Lagrangian derivation of the two coupled field equations in the Janus cosmological model

NASA Astrophysics Data System (ADS)

Petit, Jean-Pierre; D'Agostini, G.

2015-05-01

After a review citing the results obtained in previous articles introducing the Janus Cosmological Model, consisting of a set of two coupled field equations, where one metrics refers to the positive masses and the other to the negative masses, which explains the observed cosmic acceleration and the nature of dark energy, we present the Lagrangian derivation of the model.

Development of demi-span equations for predicting height among the Malaysian elderly.

PubMed

Ngoh, H J; Sakinah, H; Harsa Amylia, M S

2012-08-01

This study aimed to develop demi-span equations for predicting height in the Malaysian elderly and to explore the applicability of previous published demi-span equations derived from adult populations to the elderly. A cross-sectional study was conducted on Malaysian elderly aged 60 years and older. Subjects were residents of eight shelter homes in Peninsular Malaysia; 204 men and 124 women of Malay, Chinese and Indian ethnicity were included. Measurements of weight, height and demi-span were obtained using standard procedures. Statistical analyses were performed using SPSS version 18.0. The demi-span equations obtained were as follows: Men: Height (cm) = 67.51 + (1.29 x demi-span) - (0.12 x age) + 4.13; Women: Height (cm) = 67.51 + (1.29 x demi-span) - (0.12 x age). Height predicted from these new equations demonstrated good agreement with measured height and no significant differences were found between the mean values of predicted and measured heights in either gender (p>0.05). However, the heights predicted from previous published adult-derived demi-span equations failed to yield good agreement with the measured height of the elderly; significant over-estimation and underestimation of heights tended to occur (p>0.05). The new demi-span equations allow prediction of height with sufficient accuracy in the Malaysian elderly. However, further validation on other elderly samples is needed. Also, we recommend caution when using adult-derived demi-span equations to predict height in elderly people.

Hagedorn Temperature of AdS5/CFT4 via Integrability

NASA Astrophysics Data System (ADS)

Harmark, Troels; Wilhelm, Matthias

2018-02-01

We establish a framework for calculating the Hagedorn temperature of AdS5/CFT4 via integrability. Concretely, we derive the thermodynamic Bethe ansatz equations that yield the Hagedorn temperature of planar N =4 super Yang-Mills theory at any value of the 't Hooft coupling. We solve these equations perturbatively at weak coupling via the associated Y system, confirming the known results at tree level and one-loop order as well as deriving the previously unknown two-loop Hagedorn temperature. Finally, we comment on solving the equations at finite coupling.

Exact renormalization group equation for the Lifshitz critical point

NASA Astrophysics Data System (ADS)

Bervillier, C.

2004-10-01

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

Exergy Analysis of Rocket Systems

NASA Technical Reports Server (NTRS)

Gilbert, Andrew; Mesmer, Bryan; Watson, Michael D.

2015-01-01

Exergy is defined as the useful work available from a system in a specified environment. Exergy analysis allows for comparison between different system designs, and allows for comparison of subsystem efficiencies within system designs. The proposed paper explores the relationship between the fundamental rocket equation and an exergy balance equation. A previously derived exergy equation related to rocket systems is investigated, and a higher fidelity analysis will be derived. The exergy assessments will enable informed, value-based decision making when comparing alternative rocket system designs, and will allow the most efficient configuration among candidate configurations to be determined.

On the Melting Curve of Sulfur Hexafluoride

NASA Astrophysics Data System (ADS)

Harvey, Allan H.

2017-12-01

A previous correlation for the melting curve of sulfur hexafluoride (SF6) is inconsistent with the thermodynamic slope at the triple point derived from the Clapeyron equation. It is shown that this is probably due to the previous authors combining an accurate measurement of the triple point with melting-curve data that were distorted by impurities. A new equation is proposed that is consistent with the Clapeyron slope.

