Analytic derivation of the next-to-leading order proton structure function F2p(x ,Q2) based on the Laplace transformation

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Analysis of pulse thermography using similarities between wave and diffusion propagation

NASA Astrophysics Data System (ADS)

Gershenson, M.

2017-05-01

Pulse thermography or thermal wave imaging are commonly used as nondestructive evaluation (NDE) method. While the technical aspect has evolve with time, theoretical interpretation is lagging. Interpretation is still using curved fitting on a log log scale. A new approach based directly on the governing differential equation is introduced. By using relationships between wave propagation and the diffusive propagation of thermal excitation, it is shown that one can transform from solutions in one type of propagation to the other. The method is based on the similarities between the Laplace transforms of the diffusion equation and the wave equation. For diffusive propagation we have the Laplace variable s to the first power, while for the wave propagation similar equations occur with s2. For discrete time the transformation between the domains is performed by multiplying the temperature data vector by a matrix. The transform is local. The performance of the techniques is tested on synthetic data. The application of common back projection techniques used in the processing of wave data is also demonstrated. The combined use of the transform and back projection makes it possible to improve both depth and lateral resolution of transient thermography.

A general spectral transformation simultaneously including a Fourier transformation and a Laplace transformation

NASA Technical Reports Server (NTRS)

Marko, H.

1978-01-01

A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.

Numerical inverse Laplace transformation for determining the system response of linear systems in the time domain

NASA Technical Reports Server (NTRS)

Friedrich, R.; Drewelow, W.

1978-01-01

An algorithm is described that is based on the method of breaking the Laplace transform down into partial fractions which are then inverse-transformed separately. The sum of the resulting partial functions is the wanted time function. Any problems caused by equation system forms are largely limited by appropriate normalization using an auxiliary parameter. The practical limits of program application are reached when the degree of the denominator of the Laplace transform is seven to eight.

Unsteady aerodynamic modeling and active aeroelastic control

NASA Technical Reports Server (NTRS)

Edwards, J. W.

1977-01-01

Unsteady aerodynamic modeling techniques are developed and applied to the study of active control of elastic vehicles. The problem of active control of a supercritical flutter mode poses a definite design goal stability, and is treated in detail. The transfer functions relating the arbitrary airfoil motions to the airloads are derived from the Laplace transforms of the linearized airload expressions for incompressible two dimensional flow. The transfer function relating the motions to the circulatory part of these loads is recognized as the Theodorsen function extended to complex values of reduced frequency, and is termed the generalized Theodorsen function. Inversion of the Laplace transforms yields exact transient airloads and airfoil motions. Exact root loci of aeroelastic modes are calculated, providing quantitative information regarding subcritical and supercritical flutter conditions.

Direct conversion of rheological compliance measurements into storage and loss moduli.

PubMed

Evans, R M L; Tassieri, Manlio; Auhl, Dietmar; Waigh, Thomas A

2009-07-01

We remove the need for Laplace/inverse-Laplace transformations of experimental data, by presenting a direct and straightforward mathematical procedure for obtaining frequency-dependent storage and loss moduli [G'(omega) and G''(omega), respectively], from time-dependent experimental measurements. The procedure is applicable to ordinary rheological creep (stress-step) measurements, as well as all microrheological techniques, whether they access a Brownian mean-square displacement, or a forced compliance. Data can be substituted directly into our simple formula, thus eliminating traditional fitting and smoothing procedures that disguise relevant experimental noise.

Direct conversion of rheological compliance measurements into storage and loss moduli

NASA Astrophysics Data System (ADS)

Evans, R. M. L.; Tassieri, Manlio; Auhl, Dietmar; Waigh, Thomas A.

2009-07-01

We remove the need for Laplace/inverse-Laplace transformations of experimental data, by presenting a direct and straightforward mathematical procedure for obtaining frequency-dependent storage and loss moduli [ G'(ω) and G″(ω) , respectively], from time-dependent experimental measurements. The procedure is applicable to ordinary rheological creep (stress-step) measurements, as well as all microrheological techniques, whether they access a Brownian mean-square displacement, or a forced compliance. Data can be substituted directly into our simple formula, thus eliminating traditional fitting and smoothing procedures that disguise relevant experimental noise.

Approximation of the ruin probability using the scaled Laplace transform inversion

PubMed Central

Mnatsakanov, Robert M.; Sarkisian, Khachatur; Hakobyan, Artak

2015-01-01

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen–Weideman–Schmelzer and maximum entropy methods are presented via a simulation study. PMID:26752796

University teachers' perspectives on the role of the Laplace transform in engineering education

NASA Astrophysics Data System (ADS)

Holmberg née González Sampayo, Margarita; Bernhard, Jonte

2017-07-01

The Laplace transform is an important tool in many branches of engineering, for example, electric and control engineering, but is also regarded as a difficult topic for students to master. We have interviewed 22 university teachers from five universities in three countries (Mexico, Spain and Sweden) about their views on relationships among mathematics, physics and technology/application aspects in the process of learning the Laplace transform in engineering education. Strikingly, the teachers held a spectrum of qualitatively differing views, ranging from seeing virtually no connection (e.g. some thought the Laplace transform has no relevance in engineering), through to regarding the aspects as intimately, almost inseparably linked. The lack of awareness of the widely differing views among teachers might lead to a lack of constructive alignment among different courses that is detrimental to the quality of engineering education.

Improved FFT-based numerical inversion of Laplace transforms via fast Hartley transform algorithm

NASA Technical Reports Server (NTRS)

Hwang, Chyi; Lu, Ming-Jeng; Shieh, Leang S.

1991-01-01

The disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them. The improved method is based on introducing a new integration step length Delta(omega) = pi/mT for trapezoidal-rule approximation of the Bromwich integral, in which a new parameter, m, is introduced for controlling the accuracy of the numerical integration. Naturally, this method leads to multiple sets of complex FFT computations. A new inversion formula is derived such that N equally spaced samples of the inverse Laplace transform function can be obtained by (m/2) + 1 sets of N-point complex FFT computations or by m sets of real fast Hartley transform (FHT) computations.

Perturbative triples correction for local pair natural orbital based explicitly correlated CCSD(F12*) using Laplace transformation techniques.

PubMed

Schmitz, Gunnar; Hättig, Christof

2016-12-21

We present an implementation of pair natural orbital coupled cluster singles and doubles with perturbative triples, PNO-CCSD(T), which avoids the quasi-canonical triples approximation (T0) where couplings due to off-diagonal Fock matrix elements are neglected. A numerical Laplace transformation of the canonical expression for the perturbative (T) triples correction is used to avoid an I/O and storage bottleneck for the triples amplitudes. Results for a test set of reaction energies show that only very few Laplace grid points are needed to obtain converged energy differences and that PNO-CCSD(T) is a more robust approximation than PNO-CCSD(T0) with a reduced mean absolute deviation from canonical CCSD(T) results. We combine the PNO-based (T) triples correction with the explicitly correlated PNO-CCSD(F12*) method and investigate the use of specialized F12-PNOs in the conventional triples correction. We find that no significant additional errors are introduced and that PNO-CCSD(F12*)(T) can be applied in a black box manner.

Time-domain reflectance diffuse optical tomography with Mellin-Laplace transform for experimental detection and depth localization of a single absorbing inclusion

PubMed Central

Puszka, Agathe; Hervé, Lionel; Planat-Chrétien, Anne; Koenig, Anne; Derouard, Jacques; Dinten, Jean-Marc

2013-01-01

We show how to apply the Mellin-Laplace transform to process time-resolved reflectance measurements for diffuse optical tomography. We illustrate this method on simulated signals incorporating the main sources of experimental noise and suggest how to fine-tune the method in order to detect the deepest absorbing inclusions and optimize their localization in depth, depending on the dynamic range of the measurement. To finish, we apply this method to measurements acquired with a setup including a femtosecond laser, photomultipliers and a time-correlated single photon counting board. Simulations and experiments are illustrated for a probe featuring the interfiber distance of 1.5 cm and show the potential of time-resolved techniques for imaging absorption contrast in depth with this geometry. PMID:23577292

Application of a Laplace transform pair model for high-energy x-ray spectral reconstruction.

PubMed

Archer, B R; Almond, P R; Wagner, L K

1985-01-01

A Laplace transform pair model, previously shown to accurately reconstruct x-ray spectra at diagnostic energies, has been applied to megavoltage energy beams. The inverse Laplace transforms of 2-, 6-, and 25-MV attenuation curves were evaluated to determine the energy spectra of these beams. The 2-MV data indicate that the model can reliably reconstruct spectra in the low megavoltage range. Experimental limitations in acquiring the 6-MV transmission data demonstrate the sensitivity of the model to systematic experimental error. The 25-MV data result in a physically realistic approximation of the present spectrum.

Using Expected Value to Introduce the Laplace Transform

ERIC Educational Resources Information Center

Lutzer, Carl V.

2015-01-01

We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random. We assume only a basic understanding of probability.

A technique for increasing the accuracy of the numerical inversion of the Laplace transform with applications

NASA Technical Reports Server (NTRS)

Berger, B. S.; Duangudom, S.

1973-01-01

A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.

Analytical expression for the relaxation moduli of linear viscoelastic composites with periodic microstructure

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

Luciano, R.; Barbero, E.J.

Many micromechanical models have been used to estimate the overall stiffness of heterogeneous- materials and a large number of results and experimental data have been obtained. However, few theoretical and experimental results are available in the field of viscoelastic behavior of heterogeneous media. In this paper the viscoelastostatic problem of composite materials with periodic microstructure is studied. The matrix is assumed linear viscoelastic and the fibers elastic. The correspondence principle in viscoelasticity is applied and the problem in the Laplace domain is solved by using the Fourier series technique and assuming the Laplace transform of the homogenization eigenstrain piecewise constantmore » in the space. Formulas for the Laplace transform of the relaxation functions of the composite are obtained in terms of the properties of the matrix and the fibers and in function of nine triple series which take in account the geometry of the inclusions. The inversion to the time domain of the relaxation and the creep functions of composites reinforced by long fibers is carried out analytically when the four parameters model is used to represent the viscoelastic behavior of the matrix. Finally, comparisons with experimental results are presented.« less

Convergent radial dispersion: A note on evaluation of the Laplace transform solution

USGS Publications Warehouse

Moench, Allen F.

1991-01-01

A numerical inversion algorithm for Laplace transforms that is capable of handling rapid changes in the computed function is applied to the Laplace transform solution to the problem of convergent radial dispersion in a homogeneous aquifer. Prior attempts by the author to invert this solution were unsuccessful for highly advective systems where the Peclet number was relatively large. The algorithm used in this note allows for rapid and accurate inversion of the solution for all Peclet numbers of practical interest, and beyond. Dimensionless breakthrough curves are illustrated for tracer input in the form of a step function, a Dirac impulse, or a rectangular input.

Analytical expressions for the correlation function of a hard sphere dimer fluid

NASA Astrophysics Data System (ADS)

Kim, Soonho; Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.

Analytical expression for the correlation function of a hard sphere chain fluid

NASA Astrophysics Data System (ADS)

Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of flexible hard sphere chain fluid. A set of integral equations obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with the polymer Percus-Yevick ideal chain approximation is considered. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of individual correlation functions are obtained. By inverse Laplace transformation the inter- and intramolecular radial distribution functions (RDFs) are obtained in closed forms up to 3D(D is segment diameter). These analytical expressions for the RDFs would be useful in developing the perturbation theory of chain fluids.

Some Half-Row Sums from Pascal's Triangle via Laplace Transforms

ERIC Educational Resources Information Center

Dence, Thomas P.

2007-01-01

This article presents some identities on the sum of the entries in the first half of a row in Pascal's triangle. The results were discovered while the author was working on a problem involving Laplace transforms, which are used in proving of the identities.

An integral transform approach for a mixed boundary problem involving a flowing partially penetrating well with infinitesimal well skin

NASA Astrophysics Data System (ADS)

Chang, Chien-Chieh; Chen, Chia-Shyun

2002-06-01

A flowing partially penetrating well with infinitesimal well skin is a mixed boundary because a Cauchy condition is prescribed along the screen length and a Neumann condition of no flux is stipulated over the remaining unscreened part. An analytical approach based on the integral transform technique is developed to determine the Laplace domain solution for such a mixed boundary problem in a confined aquifer of finite thickness. First, the mixed boundary is changed into a homogeneous Neumann boundary by substituting the Cauchy condition with a Neumann condition in terms of well bore flux that varies along the screen length and is time dependent. Despite the well bore flux being unknown a priori, the modified model containing this homogeneous Neumann boundary can be solved with the Laplace and the finite Fourier cosine transforms. To determine well bore flux, screen length is discretized into a finite number of segments, to which the Cauchy condition is reinstated. This reinstatement also restores the relation between the original model and the solutions obtained. For a given time, the numerical inversion of the Laplace domain solution yields the drawdown distributions, well bore flux, and the well discharge. This analytical approach provides an alternative for dealing with the mixed boundary problems, especially when aquifer thickness is assumed to be finite.

Fractional Order Two-Temperature Dual-Phase-Lag Thermoelasticity with Variable Thermal Conductivity

PubMed Central

Mallik, Sadek Hossain; Kanoria, M.

2014-01-01

A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by using a state space approach. The inversion of Laplace transforms is computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, temperature discrepancy, and the fractional order parameter. PMID:27419210

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

Transform Methods for Precision Nonlinear Wave Models of Flexible space Structures

DTIC Science & Technology

1990-08-20

developed, each of which has motivated a structural control methodology in a natural way. The Transform Element Modelling (TEM) approach uses the Laplace...IEk A L 2 = -, c G= ( C .3 a ,b ) Talng the Laplace transfor-m (neglecting initial conditions) )ields [1+tjSZ-(,s) +S ((X’S) + al2a~ pS4 (X’S) j(X’s) (04

Analysis of blood flow with nanoparticles induced by uniform magnetic field through a circular cylinder with fractional Caputo derivatives

NASA Astrophysics Data System (ADS)

Abdullah, M.; Butt, Asma Rashid; Raza, Nauman; Alshomrani, Ali Saleh; Alzahrani, A. K.

2018-01-01

The magneto hydrodynamic blood flow in the presence of magnetic particles through a circular cylinder is investigated. To calculate the impact of externally applied uniform magnetic field, the blood is electrically charged. Initially the fluid and circular cylinder is at rest but at time t =0+ , the cylinder starts to oscillate along its axis with velocity fsin (Ωt) . To obtain the mathematical model of blood flow with fractional derivatives Caputo fractional operator is employed. The solutions for the velocities of blood and magnetic particles are procured semi analytically by using Laplace transformation method. The inverse Laplace transform has been calculated numerically by using MATHCAD computer software. The obtained results of velocities are presented in Laplace domain in terms of modified Bessel function I0 (·) . The obtained results satisfied all imposed initial and boundary conditions. The hybrid technique that is employed here less computational effort and time cost as compared to other techniques used in literature. As the limiting cases of our results the solutions of the flow model with ordinary derivatives has been procured. Finally, the impact of Reynolds number Re, fractional parameter α and Hartmann number Ha is analyzed and portrayed through graphs. It is worthy to pointing out that fractional derivatives brings remarkable differences as compared to ordinary derivatives. It also has been observed that velocity of blood and magnetic particles is weaker under the effect of transverse magnetic field.

Discovering the Laplace Transform in Undergraduate Differential Equations

ERIC Educational Resources Information Center

Quinn, Terrance J.; Rai, Sanjay

2008-01-01

The Laplace Transform is an object of fundamental importance in pure and applied mathematics. In addition, it has special pedagogical value in that it can provide a natural and concrete setting for a student to begin thinking about the modern concepts of "operator" and "functional". Most undergraduate textbooks, however, merely define the…

Receptor binding kinetics equations: Derivation using the Laplace transform method.

PubMed

Hoare, Sam R J

Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time-dependent pharmacological activities. Copyright © 2017 Elsevier Inc. All rights reserved.

Introducing the Improved Heaviside Approach to Partial Fraction Decomposition to Undergraduate Students: Results and Implications from a Pilot Study

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

The DOSY experiment provides insights into the protegrin-lipid interaction

NASA Astrophysics Data System (ADS)

Malliavin, T. E.; Louis, V.; Delsuc, M. A.

1998-02-01

The measure of translational diffusion using PFG NMR has known a renewal of interest with the development of the DOSY experiments. The extraction of diffusion coefficients from these experiments requires an inverse Laplace transform. We present here the use of the Maximum Entropy technique to perform this transform, and an application of this method to investigate the interaction protegrin-lipid. We show that the analysis by DOSY experiments permits to determine some of the interaction features. La mesure de diffusion translationnelle par gradients de champs pulsés en RMN a connu un regain d'intérêt avec le développement des expériences de DOSY. L'extraction de coefficients de diffusion à partir de ces expériences nécessite l'application d'une transformée de Laplace inverse. Nous présentons ici l'utilisation de la méthode d'Entropie Maximum pour effectuer cette transformée, ainsi qu'une application de l'expérience de DOSY pour étudier une interaction protégrine-lipide. Nous montrons que l'analyse par l'expérience de DOSY permet de déterminer certaines des caractéristiques de cette interaction.

Laplace-transformed atomic orbital-based Møller–Plesset perturbation theory for relativistic two-component Hamiltonians

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

Helmich-Paris, Benjamin, E-mail: b.helmichparis@vu.nl; Visscher, Lucas, E-mail: l.visscher@vu.nl; Repisky, Michal, E-mail: michal.repisky@uit.no

2016-07-07

We present a formulation of Laplace-transformed atomic orbital-based second-order Møller–Plesset perturbation theory (MP2) energies for two-component Hamiltonians in the Kramers-restricted formalism. This low-order scaling technique can be used to enable correlated relativistic calculations for large molecular systems. We show that the working equations to compute the relativistic MP2 energy differ by merely a change of algebra (quaternion instead of real) from their non-relativistic counterparts. With a proof-of-principle implementation we study the effect of the nuclear charge on the magnitude of half-transformed integrals and show that for light elements spin-free and spin-orbit MP2 energies are almost identical. Furthermore, we investigate themore » effect of separation of charge distributions on the Coulomb and exchange energy contributions, which show the same long-range decay with the inter-electronic/atomic distance as for non-relativistic MP2. A linearly scaling implementation is possible if the proper distance behavior is introduced to the quaternion Schwarz-type estimates as for non-relativistic MP2.« less

Flow to a well in a water-table aquifer: An improved laplace transform solution

USGS Publications Warehouse

Moench, A.F.

1996-01-01

An alternative Laplace transform solution for the problem, originally solved by Neuman, of constant discharge from a partially penetrating well in a water-table aquifer was obtained. The solution differs from existing solutions in that it is simpler in form and can be numerically inverted without the need for time-consuming numerical integration. The derivation invloves the use of the Laplace transform and a finite Fourier cosine series and avoids the Hankel transform used in prior derivations. The solution allows for water in the overlying unsaturated zone to be released either instantaneously in response to a declining water table as assumed by Neuman, or gradually as approximated by Boulton's convolution integral. Numerical evaluation yields results identical with results obtained by previously published methods with the advantage, under most well-aquifer configurations, of much reduced computation time.

Solution of the Time-Dependent Schrödinger Equation by the Laplace Transform Method

PubMed Central

Lin, S. H.; Eyring, H.

1971-01-01

The time-dependent Schrödinger equation for two quite general types of perturbation has been solved by introducing the Laplace transforms to eliminate the time variable. The resulting time-independent differential equation can then be solved by the perturbation method, the variation method, the variation-perturbation method, and other methods. PMID:16591898

Exact Analytical Solutions for Elastodynamic Impact

DTIC Science & Technology

2015-11-30

corroborated by derivation of exact discrete solutions from recursive equations for the impact problems. 15. SUBJECT TERMS One-dimensional impact; Elastic...wave propagation; Laplace transform; Floor function; Discrete solutions 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...impact Elastic wave propagation Laplace transform Floor function Discrete solutionsWe consider the one-dimensional impact problem in which a semi

University Teachers' Perspectives on the Role of the Laplace Transform in Engineering Education

ERIC Educational Resources Information Center

Holmberg, Margarita; Bernhard, Jonte

2017-01-01

The Laplace transform is an important tool in many branches of engineering, for example, electric and control engineering, but is also regarded as a difficult topic for students to master. We have interviewed 22 university teachers from five universities in three countries (Mexico, Spain and Sweden) about their views on relationships among…

Alternative formulations of the Laplace transform boundary element (LTBE) numerical method for the solution of diffusion-type equations

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

Moridis, G.

1992-03-01

The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.

Filter frequency response of time dependent signal using Laplace transform

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

Shestakov, Aleksei I.

We analyze the effect a filter has on a time dependent signal x(t). If X(s) is the Laplace transform of x and H (s) is the filter Transfer function, the response in frequency space is X (s) H (s). Consequently, in real space, the response is the convolution (x*h) (t), where hi is the Laplace inverse of H. Effects are analyzed and analytically for functions such as (t/t c) 2 e -t/tmore » $$_c$$, where t c = const. We consider lowpass, highpass and bandpass filters.« less

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

NASA Technical Reports Server (NTRS)

Cerro, J. A.; Scotti, S. J.

1991-01-01

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

Recent Advances in Laplace Transform Analytic Element Method (LT-AEM) Theory and Application to Transient Groundwater Flow

NASA Astrophysics Data System (ADS)

Kuhlman, K. L.; Neuman, S. P.

2006-12-01

Furman and Neuman (2003) proposed a Laplace Transform Analytic Element Method (LT-AEM) for transient groundwater flow. LT-AEM applies the traditionally steady-state AEM to the Laplace transformed groundwater flow equation, and back-transforms the resulting solution to the time domain using a Fourier Series numerical inverse Laplace transform method (de Hoog, et.al., 1982). We have extended the method so it can compute hydraulic head and flow velocity distributions due to any two-dimensional combination and arrangement of point, line, circular and elliptical area sinks and sources, nested circular or elliptical regions having different hydraulic properties, and areas of specified head, flux or initial condition. The strengths of all sinks and sources, and the specified head and flux values, can all vary in both space and time in an independent and arbitrary fashion. Initial conditions may vary from one area element to another. A solution is obtained by matching heads and normal fluxes along the boundary of each element. The effect which each element has on the total flow is expressed in terms of generalized Fourier series which converge rapidly (<20 terms) in most cases. As there are more matching points than unknown Fourier terms, the matching is accomplished in Laplace space using least-squares. The method is illustrated by calculating the resulting transient head and flow velocities due to an arrangement of elements in both finite and infinite domains. The 2D LT-AEM elements already developed and implemented are currently being extended to solve the 3D groundwater flow equation.

Laplace transform analysis of a multiplicative asset transfer model

NASA Astrophysics Data System (ADS)

Sokolov, Andrey; Melatos, Andrew; Kieu, Tien

2010-07-01

We analyze a simple asset transfer model in which the transfer amount is a fixed fraction f of the giver’s wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values of f∈(0,1). The Laplace transform analysis is superior to agent-based simulations as it does not depend on the number of agents, enabling us to study entropy and inequality in regimes that are costly to address with simulations. We demonstrate that Boltzmann entropy is not a suitable (e.g. non-monotonic) measure of disorder in a multiplicative asset transfer system and suggest an asymmetric stochastic process that is equivalent to the asset transfer model.

Local CC2 response method based on the Laplace transform: analytic energy gradients for ground and excited states.

PubMed

Ledermüller, Katrin; Schütz, Martin

2014-04-28

A multistate local CC2 response method for the calculation of analytic energy gradients with respect to nuclear displacements is presented for ground and electronically excited states. The gradient enables the search for equilibrium geometries of extended molecular systems. Laplace transform is used to partition the eigenvalue problem in order to obtain an effective singles eigenvalue problem and adaptive, state-specific local approximations. This leads to an approximation in the energy Lagrangian, which however is shown (by comparison with the corresponding gradient method without Laplace transform) to be of no concern for geometry optimizations. The accuracy of the local approximation is tested and the efficiency of the new code is demonstrated by application calculations devoted to a photocatalytic decarboxylation process of present interest.

The Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-LT-RIMP2) theory method

NASA Astrophysics Data System (ADS)

Kjærgaard, Thomas

2017-01-01

The divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-RI-MP2) theory method introduced in Baudin et al. [J. Chem. Phys. 144, 054102 (2016)] is significantly improved by introducing the Laplace transform of the orbital energy denominator in order to construct the double amplitudes directly in the local basis. Furthermore, this paper introduces the auxiliary reduction procedure, which reduces the set of the auxiliary functions employed in the individual fragments. The resulting Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation method is applied to the insulin molecule where we obtain a factor 9.5 speedup compared to the DEC-RI-MP2 method.

Unsteady translational motion of a slip sphere in a viscous fluid using the fractional Navier-Stokes equation

NASA Astrophysics Data System (ADS)

Ashmawy, E. A.

2017-03-01

In this paper, we investigate the translational motion of a slip sphere with time-dependent velocity in an incompressible viscous fluid. The modified Navier-Stokes equation with fractional order time derivative is used. The linear slip boundary condition is applied on the spherical boundary. The integral Laplace transform technique is employed to solve the problem. The solution in the physical domain is obtained analytically by inverting the Laplace transform using the complex inversion formula together with contour integration. An exact formula for the drag force exerted by the fluid on the spherical object is deduced. This formula is applied to some flows, namely damping oscillation, sine oscillation and sudden motion. The numerical results showed that the order of the fractional derivative contributes considerably to the drag force. The increase in this parameter resulted in an increase in the drag force. In addition, the values of the drag force increased with the increase in the slip parameter.

A homogenization approach for the effective drained viscoelastic properties of 2D porous media and an application for cortical bone.

PubMed

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

2018-02-01

Closed-form solutions for the effective rheological properties of a 2D viscoelastic drained porous medium made of a Generalized Maxwell viscoelastic matrix and pore inclusions are developed and applied for cortical bone. The in-plane (transverse) effective viscoelastic bulk and shear moduli of the Generalized Maxwell rheology of the homogenized medium are expressed as functions of the porosity and the viscoelastic properties of the solid phase. When deriving these functions, the classical inverse Laplace-Carson transformation technique is avoided, due to its complexity, by considering the short and long term approximations. The approximated results are validated against exact solutions obtained from the inverse Laplace-Carson transform for a simple configuration when the later is available. An application for cortical bone with assumption of circular pore in the transverse plane shows that the proposed approximation fit very well with experimental data. Copyright © 2017 Elsevier Ltd. All rights reserved.

Parallel Fortran-MPI software for numerical inversion of the Laplace transform and its application to oscillatory water levels in groundwater environments

USGS Publications Warehouse

Zhan, X.

2005-01-01

A parallel Fortran-MPI (Message Passing Interface) software for numerical inversion of the Laplace transform based on a Fourier series method is developed to meet the need of solving intensive computational problems involving oscillatory water level's response to hydraulic tests in a groundwater environment. The software is a parallel version of ACM (The Association for Computing Machinery) Transactions on Mathematical Software (TOMS) Algorithm 796. Running 38 test examples indicated that implementation of MPI techniques with distributed memory architecture speedups the processing and improves the efficiency. Applications to oscillatory water levels in a well during aquifer tests are presented to illustrate how this package can be applied to solve complicated environmental problems involved in differential and integral equations. The package is free and is easy to use for people with little or no previous experience in using MPI but who wish to get off to a quick start in parallel computing. ?? 2004 Elsevier Ltd. All rights reserved.

Evaluation of algorithms for geological thermal-inertia mapping

NASA Technical Reports Server (NTRS)

Miller, S. H.; Watson, K.

1977-01-01

The errors incurred in producing a thermal inertia map are of three general types: measurement, analysis, and model simplification. To emphasize the geophysical relevance of these errors, they were expressed in terms of uncertainty in thermal inertia and compared with the thermal inertia values of geologic materials. Thus the applications and practical limitations of the technique were illustrated. All errors were calculated using the parameter values appropriate to a site at the Raft River, Id. Although these error values serve to illustrate the magnitudes that can be expected from the three general types of errors, extrapolation to other sites should be done using parameter values particular to the area. Three surface temperature algorithms were evaluated: linear Fourier series, finite difference, and Laplace transform. In terms of resulting errors in thermal inertia, the Laplace transform method is the most accurate (260 TIU), the forward finite difference method is intermediate (300 TIU), and the linear Fourier series method the least accurate (460 TIU).

Laplace transforms of the Hulthén Green's function and their application to potential scattering

NASA Astrophysics Data System (ADS)

Laha, U.; Ray, S.; Panda, S.; Bhoi, J.

2017-10-01

We derive closed-form representations for the single and double Laplace transforms of the Hulthén Green's function of the outgoing wave multiplied by the Yamaguchi potential and write them in the maximally reduced form. We use the expression for the double transform to compute the low-energy phase shifts for the elastic scattering in the systems α-nucleon, α-He3, and α-H3. The calculation results agree well with the experimental data.

Transfer Functions Via Laplace- And Fourier-Borel Transforms

NASA Technical Reports Server (NTRS)

Can, Sumer; Unal, Aynur

1991-01-01

Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.

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

Boroun, G. R., E-mail: grboroun@gmail.com, E-mail: boroun@razi.ac.ir; Zarrin, S.

We derive a general scheme for the evolution of the nonsinglet structure function at the leadingorder (LO) and next-to-leading-order (NLO) by using the Laplace-transform technique. Results for the nonsinglet structure function are compared with MSTW2008, GRV, and CKMT parameterizations and also EMC experimental data in the LO and NLO analysis. The results are in good agreement with the experimental data and other parameterizations in the low- and large-x regions.

Laplace Transform Based Radiative Transfer Studies

NASA Astrophysics Data System (ADS)

Hu, Y.; Lin, B.; Ng, T.; Yang, P.; Wiscombe, W.; Herath, J.; Duffy, D.

2006-12-01

Multiple scattering is the major uncertainty for data analysis of space-based lidar measurements. Until now, accurate quantitative lidar data analysis has been limited to very thin objects that are dominated by single scattering, where photons from the laser beam only scatter a single time with particles in the atmosphere before reaching the receiver, and simple linear relationship between physical property and lidar signal exists. In reality, multiple scattering is always a factor in space-based lidar measurement and it dominates space- based lidar returns from clouds, dust aerosols, vegetation canopy and phytoplankton. While multiple scattering are clear signals, the lack of a fast-enough lidar multiple scattering computation tool forces us to treat the signal as unwanted "noise" and use simple multiple scattering correction scheme to remove them. Such multiple scattering treatments waste the multiple scattering signals and may cause orders of magnitude errors in retrieved physical properties. Thus the lack of fast and accurate time-dependent radiative transfer tools significantly limits lidar remote sensing capabilities. Analyzing lidar multiple scattering signals requires fast and accurate time-dependent radiative transfer computations. Currently, multiple scattering is done with Monte Carlo simulations. Monte Carlo simulations take minutes to hours and are too slow for interactive satellite data analysis processes and can only be used to help system / algorithm design and error assessment. We present an innovative physics approach to solve the time-dependent radiative transfer problem. The technique utilizes FPGA based reconfigurable computing hardware. The approach is as following, 1. Physics solution: Perform Laplace transform on the time and spatial dimensions and Fourier transform on the viewing azimuth dimension, and convert the radiative transfer differential equation solving into a fast matrix inversion problem. The majority of the radiative transfer computation goes to matrix inversion processes, FFT and inverse Laplace transforms. 2. Hardware solutions: Perform the well-defined matrix inversion, FFT and Laplace transforms on highly parallel, reconfigurable computing hardware. This physics-based computational tool leads to accurate quantitative analysis of space-based lidar signals and improves data quality of current lidar mission such as CALIPSO. This presentation will introduce the basic idea of this approach, preliminary results based on SRC's FPGA-based Mapstation, and how we may apply it to CALIPSO data analysis.

A practical approach to calculate the time evolutions of magnetic field effects on photochemical reactions in nano-structured materials.

PubMed

Yago, Tomoaki; Wakasa, Masanobu

2015-04-21

A practical method to calculate time evolutions of magnetic field effects (MFEs) on photochemical reactions involving radical pairs is developed on the basis of the theory of the chemically induced dynamic spin polarization proposed by Pedersen and Freed. In theory, the stochastic Liouville equation (SLE), including the spin Hamiltonian, diffusion motions of the radical pair, chemical reactions, and spin relaxations, is solved by using the Laplace and the inverse Laplace transformation technique. In our practical approach, time evolutions of the MFEs are successfully calculated by applying the Miller-Guy method instead of the final value theorem to the inverse Laplace transformation process. Especially, the SLE calculations are completed in a short time when the radical pair dynamics can be described by the chemical kinetics consisting of diffusions, reactions and spin relaxations. The SLE analysis with a short calculation time enables one to examine the various parameter sets for fitting the experimental date. Our study demonstrates that simultaneous fitting of the time evolution of the MFE and of the magnetic field dependence of the MFE provides valuable information on the diffusion motions of the radical pairs in nano-structured materials such as micelles where the lifetimes of radical pairs are longer than hundreds of nano-seconds and the magnetic field dependence of the spin relaxations play a major role for the generation of the MFE.

A novel improved method for analysis of 2D diffusion relaxation data—2D PARAFAC-Laplace decomposition

NASA Astrophysics Data System (ADS)

Tønning, Erik; Polders, Daniel; Callaghan, Paul T.; Engelsen, Søren B.

2007-09-01

This paper demonstrates how the multi-linear PARAFAC model can with advantage be used to decompose 2D diffusion-relaxation correlation NMR spectra prior to 2D-Laplace inversion to the T2- D domain. The decomposition is advantageous for better interpretation of the complex correlation maps as well as for the quantification of extracted T2- D components. To demonstrate the new method seventeen mixtures of wheat flour, starch, gluten, oil and water were prepared and measured with a 300 MHz nuclear magnetic resonance (NMR) spectrometer using a pulsed gradient stimulated echo (PGSTE) pulse sequence followed by a Carr-Purcell-Meiboom-Gill (CPMG) pulse echo train. By varying the gradient strength, 2D diffusion-relaxation data were recorded for each sample. From these double exponentially decaying relaxation data the PARAFAC algorithm extracted two unique diffusion-relaxation components, explaining 99.8% of the variation in the data set. These two components were subsequently transformed to the T2- D domain using 2D-inverse Laplace transformation and quantitatively assigned to the oil and water components of the samples. The oil component was one distinct distribution with peak intensity at D = 3 × 10 -12 m 2 s -1 and T2 = 180 ms. The water component consisted of two broad populations of water molecules with diffusion coefficients and relaxation times centered around correlation pairs: D = 10 -9 m 2 s -1, T2 = 10 ms and D = 3 × 10 -13 m 2 s -1, T2 = 13 ms. Small spurious peaks observed in the inverse Laplace transformation of original complex data were effectively filtered by the PARAFAC decomposition and thus considered artefacts from the complex Laplace transformation. The oil-to-water ratio determined by PARAFAC followed by 2D-Laplace inversion was perfectly correlated with known oil-to-water ratio of the samples. The new method of using PARAFAC prior to the 2D-Laplace inversion proved to have superior potential in analysis of diffusion-relaxation spectra, as it improves not only the interpretation, but also the quantification.

A closed form solution for constant flux pumping in a well under partial penetration condition

NASA Astrophysics Data System (ADS)

Yang, Shaw-Yang; Yeh, Hund-Der; Chiu, Pin-Yuan

2006-05-01

An analytical model for the constant flux pumping test is developed in a radial confined aquifer system with a partially penetrating well. The Laplace domain solution is derived by the application of the Laplace transforms with respect to time and the finite Fourier cosine transforms with respect to the vertical coordinates. A time domain solution is obtained using the inverse Laplace transforms, convolution theorem, and Bromwich integral method. The effect of partial penetration is apparent if the test well is completed with a short screen. An aquifer thickness 100 times larger than the screen length of the well can be considered as infinite. This solution can be used to investigate the effects of screen length and location on the drawdown distribution in a radial confined aquifer system and to produce type curves for the estimation of aquifer parameters with field pumping drawdown data.

Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane-Emden type differential equations (LETDEs).

PubMed

Tripathi, Rajnee; Mishra, Hradyesh Kumar

2016-01-01

In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.

Viscoelastic damped response of cross-ply laminated shallow spherical shells subjected to various impulsive loads

NASA Astrophysics Data System (ADS)

Şahan, Mehmet Fatih

2017-11-01

In this paper, the viscoelastic damped response of cross-ply laminated shallow spherical shells is investigated numerically in a transformed Laplace space. In the proposed approach, the governing differential equations of cross-ply laminated shallow spherical shell are derived using the dynamic version of the principle of virtual displacements. Following this, the Laplace transform is employed in the transient analysis of viscoelastic laminated shell problem. Also, damping can be incorporated with ease in the transformed domain. The transformed time-independent equations in spatial coordinate are solved numerically by Gauss elimination. Numerical inverse transformation of the results into the real domain are operated by the modified Durbin transform method. Verification of the presented method is carried out by comparing the results with those obtained by the Newmark method and ANSYS finite element software. Furthermore, the developed solution approach is applied to problems with several impulsive loads. The novelty of the present study lies in the fact that a combination of the Navier method and Laplace transform is employed in the analysis of cross-ply laminated shallow spherical viscoelastic shells. The numerical sample results have proved that the presented method constitutes a highly accurate and efficient solution, which can be easily applied to the laminated viscoelastic shell problems.

A laplace transform-based technique for solving multiscale and multidomain problems: Application to a countercurrent hemodialyzer model.

PubMed

Simon, Laurent

2017-08-01

An integral-based method was employed to evaluate the behavior of a countercurrent hemodialyzer model. Solute transfer from the blood into the dialysate was described by writing mass balance equations over a section of the device. The approach provided Laplace transform concentration profiles on both sides of the membrane. Applications of the final value theorem led to the development of the effective time constants and steady-state concentrations in the exit streams. Transient responses were derived by a numerical inversion algorithm. Simulations show that the period elapsed, before reaching equilibrium in the effluents, decreased when the blood flow rate increased from 0.25 to 0.30 ml/s. The performance index decreased from 0.80 to 0.71 when the blood-to-dialysate flow ratio increased by 20% and increased from 0.80 to 0.85 when this fraction was reduced by 17%. The analytical solution predicted methadone removal in patients undergoing dialysis. Clinicians can use these findings to predict the time required to achieve a target extraction ratio. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1985-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1986-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature

NASA Astrophysics Data System (ADS)

Lotfy, K.; Sarkar, N.

2017-11-01

In this work, a novel generalized model of photothermal theory with two-temperature thermoelasticity theory based on memory-dependent derivative (MDD) theory is performed. A one-dimensional problem for an elastic semiconductor material with isotropic and homogeneous properties has been considered. The problem is solved with a new model (MDD) under the influence of a mechanical force with a photothermal excitation. The Laplace transform technique is used to remove the time-dependent terms in the governing equations. Moreover, the general solutions of some physical fields are obtained. The surface taken into consideration is free of traction and subjected to a time-dependent thermal shock. The numerical Laplace inversion is used to obtain the numerical results of the physical quantities of the problem. Finally, the obtained results are presented and discussed graphically.

Research on numerical algorithms for large space structures

NASA Technical Reports Server (NTRS)

Denman, E. D.

1981-01-01

Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.

Numerical approach for ECT by using boundary element method with Laplace transform

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

Enokizono, M.; Todaka, T.; Shibao, K.

1997-03-01

This paper presents an inverse analysis by using BEM with Laplace transform. The method is applied to a simple problem in the eddy current testing (ECT). Some crack shapes in a conductive specimen are estimated from distributions of the transient eddy current on its sensing surface and magnetic flux density in the liftoff space. Because the transient behavior includes information on various frequency components, the method is applicable to the shape estimation of a comparative small crack.

Camera flash heating of a three-layer solid composite: An approximate solution

NASA Astrophysics Data System (ADS)

Jibrin, Sani; Moksin, Mohd Maarof; Husin, Mohd Shahril; Zakaria, Azmi; Hassan, Jumiah; Talib, Zainal Abidin

2014-03-01

Camera flash heating and the subsequent thermal wave propagation in a solid composite material is studied using the Laplace transform technique. Full-field rear surface temperature for a single-layer, two-layer and three-layer solid composites are obtained directly from the Laplace transform conversion tables as opposed to the tedious inversion process by integral transform method. This is achieved by first expressing the hyperbolic-transcendental equation in terms of negative exponentials of square root of s/α and expanded same in a series by the binomial theorem. Electrophoretic deposition (EPD) and dip coating processes were used to prepare three-layer solid composites consisting ZnO/Cu/ZnO and starch/Al/starch respectively. About 0.5ml of deionized water enclosed within an air-tight aluminium container serves as the third three layer sample (AL/water/AL). Thermal diffusivity experiments were carried out on all the three samples prepared. Using Scaled Levenberg-Marquardt algorithm, the approximate temperature curve for the three-layer solid composite is fitted with the corresponding experimental result. The agreement between the theoretical curve and the experimental data as well as that between the obtained thermal diffusivity values for the ZnO, aluminium and deionized water in this work and similar ones found in literature is found to be very good.

Solution of fractional kinetic equation by a class of integral transform of pathway type

NASA Astrophysics Data System (ADS)

Kumar, Dilip

2013-04-01

Solutions of fractional kinetic equations are obtained through an integral transform named Pα-transform introduced in this paper. The Pα-transform is a binomial type transform containing many class of transforms including the well known Laplace transform. The paper is motivated by the idea of pathway model introduced by Mathai [Linear Algebra Appl. 396, 317-328 (2005), 10.1016/j.laa.2004.09.022]. The composition of the transform with differential and integral operators are proved along with convolution theorem. As an illustration of applications to the general theory of differential equations, a simple differential equation is solved by the new transform. Being a new transform, the Pα-transform of some elementary functions as well as some generalized special functions such as H-function, G-function, Wright generalized hypergeometric function, generalized hypergeometric function, and Mittag-Leffler function are also obtained. The results for the classical Laplace transform is retrieved by letting α → 1.

Stabilization of the Inverse Laplace Transform of Multiexponential Decay through Introduction of a Second Dimension

PubMed Central

Celik, Hasan; Bouhrara, Mustapha; Reiter, David A.; Fishbein, Kenneth W.; Spencer, Richard G.

2013-01-01

We propose a new approach to stabilizing the inverse Laplace transform of a multiexponential decay signal, a classically ill-posed problem, in the context of nuclear magnetic resonance relaxometry. The method is based on extension to a second, indirectly detected, dimension, that is, use of the established framework of two-dimensional relaxometry, followed by projection onto the desired axis. Numerical results for signals comprised of discrete T1 and T2 relaxation components and experiments performed on agarose gel phantoms are presented. We find markedly improved accuracy, and stability with respect to noise, as well as insensitivity to regularization in quantifying underlying relaxation components through use of the two-dimensional as compared to the one-dimensional inverse Laplace transform. This improvement is demonstrated separately for two different inversion algorithms, nonnegative least squares and non-linear least squares, to indicate the generalizability of this approach. These results may have wide applicability in approaches to the Fredholm integral equation of the first kind. PMID:24035004

Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen; Magin, Richard L.

2016-07-01

Analytical solutions to the fractional diffusion equation are often obtained by using Laplace and Fourier transforms, which conveniently encode the order of the time and the space derivatives (α and β) as non-integer powers of the conjugate transform variables (s, and k) for the spectral and the spatial frequencies, respectively. This study presents a new solution to the fractional diffusion equation obtained using the Laplace transform and expressed as a Fox's H-function. This result clearly illustrates the kinetics of the underlying stochastic process in terms of the Laplace spectral frequency and entropy. The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss-Kronrod quadrature algorithm. Here, the properties of spectral entropy are investigated for the cases of sub-diffusion and super-diffusion. We find that the overall spectral entropy decreases with the increasing α and β, and that the normal or Gaussian case with α = 1 and β = 2, has the lowest spectral entropy (i.e., less information is needed to describe the state of a Gaussian process). In addition, as the neighborhood over which the entropy is calculated increases, the spectral entropy decreases, which implies a spatial averaging or coarse graining of the material properties. Consequently, the spectral entropy is shown to provide a new way to characterize the temporal correlation of anomalous diffusion. Future studies should be designed to examine changes of spectral entropy in physical, chemical and biological systems undergoing phase changes, chemical reactions and tissue regeneration.

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2016-01-01

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

The theory of the gravitational potential applied to orbit prediction

NASA Technical Reports Server (NTRS)

Kirkpatrick, J. C.

1976-01-01

A complete derivation of the geopotential function and its gradient is presented. Also included is the transformation of Laplace's equation from Cartesian to spherical coordinates. The analytic solution to Laplace's equation is obtained from the transformed version, in the classical manner of separating the variables. A cursory introduction to the method devised by Pines, using direction cosines to express the orientation of a point in space, is presented together with sample computer program listings for computing the geopotential function and the components of its gradient. The use of the geopotential function is illustrated.

External Theory for Stochastic Processes.