The Dissipation Rate Transport Equation and Subgrid-Scale Models in Rotating Turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Ye, Zhou

1997-01-01

The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties arc increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dissipation rate transport equation and subgrid scale models for rotating turbulence are derived from an analytical statistical theory of rotating turbulence. In the strong rotation limit, the theory predicts a turbulent steady state in which the inertial range energy spectrum scales as k(sup -2) and the turbulent time scale is the inverse rotation rate. This scaling has been derived previously by heuristic arguments.

Search algorithm complexity modeling with application to image alignment and matching

NASA Astrophysics Data System (ADS)

DelMarco, Stephen

2014-05-01

Search algorithm complexity modeling, in the form of penetration rate estimation, provides a useful way to estimate search efficiency in application domains which involve searching over a hypothesis space of reference templates or models, as in model-based object recognition, automatic target recognition, and biometric recognition. The penetration rate quantifies the expected portion of the database that must be searched, and is useful for estimating search algorithm computational requirements. In this paper we perform mathematical modeling to derive general equations for penetration rate estimates that are applicable to a wide range of recognition problems. We extend previous penetration rate analyses to use more general probabilistic modeling assumptions. In particular we provide penetration rate equations within the framework of a model-based image alignment application domain in which a prioritized hierarchical grid search is used to rank subspace bins based on matching probability. We derive general equations, and provide special cases based on simplifying assumptions. We show how previously-derived penetration rate equations are special cases of the general formulation. We apply the analysis to model-based logo image alignment in which a hierarchical grid search is used over a geometric misalignment transform hypothesis space. We present numerical results validating the modeling assumptions and derived formulation.

Thermal diffusion of Boussinesq solitons.

PubMed

Arévalo, Edward; Mertens, Franz G

2007-10-01

We consider the problem of the soliton dynamics in the presence of an external noisy force for the Boussinesq type equations. A set of ordinary differential equations (ODEs) of the relevant coordinates of the system is derived. We show that for the improved Boussinesq (IBq) equation the set of ODEs has limiting cases leading to a set of ODEs which can be directly derived either from the ill-posed Boussinesq equation or from the Korteweg-de Vries (KdV) equation. The case of a soliton propagating in the presence of damping and thermal noise is considered for the IBq equation. A good agreement between theory and simulations is observed showing the strong robustness of these excitations. The results obtained here generalize previous results obtained in the frame of the KdV equation for lattice solitons in the monatomic chain of atoms.

Geodesic Motion of Particles and Quantum Tunneling from Reissner-Nordström Black Holes in Anti-de Sitter Spacetime

NASA Astrophysics Data System (ADS)

Deng, Gao-Ming; Huang, Yong-Chang

2018-03-01

The geodesics of tunneling particles were derived unnaturally and awkwardly in previous works. For one thing, the previous derivation was inconsistent with the variational principle of action. Moreover, the definition of geodesic equations for massive particles was quite different from that of massless case. Even worse, the relativistic and nonrelativistic foundations were mixed with each other during the past derivation of geodesics. As a highlight, remedying the urgent shortcomings, we improve treatment to derive the geodesic equations of massive and massless particles in a unified and self-consistent way. Besides, we extend to investigate the Hawking radiation via tunneling from Reissner-Nordström black holes in the context of AdS spacetime. Of special interest, the trick of utilizing the first law of black hole thermodynamics manifestly simplifies the calculation of tunneling integration.

A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

NASA Technical Reports Server (NTRS)

Luo, Li-Shi

1998-01-01

A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

On the Connection Between One-and Two-Equation Models of Turbulence

NASA Technical Reports Server (NTRS)

Menter, F. R.; Rai, Man Mohan (Technical Monitor)

1994-01-01

A formalism will be presented that allows the transformation of two-equation eddy viscosity turbulence models into one-equation models. The transformation is based on an assumption that is widely accepted over a large range of boundary layer flows and that has been shown to actually improve predictions when incorporated into two-equation models of turbulence. Based on that assumption, a new one-equation turbulence model will be derived. The new model will be tested in great detail against a previously introduced one-equation model and against its parent two-equation model.

Dynamical density functional theory for arbitrary-shape colloidal fluids including inertia and hydrodynamic interactions

NASA Astrophysics Data System (ADS)

Duran-Olivencia, Miguel A.; Goddard, Ben; Kalliadasis, Serafim

2015-11-01

Over the last few decades the classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become a remarkably powerful tool in the study of colloidal fluids. Recently there has been extensive research to generalise all previous DDFTs finally yielding a general DDFT equation (for spherical particles) which takes into account both inertia and hydrodynamic interactions (HI) which strongly influence non-equilibrium properties. The present work will be devoted to a further generalisation of such a framework to systems of anisotropic particles. To this end, the kinetic equation for the Brownian particle distribution function is derived starting from the Liouville equation and making use of Zwanzig's projection-operator techniques. By averaging over all but one particle, a DDFT equation is finally obtained with some similarities to that for spherical colloids. However, there is now an inevitable translational-rotational coupling which affects the diffusivity of asymmetric particles. Lastly, in the overdamped (high friction) limit the theory is notably simplified leading to a DDFT equation which agrees with previous derivations. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.

Bäcklund Transformations in 10D SUSY Yang-Mills Theories

NASA Astrophysics Data System (ADS)

Gervais, Jean-Loup

A Bäcklund transformation is derived for the Yang's type (super) equations previously derived (hep-th/9811108) by M. Saveliev and the author, from the ten-dimensional super-Yang-Mills field equations in an on-shell light cone gauge. It is shown to be based upon a particular gauge transformation satisfying nonlinear conditions which ensure that the equations retain the same form. These Yang's type field equations are shown to be precisely such that they automatically provide a solution of these conditions. This Bäcklund transformation is similar to the one proposed by A. Leznov for self-dual Yang-Mills in four dimensions. In the introduction a personal recollection on the birth of supersymmetry is given.

A pseudoenergy wave-activity relation for ageostrophic and non-hydrostatic moist atmosphere

NASA Astrophysics Data System (ADS)

Ran, Ling-Kun; Ping, Fan

2015-05-01

By employing the energy-Casimir method, a three-dimensional virtual pseudoenergy wave-activity relation for a moist atmosphere is derived from a complete system of nonhydrostatic equations in Cartesian coordinates. Since this system of equations includes the effects of water substance, mass forcing, diabatic heating, and dissipations, the derived wave-activity relation generalizes the previous result for a dry atmosphere. The Casimir function used in the derivation is a monotonous function of virtual potential vorticity and virtual potential temperature. A virtual energy equation is employed (in place of the previous zonal momentum equation) in the derivation, and the basic state is stationary but can be three-dimensional or, at least, not necessarily zonally symmetric. The derived wave-activity relation is further used for the diagnosis of the evolution and propagation of meso-scale weather systems leading to heavy rainfall. Our diagnosis of two real cases of heavy precipitation shows that positive anomalies of the virtual pseudoenergy wave-activity density correspond well with the strong precipitation and are capable of indicating the movement of the precipitation region. This is largely due to the cyclonic vorticity perturbation and the vertically increasing virtual potential temperature over the precipitation region. Project supported by the National Basic Research Program of China (Grant No. 2013CB430105), the Key Program of the Chinese Academy of Sciences (Grant No. KZZD-EW-05), the National Natural Science Foundation of China (Grant No. 41175060), and the Project of CAMS, China (Grant No. 2011LASW-B15).

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation. The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied. The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Distribution theory for Schrödinger’s integral equation