DTIC Science & Technology

1985-11-01

1.2 1.4 1.8 11111125 11.I6 MICROCOP RESOLUTION TEST CHART M.. MW’ PAPI ~ W W ’W IV AV a a W 4 * S6 _ ~.. r dV . Unclassif’ DA 7 4 9JT FILE COPY...intensity measure has the Laplace : <-f Transform L (f)=exp(-x (l-e - f ) whereas a Compound Poisson Process has Laplace Transform (2.3.1) L (f...see Example 2.2.4 as an illustration of this). The result is a clustering of exceedances, leading to a compounding of events in the limiting point

Two-Dimensional Model for Reactive-Sorption Columns of Cylindrical Geometry: Analytical Solutions and Moment Analysis.

PubMed

Khan, Farman U; Qamar, Shamsul

2017-05-01

A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation

NASA Astrophysics Data System (ADS)

Salajegheh, Maral; Nejad, S. Mohammad Moosavi; Khanpour, Hamzeh; Tehrani, S. Atashbar

2018-05-01

In this paper, we present SMKA18 analysis, which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton g1p(x ,Q2) , neutron g1n(x ,Q2) , and deuteron g1d(x ,Q2) spin-dependent structure functions data set including the most recent high-precision measurements from COMPASS16 experiments at CERN, which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard Hessian error propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering data set and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of x .

An investigation on a two-dimensional problem of Mode-I crack in a thermoelastic medium

NASA Astrophysics Data System (ADS)

Kant, Shashi; Gupta, Manushi; Shivay, Om Namha; Mukhopadhyay, Santwana

2018-04-01

In this work, we consider a two-dimensional dynamical problem of an infinite space with finite linear Mode-I crack and employ a recently proposed heat conduction model: an exact heat conduction with a single delay term. The thermoelastic medium is taken to be homogeneous and isotropic. However, the boundary of the crack is subjected to a prescribed temperature and stress distributions. The Fourier and Laplace transform techniques are used to solve the problem. Mathematical modeling of the present problem reduces the solution of the problem into the solution of a system of four dual integral equations. The solution of these equations is equivalent to the solution of the Fredholm's integral equation of the first kind which has been solved by using the regularization method. Inverse Laplace transform is carried out by using the Bellman method, and we obtain the numerical solution for all the physical field variables in the physical domain. Results are shown graphically, and we highlight the effects of the presence of crack in the behavior of thermoelastic interactions inside the medium in the present context, and its results are compared with the results of the thermoelasticity of type-III.

A Solution of the System of Partial Differential Equations Which Describe the Propagation of Acoustic Pulses in Layered Fluid Media,

DTIC Science & Technology

transformed problem. Then using several changes of integration variables, the inverse transform is obtained by direct identification without recourse to the complex Laplace transform inversion integral. (Author)

A new approach to the problem of bulk-mediated surface diffusion.

PubMed

Berezhkovskii, Alexander M; Dagdug, Leonardo; Bezrukov, Sergey M

2015-08-28

This paper is devoted to bulk-mediated surface diffusion of a particle which can diffuse both on a flat surface and in the bulk layer above the surface. It is assumed that the particle is on the surface initially (at t = 0) and at time t, while in between it may escape from the surface and come back any number of times. We propose a new approach to the problem, which reduces its solution to that of a two-state problem of the particle transitions between the surface and the bulk layer, focusing on the cumulative residence times spent by the particle in the two states. These times are random variables, the sum of which is equal to the total observation time t. The advantage of the proposed approach is that it allows for a simple exact analytical solution for the double Laplace transform of the conditional probability density of the cumulative residence time spent on the surface by the particle observed for time t. This solution is used to find the Laplace transform of the particle mean square displacement and to analyze the peculiarities of its time behavior over the entire range of time. We also establish a relation between the double Laplace transform of the conditional probability density and the Fourier-Laplace transform of the particle propagator over the surface. The proposed approach treats the cases of both finite and infinite bulk layer thicknesses (where bulk-mediated surface diffusion is normal and anomalous at asymptotically long times, respectively) on equal footing.

Calculation of stability derivatives for slowly oscillating bodies of revolution at Mach 1.0

NASA Technical Reports Server (NTRS)

Ruo, S. Y.; Liu, D. D.

1971-01-01

A parabolic method for steady transonic flow is extended to bodies of revolution oscillating in a sonic flow field. A Laplace transform technique is employed to derive the dipole solution, and the Adams-Sears iterative technique is used in the stability derivative calculation. A computer program is developed to perform the stability derivative calculation for the slowly oscillating cone and parabolic ogive. Inputs for the program are body geometry thickness ratio, acceleration constant, and pitch axis location. Sample calculations were performed for the parabolic ogive and circular cone and results are compared with those obtained by using other techniques and the available experimental data for circular cones.

Transient excitation and data processing techniques employing the fast fourier transform for aeroelastic testing

NASA Technical Reports Server (NTRS)

Jennings, W. P.; Olsen, N. L.; Walter, M. J.

1976-01-01

The development of testing techniques useful in airplane ground resonance testing, wind tunnel aeroelastic model testing, and airplane flight flutter testing is presented. Included is the consideration of impulsive excitation, steady-state sinusoidal excitation, and random and pseudorandom excitation. Reasons for the selection of fast sine sweeps for transient excitation are given. The use of the fast fourier transform dynamic analyzer (HP-5451B) is presented, together with a curve fitting data process in the Laplace domain to experimentally evaluate values of generalized mass, model frequencies, dampings, and mode shapes. The effects of poor signal to noise ratios due to turbulence creating data variance are discussed. Data manipulation techniques used to overcome variance problems are also included. The experience is described that was gained by using these techniques since the early stages of the SST program. Data measured during 747 flight flutter tests, and SST, YC-14, and 727 empennage flutter model tests are included.

A system for rapid analysis of the femoral blood velocity waveform at the bedside.

PubMed

Capper, W L; Amoore, J N; Clifford, P C; Immelman, E J; Harries-Jones, E P

1986-01-01

The shape of the arterial blood velocity waveform varies with atherosclerotic disease and several methods of quantifying the shape in order to predict the severity of the disease have been described. These methods include pulsatility index, the Laplace transform method, and principal component analysis. This paper describes the development of a system which allows the operator to acquire, display, and store waveforms from each limb and then to quantify the waveforms at the bedside within a few minutes. The system includes a 10 MHz bi-directional Doppler unit, an instantaneous mean frequency processor, and an Apple II microcomputer fitted with an accelerator card. Both the Laplace transform parameters and the pulsatility index are computed and each result is printed in tabular form together with the averaged results of five waveforms from each limb. The printout is suitable for inclusion in the patient's folder. In initial clinical studies Laplace transform analysis exhibited a good correlation with aorto-iliac stenosis as assessed angiographically (R = 0.73 P less than 0.001 t test).

A new numerical method for inverse Laplace transforms used to obtain gluon distributions from the proton structure function

NASA Astrophysics Data System (ADS)

Block, Martin M.; Durand, Loyal

2011-11-01

We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace transforms needed to obtain gluon distributions from the proton structure function F2^{γ p}(x,Q2). We numerically inverted the function g( s), s being the variable in Laplace space, to G( v), where v is the variable in ordinary space. We have since discovered that the algorithm does not work if g( s)→0 less rapidly than 1/ s as s→∞, e.g., as 1/ s β for 0< β<1. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of β. The new algorithm is exact if the original function G( v) is given by the product of a power v β-1 and a polynomial in v. We test the algorithm numerically for very small positive β, β=10-6 obtaining numerical results that imitate the Dirac delta function δ( v). We also devolve the published MSTW2008LO gluon distribution at virtuality Q 2=5 GeV2 down to the lower virtuality Q 2=1.69 GeV2. For devolution, β is negative, giving rise to inverse Laplace transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.

Laplace transform homotopy perturbation method for the approximation of variational problems.

PubMed

Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R

2016-01-01

This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.

Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators

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

Helmich-Paris, Benjamin, E-mail: b.helmichparis@vu.nl; Visscher, Lucas, E-mail: l.visscher@vu.nl

2016-09-15

We present a robust and non-heuristic algorithm that finds all extremum points of the error distribution function of numerically Laplace-transformed orbital energy denominators. The extremum point search is one of the two key steps for finding the minimax approximation. If pre-tabulation of initial guesses is supposed to be avoided, strategies for a sufficiently robust algorithm have not been discussed so far. We compare our non-heuristic approach with a bracketing and bisection algorithm and demonstrate that 3 times less function evaluations are required altogether when applying it to typical non-relativistic and relativistic quantum chemical systems.

Time-temperature effect in adhesively bonded joints

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

The viscoelastic analysis of an adhesively bonded lap joint was reconsidered. The adherends are approximated by essentially Reissner plates and the adhesive is linearly viscoelastic. The hereditary integrals are used to model the adhesive. A linear integral differential equations system for the shear and the tensile stress in the adhesive is applied. The equations have constant coefficients and are solved by using Laplace transforms. It is shown that if the temperature variation in time can be approximated by a piecewise constant function, then the method of Laplace transforms can be used to solve the problem. A numerical example is given for a single lap joint under various loading conditions.

Numerical conversion of transient to harmonic response functions for linear viscoelastic materials.

PubMed

Buschmann, M D

1997-02-01

Viscoelastic material behavior is often characterized using one of the three measurements: creep, stress-relaxation or dynamic sinusoidal tests. A two-stage numerical method was developed to allow representation of data from creep and stress-relaxation tests on the Fourier axis in the Laplace domain. The method assumes linear behavior and is theoretically applicable to any transient test which attains an equilibrium state. The first stage numerically resolves the Laplace integral to convert temporal stress and strain data, from creep or stress-relaxation, to the stiffness function, G(s), evaluated on the positive real axis in the Laplace domain. This numerical integration alone allows the direct comparison of data from transient experiments which attain a final equilibrium state, such as creep and stress relaxation, and allows such data to be fitted to models expressed in the Laplace domain. The second stage of this numerical procedure maps the stiffness function, G(s), from the positive real axis to the positive imaginary axis to reveal the harmonic response function, or dynamic stiffness, G(j omega). The mapping for each angular frequency, s, is accomplished by fitting a polynomial to a subset of G(s) centered around a particular value of s, substituting js for s and thereby evaluating G(j omega). This two-stage transformation circumvents previous numerical difficulties associated with obtaining Fourier transforms of the stress and strain time domain signals. The accuracy of these transforms is verified using model functions from poroelasticity, corresponding to uniaxial confined compression of an isotropic material and uniaxial unconfined compression of a transversely isotropic material. The addition of noise to the model data does not significantly deteriorate the transformed results and data points need not be equally spaced in time. To exemplify its potential utility, this two-stage transform is applied to experimental stress relaxation data to obtain the dynamic stiffness which is then compared to direct measurements of dynamic stiffness using steady-state sinusoidal tests of the same cartilage disk in confined compression. In addition to allowing calculation of the dynamic stiffness from transient tests and the direct comparison of experimental data from different tests, these numerical methods should aid in the experimental analysis of linear and nonlinear material behavior, and increase the speed of curve-fitting routines by fitting creep or stress relaxation data to models expressed in the Laplace domain.

Off-axis impact of unidirectional composites with cracks: Dynamic stress intensification

NASA Technical Reports Server (NTRS)

Sih, G. C.; Chen, E. P.

1979-01-01

The dynamic response of unidirectional composites under off axis (angle loading) impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. The analytical method utilizes Fourier transform for the space variable and Laplace transform for the time variable. The off axis impact is separated into two parts, one being symmetric and the other skew-symmetric with reference to the crack plane. Transient boundary conditions of normal and shear tractions are applied to a crack embedded in the matrix of the unidirectional composite. The two boundary conditions are solved independently and the results superimposed. Mathematically, these conditions reduce the problem to a system of dual integral equations which are solved in the Laplace transform plane for the transformation of the dynamic stress intensity factor. The time inversion is carried out numerically for various combinations of the material properties of the composite and the results are displayed graphically.

Application of computerised penile arterial waveform analysis in the diagnosis of arteriogenic impotence. An initial study in potent and impotent men.

PubMed

Desai, K M; Gingell, J C; Skidmore, R; Follett, D H

1987-11-01

A new method is described for evaluating arteriogenic impotence by means of noninvasive quantification of penile Doppler arterial waveforms using computerised analysis based on the Laplace Transform model. The haemodynamic changes occurring during a papaverine-induced erection in healthy potent volunteers have been recorded by this technique, which has also been shown to be capable of discriminating between a normal and an abnormal penile arterial supply in an initial study of potent and impotent men.

Reflection and refraction of a transient temperature field at a plane interface using Cagniard-de Hoop approach.

PubMed

Shendeleva, M L

2001-09-01

An instantaneous line heat source located in the medium consisting of two half-spaces with different thermal properties is considered. Green's functions for the temperature field are derived using the Laplace and Fourier transforms in time and space and their inverting by the Cagniard-de Hoop technique known in elastodynamics. The characteristic feature of the proposed approach consists in the application of the Cagniard-de Hoop method to the transient heat conduction problem. The idea is suggested by the fact that the Laplace transform in time reduces the heat conduction equation to a Helmholtz equation, as for the wave propagation. Derived solutions exhibit some wave properties. First, the temperature field is decomposed into the source field and the reflected field in one half-space and the transmitted field in the other. Second, the laws of reflection and refraction can be deduced for the rays of the temperature field. In this connection the ray concept is briefly discussed. It is shown that the rays, introduced in such a way that they are consistent with Snell's law do not represent the directions of heat flux in the medium. Numerical computations of the temperature field as well as diagrams of rays and streamlines of the temperature field are presented.

Study on sampling of continuous linear system based on generalized Fourier transform

NASA Astrophysics Data System (ADS)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

PubMed

Murase, Kenya

2016-01-01

In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

Semi-analytic valuation of stock loans with finite maturity

NASA Astrophysics Data System (ADS)

Lu, Xiaoping; Putri, Endah R. M.

2015-10-01

In this paper we study stock loans of finite maturity with different dividend distributions semi-analytically using the analytical approximation method in Zhu (2006). Stock loan partial differential equations (PDEs) are established under Black-Scholes framework. Laplace transform method is used to solve the PDEs. Optimal exit price and stock loan value are obtained in Laplace space. Values in the original time space are recovered by numerical Laplace inversion. To demonstrate the efficiency and accuracy of our semi-analytic method several examples are presented, the results are compared with those calculated using existing methods. We also present a calculation of fair service fee charged by the lender for different loan parameters.

Use and Misuse of Laplace's Law in Ophthalmology.

PubMed

Chung, Cheuk Wang; Girard, Michaël J A; Jan, Ning-Jiun; Sigal, Ian A

2016-01-01

Laplace's Law, with its compactness and simplicity, has long been employed in ophthalmology for describing the mechanics of the corneoscleral shell. We questioned the appropriateness of Laplace's Law for computing wall stress in the eye considering the advances in knowledge of ocular biomechanics. In this manuscript we recapitulate the formulation of Laplace's Law, as well as common interpretations and uses in ophthalmology. Using numerical modeling, we study how Laplace's Law cannot account for important characteristics of the eye, such as variations in globe shape and size or tissue thickness, anisotropy, viscoelasticity, or that the eye is a living, dynamic organ. We show that accounting for various geometrical and material factors, excluded from Laplace's Law, can alter estimates of corneoscleral wall stress as much as 456% and, therefore, that Laplace's Law is unreliable. We conclude by illustrating how computational techniques, such as finite element modeling, can account for the factors mentioned above, and are thus more suitable tools to provide quantitative characterization of corneoscleral biomechanics.

Laplace and Z Transform Solutions of Differential and Difference Equations With the HP-41C.

ERIC Educational Resources Information Center

Harden, Richard C.; Simons, Fred O., Jr.

1983-01-01

A previously developed program for the HP-41C programmable calculator is extended to handle models of differential and difference equations with multiple eigenvalues. How to obtain difference equation solutions via the Z transform is described. (MNS)

Axisymmetric deformation in a micropolar thermoelastic medium under fractional order theory of thermoelasticity

NASA Astrophysics Data System (ADS)

Kumar, Rajneesh; Singh, Kulwinder; Pathania, Devinder Singh

2017-07-01

The purpose of this paper is to study the variations in temperature, radial and normal displacement, normal stress, shear stress and couple stress in a micropolar thermoelastic solid in the context of fractional order theory of thermoelasticity. Eigen value approach together with Laplace and Hankel transforms are employed to obtain the general solution of the problem. The field variables corresponding to different fractional order theories of thermoelasticity have been obtained in the transformed domain. The general solution is applied to an infinite space subjected to a concentrated load at the origin. To obtained solution in the physical domain numerical inversion technique has been applied and numerically computed results are depicted graphically to analyze the effects of fractional order parameter on the field variables.

Hall effects on unsteady MHD reactive flow of second grade fluid through porous medium in a rotating parallel plate channel

NASA Astrophysics Data System (ADS)

Krishna, M. Veera; Swarnalathamma, B. V.

2017-07-01

We considered the transient MHD flow of a reactive second grade fluid through porous medium between two infinitely long horizontal parallel plates when one of the plate is set into uniform accelerated motion in the presence of a uniform transverse magnetic field under Arrhenius reaction rate. The governing equations are solved by Laplace transform technique. The effects of the pertinent parameters on the velocity, temperature are discussed in detail. The shear stress and Nusselt number at the plates are also obtained analytically and computationally discussed with reference to governing parameters.

Closed Form Solutions for Unsteady Free Convection Flow of a Second Grade Fluid over an Oscillating Vertical Plate

PubMed Central

Ali, Farhad; Khan, Ilyas; Shafie, Sharidan

2014-01-01

Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ 0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions. PMID:24551033

Viscoelastic analysis of adhesively bonded joints

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1980-01-01

An adhesively bonded lap joint is analyzed by assuming that the adherends are elastic and the adhesive is linearly viscoelastic. After formulating the general problem a specific example for two identical adherends bonded through a three parameter viscoelastic solid adhesive is considered. The standard Laplace transform technique is used to solve the problem. The stress distribution in the adhesive layer is calculated for three different external loads, namely, membrane loading, bending, and transverse shear loading. The results indicate that the peak value of the normal stress in the adhesive is not only consistently higher than the corresponding shear stress but also decays slower.

Three-dimensional unsteady lifting surface theory in the subsonic range

NASA Technical Reports Server (NTRS)

Kuessner, H. G.

1985-01-01

The methods of the unsteady lifting surface theory are surveyed. Linearized Euler's equations are simplified by means of a Galileo-Lorentz transformation and a Laplace transformation so that the time and the compressibility of the fluid are limited to two constants. The solutions to this simplified problem are represented as integrals with a differential nucleus; these results in tolerance conditions, for which any exact solution must suffice. It is shown that none of the existing three-dimensional lifting surface theories in subsonic range satisfy these conditions. An oscillating elliptic lifting surface which satisfies the tolerance conditions is calculated through the use of Lame's functions. Numerical examples are calculated for the borderline cases of infinitely stretched elliptic lifting surfaces and of circular lifting surfaces. Out of the harmonic solutions any such temporal changes of the down current are calculated through the use of an inverse Laplace transformation.

Local CC2 response method for triplet states based on Laplace transform: excitation energies and first-order properties.

PubMed

Freundorfer, Katrin; Kats, Daniel; Korona, Tatiana; Schütz, Martin

2010-12-28

A new multistate local CC2 response method for calculating excitation energies and first-order properties of excited triplet states in extended molecular systems is presented. The Laplace transform technique is employed to partition the left/right local CC2 eigenvalue problems as well as the linear equations determining the Lagrange multipliers needed for the properties. The doubles part in the equations can then be inverted on-the-fly and only effective equations for the singles part must be solved iteratively. The local approximation presented here is adaptive and state-specific. The density-fitting method is utilized to approximate the electron-repulsion integrals. The accuracy of the new method is tested by comparison to canonical reference values for a set of 12 test molecules and 62 excited triplet states. As an illustrative application example, the lowest four triplet states of 3-(5-(5-(4-(bis(4-(hexyloxy)phenyl)amino)phenyl)thiophene-2-yl)thiophene-2-yl)-2-cyanoacrylic acid, an organic sensitizer for solar-cell applications, are computed in the present work. No triplet charge-transfer states are detected among these states. This situation contrasts with the singlet states of this molecule, where the lowest singlet state has been recently found to correspond to an excited state with a pronounced charge-transfer character having a large transition strength.

A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method

NASA Astrophysics Data System (ADS)

Vu, Q. H.; Brenner, R.; Castelnau, O.; Moulinec, H.; Suquet, P.

2012-03-01

The correspondence principle is customarily used with the Laplace-Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mécanique des Milieux Continus(Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct. 46 1599-1606) have shown the equivalence between the collocation method used to invert Laplace-Carson transforms and an internal variables formulation. In this paper, this new method is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered.

Myocardial wall thickening from gated magnetic resonance images using Laplace's equation

NASA Astrophysics Data System (ADS)

Prasad, M.; Ramesh, A.; Kavanagh, P.; Gerlach, J.; Germano, G.; Berman, D. S.; Slomka, P. J.

2009-02-01

The aim of our work is to present a robust 3D automated method for measuring regional myocardial thickening using cardiac magnetic resonance imaging (MRI) based on Laplace's equation. Multiple slices of the myocardium in short-axis orientation at end-diastolic and end-systolic phases were considered for this analysis. Automatically assigned 3D epicardial and endocardial boundaries were fitted to short-axis and long axis slices corrected for breathold related misregistration, and final boundaries were edited by a cardiologist if required. Myocardial thickness was quantified at the two cardiac phases by computing the distances between the myocardial boundaries over the entire volume using Laplace's equation. The distance between the surfaces was found by computing normalized gradients that form a vector field. The vector fields represent tangent vectors along field lines connecting both boundaries. 3D thickening measurements were transformed into polar map representation and 17-segment model (American Heart Association) regional thickening values were derived. The thickening results were then compared with standard 17-segment 6-point visual scoring of wall motion/wall thickening (0=normal; 5=greatest abnormality) performed by a consensus of two experienced imaging cardiologists. Preliminary results on eight subjects indicated a strong negative correlation (r=-0.8, p<0.0001) between the average thickening obtained using Laplace and the summed segmental visual scores. Additionally, quantitative ejection fraction measurements also correlated well with average thickening scores (r=0.72, p<0.0001). For segmental analysis, we obtained an overall correlation of -0.55 (p<0.0001) with higher agreement along the mid and apical regions (r=-0.6). In conclusion 3D Laplace transform can be used to quantify myocardial thickening in 3D.

Hipergeometric solutions to some nonhomogeneous equations of fractional order

NASA Astrophysics Data System (ADS)

Olivares, Jorge; Martin, Pablo; Maass, Fernando

2017-12-01

In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 < alpha < 1. Caputo definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.

Process Dynamics and Control, a Theory-Experiential Approach.

ERIC Educational Resources Information Center

Perna, A. J.; And Others

A required senior-level chemical engineering course at Colorado State University is described. The first nine weeks are devoted to the theory portion of the course, which includes the following topics: LaPlace transformations and time constants, block diagrams, inverse transformations, linearization, frequency response analysis, graphical…

The Cagniard Method in Complex Time Revisited

DTIC Science & Technology

1991-04-04

make the p-integral take the form of a forward Laplace transform, so that the cascade of the two integrals can be identified as a forward and inverse ... transform , thereby making the actual integration unnecessary. Typically, the method is applied to an integral that represents one body wave plus other

Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform.

PubMed

Nagy, Péter R; Kállay, Mihály

2017-06-07

An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor.

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

NASA Astrophysics Data System (ADS)

Igumnov, Leonid; Ipatov, Aleksandr; Belov, Aleksandr; Petrov, Andrey

2015-09-01

The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.

Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform

PubMed Central

2017-01-01

An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor. PMID:28576082

A Lagging Model for Describing Drawdown Induced by a Constant-Rate Pumping in a Leaky Confined Aquifer

NASA Astrophysics Data System (ADS)

Lin, Ye-Chen; Yeh, Hund-Der

2017-10-01

This study proposes a generalized Darcy's law with considering phase lags in both the water flux and drawdown gradient to develop a lagging flow model for describing drawdown induced by constant-rate pumping (CRP) in a leaky confined aquifer. The present model has a mathematical formulation similar to the dual-porosity model. The Laplace-domain solution of the model with the effect of wellbore storage is derived by the Laplace transform method. The time-domain solution for the case of neglecting the wellbore storage and well radius is developed by the use of Laplace transform and Weber transform. The results of sensitivity analysis based on the solution indicate that the drawdown is very sensitive to the change in each of the transmissivity and storativity. Also, a study for the lagging effect on the drawdown indicates that its influence is significant associated with the lag times. The present solution is also employed to analyze a data set taken from a CRP test conducted in a fractured aquifer in South Dakota, USA. The results show the prediction of this new solution with considering the phase lags has very good fit to the field data, especially at early pumping time. In addition, the phase lags seem to have a scale effect as indicated in the results. In other words, the lagging behavior is positively correlated with the observed distance in the Madison aquifer.

Some practical observations on the predictor jump method for solving the Laplace equation

NASA Astrophysics Data System (ADS)

Duque-Carrillo, J. F.; Vega-Fernández, J. M.; Peña-Bernal, J. J.; Rossell-Bueno, M. A.

1986-01-01

The best conditions for the application of the predictor jump (PJ) method in the solution of the Laplace equation are discussed and some practical considerations for applying this new iterative technique are presented. The PJ method was remarked on in a previous article entitled ``A new way for solving Laplace's problem (the predictor jump method)'' [J. M. Vega-Fernández, J. F. Duque-Carrillo, and J. J. Peña-Bernal, J. Math. Phys. 26, 416 (1985)].

Exact solution for heat transfer free convection flow of Maxwell nanofluids with graphene nanoparticles

NASA Astrophysics Data System (ADS)

Aman, Sidra; Zuki Salleh, Mohd; Ismail, Zulkhibri; Khan, Ilyas

2017-09-01

This article focuses on the flow of Maxwell nanofluids with graphene nanoparticles over a vertical plate (static) with constant wall temperature. Possessing high thermal conductivity, engine oil is useful to be chosen as base fluid with free convection. The problem is modelled in terms of PDE’s with boundary conditions. Some suitable non-dimensional variables are interposed to transform the governing equations into dimensionless form. The generated equations are solved via Laplace transform technique. Exact solutions are evaluated for velocity and temperature. These solutions are significantly controlled by some parameters involved. Temperature rises with elevation in volume fraction while Velocity decreases with increment in volume fraction. A comparison with previous published results are established and discussed. Moreover, a detailed discussion is made for influence of volume fraction on the flow and heat profile.

Decoupling the NLO-coupled QED⊗QCD, DGLAP evolution equations, using Laplace transform method

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Waveform shape analysis: extraction of physiologically relevant information from Doppler recordings.

PubMed

Ramsay, M M; Broughton Pipkin, F; Rubin, P C; Skidmore, R

1994-05-01

1. Doppler recordings were made from the brachial artery of healthy female subjects during a series of manoeuvres which altered the pressure-flow characteristics of the vessel. 2. Changes were induced in the peripheral circulation of the forearm by the application of heat or ice-packs. A sphygmomanometer cuff was used to create graded occlusion of the vessel above and below the point of measurement. Recordings were also made whilst the subjects performed a standardized Valsalva manoeuvre. 3. The Doppler recordings were analysed both with the standard waveform indices (systolic/diastolic ratio, pulsatility index and resistance index) and by the method of Laplace transform analysis. 4. The waveform parameters obtained by Laplace transform analysis distinguished the different changes in flow conditions; they thus had direct physiological relevance, unlike the standard waveform indices.

Turbulence excited frequency domain damping measurement and truncation effects

NASA Technical Reports Server (NTRS)

Soovere, J.

1976-01-01

Existing frequency domain modal frequency and damping analysis methods are discussed. The effects of truncation in the Laplace and Fourier transform data analysis methods are described. Methods for eliminating truncation errors from measured damping are presented. Implications of truncation effects in fast Fourier transform analysis are discussed. Limited comparison with test data is presented.

A new principle technic for the transformation from frequency domain to time domain

NASA Astrophysics Data System (ADS)

Gao, Ben-Qing

2017-03-01

A principle technic for the transformation from frequency domain to time domain is presented. Firstly, a special type of frequency domain transcendental equation is obtained for an expected frequency domain parameter which is a rational or irrational fraction expression. Secondly, the inverse Laplace transformation is performed. When the two time-domain factors corresponding to the two frequency domain factors at two sides of frequency domain transcendental equation are known quantities, a time domain transcendental equation is reached. At last, the expected time domain parameter corresponding to the expected frequency domain parameter can be solved by the inverse convolution process. Proceeding from rational or irrational fraction expression, all solving process is provided. In the meantime, the property of time domain sequence is analyzed and the strategy for choosing the parameter values is described. Numerical examples are presented to verify the proposed theory and technic. Except for rational or irrational fraction expressions, examples of complex relative permittivity of water and plasma are used as verification method. The principle method proposed in the paper can easily solve problems which are difficult to be solved by Laplace transformation.

Viscoelastic analysis of adhesively bonded joints

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

In this paper an adhesively bonded lap joint is analyzed by assuming that the adherends are elastic and the adhesive is linearly viscoelastic. After formulating the general problem a specific example for two identical adherends bonded through a three parameter viscoelastic solid adhesive is considered. The standard Laplace transform technique is used to solve the problem. The stress distribution in the adhesive layer is calculated for three different external loads namely, membrane loading, bending, and transverse shear loading. The results indicate that the peak value of the normal stress in the adhesive is not only consistently higher than the corresponding shear stress but also decays slower.

Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems

NASA Astrophysics Data System (ADS)

Lenka, Bichitra Kumar; Banerjee, Soumitro

2018-03-01

We discuss the asymptotic stability of autonomous linear and nonlinear fractional order systems where the state equations contain same or different fractional orders which lie between 0 and 2. First, we use the Laplace transform method to derive some sufficient conditions which ensure asymptotic stability of linear fractional order systems. Then by using the obtained results and linearization technique, a stability theorem is presented for autonomous nonlinear fractional order system. Finally, we design a control strategy for stabilization of autonomous nonlinear fractional order systems, and apply the results to the chaotic fractional order Lorenz system in order to verify its effectiveness.

Hybrid asymptotic-numerical approach for estimating first-passage-time densities of the two-dimensional narrow capture problem.

PubMed

Lindsay, A E; Spoonmore, R T; Tzou, J C

2016-10-01

A hybrid asymptotic-numerical method is presented for obtaining an asymptotic estimate for the full probability distribution of capture times of a random walker by multiple small traps located inside a bounded two-dimensional domain with a reflecting boundary. As motivation for this study, we calculate the variance in the capture time of a random walker by a single interior trap and determine this quantity to be comparable in magnitude to the mean. This implies that the mean is not necessarily reflective of typical capture times and that the full density must be determined. To solve the underlying diffusion equation, the method of Laplace transforms is used to obtain an elliptic problem of modified Helmholtz type. In the limit of vanishing trap sizes, each trap is represented as a Dirac point source that permits the solution of the transform equation to be represented as a superposition of Helmholtz Green's functions. Using this solution, we construct asymptotic short-time solutions of the first-passage-time density, which captures peaks associated with rapid capture by the absorbing traps. When numerical evaluation of the Helmholtz Green's function is employed followed by numerical inversion of the Laplace transform, the method reproduces the density for larger times. We demonstrate the accuracy of our solution technique with a comparison to statistics obtained from a time-dependent solution of the diffusion equation and discrete particle simulations. In particular, we demonstrate that the method is capable of capturing the multimodal behavior in the capture time density that arises when the traps are strategically arranged. The hybrid method presented can be applied to scenarios involving both arbitrary domains and trap shapes.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

Comparison of methods applied in photoinduced transient spectroscopy to determining the defect center parameters: The correlation procedure and the signal analysis based on inverse Laplace transformation

NASA Astrophysics Data System (ADS)

Suproniuk, M.; Pawłowski, M.; Wierzbowski, M.; Majda-Zdancewicz, E.; Pawłowski, Ma.

2018-04-01

The procedure for determination of trap parameters by photo-induced transient spectroscopy is based on the Arrhenius plot that illustrates a thermal dependence of the emission rate. In this paper, we show that the Arrhenius plot obtained by the correlation method is shifted toward lower temperatures as compared to the one obtained with the inverse Laplace transformation. This shift is caused by the model adequacy error of the correlation method and introduces errors to a calculation procedure of defect center parameters. The effect is exemplified by comparing the results of the determination of trap parameters with both methods based on photocurrent transients for defect centers observed in tin-doped neutron-irradiated silicon crystals and in gallium arsenide grown with the Vertical Gradient Freeze method.

Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-11-01

The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

Electromagnetic field scattering by a triangular aperture.

PubMed

Harrison, R E; Hyman, E

1979-03-15

The multiple Laplace transform has been applied to analysis and computation of scattering by a double triangular aperture. Results are obtained which match far-field intensity distributions observed in experiments. Arbitrary polarization components, as well as in-phase and quadrature-phase components, may be determined, in the transform domain, as a continuous function of distance from near to far-field for any orientation, aperture, and transformable waveform. Numerical results are obtained by application of numerical multiple inversions of the fully transformed solution.

Ultrasonic wave propagation in viscoelastic cortical bone plate coupled with fluids: a spectral finite element study.

PubMed

Nguyen, Vu-Hieu; Naili, Salah

2013-01-01

This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally graded anisotropic material coupled with fluids. The viscous effects are taken into account. The geometrical configuration mimics the one of axial transmission technique used for evaluating the bone quality. We present a numerical procedure adapted for this purpose which is based on the spectral finite element method (FEM). By using a combined Laplace-Fourier transform, the vibroacoustic problem may be transformed into the frequency-wavenumber domain in which, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analysed using FEM. Several numerical tests are presented showing very good performance of the proposed approach. We present some results to study the influence of the frequency on the first arriving signal velocity in (visco)elastic bone plate.

Statistical Modeling of Retinal Optical Coherence Tomography.

PubMed

Amini, Zahra; Rabbani, Hossein

2016-06-01

In this paper, a new model for retinal Optical Coherence Tomography (OCT) images is proposed. This statistical model is based on introducing a nonlinear Gaussianization transform to convert the probability distribution function (pdf) of each OCT intra-retinal layer to a Gaussian distribution. The retina is a layered structure and in OCT each of these layers has a specific pdf which is corrupted by speckle noise, therefore a mixture model for statistical modeling of OCT images is proposed. A Normal-Laplace distribution, which is a convolution of a Laplace pdf and Gaussian noise, is proposed as the distribution of each component of this model. The reason for choosing Laplace pdf is the monotonically decaying behavior of OCT intensities in each layer for healthy cases. After fitting a mixture model to the data, each component is gaussianized and all of them are combined by Averaged Maximum A Posterior (AMAP) method. To demonstrate the ability of this method, a new contrast enhancement method based on this statistical model is proposed and tested on thirteen healthy 3D OCTs taken by the Topcon 3D OCT and five 3D OCTs from Age-related Macular Degeneration (AMD) patients, taken by Zeiss Cirrus HD-OCT. Comparing the results with two contending techniques, the prominence of the proposed method is demonstrated both visually and numerically. Furthermore, to prove the efficacy of the proposed method for a more direct and specific purpose, an improvement in the segmentation of intra-retinal layers using the proposed contrast enhancement method as a preprocessing step, is demonstrated.

Compression of 3D Point Clouds Using a Region-Adaptive Hierarchical Transform.

PubMed

De Queiroz, Ricardo; Chou, Philip A

2016-06-01

In free-viewpoint video, there is a recent trend to represent scene objects as solids rather than using multiple depth maps. Point clouds have been used in computer graphics for a long time and with the recent possibility of real time capturing and rendering, point clouds have been favored over meshes in order to save computation. Each point in the cloud is associated with its 3D position and its color. We devise a method to compress the colors in point clouds which is based on a hierarchical transform and arithmetic coding. The transform is a hierarchical sub-band transform that resembles an adaptive variation of a Haar wavelet. The arithmetic encoding of the coefficients assumes Laplace distributions, one per sub-band. The Laplace parameter for each distribution is transmitted to the decoder using a custom method. The geometry of the point cloud is encoded using the well-established octtree scanning. Results show that the proposed solution performs comparably to the current state-of-the-art, in many occasions outperforming it, while being much more computationally efficient. We believe this work represents the state-of-the-art in intra-frame compression of point clouds for real-time 3D video.

Performance of some numerical Laplace inversion methods on American put option formula

NASA Astrophysics Data System (ADS)

Octaviano, I.; Yuniar, A. R.; Anisa, L.; Surjanto, S. D.; Putri, E. R. M.

2018-03-01

Numerical inversion approaches of Laplace transform is used to obtain a semianalytic solution. Some of the mathematical inversion methods such as Durbin-Crump, Widder, and Papoulis can be used to calculate American put options through the optimal exercise price in the Laplace space. The comparison of methods on some simple functions is aimed to know the accuracy and parameters which used in the calculation of American put options. The result obtained is the performance of each method regarding accuracy and computational speed. The Durbin-Crump method has an average error relative of 2.006e-004 with computational speed of 0.04871 seconds, the Widder method has an average error relative of 0.0048 with computational speed of 3.100181 seconds, and the Papoulis method has an average error relative of 9.8558e-004 with computational speed of 0.020793 seconds.

Simultaneous Gaussian and exponential inversion for improved analysis of shales by NMR relaxometry

USGS Publications Warehouse

Washburn, Kathryn E.; Anderssen, Endre; Vogt, Sarah J.; Seymour, Joseph D.; Birdwell, Justin E.; Kirkland, Catherine M.; Codd, Sarah L.

2014-01-01

Nuclear magnetic resonance (NMR) relaxometry is commonly used to provide lithology-independent porosity and pore-size estimates for petroleum resource evaluation based on fluid-phase signals. However in shales, substantial hydrogen content is associated with solid and fluid signals and both may be detected. Depending on the motional regime, the signal from the solids may be best described using either exponential or Gaussian decay functions. When the inverse Laplace transform, the standard method for analysis of NMR relaxometry results, is applied to data containing Gaussian decays, this can lead to physically unrealistic responses such as signal or porosity overcall and relaxation times that are too short to be determined using the applied instrument settings. We apply a new simultaneous Gaussian-Exponential (SGE) inversion method to simulated data and measured results obtained on a variety of oil shale samples. The SGE inversion produces more physically realistic results than the inverse Laplace transform and displays more consistent relaxation behavior at high magnetic field strengths. Residuals for the SGE inversion are consistently lower than for the inverse Laplace method and signal overcall at short T2 times is mitigated. Beyond geological samples, the method can also be applied in other fields where the sample relaxation consists of both Gaussian and exponential decays, for example in material, medical and food sciences.

Influence of wall couple stress in MHD flow of a micropolar fluid in a porous medium with energy and concentration transfer

NASA Astrophysics Data System (ADS)

Khalid, Asma; Khan, Ilyas; Khan, Arshad; Shafie, Sharidan

2018-06-01

The intention here is to investigate the effects of wall couple stress with energy and concentration transfer in magnetohydrodynamic (MHD) flow of a micropolar fluid embedded in a porous medium. The mathematical model contains the set of linear conservation forms of partial differential equations. Laplace transforms and convolution technique are used for computation of exact solutions of velocity, microrotations, temperature and concentration equations. Numerical values of skin friction, couple wall stress, Nusselt and Sherwood numbers are also computed. Characteristics for the significant variables on the physical quantities are graphically discussed. Comparison with previously published work in limiting sense shows an excellent agreement.

Applications of Laplace transform methods to airfoil motion and stability calculations

NASA Technical Reports Server (NTRS)

Edwards, J. W.

1979-01-01

This paper reviews the development of generalized unsteady aerodynamic theory and presents a derivation of the generalized Possio integral equation. Numerical calculations resolve questions concerning subsonic indicial lift functions and demonstrate the generation of Kutta waves at high values of reduced frequency, subsonic Mach number, or both. The use of rational function approximations of unsteady aerodynamic loads in aeroelastic stability calculations is reviewed, and a reformulation of the matrix Pade approximation technique is given. Numerical examples of flutter boundary calculations for a wing which is to be flight tested are given. Finally, a simplified aerodynamic model of transonic flow is used to study the stability of an airfoil exposed to supersonic and subsonic flow regions.

Hyperasymptotics and quark-hadron duality violations in QCD

NASA Astrophysics Data System (ADS)

Boito, Diogo; Caprini, Irinel; Golterman, Maarten; Maltman, Kim; Peris, Santiago

2018-03-01

We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex q2 plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality-violating contributions. Starting with the assumption that for QCD at Nc=∞ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite Nc.

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

Boroun, G. R., E-mail: grboroun@gmail.com, E-mail: boroun@razi.ac.ir; Zarrin, S.; Dadfar, S.

We evaluate the non-singlet spin-dependent structure function g{sub 1}{sup NS} at leading order (LO) and next-to-leading order (NLO) by using the Laplace-transform technique and method of characteristics and also obtain its first moment at NLO. The polarized non-singlet structure function results are compared with the data from HERMES (A. Airapetian et al., Phys. Rev. D 75, 012007 (2007)) and E143 (K. Abe et al. (E143 Collab.), Phys. Rev. D 58, 112003 (1998)) at LO and NLO analyses and the first-moment the result at NLO is compared with the result of the NLO GRSV2000 fit. Considering the solution, this method ismore » valid at low- and large-x regions.« less

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 reconstruction of dental X-ray tubes using laplace inverse transform of the attenuation curve

NASA Astrophysics Data System (ADS)

Malezan, A.; Tomal, A.; Antoniassi, M.; Watanabe, P. C. A.; Albino, L. D.; Poletti, M. E.

2015-11-01

In this work, a spectral reconstruction methodology for diagnostic X-ray, using Laplace inverse transform of the attenuation, was successfully applied to dental X-ray equipments. The attenuation curves of 8 commercially available dental X-ray equipment, from 3 different manufactures (Siemens, Gnatus and Dabi Atlante), were obtained by using an ionization chamber and high purity aluminium filters, while the kVp was obtained with a specific meter. A computational routine was implemented in order to adjust a model function, whose inverse Laplace transform is analytically known, to the attenuation curve. This methodology was validated by comparing the reconstructed and the measured (using semiconductor detector of cadmium telluride) spectra of a given dental X-ray unit. The spectral reconstruction showed the Dabi Atlante equipments generating similar shape spectra. This is a desirable feature from clinic standpoint because it produces similar levels of image quality and dose. We observed that equipments from Siemens and Gnatus generate significantly different spectra, suggesting that, for a given operating protocol, these units will present different levels of image quality and dose. This fact claims for the necessity of individualized operating protocols that maximize image quality and dose. The proposed methodology is suitable to perform a spectral reconstruction of dental X-ray equipments from the simple measurements of attenuation curve and kVp. The simplified experimental apparatus and the low level of technical difficulty make this methodology accessible to a broad range of users. The knowledge of the spectral distribution can help in the development of operating protocols that maximize image quality and dose.

Computing the Distribution of Pareto Sums Using Laplace Transformation and Stehfest Inversion

NASA Astrophysics Data System (ADS)

Harris, C. K.; Bourne, S. J.

2017-05-01

In statistical seismology, the properties of distributions of total seismic moment are important for constraining seismological models, such as the strain partitioning model (Bourne et al. J Geophys Res Solid Earth 119(12): 8991-9015, 2014). This work was motivated by the need to develop appropriate seismological models for the Groningen gas field in the northeastern Netherlands, in order to address the issue of production-induced seismicity. The total seismic moment is the sum of the moments of individual seismic events, which in common with many other natural processes, are governed by Pareto or "power law" distributions. The maximum possible moment for an induced seismic event can be constrained by geomechanical considerations, but rather poorly, and for Groningen it cannot be reliably inferred from the frequency distribution of moment magnitude pertaining to the catalogue of observed events. In such cases it is usual to work with the simplest form of the Pareto distribution without an upper bound, and we follow the same approach here. In the case of seismicity, the exponent β appearing in the power-law relation is small enough for the variance of the unbounded Pareto distribution to be infinite, which renders standard statistical methods concerning sums of statistical variables, based on the central limit theorem, inapplicable. Determinations of the properties of sums of moderate to large numbers of Pareto-distributed variables with infinite variance have traditionally been addressed using intensive Monte Carlo simulations. This paper presents a novel method for accurate determination of the properties of such sums that is accurate, fast and easily implemented, and is applicable to Pareto-distributed variables for which the power-law exponent β lies within the interval [0, 1]. It is based on shifting the original variables so that a non-zero density is obtained exclusively for non-negative values of the parameter and is identically zero elsewhere, a property that is shared by the sum of an arbitrary number of such variables. The technique involves applying the Laplace transform to the normalized sum (which is simply the product of the Laplace transforms of the densities of the individual variables, with a suitable scaling of the Laplace variable), and then inverting it numerically using the Gaver-Stehfest algorithm. After validating the method using a number of test cases, it was applied to address the distribution of total seismic moment, and the quantiles computed for various numbers of seismic events were compared with those obtained in the literature using Monte Carlo simulation. Excellent agreement was obtained. As an application, the method was applied to the evolution of total seismic moment released by tremors due to gas production in the Groningen gas field in the northeastern Netherlands. The speed, accuracy and ease of implementation of the method allows the development of accurate correlations for constraining statistical seismological models using, for example, the maximum-likelihood method. It should also be of value in other natural processes governed by Pareto distributions with exponent less than unity.