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

Lange, Rutger-Jan, E-mail: rutger-jan.lange@cantab.net

2015-12-15

Much of the literature on point interactions in quantum mechanics has focused on the differential form of Schrödinger’s equation. This paper, in contrast, investigates the integral form of Schrödinger’s equation. While both forms are known to be equivalent for smooth potentials, this is not true for distributional potentials. Here, we assume that the potential is given by a distribution defined on the space of discontinuous test functions. First, by using Schrödinger’s integral equation, we confirm a seminal result by Kurasov, which was originally obtained in the context of Schrödinger’s differential equation. This hints at a possible deeper connection between bothmore » forms of the equation. We also sketch a generalisation of Kurasov’s [J. Math. Anal. Appl. 201(1), 297–323 (1996)] result to hypersurfaces. Second, we derive a new closed-form solution to Schrödinger’s integral equation with a delta prime potential. This potential has attracted considerable attention, including some controversy. Interestingly, the derived propagator satisfies boundary conditions that were previously derived using Schrödinger’s differential equation. Third, we derive boundary conditions for “super-singular” potentials given by higher-order derivatives of the delta potential. These boundary conditions cannot be incorporated into the normal framework of self-adjoint extensions. We show that the boundary conditions depend on the energy of the solution and that probability is conserved. This paper thereby confirms several seminal results and derives some new ones. In sum, it shows that Schrödinger’s integral equation is a viable tool for studying singular interactions in quantum mechanics.« less

Protein osmotic pressure gradients and microvascular reflection coefficients.

PubMed

Drake, R E; Dhother, S; Teague, R A; Gabel, J C

1997-08-01

Microvascular membranes are heteroporous, so the mean osmotic reflection coefficient for a microvascular membrane (sigma d) is a function of the reflection coefficient for each pore. Investigators have derived equations for sigma d based on the assumption that the protein osmotic pressure gradient across the membrane (delta II) does not vary from pore to pore. However, for most microvascular membranes, delta II probably does vary from pore to pore. In this study, we derived a new equation for sigma d. According to our equation, pore-to-pore differences in delta II increase the effect of small pores and decrease the effect of large pores on the overall membrane osmotic reflection coefficient. Thus sigma d for a heteroporous membrane may be much higher than previously derived equations indicate. Furthermore, pore-to-pore delta II differences increase the effect of plasma protein osmotic pressure to oppose microvascular fluid filtration.

Simulation of the pulse propagation by the interacting mode parabolic equation method

NASA Astrophysics Data System (ADS)

Trofimov, M. Yu.; Kozitskiy, S. B.; Zakharenko, A. D.

2018-07-01

A broadband modeling of pulses has been performed by using the previously derived interacting mode parabolic equation through the Fourier synthesis. Test examples on the wedge with the angle 2.86∘ (known as the ASA benchmark) show excellent agreement with the source images method.

Unstable solitary-wave solutions of the generalized Benjamin-Bona-Mahony equation

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

McKinney, W.R.; Restrepo, J.M.; Bona, J.L.

1994-06-01

The evolution of solitary waves of the gBBM equation is investigated computationally. The experiments confirm previously derived theoretical stability estimates and, more importantly, yield insights into their behavior. For example, highly energetic unstable solitary waves when perturbed are shown to evolve into several stable solitary waves.

Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation

NASA Technical Reports Server (NTRS)

Spangler, Steven R.

1990-01-01

A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.

Incompressible spectral-element method: Derivation of equations

NASA Technical Reports Server (NTRS)

Deanna, Russell G.

1993-01-01

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

Modeling transport across the running-sandpile cellular automaton by means of fractional transport equations

NASA Astrophysics Data System (ADS)

Sánchez, R.; Newman, D. E.; Mier, J. A.

2018-05-01

Fractional transport equations are used to build an effective model for transport across the running sandpile cellular automaton [Hwa et al., Phys. Rev. A 45, 7002 (1992), 10.1103/PhysRevA.45.7002]. It is shown that both temporal and spatial fractional derivatives must be considered to properly reproduce the sandpile transport features, which are governed by self-organized criticality, at least over sufficiently long or large scales. In contrast to previous applications of fractional transport equations to other systems, the specifics of sand motion require in this case that the spatial fractional derivatives used for the running sandpile must be of the completely asymmetrical Riesz-Feller type. Appropriate values for the fractional exponents that define these derivatives in the case of the running sandpile are obtained numerically.

A unifying fractional wave equation for compressional and shear waves.

PubMed

Holm, Sverre; Sinkus, Ralph

2010-01-01

This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.

Equations of motion of slung load systems with results for dual lift

NASA Technical Reports Server (NTRS)

Cicolani, Luigi S.; Kanning, Gerd

1990-01-01

General simulation equations are derived for the rigid body motion of slung load systems. These systems are viewed as consisting of several rigid bodies connected by straight-line cables or links. The suspension can be assumed to be elastic or inelastic, both cases being of interest in simulation and control studies. Equations for the general system are obtained via D'Alembert's principle and the introduction of generalized velocity coordinates. Three forms are obtained. Two of these generalize previous case-specific results for single helicopter systems with elastic or inelastic suspensions. The third is a new formulation for inelastic suspensions. It is derived from the elastic suspension equations by choosing the generalized coordinates so as to separate motion due to cable stretching from motion with invariant cable lengths. The result is computationally more efficient than the conventional formulation, and is readily integrated with the elastic suspension formulation and readily applied to the complex dual lift and multilift systems. Equations are derived for dual lift systems. Three proposed suspension arrangements can be integrated in a single equation set. The equations are given in terms of the natural vectors and matrices of three-dimensional rigid body mechanics and are tractable for both analysis and programming.

Modeling of Inverted Annular Film Boiling using an integral method

NASA Astrophysics Data System (ADS)

Sridharan, Arunkumar

In modeling Inverted Annular Film Boiling (IAFB), several important phenomena such as interaction between the liquid and the vapor phases and irregular nature of the interface, which greatly influence the momentum and heat transfer at the interface, need to be accounted for. However, due to the complexity of these phenomena, they were not modeled in previous studies. Since two-phase heat transfer equations and relationships rely heavily on experimental data, many closure relationships that were used in previous studies to solve the problem are empirical in nature. Also, in deriving the relationships, the experimental data were often extrapolated beyond the intended range of conditions, causing errors in predictions. In some cases, empirical correlations that were derived from situations other than IAFB, and whose applicability to IAFB was questionable, were used. Moreover, arbitrary constants were introduced in the model developed in previous studies to provide good fit to the experimental data. These constants have no physical basis, thereby leading to questionable accuracy in the model predictions. In the present work, modeling of Inverted Annular Film Boiling (IAFB) is done using Integral Method. Two-dimensional formulation of IAFB is presented. Separate equations for the conservation of mass, momentum and energy are derived from first principles, for the vapor film and the liquid core. Turbulence is incorporated in the formulation. The system of second-order partial differential equations is integrated over the radial direction to obtain a system of integral differential equations. In order to solve the system of equations, second order polynomial profiles are used to describe the nondimensional velocity and temperatures. The unknown coefficients in the profiles are functions of the axial direction alone. Using the boundary conditions that govern the physical problem, equations for the unknown coefficients are derived in terms of the primary dependent variables: wall shear stress, interfacial shear stress, film thickness, pressure, wall temperature and the mass transfer rate due to evaporation. A system of non-linear first order coupled ordinary differential equations is obtained. Due to the inherent mathematical complexity of the system of equations, simplifying assumptions are made to obtain a numerical solution. The system of equations is solved numerically to obtain values of the unknown quantities at each subsequent axial location. Derived quantities like void fraction and heat transfer coefficient are calculated at each axial location. The calculation is terminated when the void fraction reaches a value of 0.6, the upper limit of IAFB. The results obtained agree with the experimental trends observed. Void fraction increases along the heated length, while the heat transfer coefficient drops due to the increased resistance of the vapor film as expected.