Solution of Fifth-order Korteweg and de Vries Equation by Homotopy perturbation Transform Method using He's Polynomial

NASA Astrophysics Data System (ADS)

Sharma, Dinkar; Singh, Prince; Chauhan, Shubha

2017-06-01

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is applied to solve nonlinear fifth order Korteweg de Vries (KdV) equations. The method is known as homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He's polynomials. Two test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM).

Experimental demonstration of conformal phased array antenna via transformation optics.

PubMed

Lei, Juan; Yang, Juxing; Chen, Xi; Zhang, Zhiya; Fu, Guang; Hao, Yang

2018-02-28

Transformation Optics has been proven a versatile technique for designing novel electromagnetic devices and it has much wider applicability in many subject areas related to general wave equations. Among them, quasi-conformal transformation optics (QCTO) can be applied to minimize anisotropy of transformed media and has opened up the possibility to the design of broadband antennas with arbitrary geometries. In this work, a wide-angle scanning conformal phased array based on all-dielectric QCTO lens is designed and experimentally demonstrated. Excited by the same current distribution as such in a conventional planar array, the conformal system in presence of QCTO lens can preserve the same radiation characteristics of a planar array with wide-angle beam-scanning and low side lobe level (SLL). Laplace's equation subject to Dirichlet-Neumann boundary conditions is adopted to construct the mapping between the virtual and physical spaces. The isotropic lens with graded refractive index is realized by all-dielectric holey structure after an effective parameter approximation. The measurements of the fabricated system agree well with the simulated results, which demonstrate its excellent wide-angle beam scanning performance. Such demonstration paves the way to a robust but efficient array synthesis, as well as multi-beam and beam forming realization of conformal arrays via transformation optics.

The acoustic response of rooms with open windows to airborne sounds.

NASA Technical Reports Server (NTRS)

Vaidya, P. G.

1972-01-01

The objective of the work described in this and the companion paper was to establish a theory for predicting the sound field generated in a room by a sonic boom incident on an open window. In this paper, some basic theoretical results are presented. First, the case of a normally incident harmonic wave was considered. Expressions for the pressure field were obtained by viewing the room as a terminated duct and by using a Green function method. The concept of mode excitation distribution functions was formulated and used to match the boundary conditions. This concept has been extended for oblique incidence. A modified form of Laplace transform technique was used to obtain expressions in the time domain for transient signals.

Finite state modeling of aeroelastic systems

NASA Technical Reports Server (NTRS)

Vepa, R.

1977-01-01

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

Variable mass diffusion effects on free convection flow past an impulsively started infinite vertical plate

NASA Astrophysics Data System (ADS)

Rushi Kumar, B.; Jayakar, R.; Vijay Kumar, A. G.

2017-11-01

An exact analysis of the problem of free convection flow of a viscous incompressible chemically reacting fluid past an infinite vertical plate with the flow due to impulsive motion of the plate with Newtonian heating in the presence of thermal radiation and variable mass diffusion is performed. The resulting governing equations were tackled by Laplace transform technique. Finally the effects of pertinent flow parameters such as the radiation parameter, chemical reaction parameter, buoyancy ratio parameter, thermal Grashof number, Schmidt number, Prandtl number and time on the velocity, temperature, concentration and skin friction for both aiding and opposing flows were examined in detail when Pr=0.71(conducting air) and Pr=7.0(water).

A Semi-Analytical Solution to Time Dependent Groundwater Flow Equation Incorporating Stream-Wetland-Aquifer Interactions

NASA Astrophysics Data System (ADS)

Boyraz, Uǧur; Melek Kazezyılmaz-Alhan, Cevza

2017-04-01

Groundwater is a vital element of hydrologic cycle and the analytical & numerical solutions of different forms of groundwater flow equations play an important role in understanding the hydrological behavior of subsurface water. The interaction between groundwater and surface water bodies can be determined using these solutions. In this study, new hypothetical approaches are implemented to groundwater flow system in order to contribute to the studies on surface water/groundwater interactions. A time dependent problem is considered in a 2-dimensional stream-wetland-aquifer system. The sloped stream boundary is used to represent the interaction between stream and aquifer. The rest of the aquifer boundaries are assumed as no-flux boundary. In addition, a wetland is considered as a surface water body which lies over the whole aquifer. The effect of the interaction between the wetland and the aquifer is taken into account with a source/sink term in the groundwater flow equation and the interaction flow is calculated by using Darcy's approach. A semi-analytical solution is developed for the 2-dimensional groundwater flow equation in 5 steps. First, Laplace and Fourier cosine transforms are employed to obtain the general solution in Fourier and Laplace domain. Then, the initial and boundary conditions are applied to obtain the particular solution. Finally, inverse Fourier transform is carried out analytically and inverse Laplace transform is carried out numerically to obtain the final solution in space and time domain, respectively. In order to verify the semi-analytical solution, an explicit finite difference algorithm is developed and analytical and numerical solutions are compared for synthetic examples. The comparison of the analytical and numerical solutions shows that the analytical solution gives accurate results.

An Overview of the Common Fluid Models Used in Fluid-Structure Interactions

DTIC Science & Technology

1991-08-05

inverse transform of (63) and us- ing the relation f (t - a) = exp (iwa)f(0) (64) for arbitrary (reasonably behaved) f, with f = C and a = r/c since...lri( r - ) - F -la* exp(ikr)dS’ using (53). The inverse transform of this equation gives 3 rV (Xi, t) = 2Vi c + T r3’fV+(- C (an ))dS’ (72) upon...T, when it exists, has the property rl-Tf= T=rf = f for a generic function f, the Laplace transform and inverse transform being examples of such a T

The Relationship between Ground Permittivity and the Input Impedance of a Horizontal Dipole near Ground

DTIC Science & Technology

1989-04-01

only one of the terms. Thus, the inverse transform of the dyadic part of R is accomplished by simply replacing KK with -VtV t, where Vt is the x-y...KK/k2 . (2.30) The inverse transform of RTE can be found in the Laplace transform tables [18] or [19] to be L-I RE)=-2 J2 (kt4 iT)L-tRTE) = (2.31) -2...discussed in further detail in the next chapter. 9 The inverse transform of the second term of the reflection dyadic, Ro, is somewhat more difficult than

Investigation into the Effects of Weapon Setback on Various Materials and Geometries.

DTIC Science & Technology

1978-07-01

taking the Laplace Transform of the dynamic equation, rearrangement and taking the inverse transform to find the time-dependent strain. The "dynamic...taking the inverse transform of the above equation: ■»-«fa-to*« 1 E’ ♦ ¥®*> B’ (s+-fj- )(S2+f )T If we neglect the residual strain on the system...partial fractions yields: *t) --f (fr JC-> K, K2 —L_ + + K3 »+-^ s+i(f) s-i(f) performing the inverse transform yields: 4©[K,^> ♦ K2

Spatially resolved D-T(2) correlation NMR of porous media.

PubMed

Zhang, Yan; Blümich, Bernhard

2014-05-01

Within the past decade, 2D Laplace nuclear magnetic resonance (NMR) has been developed to analyze pore geometry and diffusion of fluids in porous media on the micrometer scale. Many objects like rocks and concrete are heterogeneous on the macroscopic scale, and an integral analysis of microscopic properties provides volume-averaged information. Magnetic resonance imaging (MRI) resolves this spatial average on the contrast scale set by the particular MRI technique. Desirable contrast parameters for studies of fluid transport in porous media derive from the pore-size distribution and the pore connectivity. These microscopic parameters are accessed by 1D and 2D Laplace NMR techniques. It is therefore desirable to combine MRI and 2D Laplace NMR to image functional information on fluid transport in porous media. Because 2D Laplace resolved MRI demands excessive measuring time, this study investigates the possibility to restrict the 2D Laplace analysis to the sum signals from low-resolution pixels, which correspond to pixels of similar amplitude in high-resolution images. In this exploratory study spatially resolved D-T2 correlation maps from glass beads and mortar are analyzed. Regions of similar contrast are first identified in high-resolution images to locate corresponding pixels in low-resolution images generated with D-T2 resolved MRI for subsequent pixel summation to improve the signal-to-noise ratio of contrast-specific D-T2 maps. This method is expected to contribute valuable information on correlated sample heterogeneity from the macroscopic and the microscopic scales in various types of porous materials including building materials and rock. Copyright © 2014 Elsevier Inc. All rights reserved.

Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags

NASA Astrophysics Data System (ADS)

Karmakar, R.; Sur, A.; Kanoria, M.

2016-07-01

The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord-Shulman and dual-phase-lag models.

Two-Compartment Pharmacokinetic Models for Chemical Engineers

ERIC Educational Resources Information Center

Kanneganti, Kumud; Simon, Laurent

2011-01-01

The transport of potassium permanganate between two continuous-stirred vessels was investigated to help chemical and biomedical engineering students understand two-compartment pharmacokinetic models. Concepts of modeling, mass balance, parameter estimation and Laplace transform were applied to the two-unit process. A good agreement was achieved…

Improved pulse shape discrimination in EJ-301 liquid scintillators

NASA Astrophysics Data System (ADS)

Lang, R. F.; Masson, D.; Pienaar, J.; Röttger, S.

2017-06-01

Digital pulse shape discrimination has become readily available to distinguish nuclear recoil and electronic recoil events in scintillation detectors. We evaluate digital implementations of pulse shape discrimination algorithms discussed in the literature, namely the Charge Comparison Method, Pulse-Gradient Analysis, Fourier Series and Standard Event Fitting. In addition, we present a novel algorithm based on a Laplace Transform. Instead of comparing the performance of these algorithms based on a single Figure of Merit, we evaluate them as a function of recoil energy. Specifically, using commercial EJ-301 liquid scintillators, we examined both the resulting acceptance of nuclear recoils at a given rejection level of electronic recoils, as well as the purity of the selected nuclear recoil event samples. We find that both a Standard Event fit and a Laplace Transform can be used to significantly improve the discrimination capabilities over the whole considered energy range of 0 - 800keVee . Furthermore, we show that the Charge Comparison Method performs poorly in accurately identifying nuclear recoils.

Application of a Three-Dimensional Poroelastic BEM to Modeling the Biphasic Mechanics of Cell-Matrix Interactions in Articular Cartilage (REVISION)

PubMed Central

Haider, Mansoor A.; Guilak, Farshid

2009-01-01

Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain. PMID:19851478

Application of a Three-Dimensional Poroelastic BEM to Modeling the Biphasic Mechanics of Cell-Matrix Interactions in Articular Cartilage (REVISION).

PubMed

Haider, Mansoor A; Guilak, Farshid

2007-06-15

Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.

Aquifer response to stream-stage and recharge variations. I. Analytical step-response functions

USGS Publications Warehouse

Moench, A.F.; Barlow, P.M.

2000-01-01

Laplace transform step-response functions are presented for various homogeneous confined and leaky aquifer types and for anisotropic, homogeneous unconfined aquifers interacting with perennial streams. Flow is one-dimensional, perpendicular to the stream in the confined and leaky aquifers, and two-dimensional in a plane perpendicular to the stream in the water-table aquifers. The stream is assumed to penetrate the full thickness of the aquifer. The aquifers may be semi-infinite or finite in width and may or may not be bounded at the stream by a semipervious streambank. The solutions are presented in a unified manner so that mathematical relations among the various aquifer configurations are clearly demonstrated. The Laplace transform solutions are inverted numerically to obtain the real-time step-response functions for use in the convolution (or superposition) integral. To maintain linearity in the case of unconfined aquifers, fluctuations in the elevation of the water table are assumed to be small relative to the saturated thickness, and vertical flow into or out of the zone above the water table is assumed to occur instantaneously. Effects of hysteresis in the moisture distribution above the water table are therefore neglected. Graphical comparisons of the new solutions are made with known closed-form solutions.Laplace transform step-response functions are presented for various homogeneous confined and leaky aquifer types and for anisotropic, homogeneous unconfined aquifers interacting with perennial streams. Flow is one-dimensional, perpendicular to the stream in the confined and leaky aquifers, and two-dimensional in a plane perpendicular to the stream in the water-table aquifers. The stream is assumed to penetrate the full thickness of the aquifer. The aquifers may be semi-infinite or finite in width and may or may not be bounded at the stream by a semipervious streambank. The solutions are presented in a unified manner so that mathematical relations among the various aquifer configurations are clearly demonstrated. The Laplace transform solutions are inverted numerically to obtain the real-time step-response functions for use in the convolution (or superposition) integral. To maintain linearity in the case of unconfined aquifers, fluctuations in the elevation of the water table are assumed to be small relative to the saturated thickness, and vertical flow into or out of the zone above the water table is assumed to occur instantaneously. Effects of hysteresis in the moisture distribution above the water table are therefore neglected. Graphical comparisons of the new solutions are made with known closed-form solutions.

Simulation of Simple Controlled Processes with Dead-Time.

ERIC Educational Resources Information Center

Watson, Keith R.; And Others

1985-01-01

The determination of closed-loop response of processes containing dead-time is typically not covered in undergraduate process control, possibly because the solution by Laplace transforms requires the use of Pade approximation for dead-time, which makes the procedure lengthy and tedious. A computer-aided method is described which simplifies the…

Using 3D Simulation of Elastic Wave Propagation in Laplace Domain for Electromagnetic-Seismic Inverse Modeling

NASA Astrophysics Data System (ADS)

Petrov, P.; Newman, G. A.

2010-12-01

Quantitative imaging of the subsurface objects is essential part of modern geophysical technology important in oil and gas exploration and wide-range engineering applications. A significant advancement in developing a robust, high resolution imaging technology is concerned with using the different geophysical measurements (gravity, EM and seismic) sense the subsurface structure. A joint image of the subsurface geophysical attributes (velocity, electrical conductivity and density) requires the consistent treatment of the different geophysical data (electromagnetic and seismic) due to their differing physical nature - diffusive and attenuated propagation of electromagnetic energy and nonlinear, multiple scattering wave propagation of seismic energy. Recent progress has been reported in the solution of this problem by reducing the complexity of seismic wave field. Works formed by Shin and Cha (2009 and 2008) suggests that low-pass filtering the seismic trace via Laplace-Fourier transformation can be an effective approach for obtaining seismic data that has similar spatial resolution to EM data. The effect of Laplace- Fourier transformation on the low-pass filtered trace changes the modeling of the seismic wave field from multi-wave propagation to diffusion. The key benefit of transformation is that diffusive wave-field inversion works well for both data sets seismic (Shin and Cha, 2008) and electromagnetic (Commer and Newman 2008, Newman et al., 2010). Moreover the different data sets can also be matched for similar and consistent resolution. Finally, the low pass seismic image is also an excellent choice for a starting model when analyzing the entire seismic waveform to recover the high spatial frequency components of the seismic image; its reflectivity (Shin and Cha, 2009). Without a good starting model full waveform seismic imaging and migration can encounter serious difficulties. To produce seismic wave fields consistent for joint imaging in the Laplace-Fourier domain we had developed 3D code for full-wave field simulation in the elastic media which take into account nonlinearity introduced by free-surface effects. Our approach is based on the velocity-stress formulation. In the contrast to conventional formulation we defined the material properties such as density and Lame constants not at nodal points but within cells. This second order finite differences method formulated in the cell-based grid, generate numerical solutions compatible with analytical ones within the range errors determinate by dispersion analysis. Our simulator will be embedded in an inversion scheme for joint seismic- electromagnetic imaging. It also offers possibilities for preconditioning the seismic wave propagation problems in the frequency domain. References. Shin, C. & Cha, Y. (2009), Waveform inversion in the Laplace-Fourier domain, Geophys. J. Int. 177(3), 1067- 1079. Shin, C. & Cha, Y. H. (2008), Waveform inversion in the Laplace domain, Geophys. J. Int. 173(3), 922-931. Commer, M. & Newman, G. (2008), New advances in three-dimensional controlled-source electromagnetic inversion, Geophys. J. Int. 172(2), 513-535. Newman, G. A., Commer, M. & Carazzone, J. J. (2010), Imaging CSEM data in the presence of electrical anisotropy, Geophysics, in press.

Unsteady magnetohydrodynamics mixed convection flow in a rotating medium with double diffusion

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

Jiann, Lim Yeou; Ismail, Zulkhibri; Khan, Ilyas

2015-05-15

Exact solutions of an unsteady Magnetohydrodynamics (MHD) flow over an impulsively started vertical plate in a rotating medium are presented. The effects of thermal radiative and thermal diffusion on the fluid flow are also considered. The governing equations are modelled and solved for velocity, temperature and concentration using Laplace transforms technique. Expressions of velocity, temperature and concentration profiles are obtained and their numerical results are presented graphically. Skin friction, Sherwood number and Nusselt number are also computed and presented in tabular forms. The determined solutions can generate a large class of solutions as special cases corresponding to different motions withmore » technical relevance. The results obtained herein may be used to verify the validation of obtained numerical solutions for more complicated fluid flow problems.« less

Tissue responses to fractional transient heating with sinusoidal heat flux condition on skin surface.

PubMed

Ezzat, Magdy A; El-Bary, Alaa A; Al-Sowayan, Noorah S

2016-10-01

A fractional model of Bioheat equation for describing quantitatively the thermal responses of skin tissue under sinusoidal heat flux conditions on skin surface is given. Laplace transform technique is used to obtain the solution in a closed form. The resulting formulation is applied to one-dimensional application to investigate the temperature distribution in skin with instantaneous surface heating for different cases. According to the numerical results and its graphs, conclusion about the fractional bioheat transfer equation has been constructed. Sensitivity analysis is performed to explore the thermal effects of various control parameters on tissue temperature. The comparisons are made with the results obtained in the case of the absence of time-fractional order. © 2016 Japanese Society of Animal Science. © 2016 Japanese Society of Animal Science.

A multidimensional subdiffusion model: An arbitrage-free market

NASA Astrophysics Data System (ADS)

Li, Guo-Hua; Zhang, Hong; Luo, Mao-Kang

2012-12-01

To capture the subdiffusive characteristics of financial markets, the subordinated process, directed by the inverse α-stale subordinator Sα(t) for 0 < α < 1, has been employed as the model of asset prices. In this article, we introduce a multidimensional subdiffusion model that has a bond and K correlated stocks. The stock price process is a multidimensional subdiffusion process directed by the inverse α-stable subordinator. This model describes the period of stagnation for each stock and the behavior of the dependency between multiple stocks. Moreover, we derive the multidimensional fractional backward Kolmogorov equation for the subordinated process using the Laplace transform technique. Finally, using a martingale approach, we prove that the multidimensional subdiffusion model is arbitrage-free, and also gives an arbitrage-free pricing rule for contingent claims associated with the martingale measure.

Stability and Control. Volume 2. Stability and Control Flight Test Theory

DTIC Science & Technology

1974-07-01

e we have 2 mx , . mx , mx n am e + bme + ce = 0 or (am2 + bm + c)emx = 0 (1.21) mx , n Since e ? 0...1.97) (1.98) Substituting 2 mt , , mt , mt n am e + bme + ce =0 (1.99) and emt (am2 + bm + c) =0 (1.100) led us to assert that 1.98 would...derive Laplace transforms each time we use them. Extensive tables of transforms exist in most advanced mathe- matics and control system textbooks . We

Axisymmetric deformation of a poroelastic layer overlying an elastic half-space due to surface loading

NASA Astrophysics Data System (ADS)

Rani, Sunita; Rani, Sunita

2017-11-01

The axisymmetric deformation of a homogeneous, isotropic, poroelastic layer of uniform thickness overlying a homogeneous, isotropic, elastic half-space due to surface loads has been obtained. The fluid and the solid constituents of the porous layer are compressible and the permeability in vertical direction is different from its permeability in horizontal direction. The displacements and pore-pressure are taken as basic state variables. An analytical solution for the pore-pressure, displacements and stresses has been obtained using the Laplace-Hankel transform technique. The case of normal disc loading is discussed in detail. Diffusion of pore-pressure is obtained in the space-time domain. The Laplace inversion is evaluated using the fixed Talbot algorithm and the Hankel inversion using the extended Simpson's rule. Two different models of the Earth have been considered: continental crust model and oceanic crust model. For continental crust model, the layer is assumed to be of Westerly Granite and for the oceanic crust model of Hanford Basalt. The effect of the compressibilities of the fluid as well as solid constituents and anisotropy in permeability has been studied on the diffusion of pore-pressure. Contour maps have been plotted for the diffusion of pore-pressure for both models. It is observed that the pore-pressure changes to compression for the continental crust model with time, which is not true for the oceanic crust.

Numerical time-domain electromagnetics based on finite-difference and convolution

NASA Astrophysics Data System (ADS)

Lin, Yuanqu

Time-domain methods posses a number of advantages over their frequency-domain counterparts for the solution of wideband, nonlinear, and time varying electromagnetic scattering and radiation phenomenon. Time domain integral equation (TDIE)-based methods, which incorporate the beneficial properties of integral equation method, are thus well suited for solving broadband scattering problems for homogeneous scatterers. Widespread adoption of TDIE solvers has been retarded relative to other techniques by their inefficiency, inaccuracy and instability. Moreover, two-dimensional (2D) problems are especially problematic, because 2D Green's functions have infinite temporal support, exacerbating these difficulties. This thesis proposes a finite difference delay modeling (FDDM) scheme for the solution of the integral equations of 2D transient electromagnetic scattering problems. The method discretizes the integral equations temporally using first- and second-order finite differences to map Laplace-domain equations into the Z domain before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z-domain mapping. The first FDDM method developed in this thesis uses second-order Lagrange basis functions with Galerkin's method for spatial discretization. The second application of the FDDM method discretizes the space using a locally-corrected Nystrom method, which accelerates the precomputation phase and achieves high order accuracy. The Fast Fourier Transform (FFT) is applied to accelerate the marching-on-time process in both methods. While FDDM methods demonstrate impressive accuracy and stability in solving wideband scattering problems for homogeneous scatterers, they still have limitations in analyzing interactions between several inhomogenous scatterers. Therefore, this thesis devises a multi-region finite-difference time-domain (MR-FDTD) scheme based on domain-optimal Green's functions for solving sparsely-populated problems. The scheme uses a discrete Green's function (DGF) on the FDTD lattice to truncate the local subregions, and thus reduces reflection error on the local boundary. A continuous Green's function (CGF) is implemented to pass the influence of external fields into each FDTD region which mitigates the numerical dispersion and anisotropy of standard FDTD. Numerical results will illustrate the accuracy and stability of the proposed techniques.

Student Learning in an Electric Circuit Theory Course: Critical Aspects and Task Design

ERIC Educational Resources Information Center

Carstensen, Anna-Karin; Bernhard, Jonte

2009-01-01

Understanding time-dependent responses, such as transients, is important in electric circuit theory and other branches of engineering. However, transient response is considered difficult to learn since familiarity with advanced mathematical tools such as Laplace transforms is required. Here, we analyse and describe a novel learning environment…

An Improvement to the Fourier Series Method for Inversion of Laplace Transforms Applied to Elastic and Viscoelastic Waves

DTIC Science & Technology

2007-01-01

Lawrence Livermore National Laboratory Report UCRL -MA-107254 Rev. 1. NO. OF COPIES ORGANIZATION 1 DEFENSE TECHNICAL (PDF INFORMATION CTR...AFB FL 32542 3 DARPA L CHRISTODOULOU W COBLENZ S WAX 3701 N FAIRFAX DR ARLINGTON VA 22203-1714 1 DIRECTOR US ARMY ARDEC

Silencer! A Tool for Substrate Noise Coupling Analysis

DTIC Science & Technology

2004-01-09

network for up to one hundred substrate ports. The solver uses the Laplace equation and then 17 transforms it with Green’s theorem into a...the contact center points can be calculated (using Pythagoras ) and saved in a n x n matrix: ( ) ( ) 2 2 xij cxj cxi yij cyj cyi dij xij yij

One-dimensional wave propagation in particulate suspensions

NASA Technical Reports Server (NTRS)

Rochelle, S. G.; Peddieson, J., Jr.

1976-01-01

One-dimensional small-amplitude wave motion in a two-phase system consisting of an inviscid gas and a cloud of suspended particles is analyzed using a continuum theory of suspensions. Laplace transform methods are used to obtain several approximate solutions. Properties of acoustic wave motion in particulate suspensions are inferred from these solutions.

A hybrid method for transient wave propagation in a multilayered solid

NASA Astrophysics Data System (ADS)

Tian, Jiayong; Xie, Zhoumin

2009-08-01

We present a hybrid method for the evaluation of transient elastic-wave propagation in a multilayered solid, integrating reverberation matrix method with the theory of generalized rays. Adopting reverberation matrix formulation, Laplace-Fourier domain solutions of elastic waves in the multilayered solid are expanded into the sum of a series of generalized-ray group integrals. Each generalized-ray group integral containing Kth power of reverberation matrix R represents the set of K-times reflections and refractions of source waves arriving at receivers in the multilayered solid, which was computed by fast inverse Laplace transform (FILT) and fast Fourier transform (FFT) algorithms. However, the calculation burden and low precision of FILT-FFT algorithm limit the application of reverberation matrix method. In this paper, we expand each of generalized-ray group integrals into the sum of a series of generalized-ray integrals, each of which is accurately evaluated by Cagniard-De Hoop method in the theory of generalized ray. The numerical examples demonstrate that the proposed method makes it possible to calculate the early-time transient response in the complex multilayered-solid configuration efficiently.

Time-dependent flow model of a generalized Burgers' fluid with fractional derivatives through a cylindrical domain: An exact and numerical approach

NASA Astrophysics Data System (ADS)

Safdar, Rabia; Imran, M.; Khalique, Chaudry Masood

2018-06-01

Exact solutions for velocity field and tangential stress for rotational flow of a generalized Burgers' fluid within an infinite circular pipe are derived by using the methods of Laplace and finite Hankel transformations. Firstly we take the position of fluid at rest and then the fluid flow due to the rotation of the pipe around the axis of flow having time dependant angular velocity. The exact solutions are presented in terms of the generalized Ga,b,c (., t) -functions. The corresponding results can be freely specified for the same results of Burgers', Oldroyd B, Maxwell, second grade and Newtonian fluids (performing the same motion) as particular cases of the results obtained earlier. The impact of the different parameters, individually and in comparison, are represented by graphical demonstrations. Secondly the numerical solutions for velocity and stress are also obtained with the help of Laplace transformation, Gaver Stehfest's algorithm and MATHCAD. Finally a comparison of both methods for the same problem is done and shows the consistency of results.

A novel method for identification of lithium-ion battery equivalent circuit model parameters considering electrochemical properties

NASA Astrophysics Data System (ADS)

Zhang, Xi; Lu, Jinling; Yuan, Shifei; Yang, Jun; Zhou, Xuan

2017-03-01

This paper proposes a novel parameter identification method for the lithium-ion (Li-ion) battery equivalent circuit model (ECM) considering the electrochemical properties. An improved pseudo two-dimension (P2D) model is established on basis of partial differential equations (PDEs), since the electrolyte potential is simplified from the nonlinear to linear expression while terminal voltage can be divided into the electrolyte potential, open circuit voltage (OCV), overpotential of electrodes, internal resistance drop, and so on. The model order reduction process is implemented by the simplification of the PDEs using the Laplace transform, inverse Laplace transform, Pade approximation, etc. A unified second order transfer function between cell voltage and current is obtained for the comparability with that of ECM. The final objective is to obtain the relationship between the ECM resistances/capacitances and electrochemical parameters such that in various conditions, ECM precision could be improved regarding integration of battery interior properties for further applications, e.g., SOC estimation. Finally simulation and experimental results prove the correctness and validity of the proposed methodology.

Angular rate optimal design for the rotary strapdown inertial navigation system.

PubMed

Yu, Fei; Sun, Qian

2014-04-22

Due to the characteristics of high precision for a long duration, the rotary strapdown inertial navigation system (RSINS) has been widely used in submarines and surface ships. Nowadays, the core technology, the rotating scheme, has been studied by numerous researchers. It is well known that as one of the key technologies, the rotating angular rate seriously influences the effectiveness of the error modulating. In order to design the optimal rotating angular rate of the RSINS, the relationship between the rotating angular rate and the velocity error of the RSINS was analyzed in detail based on the Laplace transform and the inverse Laplace transform in this paper. The analysis results showed that the velocity error of the RSINS depends on not only the sensor error, but also the rotating angular rate. In order to minimize the velocity error, the rotating angular rate of the RSINS should match the sensor error. One optimal design method for the rotating rate of the RSINS was also proposed in this paper. Simulation and experimental results verified the validity and superiority of this optimal design method for the rotating rate of the RSINS.

Invertibility of retarded response functions for Laplace transformable potentials: Application to one-body reduced density matrix functional theory.

PubMed

Giesbertz, K J H

2015-08-07

A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especially for time-dependent one-body reduced density matrix (1RDM) functional theory, this is an important step forward, since a solid foundation has currently been lacking. The theorem is equally valid for static response functions in the non-degenerate case, so can be used to characterize the uniqueness of the potential in the ground state version of the corresponding density-functional-like theory. Such a classification of the uniqueness of the non-local potential in ground state 1RDM functional theory has been lacking for decades. With the aid of presented invertibility theorem presented here, a complete classification of the non-uniqueness of the non-local potential in 1RDM functional theory can be given for the first time.

Estimation for general birth-death processes

PubMed Central

Crawford, Forrest W.; Minin, Vladimir N.; Suchard, Marc A.

2013-01-01

Birth-death processes (BDPs) are continuous-time Markov chains that track the number of “particles” in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear BDPs in which per-particle birth and death rates are constant. Researchers often observe the number of particles at discrete times, necessitating data augmentation procedures such as expectation-maximization (EM) to find maximum likelihood estimates. For BDPs on finite state-spaces, there are powerful matrix methods for computing the conditional expectations needed for the E-step of the EM algorithm. For BDPs on infinite state-spaces, closed-form solutions for the E-step are available for some linear models, but most previous work has resorted to time-consuming simulation. Remarkably, we show that the E-step conditional expectations can be expressed as convolutions of computable transition probabilities for any general BDP with arbitrary rates. This important observation, along with a convenient continued fraction representation of the Laplace transforms of the transition probabilities, allows for novel and efficient computation of the conditional expectations for all BDPs, eliminating the need for truncation of the state-space or costly simulation. We use this insight to derive EM algorithms that yield maximum likelihood estimation for general BDPs characterized by various rate models, including generalized linear models. We show that our Laplace convolution technique outperforms competing methods when they are available and demonstrate a technique to accelerate EM algorithm convergence. We validate our approach using synthetic data and then apply our methods to cancer cell growth and estimation of mutation parameters in microsatellite evolution. PMID:25328261

Estimation for general birth-death processes.

PubMed

Crawford, Forrest W; Minin, Vladimir N; Suchard, Marc A

2014-04-01

Birth-death processes (BDPs) are continuous-time Markov chains that track the number of "particles" in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear BDPs in which per-particle birth and death rates are constant. Researchers often observe the number of particles at discrete times, necessitating data augmentation procedures such as expectation-maximization (EM) to find maximum likelihood estimates. For BDPs on finite state-spaces, there are powerful matrix methods for computing the conditional expectations needed for the E-step of the EM algorithm. For BDPs on infinite state-spaces, closed-form solutions for the E-step are available for some linear models, but most previous work has resorted to time-consuming simulation. Remarkably, we show that the E-step conditional expectations can be expressed as convolutions of computable transition probabilities for any general BDP with arbitrary rates. This important observation, along with a convenient continued fraction representation of the Laplace transforms of the transition probabilities, allows for novel and efficient computation of the conditional expectations for all BDPs, eliminating the need for truncation of the state-space or costly simulation. We use this insight to derive EM algorithms that yield maximum likelihood estimation for general BDPs characterized by various rate models, including generalized linear models. We show that our Laplace convolution technique outperforms competing methods when they are available and demonstrate a technique to accelerate EM algorithm convergence. We validate our approach using synthetic data and then apply our methods to cancer cell growth and estimation of mutation parameters in microsatellite evolution.

Coherent pulses in the diffusive transport of charged particles`

NASA Technical Reports Server (NTRS)

Kota, J.

1994-01-01

We present exact solutions to the diffusive transport of charged particles following impulsive injection for a simple model of scattering. A modified, two-parameter relaxation-time model is considered that simulates the low rate of scattering through perpendicular pitch-angle. Scattering is taken to be isotropic within each of the foward- and backward-pointing hemispheres, respectively, but, at the same time, a reduced rate of sccattering is assumed from one hemisphere to the other one. By applying a technique of Fourier- and Laplace-transform, the inverse transformation can be performed and exact solutions can be reached. By contrast with the first, and so far only exact solutions of Federov and Shakov, this wider class of solutions gives rise to coherent pulses to appear. The present work addresses omnidirectional densities for isotropic injection from an instantaneous and localized source. The dispersion relations are briefly discussed. We find, for this particular model, two diffusive models to exist up to a certain limiting wavenumber. The corresponding eigenvalues are real at the lowest wavenumbers. Complex eigenvalues, which are responsible for coherent pulses, appear at higher wavenumbers.

Method of Improved Fuzzy Contrast Combined Adaptive Threshold in NSCT for Medical Image Enhancement

PubMed Central

Yang, Jie; Kasabov, Nikola

2017-01-01

Noises and artifacts are introduced to medical images due to acquisition techniques and systems. This interference leads to low contrast and distortion in images, which not only impacts the effectiveness of the medical image but also seriously affects the clinical diagnoses. This paper proposes an algorithm for medical image enhancement based on the nonsubsampled contourlet transform (NSCT), which combines adaptive threshold and an improved fuzzy set. First, the original image is decomposed into the NSCT domain with a low-frequency subband and several high-frequency subbands. Then, a linear transformation is adopted for the coefficients of the low-frequency component. An adaptive threshold method is used for the removal of high-frequency image noise. Finally, the improved fuzzy set is used to enhance the global contrast and the Laplace operator is used to enhance the details of the medical images. Experiments and simulation results show that the proposed method is superior to existing methods of image noise removal, improves the contrast of the image significantly, and obtains a better visual effect. PMID:28744464

Analysis of 3D poroelastodynamics using BEM based on modified time-step scheme

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Petrov, A. N.; Vorobtsov, I. V.

2017-10-01

The development of 3d boundary elements modeling of dynamic partially saturated poroelastic media using a stepping scheme is presented in this paper. Boundary Element Method (BEM) in Laplace domain and the time-stepping scheme for numerical inversion of the Laplace transform are used to solve the boundary value problem. The modified stepping scheme with a varied integration step for quadrature coefficients calculation using the symmetry of the integrand function and integral formulas of Strongly Oscillating Functions was applied. The problem with force acting on a poroelastic prismatic console end was solved using the developed method. A comparison of the results obtained by the traditional stepping scheme with the solutions obtained by this modified scheme shows that the computational efficiency is better with usage of combined formulas.

The boundary element method applied to 3D magneto-electro-elastic dynamic problems

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

2017-11-01

Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

Finite-time synchronization of fractional-order memristor-based neural networks with time delays.

PubMed

Velmurugan, G; Rakkiyappan, R; Cao, Jinde

2016-01-01

In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1<α<2 and 0<α<1. The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Analytical solutions for a soil vapor extraction model that incorporates gas phase dispersion and molecular diffusion

NASA Astrophysics Data System (ADS)

Huang, Junqi; Goltz, Mark N.

2017-06-01

To greatly simplify their solution, the equations describing radial advective/dispersive transport to an extraction well in a porous medium typically neglect molecular diffusion. While this simplification is appropriate to simulate transport in the saturated zone, it can result in significant errors when modeling gas phase transport in the vadose zone, as might be applied when simulating a soil vapor extraction (SVE) system to remediate vadose zone contamination. A new analytical solution for the equations describing radial gas phase transport of a sorbing contaminant to an extraction well is presented. The equations model advection, dispersion (including both mechanical dispersion and molecular diffusion), and rate-limited mass transfer of dissolved, separate phase, and sorbed contaminants into the gas phase. The model equations are analytically solved by using the Laplace transform with respect to time. The solutions are represented by confluent hypergeometric functions in the Laplace domain. The Laplace domain solutions are then evaluated using a numerical Laplace inversion algorithm. The solutions can be used to simulate the spatial distribution and the temporal evolution of contaminant concentrations during operation of a soil vapor extraction well. Results of model simulations show that the effect of gas phase molecular diffusion upon concentrations at the extraction well is relatively small, although the effect upon the distribution of concentrations in space is significant. This study provides a tool that can be useful in designing SVE remediation strategies, as well as verifying numerical models used to simulate SVE system performance.

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Temperature Rise in a Two-Layer Structure Induced by a Rotating or Dithering Laser Beam

DTIC Science & Technology

2012-01-01

References [1] G. Araya and G. Gutierrez, Analytical solution for a transient, three-dimensional temperature dis- tribution due to a moving laser...beam, Int. J. Heat and Mass Transfer 49 ( 2006 ), 4124-4131. [2] R. Bellman, R.E. Marshak, and G.M. Wing, Laplace transform solution of two-medium neutron

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

ALARA: The next link in a chain of activation codes

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

Wilson, P.P.H.; Henderson, D.L.

1996-12-31

The Adaptive Laplace and Analytic Radioactivity Analysis [ALARA] code has been developed as the next link in the chain of DKR radioactivity codes. Its methods address the criticisms of DKR while retaining its best features. While DKR ignored loops in the transmutation/decay scheme to preserve the exactness of the mathematical solution, ALARA incorporates new computational approaches without jeopardizing the most important features of DKR`s physical modelling and mathematical methods. The physical model uses `straightened-loop, linear chains` to achieve the same accuracy in the loop solutions as is demanded in the rest of the scheme. In cases where a chain hasmore » no loops, the exact DKR solution is used. Otherwise, ALARA adaptively chooses between a direct Laplace inversion technique and a Laplace expansion inversion technique to optimize the accuracy and speed of the solution. All of these methods result in matrix solutions which allow the fastest and most accurate solution of exact pulsing histories. Since the entire history is solved for each chain as it is created, ALARA achieves the optimum combination of high accuracy, high speed and low memory usage. 8 refs., 2 figs.« less

The effect of viscoelasticity on the stress distribution of adhesively single-lap joint with an internal break in the composite adherends

NASA Astrophysics Data System (ADS)

Reza, Arash; Shishesaz, Mohammad

2017-09-01

The aim of this research is to study the effect of a break in the laminated composite adherends on stress distribution in the adhesively single-lap joint with viscoelastic adhesive and matrix. The proposed model involves two adherends with E-glass fibers and poly-methyl-methacrylate matrix that have been adhered to each other by phenolic-epoxy resin. The equilibrium equations that are based on shear-lag theory have been derived in the Laplace domain, and the governing differential equations of the model have been derived analytically in the Laplace domain. A numerical inverse Laplace transform, which is called Gaver-Stehfest method, has been used to extract desired results in the time domain. The results obtained at the initial time completely matched with the results of elastic solution. Also, a comparison between results obtained from the analytical and finite element models show a relatively good match. The results show that viscoelastic behavior decreases the peak of stress near the break. Finally, the effect of size and location of the break, as well as volume fraction of fibers, on the stress distribution in the adhesive layer is fully investigated.

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Sandri, G.; Scudder, J. D.; Howell, D. R.

1976-01-01

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Spectrum response estimation for deep-water floating platforms via retardation function representation

NASA Astrophysics Data System (ADS)

Liu, Fushun; Liu, Chengcheng; Chen, Jiefeng; Wang, Bin

2017-08-01

The key concept of spectrum response estimation with commercial software, such as the SESAM software tool, typically includes two main steps: finding a suitable loading spectrum and computing the response amplitude operators (RAOs) subjected to a frequency-specified wave component. In this paper, we propose a nontraditional spectrum response estimation method that uses a numerical representation of the retardation functions. Based on estimated added mass and damping matrices of the structure, we decompose and replace the convolution terms with a series of poles and corresponding residues in the Laplace domain. Then, we estimate the power density corresponding to each frequency component using the improved periodogram method. The advantage of this approach is that the frequency-dependent motion equations in the time domain can be transformed into the Laplace domain without requiring Laplace-domain expressions for the added mass and damping. To validate the proposed method, we use a numerical semi-submerged pontoon from the SESAM. The numerical results show that the responses of the proposed method match well with those obtained from the traditional method. Furthermore, the estimated spectrum also matches well, which indicates its potential application to deep-water floating structures.

Laplacian versus topography in the solution of the linear gravimetric boundary value problem by means of successive approximations

NASA Astrophysics Data System (ADS)

Holota, Petr; Nesvadba, Otakar

2017-04-01

The aim of this paper is to discuss the solution of the linearized gravimetric boundary value problem by means of the method of successive approximations. We start with the relation between the geometry of the solution domain and the structure of Laplace's operator. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. Laplace's operator has a relatively simple structure in terms of ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from an oblate ellipsoid of revolution, even if it is optimally fitted. Therefore, an alternative is discussed. A system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces is used. Clearly, the structure of Laplace's operator is more complicated in this case. It was deduced by means of tensor calculus and in a sense it represents the topography of the physical surface of the Earth. Nevertheless, the construction of the respective Green's function is more simple, if the solution domain is transformed. This enables the use of the classical Green's function method together with the method of successive approximations for the solution of the linear gravimetric boundary value problem expressed in terms of new coordinates. The structure of iteration steps is analyzed and where useful also modified by means of the integration by parts. Comparison with other methods is discussed.

Cotton-type and joint invariants for linear elliptic systems.

PubMed

Aslam, A; Mahomed, F M

2013-01-01

Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.

Evolutionary model of stock markets

NASA Astrophysics Data System (ADS)

Kaldasch, Joachim

2014-12-01

The paper presents an evolutionary economic model for the price evolution of stocks. Treating a stock market as a self-organized system governed by a fast purchase process and slow variations of demand and supply the model suggests that the short term price distribution has the form a logistic (Laplace) distribution. The long term return can be described by Laplace-Gaussian mixture distributions. The long term mean price evolution is governed by a Walrus equation, which can be transformed into a replicator equation. This allows quantifying the evolutionary price competition between stocks. The theory suggests that stock prices scaled by the price over all stocks can be used to investigate long-term trends in a Fisher-Pry plot. The price competition that follows from the model is illustrated by examining the empirical long-term price trends of two stocks.

Cotton-Type and Joint Invariants for Linear Elliptic Systems

PubMed Central

Aslam, A.; Mahomed, F. M.

2013-01-01

Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results. PMID:24453871

Reversible Energy Transfer and Fluorescence Decay in Solid Solutions

NASA Astrophysics Data System (ADS)

Shealy, David L.; Hoover, Richard B.; Gabardi, David R.

1988-07-01

The article deals with the influence of reversible excitation energy transfer on the fluorescence decay in systems with random distribution of molecules. On the basis of a hopping model, we have obtained an expression for the Laplace transform of the decay function and an expression for the average decay time. The case of dipole-dipole interaction is discussed in detail.

A superparticle on the “super” Poincaré upper half plane

NASA Astrophysics Data System (ADS)

Uehara, S.; Yasui, Yukinori

1988-03-01

A non-relativistic superparticle moving freely on the “super” Poincaré upper half plane is investigated. The lagrangian is invariant under the super Möbius transformations SPL(2, R), so that it can be projected into the lagrangian on the super Riemann surface. The quantum hamiltonian becomes the “super” Laplace-Beltrami operator in the curved superspace.

A scale-invariant internal representation of time.

PubMed

Shankar, Karthik H; Howard, Marc W

2012-01-01

We propose a principled way to construct an internal representation of the temporal stimulus history leading up to the present moment. A set of leaky integrators performs a Laplace transform on the stimulus function, and a linear operator approximates the inversion of the Laplace transform. The result is a representation of stimulus history that retains information about the temporal sequence of stimuli. This procedure naturally represents more recent stimuli more accurately than less recent stimuli; the decrement in accuracy is precisely scale invariant. This procedure also yields time cells that fire at specific latencies following the stimulus with a scale-invariant temporal spread. Combined with a simple associative memory, this representation gives rise to a moment-to-moment prediction that is also scale invariant in time. We propose that this scale-invariant representation of temporal stimulus history could serve as an underlying representation accessible to higher-level behavioral and cognitive mechanisms. In order to illustrate the potential utility of this scale-invariant representation in a variety of fields, we sketch applications using minimal performance functions to problems in classical conditioning, interval timing, scale-invariant learning in autoshaping, and the persistence of the recency effect in episodic memory across timescales.

Post-earthquake relaxation using a spectral element method: 2.5-D case

USGS Publications Warehouse

Pollitz, Fred

2014-01-01

The computation of quasi-static deformation for axisymmetric viscoelastic structures on a gravitating spherical earth is addressed using the spectral element method (SEM). A 2-D spectral element domain is defined with respect to spherical coordinates of radius and angular distance from a pole of symmetry, and 3-D viscoelastic structure is assumed to be azimuthally symmetric with respect to this pole. A point dislocation source that is periodic in azimuth is implemented with a truncated sequence of azimuthal order numbers. Viscoelasticity is limited to linear rheologies and is implemented with the correspondence principle in the Laplace transform domain. This leads to a series of decoupled 2-D problems which are solved with the SEM. Inverse Laplace transform of the independent 2-D solutions leads to the time-domain solution of the 3-D equations of quasi-static equilibrium imposed on a 2-D structure. The numerical procedure is verified through comparison with analytic solutions for finite faults embedded in a laterally homogeneous viscoelastic structure. This methodology is applicable to situations where the predominant structure varies in one horizontal direction, such as a structural contrast across (or parallel to) a long strike-slip fault.