An integrable semi-discrete Degasperis-Procesi equation

NASA Astrophysics Data System (ADS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-06-01

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota’s bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

Strong Langmuir Turbulence and Four-Wave Mixing

NASA Astrophysics Data System (ADS)

Glanz, James

1991-02-01

The staircase expansion is a new mathematical technique for deriving reduced, nonlinear-PDE descriptions from the plasma-moment equations. Such descriptions incorporate only the most significant linear and nonlinear terms of more complex systems. The technique is used to derive a set of Dawson-Zakharov or "master" equations, which unify and generalize previous work and show the limitations of models commonly used to describe nonlinear plasma waves. Fundamentally new wave-evolution equations are derived that admit of exact nonlinear solutions (solitary waves). Analytic calculations illustrate the competition between well-known effects of self-focusing, which require coupling to ion motion, and pure-electron nonlinearities, which are shown to be especially important in curved geometries. Also presented is an N -moment hydrodynamic model derived from the Vlasov equation. In this connection, the staircase expansion is shown to remain useful for all values of N >= 3. The relevance of the present work to nonlocally truncated hierarchies, which more accurately model dissipation, is briefly discussed. Finally, the general formalism is applied to the problem of electromagnetic emission from counterpropagating Langmuir pumps. It is found that previous treatments have neglected order-unity effects that increase the emission significantly. Detailed numerical results are presented to support these conclusions. The staircase expansion--so called because of its appearance when written out--should be effective whenever the largest contribution to the nonlinear wave remains "close" to some given frequency. Thus the technique should have application to studies of wake-field acceleration schemes and anomalous damping of plasma waves.

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

Sano, Yukio; Sano, Tomokazu

A quadratic equation for the temperature-independent Grueneisen coefficient {gamma} was derived by a method in which the Walsh-Christian and Mie-Grueneisen equations are combined. Some previously existing ab initio temperature Hugoniots for hexagonal close-packed solid Fe are inaccurate because the constant-volume specific heats on the Hugoniots CVH, which are related uniquely to the solutions of the quadratic equation, have values that are too small. A CVH distribution in the solid phase range was demonstrated to agree approximately with a previous ab initio distribution. In contrast, the corresponding {gamma} distribution was significantly different from the ab initio distribution in the lower pressuremore » region. The causes of these disagreements are clarified.« less

Comment on "Defocusing complex short-pulse equation and its multi-dark-soliton solution"

NASA Astrophysics Data System (ADS)

Youssoufa, Saliou; Kuetche, Victor K.; Kofane, Timoleon C.

2017-08-01

In their recent paper, Feng et al. [Phys. Rev. E 93, 052227 (2016), 10.1103/PhysRevE.93.052227] proposed a complex short-pulse equation of both focusing and defocusing types. They studied in detail the defocusing case and derived its multi-dark-soliton solutions. Nonetheless, from a physical viewpoint in order to better and deeply understand their genuine implications, we find it useful to provide a real and proper background for the derivation of the previous evolution system while showing that the expression of the nonlinear electric polarization the above authors used in their scheme is not suitable for getting the defocusing complex short-pulse equation.

Comment on "Defocusing complex short-pulse equation and its multi-dark-soliton solution".

PubMed

Youssoufa, Saliou; Kuetche, Victor K; Kofane, Timoleon C

2017-08-01

In their recent paper, Feng et al. [Phys. Rev. E 93, 052227 (2016)PREHBM2470-004510.1103/PhysRevE.93.052227] proposed a complex short-pulse equation of both focusing and defocusing types. They studied in detail the defocusing case and derived its multi-dark-soliton solutions. Nonetheless, from a physical viewpoint in order to better and deeply understand their genuine implications, we find it useful to provide a real and proper background for the derivation of the previous evolution system while showing that the expression of the nonlinear electric polarization the above authors used in their scheme is not suitable for getting the defocusing complex short-pulse equation.

Asymptotic Standard Errors for Item Response Theory True Score Equating of Polytomous Items

ERIC Educational Resources Information Center

Cher Wong, Cheow

2015-01-01

Building on previous works by Lord and Ogasawara for dichotomous items, this article proposes an approach to derive the asymptotic standard errors of item response theory true score equating involving polytomous items, for equivalent and nonequivalent groups of examinees. This analytical approach could be used in place of empirical methods like…

Sex-specific lean body mass predictive equations are accurate in the obese paediatric population

PubMed Central

Jackson, Lanier B.; Henshaw, Melissa H.; Carter, Janet; Chowdhury, Shahryar M.