Angular Rate Optimal Design for the Rotary Strapdown Inertial Navigation System

PubMed Central

Yu, Fei; Sun, Qian

2014-01-01

Due to the characteristics of high precision for a long duration, the rotary strapdown inertial navigation system (RSINS) has been widely used in submarines and surface ships. Nowadays, the core technology, the rotating scheme, has been studied by numerous researchers. It is well known that as one of the key technologies, the rotating angular rate seriously influences the effectiveness of the error modulating. In order to design the optimal rotating angular rate of the RSINS, the relationship between the rotating angular rate and the velocity error of the RSINS was analyzed in detail based on the Laplace transform and the inverse Laplace transform in this paper. The analysis results showed that the velocity error of the RSINS depends on not only the sensor error, but also the rotating angular rate. In order to minimize the velocity error, the rotating angular rate of the RSINS should match the sensor error. One optimal design method for the rotating rate of the RSINS was also proposed in this paper. Simulation and experimental results verified the validity and superiority of this optimal design method for the rotating rate of the RSINS. PMID:24759115

A Unified Mathematical Framework for Coding Time, Space, and Sequences in the Hippocampal Region

PubMed Central

MacDonald, Christopher J.; Tiganj, Zoran; Shankar, Karthik H.; Du, Qian; Hasselmo, Michael E.; Eichenbaum, Howard

2014-01-01

The medial temporal lobe (MTL) is believed to support episodic memory, vivid recollection of a specific event situated in a particular place at a particular time. There is ample neurophysiological evidence that the MTL computes location in allocentric space and more recent evidence that the MTL also codes for time. Space and time represent a similar computational challenge; both are variables that cannot be simply calculated from the immediately available sensory information. We introduce a simple mathematical framework that computes functions of both spatial location and time as special cases of a more general computation. In this framework, experience unfolding in time is encoded via a set of leaky integrators. These leaky integrators encode the Laplace transform of their input. The information contained in the transform can be recovered using an approximation to the inverse Laplace transform. In the temporal domain, the resulting representation reconstructs the temporal history. By integrating movements, the equations give rise to a representation of the path taken to arrive at the present location. By modulating the transform with information about allocentric velocity, the equations code for position of a landmark. Simulated cells show a close correspondence to neurons observed in various regions for all three cases. In the temporal domain, novel secondary analyses of hippocampal time cells verified several qualitative predictions of the model. An integrated representation of spatiotemporal context can be computed by taking conjunctions of these elemental inputs, leading to a correspondence with conjunctive neural representations observed in dorsal CA1. PMID:24672015

Solution of QCD⊗QED coupled DGLAP equations at NLO

NASA Astrophysics Data System (ADS)

Zarrin, S.; Boroun, G. R.

2017-09-01

In this work, we present an analytical solution for QCD⊗QED coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at the leading order (LO) accuracy in QED and next-to-leading order (NLO) accuracy in perturbative QCD using double Laplace transform. This technique is applied to obtain the singlet, gluon and photon distribution functions and also the proton structure function. We also obtain contribution of photon in proton at LO and NLO at high energy and successfully compare the proton structure function with HERA data [1] and APFEL results [2]. Some comparisons also have been done for the singlet and gluon distribution functions with the MSTW results [3]. In addition, the contribution of photon distribution function inside the proton has been compared with results of MRST [4] and with the contribution of sea quark distribution functions which obtained by MSTW [3] and CTEQ6M [5].

The spectrum, radiation conditions and the Fredholm property for the Dirichlet Laplacian in a perforated plane with semi-infinite inclusions

NASA Astrophysics Data System (ADS)

Cardone, G.; Durante, T.; Nazarov, S. A.

2017-07-01

We consider the spectral Dirichlet problem for the Laplace operator in the plane Ω∘ with double-periodic perforation but also in the domain Ω• with a semi-infinite foreign inclusion so that the Floquet-Bloch technique and the Gelfand transform do not apply directly. We describe waves which are localized near the inclusion and propagate along it. We give a formulation of the problem with radiation conditions that provides a Fredholm operator of index zero. The main conclusion concerns the spectra σ∘ and σ• of the problems in Ω∘ and Ω•, namely we present a concrete geometry which supports the relation σ∘ ⫋σ• due to a new non-empty spectral band caused by the semi-infinite inclusion called an open waveguide in the double-periodic medium.

Longitudinal structure function from logarithmic slopes of F2 at low x

NASA Astrophysics Data System (ADS)

Boroun, G. R.

2018-01-01

Using Laplace transform techniques, I calculate the longitudinal structure function FL(x ,Q2) from the scaling violations of the proton structure function F2(x ,Q2) and make a critical study of this relationship between the structure functions at leading order (LO) up to next-to-next-to leading order (NNLO) analysis at small x . Furthermore, I consider heavy quark contributions to the relation between the structure functions, which leads to compact formula for Nf=3 +Heavy . The nonlinear corrections to the longitudinal structure function at LO up to NNLO analysis are shown in the Nf=4 (light quark flavor) based on the nonlinear corrections at R =2 and R =4 GeV-1 . The results are compared with experimental data of the longitudinal proton structure function FL in the range of 6.5 ≤Q2≤800 GeV2 .

Hall effects on unsteady MHD flow of second grade fluid through porous medium with ramped wall temperature and ramped surface concentration

NASA Astrophysics Data System (ADS)

VeeraKrishna, M.; Chamkha, Ali J.

2018-05-01

The heat generation/absorption and thermo-diffusion on an unsteady free convective MHD flow of radiating and chemically reactive second grade fluid near an infinite vertical plate through a porous medium and taking the Hall current into account have been studied. Assume that the bounding plate has a ramped temperature with a ramped surface concentration and isothermal temperature with a ramped surface concentration. The analytical solutions for the governing equations are obtained by making use of the Laplace transforms technique. The velocity, temperature, and concentration profiles are discussed through graphs. We also found that velocity, temperature, and concentration profiles in the case of ramped temperature with ramped surface concentrations are less than those of isothermal temperature with ramped surface concentrations. Also, the expressions of the skin friction, Nusselt number, and Sherwood number are obtained and represented computationally through a tabular form.

Duality of force laws and conformal transformations

NASA Astrophysics Data System (ADS)

Kothawala, Dawood

2011-06-01

As was first noted by Isaac Newton, the two most famous ellipses of classical mechanics, arising from the force laws F ∝r and F ∝1/r2, can be mapped onto each other by changing the location of the center of force. Less well known is that this mapping can also be achieved by the complex transformation, z →z2. We derive this result and its generalization by writing the Gaussian curvature in its covariant form, and then changing the metric by a conformal transformation which mimics this mapping of the curves. We indicate how the conserved Laplace-Runge-Lenz vector for the 1/r2 force law transforms under this transformation, and compare it with the corresponding quantities for the linear force law. Our main aim is to present this duality by introducing concepts from differential geometry.

Automatic defects recognition in composite aerospace structures from experimental and theoretical analysis as part of an intelligent infrared thermographic inspection system

NASA Astrophysics Data System (ADS)

David, Denis G. F.; Marin, J. Y.; Tretout, Herve R.

An original concept for IR thermography nondestructive testing is validated. The principles of image and data processing investigated and developed as well as the utilization of AI should be transposable to other nondestructive techniques such as ultrasounds and X-rays. It is shown that modeling can be used in different ways to play a great part in the detection, the interpretation, and the sizing of the defects. The original concept lies in the comparison of experimental data with theoretical ones in order to identify regions of abnormal behavior related to defects. A Laplace transforms analytical method is successfully implemented in the case of composite materials such as graphite epoxy to identify a set of thermal parameters which contributes to the expertise. This approach is extended to a more complicated composite material such as Kevlar, which presents semitransparent characteristics. This modeling technique, which expresses experimental data in terms of thermal parameters, makes it possible to increase SNR and reduce the number of thermal images to be processed.

Automatic defects recognition in composite aerospace structures from experimental and theoretical analysis as part of an intelligent infrared thermographic inspection system

NASA Astrophysics Data System (ADS)

David, D.; Marin, J. Y.; Tretout, H.

1992-04-01

An original concept for IR thermography nondestructive testing is validated. The principles of image and data processing investigated and developed as well as the utilization of AI should be transposable to other nondestructive techniques such as ultrasounds and X-rays. It is shown that modeling can be used in different ways to play a great part in the detection, the interpretation, and the sizing of the defects. The original concept lies in the comparison of experimental data with theoretical ones in order to identify regions of abnormal behavior related to defects. A Laplace transforms analytical method is successfully implemented in the case of composite materials such as graphite epoxy to identify a set of thermal parameters which contributes to the expertise. This approach is extended to a more complicated composite material such as Kevlar, which presents semitransparent characteristics. This modeling technique, which expresses experimental data in terms of thermal parameters, makes it possible to increase SNR and reduce the number of thermal images to be processed.

Wave propagation in strain gradient poroelastic medium with microinertia: closed-form and finite element solutions

NASA Astrophysics Data System (ADS)

Rosi, Giuseppe; Scala, Ilaria; Nguyen, Vu-Hieu; Naili, Salah

2017-06-01

This article is about ultrasonic wave propagation in microstructured porous media. The classic Biot's model is enriched using a strain gradient approach to be able to capture high-order effects when the wavelength approaches the characteristic size of the microstructure. In order to reproduce actual transmission/reflection experiments performed on poroelastic samples, and to validate the choice of the model, the computation of the time domain response is necessary, as it allows for a direct comparison with experimental results. For obtaining the time response, we use two strategies: on the one hand we compute the closed form solution by using the Laplace and Fourier transforms techniques; on the other hand we used a finite element method. The results are presented for a transmission/reflection test performed on a poroelastic sample immersed in water. The effects introduced by the strain gradient terms are visible in the time response and in agreement with experimental observations. The results can be exploited in characterization of mechanical properties of poroelastic media by enhancing the reliability of quantitative ultrasound techniques.

Multi-Rate Digital Control Systems with Simulation Applications. Volume II. Computer Algorithms

DTIC Science & Technology

1980-09-01

OREWORD The research described in this report was performed by Systems Technology, Inc., Hawthorne, California, under Air Force Contract F33615-79-C-3601...zero to plus infinity . - K ST(t) = 6(t) + 5(t - T) + 6(t - 2T) + .... J 6(t - kT) (4) k=O The Laplace transform of 6 T(t) is given in closed form as...The definition of the z-transform stems from the infinite summation cT(t) = • c( kfc ) 6(t - kT) k = 0, 1, 2, ... (16) k=0 where cT(t), the sampled

Experimental validation of a transformation optics based lens for beam steering

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

Yi, Jianjia; Burokur, Shah Nawaz, E-mail: shah-nawaz.burokur@u-psud.fr; Lustrac, André de

2015-10-12

A transformation optics based lens for beam control is experimentally realized and measured at microwave frequencies. Laplace's equation is adopted to construct the mapping between the virtual and physical spaces. The metamaterial-based lens prototype is designed using electric LC resonators. A planar microstrip antenna source is used as transverse electric polarized wave launcher for the lens. Both the far field radiation patterns and the near-field distributions have been measured to experimentally demonstrate the beam steering properties. Measurements agree quantitatively and qualitatively with numerical simulations, and a non-narrow frequency bandwidth operation is observed.

Some composition formulae for the M-S-M fractional integral operator with the multi-index Mittag-Leffler functions

NASA Astrophysics Data System (ADS)

Jain, Shilpi; Agarwal, Praveen; Kıymaz, I. Onur; ćetinkaya, Ayá¹£egül

2018-01-01

Authors presented some composition formulae for the Marichev-Saigo-Maeda (M-S-M) fractional integral operator with the multi-index Mittag-Leffler functions. Our results are generalizes the results obtained by Choi and Agarwal [3]. Here, we record some particular cases of our main result. Finally, we obtain Laplace transforms of the composition formulae.

Comparative study of palm print authentication system using geometric features

NASA Astrophysics Data System (ADS)

Shreyas, Kamath K. M.; Rajeev, Srijith; Panetta, Karen; Agaian, Sos S.

2017-05-01

Biometrics, particularly palm print authentication has been a stimulating research area due to its abundance of features. Stable features and effective matching are the most crucial steps for an authentication system. In conventional palm print authentication systems, matching is based on flexion creases, friction ridges, and minutiae points. Currently, contactless palm print imaging is an emerging technology. However, they tend to involve fluctuations in the image quality and texture loss due to factors such as varying illumination conditions, occlusions, noise, pose, and ghosting. These variations decrease the performance of the authentication systems. Furthermore, real-time palm print authentication in large databases continue to be a challenging task. In order to effectively solve these problems, features which are invariant to these anomalies are required. This paper proposes a robust palm print matching framework by making a comparative study of different local geometric features such as Difference-of-Gaussian, Hessian, Hessian-Laplace, Harris-Laplace, and Multiscale Harris for feature detection. These detectors are coupled with Scale Invariant Feature Transformation (SIFT) descriptor to describe the identified features. Additionally, a two-stage refinement process is carried out to obtain the best stable matches. Computer simulations demonstrate that the accuracy of the system has increased effectively with an EER of 0.86% when Harris-Laplace detector is used on IITD database.

Extracting Low-Frequency Information from Time Attenuation in Elastic Waveform Inversion

NASA Astrophysics Data System (ADS)

Guo, Xuebao; Liu, Hong; Shi, Ying; Wang, Weihong

2017-03-01

Low-frequency information is crucial for recovering background velocity, but the lack of low-frequency information in field data makes inversion impractical without accurate initial models. Laplace-Fourier domain waveform inversion can recover a smooth model from real data without low-frequency information, which can be used for subsequent inversion as an ideal starting model. In general, it also starts with low frequencies and includes higher frequencies at later inversion stages, while the difference is that its ultralow frequency information comes from the Laplace-Fourier domain. Meanwhile, a direct implementation of the Laplace-transformed wavefield using frequency domain inversion is also very convenient. However, because broad frequency bands are often used in the pure time domain waveform inversion, it is difficult to extract the wavefields dominated by low frequencies in this case. In this paper, low-frequency components are constructed by introducing time attenuation into the recorded residuals, and the rest of the method is identical to the traditional time domain inversion. Time windowing and frequency filtering are also applied to mitigate the ambiguity of the inverse problem. Therefore, we can start at low frequencies and to move to higher frequencies. The experiment shows that the proposed method can achieve a good inversion result in the presence of a linear initial model and records without low-frequency information.

A new analytical solution solved by triple series equations method for constant-head tests in confined aquifers

NASA Astrophysics Data System (ADS)

Chang, Ya-Chi; Yeh, Hund-Der

2010-06-01

The constant-head pumping tests are usually employed to determine the aquifer parameters and they can be performed in fully or partially penetrating wells. Generally, the Dirichlet condition is prescribed along the well screen and the Neumann type no-flow condition is specified over the unscreened part of the test well. The mathematical model describing the aquifer response to a constant-head test performed in a fully penetrating well can be easily solved by the conventional integral transform technique under the uniform Dirichlet-type condition along the rim of wellbore. However, the boundary condition for a test well with partial penetration should be considered as a mixed-type condition. This mixed boundary value problem in a confined aquifer system of infinite radial extent and finite vertical extent is solved by the Laplace and finite Fourier transforms in conjunction with the triple series equations method. This approach provides analytical results for the drawdown in a partially penetrating well for arbitrary location of the well screen in a finite thickness aquifer. The semi-analytical solutions are particularly useful for the practical applications from the computational point of view.

Hierarchical coarse-graining transform.

PubMed

Pancaldi, Vera; King, Peter R; Christensen, Kim

2009-03-01

We present a hierarchical transform that can be applied to Laplace-like differential equations such as Darcy's equation for single-phase flow in a porous medium. A finite-difference discretization scheme is used to set the equation in the form of an eigenvalue problem. Within the formalism suggested, the pressure field is decomposed into an average value and fluctuations of different kinds and at different scales. The application of the transform to the equation allows us to calculate the unknown pressure with a varying level of detail. A procedure is suggested to localize important features in the pressure field based only on the fine-scale permeability, and hence we develop a form of adaptive coarse graining. The formalism and method are described and demonstrated using two synthetic toy problems.

Operator based integration of information in multimodal radiological search mission with applications to anomaly detection

NASA Astrophysics Data System (ADS)

Benedetto, J.; Cloninger, A.; Czaja, W.; Doster, T.; Kochersberger, K.; Manning, B.; McCullough, T.; McLane, M.

2014-05-01

Successful performance of radiological search mission is dependent on effective utilization of mixture of signals. Examples of modalities include, e.g., EO imagery and gamma radiation data, or radiation data collected during multiple events. In addition, elevation data or spatial proximity can be used to enhance the performance of acquisition systems. State of the art techniques in processing and exploitation of complex information manifolds rely on diffusion operators. Our approach involves machine learning techniques based on analysis of joint data- dependent graphs and their associated diffusion kernels. Then, the significant eigenvectors of the derived fused graph Laplace and Schroedinger operators form the new representation, which provides integrated features from the heterogeneous input data. The families of data-dependent Laplace and Schroedinger operators on joint data graphs, shall be integrated by means of appropriately designed fusion metrics. These fused representations are used for target and anomaly detection.

Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization

NASA Technical Reports Server (NTRS)

Tiffany, S. H.; Adams, W. M., Jr.

1984-01-01

A technique which employs both linear and nonlinear methods in a multilevel optimization structure to best approximate generalized unsteady aerodynamic forces for arbitrary motion is described. Optimum selection of free parameters is made in a rational function approximation of the aerodynamic forces in the Laplace domain such that a best fit is obtained, in a least squares sense, to tabular data for purely oscillatory motion. The multilevel structure and the corresponding formulation of the objective models are presented which separate the reduction of the fit error into linear and nonlinear problems, thus enabling the use of linear methods where practical. Certain equality and inequality constraints that may be imposed are identified; a brief description of the nongradient, nonlinear optimizer which is used is given; and results which illustrate application of the method are presented.

Traveling waves in a delayed SIR model with nonlocal dispersal and nonlinear incidence

NASA Astrophysics Data System (ADS)

Zhang, Shou-Peng; Yang, Yun-Rui; Zhou, Yong-Hui

2018-01-01

This paper is concerned with traveling waves of a delayed SIR model with nonlocal dispersal and a general nonlinear incidence. The existence and nonexistence of traveling waves of the system are established respectively by Schauder's fixed point theorem and two-sided Laplace transform. It is also shown that the spread speed c is influenced by the dispersal rate of the infected individuals and the delay τ.

A small-plane heat source method for measuring the thermal conductivities of anisotropic materials

NASA Astrophysics Data System (ADS)

Cheng, Liang; Yue, Kai; Wang, Jun; Zhang, Xinxin

2017-07-01

A new small-plane heat source method was proposed in this study to simultaneously measure the in-plane and cross-plane thermal conductivities of anisotropic insulating materials. In this method the size of the heat source element is smaller than the sample size and the boundary condition is thermal insulation due to no heat flux at the edge of the sample during the experiment. A three-dimensional model in a rectangular coordinate system was established to exactly describe the heat transfer process of the measurement system. Using the Laplace transform, variable separation, and Laplace inverse transform methods, the analytical solution of the temperature rise of the sample was derived. The temperature rises calculated by the analytical solution agree well with the results of numerical calculation. The result of the sensitivity analysis shows that the sensitivity coefficients of the estimated thermal conductivities are high and uncorrelated to each other. At room temperature and in a high-temperature environment, experimental measurements of anisotropic silica aerogel were carried out using the traditional one-dimensional plane heat source method and the proposed method, respectively. The results demonstrate that the measurement method developed in this study is effective and feasible for simultaneously obtaining the in-plane and cross-plane thermal conductivities of the anisotropic materials.

Transform methods for precision continuum and control models of flexible space structures

NASA Technical Reports Server (NTRS)

Lupi, Victor D.; Turner, James D.; Chun, Hon M.

1991-01-01

An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality.

Comparison of the convolution quadrature method and enhanced inverse FFT with application in elastodynamic boundary element method

NASA Astrophysics Data System (ADS)

Schanz, Martin; Ye, Wenjing; Xiao, Jinyou

2016-04-01

Transient problems can often be solved with transformation methods, where the inverse transformation is usually performed numerically. Here, the discrete Fourier transform in combination with the exponential window method is compared with the convolution quadrature method formulated as inverse transformation. Both are inverse Laplace transforms, which are formally identical but use different complex frequencies. A numerical study is performed, first with simple convolution integrals and, second, with a boundary element method (BEM) for elastodynamics. Essentially, when combined with the BEM, the discrete Fourier transform needs less frequency calculations, but finer mesh compared to the convolution quadrature method to obtain the same level of accuracy. If further fast methods like the fast multipole method are used to accelerate the boundary element method the convolution quadrature method is better, because the iterative solver needs much less iterations to converge. This is caused by the larger real part of the complex frequencies necessary for the calculation, which improves the conditions of system matrix.

Explicit solutions for exit-only radioactive decay chains

NASA Astrophysics Data System (ADS)

Yuan, Ding; Kernan, Warnick

2007-05-01

In this study, we extended Bateman's [Proc. Cambridge Philos. Soc. 15, 423 (1910)] original work for solving radioactive decay chains and explicitly derived analytic solutions for generic exit-only radioactive decay problems under given initial conditions. Instead of using the conventional Laplace transform for solving Bateman's equations, we used a much simpler algebraic approach. Finally, we discuss methods of breaking down certain classes of large decay chains into collections of simpler chains for easy handling.

A Method of Evaluating Laplace Transforms with Series of Complete or Incomplete Beta Functions,

DTIC Science & Technology

1982-12-01

DEVELOPMENT COMMAND BALLISTIC RESEARCH LABORATORY ABERDEEN PROVING GROUND , MARYLAND A i ’:-Approved for public rlease; distribution unlimited. c...BLI Aberden Provin Ground 100161102.143 I. CONTROLLING OFFICE NAME AND ADDRESS Q?. REPORT DATE US Army Armament Research & Development Command...December 1982 US Arm), Ballistic Research Laboratory (DRDAR-BL 13. ’NUMBER OF PAGES Aberdeen Proving Ground , NMD 21005 33 14 MC5NiTORING AGENCY NAME

A new fractional operator of variable order: Application in the description of anomalous diffusion

NASA Astrophysics Data System (ADS)

Yang, Xiao-Jun; Machado, J. A. Tenreiro

2017-09-01

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

Using a quasi-heat-pulse method to determine heat and moisture transfer properties for porous orthotropic wood products or cellular solid materials

Treesearch

M. A. Dietenberger

2006-01-01

Understanding heat and moisture transfer in a wood specimen as used in the K-tester has led to an unconventional numerical solution arid intriguing protocol to deriving the transfer properties. Laplace transform solutions of Luikov’s differential equations are derived for one-dimensional heat and moisture transfer in porous hygroscopic orthotropic materials and for a...

Application of Quasi-Heat-Pulse Solutions for Luikov’s Equations of Heat and Moisture Transfer for Calibrating and Utilizing Thermal Properties Apparatus

Treesearch

Mark A. Dietenberger; Charles R. Boardman

2014-01-01

Several years ago the Laplace transform solutions of Luikov’s differential equations were presented for one-dimensional heat and moisture transfer in porous hydroscopic orthotropic materials for the boundary condition of a gradual heat pulse applied to both surfaces of a flat slab. This paper presents calibration methods and data for the K-tester 637 (Lasercomp),...

Three-dimensional semi-analytical solution to groundwater flow in confined and unconfined wedge-shaped aquifers

NASA Astrophysics Data System (ADS)

Sedghi, Mohammad Mahdi; Samani, Nozar; Sleep, Brent

2009-06-01

The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471-80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.

Stress wave calculations in composite plates using the fast Fourier transform.

NASA Technical Reports Server (NTRS)

Moon, F. C.

1973-01-01

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

A Modified Normalization Technique for Frequency-Domain Full Waveform Inversion

NASA Astrophysics Data System (ADS)

Hwang, J.; Jeong, G.; Min, D. J.; KIM, S.; Heo, J. Y.

2016-12-01

Full waveform inversion (FWI) is a technique to estimate subsurface material properties minimizing the misfit function built with residuals between field and modeled data. To achieve computational efficiency, FWI has been performed in the frequency domain by carrying out modeling in the frequency domain, whereas observed data (time-series data) are Fourier-transformed.One of the main drawbacks of seismic FWI is that it easily gets stuck in local minima because of lacking of low-frequency data. To compensate for this limitation, damped wavefields are used, as in the Laplace-domain waveform inversion. Using damped wavefield in FWI plays a role in generating low-frequency components and help recover long-wavelength structures. With these newly generated low-frequency components, we propose a modified frequency-normalization technique, which has an effect of boosting contribution of low-frequency components to model parameter update.In this study, we introduce the modified frequency-normalization technique which effectively amplifies low-frequency components of damped wavefields. Our method is demonstrated for synthetic data for the SEG/EAGE salt model. AcknowledgementsThis work was supported by the Korea Institute of Energy Technology Evaluation and Planning(KETEP) and the Ministry of Trade, Industry & Energy(MOTIE) of the Republic of Korea (No. 20168510030830) and by the Dual Use Technology Program, granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea.

Mixed convection flow of sodium alginate (SA-NaAlg) based molybdenum disulphide (MoS2) nanofluids: Maxwell Garnetts and Brinkman models

NASA Astrophysics Data System (ADS)

Ahmed, Tarek Nabil; Khan, Ilyas

2018-03-01

This article aims to study the mixed convection heat transfer in non-Newtonian nanofluids over an infinite vertical plate. Mixed convection is caused due to buoyancy force and sudden plate motion. Sodium alginate (SA-NaAlg) is considered as non-Newtonian base fluid and molybdenum disulphide (MoS2) as nanoparticles are suspended in it. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell-Garnetts (MG) and Brinkman models, respectively. The flow is modeled in the form of partial differential equations with imposed physical conditions. Exact solutions for velocity and temperature fields are developed by means of the Laplace transform technique. Numerical computations are performed for different governing parameters such as non-Newtonian parameter, Grashof number and nanoparticle volume fraction and the results are plotted in various graphs. Results for skin friction and Nusselt number are presented in tabular form which show that increasing nanoparticle volume fraction leads to heat transfer enhancement and increasing skin friction.

Generalized stochastic resonance for a fractional harmonic oscillator with bias-signal-modulated trichotomous noise

NASA Astrophysics Data System (ADS)

Lin, Lifeng; Wang, Huiqi; Huang, Xipei; Wen, Yongxian

2018-03-01

For a fractional linear oscillator subjected to both parametric excitation of trichotomous noise and external excitation of bias-signal-modulated trichotomous noise, the generalized stochastic resonance (GSR) phenomena are investigated in this paper in case the noises are cross-correlative. First, the generalized Shapiro-Loginov formula and generalized fractional Shapiro-Loginov formula are derived. Then, by using the generalized (fractional) Shapiro-Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is obtained. The numerical results show that the evolution of the output amplitude amplification is nonmonotonic with the frequency of periodic signal, the noise parameters, and the fractional order. The GSR phenomena, including single-peak GSR, double-peak GSR and triple-peak GSR, are observed in this system. In addition, the interplay of the multiplicative trichotomous noise, bias-signal-modulated trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena, and the two kinds of trichotomous noises play opposite roles on the GSR.

A Study of Chemically Reactive Species and Thermal Radiation Effects on an Unsteady MHD Free Convection Flow Through a Porous Medium Past a Flat Plate with Ramped Wall Temperature

NASA Astrophysics Data System (ADS)

Pandit, K. K.; Sarma, D.; Singh, S. I.

2017-12-01

An investigation of the effects of a chemical reaction and thermal radiation on unsteady MHD free convection heat and mass transfer flow of an electrically conducting, viscous, incompressible fluid past a vertical infinite flat plate embedded in a porous medium is carried out. The flow is induced by a general time-dependent movement of the vertical plate, and the cases of ramped temperature and isothermal plates are studied. An exact solution of the governing equations is obtained in closed form by the Laplace Transform technique. Some applications of practical interest for different types of plate motions are discussed. The numerical values of fluid velocity, temperature and species concentration are displayed graphically whereas the numerical values of skin friction, Nusselt number and Sherwood number are presented in a tabular form for various values of pertinent flow parameters for both ramped temperature and isothermal plates.

Unsteady free convection flow of viscous fluids with analytical results by employing time-fractional Caputo-Fabrizio derivative (without singular kernel)

NASA Astrophysics Data System (ADS)

Ali Shah, Nehad; Mahsud, Yasir; Ali Zafar, Azhar

2017-10-01

This article introduces a theoretical study for unsteady free convection flow of an incompressible viscous fluid. The fluid flows near an isothermal vertical plate. The plate has a translational motion with time-dependent velocity. The equations governing the fluid flow are expressed in fractional differential equations by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Explicit solutions for velocity, temperature and solute concentration are obtained by applying the Laplace transform technique. As the fractional parameter approaches to one, solutions for the ordinary fluid model are extracted from the general solutions of the fractional model. The results showed that, for the fractional model, the obtained solutions for velocity, temperature and concentration exhibit stationary jumps discontinuity across the plane at t=0 , while the solutions are continuous functions in the case of the ordinary model. Finally, numerical results for flow features at small-time are illustrated through graphs for various pertinent parameters.

Shock-induced thermal wave propagation and response analysis of a viscoelastic thin plate under transient heating loads

NASA Astrophysics Data System (ADS)

Li, Chenlin; Guo, Huili; Tian, Xiaogeng

2018-04-01

This paper is devoted to the thermal shock analysis for viscoelastic materials under transient heating loads. The governing coupled equations with time-delay parameter and nonlocal scale parameter are derived based on the generalized thermo-viscoelasticity theory. The problem of a thin plate composed of viscoelastic material, subjected to a sudden temperature rise at the boundary plane, is solved by employing Laplace transformation techniques. The transient responses, i.e. temperature, displacement, stresses, heat flux as well as strain, are obtained and discussed. The effects of time-delay and nonlocal scale parameter on the transient responses are analyzed and discussed. It can be observed that: the propagation of thermal wave is dynamically smoothed and changed with the variation of time-delay; while the displacement, strain, and stress can be rapidly reduced by nonlocal scale parameter, which can be viewed as an important indicator for predicting the stiffness softening behavior for viscoelastic materials.

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

Trainham, Clifford P.; O'Neill, Mary D.; McKenna, Ian J.

The rate equations found in frequency domain fluorescence spectroscopy are the same as those found in electronics under analog filter theory. Laplace transform methods are a natural way to solve the equations, and the methods can provide solutions for arbitrary excitation functions. The fluorescence terms can be modeled as circuit components and cascaded with drive and detection electronics to produce a global transfer function. Electronics design tools such as Spicea can be used to model fluorescence problems. In applications, such as remote sensing, where detection electronics are operated at high gain and limited bandwidth, a global modeling of the entiremore » system is important, since the filter terms of the drive and detection electronics affect the measured response of the fluorescence signals. Furthermore, the techniques described here can be used to separate signals from fast and slow fluorophores emitting into the same spectral band, and data collection can be greatly accelerated by means of a frequency comb driver waveform and appropriate signal processing of the response.« less

Functional determinants of radial operators in AdS 2

NASA Astrophysics Data System (ADS)

Aguilera-Damia, Jeremías; Faraggi, Alberto; Zayas, Leopoldo Pando; Rathee, Vimal; Silva, Guillermo A.

2018-06-01

We study the zeta-function regularization of functional determinants of Laplace and Dirac-type operators in two-dimensional Euclidean AdS 2 space. More specifically, we consider the ratio of determinants between an operator in the presence of background fields with circular symmetry and the free operator in which the background fields are absent. By Fourier-transforming the angular dependence, one obtains an infinite number of one-dimensional radial operators, the determinants of which are easy to compute. The summation over modes is then treated with care so as to guarantee that the result coincides with the two-dimensional zeta-function formalism. The method relies on some well-known techniques to compute functional determinants using contour integrals and the construction of the Jost function from scattering theory. Our work generalizes some known results in flat space. The extension to conformal AdS 2 geometries is also considered. We provide two examples, one bosonic and one fermionic, borrowed from the spectrum of fluctuations of the holographic 1/4 -BPS latitude Wilson loop.

Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.

PubMed

Nguyen, Vu-Hieu; Naili, Salah

2012-08-01

This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. Copyright © 2012 John Wiley & Sons, Ltd.

An analog filter approach to frequency domain fluorescence spectroscopy

DOE PAGES

Trainham, Clifford P.; O'Neill, Mary D.; McKenna, Ian J.

2015-10-01

The rate equations found in frequency domain fluorescence spectroscopy are the same as those found in electronics under analog filter theory. Laplace transform methods are a natural way to solve the equations, and the methods can provide solutions for arbitrary excitation functions. The fluorescence terms can be modeled as circuit components and cascaded with drive and detection electronics to produce a global transfer function. Electronics design tools such as Spicea can be used to model fluorescence problems. In applications, such as remote sensing, where detection electronics are operated at high gain and limited bandwidth, a global modeling of the entiremore » system is important, since the filter terms of the drive and detection electronics affect the measured response of the fluorescence signals. Furthermore, the techniques described here can be used to separate signals from fast and slow fluorophores emitting into the same spectral band, and data collection can be greatly accelerated by means of a frequency comb driver waveform and appropriate signal processing of the response.« less

Lévy flights in the presence of a point sink of finite strength

NASA Astrophysics Data System (ADS)

Janakiraman, Deepika

2017-01-01

In this paper, the absorption of a particle undergoing Lévy flight in the presence of a point sink of arbitrary strength and position is studied. The motion of such a particle is given by a modified Fokker-Planck equation whose exact solution in the Laplace domain can be described in terms of the Laplace transform of the unperturbed (absence of the sink) Green's function. This solution for the Green's function is a well-studied, generic result which applies to both fractional and usual Fokker-Planck equations alike. Using this result, the propagator and the absorption-time distribution are obtained for free Lévy flight and Lévy flight in linear and harmonic potentials in the presence of a delta function sink, and their dependence on the sink strength is analyzed. Analytical results are presented for the long-time behavior of the absorption-time distribution in all three above-mentioned potentials. Simulation results are found to corroborate closely with analytical results.

Analysis of heat transfer for unsteady MHD free convection flow of rotating Jeffrey nanofluid saturated in a porous medium

NASA Astrophysics Data System (ADS)

Mohd Zin, Nor Athirah; Khan, Ilyas; Shafie, Sharidan; Alshomrani, Ali Saleh

In this article, the influence of thermal radiation on unsteady magnetohydrodynamics (MHD) free convection flow of rotating Jeffrey nanofluid passing through a porous medium is studied. The silver nanoparticles (AgNPs) are dispersed in the Kerosene Oil (KO) which is chosen as conventional base fluid. Appropriate dimensionless variables are used and the system of equations is transformed into dimensionless form. The resulting problem is solved using the Laplace transform technique. The impact of pertinent parameters including volume fraction φ , material parameters of Jeffrey fluid λ1 , λ , rotation parameter r , Hartmann number Ha , permeability parameter K , Grashof number Gr , Prandtl number Pr , radiation parameter Rd and dimensionless time t on velocity and temperature profiles are presented graphically with comprehensive discussions. It is observed that, the rotation parameter, due to the Coriolis force, tends to decrease the primary velocity but reverse effect is observed in the secondary velocity. It is also observed that, the Lorentz force retards the fluid flow for both primary and secondary velocities. The expressions for skin friction and Nusselt number are also evaluated for different values of emerging parameters. A comparative study with the existing published work is provided in order to verify the present results. An excellent agreement is found.

An annual model of SSM/I radiobrightness for dry soil

NASA Technical Reports Server (NTRS)

Liou, Yuei-An; England, A. W.

1992-01-01

An annual model is presented of the temperature structure within a homogeneous, dry soil halfspace that is subject to both diurnal and annual insolation, radiant heating from the atmosphere, sensible heat exchange with the atmosphere, and radiant cooling. The thermal constitutive properties of the soil are assumed to be constant so that the heat flow equation can be solved analytically. For computational economy, a variable time interval Laplace transform method is developed to predict the temperature.

Propagator for finite range potentials: The case of reflection

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

Cacciari, Ilaria; Moretti, Paolo; Istituto dei Sistemi Complessi, CNR, Sezione di Firenze, via Madonna del Piano 10, Sesto Fiorentino, Florence 50019

2007-04-15

Following a previous study on the transmission propagator for a finite range potential, the problem of reflection is considered. It is found that the Laplace transform of the reflection propagator can be expressed in terms of the usual Fredholm determinant {delta} and of a new similar determinant {gamma}, containing the peculiar characteristics of reflection. As an example, an array of delta potentials is considered. Moreover, a possible application to the calculation of quantum traversal time is shown.

Lossy radial diffusion of relativistic Jovian electrons. [calculation of synchrotron radiation and electron radiation for Jupiter

NASA Technical Reports Server (NTRS)

Barbosa, D. D.; Coroniti, F. V.

1976-01-01

The radial diffusion equation with synchrotron losses was solved by the Laplace transform method for near-equatorially mirroring relativistic electrons. The evolution of a power law distribution function was found and the characteristics of synchrotron burn-off are stated in terms of explicit parameters for an arbitrary diffusion coefficient. Emissivity from the radiation belts of Jupiter was studied. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.

LaPlace Transform1 Adaptive Control Law in Support of Large Flight Envelope Modeling Work

NASA Technical Reports Server (NTRS)

Gregory, Irene M.; Xargay, Enric; Cao, Chengyu; Hovakimyan, Naira

2011-01-01

This paper presents results of a flight test of the L1 adaptive control architecture designed to directly compensate for significant uncertain cross-coupling in nonlinear systems. The flight test was conducted on the subscale turbine powered Generic Transport Model that is an integral part of the Airborne Subscale Transport Aircraft Research system at the NASA Langley Research Center. The results presented are in support of nonlinear aerodynamic modeling and instrumentation calibration.

Effects of Unsaturated Zones on Baseflow Recession: Analytical Solution and Application

NASA Astrophysics Data System (ADS)

Zhan, H.; Liang, X.; Zhang, Y. K.

2017-12-01

Unsaturated flow is an important process in baseflow recessions and its effect is rarely investigated. A mathematical model for a coupled unsaturated-saturated flow in a horizontally unconfined aquifer with time-dependent infiltrations is presented. Semi-analytical solutions for hydraulic heads and discharges are derived using Laplace transform and Cosine transform. The solutions are compared with solutions of the linearized Boussinesq equation (LB solution) and the linearized Laplace equation (LL solution), respectively. The result indicates that a larger dimensionless constitutive exponent κD of the unsaturated zone leads to a smaller discharge during the infiltration period and a larger discharge after the infiltration. The lateral discharge of the unsaturated zone is significant when κD≤1, and becomes negligible when κD≥100. For late times, the power index b of the recession curve-dQ/dt aQb, is 1 and independent of κD, where Q is the baseflow and a is a constant lumped aquifer parameter. For early times, b is approximately equal to 3 but it approaches infinity when t→1. The present solution is applied to synthetic and field cases. The present solution matched the synthetic data better than both the LL and LB solutions, with a minimum relative error of 16% for estimate of hydraulic conductivity. The present solution was applied to the observed streamflow discharge in Iowa, and the estimated values of the aquifer parameters were reasonable.

The Importance of the Numerical Resolution of the Laplace Equation in the optimization of a Neuronal Stimulation Technique

NASA Astrophysics Data System (ADS)

Faria, Paula

2010-09-01

For the past few years, the potential of transcranial direct current stimulation (tDCS) for the treatment of several pathologies has been investigated. Knowledge of the current density distribution is an important factor in optimizing such applications of tDCS. For this goal, we used the finite element method to solve the Laplace equation in a spherical head model in order to investigate the three dimensional distribution of the current density and the variation of its intensity with depth using different electrodes montages: the traditional one with two sponge electrodes and new electrode montages: with sponge and EEG electrodes and with EEG electrodes varying the numbers of electrodes. The simulation results confirm the effectiveness of the mixed system which may allow the use of tDCS and EEG recording concomitantly and may help to optimize this neuronal stimulation technique. The numerical results were used in a promising application of tDCS in epilepsy.

CMB B-mode auto-bispectrum produced by primordial gravitational waves

NASA Astrophysics Data System (ADS)

Tahara, Hiroaki W. H.; Yokoyama, Jun'ichi

2018-01-01

Gravitational waves from inflation induce polarization patterns in the cosmic microwave background (CMB). It is known that there are only two types of non-Gaussianities of the gravitational waves in the most general covariant scalar field theory having second-order field equations, namely, generalized G-inflation. One originates from the inherent non-Gaussianity in general relativity, and the other from a derivative coupling between the Einstein tensor and the scalar field. We calculate polarization bispectra induced by these non-Gaussianities by transforming them into separable forms by virtue of the Laplace transformation. It is shown that future experiments can constrain the new one but cannot detect the general relativistic one.

Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

NASA Astrophysics Data System (ADS)

Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

2017-03-01

Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

On the solutions of fractional order of evolution equations

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-01-01

In this paper we present a discussion of generalized Cauchy problems in a diffusion wave process, we consider bi-fractional-order evolution equations in the Riemann-Liouville, Liouville-Caputo, and Caputo-Fabrizio sense. Through Fourier transforms and Laplace transform we derive closed-form solutions to the Cauchy problems mentioned above. Similarly, we establish fundamental solutions. Finally, we give an application of the above results to the determination of decompositions of Dirac type for bi-fractional-order equations and write a formula for the moments for the fractional vibration of a beam equation. This type of decomposition allows us to speak of internal degrees of freedom in the vibration of a beam equation.

Laplace deep level transient spectroscopy: Embodiment and evolution

NASA Astrophysics Data System (ADS)

Peaker, A. R.; Markevich, V. P.; Hawkins, I. D.; Hamilton, B.; Bonde Nielsen, K.; Gościński, K.

2012-08-01

This paper is to commemorate the work of Leszek Dobaczewski who devoted much of his life to the development and application of high resolution DLTS. Under good experimental conditions Laplace DLTS provides an order of magnitude higher energy resolution than conventional DLTS techniques. This has had a profound effect on electrical defect spectroscopy enabling the effect of external probes, such as uniaxial stress, and internal perturbations, such as the proximity of atoms isovalent with the host, to be quantified in terms of electronic behaviour. Laplace DLTS provides a synergy with other techniques that was difficult or impossible to achieve previously. In this paper we present an overview of the development of LDLTS and illustrate some of its uses by describing its application in a number of key areas of defect research. Leszek Dobaczewski was born on 25th December 1954. He received his education in Warsaw taking his PhD in 1986 with Jerzy Langer at the Institute of Physics on “Recombination Processes at defects with the large lattice relaxation”. He held a research position at the institute in Warsaw until he came to Manchester in 1990 and thereafter alternated between Manchester and Warsaw. He worked primarily on the development and application of high resolution DLTS. He was awarded the degree of DSc in 1994 for his work on DX centres and held an appointment as full professor in Warsaw with Visiting Professor posts at Manchester and Aarhus. Professor Leszek Dobaczewski died in April 2010.

Exact finite element method analysis of viscoelastic tapered structures to transient loads

NASA Technical Reports Server (NTRS)

Spyrakos, Constantine Chris

1987-01-01

A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.

Unsteady transonic flow analysis for low aspect ratio, pointed wings.

NASA Technical Reports Server (NTRS)

Kimble, K. R.; Ruo, S. Y.; Wu, J. M.; Liu, D. Y.

1973-01-01

Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flow field. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms.

On the Analytical and Numerical Properties of the Truncated Laplace Transform I

DTIC Science & Technology

2014-09-05

contains generalizations and conclusions. 2 2 Preliminaries 2.1 The Legendre Polynomials In this subsection we summarize some of the properties of the the...standard Legendre Polynomi - als, and restate these properties for shifted and normalized forms of the Legendre Polynomials . We define the Shifted... Legendre Polynomial of degree k = 0, 1, ..., which we will be denoting by P ∗k , by the formula P ∗k (x) = Pk(2x− 1), (5) where Pk is the Legendre

Applications of Functional Analytic and Martingale Methods to Problems in Queueing Network Theory.

DTIC Science & Technology

1983-05-14

8217’") Air Force Office of Scientific Research Sf. ADDRESS (Cllty. State and ZIP Code) 7b. ADDRESS (City. State and ZIP Code) Directorate of Mathematical... Scientific Report on Air Force Grant #82-0167 Principal Investigator: Professor Walter A. Rosenkrantz I. Publications (1) Calculation of the LaPlace transform...whether or not a protocol for accessing a comunications channel is stable. In AFOSR 82-0167, Report No. 3 we showed that the SLOTTED ALOHA Multi access

Asymptotic Analysis of the parton branching equation at LHC Energies

NASA Astrophysics Data System (ADS)

Wang, W. Y.; Lau, H. P.; Leong, Q.; Chan, A. H.; Oh, C. H.

2018-01-01

An asymptotic solution to the QCD parton branching equation is derived using the method of Laplace transformation and saddle point approximation. The distribution is applied to charged particle multiplicity distributions in proton-proton collisions at √s = 0.9, 2.36, and 7 TeV for |ƞ| < 0.5, 1.0, 1.5, 2.0, 2.4, and 8 TeV for |ƞ| < 0.5, 1.0, 1.5, as well as 13 TeV data for |ƞ| < 0.8 and 2.5.

Fractional Number Operator and Associated Fractional Diffusion Equations

NASA Astrophysics Data System (ADS)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

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

Brezov, D. S.; Mladenova, C. D.; Mladenov, I. M., E-mail: mladenov@bio21.bas.bg

In this paper we obtain the Lie derivatives of the scalar parameters in the generalized Euler decomposition with respect to arbitrary axes under left and right deck transformations. This problem can be directly related to the representation of the angular momentum in quantum mechanics. As a particular example, we calculate the angular momentum and the corresponding quantum hamiltonian in the standard Euler and Bryan representations. Similarly, in the hyperbolic case, the Laplace-Beltrami operator is retrieved for the Iwasawa decomposition. The case of two axes is considered as well.

Markov and semi-Markov processes as a failure rate

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

Grabski, Franciszek

2016-06-08

In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

On the dielectric conductivity of molecular ionic liquids.

PubMed

Schröder, Christian; Steinhauser, Othmar

2009-09-21

The contribution of the conductivity to the spectrum of the generalized dielectric constant or susceptibility of molecular ionic liquids is analyzed, both in theoretical terms and computationally by means of molecular dynamics simulation of the concrete system 1-ethyl-3-methyl-imidazolium dicyanoamide at 300 K. As a central quantity the simulated current autocorrelation function is modeled by a carefully designed fit function. This not only gives a satisfactory numerical representation but yields the correct conductivity upon integration. In addition the fit function can be Fourier-Laplace transformed analytically. Both, the real and imaginary parts of the transform show expected behavior, in particular, the right limits for zero frequency. This altogether demonstrates that the components of the fit function are of physical relevance.

Comparison of the Young-Laplace law and finite element based calculation of ventricular wall stress: implications for postinfarct and surgical ventricular remodeling.

PubMed

Zhang, Zhihong; Tendulkar, Amod; Sun, Kay; Saloner, David A; Wallace, Arthur W; Ge, Liang; Guccione, Julius M; Ratcliffe, Mark B

2011-01-01

Both the Young-Laplace law and finite element (FE) based methods have been used to calculate left ventricular wall stress. We tested the hypothesis that the Young-Laplace law is able to reproduce results obtained with the FE method. Magnetic resonance imaging scans with noninvasive tags were used to calculate three-dimensional myocardial strain in 5 sheep 16 weeks after anteroapical myocardial infarction, and in 1 of those sheep 6 weeks after a Dor procedure. Animal-specific FE models were created from the remaining 5 animals using magnetic resonance images obtained at early diastolic filling. The FE-based stress in the fiber, cross-fiber, and circumferential directions was calculated and compared to stress calculated with the assumption that wall thickness is very much less than the radius of curvature (Young-Laplace law), and without that assumption (modified Laplace). First, circumferential stress calculated with the modified Laplace law is closer to results obtained with the FE method than stress calculated with the Young-Laplace law. However, there are pronounced regional differences, with the largest difference between modified Laplace and FE occurring in the inner and outer layers of the infarct borderzone. Also, stress calculated with the modified Laplace is very different than stress in the fiber and cross-fiber direction calculated with FE. As a consequence, the modified Laplace law is inaccurate when used to calculate the effect of the Dor procedure on regional ventricular stress. The FE method is necessary to determine stress in the left ventricle with postinfarct and surgical ventricular remodeling. Copyright © 2011 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.

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

PubMed

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

2000-08-20

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

Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere

NASA Astrophysics Data System (ADS)

Fadly Nurullah Rasedee, Ahmad; Ahmedov, Anvarjon; Sathar, Mohammad Hasan Abdul

2017-09-01

The mathematical models of the heat and mass transfer processes on the ball type solids can be solved using the theory of convergence of Fourier-Laplace series on unit sphere. Many interesting models have divergent Fourier-Laplace series, which can be made convergent by introducing Riesz and Cesaro means of the series. Partial sums of the Fourier-Laplace series summed by Riesz method are integral operators with the kernel known as Riesz means of the spectral function. In order to obtain the convergence results for the partial sums by Riesz means we need to know an asymptotic behavior of the latter kernel. In this work the estimations for Riesz means of spectral function of Laplace-Beltrami operator which guarantees the convergence of the Fourier-Laplace series by Riesz method are obtained.

Object-oriented Persistent Homology

PubMed Central

Wang, Bao; Wei, Guo-Wei

2015-01-01

Persistent homology provides a new approach for the topological simplification of big data via measuring the life time of intrinsic topological features in a filtration process and has found its success in scientific and engineering applications. However, such a success is essentially limited to qualitative data classification and analysis. Indeed, persistent homology has rarely been employed for quantitative modeling and prediction. Additionally, the present persistent homology is a passive tool, rather than a proactive technique, for classification and analysis. In this work, we outline a general protocol to construct object-oriented persistent homology methods. By means of differential geometry theory of surfaces, we construct an objective functional, namely, a surface free energy defined on the data of interest. The minimization of the objective functional leads to a Laplace-Beltrami operator which generates a multiscale representation of the initial data and offers an objective oriented filtration process. The resulting differential geometry based object-oriented persistent homology is able to preserve desirable geometric features in the evolutionary filtration and enhances the corresponding topological persistence. The cubical complex based homology algorithm is employed in the present work to be compatible with the Cartesian representation of the Laplace-Beltrami flow. The proposed Laplace-Beltrami flow based persistent homology method is extensively validated. The consistence between Laplace-Beltrami flow based filtration and Euclidean distance based filtration is confirmed on the Vietoris-Rips complex for a large amount of numerical tests. The convergence and reliability of the present Laplace-Beltrami flow based cubical complex filtration approach are analyzed over various spatial and temporal mesh sizes. The Laplace-Beltrami flow based persistent homology approach is utilized to study the intrinsic topology of proteins and fullerene molecules. Based on a quantitative model which correlates the topological persistence of fullerene central cavity with the total curvature energy of the fullerene structure, the proposed method is used for the prediction of fullerene isomer stability. The efficiency and robustness of the present method are verified by more than 500 fullerene molecules. It is shown that the proposed persistent homology based quantitative model offers good predictions of total curvature energies for ten types of fullerene isomers. The present work offers the first example to design object-oriented persistent homology to enhance or preserve desirable features in the original data during the filtration process and then automatically detect or extract the corresponding topological traits from the data. PMID:26705370

Analytical solution for the transient response of a fluid/saturated porous medium halfspace system subjected to an impulsive line source

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng; Jing, Liping; Li, Yongqiang

2018-05-01

In this paper, transient wave propagation is investigated within a fluid/saturated porous medium halfspace system with a planar interface that is subjected to a cylindrical P-wave line source. Assuming the permeability coefficient is sufficiently large, analytical solutions for the transient response of the fluid/saturated porous medium halfspace system are developed. Moreover, the analytical solutions are presented in simple closed forms wherein each term represents a transient physical wave, especially the expressions for head waves. The methodology utilised to determine where the head wave can emerge within the system is also given. The wave fields within the fluid and porous medium are first defined considering the behaviour of two compressional waves and one tangential wave in the saturated porous medium and one compressional wave in the fluid. Substituting these wave fields into the interface continuity conditions, the analytical solutions in the Laplace domain are then derived. To transform the solutions into the time domain, a suitable distortion of the contour is provided to change the integration path of the solution, after which the analytical solutions in the Laplace domain are transformed into the time domain by employing Cagniard's method. Numerical examples are provided to illustrate some interesting features of the fluid/saturated porous medium halfspace system. In particular, the interface wave and head waves that propagate along the interface between the fluid and saturated porous medium can be observed.

A Semianalytical Model for Pumping Tests in Finite Heterogeneous Confined Aquifers With Arbitrarily Shaped Boundary

NASA Astrophysics Data System (ADS)

Wang, Lei; Dai, Cheng; Xue, Liang

2018-04-01

This study presents a Laplace-transform-based boundary element method to model the groundwater flow in a heterogeneous confined finite aquifer with arbitrarily shaped boundaries. The boundary condition can be Dirichlet, Neumann or Robin-type. The derived solution is analytical since it is obtained through the Green's function method within the domain. However, the numerical approximation is required on the boundaries, which essentially renders it a semi-analytical solution. The proposed method can provide a general framework to derive solutions for zoned heterogeneous confined aquifers with arbitrarily shaped boundary. The requirement of the boundary element method presented here is that the Green function must exist for a specific PDE equation. In this study, the linear equations for the two-zone and three-zone confined aquifers with arbitrarily shaped boundary is established in Laplace space, and the solution can be obtained by using any linear solver. Stehfest inversion algorithm can be used to transform it back into time domain to obtain the transient solution. The presented solution is validated in the two-zone cases by reducing the arbitrarily shaped boundaries to circular ones and comparing it with the solution in Lin et al. (2016, https://doi.org/10.1016/j.jhydrol.2016.07.028). The effect of boundary shape and well location on dimensionless drawdown in two-zone aquifers is investigated. Finally the drawdown distribution in three-zone aquifers with arbitrarily shaped boundary for constant-rate tests (CRT) and flow rate distribution for constant-head tests (CHT) are analyzed.

Immittance Data Validation by Kramers‐Kronig Relations – Derivation and Implications

PubMed Central

2017-01-01

Abstract Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers‐Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two‐sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non‐linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences. PMID:29577007

Speech Enhancement, Gain, and Noise Spectrum Adaptation Using Approximate Bayesian Estimation

PubMed Central

Hao, Jiucang; Attias, Hagai; Nagarajan, Srikantan; Lee, Te-Won; Sejnowski, Terrence J.

2010-01-01

This paper presents a new approximate Bayesian estimator for enhancing a noisy speech signal. The speech model is assumed to be a Gaussian mixture model (GMM) in the log-spectral domain. This is in contrast to most current models in frequency domain. Exact signal estimation is a computationally intractable problem. We derive three approximations to enhance the efficiency of signal estimation. The Gaussian approximation transforms the log-spectral domain GMM into the frequency domain using minimal Kullback–Leiber (KL)-divergency criterion. The frequency domain Laplace method computes the maximum a posteriori (MAP) estimator for the spectral amplitude. Correspondingly, the log-spectral domain Laplace method computes the MAP estimator for the log-spectral amplitude. Further, the gain and noise spectrum adaptation are implemented using the expectation–maximization (EM) algorithm within the GMM under Gaussian approximation. The proposed algorithms are evaluated by applying them to enhance the speeches corrupted by the speech-shaped noise (SSN). The experimental results demonstrate that the proposed algorithms offer improved signal-to-noise ratio, lower word recognition error rate, and less spectral distortion. PMID:20428253

On a difficulty in eigenfunction expansion solutions for the start-up of fluid flow

NASA Astrophysics Data System (ADS)

Christov, Ivan C.

2015-11-01

Most mathematics and engineering textbooks describe the process of ``subtracting off'' the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundary-value problem with homogeneous boundary conditions that can be solved by separation of variables (i.e., eigenfunction expansions). While this method produces the correct solution for the start-up of the flow of, e.g., a Newtonian fluid between parallel plates, it can lead to erroneous solutions to the corresponding problem for a class of non-Newtonian fluids. We show that the reason for this is the non-rigorous enforcement of the start-up condition in the textbook approach, which leads to a violation of the principle of causality. Nevertheless, these boundary-value problems can be solved correctly using eigenfunction expansions, and we present the formulation that makes this possible (in essence, an application of Duhamel's principle). The solutions obtained by this new approach are shown to agree identically with those obtained by using the Laplace transform in time only, a technique that enforces the proper start-up condition implicitly (hence, the same error cannot be committed). Supported, in part, by NSF Grant DMS-1104047 and the U.S. DOE (Contract No. DE-AC52-06NA25396) through the LANL/LDRD Program.

Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

NASA Astrophysics Data System (ADS)

Chen, Jing-Bo

2014-06-01

By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

Image compression technique

DOEpatents

Fu, C.Y.; Petrich, L.I.

1997-03-25

An image is compressed by identifying edge pixels of the image; creating a filled edge array of pixels each of the pixels in the filled edge array which corresponds to an edge pixel having a value equal to the value of a pixel of the image array selected in response to the edge pixel, and each of the pixels in the filled edge array which does not correspond to an edge pixel having a value which is a weighted average of the values of surrounding pixels in the filled edge array which do correspond to edge pixels; and subtracting the filled edge array from the image array to create a difference array. The edge file and the difference array are then separately compressed and transmitted or stored. The original image is later reconstructed by creating a preliminary array in response to the received edge file, and adding the preliminary array to the received difference array. Filling is accomplished by solving Laplace`s equation using a multi-grid technique. Contour and difference file coding techniques also are described. The techniques can be used in a method for processing a plurality of images by selecting a respective compression approach for each image, compressing each of the images according to the compression approach selected, and transmitting each of the images as compressed, in correspondence with an indication of the approach selected for the image. 16 figs.

Laplace approximation for Bessel functions of matrix argument

NASA Astrophysics Data System (ADS)

Butler, Ronald W.; Wood, Andrew T. A.

2003-06-01

We derive Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel A[nu]; matrix Bessel B[nu]; and the type II confluent hypergeometric function of matrix argument, [Psi]. We examine the theoretical and numerical properties of the approximations. On the theoretical side, it is shown that the Laplace approximations to A[nu], B[nu] and [Psi] given here, together with the Laplace approximations to the matrix argument functions 1F1 and 2F1 presented in Butler and Wood (Laplace approximations to hyper-geometric functions with matrix argument, Ann. Statist. (2002)), satisfy all the important confluence relations and symmetry relations enjoyed by the original functions.

Temperature field for radiative tomato peeling

NASA Astrophysics Data System (ADS)

Cuccurullo, G.; Giordano, L.

2017-01-01

Nowadays peeling of tomatoes is performed by using steam or lye, which are expensive and polluting techniques, thus sustainable alternatives are searched for dry peeling and, among that, radiative heating seems to be a fairly promising method. This paper aims to speed up the prediction of surface temperatures useful for realizing dry-peeling, thus a 1D-analytical model for the unsteady temperature field in a rotating tomato exposed to a radiative heating source is presented. Since only short times are of interest for the problem at hand, the model involves a semi-infinite slab cooled by convective heat transfer while heated by a pulsating heat source. The model being linear, the solution is derived following the Laplace Transform method. A 3D finite element model of the rotating tomato is introduced as well in order to validate the analytical solution. A satisfactory agreement is attained. Therefore, two different ways to predict the onset of the peeling conditions are available which can be of help for proper design of peeling plants. Particular attention is paid to study surface temperature uniformity, that being a critical parameter for realizing an easy tomato peeling.

On the Misuse of the Laplace Law in Bio Fluid Dynamics

NASA Astrophysics Data System (ADS)

Thatte, Azam

2005-11-01

The Laplace law is commonly applied in biomechanical analyses of blood vessels, lung alveoli, and the gastrointestinal tract, often without concern to assumptions that underlie its use. This ``law'' is a simple force balance applied across the wall of a static pressurized (δP) vessel for small thickness-to-radius ratio τ/r. However, the true thin-wall requirement is more severe than τ/r << 1. Furthermore, because the Laplace law estimates total stress rather than deviatoric stress, the common practice of evaluating material stiffness by plotting Laplace law stress against strain is, in principle, incorrect. To study the validity of the Laplace law in biomechanical applications, we solved exactly the model problem of an axisymmetric pressurized cylinder of arbitrary thickness, linearly elastic isotropic material, in steady state, with the no-load state (δP = 0) as the zero stress state. Vessel radii and all stresses (total, deviatoric, hydrostatic) are predicted as functions of δP. We find that the Laplace law is invalid for many biomechanical applications and that total stress is not an appropriate surrogate for deviatoric stress to evaluate stiffness. We propose a model for deviatoric stress that we argue should replace the Laplace law for many biomechanical applications.

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.

Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

NASA Astrophysics Data System (ADS)

Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

2017-12-01

The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

The complex variable boundary element method: Applications in determining approximative boundaries

USGS Publications Warehouse

Hromadka, T.V.

1984-01-01

The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

PubMed

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

Kinetics of heterogeneous chemical reactions: a theoretical model for the accumulation of pesticides in soil.

PubMed

Lin, S H; Sahai, R; Eyring, H

1971-04-01

A theoretical model for the accumulation of pesticides in soil has been proposed and discussed from the viewpoint of heterogeneous reaction kinetics with a basic aim to understand the complex nature of soil processes relating to the environmental pollution. In the bulk of soil, the pesticide disappears by diffusion and a chemical reaction; the rate processes considered on the surface of soil are diffusion, chemical reaction, vaporization, and regular pesticide application. The differential equations involved have been solved analytically by the Laplace-transform method.

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.

Kinetics of Heterogeneous Chemical Reactions: A Theoretical Model for the Accumulation of Pesticides in Soil

PubMed Central

Lin, S. H.; Sahai, R.; Eyring, H.

1971-01-01

A theoretical model for the accumulation of pesticides in soil has been proposed and discussed from the viewpoint of heterogeneous reaction kinetics with a basic aim to understand the complex nature of soil processes relating to the environmental pollution. In the bulk of soil, the pesticide disappears by diffusion and a chemical reaction; the rate processes considered on the surface of soil are diffusion, chemical reaction, vaporization, and regular pesticide application. The differential equations involved have been solved analytically by the Laplace-transform method. PMID:5279519

Generalized thermoelastic interaction in an isotropic solid cylinder without energy dissipation

NASA Astrophysics Data System (ADS)

Alshaikh, Fatimah

2018-04-01

In this paper, we constructed the generalized thermoelastic equations of an isotropic solid cylinder. The formulation is applied in the context of Green and Naghdi theory of types II (without energy dissipation). The material of the cylinder is supposed to be homogeneous isotropic both mechanically and thermally. The governing equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical results for the temperature distribution, displacement and radial stress are represented graphically.

Drag Minimization for Wings and Bodies in Supersonic Flow

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Fuller, Franklyn B

1958-01-01

The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.

A Tutorial Review on Fractal Spacetime and Fractional Calculus

NASA Astrophysics Data System (ADS)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

NASA Astrophysics Data System (ADS)

Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier

2018-01-01

The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.

Discrete transparent boundary conditions for the mixed KDV-BBM equation

NASA Astrophysics Data System (ADS)

Besse, Christophe; Noble, Pascal; Sanchez, David

2017-09-01

In this paper, we consider artificial boundary conditions for the linearized mixed Korteweg-de Vries (KDV) and Benjamin-Bona-Mahoney (BBM) equation which models water waves in the small amplitude, large wavelength regime. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z-transform of an holomorphic function). In this paper, we propose a new, stable and fairly general strategy to carry out this crucial step in the design of transparent boundary conditions. For large time simulations, we also introduce a methodology based on the asymptotic expansion of coefficients involved in exact direct transparent boundary conditions. We illustrate the accuracy of our methods for Gaussian and wave packets initial data.

Effect of Box-Cox transformation on power of Haseman-Elston and maximum-likelihood variance components tests to detect quantitative trait Loci.

PubMed

Etzel, C J; Shete, S; Beasley, T M; Fernandez, J R; Allison, D B; Amos, C I

2003-01-01

Non-normality of the phenotypic distribution can affect power to detect quantitative trait loci in sib pair studies. Previously, we observed that Winsorizing the sib pair phenotypes increased the power of quantitative trait locus (QTL) detection for both Haseman-Elston (HE) least-squares tests [Hum Hered 2002;53:59-67] and maximum likelihood-based variance components (MLVC) analysis [Behav Genet (in press)]. Winsorizing the phenotypes led to a slight increase in type 1 error in H-E tests and a slight decrease in type I error for MLVC analysis. Herein, we considered transforming the sib pair phenotypes using the Box-Cox family of transformations. Data were simulated for normal and non-normal (skewed and kurtic) distributions. Phenotypic values were replaced by Box-Cox transformed values. Twenty thousand replications were performed for three H-E tests of linkage and the likelihood ratio test (LRT), the Wald test and other robust versions based on the MLVC method. We calculated the relative nominal inflation rate as the ratio of observed empirical type 1 error divided by the set alpha level (5, 1 and 0.1% alpha levels). MLVC tests applied to non-normal data had inflated type I errors (rate ratio greater than 1.0), which were controlled best by Box-Cox transformation and to a lesser degree by Winsorizing. For example, for non-transformed, skewed phenotypes (derived from a chi2 distribution with 2 degrees of freedom), the rates of empirical type 1 error with respect to set alpha level=0.01 were 0.80, 4.35 and 7.33 for the original H-E test, LRT and Wald test, respectively. For the same alpha level=0.01, these rates were 1.12, 3.095 and 4.088 after Winsorizing and 0.723, 1.195 and 1.905 after Box-Cox transformation. Winsorizing reduced inflated error rates for the leptokurtic distribution (derived from a Laplace distribution with mean 0 and variance 8). Further, power (adjusted for empirical type 1 error) at the 0.01 alpha level ranged from 4.7 to 17.3% across all tests using the non-transformed, skewed phenotypes, from 7.5 to 20.1% after Winsorizing and from 12.6 to 33.2% after Box-Cox transformation. Likewise, power (adjusted for empirical type 1 error) using leptokurtic phenotypes at the 0.01 alpha level ranged from 4.4 to 12.5% across all tests with no transformation, from 7 to 19.2% after Winsorizing and from 4.5 to 13.8% after Box-Cox transformation. Thus the Box-Cox transformation apparently provided the best type 1 error control and maximal power among the procedures we considered for analyzing a non-normal, skewed distribution (chi2) while Winzorizing worked best for the non-normal, kurtic distribution (Laplace). We repeated the same simulations using a larger sample size (200 sib pairs) and found similar results. Copyright 2003 S. Karger AG, Basel

Towards Informetrics: Haitun, Laplace, Zipf, Bradford and the Alvey Programme.

ERIC Educational Resources Information Center

Brookes, B. C.

1984-01-01

Review of recent developments in statistical theories for social sciences highlights Haitun's statistical distributions, Laplace's "Law of Succession" and distribution, Laplace and Bradford analysis of book-index data, inefficiency of frequency distribution analysis, Laws of Bradford and Zipf, natural categorization, and Bradford Law and…

Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: Basic theory and applications

NASA Astrophysics Data System (ADS)

Doungmo Goufo, Emile Franc

2016-08-01

After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function E α , β ( z ) , z ∈ ℂ ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89, 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on Eα,β(z). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β. Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of Eα,β(z), certainly opening new doors to modeling with two-parameter derivatives.

Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: Basic theory and applications.

PubMed

Doungmo Goufo, Emile Franc

2016-08-01

After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function Eα,β(z), z∈ℂ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89, 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on Eα , β(z). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β. Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of Eα , β(z), certainly opening new doors to modeling with two-parameter derivatives.

Research on HDR image fusion algorithm based on Laplace pyramid weight transform with extreme low-light CMOS

NASA Astrophysics Data System (ADS)

Guan, Wen; Li, Li; Jin, Weiqi; Qiu, Su; Zou, Yan

2015-10-01

Extreme-Low-Light CMOS has been widely applied in the field of night-vision as a new type of solid image sensor. But if the illumination in the scene has drastic changes or the illumination is too strong, Extreme-Low-Light CMOS can't both clearly present the high-light scene and low-light region. According to the partial saturation problem in the field of night-vision, a HDR image fusion algorithm based on the Laplace Pyramid was researched. The overall gray value and the contrast of the low light image is very low. We choose the fusion strategy based on regional average gradient for the top layer of the long exposure image and short exposure image, which has rich brightness and textural features. The remained layers which represent the edge feature information of the target are based on the fusion strategy based on regional energy. In the process of source image reconstruction with Laplacian pyramid image, we compare the fusion results with four kinds of basal images. The algorithm is tested using Matlab and compared with the different fusion strategies. We use information entropy, average gradient and standard deviation these three objective evaluation parameters for the further analysis of the fusion result. Different low illumination environment experiments show that the algorithm in this paper can rapidly get wide dynamic range while keeping high entropy. Through the verification of this algorithm features, there is a further application prospect of the optimized algorithm. Keywords: high dynamic range imaging, image fusion, multi-exposure image, weight coefficient, information fusion, Laplacian pyramid transform.

Homogenization of Electromagnetic and Seismic Wavefields for Joint Inverse Modeling

NASA Astrophysics Data System (ADS)

Newman, G. A.; Commer, M.; Petrov, P.; Um, E. S.

2011-12-01

A significant obstacle in developing a robust joint imaging technology exploiting seismic and electromagnetic (EM) wave fields is the resolution at which these different geophysical measurements sense the subsurface. Imaging of seismic reflection data is an order of magnitude finer in resolution and scale compared to images produced with EM data. A consistent joint image of the subsurface geophysical attributes (velocity, electrical conductivity) requires/demands the different geophysical data types be similar in their resolution of the subsurface. The superior resolution of seismic data results from the fact that the energy propagates as a wave, while propagation of EM energy is diffusive and attenuates with distance. On the other hand, the complexity of the seismic wave field can be a significant problem due to high reflectivity of the subsurface and the generation of multiple scattering events. While seismic wave fields have been very useful in mapping the subsurface for energy resources, too much scattering and too many reflections can lead to difficulties in imaging and interpreting seismic data. To overcome these obstacles a formulation for joint imaging of seismic and EM wave fields is introduced, where each data type is matched in resolution. In order to accomplish this, seismic data are first transformed into the Laplace-Fourier Domain, which changes the modeling of the seismic wave field from wave propagation to diffusion. Though high frequency information (reflectivity) is lost with this transformation, several benefits follow: (1) seismic and EM data can be easily matched in resolution, governed by the same physics of diffusion, (2) standard least squares inversion works well with diffusive type problems including both transformed seismic and EM, (3) joint imaging of seismic and EM data may produce better starting velocity models critical for successful reverse time migration or full waveform imaging of seismic data (non transformed) and (4) possibilities to image across multiple scale lengths, incorporating different types of geophysical data and attributes in the process. Important numerical details of 3D seismic wave field simulation in the Laplace-Fourier domain for both acoustic and elastic cases will also be discussed.

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

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

Meng, Da; Zheng, Bin; Lin, Guang

2014-08-29

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is themore » number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.« less

On the coupled unsaturated-saturated flow process induced by vertical, horizontal, and slant wells in unconfined aquifers

NASA Astrophysics Data System (ADS)

Liang, Xiuyu; Zhan, Hongbin; Zhang, You-Kuan; Liu, Jin

2017-03-01

Conventional models of pumping tests in unconfined aquifers often neglect the unsaturated flow process. This study concerns the coupled unsaturated-saturated flow process induced by vertical, horizontal, and slant wells positioned in an unconfined aquifer. A mathematical model is established with special consideration of the coupled unsaturated-saturated flow process and the well orientation. Groundwater flow in the saturated zone is described by a three-dimensional governing equation and a linearized three-dimensional Richards' equation in the unsaturated zone. A solution in the Laplace domain is derived by the Laplace-finite-Fourier-transform and the method of separation of variables, and the semi-analytical solutions are obtained using a numerical inverse Laplace method. The solution is verified by a finite-element numerical model. It is found that the effects of the unsaturated zone on the drawdown of a pumping test exist at any angle of inclination of the pumping well, and this impact is more significant in the case of a horizontal well. The effects of the unsaturated zone on the drawdown are independent of the length of the horizontal well screen. The vertical well leads to the largest water volume drained from the unsaturated zone (W) during the early pumping time, and the effects of the well orientation on W values become insignificant at the later time. The screen length of the horizontal well does not affect W for the whole pumping period. The proposed solutions are useful for the parameter identification of pumping tests with a general well orientation (vertical, horizontal, and slant) in unconfined aquifers affected from above by the unsaturated flow process.

Analytical and numerical construction of equivalent cables.

PubMed

Lindsay, K A; Rosenberg, J R; Tucker, G

2003-08-01

The mathematical complexity experienced when applying cable theory to arbitrarily branched dendrites has lead to the development of a simple representation of any branched dendrite called the equivalent cable. The equivalent cable is an unbranched model of a dendrite and a one-to-one mapping of potentials and currents on the branched model to those on the unbranched model, and vice versa. The piecewise uniform cable, with a symmetrised tri-diagonal system matrix, is shown to represent the canonical form for an equivalent cable. Through a novel application of the Laplace transform it is demonstrated that an arbitrary branched model of a dendrite can be transformed to the canonical form of an equivalent cable. The characteristic properties of the equivalent cable are extracted from the matrix for the transformed branched model. The one-to-one mapping follows automatically from the construction of the equivalent cable. The equivalent cable is used to provide a new procedure for characterising the location of synaptic contacts on spinal interneurons.

Inverse Transformation: Unleashing Spatially Heterogeneous Dynamics with an Alternative Approach to XPCS Data Analysis.

PubMed

Andrews, Ross N; Narayanan, Suresh; Zhang, Fan; Kuzmenko, Ivan; Ilavsky, Jan

2018-02-01

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables probing dynamics in a broad array of materials with XPCS, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fails. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. In this paper, we propose an alternative analysis scheme based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. Using XPCS data measured from colloidal gels, we demonstrate the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.

Inverse Transformation: Unleashing Spatially Heterogeneous Dynamics with an Alternative Approach to XPCS Data Analysis

PubMed Central

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan; Kuzmenko, Ivan; Ilavsky, Jan

2018-01-01

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables probing dynamics in a broad array of materials with XPCS, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fails. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. In this paper, we propose an alternative analysis scheme based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. Using XPCS data measured from colloidal gels, we demonstrate the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS. PMID:29875506

Reactive solute transport in an asymmetric aquifer-aquitard system with scale-dependent dispersion

NASA Astrophysics Data System (ADS)

Zhou, R.; Zhan, H.

2017-12-01

Abstract: The understanding of reactive solute transport in an aquifer-aquitard system is important to study transport behavior in the more complex porous media. When transport properties are asymmetric in the upper and lower aquitards, reactive solute transport in such an aquifer-aquitard system becomes a coupled three domain problem that is more complex than the symmetric case in which the upper and lower aquitards have identical transport properties. Meanwhile, the dispersivity of transport in the aquifer is considered as a linear or exponential function of travel distance due to the heterogeneity of aquifer. This study proposed new transport models to describe reactive solute transport in such an asymmetric aquifer-aquitard system with scale-dependent dispersion. Mathematical models were developed for such problems under the first-type and third-type boundary conditions to analyze the spatial-temporal concentration and mass distribution in the aquifer and aquitards with the help of Laplace transform technique and the de Hoog numerical Laplace inversion method. Breakthrough curves (BTCs) and residence time distribution curves (RTDs) obtained from the models with scale-dependent dispersion, constant dispersion and constant effective dispersivity were compared to reflect the lumped scale-dispersion effect in the aquifer-aquitard system. The newly acquired solutions were then tested extensively against previous analytical and numerical solutions and were proven to be robust and accurate. Furthermore, to study the back diffusion of contaminant mass in aquitards, a zero-contaminant mass concentration boundary condition was imposed on the inlet boundary of the system after a certain time, which is also called the process of water flushing. The diffusion loss alone the aquifer/aquitard interfaces and mass stored ratio change in each of three domains (upper aquitard, aquifer, and lower aquitard) after water flushing provided an insightful and comprehensive analysis of transport behavior with asymmetric distribution of transport properties.

Reactive solute transport in an asymmetrical fracture-rock matrix system

NASA Astrophysics Data System (ADS)

Zhou, Renjie; Zhan, Hongbin

2018-02-01

The understanding of reactive solute transport in a single fracture-rock matrix system is the foundation of studying transport behavior in the complex fractured porous media. When transport properties are asymmetrically distributed in the adjacent rock matrixes, reactive solute transport has to be considered as a coupled three-domain problem, which is more complex than the symmetric case with identical transport properties in the adjacent rock matrixes. This study deals with the transport problem in a single fracture-rock matrix system with asymmetrical distribution of transport properties in the rock matrixes. Mathematical models are developed for such a problem under the first-type and the third-type boundary conditions to analyze the spatio-temporal concentration and mass distribution in the fracture and rock matrix with the help of Laplace transform technique and de Hoog numerical inverse Laplace algorithm. The newly acquired solutions are then tested extensively against previous analytical and numerical solutions and are proven to be robust and accurate. Furthermore, a water flushing phase is imposed on the left boundary of system after a certain time. The diffusive mass exchange along the fracture/rock matrixes interfaces and the relative masses stored in each of three domains (fracture, upper rock matrix, and lower rock matrix) after the water flushing provide great insights of transport with asymmetric distribution of transport properties. This study has the following findings: 1) Asymmetric distribution of transport properties imposes greater controls on solute transport in the rock matrixes. However, transport in the fracture is mildly influenced. 2) The mass stored in the fracture responses quickly to water flushing, while the mass stored in the rock matrix is much less sensitive to the water flushing. 3) The diffusive mass exchange during the water flushing phase has similar patterns under symmetric and asymmetric cases. 4) The characteristic distance which refers to the zero diffusion between the fracture and the rock matrix during the water flushing phase is closely associated with dispersive process in the fracture.

Correlation Filtering of Modal Dynamics using the Laplace Wavelet

NASA Technical Reports Server (NTRS)

Freudinger, Lawrence C.; Lind, Rick; Brenner, Martin J.

1997-01-01

Wavelet analysis allows processing of transient response data commonly encountered in vibration health monitoring tasks such as aircraft flutter testing. The Laplace wavelet is formulated as an impulse response of a single mode system to be similar to data features commonly encountered in these health monitoring tasks. A correlation filtering approach is introduced using the Laplace wavelet to decompose a signal into impulse responses of single mode subsystems. Applications using responses from flutter testing of aeroelastic systems demonstrate modal parameters and stability estimates can be estimated by correlation filtering free decay data with a set of Laplace wavelets.

The nonlinear oil-water two-phase flow behavior for a horizontal well in triple media carbonate reservoir

NASA Astrophysics Data System (ADS)

Wang, Yong; Tao, Zhengwu; Chen, Liang; Ma, Xin

2017-10-01

Carbonate reservoir is one of the important reservoirs in the world. Because of the characteristics of carbonate reservoir, horizontal well has become a key technology for efficiently developing carbonate reservoir. Establishing corresponding mathematical models and analyzing transient pressure behaviors of this type of well-reservoir configuration can provide a better understanding of fluid flow patterns in formation as well as estimations of important parameters. A mathematical model for a oil-water two-phase flow horizontal well in triple media carbonate reservoir by conceptualizing vugs as spherical shapes are presented in this article. A semi-analytical solution is obtained in the Laplace domain using source function theory, Laplace transformation, and superposition principle. Analysis of transient pressure responses indicates that seven characteristic flow periods of horizontal well in triple media carbonate reservoir can be identified. Parametric analysis shows that water saturation of matrix, vug and fracture system, horizontal section length, and horizontal well position can significantly influence the transient pressure responses of horizontal well in triple media carbonate reservoir. The model presented in this article can be applied to obtain important parameters pertinent to reservoir by type curve matching.

Single molecule diffusion and the solution of the spherically symmetric residence time equation.

PubMed

Agmon, Noam

2011-06-16

The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work. © 2011 American Chemical Society

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods

PubMed Central

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-01-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72–88, 2013. PMID:23847452

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods.

PubMed

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-05-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L 2 -norm regularization. However, sparse representation methods via L 1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L 1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72-88, 2013.

Illustrating dynamical symmetries in classical mechanics: The Laplace-Runge-Lenz vector revisited

NASA Astrophysics Data System (ADS)

O'Connell, Ross C.; Jagannathan, Kannan

2003-03-01

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and degeneracy associated with this vector and with analogous dynamical symmetries. We define a conserved dynamical variable α that characterizes the orientation of the orbit in two-dimensional configuration space for the Kepler problem and an analogous variable β for the isotropic harmonic oscillator. This orbit orientation variable is canonically conjugate to the angular momentum component normal to the plane of motion. We explore the canonical one-parameter group of transformations generated by α(β). Because we have an obvious pair of conserved canonically conjugate variables, it is desirable to use them as a coordinate-momentum pair. In terms of these phase space coordinates, the form of the Hamiltonian is nearly trivial because neither member of the pair can occur explicitly in the Hamiltonian. From these considerations we gain a simple picture of dynamics in phase space. The procedure we use is in the spirit of the Hamilton-Jacobi method.

General well function for pumping from a confined, leaky, or unconfined aquifer

NASA Astrophysics Data System (ADS)

Perina, Tomas; Lee, Tien-Chang

2006-02-01

A general well function for groundwater flow toward an extraction well with non-uniform radial flux along the screen and finite-thickness skin, partially penetrating an unconfined, leaky-boundary flux, or confined aquifer is derived via the Laplace and generalized finite Fourier transforms. The mixed boundary condition at the well face is solved as the discretized Fredholm integral equation. The general well function reduces to a uniform radial flux solution as a special case. In the Laplace domain, the relation between the drawdown in the extraction well and flowrate is linear and the formulations for specified flowrate or specified drawdown pumping are interchangeable. The deviation in drawdown of the uniform from non-uniform radial flux solutions depends on the relative positions of the extraction and observation well screens, aquifer properties, and time of observation. In an unconfined aquifer the maximum deviation occurs during the period of delayed drawdown when the effect of vertical flow is most apparent. The skin and wellbore storage in an observation well are included as model parameters. A separate solution is developed for a fully penetrating well with the radial flux being a continuous function of depth.

Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating.

PubMed

Hussanan, Abid; Zuki Salleh, Mohd; Tahar, Razman Mat; Khan, Ilyas

2014-01-01

In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform method and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.

Tables of the Inverse Laplace Transform of the Function [Formula: see text].

PubMed

Dishon, Menachem; Bendler, John T; Weiss, George H

1990-01-01

The inverse transform, [Formula: see text], 0 < β < 1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state physics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to g ( t ). However, there have so far been no accurately calculated values available for checking or other purposes. We present here tables, accurate to six figures, of g ( t ) for a number of values of β between 0.25 and 0.999. In addition, since g ( t ), regarded as a function of β , is uni-modal with a peak occurring at t = t max we both tabulate and graph t max and 1/ g ( t max ) as a function of β , as well as giving polynomial approximations to 1/ g ( t max ).

Tables of the Inverse Laplace Transform of the Function e−sβ

PubMed Central

Dishon, Menachem; Bendler, John T.; Weiss, George H.

1990-01-01

The inverse transform, g(t)=L−1(e−sβ), 0 < β < 1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state physics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to g(t). However, there have so far been no accurately calculated values available for checking or other purposes. We present here tables, accurate to six figures, of g(t) for a number of values of β between 0.25 and 0.999. In addition, since g(t), regarded as a function of β, is uni-modal with a peak occurring at t = tmax we both tabulate and graph tmax and 1/g(tmax) as a function of β, as well as giving polynomial approximations to 1/g(tmax). PMID:28179785

Torsional vibration of a pipe pile in transversely isotropic saturated soil

NASA Astrophysics Data System (ADS)

Zheng, Changjie; Hua, Jianmin; Ding, Xuanming

2016-09-01

This study considers the torsional vibration of a pipe pile in a transversely isotropic saturated soil layer. Based on Biot's poroelastic theory and the constitutive relations of the transversely isotropic medium, the dynamic governing equations of the outer and inner transversely isotropic saturated soil layers are derived. The Laplace transform is used to solve the governing equations of the outer and inner soil layers. The dynamic torsional response of the pipe pile in the frequency domain is derived utilizing 1D elastic theory and the continuous conditions at the interfaces between the pipe pile and the soils. The time domain solution is obtained by Fourier inverse transform. A parametric study is conducted to demonstrate the influence of the anisotropies of the outer and inner soil on the torsional dynamic response of the pipe pile.

Computational methods for yeast prion curing curves.

PubMed

Ridout, Martin S

2008-10-01

If the chemical guanidine hydrochloride is added to a dividing culture of yeast cells in which some of the protein Sup35p is in its prion form, the proportion of cells that carry replicating units of the prion, termed propagons, decreases gradually over time. Stochastic models to describe this process of 'curing' have been developed in earlier work. The present paper investigates the use of numerical methods of Laplace transform inversion to calculate curing curves and contrasts this with an alternative, more direct, approach that involves numerical integration. Transform inversion is found to provide a much more efficient computational approach that allows different models to be investigated with minimal programming effort. The method is used to investigate the robustness of the curing curve to changes in the assumed distribution of cell generation times. Matlab code is available for carrying out the calculations.

Resolvent estimates in homogenisation of periodic problems of fractional elasticity

NASA Astrophysics Data System (ADS)

Cherednichenko, Kirill; Waurick, Marcus

2018-03-01

We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients that represent the material properties of a viscoelastic composite medium. Assuming periodicity in the coefficients, we prove operator-norm convergence estimates for an operator fibre decomposition obtained by applying to the original fractional elasticity problem the Fourier-Laplace transform in time and Gelfand transform in space. We obtain estimates on each fibre that are uniform in the quasimomentum of the decomposition and in the period of oscillations of the coefficients as well as quadratic with respect to the spectral variable. On the basis of these uniform estimates we derive operator-norm-type convergence estimates for the original fractional elasticity problem, for a class of sufficiently smooth densities of applied forces.

Feeling Wall Tension in an Interactive Demonstration of Laplace's Law

ERIC Educational Resources Information Center

Letic, Milorad

2012-01-01

Laplace's Law plays a major role in explanations of the wall tension of structures like blood vessels, the bladder, the uterus in pregnancy, bronchioles, eyeballs, and the behavior of aneurisms or the enlarged heart. The general relation of Laplace's law, expressing that the product of the radius of curvature (r) and pressure (P) is equal to wall…

On the singular perturbations for fractional differential equation.

PubMed

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Analytical solutions for the motion of a charged particle in electric and magnetic fields via non-singular fractional derivatives

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Taneco-Hernandez, M. A.

2017-12-01

In this work we propose fractional differential equations for the motion of a charged particle in electric, magnetic and electromagnetic fields. Exact solutions are obtained for the fractional differential equations by employing the Laplace transform method. The temporal fractional differential equations are considered in the Caputo-Fabrizio-Caputo and Atangana-Baleanu-Caputo sense. Application examples consider constant, ramp and harmonic fields. In addition, we present numerical results for different values of the fractional order. In all cases, when α = 1, we recover the standard electrodynamics.

Optimal positions and parameters of translational and rotational mass dampers in beams subjected to random excitation

NASA Astrophysics Data System (ADS)

Łatas, Waldemar

2018-01-01

The problem of vibrations of the beam with the attached system of translational and rotational dynamic mass dampers subjected to random excitations with peaked power spectral densities, is presented in the hereby paper. The Euler-Bernoulli beam model is applied, while for solving the equation of motion the Galerkin method and the Laplace time transform are used. The obtained transfer functions allow to determine power spectral densities of the beam deflection and other dependent variables. Numerical examples present simple optimization problems of mass dampers parameters for local and global objective functions.

Laplace-transform-based method to calculate back-reflected radiance from an isotropically scattering half-space

NASA Astrophysics Data System (ADS)

Rinzema, K.; Hoenders, B. J.; Ferwerda, H. A.

1997-07-01

We present a method to determine the back-reflected radiance from an isotropically scattering half-space with matched boundary. This method has the advantage that it leads very quickly to the relevant equations, the numerical solution of which is also quite easy. Essentially, the method is derived from a mathematical criterion that effectively forbids the existence of solutions to the transport equation which grow exponentially as one moves away from the surface and deeper into the medium. Preliminary calculations for infinitely wide beams yield results which agree very well with what is found in the literature.

Application of queueing models to multiprogrammed computer systems operating in a time-critical environment

NASA Technical Reports Server (NTRS)

Eckhardt, D. E., Jr.

1979-01-01

A model of a central processor (CPU) which services background applications in the presence of time critical activity is presented. The CPU is viewed as an M/M/1 queueing system subject to periodic interrupts by deterministic, time critical process. The Laplace transform of the distribution of service times for the background applications is developed. The use of state of the art queueing models for studying the background processing capability of time critical computer systems is discussed and the results of a model validation study which support this application of queueing models are presented.

On the Analytical and Numerical Properties of the Truncated Laplace Transform II

DTIC Science & Technology

2015-05-29

La,b)∗ ◦ La,b) (un)) (t) = ∫ b a 1 t+ s un(s)ds = α 2 nun (t). (32) Similarly, the left singular functions vn of La,b are eigenfunctions of the...odd in the sense that Un(s) = (−1) nUn (−s). (83) 3.5 Decay of the coefficients Since the left singular function vn (defined in (27)) is a smooth...is associated with the right singular function un via (41) and (42) and it is studied in [12]. Lemma 3.13. Suppose that un be the n+ 1-th right

Thermomechanical Fractional Model of TEMHD Rotational Flow

PubMed Central

Hamza, F.; Abd El-Latief, A.; Khatan, W.