2015-01-01

Background The clinical assessment of lean body mass (LBM) is challenging in obese children. A sex-specific predictive equation for LBM derived from anthropometric data was recently validated in children. Aim The purpose of this study was to independently validate these predictive equations in the obese paediatric population. Subjects and methods Obese subjects aged 4–21 were analysed retrospectively. Predicted LBM (LBMp) was calculated using equations previously developed in children. Measured LBM (LBMm) was derived from dual-energy x-ray absorptiometry. Agreement was expressed as [(LBMm-LBMp)/LBMm] with 95% limits of agreement. Results Of 310 enrolled patients, 195 (63%) were females. The mean age was 11.8 ± 3.4 years and mean BMI Z-score was 2.3 ± 0.4. The average difference between LBMm and LBMp was −0.6% (−17.0%, 15.8%). Pearson’s correlation revealed a strong linear relationship between LBMm and LBMp (r=0.97, p<0.01). Conclusion This study validates the use of these clinically-derived sex-specific LBM predictive equations in the obese paediatric population. Future studies should use these equations to improve the ability to accurately classify LBM in obese children. PMID:26287383

A resonance shift prediction based on the Boltzmann-Ehrenfest principle for cylindrical cavities with a rigid sphere.

PubMed

Santillan, Arturo O; Cutanda-Henríquez, Vicente

2008-11-01

An investigation on the resonance frequency shift for a plane-wave mode in a cylindrical cavity produced by a rigid sphere is reported in this paper. This change of the resonance frequency has been previously considered as a cause of oscillational instabilities in single-mode acoustic levitation devices. It is shown that the use of the Boltzmann-Ehrenfest principle of adiabatic invariance allows the derivation of an expression for the resonance frequency shift in a simpler and more direct way than a method based on a Green's function reported in literature. The position of the sphere can be any point along the axis of the cavity. Obtained predictions of the resonance frequency shift with the deduced equation agree quite well with numerical simulations based on the boundary element method. The results are also confirmed by experiments. The equation derived from the Boltzmann-Ehrenfest principle appears to be more general, and for large spheres, it gives a better approximation than the equation previously reported.

Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II

NASA Astrophysics Data System (ADS)

Kazeykina, Anna; Muñoz, Claudio

2018-04-01

We continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensional Schrödinger operator at a fixed energy parameter. This work is concerned with the more involved case of a positive energy parameter. For the solution of the linearized equation we derive smoothing and Strichartz estimates by combining new estimates for two different frequency regimes, extending our previous results for the negative energy case [18]. The low frequency regime, which our previous result was not able to treat, is studied in detail. At non-low frequencies we also derive improved smoothing estimates with gain of almost one derivative. Then we combine the linear estimates with a Fourier decomposition method and Xs,b spaces to obtain local well-posedness of NV at positive energy in Hs, s > 1/2. Our result implies, in particular, that at least for s > 1/2, NV does not change its behavior from semilinear to quasilinear as energy changes sign, in contrast to the closely related Kadomtsev-Petviashvili equations. As a complement to our LWP results, we also provide some new explicit solutions of NV at zero energy, generalizations of the lumps solutions, which exhibit new and nonstandard long time behavior. In particular, these solutions blow up in infinite time in L2.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

NASA Astrophysics Data System (ADS)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

BRIEF COMMUNICATION: On the drift kinetic equation driven by plasma flows

NASA Astrophysics Data System (ADS)

Shaing, K. C.

2010-07-01

A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators.

Global solution branches for a nonlocal Allen-Cahn equation

NASA Astrophysics Data System (ADS)

Kuto, Kousuke; Mori, Tatsuki; Tsujikawa, Tohru; Yotsutani, Shoji

2018-05-01

We consider the Neumann problem of a 1D stationary Allen-Cahn equation with nonlocal term. Our previous paper [4] obtained a local branch of asymmetric solutions which bifurcates from a point on the branch of odd-symmetric solutions. This paper derives the global behavior of the branch of asymmetric solutions, and moreover, determines the set of all solutions to the nonlocal Allen-Cahn equation. Our proof is based on a level set analysis for an integral map associated with the nonlocal term.