2017-01-01

In this work, the fractional mathematical model of an unsteady rotational flow of Xanthan gum (XG) between two cylinders in the presence of a transverse magnetic field has been studied. This model consists of two fractional parameters α and β representing thermomechanical effects. The Laplace transform is used to obtain the numerical solutions. The fractional parameter influence has been discussed graphically for the functions field distribution (temperature, velocity, stress and electric current distributions). The relationship between the rotation of both cylinders and the fractional parameters has been discussed on the functions field distribution for small and large values of time. PMID:28045941

Linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2011-06-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and the variation of constants method. The approach presented here can be used in a first course on differential equations for science and engineering majors.

Wave computation on the Poincaré dodecahedral space

NASA Astrophysics Data System (ADS)

Bachelot-Motet, Agnès

2013-12-01

We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non-trivial topology: the Poincaré dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We adopt a variational approach using a space of finite elements that is invariant under the action of the binary icosahedral group. The computation of the transient waves is validated with their spectral analysis by computing a lot of eigenvalues of the Laplace-Beltrami operator.

DLSanalysis.org: a web interface for analysis of dynamic light scattering data.

PubMed

Hansen, Steen

2018-03-01

A web interface ( www.DLSanalysis.org ) for indirect Laplace transformation of dynamic light scattering data is presented. When experimental data are uploaded to the server they are processed in a few seconds, and the result is displayed on the screen in the form of a size distribution together with the experimental data and the fit to the data. No other user input than the experimental data is necessary, but various options for the analysis may be selected. No local installation of software or registration is necessary. The result of the analysis can be downloaded.

The effects of magnetohydrodynamic and radiation on flow of second grade fluid past an infinite inclined plate in porous medium

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

Ismail, Zulkhibri; Khan, Ilyas; Nasir, Nadirah Mohd

2015-02-03

An analysis of the exact solutions of second grade fluid problem for unsteady magnetohydrodynamic (MHD) flows past an infinite inclined plate in a porous medium is presented. It is assumed that the bounding infinite inclined plate has a constant temperature with radiation effects. Based on Boussinesq approximation the expressions for dimensionless velocity, temperature and concentration are obtained by using Laplace transform method. The derived solutions satisfying the involved differential equations, and all the boundary and initial conditions. The influence of various parameters on the velocity has been illustrated graphically and analyzed.

The Masked Sample Covariance Estimator: An Analysis via the Matrix Laplace Transform

DTIC Science & Technology

2012-02-01

Variables: Suppose that we divide the stock market into disjoint sectors, and we would like to study the interactions among the monthly returns for...vector to conform with the market sectors, and we estimate only the entries in the diagonal blocks. Spatial or Temporal Localization: A simple random model...eαW1A c ] ≤ 4p e−B/2κ 2 = 1 n . Introduce this expression into (4.11) to conclude that E[exp(2θεM xx∗)1A c ] 4 1 n · I. (4.17) 20 RICHARD Y. CHEN

Fourth order difference methods for hyperbolic IBVP's

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Products of random matrices from fixed trace and induced Ginibre ensembles

NASA Astrophysics Data System (ADS)

Akemann, Gernot; Cikovic, Milan

2018-05-01

We investigate the microcanonical version of the complex induced Ginibre ensemble, by introducing a fixed trace constraint for its second moment. Like for the canonical Ginibre ensemble, its complex eigenvalues can be interpreted as a two-dimensional Coulomb gas, which are now subject to a constraint and a modified, collective confining potential. Despite the lack of determinantal structure in this fixed trace ensemble, we compute all its density correlation functions at finite matrix size and compare to a fixed trace ensemble of normal matrices, representing a different Coulomb gas. Our main tool of investigation is the Laplace transform, that maps back the fixed trace to the induced Ginibre ensemble. Products of random matrices have been used to study the Lyapunov and stability exponents for chaotic dynamical systems, where the latter are based on the complex eigenvalues of the product matrix. Because little is known about the universality of the eigenvalue distribution of such product matrices, we then study the product of m induced Ginibre matrices with a fixed trace constraint—which are clearly non-Gaussian—and M  ‑  m such Ginibre matrices without constraint. Using an m-fold inverse Laplace transform, we obtain a concise result for the spectral density of such a mixed product matrix at finite matrix size, for arbitrary fixed m and M. Very recently local and global universality was proven by the authors and their coworker for a more general, single elliptic fixed trace ensemble in the bulk of the spectrum. Here, we argue that the spectral density of mixed products is in the same universality class as the product of M independent induced Ginibre ensembles.

The heterogeneity of segmental dynamics of filled EPDM by (1)H transverse relaxation NMR.

PubMed

Moldovan, D; Fechete, R; Demco, D E; Culea, E; Blümich, B; Herrmann, V; Heinz, M

2011-01-01

Residual second moment of dipolar interactions M(2) and correlation time segmental dynamics distributions were measured by Hahn-echo decays in combination with inverse Laplace transform for a series of unfilled and filled EPDM samples as functions of carbon-black N683 filler content. The fillers-polymer chain interactions which dramatically restrict the mobility of bound rubber modify the dynamics of mobile chains. These changes depend on the filler content and can be evaluated from distributions of M(2). A dipolar filter was applied to eliminate the contribution of bound rubber. In the first approach the Hahn-echo decays were fitted with a theoretical relationship to obtain the average values of the (1)H residual second moment and correlation time <τ(c)>. For the mobile EPDM segments the power-law distribution of correlation function was compared to the exponential correlation function and found inadequate in the long-time regime. In the second approach a log-Gauss distribution for the correlation time was assumed. Furthermore, using an averaged value of the correlation time, the distributions of the residual second moment were determined using an inverse Laplace transform for the entire series of measured samples. The unfilled EPDM sample shows a bimodal distribution of residual second moments, which can be associated to the mobile polymer sub-chains (M(2) ≅ 6.1 rad (2) s(-2)) and the second one associated to the dangling chains M(2) ≅ 5.4 rad(2) s(-2)). By restraining the mobility of bound rubber, the carbon-black fillers induce diversity in the segmental dynamics like the apparition of a distinct mobile component and changes in the distribution of mobile and free-end polymer segments. Copyright © 2010 Elsevier Inc. All rights reserved.

The heterogeneity of segmental dynamics of filled EPDM by 1H transverse relaxation NMR

NASA Astrophysics Data System (ADS)

Moldovan, D.; Fechete, R.; Demco, D. E.; Culea, E.; Blümich, B.; Herrmann, V.; Heinz, M.

2011-01-01

Residual second moment of dipolar interactions M∼2 and correlation time segmental dynamics distributions were measured by Hahn-echo decays in combination with inverse Laplace transform for a series of unfilled and filled EPDM samples as functions of carbon-black N683 filler content. The fillers-polymer chain interactions which dramatically restrict the mobility of bound rubber modify the dynamics of mobile chains. These changes depend on the filler content and can be evaluated from distributions of M∼2. A dipolar filter was applied to eliminate the contribution of bound rubber. In the first approach the Hahn-echo decays were fitted with a theoretical relationship to obtain the average values of the 1H residual second moment and correlation time <τc>. For the mobile EPDM segments the power-law distribution of correlation function was compared to the exponential correlation function and found inadequate in the long-time regime. In the second approach a log-Gauss distribution for the correlation time was assumed. Furthermore, using an averaged value of the correlation time, the distributions of the residual second moment were determined using an inverse Laplace transform for the entire series of measured samples. The unfilled EPDM sample shows a bimodal distribution of residual second moments, which can be associated to the mobile polymer sub-chains (M∼2≅6.1 rad s) and the second one associated to the dangling chains M∼2≅5.4 rad s). By restraining the mobility of bound rubber, the carbon-black fillers induce diversity in the segmental dynamics like the apparition of a distinct mobile component and changes in the distribution of mobile and free-end polymer segments.

Integrated aquitard-aquifer flow with a mixed-type well-face boundary and skin effect

NASA Astrophysics Data System (ADS)

Feng, Qinggao; Zhan, Hongbin

2016-03-01

A general analytical model describing groundwater flow to a partially penetrating well pumped at a constant rate in a leaky confined aquifer is developed. The model incorporates the effects of aquitard storage, aquifer anisotropy, wellbore storage and a finite well skin by treating the aquitard leakage as an aquitard-aquifer interface flow problem, and considers the well-face as a mixed-type or non-uniform flux (NUF) rather than a uniform flux (UF) boundary condition, which is novel. The solution is obtained using the Laplace transform coupled with separation of variables and discretization methods, followed by the numerical inverse Laplace transform. Moreover, the solution unifies some cases for flow to a partially penetrating well in a leaky confined aquifer including Perina and Lee (2006), Feng and Zhan (2015) and Hunt (2005) or confined aquifer including Chiu et al. (2007), Yang et al. (2006) and Hantush (1964). The newly developed NUF solution is compared with the UF solution. The NUF drawdown is larger than the UF drawdown at early time, while the NUF drawdown is smaller than the UF drawdown at intermediate and late times. The non-uniform flux along the well-face has significant impact on drawdown in the skin zone, while the UF solution can completely replace the NUF solution at a radial distance from the pumped well equaling to or greater than the aquifer thickness. The NUF and UF drawdowns for no skin case are remarkably smaller than that for the positive skin case and larger than that for the negative skin case. A thicker well skin results in a smaller drawdown in the skin zone.

Base flow recession from unsaturated-saturated porous media considering lateral unsaturated discharge and aquifer compressibility

NASA Astrophysics Data System (ADS)

Liang, Xiuyu; Zhan, Hongbin; Zhang, You-Kuan; Schilling, Keith

2017-09-01

Unsaturated flow is an important process in base flow recessions and its effect is rarely investigated. A mathematical model for a coupled unsaturated-saturated flow in a horizontally unconfined aquifer with time-dependent infiltrations is presented. The effects of the lateral discharge of the unsaturated zone and aquifer compressibility are specifically taken into consideration. Semianalytical solutions for hydraulic heads and discharges are derived using Laplace transform and Cosine transform. The solutions are compared with solutions of the linearized Boussinesq equation (LB solution) and the linearized Laplace equation (LL solution), respectively. A larger dimensionless constitutive exponent κD (a smaller retention capacity) of the unsaturated zone leads to a smaller discharge during the infiltration period and a larger discharge after the infiltration. The lateral discharge of the unsaturated zone is significant when κD≤1, and becomes negligible when κD≥100. The compressibility of the aquifer has a nonnegligible impact on the discharge at early times. For late times, the power index b of the recession curve -dQ/dt˜ aQb, is 1 and independent of κD, where Q is the base flow and a is a constant lumped aquifer parameter. For early times, b is approximately equal to 3 but it approaches infinity when t→0. The present solution is applied to synthetic and field cases. The present solution matched the synthetic data better than both the LL and LB solutions, with a minimum relative error of 16% for estimate of hydraulic conductivity. The present solution was applied to the observed streamflow discharge in Iowa, and the estimated values of the aquifer parameters were reasonable.

Force on a storage ring vacuum chamber after sudden turn-off of a magnet power supply

NASA Astrophysics Data System (ADS)

Sinha, Gautam; Prabhu, S. S.

2011-10-01

We are commissioning a 2.5 GeV synchrotron radiation source (SRS) where electrons travel in high vacuum inside the vacuum chambers made of aluminum alloys. These chambers are kept between the pole gaps of magnets and are made to facilitate the radiation coming out of the storage ring to the experimental station. These chambers are connected by metallic bellows. During the commissioning phase of the SRS, the metallic bellows became ruptured due to the frequent tripping of the dipole magnet power supply. The machine was down for quite some time. In the case of a power supply trip, the current in the magnets decays exponentially. It was observed experimentally that the fast B field decay generates a large eddy current in the chambers and consequently the chambers are subjected to a huge Lorentz force. This motivated us to develop a theoretical model to study the force acting on a metallic plate when exposed to an exponentially decaying field and then to extend it for a rectangular vacuum chamber. The problem is formulated using Maxwell’s equations and converted to the inhomogeneous Helmholtz equation. After taking the Laplace transform, the equation is solved with appropriate boundary conditions. Final results are obtained after taking the appropriate inverse Laplace transform. The expressions for eddy current contour and magnetic field produced by the eddy current are also derived. Variations of the force on chambers of different wall thickness due to spatially varying and exponentially time decaying field are presented. The result is a general theory which can be applied to different geometries and calculation of power loss as well. Comparisons are made with results obtained by simulation using a finite element based code, for quick verification of the theoretical model.

Effect of wellbore storage and finite thickness skin on flow to a partially penetrating well in a phreatic aquifer

NASA Astrophysics Data System (ADS)

Pasandi, M.; Samani, N.; Barry, D. A.

2008-02-01

An analytical model is presented for the analysis of constant flux tests conducted in a phreatic aquifer having a partially penetrating well with a finite thickness skin. The solution is derived in the Laplace transform domain for the drawdown in the pumping well, skin and formation regions. The time-domain solution in terms of the aquifer drawdown is then obtained from the numerical inversion of the Laplace transform and presented as dimensionless drawdown-time curves. The derived solution is used to investigate the effects of the hydraulic conductivity contrast between the skin and formation, in addition to wellbore storage, skin thickness, delayed yield, partial penetration and distance to the observation well. The results of the developed solution were compared with those from an existing solution for the case of an infinitesimally thin skin. The latter solution can never approximate that for the developed finite skin. Dimensionless drawdown-time curves were compared with the other published results for a confined aquifer. Positive skin effects are reflected in the early time and disappear in the intermediate and late time aquifer responses. But in the case of negative skin this is reversed and the negative skin also tends to disguise the wellbore storage effect. A thick negative skin lowers the overall drawdown in the aquifer and leads to more persistent delayed drainage. Partial penetration increases the drawdown in the case of a positive skin; however its effect is masked by the negative skin. The influence of a negative skin is pronounced over a broad range of radial distances. At distant observation points the influence of a positive skin is too small to be reflected in early and intermediate time pumping test data and consequently the type curve takes its asymptotic form.

A nonequilibrium model for reactive contaminant transport through fractured porous media: Model development and semianalytical solution

NASA Astrophysics Data System (ADS)

Joshi, Nitin; Ojha, C. S. P.; Sharma, P. K.

2012-10-01

In this study a conceptual model that accounts for the effects of nonequilibrium contaminant transport in a fractured porous media is developed. Present model accounts for both physical and sorption nonequilibrium. Analytical solution was developed using the Laplace transform technique, which was then numerically inverted to obtain solute concentration in the fracture matrix system. The semianalytical solution developed here can incorporate both semi-infinite and finite fracture matrix extent. In addition, the model can account for flexible boundary conditions and nonzero initial condition in the fracture matrix system. The present semianalytical solution was validated against the existing analytical solutions for the fracture matrix system. In order to differentiate between various sorption/transport mechanism different cases of sorption and mass transfer were analyzed by comparing the breakthrough curves and temporal moments. It was found that significant differences in the signature of sorption and mass transfer exists. Applicability of the developed model was evaluated by simulating the published experimental data of Calcium and Strontium transport in a single fracture. The present model simulated the experimental data reasonably well in comparison to the model based on equilibrium sorption assumption in fracture matrix system, and multi rate mass transfer model.

The development of a peak-time criterion for designing controlled-release devices.

PubMed

Simon, Laurent; Ospina, Juan

2016-08-25

This work consists of estimating dynamic characteristics for topically-applied drugs when the magnitude of the flux increases to a maximum value, called peak flux, before declining to zero. This situation is typical of controlled-released systems with a finite donor or vehicle volume. Laplace transforms were applied to the governing equations and resulted in an expression for the flux in terms of the physical characteristics of the system. After approximating this function by a second-order model, three parameters of this reduced structure captured the essential features of the original process. Closed-form relationships were then developed for the peak flux and time-to-peak based on the empirical representation. Three case studies that involve mechanisms, such as diffusion, partitioning, dissolution and elimination, were selected to illustrate the procedure. The technique performed successfully as shown by the ability of the second-order flux to match the prediction of the original transport equations. A main advantage of the proposed method is that it does not require a solution of the original partial differential equations. Less accurate results were noted for longer lag times. Copyright © 2016 Elsevier B.V. All rights reserved.

Analysis of classical Fourier, SPL and DPL heat transfer model in biological tissues in presence of metabolic and external heat source

NASA Astrophysics Data System (ADS)

Kumar, Dinesh; Singh, Surjan; Rai, K. N.

2016-06-01

In this paper, the temperature distribution in a finite biological tissue in presence of metabolic and external heat source when the surface subjected to different type of boundary conditions is studied. Classical Fourier, single-phase-lag (SPL) and dual-phase-lag (DPL) models were developed for bio-heat transfer in biological tissues. The analytical solution obtained for all the three models using Laplace transform technique and results are compared. The effect of the variability of different parameters such as relaxation time, metabolic heat source, spatial heat source, different type boundary conditions on temperature distribution in different type of the tissues like muscle, tumor, fat, dermis and subcutaneous based on three models are analyzed and discussed in detail. The result obtained in three models is compared with experimental observation of Stolwijk and Hardy (Pflug Arch 291:129-162, 1966). It has been observe that the DPL bio-heat transfer model provides better result in comparison of other two models. The value of metabolic and spatial heat source in boundary condition of first, second and third kind for different type of thermal therapies are evaluated.

Using low-field NMR to infer the physical properties of glassy oligosaccharide/water mixtures.

PubMed

Aeberhardt, Kasia; Bui, Quang D; Normand, Valéry

2007-03-01

Low-field NMR (LF-NMR) is usually used as an analytical technique, for instance, to determine water and oil contents. For this application, no attempt is made to understand the physical origin of the data. Here we build a physical model to explain the five fit parameters of the conventional free induction decay (FID) for glassy oligosaccharide/water mixtures. The amplitudes of the signals from low-mobility and high-mobility protons correspond to the density of oligosaccharide protons and water protons, respectively. The relaxation time of the high-mobility protons is described using a statistical model for the probability that oligosaccharide hydroxyl groups form multiple hydrogen bonds. The variation of energy of the hydrogen bond is calculated from the average bond distance and the average angle contribution. Applying the model to experimental data shows that hydrogen atoms screen the water oxygen atoms when two water molecules solvate a single hydroxyl group. Furthermore, the relaxation time of the oligosaccharide protons is independent of its molecular weight and the water content. Finally, inversion of the FID using the inverse Laplace transform gives the continuous spectrum of relaxation times, which is a fingerprint of the oligosaccharide.

Heat transfer enhancement in free convection flow of CNTs Maxwell nanofluids with four different types of molecular liquids.

PubMed

Aman, Sidra; Khan, Ilyas; Ismail, Zulkhibri; Salleh, Mohd Zuki; Al-Mdallal, Qasem M

2017-05-26

This article investigates heat transfer enhancement in free convection flow of Maxwell nanofluids with carbon nanotubes (CNTs) over a vertically static plate with constant wall temperature. Two kinds of CNTs i.e. single walls carbon nanotubes (SWCNTs) and multiple walls carbon nanotubes (MWCNTs) are suspended in four different types of base liquids (Kerosene oil, Engine oil, water and ethylene glycol). Kerosene oil-based nanofluids are given a special consideration due to their higher thermal conductivities, unique properties and applications. The problem is modelled in terms of PDE's with initial and boundary conditions. Some relevant non-dimensional variables are inserted in order to transmute the governing problem into dimensionless form. The resulting problem is solved via Laplace transform technique and exact solutions for velocity, shear stress and temperature are acquired. These solutions are significantly controlled by the variations of parameters including the relaxation time, Prandtl number, Grashof number and nanoparticles volume fraction. Velocity and temperature increases with elevation in Grashof number while Shear stress minimizes with increasing Maxwell parameter. A comparison between SWCNTs and MWCNTs in each case is made. Moreover, a graph showing the comparison amongst four different types of nanofluids for both CNTs is also plotted.

Analytical model of contamination during the drying of cylinders of jamonable muscle

NASA Astrophysics Data System (ADS)

Montoya Arroyave, Isabel

2014-05-01

For a cylinder of jamonable muscle of radius R and length much greater than R; considering that the internal resistance to the transfer of water is much greater than the external and that the internal resistance is one certain function of the distance to the axis; the distribution of the punctual moisture in the jamonable cylinder is analytically computed in terms of the Bessel's functions. During the process of drying and salted the jamonable cylinder is sensitive to contaminate with bacterium and protozoa that come from the environment. An analytical model of contamination is presents using the diffusion equation with sources and sinks, which is solve by the method of the Laplace transform, the Bromwich integral, the residue theorem and some special functions like Bessel and Heun. The critical times intervals of drying and salted are computed in order to obtain the minimum possible contamination. It is assumed that both external moisture and contaminants decrease exponentially with time. Contaminants profiles are plotted and discussed some possible techniques of contaminants detection. All computations are executed using Computer Algebra, specifically Maple. It is said that the results are important for the food industry and it is suggested some future research lines.

The motions and wave fields produced by an ellipse moving through a stratified fluid

NASA Astrophysics Data System (ADS)

Hurlen, Erik Curtis

Solid-fluid interactions are ubiquitous in nature, from leaves falling from trees to fish swimming in the ocean. This dissertation examines a certain class of these interactions, namely asymmetric objects moving through stratified fluids. In the first part, the equations of motion are derived and subsequently solved for a displaced neutrally buoyant ellipse of varying aspect ratio. This is accomplished by using a spectral numerical algorithm, although in certain specific cases the equations can also be solved analytically using Laplace transform techniques. Experiments are conducted to which these analytical and numerical results are compared. General quantitative agreement is observed between the two sets of data. The discrepancies which are observed are consistent with both previous research and expectation. In the second part, the focus is shifted from the solid to the fluid, as the primary concern is now the wave field produced by these moving bodies. The spectral method developed in the first part is easily adapted to this second situation, in which the drag forces on the solid are also easily extracted. The results from this section are compared to previous results, and match very well. The results are then expanded to cases which have not been previously studied.

Influence of non-integer-order derivatives on unsteady unidirectional motions of an Oldroyd-B fluid with generalized boundary conditions

NASA Astrophysics Data System (ADS)

Zafar, A. A.; Riaz, M. B.; Shah, N. A.; Imran, M. A.

2018-03-01

The objective of this article is to study some unsteady Couette flows of an Oldroyd-B fluid with non-integer derivatives. The fluid fills an annular region of two infinite co-axial circular cylinders. Flows are due to the motion of the outer cylinder, that rotates about its axis with an arbitrary time-dependent velocity while the inner cylinder is held fixed. Closed form solutions of dimensionless velocity field and tangential tension are obtained by means of the finite Hankel transform and the theory of Laplace transform for fractional calculus. Several results in the literature including the rotational flows through an infinite cylinder can be obtained as limiting cases of our general solutions. Finally, the control of the fractional framework on the dynamics of fluid is analyzed by numerical simulations and graphical illustrations.

Stochastic evaluation of second-order many-body perturbation energies.

PubMed

Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So

2012-11-28

With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mE(h) of the correct values after 10(8) Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories.

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

Radial flow to a partially penetrating well with storage in an anisotropic confined aquifer

NASA Astrophysics Data System (ADS)

Mishra, Phoolendra Kumar; Vesselinov, Velimir V.; Neuman, Shlomo P.

2012-07-01

SummaryDrawdowns generated by extracting water from large diameter (e.g. water supply) well are affected by wellbore storage. We present an analytical solution in Laplace transformed space for drawdown in a uniform anisotropic aquifer caused by withdrawing water at a constant rate from partially penetrating well with storage. The solution is back transformed into the time domain numerically. When the pumping well is fully penetrating our solution reduces to that of Papadopulos and Cooper (1967); Hantush (1964) when the pumping well has no wellbore storage; Theis (1935) when both conditions are fulfilled and Yang (2006) when the pumping well is partially penetrating, has finite radius but lacks storage. Newly developed solution is then used to explore graphically the effects of partial penetration, wellbore storage and anisotropy on time evolutions of drawdown in the pumping well and in observation wells. We concluded after validating the developed analytical solution using synthetic pumping test.

A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel

NASA Astrophysics Data System (ADS)

Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru

2018-02-01

The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.

Laplace-SGBEM analysis of the dynamic stress intensity factors and the dynamic T-stress for the interaction between a crack and auxetic inclusions

NASA Astrophysics Data System (ADS)

Kwon, Kibum

A dynamic analysis of the interaction between a crack and an auxetic (negative Poisson ratio)/non-auxetic inclusion is presented. The two most important fracture parameters, namely the stress intensity factors and the T-stress are analyzed by using the symmetric Galerkin boundary element method in the Laplace domain for three different models of crack-inclusion interaction. To investigate the effects of auxetic inclusions on the fracture behavior of composites reinforced by this new type of material, comparisons of the dynamic stress intensity factors and the dynamic T-stress are made between the use of auxetic inclusions as opposed to the use of traditional inclusions. Furthermore, the technique presented in this research can be employed to analyze for the interaction between a crack and a cluster of auxetic/non-auxetic inclusions. Results from the latter models can be employed in crack growth analysis in auxetic-fiber-reinforced composites.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

The pulsating orb: solving the wave equation outside a ball

PubMed Central

2016-01-01

Transient acoustic waves are generated by the oscillations of an object or are scattered by the object. This leads to initial-boundary value problems (IBVPs) for the wave equation. Basic properties of this equation are reviewed, with emphasis on characteristics, wavefronts and compatibility conditions. IBVPs are formulated and their properties reviewed, with emphasis on weak solutions and the constraints imposed by the underlying continuum mechanics. The use of the Laplace transform to treat the IBVPs is also reviewed, with emphasis on situations where the solution is discontinuous across wavefronts. All these notions are made explicit by solving simple IBVPs for a sphere in some detail. PMID:27279773

On the Singular Perturbations for Fractional Differential Equation

PubMed Central

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. PMID:24683357

Competing bosonic condensates in optical lattice with a mixture of single and pair hoppings

NASA Astrophysics Data System (ADS)

Travin, V. M.; Kopeć, T. K.

2017-01-01

A system of ultra-cold atoms with single boson and pair tunneling of bosonic atoms is considered in an optical lattice at arbitrary temperature. A mean-field theory was applied to the extended Bose-Hubbard Hamiltonian describing the system in order to investigate the competition between superfluid and pair superfluid as a function of the chemical potential and the temperature. To this end we have applied a method based on the Laplace transform method for the efficient calculation of the statistical sum for the quantum Hamiltonian. These results may be of interest for experiments on cold atom systems in optical lattices.

State-to-state models of vibrational relaxation in Direct Simulation Monte Carlo (DSMC)

NASA Astrophysics Data System (ADS)

Oblapenko, G. P.; Kashkovsky, A. V.; Bondar, Ye A.

2017-02-01

In the present work, the application of state-to-state models of vibrational energy exchanges to the Direct Simulation Monte Carlo (DSMC) is considered. A state-to-state model for VT transitions of vibrational energy in nitrogen and oxygen, based on the application of the inverse Laplace transform to results of quasiclassical trajectory calculations (QCT) of vibrational energy transitions, along with the Forced Harmonic Oscillator (FHO) state-to-state model is implemented in DSMC code and applied to flows around blunt bodies. Comparisons are made with the widely used Larsen-Borgnakke model and the in uence of multi-quantum VT transitions is assessed.

Heat transfer characteristics of an emergent strand

NASA Technical Reports Server (NTRS)

Simon, W. E.; Witte, L. C.; Hedgcoxe, P. G.

1974-01-01

A mathematical model was developed to describe the heat transfer characteristics of a hot strand emerging into a surrounding coolant. A stable strand of constant efflux velocity is analyzed, with a constant (average) heat transfer coefficient on the sides and leading surface of the strand. After developing a suitable governing equation to provide an adequate description of the physical system, the dimensionless governing equation is solved with Laplace transform methods. The solution yields the temperature within the strand as a function of axial distance and time. Generalized results for a wide range of parameters are presented, and the relationship of the results and experimental observations is discussed.

Some effects of nonlinear variation in the directional-stability and damping-in-yawing derivatives on the lateral stability of an airplane

NASA Technical Reports Server (NTRS)

Sternfield, Leonard

1951-01-01

A theoretical investigation has been made to determine the effect of nonlinear stability derivatives on the lateral stability of an airplane. Motions were calculated on the assumption that the directional-stability and the damping-in-yawing derivatives are functions of the angle of sideslip. The application of the Laplace transform to the calculation of an airplane motion when certain types of nonlinear derivatives are present is described in detail. The types of nonlinearities assumed correspond to the condition in which the values of the directional-stability and damping-in-yawing derivatives are zero for small angle of sideslip.

On the Analytical and Numerical Properties of the Truncated Laplace Transform

DTIC Science & Technology

2014-05-01

classical study of the truncated Fourier trans- form. The resulting algorithms are applicable to all environments likely to be encountered in applications...other words, (((La,b)∗ ◦ La,b) (un)) (t) = ∫ b a 1 t+ s un(s)ds = α 2 nun (t). (2.69) Observation 2.22. Similarly, La,b ◦ (La,b)∗ of a function g ∈ L2(0...3.20)) are even and odd functions in the regular sense: Un(s) = (Cγ(un)) (s) = (−1) nUn (−s). (3.25) In particular, at the point s = 0, we have: U2j+1(0

Asymptotic expansions of solutions of the heat conduction equation in internally bounded cylindrical geometry

USGS Publications Warehouse

Ritchie, R.H.; Sakakura, A.Y.

1956-01-01

The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.

A renewal jump-diffusion process with threshold dividend strategy

NASA Astrophysics Data System (ADS)

Li, Bo; Wu, Rong; Song, Min

2009-06-01

In this paper, we consider a jump-diffusion risk process with the threshold dividend strategy. Both the distributions of the inter-arrival times and the claims are assumed to be in the class of phase-type distributions. The expected discounted dividend function and the Laplace transform of the ruin time are discussed. Motivated by Asmussen [S. Asmussen, Stationary distributions for fluid flow models with or without Brownian noise, Stochastic Models 11 (1) (1995) 21-49], instead of studying the original process, we study the constructed fluid flow process and their closed-form formulas are obtained in terms of matrix expression. Finally, numerical results are provided to illustrate the computation.

Delta function excitation of waves in the earth's ionosphere

NASA Technical Reports Server (NTRS)

Vidmar, R. J.; Crawford, F. W.; Harker, K. J.

1983-01-01

Excitation of the earth's ionosphere by delta function current sheets is considered, and the temporal and spatial evolution of wave packets is analyzed for a two-component collisional F2 layer. Approximations of an inverse Fourier-Laplace transform via saddle point methods provide plots of typical wave packets. These illustrate cold plasma wave theory and may be used as a diagnostic tool since it is possible to relate specific features, e.g., the frequency of a modulation envelope, to plasma parameters such as the electron cyclotron frequency. It is also possible to deduce the propagation path length and orientation of a remote radio beacon.

A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].

PubMed

Murase, Kenya

2015-01-01

In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.

Modeling transient heat transfer in nuclear waste repositories.

PubMed

Yang, Shaw-Yang; Yeh, Hund-Der

2009-09-30

The heat of high-level nuclear waste may be generated and released from a canister at final disposal sites. The waste heat may affect the engineering properties of waste canisters, buffers, and backfill material in the emplacement tunnel and the host rock. This study addresses the problem of the heat generated from the waste canister and analyzes the heat distribution between the buffer and the host rock, which is considered as a radial two-layer heat flux problem. A conceptual model is first constructed for the heat conduction in a nuclear waste repository and then mathematical equations are formulated for modeling heat flow distribution at repository sites. The Laplace transforms are employed to develop a solution for the temperature distributions in the buffer and the host rock in the Laplace domain, which is numerically inverted to the time-domain solution using the modified Crump method. The transient temperature distributions for both the single- and multi-borehole cases are simulated in the hypothetical geological repositories of nuclear waste. The results show that the temperature distributions in the thermal field are significantly affected by the decay heat of the waste canister, the thermal properties of the buffer and the host rock, the disposal spacing, and the thickness of the host rock at a nuclear waste repository.

Inverse transformation: unleashing spatially heterogeneous dynamics with an alternative approach to XPCS data analysis

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

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering-vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables XPCS to probe the dynamics in a broad array of materials, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fail. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. This paper proposes an alternative analysis schememore » based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. In conclusion, using XPCS data measured from colloidal gels, it is demonstrated that the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.« less

Inverse transformation: unleashing spatially heterogeneous dynamics with an alternative approach to XPCS data analysis

DOE PAGES

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan; ...

2018-02-01

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering-vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables XPCS to probe the dynamics in a broad array of materials, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fail. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. This paper proposes an alternative analysis schememore » based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. In conclusion, using XPCS data measured from colloidal gels, it is demonstrated that the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.« less

On computing Laplace's coefficients and their derivatives.

NASA Astrophysics Data System (ADS)

Gerasimov, I. A.; Vinnikov, E. L.

The algorithm of computing Laplace's coefficients and their derivatives is proposed with application of recurrent relations. The A.G.M.-method is used for the calculation of values L0(0), L0(1). The FORTRAN-program corresponding to the algorithm is given. The precision control was provided with numerical integrating by Simpsons method. The behavior of Laplace's coefficients and their third derivatives whith varying indices K, n for fixed values of the α-parameter is presented graphically.

Comments on numerical solution of boundary value problems of the Laplace equation and calculation of eigenvalues by the grid method

NASA Technical Reports Server (NTRS)

Lyusternik, L. A.

1980-01-01

The mathematics involved in numerically solving for the plane boundary value of the Laplace equation by the grid method is developed. The approximate solution of a boundary value problem for the domain of the Laplace equation by the grid method consists of finding u at the grid corner which satisfies the equation at the internal corners (u=Du) and certain boundary value conditions at the boundary corners.

Coarsening strategies for unstructured multigrid techniques with application to anisotropic problems

NASA Technical Reports Server (NTRS)

Morano, E.; Mavriplis, D. J.; Venkatakrishnan, V.

1995-01-01

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e., the aspect-ratio AR = delta y/delta x is much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotopic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.

Coarsening Strategies for Unstructured Multigrid Techniques with Application to Anisotropic Problems

NASA Technical Reports Server (NTRS)

Morano, E.; Mavriplis, D. J.; Venkatakrishnan, V.

1996-01-01

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e. the aspect-ratio AR = (delta)y/(delta)x much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotropic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.

Who let the demon out? Laplace and Boscovich on determinism.

PubMed

Kožnjak, Boris

2015-06-01

In this paper, I compare Pierre-Simon Laplace's celebrated formulation of the principle of determinism in his 1814 Essai philosophique sur les probabilités with the formulation of the same principle offered by Roger Joseph Boscovich in his Theoria philosophiae naturalis, published 56 years earlier. This comparison discloses a striking general similarity between the two formulations of determinism as well as certain important differences. Regarding their similarities, both Boscovich's and Laplace's conceptions of determinism involve two mutually interdependent components-ontological and epistemic-and they are both intimately linked with the principles of causality and continuity. Regarding their differences, however, Boscovich's formulation of the principle of determinism turns out not only to be temporally prior to Laplace's but also-being founded on fewer metaphysical principles and more rooted in and elaborated by physical assumptions-to be more precise, complete and comprehensive than Laplace's somewhat parenthetical statement of the doctrine. A detailed analysis of these similarities and differences, so far missing in the literature on the history and philosophy of the concept of determinism, is the main goal of the present paper. Copyright © 2015 Elsevier Ltd. All rights reserved.

On the origins and foundations of Laplacian determinism.

PubMed

van Strien, Marij

2014-03-01

In this paper I examine the foundations of Laplace's famous statement of determinism in 1814, and argue that rather than derived from his mechanics, this statement is based on general philosophical principles, namely the principle of sufficient reason and the law of continuity. It is usually supposed that Laplace's statement is based on the fact that each system in classical mechanics has an equation of motion which has a unique solution. But Laplace never proved this result, and in fact he could not have proven it, since it depends on a theorem about uniqueness of solutions to differential equations that was only developed later on. I show that the idea that is at the basis of Laplace's determinism was in fact widespread in enlightenment France, and is ultimately based on a re-interpretation of Leibnizian metaphysics, specifically the principle of sufficient reason and the law of continuity. Since the law of continuity also lies at the basis of the application of differential calculus in physics, one can say that Laplace's determinism and the idea that systems in physics can be described by differential equations with unique solutions have a common foundation.

Analytical model for advective-dispersive transport involving flexible boundary inputs, initial distributions and zero-order productions

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Li, Loretta Y.; Lai, Keng-Hsin; Liang, Ching-Ping

2017-11-01

A novel solution method is presented which leads to an analytical model for the advective-dispersive transport in a semi-infinite domain involving a wide spectrum of boundary inputs, initial distributions, and zero-order productions. The novel solution method applies the Laplace transform in combination with the generalized integral transform technique (GITT) to obtain the generalized analytical solution. Based on this generalized analytical expression, we derive a comprehensive set of special-case solutions for some time-dependent boundary distributions and zero-order productions, described by the Dirac delta, constant, Heaviside, exponentially-decaying, or periodically sinusoidal functions as well as some position-dependent initial conditions and zero-order productions specified by the Dirac delta, constant, Heaviside, or exponentially-decaying functions. The developed solutions are tested against an analytical solution from the literature. The excellent agreement between the analytical solutions confirms that the new model can serve as an effective tool for investigating transport behaviors under different scenarios. Several examples of applications, are given to explore transport behaviors which are rarely noted in the literature. The results show that the concentration waves resulting from the periodically sinusoidal input are sensitive to dispersion coefficient. The implication of this new finding is that a tracer test with a periodic input may provide additional information when for identifying the dispersion coefficients. Moreover, the solution strategy presented in this study can be extended to derive analytical models for handling more complicated problems of solute transport in multi-dimensional media subjected to sequential decay chain reactions, for which analytical solutions are not currently available.

Application of Advanced Concepts and Techniques in Electromagnetic Topology Based Simulations: CRIPTE and Related Codes

DTIC Science & Technology

2008-12-01

multiconductor transmission line theory. The per-unit capacitance, inductance , and characteristic impedance matrices generated from the companion LAPLACE...code based on the Method of Moments application, by meshing different sections of the multiconductor cable for capacitance and inductance matrices [21...conductors held together in four pairs and resided in the cable jacket. Each of eight conductors was also designed with the per unit length resistance

Stability of outer planetary orbits around binary stars - A comparison of Hill's and Laplace's stability criteria

NASA Technical Reports Server (NTRS)

Kubala, A.; Black, D.; Szebehely, V.

1993-01-01

A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and coworkers and the general, numerically integrated results of Laplace's method by Graziani and Black (1981) are compared for varying values of the mass parameter mu. For mu = 0 to 0.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For mu greater than 0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of mu.

Double negatively charged carbon vacancy at the h- and k-sites in 4H-SiC: Combined Laplace-DLTS and DFT study

NASA Astrophysics Data System (ADS)

Capan, Ivana; Brodar, Tomislav; Pastuović, Željko; Siegele, Rainer; Ohshima, Takeshi; Sato, Shin-ichiro; Makino, Takahiro; Snoj, Luka; Radulović, Vladimir; Coutinho, José; Torres, Vitor J. B.; Demmouche, Kamel

2018-04-01

We present results from combined Laplace-Deep Level Transient Spectroscopy (Laplace-DLTS) and density functional theory studies of the carbon vacancy (VC) in n-type 4H-SiC. Using Laplace-DLTS, we were able to distinguish two previously unresolved sub-lattice-inequivalent emissions, causing the broad Z1/2 peak at 290 K that is commonly observed by conventional DLTS in n-type 4H-SiC. This peak has two components with activation energies for electron emission of 0.58 eV and 0.65 eV. We compared these results with the acceptor levels of VC obtained by means of hybrid density functional supercell calculations. The calculations support the assignment of the Z1/2 signal to a superposition of emission peaks from double negatively charged VC defects. Taking into account the measured and calculated energy levels, the calculated relative stability of VC in hexagonal (h) and cubic (k) lattice sites, as well as the observed relative amplitude of the Laplace-DLTS peaks, we assign Z1 and Z2 to VC(h) and VC(k), respectively. We also present the preliminary results of DLTS and Laplace-DLTS measurements on deep level defects (ET1 and ET2) introduced by fast neutron irradiation and He ion implantation in 4H-SiC. The origin of ET1 and ET2 is still unclear.

Reconfigurable liquid metal circuits by Laplace pressure shaping

NASA Astrophysics Data System (ADS)

Cumby, Brad L.; Hayes, Gerard J.; Dickey, Michael D.; Justice, Ryan S.; Tabor, Christopher E.; Heikenfeld, Jason C.

2012-10-01

We report reconfigurable circuits formed by liquid metal shaping with <10 pounds per square inch (psi) Laplace and vacuum pressures. Laplace pressure drives liquid metals into microreplicated trenches, and upon release of vacuum, the liquid metal dewets into droplets that are compacted to 10-100× less area than when in the channel. Experimental validation includes measurements of actuation speeds exceeding 30 cm/s, simple erasable resistive networks, and switchable 4.5 GHz antennas. Such capability may be of value for next generation of simple electronic switches, tunable antennas, adaptive reflectors, and switchable metamaterials.

Transient well flow in vertically heterogeneous aquifers

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1999-11-01

A solution for the general problem of computing well flow in vertically heterogeneous aquifers is found by an integration of both analytical and numerical techniques. The radial component of flow is treated analytically; the drawdown is a continuous function of the distance to the well. The finite-difference technique is used for the vertical flow component only. The aquifer is discretized in the vertical dimension and the heterogeneous aquifer is considered to be a layered (stratified) formation with a finite number of homogeneous sublayers, where each sublayer may have different properties. The transient part of the differential equation is solved with Stehfest's algorithm, a numerical inversion technique of the Laplace transform. The well is of constant discharge and penetrates one or more of the sublayers. The effect of wellbore storage on early drawdown data is taken into account. In this way drawdowns are found for a finite number of sublayers as a continuous function of radial distance to the well and of time since the pumping started. The model is verified by comparing results with published analytical and numerical solutions for well flow in homogeneous and heterogeneous, confined and unconfined aquifers. Instantaneous and delayed drainage of water from above the water table are considered, combined with the effects of partially penetrating and finite-diameter wells. The model is applied to demonstrate that the transient effects of wellbore storage in unconfined aquifers are less pronounced than previous numerical experiments suggest. Other applications of the presented solution technique are given for partially penetrating wells in heterogeneous formations, including a demonstration of the effect of decreasing specific storage values with depth in an otherwise homogeneous aquifer. The presented solution can be a powerful tool for the analysis of drawdown from pumping tests, because hydraulic properties of layered heterogeneous aquifer systems with partially penetrating wells may be estimated without the need to construct transient numerical models. A computer program based on the hybrid analytical-numerical technique is available from the author.

Tidal Friction in the Earth-Moon System and Laplace Planes: Darwin Redux

NASA Technical Reports Server (NTRS)

Rubincam, David P.

2015-01-01

The dynamical evolution of the Earth-Moon system due to tidal friction is treated here. George H. Darwin used Laplace planes (also called proper planes) in his study of tidal evolution. The Laplace plane approach is adapted here to the formalisms of W.M. Kaula and P. Goldreich. Like Darwin, the approach assumes a three-body problem: Earth, Moon, and Sun, where the Moon and Sun are point-masses. The tidal potential is written in terms of the Laplace plane angles. The resulting secular equations of motion can be easily integrated numerically assuming the Moon is in a circular orbit about the Earth and the Earth is in a circular orbit about the Sun. For Earth-Moon distances greater than 10 Earth radii, the Earth's approximate tidal response can be characterized with a single parameter, which is a ratio: a Love number times the sine of a lag angle divided by another such product. For low parameter values it can be shown that Darwin's low-viscosity molten Earth, M. Ross's and G. Schubert's model of an Earth near melting, and Goldreich's equal tidal lag angles must all give similar histories. For higher parameter values, as perhaps has been the case at times with the ocean tides, the Earth's obliquity may have decreased slightly instead of increased once the Moon's orbit evolved further than 50 Earth radii from the Earth, with possible implications for climate. This is contrast to the other tidal friction models mentioned, which have the obliquity always increasing with time. As for the Moon, its orbit is presently tilted to its Laplace plane by 5.2deg. The equations do not allow the Moon to evolve out of its Laplace plane by tidal friction alone, so that if it was originally in its Laplace plane, the tilt arose with the addition of other mechanisms, such as resonance passages.

Nonadditivity of van der Waals forces on liquid surfaces

NASA Astrophysics Data System (ADS)

Venkataram, Prashanth S.; Whitton, Jeremy D.; Rodriguez, Alejandro W.

2016-09-01

We present an approach for modeling nanoscale wetting and dewetting of textured solid surfaces that exploits recently developed, sophisticated techniques for computing exact long-range dispersive van der Waals (vdW) or (more generally) Casimir forces in arbitrary geometries. We apply these techniques to solve the variational formulation of the Young-Laplace equation and predict the equilibrium shapes of liquid-vacuum interfaces near solid gratings. We show that commonly employed methods of computing vdW interactions based on additive Hamaker or Derjaguin approximations, which neglect important electromagnetic boundary effects, can result in large discrepancies in the shapes and behaviors of liquid surfaces compared to exact methods.

Activity computer program for calculating ion irradiation activation

NASA Astrophysics Data System (ADS)

Palmer, Ben; Connolly, Brian; Read, Mark

2017-07-01

A computer program, Activity, was developed to predict the activity and gamma lines of materials irradiated with an ion beam. It uses the TENDL (Koning and Rochman, 2012) [1] proton reaction cross section database, the Stopping and Range of Ions in Matter (SRIM) (Biersack et al., 2010) code, a Nuclear Data Services (NDS) radioactive decay database (Sonzogni, 2006) [2] and an ENDF gamma decay database (Herman and Chadwick, 2006) [3]. An extended version of Bateman's equation is used to calculate the activity at time t, and this equation is solved analytically, with the option to also solve by numeric inverse Laplace Transform as a failsafe. The program outputs the expected activity and gamma lines of the activated material.

A remark on fractional differential equation involving I-function

NASA Astrophysics Data System (ADS)

Mishra, Jyoti

2018-02-01

The present paper deals with the solution of the fractional differential equation using the Laplace transform operator and its corresponding properties in the fractional calculus; we derive an exact solution of a complex fractional differential equation involving a special function known as I-function. The analysis of the some fractional integral with two parameters is presented using the suggested Theorem 1. In addition, some very useful corollaries are established and their proofs presented in detail. Some obtained exact solutions are depicted to see the effect of each fractional order. Owing to the wider applicability of the I-function, we can conclude that, the obtained results in our work generalize numerous well-known results obtained by specializing the parameters.

Vacuum polarization in Coulomb field revisited

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

Zamastil, J., E-mail: zamastil@karlov.mff.cuni.cz; Šimsa, D.

2017-04-15

Simplified derivation of Wichmann–Kroll term is presented. The derivation uses two formulas for hypergeometric functions, but otherwise is elementary. It is found that Laplace transform of the vacuum charge density diverges at zero momentum transfer. This divergence has nothing to do with known ultraviolet divergence. The latter is related to the large momentum behavior of the pertinent integral, while the former to the small momentum behavior. When these divergences are removed, the energy shift caused by vacuum polarization for an ordinary hydrogen obtained here is in an exact agreement with the result obtained by Wichmann and Kroll. Also, for muonicmore » hydrogen the result obtained here reasonably agrees with that given in literature.« less

Three-dimensional solutions of the magnetohydrostatic equations for rigidly rotating magnetospheres in cylindrical coordinates

NASA Astrophysics Data System (ADS)

Wilson, F.; Neukirch, T.

2018-01-01

We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary magnetospheres and stellar coronae. We consider the case with centrifugal force only, and use a transformation method in which the governing equation for the "pseudo-potential" (from which the magnetic field can be calculated) becomes the Laplace partial differential equation. The new solutions extend the set of previously found solutions to those of a "fractional multipole" nature, and offer wider possibilities for modelling than before. We consider some special cases, and present example solutions.

Analysis on ultrashort-pulse laser ablation for nanoscale film of ceramics

NASA Astrophysics Data System (ADS)

Ho, C. Y.; Tsai, Y. H.; Chiou, Y. J.

2017-06-01

This paper uses the dual-phase-lag model to study the ablation characteristics of femtosecond laser processing for nanometer-sized ceramic films. In ultrafast process and ultrasmall size where the two lags occur, a dual-phase-lag can be applied to analyse the ablation characteristics of femtosecond laser processing for materials. In this work, the ablation rates of nanometer-sized lead zirconate titanate (PZT) ceramics are investigated using a dual-phase-lag and the model is solved by Laplace transform method. The results obtained from this work are validated by the available experimental data. The effects of material thermal properties on the ablation characteristics of femtosecond laser processing for ceramics are also discussed.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Magnetic field effect on blood flow of Casson fluid in axisymmetric cylindrical tube: A fractional model

NASA Astrophysics Data System (ADS)

Ali, Farhad; Sheikh, Nadeem Ahmad; Khan, Ilyas; Saqib, Muhammad

2017-02-01

The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.

An analytical solution for percutaneous drug absorption: application and removal of the vehicle.

PubMed

Simon, L; Loney, N W

2005-10-01

The methods of Laplace transform were used to solve a mathematical model developed for percutaneous drug absorption. This model includes application and removal of the vehicle from the skin. A system of two linear partial differential equations was solved for the application period. The concentration of the medicinal agent in the skin at the end of the application period was used as the initial condition to determine the distribution of the drug in the skin following instantaneous removal of the vehicle. The influences of the diffusion and partition coefficients, clearance factor and vehicle layer thickness on the amount of drug in the vehicle and the skin were discussed.

Generalization of Wilemski-Fixman-Weiss decoupling approximation to the case involving multiple sinks of different sizes, shapes, and reactivities.

PubMed

Uhm, Jesik; Lee, Jinuk; Eun, Changsun; Lee, Sangyoub

2006-08-07

We generalize the Wilemski-Fixman-Weiss decoupling approximation to calculate the transient rate of absorption of point particles into multiple sinks of different sizes, shapes, and reactivities. As an application we consider the case involving two spherical sinks. We obtain a Laplace-transform expression for the transient rate that is in excellent agreement with computer simulations. The long-time steady-state rate has a relatively simple expression, which clearly shows the dependence on the diffusion constant of the particles and on the sizes and reactivities of sinks, and its numerical result is in good agreement with the known exact result that is given in terms of recursion relations.

Exact analytical solution to a transient conjugate heat-transfer problem

NASA Technical Reports Server (NTRS)

Sucec, J.

1973-01-01

An exact analytical solution is found for laminar, constant-property, slug flow over a thin plate which is also convectively cooled from below. The solution is found by means of two successive Laplace transformations when a transient in the plate and the fluid is initiated by a step change in the fluid inlet temperature. The exact solution yields the transient fluid temperature, surface heat flux, and surface temperature distributions. The results of the exact transient solution for the surface heat flux are compared to the quasi-steady values, and a criterion for the validity of the quasi-steady results is found. Also the effect of the plate coupling parameter on the surface heat flux are investigated.

A DPL model of photo-thermal interaction in an infinite semiconductor material containing a spherical hole

NASA Astrophysics Data System (ADS)

Hobiny, Aatef D.; Abbas, Ibrahim A.

2018-01-01

The dual phase lag (DPL) heat transfer model is applied to study the photo-thermal interaction in an infinite semiconductor medium containing a spherical hole. The inner surface of the cavity was traction free and loaded thermally by pulse heat flux. By using the eigenvalue approach methodology and Laplace's transform, the physical variable solutions are obtained analytically. The numerical computations for the silicon-like semiconductor material are obtained. The comparison among the theories, i.e., dual phase lag (DPL), Lord and Shulman's (LS) and the classically coupled thermoelastic (CT) theory is presented graphically. The results further show that the analytical scheme can overcome mathematical problems by analyzing these problems.

Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids

NASA Astrophysics Data System (ADS)

Wang, Xiaoping; Qi, Haitao; Yu, Bo; Xiong, Zhen; Xu, Huanying

2017-09-01

This work investigates the unsteady electroosmotic slip flow of viscoelastic fluid through a parallel plate micro-channel under combined influence of electroosmotic and pressure gradient forcings with asymmetric zeta potentials at the walls. The generalized second grade fluid with fractional derivative was used for the constitutive equation. The Navier slip model with different slip coefficients at both walls was also considered. By employing the Debye-Hückel linearization and the Laplace and sin-cos-Fourier transforms, the analytical solutions for the velocity distribution are derived. And the finite difference method for this problem was also given. Finally, the influence of pertinent parameters on the generation of flow is presented graphically.

Transport of a decay chain in homogenous porous media: analytical solutions.

PubMed

Bauer, P; Attinger, S; Kinzelbach, W

2001-06-01

With the aid of integral transforms, analytical solutions for the transport of a decay chain in homogenous porous media are derived. Unidirectional steady-state flow and radial steady-state flow in single and multiple porosity media are considered. At least in Laplace domain, all solutions can be written in closed analytical formulae. Partly, the solutions can also be inverted analytically. If not, analytical calculation of the steady-state concentration distributions, evaluation of temporal moments and numerical inversion are still possible. Formulae for several simple boundary conditions are given and visualized in this paper. The derived novel solutions are widely applicable and are very useful for the validation of numerical transport codes.

On Time-II: Newton's Time.

ERIC Educational Resources Information Center

Raju, C. K.

1991-01-01

A study of time in Newtonian physics is presented. Newton's laws of motion, falsifiability and physical theories, laws of motion and law of gravitation, and Laplace's demon are discussed. Short bibliographic sketches of Laplace and Karl Popper are included. (KR)

4. Historic American Buildings Survey Drawing by LaPlace VIEW FROM ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

4. Historic American Buildings Survey Drawing by LaPlace VIEW FROM HILL TO REAR OF MISSION GROUNDS - 1839 - Mission San Carlos Borromeo, Rio Road & Lausen Drive, Carmel-by-the-Sea, Monterey County, CA

Advanced Russian Mission Laplace-P to Study the Planetary System of Jupiter: Scientific Goals, Objectives, Special Features and Mission Profile

NASA Astrophysics Data System (ADS)

Martynov, M. B.; Merkulov, P. V.; Lomakin, I. V.; Vyatlev, P. A.; Simonov, A. V.; Leun, E. V.; Barabanov, A. A.; Nasyrov, A. F.

2017-12-01

The advanced Russian project Laplace-P is aimed at developing and launching two scientific spacecraft (SC)— Laplace-P1 ( LP1 SC) and Laplace-P2 ( LP2 SC)—designed for remote and in-situ studies of the system of Jupiter and its moon Ganymede. The LP1 and LP2 spacecraft carry an orbiter and a lander onboard, respectively. One of the orbiter's objectives is to map the surface of Ganymede from the artificial satellite's orbit and to acquire the data for the landing site selection. The main objective of the lander is to carry out in-situ investigations of Ganymede's surface. The paper describes the scientific goals and objectives of the mission, its special features, and the LP1 and LP2 mission profiles during all of the phases—from the launch to the landing on the surface of Ganymede.

Burton-Miller-type singular boundary method for acoustic radiation and scattering

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Gu, Yan

2014-08-01

This paper proposes the singular boundary method (SBM) in conjunction with Burton and Miller's formulation for acoustic radiation and scattering. The SBM is a strong-form collocation boundary discretization technique using the singular fundamental solutions, which is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors (SIFs) to eliminate the singularities of the fundamental solutions. Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS). In the present method, we derive the SIFs of exterior Helmholtz equation by means of the SIFs of exterior Laplace equation owing to the same order of singularities between the Laplace and Helmholtz fundamental solutions. In conjunction with the Burton-Miller formulation, the SBM enhances the quality of the solution, particularly in the vicinity of the corresponding interior eigenfrequencies. Numerical illustrations demonstrate efficiency and accuracy of the present scheme on some benchmark examples under 2D and 3D unbounded domains in comparison with the analytical solutions, the boundary element solutions and Dirichlet-to-Neumann finite element solutions.

The discrete Laplace exponential family and estimation of Y-STR haplotype frequencies.

PubMed

Andersen, Mikkel Meyer; Eriksen, Poul Svante; Morling, Niels

2013-07-21

Estimating haplotype frequencies is important in e.g. forensic genetics, where the frequencies are needed to calculate the likelihood ratio for the evidential weight of a DNA profile found at a crime scene. Estimation is naturally based on a population model, motivating the investigation of the Fisher-Wright model of evolution for haploid lineage DNA markers. An exponential family (a class of probability distributions that is well understood in probability theory such that inference is easily made by using existing software) called the 'discrete Laplace distribution' is described. We illustrate how well the discrete Laplace distribution approximates a more complicated distribution that arises by investigating the well-known population genetic Fisher-Wright model of evolution by a single-step mutation process. It was shown how the discrete Laplace distribution can be used to estimate haplotype frequencies for haploid lineage DNA markers (such as Y-chromosomal short tandem repeats), which in turn can be used to assess the evidential weight of a DNA profile found at a crime scene. This was done by making inference in a mixture of multivariate, marginally independent, discrete Laplace distributions using the EM algorithm to estimate the probabilities of membership of a set of unobserved subpopulations. The discrete Laplace distribution can be used to estimate haplotype frequencies with lower prediction error than other existing estimators. Furthermore, the calculations could be performed on a normal computer. This method was implemented in the freely available open source software R that is supported on Linux, MacOS and MS Windows. Copyright © 2013 Elsevier Ltd. All rights reserved.

Cluster analysis of European Y-chromosomal STR haplotypes using the discrete Laplace method.

PubMed

Andersen, Mikkel Meyer; Eriksen, Poul Svante; Morling, Niels

2014-07-01

The European Y-chromosomal short tandem repeat (STR) haplotype distribution has previously been analysed in various ways. Here, we introduce a new way of analysing population substructure using a new method based on clustering within the discrete Laplace exponential family that models the probability distribution of the Y-STR haplotypes. Creating a consistent statistical model of the haplotypes enables us to perform a wide range of analyses. Previously, haplotype frequency estimation using the discrete Laplace method has been validated. In this paper we investigate how the discrete Laplace method can be used for cluster analysis to further validate the discrete Laplace method. A very important practical fact is that the calculations can be performed on a normal computer. We identified two sub-clusters of the Eastern and Western European Y-STR haplotypes similar to results of previous studies. We also compared pairwise distances (between geographically separated samples) with those obtained using the AMOVA method and found good agreement. Further analyses that are impossible with AMOVA were made using the discrete Laplace method: analysis of the homogeneity in two different ways and calculating marginal STR distributions. We found that the Y-STR haplotypes from e.g. Finland were relatively homogeneous as opposed to the relatively heterogeneous Y-STR haplotypes from e.g. Lublin, Eastern Poland and Berlin, Germany. We demonstrated that the observed distributions of alleles at each locus were similar to the expected ones. We also compared pairwise distances between geographically separated samples from Africa with those obtained using the AMOVA method and found good agreement. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Reactive silica transport in fractured porous media: Analytical solutions for a system of parallel fractures

NASA Astrophysics Data System (ADS)

Yang, Jianwen

2012-04-01

A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a set of parallel fractures embedded in an impermeable host rock matrix, taking into account of hydrodynamic dispersion and advection of silica transport along the fractures, molecular diffusion from each fracture to the intervening rock matrix, and dissolution of quartz. A special analytical solution is also developed by ignoring the longitudinal hydrodynamic dispersion term but remaining other conditions the same. The general and special solutions are in the form of a double infinite integral and a single infinite integral, respectively, and can be evaluated using Gauss-Legendre quadrature technique. A simple criterion is developed to determine under what conditions the general analytical solution can be approximated by the special analytical solution. It is proved analytically that the general solution always lags behind the special solution, unless a dimensionless parameter is less than a critical value. Several illustrative calculations are undertaken to demonstrate the effect of fracture spacing, fracture aperture and fluid flow rate on silica transport. The analytical solutions developed here can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.

Observing secretory granules with a multiangle evanescent wave microscope.

PubMed Central

Rohrbach, A

2000-01-01

In total internal reflection fluorescence microscopy (TIRFM), fluorophores near a surface can be excited with evanescent waves, which decay exponentially with distance from the interface. Penetration depths of evanescent waves from 60 nm to 300 nm were generated by varying the angle of incidence of a laser beam. With a novel telecentric multiangle evanescent wave microscope, we monitored and investigated both single secretory granules and pools of granules in bovine chromaffin cells. By measuring the fluorescence intensity as a function of penetration depth, it is possible through a Laplace transform to obtain the fluorophore distribution as a function of axial position. We discuss the extent to which it is possible to determine distances and diameters of granules with this microscopy technique by modeling the fluorescent volumes of spheres in evanescent fields. The anisotropic near-field detection of fluorophores and the influence of the detection point-spread function are considered. The diameters of isolated granules between 70 nm and 300 nm have been reconstructed, which is clearly beyond the resolution limit of a confocal microscope. Furthermore, the paper demonstrates how evanescent waves propagate along surfaces and scatter at objects with a higher refractive index. TIRFM will have a limited applicability for quantitative measurements when the parameters used to define evanescent waves are not optimally selected. PMID:10777760

An exact solution on unsteady MHD free convection chemically reacting silver nanofluid flow past an exponentially accelerated vertical plate through porous medium

NASA Astrophysics Data System (ADS)

Kumaresan, E.; Vijaya Kumar, A. G.; Rushi Kumar, B.

2017-11-01

This article studies, an exact solution of unsteady MHD free convection boundary-layer flow of a silver nanofluid past an exponentially accelerated moving vertical plate through aporous medium in the presence of thermal radiation, transverse applied amagnetic field, radiation absorption and Heat generation or absorption with chemical reaction are investigated theoretically. We consider nanofluids contain spherical shaped nanoparticle of silverwith a nanoparticle volume concentration range smaller than or equal to 0.04. This phenomenon is modeled in the form of partial differential equations with initial boundary conditions. Some suitable dimensional variables are introduced. The corresponding dimensionless equations with boundary conditions are solved by using Laplace transform technique. The exact solutions for velocity, energy, and species are obtained, also the corresponding numerical values of nanofluid velocity, temperature and concentration profiles are represented graphically. The expressions for skin friction coefficient, the rate of heat transfer and mass transfer are derived. The present study finds applications involving heat transfer, enhancement of thermal conductivity and other applications like transportation, industrial cooling applications, heating buildings and reducing pollution, energy applications and solar absorption. The effect of heat transfer is found to be more pronounced in a silver-water nanofluid than in the other nanofluids.

Controlled destruction and temperature distributions in biological tissues subjected to monoactive electrocoagulation.

PubMed

Erez, A; Shitzer, A

1980-02-01

An analysis of the temperature fields developed in a biological tissue undergoing a monoactive electrical coagulating process is presented, including thermal recovery following prolonged heating. The analysis is performed for the passage of alternating current and assumes a homogeneous and isotropic tissue model which is uniformly perfused by blood at arterial temperature. Solution for the one-dimensional spherical geometry is obtained by a Laplace transform and numerical integrations. Results obtained indicate the major role which blood perfusion plays in determining the effects of the coagulating process; tissue temperatures and depth of destruction are drastically reduced as blood perfusion increases. Metabolic heat generation rate is found to have negligible effects on tissue temperatures whereas electrode thermal inertia affects temperature levels appreciably. However, electrodes employed in practice would have a low thermal inertia which might be regarded as zero for all practical purposes. It is also found that the depth of tissue destruction is almost directly proportional to the electrical power and duration of application. To avoid excessively high temperatures and charring, it would be advantageous to reduce power and increase the time of application. Results of this study should be regarded as a first approximation to the rather complex phenomena associated with electrocoagulation. They may, nevertheless, serve as preliminary guidelines to practicing surgeons applying this technique.

Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system

NASA Astrophysics Data System (ADS)

Sedghi, Mohammad M.; Samani, Nozar

2015-09-01

Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a constant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to estimate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated.

Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis

NASA Astrophysics Data System (ADS)

Schäfer, Tobias; Ramberger, Benjamin; Kresse, Georg

2017-03-01

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O ( N 4 ) , with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

Transient reaction of an elastic half-plane on a source of a concentrated boundary disturbance

NASA Astrophysics Data System (ADS)

Okonechnikov, A. S.; Tarlakovski, D. V.; Ul'yashina, A. N.; Fedotenkov, G. V.

2016-11-01

One of the key problems in studying the non-stationary processes of solid mechanics is obtaining of influence functions. These functions serve as solutions for the problems of effect of sudden concentrated loads on a body with linear elastic properties. Knowledge of the influence functions allows us to obtain the solutions for the problems with non-mixed boundary and initial conditions in the form of quadrature formulae with the help of superposition principle, as well as get the integral governing equations for the problems with mixed boundary and initial conditions. This paper offers explicit derivations for all nonstationary surface influence functions of an elastic half-plane in a plane strain condition. It is achieved with the help of combined inverse transform of a Fourier-Laplace integral transformation. The external disturbance is both dynamic and kinematic. The derived functions in xτ-domain are studied to find and describe singularities and are supplemented with graphs.

Communication: A reduced scaling J-engine based reformulation of SOS-MP2 using graphics processing units.

PubMed

Maurer, S A; Kussmann, J; Ochsenfeld, C

2014-08-07

We present a low-prefactor, cubically scaling scaled-opposite-spin second-order Møller-Plesset perturbation theory (SOS-MP2) method which is highly suitable for massively parallel architectures like graphics processing units (GPU). The scaling is reduced from O(N⁵) to O(N³) by a reformulation of the MP2-expression in the atomic orbital basis via Laplace transformation and the resolution-of-the-identity (RI) approximation of the integrals in combination with efficient sparse algebra for the 3-center integral transformation. In contrast to previous works that employ GPUs for post Hartree-Fock calculations, we do not simply employ GPU-based linear algebra libraries to accelerate the conventional algorithm. Instead, our reformulation allows to replace the rate-determining contraction step with a modified J-engine algorithm, that has been proven to be highly efficient on GPUs. Thus, our SOS-MP2 scheme enables us to treat large molecular systems in an accurate and efficient manner on a single GPU-server.

Computation of type curves for flow to partially penetrating wells in water-table aquifers

USGS Publications Warehouse

Moench, Allen F.

1993-01-01

Evaluation of Neuman's analytical solution for flow to a well in a homogeneous, anisotropic, water-table aquifer commonly requires large amounts of computation time and can produce inaccurate results for selected combinations of parameters. Large computation times occur because the integrand of a semi-infinite integral involves the summation of an infinite series. Each term of the series requires evaluation of the roots of equations, and the series itself is sometimes slowly convergent. Inaccuracies can result from lack of computer precision or from the use of improper methods of numerical integration. In this paper it is proposed to use a method of numerical inversion of the Laplace transform solution, provided by Neuman, to overcome these difficulties. The solution in Laplace space is simpler in form than the real-time solution; that is, the integrand of the semi-infinite integral does not involve an infinite series or the need to evaluate roots of equations. Because the integrand is evaluated rapidly, advanced methods of numerical integration can be used to improve accuracy with an overall reduction in computation time. The proposed method of computing type curves, for which a partially documented computer program (WTAQ1) was written, was found to reduce computation time by factors of 2 to 20 over the time needed to evaluate the closed-form, real-time solution.

Method based on the Laplace equations to reconstruct the river terrain for two-dimensional hydrodynamic numerical modeling

NASA Astrophysics Data System (ADS)

Lai, Ruixun; Wang, Min; Yang, Ming; Zhang, Chao

2018-02-01

The accuracy of the widely-used two-dimensional hydrodynamic numerical model depends on the quality of the river terrain model, particularly in the main channel. However, in most cases, the bathymetry of the river channel is difficult or expensive to obtain in the field, and there is a lack of available data to describe the geometry of the river channel. We introduce a method that originates from the grid generation with the elliptic equation to generate streamlines of the river channel. The streamlines are numerically solved with the Laplace equations. In the process, streamlines in the physical domain are first computed in a computational domain, and then transformed back to the physical domain. The interpolated streamlines are integrated with the surrounding topography to reconstruct the entire river terrain model. The approach was applied to a meandering reach in the Qinhe River, which is a tributary in the middle of the Yellow River, China. Cross-sectional validation and the two-dimensional shallow-water equations are used to test the performance of the river terrain generated. The results show that the approach can reconstruct the river terrain using the data from measured cross-sections. Furthermore, the created river terrain can maintain a geometrical shape consistent with the measurements, while generating a smooth main channel. Finally, several limitations and opportunities for future research are discussed.

A versatile approach to the study of the transient response of a submerged thin shell

NASA Astrophysics Data System (ADS)

Leblond, C.; Sigrist, J.-F.

2010-01-01

The transient response of submerged two-dimensional thin shell subjected to weak acoustical or mechanical excitations is addressed in this paper. The proposed approach is first exposed in a detailed manner: it is based on Laplace transform in time, in vacuo eigenvector expansion with time-dependent coefficients for the structural dynamics and boundary-integral formulation for the fluid. The projection of the fluid pressure on the in vacuo eigenvectors leads to a fully coupled system involving the modal time-dependent displacement coefficients, which are the problem unknowns. They are simply determined by matrix inversion in the Laplace domain. Application of the method to the response of a two-dimensional immersed shell to a weak acoustical excitation is then exposed: the proposed test-case corresponds to the design of immersed structures subjected to underwater explosions, which is of paramount importance in naval shipbuilding. Comparison of a numerical calculation based on the proposed approach with an analytical solution is exposed; versatility of the method is also highlighted by referring to "classical" FEM/FEM or FEM/BEM simulations. As a conspicuous feature of the method, calculation of the fluid response functions corresponding to a given geometry has to be performed once, allowing various simulations for different material properties of the structure, as well as for various excitations on the structure. This versatile approach can therefore be efficiently and extensively used for design purposes.

Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis

PubMed Central

Reuter, Martin; Wolter, Franz-Erich; Shenton, Martha; Niethammer, Marc

2009-01-01

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and -functions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel. PMID:20161035

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

The Laplace method for probability measures in Banach spaces

NASA Astrophysics Data System (ADS)

Piterbarg, V. I.; Fatalov, V. R.

1995-12-01

Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Hölder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces L_k^p and l^2. Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the l_k^p-norm of a Gaussian finite-dimensional vector with dependent coordinates, p > 1 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type \\chi^2 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of l^2-valued Gaussian processes 8.5. Exact asymptotics of large deviations for the l^2-valued Ornstein-Uhlenbeck process Bibliography

Dipole and quadrupole synthesis of electric potential fields. M.S. Thesis

NASA Technical Reports Server (NTRS)

Tilley, D. G.

1979-01-01

A general technique for expanding an unknown potential field in terms of a linear summation of weighted dipole or quadrupole fields is described. Computational methods were developed for the iterative addition of dipole fields. Various solution potentials were compared inside the boundary with a more precise calculation of the potential to derive optimal schemes for locating the singularities of the dipole fields. Then, the problem of determining solutions to Laplace's equation on an unbounded domain as constrained by pertinent electron trajectory data was considered.

Free Wake Analysis of Helicopter Rotor Blades in Hover Using a Finite Volume Technique

DTIC Science & Technology

1988-10-01

inboard, and root) which were replaced by a far wake model after four revolutions. Murman and Stremel 1121 calculated j two-dimensional unsteady wake...distributed to a fixed mesh, on which the velocities were calculated by a finite difference solution of Laplace’s equation. Stremel [131 applied this two...Analysis of a Hovering Rotor," Vertica, Vol. 6, No. 2, 1982. 12. Murman, E.M., and Stremel , P.M., "A Vortex Wake Capturing Method Po- tential Flow

Stress and reliability analyses of multilayered composite cylinder under thermal and mechanical loads

NASA Astrophysics Data System (ADS)

Wang, Xiaohua

The coupling resulting from the mutual influence of material thermal and mechanical parameters is examined in the thermal stress analysis of a multilayered isotropic composite cylinder subjected to sudden axisymmetric external and internal temperature. The method of complex frequency response functions together with the Fourier transform technique is utilized. Because the coupling parameters for some composite materials, such as carbon-carbon, are very small, the effect of coupling is neglected in the orthotropic thermal stress analysis. The stress distributions in multilayered orthotropic cylinders subjected to sudden axisymmetric temperature loading combined with dynamic pressure as well as asymmetric temperature loading are also obtained. The method of Fourier series together with the Laplace transform is utilized in solving the heat conduction equation and thermal stress analysis. For brittle materials, like carbon-carbon composites, the strength variability is represented by two or three parameter Weibull distributions. The 'weakest link' principle which takes into account both the carbon-carbon composite cylinders. The complex frequency response analysis is performed on a multilayered orthotropic cylinder under asymmetrical thermal load. Both deterministic and random thermal stress and reliability analyses can be based on the results of this frequency response analysis. The stress and displacement distributions and reliability of rocket motors under static or dynamic line loads are analyzed by an elasticity approach. Rocket motors are modeled as long hollow multilayered cylinders with an air core, a thick isotropic propellant inner layer and a thin orthotropic kevlar-epoxy case. The case is treated as a single orthotropic layer or a ten layered orthotropic structure. Five material properties and the load are treated as random variable with normal distributions when the reliability of the rocket motor is analyzed by the first-order, second-moment method (FOSM).

Gradient estimates on the weighted p-Laplace heat equation

NASA Astrophysics Data System (ADS)

Wang, Lin Feng

2018-01-01

In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.

Locating CVBEM collocation points for steady state heat transfer problems

USGS Publications Warehouse

Hromadka, T.V.

1985-01-01

The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.

An Elementary Proof of Laplace's Formula on Determinants

ERIC Educational Resources Information Center

Aversa, Vincenzo; De Simone, Anna

2012-01-01

A well known result due to Laplace states the equivalence between two different ways of defining the determinant of a square matrix. We give here a short proof of this result, in a form that can be presented, in our opinion, at any level of undergraduate studies.

Mathematical model of an indirect action fuel flow controller for aircraft jet engines

NASA Astrophysics Data System (ADS)

Tudosie, Alexandru-Nicolae

2017-06-01

The paper deals with a fuel mass flow rate controller with indirect action for aircraft jet engines. The author has identified fuel controller's main parts and its operation mode, then, based on these observations, one has determined motion equations of each main part, which have built system's non-linear mathematical model. In order to realize a better study this model was linearised (using the finite differences method) and then adimensionalized. Based on this new form of the mathematical model, after applying Laplace transformation, the embedded system (controller+engine) was described by the block diagram with transfer functions. Some Simulink-Matlab simulations were performed, concerning system's time behavior for step input, which lead to some useful conclusions and extension possibilities.

MHD Flow of Sodium Alginate-Based Casson Type Nanofluid Passing Through A Porous Medium With Newtonian Heating.

PubMed

Khan, Arshad; Khan, Dolat; Khan, Ilyas; Ali, Farhad; Karim, Faizan Ul; Imran, Muhammad

2018-06-05

Casson nanofluid, unsteady flow over an isothermal vertical plate with Newtonian heating (NH) is investigated. Sodium alginate (base fluid)is taken as counter example of Casson fluid. MHD and porosity effects are considered. Effects of thermal radiation along with heat generation are examined. Sodium alginate with Silver, Titanium oxide, Copper and Aluminum oxide are added as nano particles. Initial value problem with physical boundary condition is solved by using Laplace transform method. Exact results are obtained for temperature and velocity fields. Skin-friction and Nusselt number are calculated. The obtained results are analyzed graphically for emerging flow parameters and discussed. It is bring into being that temperature and velocity profile are decreasing with increasing nano particles volume fraction.

Mean first passage times of Brownian rotators from differential recurrence relations

NASA Astrophysics Data System (ADS)

Coffey, W. T.

1999-11-01

An exact method of calculation of mean first passage times (analogous to that previously used [W. T. Coffey, Yu. P. Kalmykov, E. S. Massawe, and J. T. Waldron, J. Chem. Phys. 99, 4011 (1993)] for the correlation time) is developed in terms of continued fractions from the zero frequency limit of the Laplace transform of the set of differential recurrence relations generated by the Fokker-Planck or Langevin equations. The method because it is based on a Floquet representation avoids the use of quadratures and so may be easily generalized to multidegree of freedom systems by the use of matrix continued fractions. The procedure is illustrated by considering the mean first passage time of a fixed axis rotator with two equivalent sites.

Main Battle Tank Flexible Gun Tube Disturbance Model: Three-Segment Model

DTIC Science & Technology

2002-10-01

Laplace transform of equation (1) yields Ix,(s) F. (s)l [a] o2(s)[ = 2 , (s) (2) Theelmets f a]and[ 0{2(S) jjSO,(S)13o( s )) oP (S)J The elements of [a...contain the actuator force, F,, and the actuator displacement, x,, in addition to disturbances (s2y,(s), sOp( s ), Op (s)) and the responses 01(s), 02(s), •3...function. The portion of the response due to the disturbance is X, (s) B2 B13 B14 1fs2y(s) 2°s(s) B4 s OP (s) J (7) 02(S) B2 B33 B34 op (S)J 103S) -B2

Relaxation distribution function of intracellular dielectric zones as an indicator of tumorous transition of living cells.

PubMed

Thornton, B S; Hung, W T; Irving, J

1991-01-01

The response decay data of living cells subject to electric polarization is associated with their relaxation distribution function (RDF) and can be determined using the inverse Laplace transform method. A new polynomial, involving a series of associated Laguerre polynomials, has been used as the approximating function for evaluating the RDF, with the advantage of avoiding the usual arbitrary trial values of a particular parameter in the numerical computations. Some numerical examples are given, followed by an application to cervical tissue. It is found that the average relaxation time and the peak amplitude of the RDF exhibit higher values for tumorous cells than normal cells and might be used as parameters to differentiate them and their associated tissues.

A time domain inverse dynamic method for the end point tracking control of a flexible manipulator

NASA Technical Reports Server (NTRS)

Kwon, Dong-Soo; Book, Wayne J.

1991-01-01

The inverse dynamic equation of a flexible manipulator was solved in the time domain. By dividing the inverse system equation into the causal part and the anticausal part, we calculated the torque and the trajectories of all state variables for a given end point trajectory. The interpretation of this method in the frequency domain was explained in detail using the two-sided Laplace transform and the convolution integral. The open loop control of the inverse dynamic method shows an excellent result in simulation. For real applications, a practical control strategy is proposed by adding a feedback tracking control loop to the inverse dynamic feedforward control, and its good experimental performance is presented.

On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid

NASA Astrophysics Data System (ADS)

Khan, M.; Anjum, Asia; Qi, Haitao; Fetecau, C.

2010-02-01

This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag-Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

NASA Technical Reports Server (NTRS)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Dirac delta representation by exact parametric equations.. Application to impulsive vibration systems

NASA Astrophysics Data System (ADS)

Chicurel-Uziel, Enrique

2007-08-01

A pair of closed parametric equations are proposed to represent the Heaviside unit step function. Differentiating the step equations results in two additional parametric equations, that are also hereby proposed, to represent the Dirac delta function. These equations are expressed in algebraic terms and are handled by means of elementary algebra and elementary calculus. The proposed delta representation complies exactly with the values of the definition. It complies also with the sifting property and the requisite unit area and its Laplace transform coincides with the most general form given in the tables. Furthermore, it leads to a very simple method of solution of impulsive vibrating systems either linear or belonging to a large class of nonlinear problems. Two example solutions are presented.

Time-resolved measurements in diffuse reflectance: effects of the instrument response function of different detection systems on the depth sensitivity

NASA Astrophysics Data System (ADS)

Puszka, Agathe; Planat-Chrétien, Anne; Berger, Michel; Hervé, Lionel; Dinten, Jean-Marc

2014-02-01

We demonstrate the loss of depth sensitivity induced by the instrument response function on reflectance time-resolved diffuse optical tomography through the comparison of 3 detection systems: on one hand a photomultiplier tube (PMT) and a hybrid PMT coupled with a time-correlated single-photon counting card and on the other hand a high rate intensified camera. We experimentally evaluate the depth sensitivity achieved for each detection module with an absorbing inclusion embedded in a turbid medium. The different interfiber distances of 5, 10 and 15 mm are considered. Finally, we determine a maximal depth reached for each detection system by using 3D tomographic reconstructions based on the Mellin-Laplace transform.

Lock-in amplifier error prediction and correction in frequency sweep measurements.

PubMed

Sonnaillon, Maximiliano Osvaldo; Bonetto, Fabian Jose

2007-01-01

This article proposes an analytical algorithm for predicting errors in lock-in amplifiers (LIAs) working with time-varying reference frequency. Furthermore, a simple method for correcting such errors is presented. The reference frequency can be swept in order to measure the frequency response of a system within a given spectrum. The continuous variation of the reference frequency produces a measurement error that depends on three factors: the sweep speed, the LIA low-pass filters, and the frequency response of the measured system. The proposed error prediction algorithm is based on the final value theorem of the Laplace transform. The correction method uses a double-sweep measurement. A mathematical analysis is presented and validated with computational simulations and experimental measurements.

Electromagnetic plasma wave propagation along a magnetic field. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Olson, C. L.

1970-01-01

The linearized response of a Vlasov plasma to the steady-state excitation of transverse plasma waves along an external magnetic field is examined. Assuming a delta-function excitation mechanism, and performing a detailed Vlasov-Maxwell equation analysis using Fourier-Laplace transforms, the plasma response is found to consist of three terms: a branch-cut term, a free-streaming term, and a dielectric-pole term. Also considered is the phenomenon of plasma wave echoes. The case of longitudinal electrostatic waves is extended to the case of transverse plasma waves that propagate along an external magnetic field. It is shown that a transverse echo results in lowest order only when one excitation is transverse and the other is longitudinal.

Molecular dynamics in aluminum layered double hydroxides as studied by 1H T1ρ NMR measurements

NASA Astrophysics Data System (ADS)

Vyalikh, Anastasia; Wang, De-Yi; Wagenknecht, Udo; Heinrich, Gert; Scheler, Ulrich

2011-06-01

Proton dynamics in pristine and organically-modified layered double hydroxide has been studied by 1H T1ρ. Inverse Laplace transform with spectral resolution results in a correlation of T1ρ and chemical shift. In LDH two contributions are resolved. They are assigned to the metal hydroxides, forming the LDH sheets (4-8 ms), and mobile interlayer water (2 ms). Apparent T1ρ values of OH-protons in surfactant-modified LDH are different in dodecylbenzenesulfonate- (SDBS) and sodium octasulfonate- (C8) modified LDH. This difference is explained by the presence of water in LDH-SDBS. The effects of spin diffusion have been studied by performing 2D 1H RFDR in the LDH-SDBS.

Bayesian Estimation of Multivariate Latent Regression Models: Gauss versus Laplace

ERIC Educational Resources Information Center

Culpepper, Steven Andrew; Park, Trevor

2017-01-01

A latent multivariate regression model is developed that employs a generalized asymmetric Laplace (GAL) prior distribution for regression coefficients. The model is designed for high-dimensional applications where an approximate sparsity condition is satisfied, such that many regression coefficients are near zero after accounting for all the model…

Evaluation of the Laplace Integral. Classroom Notes

ERIC Educational Resources Information Center

Chen, Hongwei

2004-01-01

Based on the dominated convergence theorem and parametric differentiation, two different evaluations of the Laplace integral are displayed. This article presents two different proofs of (1) which may be of interest since they are based on principles within the realm of real analysis. The first method applies the dominated convergence theorem to…

Giant graviton interactions and M2-branes ending on multiple M5-branes

NASA Astrophysics Data System (ADS)

Hirano, Shinji; Sato, Yuki

2018-05-01

We study splitting and joining interactions of giant gravitons with angular momenta N 1/2 ≪ J ≪ N in the type IIB string theory on AdS 5 × S 5 by describing them as instantons in the tiny graviton matrix model introduced by Sheikh-Jabbari. At large J the instanton equation can be mapped to the four-dimensional Laplace equation and the Coulomb potential for m point charges in an n-sheeted Riemann space corresponds to the m-to- n interaction process of giant gravitons. These instantons provide the holographic dual of correlators of all semi-heavy operators and the instanton amplitudes exactly agree with the pp-wave limit of Schur polynomial correlators in N = 4 SYM computed by Corley, Jevicki and Ramgoolam. By making a slight change of variables the same instanton equation is mathematically transformed into the Basu-Harvey equation which describes the system of M2-branes ending on M5-branes. As it turns out, the solutions to the sourceless Laplace equation on an n-sheeted Riemann space correspond to n M5-branes connected by M2-branes and we find general solutions representing M2-branes ending on multiple M5-branes. Among other solutions, the n = 3 case describes an M2-branes junction ending on three M5-branes. The effective theory on the moduli space of our solutions might shed light on the low energy effective theory of multiple M5-branes.

On the aquitard-aquifer interface flow and the drawdown sensitivity with a partially penetrating pumping well in an anisotropic leaky confined aquifer

NASA Astrophysics Data System (ADS)

Feng, Qinggao; Zhan, Hongbin

2015-02-01

A mathematical model for describing groundwater flow to a partially penetrating pumping well of a finite diameter in an anisotropic leaky confined aquifer is developed. The model accounts for the jointed effects of aquitard storage, aquifer anisotropy, and wellbore storage by treating the aquitard leakage as a boundary condition at the aquitard-aquifer interface rather than a volumetric source/sink term in the governing equation, which has never developed before. A new semi-analytical solution for the model is obtained by the Laplace transform in conjunction with separation of variables. Specific attention was paid on the flow across the aquitard-aquifer interface, which is of concern if aquitard and aquifer have different pore water chemistry. Moreover, Laplace-domain and steady-state solutions are obtained to calculate the rate and volume of (total) leakage through the aquitard-aquifer interface due to pump in a partially penetrating well, which is also useful for engineers to manager water resources. The sensitivity analyses for the drawdown illustrate that the drawdown is most sensitive to the well partial penetration. It is apparently sensitive to the aquifer anisotropic ratio over the entire time of pumping. It is moderately sensitive to the aquitard/aquifer specific storage ratio at the intermediate times only. It is moderately sensitive to the aquitard/aquifer vertical hydraulic conductivity ratio and the aquitard/aquifer thickness ratio with the identical influence at late times.

Laplace, Pierre-Simon (1749-1827)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Celestial mechanician, born in Beaumont-en-Auge, Normandy, France, became professor of mathematics at the Ecole Militaire in Paris, examining the cadet Napoleon Bonaparte. This position made Laplace well known to people in positions of power, which he opportunistically exploited, becoming, under Napoleon, Minister of the Interior (Napoleon soon removed him from office `because he brought the spir...

From entropy-maximization to equality-maximization: Gauss, Laplace, Pareto, and Subbotin

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2014-12-01

The entropy-maximization paradigm of statistical physics is well known to generate the omnipresent Gauss law. In this paper we establish an analogous socioeconomic model which maximizes social equality, rather than physical disorder, in the context of the distributions of income and wealth in human societies. We show that-on a logarithmic scale-the Laplace law is the socioeconomic equality-maximizing counterpart of the physical entropy-maximizing Gauss law, and that this law manifests an optimized balance between two opposing forces: (i) the rich and powerful, striving to amass ever more wealth, and thus to increase social inequality; and (ii) the masses, struggling to form more egalitarian societies, and thus to increase social equality. Our results lead from log-Gauss statistics to log-Laplace statistics, yield Paretian power-law tails of income and wealth distributions, and show how the emergence of a middle-class depends on the underlying levels of socioeconomic inequality and variability. Also, in the context of asset-prices with Laplace-distributed returns, our results imply that financial markets generate an optimized balance between risk and predictability.

Wetting transitions on patterned surfaces with diffuse interaction potentials embedded in a Young-Laplace formulation

NASA Astrophysics Data System (ADS)

Pashos, G.; Kokkoris, G.; Papathanasiou, A. G.; Boudouvis, A. G.

2016-01-01

The Minimum Energy Paths (MEPs) of wetting transitions on pillared surfaces are computed with the Young-Laplace equation, augmented with a pressure term that accounts for liquid-solid interactions. The interactions are smoothed over a short range from the solid phase, therefore facilitating the numerical solution of problems concerning wetting on complex surface patterns. The patterns may include abrupt geometric features, e.g., arrays of rectangular pillars, where the application of the unmodified Young-Laplace is not practical. The MEPs are obtained by coupling the augmented Young-Laplace with the modified string method from which the energy barriers of wetting transitions are eventually extracted. We demonstrate the method on a wetting transition that is associated with the breakdown of superhydrophobic behavior, i.e., the transition from the Cassie-Baxter state to the Wenzel state, taking place on a superhydrophobic pillared surface. The computed energy barriers quantify the resistance of the system to these transitions and therefore, they can be used to evaluate superhydrophobic performance or provide guidelines for optimal pattern design.

Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations

NASA Astrophysics Data System (ADS)

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

2018-02-01

The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.

Deep levels in H-irradiated GaAs1-xNx (x < 0.01) grown by molecular beam epitaxy

NASA Astrophysics Data System (ADS)

Shafi, M.; Mari, R. H.; Khatab, A.; Henini, M.; Polimeni, A.; Capizzi, M.; Hopkinson, M.

2011-12-01

Dilute nitride GaAs1-xNx layers have been grown by molecular beam epitaxy with nitrogen concentration ranging from 0.2% to 0.8%. These samples have been studied before and after hydrogen irradiation by using standard deep level transient spectroscopy (DLTS) and high resolution Laplace DLTS techniques. The activation energy, capture cross section and density of the electron traps have been estimated and compared with results obtained in N-free as-grown and H-irradiated bulk GaAs.

Natural and Artificial Satellite Dynamics and Evolution around Near-Earth Asteroids with Solar Radiation Pressure

NASA Astrophysics Data System (ADS)

Rieger, Samantha M.

Natural and artificial satellites are subject to perturbations when orbiting near-Earth asteroids. These perturbations include non-uniform gravity from the asteroid, third-body disturbances from the Sun, and solar radiation pressure. For small natural (1 cm-15 m) and artificial satellites, solar radiation pressure is the primary perturbation that will cause their orbits to go unstable. For the asteroid Bennu, the future target of the spacecraft OSIRIS-REx, the possibility of natural satellites having stable orbits around the asteroid and characterize these stable regions is investigated. It has been found that the main orbital phenomena responsible for the stability or instability of these possible natural satellites are Sun-synchronous orbits, the modified Laplace plane, and the Kozai resonance. These findings are applied to other asteroids as well as to artificial satellites. The re-emission of solar radiation pressure through BYORP is also investigated for binary asteroid systems. Specifically, the BYORP force is combined with the Laplace plane such that BYORP expands the orbit of the binary system along the Laplace surface where the secondary increases in inclination. For obliquities from 68.875° - 111.125° the binary will eventually extend into the Laplace instability region, where the eccentricity of the orbit will increase. A subset of the instability region leads to eccentricities high enough that the secondary will impact the primary. This result inspired the development of a hypothesis of a contact-binary binary cycle described briefly in the following. YORP will increase the spin rate of a contact binary while also driving the spin-pole to an obliquity of 90°. Eventually, the contact binary will fission. The binary will subsequently become double-synchronous, thus allowing the BYORP acceleration to have secular effects on the orbit. The orbit will then expand along the Laplace surface to the Laplace plane instability region eventually leading to an impact and the start of a new cycle with the YORP process.

NMR spin-rotation relaxation and diffusion of methane

NASA Astrophysics Data System (ADS)

Singer, P. M.; Asthagiri, D.; Chapman, W. G.; Hirasaki, G. J.

2018-05-01

The translational diffusion-coefficient and the spin-rotation contribution to the 1H NMR relaxation rate for methane (CH4) are investigated using MD (molecular dynamics) simulations, over a wide range of densities and temperatures, spanning the liquid, supercritical, and gas phases. The simulated diffusion-coefficients agree well with measurements, without any adjustable parameters in the interpretation of the simulations. A minimization technique is developed to compute the angular velocity for non-rigid spherical molecules, which is used to simulate the autocorrelation function for spin-rotation interactions. With increasing diffusivity, the autocorrelation function shows increasing deviations from the single-exponential decay predicted by the Langevin theory for rigid spheres, and the deviations are quantified using inverse Laplace transforms. The 1H spin-rotation relaxation rate derived from the autocorrelation function using the "kinetic model" agrees well with measurements in the supercritical/gas phase, while the relaxation rate derived using the "diffusion model" agrees well with measurements in the liquid phase. 1H spin-rotation relaxation is shown to dominate over the MD-simulated 1H-1H dipole-dipole relaxation at high diffusivity, while the opposite is found at low diffusivity. At high diffusivity, the simulated spin-rotation correlation time agrees with the kinetic collision time for gases, which is used to derive a new expression for 1H spin-rotation relaxation, without any adjustable parameters.

Flow of magnetic particles in blood with isothermal heating: A fractional model for two-phase flow

NASA Astrophysics Data System (ADS)

Ali, Farhad; Imtiaz, Anees; Khan, Ilyas; Sheikh, Nadeem Ahmad

2018-06-01

In the sixteenth century, medical specialists were of the conclusion that magnet can be utilized for the treatment or wipe out the illnesses from the body. On this basis, the research on magnet advances day by day for the treatment of different types of diseases in mankind. This study aims to investigate the effect of magnetic field and their applications in human body specifically in blood. Blood is a non-Newtonian fluid because its viscosity depends strongly on the fraction of volume occupied by red cells also called the hematocrit. Therefore, in this paper blood is considered as an example of non-Newtonian Casson fluid. The blood flow is considered in a vertical cylinder together with heat transfer due to mixed conviction caused by buoyancy force and the external pressure gradient. Effect of magnetic field on the velocities of blood and magnetic particles is also considered. The problem is modelled using the Caputo-Fabrizio derivative approach. The governing fractional partial differential equations are solved using Laplace and Hankel transformation techniques and exact solutions are obtained. Effects of different parameters such as Grashof number, Prandtl number, Casson fluid parameter and fractional parameters, and magnetic field are shown graphically. Both velocity profiles increase with the increase of Grashoff number and Casson fluid parameter and reduce with the increase of magnetic field.

One-dimensional analytical solution for hydraulic head and numerical solution for solute transport through a horizontal fracture for submarine groundwater discharge.

PubMed

He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J; Zhan, Hongbin

2017-11-01

Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions. Copyright © 2017 Elsevier B.V. All rights reserved.

One-dimensional analytical solution for hydraulic head and numerical solution for solute transport through a horizontal fracture for submarine groundwater discharge

NASA Astrophysics Data System (ADS)

He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J.; Zhan, Hongbin

2017-11-01

Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions.

Communication: A reduced scaling J-engine based reformulation of SOS-MP2 using graphics processing units

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

Maurer, S. A.; Kussmann, J.; Ochsenfeld, C., E-mail: Christian.Ochsenfeld@cup.uni-muenchen.de

2014-08-07

We present a low-prefactor, cubically scaling scaled-opposite-spin second-order Møller-Plesset perturbation theory (SOS-MP2) method which is highly suitable for massively parallel architectures like graphics processing units (GPU). The scaling is reduced from O(N{sup 5}) to O(N{sup 3}) by a reformulation of the MP2-expression in the atomic orbital basis via Laplace transformation and the resolution-of-the-identity (RI) approximation of the integrals in combination with efficient sparse algebra for the 3-center integral transformation. In contrast to previous works that employ GPUs for post Hartree-Fock calculations, we do not simply employ GPU-based linear algebra libraries to accelerate the conventional algorithm. Instead, our reformulation allows tomore » replace the rate-determining contraction step with a modified J-engine algorithm, that has been proven to be highly efficient on GPUs. Thus, our SOS-MP2 scheme enables us to treat large molecular systems in an accurate and efficient manner on a single GPU-server.« less

Observatory geoelectric fields induced in a two-layer lithosphere during magnetic storms

USGS Publications Warehouse

Love, Jeffrey J.; Swidinsky, Andrei

2015-01-01

We report on the development and validation of an algorithm for estimating geoelectric fields induced in the lithosphere beneath an observatory during a magnetic storm. To accommodate induction in three-dimensional lithospheric electrical conductivity, we analyze a simple nine-parameter model: two horizontal layers, each with uniform electrical conductivity properties given by independent distortion tensors. With Laplace transformation of the induction equations into the complex frequency domain, we obtain a transfer function describing induction of observatory geoelectric fields having frequency-dependent polarization. Upon inverse transformation back to the time domain, the convolution of the corresponding impulse-response function with a geomagnetic time series yields an estimated geoelectric time series. We obtain an optimized set of conductivity parameters using 1-s resolution geomagnetic and geoelectric field data collected at the Kakioka, Japan, observatory for five different intense magnetic storms, including the October 2003 Halloween storm; our estimated geoelectric field accounts for 93% of that measured during the Halloween storm. This work demonstrates the need for detailed modeling of the Earth’s lithospheric conductivity structure and the utility of co-located geomagnetic and geoelectric monitoring.

Comb model for the anomalous diffusion with dual-phase-lag constitutive relation

NASA Astrophysics Data System (ADS)

Liu, Lin; Zheng, Liancun; Fan, Yu; Chen, Yanping; Liu, Fawang

2018-10-01

As a development of the Fick's model, the dual-phase-lag constitutive relationship with macroscopic and microscopic relaxation characteristics is introduced to describe the anomalous diffusion in comb model. The Dirac delta function in the formulated governing equation represents the special spatial structure of comb model that the horizontal current only exists on the x axis. Solutions are obtained by analytical method with Laplace transform and Fourier transform. The dependence of concentration field and mean square displacement on different parameters are presented and discussed. Results show that the macroscopic and microscopic relaxation parameters have opposite effects on the particle distribution and mean square displacement. Furthermore, four significant results with constant 1/2 are concluded, namely the product of the particle number and the mean square displacement on the x axis equals to 1/2, the exponent of mean square displacement is 1/2 at the special case τq= τP, an asymptotic form of mean square displacement (MSD∼t1/2 as t→0, ∞) is obtained as well at the short time behavior and the long time behavior.

Solute transport in a single fracture involving an arbitrary length decay chain with rock matrix comprising different geological layers.

PubMed

Mahmoudzadeh, Batoul; Liu, Longcheng; Moreno, Luis; Neretnieks, Ivars

2014-08-01

A model is developed to describe solute transport and retention in fractured rocks. It accounts for advection along the fracture, molecular diffusion from the fracture to the rock matrix composed of several geological layers, adsorption on the fracture surface, adsorption in the rock matrix layers and radioactive decay-chains. The analytical solution, obtained for the Laplace-transformed concentration at the outlet of the flowing channel, can conveniently be transformed back to the time domain by the use of the de Hoog algorithm. This allows one to readily include it into a fracture network model or a channel network model to predict nuclide transport through channels in heterogeneous fractured media consisting of an arbitrary number of rock units with piecewise constant properties. More importantly, the simulations made in this study recommend that it is necessary to account for decay-chains and also rock matrix comprising at least two different geological layers, if justified, in safety and performance assessment of the repositories for spent nuclear fuel. Copyright © 2014 Elsevier B.V. All rights reserved.

Semianalytical solutions for transport in aquifer and fractured clay matrix system

NASA Astrophysics Data System (ADS)

Huang, Junqi; Goltz, Mark N.

2015-09-01

A three-dimensional mathematical model that describes transport of contaminant in a horizontal aquifer with simultaneous diffusion into a fractured clay formation is proposed. A group of semianalytical solutions is derived based on specific initial and boundary conditions as well as various source functions. The analytical model solutions are evaluated by numerical Laplace inverse transformation and analytical Fourier inverse transformation. The model solutions can be used to study the fate and transport in a three-dimensional spatial domain in which a nonaqueous phase liquid exists as a pool atop a fractured low-permeability clay layer. The nonaqueous phase liquid gradually dissolves into the groundwater flowing past the pool, while simultaneously diffusing into the fractured clay formation below the aquifer. Mass transfer of the contaminant into the clay formation is demonstrated to be significantly enhanced by the existence of the fractures, even though the volume of fractures is relatively small compared to the volume of the clay matrix. The model solution is a useful tool in assessing contaminant attenuation processes in a confined aquifer underlain by a fractured clay formation.

An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion

NASA Astrophysics Data System (ADS)

Messelmi, Farid

2017-12-01

We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray-Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem.

A Boundary Value Problem for Introductory Physics?

ERIC Educational Resources Information Center

Grundberg, Johan

2008-01-01

The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…

Against Laplacian Reduction of Newtonian Mass to Spatiotemporal Quantities

NASA Astrophysics Data System (ADS)

Martens, Niels C. M.

2018-05-01

Laplace wondered about the minimal choice of initial variables and parameters corresponding to a well-posed initial value problem. Discussions of Laplace's problem in the literature have focused on choosing between spatiotemporal variables relative to absolute space (i.e. substantivalism) or merely relative to other material bodies (i.e. relationalism) and between absolute masses (i.e. absolutism) or merely mass ratios (i.e. comparativism). This paper extends these discussions of Laplace's problem, in the context of Newtonian Gravity, by asking whether mass needs to be included in the initial state at all, or whether a purely spatiotemporal initial state suffices. It is argued that mass indeed needs to be included; removing mass from the initial state drastically reduces the predictive and explanatory power of Newtonian Gravity.

Against Laplacian Reduction of Newtonian Mass to Spatiotemporal Quantities

NASA Astrophysics Data System (ADS)

Martens, Niels C. M.

2018-03-01

Laplace wondered about the minimal choice of initial variables and parameters corresponding to a well-posed initial value problem. Discussions of Laplace's problem in the literature have focused on choosing between spatiotemporal variables relative to absolute space (i.e. substantivalism) or merely relative to other material bodies (i.e. relationalism) and between absolute masses (i.e. absolutism) or merely mass ratios (i.e. comparativism). This paper extends these discussions of Laplace's problem, in the context of Newtonian Gravity, by asking whether mass needs to be included in the initial state at all, or whether a purely spatiotemporal initial state suffices. It is argued that mass indeed needs to be included; removing mass from the initial state drastically reduces the predictive and explanatory power of Newtonian Gravity.

Heat Transfer Analysis of Thermal Protection Structures for Hypersonic Vehicles

NASA Astrophysics Data System (ADS)

Zhou, Chen; Wang, Zhijin; Hou, Tianjiao

2017-11-01

This research aims to develop an analytical approach to study the heat transfer problem of thermal protection systems (TPS) for hypersonic vehicles. Laplace transform and integral method are used to describe the temperature distribution through the TPS subject to aerodynamic heating during flight. Time-dependent incident heat flux is also taken into account. Two different cases with heat flux and radiation boundary conditions are studied and discussed. The results are compared with those obtained by finite element analyses and show a good agreement. Although temperature profiles of such problems can be readily accessed via numerical simulations, analytical solutions give a greater insight into the physical essence of the heat transfer problem. Furthermore, with the analytical approach, rapid thermal analyses and even thermal optimization can be achieved during the preliminary TPS design.

Radon transport model into a porous ground layer of finite capacity

NASA Astrophysics Data System (ADS)

Parovik, Roman

2017-10-01

The model of radon transfer is considered in a porous ground layer of finite power. With the help of the Laplace integral transformation, a numerical solution of this model is obtained which is based on the construction of a generalized quadrature formula of the highest degree of accuracy for the transition to the original - the function of solving this problem. The calculated curves are constructed and investigated depending on the diffusion and advection coefficients.The work was a mathematical model that describes the effect of the sliding attachment (stick-slip), taking into account hereditarity. This model can be regarded as a mechanical model of earthquake preparation. For such a model was proposed explicit finite- difference scheme, on which were built the waveform and phase trajectories hereditarity effect of stick-slip.

Exact solution and precise asymptotics of a Fisher-KPP type front

NASA Astrophysics Data System (ADS)

Berestycki, Julien; Brunet, Éric; Derrida, Bernard

2018-01-01

The present work concerns a version of the Fisher-KPP equation where the nonlinear term is replaced by a saturation mechanism, yielding a free boundary problem with mixed conditions. Following an idea proposed in Brunet and Derrida (2015 J. Stat. Phys. 161 801), we show that the Laplace transform of the initial condition is directly related to some functional of the front position μt . We then obtain precise asymptotics of the front position by means of singularity analysis. In particular, we recover the so-called Ebert and van Saarloos correction (Ebert and van Saarloos 2000 Physica D 146 1), we obtain an additional term of order log t /t in this expansion, and we give precise conditions on the initial condition for those terms to be present.

Steady/unsteady aerodynamic analysis of wings at subsonic, sonic and supersonic Mach numbers using a 3D panel method

NASA Astrophysics Data System (ADS)

Cho, Jeonghyun; Han, Cheolheui; Cho, Leesang; Cho, Jinsoo

2003-08-01

This paper treats the kernel function of an integral equation that relates a known or prescribed upwash distribution to an unknown lift distribution for a finite wing. The pressure kernel functions of the singular integral equation are summarized for all speed range in the Laplace transform domain. The sonic kernel function has been reduced to a form, which can be conveniently evaluated as a finite limit from both the subsonic and supersonic sides when the Mach number tends to one. Several examples are solved including rectangular wings, swept wings, a supersonic transport wing and a harmonically oscillating wing. Present results are given with other numerical data, showing continuous results through the unit Mach number. Computed results are in good agreement with other numerical results.

Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass

NASA Technical Reports Server (NTRS)

Saleh, B. E. A.; Tavolacci, J. T.; Teich, M. C.

1981-01-01

Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.

Kinetics analysis and quantitative calculations for the successive radioactive decay process

NASA Astrophysics Data System (ADS)

Zhou, Zhiping; Yan, Deyue; Zhao, Yuliang; Chai, Zhifang

2015-01-01

The general radioactive decay kinetics equations with branching were developed and the analytical solutions were derived by Laplace transform method. The time dependence of all the nuclide concentrations can be easily obtained by applying the equations to any known radioactive decay series. Taking the example of thorium radioactive decay series, the concentration evolution over time of various nuclide members in the family has been given by the quantitative numerical calculations with a computer. The method can be applied to the quantitative prediction and analysis for the daughter nuclides in the successive decay with branching of the complicated radioactive processes, such as the natural radioactive decay series, nuclear reactor, nuclear waste disposal, nuclear spallation, synthesis and identification of superheavy nuclides, radioactive ion beam physics and chemistry, etc.

Three novel approaches to structural identifiability analysis in mixed-effects models.

PubMed

Janzén, David L I; Jirstrand, Mats; Chappell, Michael J; Evans, Neil D

2016-05-06

Structural identifiability is a concept that considers whether the structure of a model together with a set of input-output relations uniquely determines the model parameters. In the mathematical modelling of biological systems, structural identifiability is an important concept since biological interpretations are typically made from the parameter estimates. For a system defined by ordinary differential equations, several methods have been developed to analyse whether the model is structurally identifiable or otherwise. Another well-used modelling framework, which is particularly useful when the experimental data are sparsely sampled and the population variance is of interest, is mixed-effects modelling. However, established identifiability analysis techniques for ordinary differential equations are not directly applicable to such models. In this paper, we present and apply three different methods that can be used to study structural identifiability in mixed-effects models. The first method, called the repeated measurement approach, is based on applying a set of previously established statistical theorems. The second method, called the augmented system approach, is based on augmenting the mixed-effects model to an extended state-space form. The third method, called the Laplace transform mixed-effects extension, is based on considering the moment invariants of the systems transfer function as functions of random variables. To illustrate, compare and contrast the application of the three methods, they are applied to a set of mixed-effects models. Three structural identifiability analysis methods applicable to mixed-effects models have been presented in this paper. As method development of structural identifiability techniques for mixed-effects models has been given very little attention, despite mixed-effects models being widely used, the methods presented in this paper provides a way of handling structural identifiability in mixed-effects models previously not possible. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Existence results for degenerate p(x)-Laplace equations with Leray-Lions type operators

NASA Astrophysics Data System (ADS)

Ho, Ky; Sim, Inbo

2017-01-01

We show the various existence results for degenerate $p(x)$-Laplace equations with Leray-Lions type operators. A suitable condition on degeneracy is discussed and proofs are mainly based on direct methods and critical point theories in Calculus of Variations. In particular, we investigate the various situations of the growth rates between principal operators and nonlinearities.

Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

PubMed

Kiselev, Aleksei P; Plachenov, Alexandr B

2016-04-01

The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.

Anisotropic Laplace-Beltrami Eigenmaps: Bridging Reeb Graphs and Skeletons*

PubMed Central

Shi, Yonggang; Lai, Rongjie; Krishna, Sheila; Sicotte, Nancy; Dinov, Ivo; Toga, Arthur W.

2010-01-01

In this paper we propose a novel approach of computing skeletons of robust topology for simply connected surfaces with boundary by constructing Reeb graphs from the eigenfunctions of an anisotropic Laplace-Beltrami operator. Our work brings together the idea of Reeb graphs and skeletons by incorporating a flux-based weight function into the Laplace-Beltrami operator. Based on the intrinsic geometry of the surface, the resulting Reeb graph is pose independent and captures the global profile of surface geometry. Our algorithm is very efficient and it only takes several seconds to compute on neuroanatomical structures such as the cingulate gyrus and corpus callosum. In our experiments, we show that the Reeb graphs serve well as an approximate skeleton with consistent topology while following the main body of conventional skeletons quite accurately. PMID:21339850

X-ray analysis of residual stress gradients in TiN coatings by a Laplace space approach and cross-sectional nanodiffraction: a critical comparison.

PubMed

Stefenelli, Mario; Todt, Juraj; Riedl, Angelika; Ecker, Werner; Müller, Thomas; Daniel, Rostislav; Burghammer, Manfred; Keckes, Jozef

2013-10-01

Novel scanning synchrotron cross-sectional nanobeam and conventional laboratory as well as synchrotron Laplace X-ray diffraction methods are used to characterize residual stresses in exemplary 11.5 µm-thick TiN coatings. Both real and Laplace space approaches reveal a homogeneous tensile stress state and a very pronounced compressive stress gradient in as-deposited and blasted coatings, respectively. The unique capabilities of the cross-sectional approach operating with a beam size of 100 nm in diameter allow the analysis of stress variation with sub-micrometre resolution at arbitrary depths and the correlation of the stress evolution with the local coating microstructure. Finally, advantages and disadvantages of both approaches are extensively discussed.

On initial orbit determination

NASA Technical Reports Server (NTRS)

Taff, L. G.

1984-01-01

The classical methods of initial orbit determination are brought together within a larger viewpoint. This new synthesis stresses that all such techniques follow one of three approaches. Either they seek to compute the orbital element set, or its equivalent, by attacking the differential equations of motion (Laplace), the first integrals of the equations of motion (Taff), or the solution itself (Gauss). The particular technique pursued within a given type of approach should depend upon the nature of the observational data, the amount of a priori information one is willing to presume, and the object of the exercise. This might be a binary star system, a moon, a minor planet, or an artificial satellite. The efficacy of some algorithms for each approach is discussed briefly. Unfortunately, none of them work very well. Extensions of these techniques to radars or laser radars are trivial and have provided no new insights into the overall problem.

Solving the transient water age distribution problem in environmental flow systems

NASA Astrophysics Data System (ADS)

Cornaton, F. J.

2011-12-01

The temporal evolution of groundwater age and its frequency distributions can display important changes as flow regimes vary due to the natural change in climate and hydrologic conditions and/or to human induced pressures on the resource to satisfy the water demand. Groundwater age being nowadays frequently used to investigate reservoir properties and recharge conditions, special attention needs to be put on the way this property is characterized, would it be using isotopic methods, multiple tracer techniques, or mathematical modelling. Steady-state age frequency distributions can be modelled using standard numerical techniques, since the general balance equation describing age transport under steady-state flow conditions is exactly equivalent to a standard advection-dispersion equation. The time-dependent problem is however described by an extended transport operator that incorporates an additional coordinate for water age. The consequence is that numerical solutions can hardly be achieved, especially for real 3-D applications over large time periods of interest. The absence of any robust method has thus left us in the quantitative hydrogeology community dodging the issue of transience. Novel algorithms for solving the age distribution problem under time-varying flow regimes are presented and, for some specific configurations, extended to the problem of generalized component exposure time. The solution strategy is based on the combination of the Laplace Transform technique applied to the age (or exposure time) coordinate with standard time-marching schemes. The method is well-suited for groundwater problems with possible density-dependency of fluid flow (e.g. coupled flow and heat/salt concentration problems), but also presents significance to the homogeneous flow (compressible case) problem. The approach is validated using 1-D analytical solutions and exercised on some demonstration problems that are relevant to topical issues in groundwater age, including analysis of transfer times in the vadose zone, aquifer-aquitard interactions and the induction of transient age distributions when a well pump is started.

Analytical solutions to compartmental indoor air quality models with application to environmental tobacco smoke concentrations measured in a house.

PubMed

Ott, Wayne R; Klepeis, Neil E; Switzer, Paul

2003-08-01

This paper derives the analytical solutions to multi-compartment indoor air quality models for predicting indoor air pollutant concentrations in the home and evaluates the solutions using experimental measurements in the rooms of a single-story residence. The model uses Laplace transform methods to solve the mass balance equations for two interconnected compartments, obtaining analytical solutions that can be applied without a computer. Environmental tobacco smoke (ETS) sources such as the cigarette typically emit pollutants for relatively short times (7-11 min) and are represented mathematically by a "rectangular" source emission time function, or approximated by a short-duration source called an "impulse" time function. Other time-varying indoor sources also can be represented by Laplace transforms. The two-compartment model is more complicated than the single-compartment model and has more parameters, including the cigarette or combustion source emission rate as a function of time, room volumes, compartmental air change rates, and interzonal air flow factors expressed as dimensionless ratios. This paper provides analytical solutions for the impulse, step (Heaviside), and rectangular source emission time functions. It evaluates the indoor model in an unoccupied two-bedroom home using cigars and cigarettes as sources with continuous measurements of carbon monoxide (CO), respirable suspended particles (RSP), and particulate polycyclic aromatic hydrocarbons (PPAH). Fine particle mass concentrations (RSP or PM3.5) are measured using real-time monitors. In our experiments, simultaneous measurements of concentrations at three heights in a bedroom confirm an important assumption of the model-spatial uniformity of mixing. The parameter values of the two-compartment model were obtained using a "grid search" optimization method, and the predicted solutions agreed well with the measured concentration time series in the rooms of the home. The door and window positions in each room had considerable effect on the pollutant concentrations observed in the home. Because of the small volumes and low air change rates of most homes, indoor pollutant concentrations from smoking activity in a home can be very high and can persist at measurable levels indoors for many hours.

Kepler unbound: Some elegant curiosities of classical mechanics

NASA Astrophysics Data System (ADS)

MacKay, Niall J.; Salour, Sam

2015-01-01

We explain two exotic systems of classical mechanics: the McIntosh-Cisneros-Zwanziger ("MICZ") Kepler system, of motion of a charged particle in the presence of a modified dyon; and Gibbons and Manton's description of the slow motion of well-separated solitonic ("BPS") monopoles using Taub-NUT space. Each system is characterized by the conservation of a Laplace-Runge-Lenz vector, and we use elementary vector techniques to show that each obeys a subtly different variation on Kepler's three laws for the Newton-Coulomb two-body problem, including a new modified Kepler third law for BPS monopoles.

Piecewise uniform conduction-like flow channels and method therefor

DOEpatents

Cummings, Eric B [Livermore, CA; Fiechtner, Gregory J [Livermore, CA

2006-02-28

A low-dispersion methodology for designing microfabricated conduction channels for on-chip electrokinetic-based systems is presented. The technique relies on trigonometric relations that apply for ideal electrokinetic flows, allowing faceted channels to be designed on chips using common drafting software and a hand calculator. Flows are rotated and stretched along the abrupt interface between adjacent regions with differing permeability. Regions bounded by interfaces form flow "prisms" that can be combined with other designed prisms to obtain a wide range of turning angles and expansion ratios while minimizing dispersion. Designs are demonstrated using two-dimensional numerical solutions of the Laplace equation.

Diffusion accessibility as a method for visualizing macromolecular surface geometry.

PubMed

Tsai, Yingssu; Holton, Thomas; Yeates, Todd O

2015-10-01

Important three-dimensional spatial features such as depth and surface concavity can be difficult to convey clearly in the context of two-dimensional images. In the area of macromolecular visualization, the computer graphics technique of ray-tracing can be helpful, but further techniques for emphasizing surface concavity can give clearer perceptions of depth. The notion of diffusion accessibility is well-suited for emphasizing such features of macromolecular surfaces, but a method for calculating diffusion accessibility has not been made widely available. Here we make available a web-based platform that performs the necessary calculation by solving the Laplace equation for steady state diffusion, and produces scripts for visualization that emphasize surface depth by coloring according to diffusion accessibility. The URL is http://services.mbi.ucla.edu/DiffAcc/. © 2015 The Protein Society.

SPHARA--a generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: application to EEG.

PubMed

Graichen, Uwe; Eichardt, Roland; Fiedler, Patrique; Strohmeier, Daniel; Zanow, Frank; Haueisen, Jens

2015-01-01

Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.

Solar System constraints on renormalization group extended general relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

NASA Astrophysics Data System (ADS)

Rodrigues, Davi C.; Mauro, Sebastião; de Almeida, Álefe O. F.

2016-10-01

General relativity extensions based on renormalization group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post-Newtonian limits of a realization called renormalization group extended general relativity (RGGR). Special attention is given to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter ν¯⊙, and this parameter is such that for ν¯⊙=0 one fully recovers GR in the Solar System. Previously this parameter was constrained to be |ν¯ ⊙|≲10-21 , without considering the external potential effect. Here we show that under a certain approximation RGGR can be cast in a form compatible with the parametrized post-Newtonian (PPN) formalism, and we use both the PPN formalism and the Laplace-Runge-Lenz technique to put new bounds on ν¯⊙, either considering or not the external potential effect. With the external potential effect the new bound reads |ν¯ ⊙|≲10-16 . We discuss the possible consequences of this bound on the dark matter abundance in galaxies.

PULSAR SIGNAL DENOISING METHOD BASED ON LAPLACE DISTRIBUTION IN NO-SUBSAMPLING WAVELET PACKET DOMAIN

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

Wenbo, Wang; Yanchao, Zhao; Xiangli, Wang

2016-11-01

In order to improve the denoising effect of the pulsar signal, a new denoising method is proposed in the no-subsampling wavelet packet domain based on the local Laplace prior model. First, we count the true noise-free pulsar signal’s wavelet packet coefficient distribution characteristics and construct the true signal wavelet packet coefficients’ Laplace probability density function model. Then, we estimate the denosied wavelet packet coefficients by using the noisy pulsar wavelet coefficients based on maximum a posteriori criteria. Finally, we obtain the denoisied pulsar signal through no-subsampling wavelet packet reconstruction of the estimated coefficients. The experimental results show that the proposed method performs better when calculating the pulsar time of arrival than the translation-invariant wavelet denoising method.

How do output growth-rate distributions look like? Some cross-country, time-series evidence

NASA Astrophysics Data System (ADS)

Fagiolo, G.; Napoletano, M.; Roventini, A.

2007-05-01

This paper investigates the statistical properties of within-country gross domestic product (GDP) and industrial production (IP) growth-rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether also within-country, time-series GDP and IP growth rates can be approximated by tent-shaped distributions. We fit output growth rates with the exponential-power (Subbotin) family of densities, which includes as particular cases both Gaussian and Laplace distributions. We find that, for a large number of OECD (Organization for Economic Cooperation and Development) countries including the US, both GDP and IP growth rates are Laplace distributed. Moreover, we show that fat-tailed distributions robustly emerge even after controlling for outliers, autocorrelation and heteroscedasticity.

Tests of Fit for Asymmetric Laplace Distributions with Applications on Financial Data

NASA Astrophysics Data System (ADS)

Fragiadakis, Kostas; Meintanis, Simos G.

2008-11-01

New goodness-of-fit tests for the family of asymmetric Laplace distributions are constructed. The proposed tests are based on a weighted integral incorporating the empirical characteristic function of suitably standardized data, and can be written in a closed form appropriate for computer implementation. Monte Carlo results show that the new procedure are competitive with classical goodness-of-fit methods. Applications with financial data are also included.

DYNAMICAL INSTABILITIES IN HIGH-OBLIQUITY SYSTEMS

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

Tamayo, D.; Nicholson, P. D.; Burns, J. A.

2013-03-01

High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations-large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. found that, for planets with obliquities >68. Degree-Sign 875, orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range and execute large-amplitude chaotic oscillations in eccentricity and inclination. In the hope of making that treatment more easily understandable, we analyze the problem using orbital elements, confirming this threshold obliquity. Furthermore, we findmore » that orbits inclined to the Laplace plane will be unstable over a broader radial range, and that such orbits can go unstable for obliquities less than 68. Degree-Sign 875. Finally, we analyze the added effects of radiation pressure, which are important for dust grains and provide a natural mechanism for particle semimajor axes to sweep via Poynting-Robertson drag through any unstable range. For low-eccentricity orbits in the equilibrium Laplace plane, we find that generally the effect persists; however, the unstable radial range is shifted and small retrograde particles can avoid the instability altogether. We argue that this occurs because radiation pressure modifies the equilibrium Laplace plane.« less

Chaotic diffusion in the Gliese-876 planetary system

NASA Astrophysics Data System (ADS)

Martí, J. G.; Cincotta, P. M.; Beaugé, C.

2016-07-01

Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disc, and a natural consequence of irregular motion. In this paper, we show that resonant multiplanetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and may still survive virtually unchanged over time-scales comparable to their age. Using the GJ-876 system as an example, we analyse the chaotic diffusion of the outermost (and less massive) planet. We construct a set of stability maps in the surrounding regions of the Laplace resonance. We numerically integrate ensembles of close initial conditions, compute Poincaré maps and estimate the chaotic diffusion present in this system. Our results show that, the Laplace resonance contains two different regions: an inner domain characterized by low chaoticity and slow diffusion, and an outer one displaying larger values of dynamical indicators. In the outer resonant domain, the stochastic borders of the Laplace resonance seem to prevent the complete destruction of the system. We characterize the diffusion for small ensembles along the parameters of the outermost planet. Finally, we perform a stability analysis of the inherent chaotic, albeit stable Laplace resonance, by linking the behaviour of the resonant variables of the configurations to the different sub-structures inside the three-body resonance.

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

A novel model of photothermal diffusion (PTD) for polymer nano-composite semiconducting of thin circular plate

NASA Astrophysics Data System (ADS)

Lotfy, Kh.

2018-05-01

In this article, theoretical discussions for a novel mathematical-physical Photothermal diffusion (PTD) model in the generalized thermoelasticity theory with photothermal processes and chemical action are introduced. The mean idea of this model depends on the interaction between quasi-particles (plasma waves) that depends on the kind of the used materials, the mechanical forces acting on the surface, the generalized thermo and mass diffusion (due to coupling of temperature fields with thermal waves and chemical potential) and the elastic waves. The one dimensional Laplace transforms is used to obtain the exact solution for some physical and chemical quantities for a thin circular plate of a semiconducting polymer nanocomposite such as silicon (Si). New variables are deduced and discussed. The obtained results of the physical quantities are presented analytically and illustrated graphically with some important applications.

Bending and stretching finite element analysis of anisotropic viscoelastic composite plates

NASA Technical Reports Server (NTRS)

Hilton, Harry H.; Yi, Sung

1990-01-01

Finite element algorithms have been developed to analyze linear anisotropic viscoelastic plates, with or without holes, subjected to mechanical (bending, tension), temperature, and hygrothermal loadings. The analysis is based on Laplace transforms rather than direct time integrations in order to improve the accuracy of the results and save on extensive computational time and storage. The time dependent displacement fields in the transverse direction for the cross ply and angle ply laminates are calculated and the stacking sequence effects of the laminates are discussed in detail. Creep responses for the plates with or without a circular hole are also studied. The numerical results compare favorably with analytical solutions, i.e. within 1.8 percent for bending and 10(exp -3) 3 percent for tension. The tension results of the present method are compared with those using the direct time integration scheme.

FDTD modelling of induced polarization phenomena in transient electromagnetics

NASA Astrophysics Data System (ADS)

Commer, Michael; Petrov, Peter V.; Newman, Gregory A.

2017-04-01

The finite-difference time-domain scheme is augmented in order to treat the modelling of transient electromagnetic signals containing induced polarization effects from 3-D distributions of polarizable media. Compared to the non-dispersive problem, the discrete dispersive Maxwell system contains costly convolution operators. Key components to our solution for highly digitized model meshes are Debye decomposition and composite memory variables. We revert to the popular Cole-Cole model of dispersion to describe the frequency-dependent behaviour of electrical conductivity. Its inversely Laplace-transformed Debye decomposition results in a series of time convolutions between electric field and exponential decay functions, with the latter reflecting each Debye constituents' individual relaxation time. These function types in the discrete-time convolution allow for their substitution by memory variables, annihilating the otherwise prohibitive computing demands. Numerical examples demonstrate the efficiency and practicality of our algorithm.

Dynamic response of porous functionally graded material nanobeams subjected to moving nanoparticle based on nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Barati, Mohammad Reza

2017-11-01

Up to now, nonlocal strain gradient theory (NSGT) is broadly applied to examine free vibration, static bending and buckling of nanobeams. This theory captures nonlocal stress field effects together with the microstructure-dependent strain gradient effects. In this study, forced vibrations of NSGT nanobeams on elastic substrate subjected to moving loads are examined. The nanobeam is made of functionally graded material (FGM) with even and uneven porosity distributions inside the material structure. The graded material properties with porosities are described by a modified power-law model. Dynamic deflection of the nanobeam is obtained via Galerkin and inverse Laplace transform methods. The importance of nonlocal parameter, strain gradient parameter, moving load velocity, porosity volume fraction, type of porosity distribution and elastic foundation on forced vibration behavior of nanobeams are discussed.

Propagation of waves from an arbitrary shaped surface-A generalization of the Fresnel diffraction integral

NASA Astrophysics Data System (ADS)

Feshchenko, R. M.; Vinogradov, A. V.; Artyukov, I. A.

2018-04-01

Using the method of Laplace transform the field amplitude in the paraxial approximation is found in the two-dimensional free space using initial values of the amplitude specified on an arbitrary shaped monotonic curve. The obtained amplitude depends on one a priori unknown function, which can be found from a Volterra first kind integral equation. In a special case of field amplitude specified on a concave parabolic curve the exact solution is derived. Both solutions can be used to study the light propagation from arbitrary surfaces including grazing incidence X-ray mirrors. They can find applications in the analysis of coherent imaging problems of X-ray optics, in phase retrieval algorithms as well as in inverse problems in the cases when the initial field amplitude is sought on a curved surface.

Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays

NASA Astrophysics Data System (ADS)

Yang, Hongyong; Han, Fujun; Zhao, Mei; Zhang, Shuning; Yue, Jun

2017-08-01

Because many networked systems can only be characterized with fractional-order dynamics in complex environments, fractional-order calculus has been studied deeply recently. When diverse individual features are shown in different agents of networked systems, heterogeneous fractional-order dynamics will be used to describe the complex systems. Based on the distinguishing properties of agents, heterogeneous fractional-order multi-agent systems (FOMAS) are presented. With the supposition of multiple leader agents in FOMAS, distributed containment control of FOMAS is studied in directed weighted topologies. By applying Laplace transformation and frequency domain theory of the fractional-order operator, an upper bound of delays is obtained to ensure containment consensus of delayed heterogenous FOMAS. Consensus results of delayed FOMAS in this paper can be extended to systems with integer-order models. Finally, numerical examples are used to verify our results.

Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

NASA Astrophysics Data System (ADS)

Azadbakht, F. Teimoury; Boroun, G. R.

2018-02-01

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions δ FS(x,Q2)=F[partial δ FS0(x), δ FS0(x)] and {δ G}(x,Q2)=G[partial δ G0(x), δ G0(x)]. We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC'08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.

``Models'' CAVEAT EMPTOR!!!: ``Toy Models Too-Often Yield Toy-Results''!!!: Statistics, Polls, Politics, Economics, Elections!!!: GRAPH/Network-Physics: ``Equal-Distribution for All'' TRUMP-ED BEC ``Winner-Take-All'' ``Doctor Livingston I Presume?''

NASA Astrophysics Data System (ADS)

Preibus-Norquist, R. N. C.-Grover; Bush-Romney, G. W.-Willard-Mitt; Dimon, J. P.; Adelson-Koch, Sheldon-Charles-David-Sheldon; Krugman-Axelrod, Paul-David; Siegel, Edward Carl-Ludwig; D. N. C./O. F. P./''47''%/50% Collaboration; R. N. C./G. O. P./''53''%/49% Collaboration; Nyt/Wp/Cnn/Msnbc/Pbs/Npr/Ft Collaboration; Ftn/Fnc/Fox/Wsj/Fbn Collaboration; Lb/Jpmc/Bs/Boa/Ml/Wamu/S&P/Fitch/Moodys/Nmis Collaboration

2013-03-01

``Models''? CAVEAT EMPTOR!!!: ``Toy Models Too-Often Yield Toy-Results''!!!: Goldenfeld[``The Role of Models in Physics'', in Lects.on Phase-Transitions & R.-G.(92)-p.32-33!!!]: statistics(Silver{[NYTimes; Bensinger, ``Math-Geerks Clearly-Defeated Pundits'', LATimes, (11/9/12)])}, polls, politics, economics, elections!!!: GRAPH/network/net/...-PHYSICS Barabasi-Albert[RMP (02)] (r,t)-space VERSUS(???) [Where's the Inverse/ Dual/Integral-Transform???] (Benjamin)Franklin(1795)-Fourier(1795; 1897;1822)-Laplace(1850)-Mellin (1902) Brillouin(1922)-...(k,)-space, {Hubbard [The World According to Wavelets,Peters (96)-p.14!!!/p.246: refs.-F2!!!]},and then (2) Albert-Barabasi[]Bose-Einstein quantum-statistics(BEQS) Bose-Einstein CONDENSATION (BEC) versus Bianconi[pvt.-comm.; arXiv:cond-mat/0204506; ...] -Barabasi [???] Fermi-Dirac

Generalized Langevin equation with a three parameter Mittag-Leffler noise

NASA Astrophysics Data System (ADS)

Sandev, Trifce; Tomovski, Živorad; Dubbeldam, Johan L. A.

2011-10-01

The relaxation functions for a given generalized Langevin equation in the presence of a three parameter Mittag-Leffler noise are studied analytically. The results are represented by three parameter Mittag-Leffler functions. Exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the Laplace transform method. The asymptotic behavior of the particle in the short and long time limits are found by using the Tauberian theorems. It is shown that for large times the particle motion is subdiffusive for β-1<αδ<β, and superdiffusive for β<αδ. Many previously obtained results are recovered. Due to the many parameters contained in the noise term, the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media.

The theory of nonstationary thermophoresis of a solid spherical particle

NASA Astrophysics Data System (ADS)

Kuzmin, M. K.; Yalamov, Yu. I.

2007-06-01

The theory of nonstationary thermophoresis of a solid spherical particle in a viscous gaseous medium is presented. The theory is constructed on the solutions of fluid-dynamics and thermal problems, each of which is split into stationary and strictly nonstationary parts. The solution of the stationary parts of the problems gives the final formula for determining the stationary component of the thermophoretic velocity of this particle. To determine the nonstationary component of the thermophoretic velocity of the particle, the corresponding formula in the space of Laplace transforms is derived. The limiting value theorems from operational calculus are used for obtaining the dependence of the nonstationary component of the thermophoretic velocity of the spherical particle on the strictly nonstationary temperature gradient for large and small values of time. The factors determining the thermophoretic velocity of the particle under investigation are determined.

A simple method to calculate first-passage time densities with arbitrary initial conditions

NASA Astrophysics Data System (ADS)

Nyberg, Markus; Ambjörnsson, Tobias; Lizana, Ludvig

2016-06-01

Numerous applications all the way from biology and physics to economics depend on the density of first crossings over a boundary. Motivated by the lack of general purpose analytical tools for computing first-passage time densities (FPTDs) for complex problems, we propose a new simple method based on the independent interval approximation (IIA). We generalise previous formulations of the IIA to include arbitrary initial conditions as well as to deal with discrete time and non-smooth continuous time processes. We derive a closed form expression for the FPTD in z and Laplace-transform space to a boundary in one dimension. Two classes of problems are analysed in detail: discrete time symmetric random walks (Markovian) and continuous time Gaussian stationary processes (Markovian and non-Markovian). Our results are in good agreement with Langevin dynamics simulations.

Multidimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rodrigues, M. M.; Vieira, N.

2012-11-01

This work is intended to investigate the multi-dimensional space-time fractional Schrödinger equation of the form (CDt0+αu)(t,x) = iħ/2m(C∇βu)(t,x), with ħ the Planck's constant divided by 2π, m is the mass and u(t,x) is a wave function of the particle. Here (CDt0+α,C∇β are operators of the Caputo fractional derivatives, where α ∈]0,1] and β ∈]1,2]. The wave function is obtained using Laplace and Fourier transforms methods and a symbolic operational form of solutions in terms of the Mittag-Leffler functions is exhibited. It is presented an expression for the wave function and for the quantum mechanical probability density. Using Banach fixed point theorem, the existence and uniqueness of solutions is studied for this kind of fractional differential equations.

Relaxation in a two-body Fermi-Pasta-Ulam system in the canonical ensemble

NASA Astrophysics Data System (ADS)

Sen, Surajit; Barrett, Tyler

The study of the dynamics of the Fermi-Pasta-Ulam (FPU) chain remains a challenging problem. Inspired by the recent work of Onorato et al. on thermalization in the FPU system, we report a study of relaxation processes in a two-body FPU system in the canonical ensemble. The studies have been carried out using the Recurrence Relations Method introduced by Zwanzig, Mori, Lee and others. We have obtained exact analytical expressions for the first thirteen levels of the continued fraction representation of the Laplace transformed velocity autocorrelation function of the system. Using simple and reasonable extrapolation schemes and known limits we are able to estimate the relaxation behavior of the oscillators in the two-body FPU system and recover the expected behavior in the harmonic limit. Generalizations of the calculations to larger systems will be discussed.

Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics, production version (SOUSSA-P 1.1). Volume 1: Theoretical manual. [Green function

NASA Technical Reports Server (NTRS)

Morino, L.

1980-01-01

Recent developments of the Green's function method and the computer program SOUSSA (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed and summarized. Applying the Green's function method to the fully unsteady (transient) potential equation yields an integro-differential-delay equation. With spatial discretization by the finite-element method, this equation is approximated by a set of differential-delay equations in time. Time solution by Laplace transform yields a matrix relating the velocity potential to the normal wash. Premultiplying and postmultiplying by the matrices relating generalized forces to the potential and the normal wash to the generalized coordinates one obtains the matrix of the generalized aerodynamic forces. The frequency and mode-shape dependence of this matrix makes the program SOUSSA useful for multiple frequency and repeated mode-shape evaluations.

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

NASA Astrophysics Data System (ADS)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Pattern formation in superdiffusion Oregonator model

NASA Astrophysics Data System (ADS)

Feng, Fan; Yan, Jia; Liu, Fu-Cheng; He, Ya-Feng

2016-10-01

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional (2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction-diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor. Project supported by the National Natural Science Foundation of China (Grant Nos. 11205044 and 11405042), the Research Foundation of Education Bureau of Hebei Province, China (Grant Nos. Y2012009 and ZD2015025), the Program for Young Principal Investigators of Hebei Province, China, and the Midwest Universities Comprehensive Strength Promotion Project.