Dynamic analysis of a system of hinge-connected rigid bodies with nonrigid appendages. [equations of motion

NASA Technical Reports Server (NTRS)

Likins, P. W.

1974-01-01

Equations of motion are derived for use in simulating a spacecraft or other complex electromechanical system amenable to idealization as a set of hinge-connected rigid bodies of tree topology, with rigid axisymmetric rotors and nonrigid appendages attached to each rigid body in the set. In conjunction with a previously published report on finite-element appendage vibration equations, this report provides a complete minimum-dimension formulation suitable for generic programming for digital computer numerical integration.

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

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

Jarman, Kenneth D.; Tartakovsky, Alexandre M.

2015-01-01

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

Second order nonlinear equations of motion for spinning highly flexible line-elements. [for spacecraft solar sail

NASA Technical Reports Server (NTRS)

Salama, M.; Trubert, M.

1979-01-01

A formulation is given for the second order nonlinear equations of motion for spinning line-elements having little or no intrinsic structural stiffness. Such elements have been employed in recent studies of structural concepts for future large space structures such as the Heliogyro solar sailer. The derivation is based on Hamilton's variational principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line-element dynamics. For comparison with previous work, the nonlinear equations are reduced to a linearized form frequently found in the literature. The comparison has revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.

Introducing time-dependent molecular fields: a new derivation of the wave equations

NASA Astrophysics Data System (ADS)

Baer, Michael

2018-02-01

This article is part of a series of articles trying to establish the concept molecular field. The theory that induced us to introduce this novel concept is based on the Born-Huang expansion as applied to the Schroedinger equation that describes the interaction of a molecular system with an external electric field. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from a single spatial curl equation, two space-time curl equations and one single space-time divergent equation to a pair of decoupled wave equations usually encountered within the theory of fields. In the present study, just like in the previous study [see Baer et al., Mol. Phys. 114, 227 (2016)] the wave equations are derived for an electric field having two features: (a) its intensity is high enough; (b) its duration is short enough. Although not all the findings are new the derivation, in the present case, is new, straightforward, fluent and much friendlier as compared to the previous one and therefore should be presented again. For this situation the study reveals that the just described interaction creates two fields that coexist within a molecule: one is a novel vectorial field formed via the interaction of the electric field with the Born-Huang non-adiabatic coupling terms (NACTs) and the other is an ordinary, scalar, electric field essentially identical to the original electric field. Section 4 devoted to the visualization of the outcomes via two intersecting Jahn-Teller cones which contain NACTs that become singular at the intersection point of these cones. Finally, the fact that eventually we are facing a kind of a cosmic situation may bring us to speculate that singular NACTs are a result of cosmic phenomena. Thus, if indeed this singularity is somehow connected to reality then, like other singularities in physics, it is formed at (or immediately after) the Big Bang and consequently, guarantees the formation of molecules.

Density-velocity equations with bulk modulus for computational hydro-acoustics

NASA Astrophysics Data System (ADS)

Lin, Po-Hsien; Chen, Yung-Yu; John Yu, S.-T.

2014-02-01

This paper reports a new set of model equations for Computational Hydro Acoustics (CHA). The governing equations include the continuity and the momentum equations. The definition of bulk modulus is used to relate density with pressure. For 3D flow fields, there are four equations with density and velocity components as the unknowns. The inviscid equations are proved to be hyperbolic because an arbitrary linear combination of the three Jacobian matrices is diagonalizable and has a real spectrum. The left and right eigenvector matrices are explicitly derived. Moreover, an analytical form of the Riemann invariants are derived. The model equations are indeed suitable for modeling wave propagation in low-speed, nearly incompressible air and water flows. To demonstrate the capability of the new formulation, we use the CESE method to solve the 2D equations for aeolian tones generated by air flows passing a circular cylinder at Re = 89,000, 46,000, and 22,000. Numerical results compare well with previously published data. By simply changing the value of the bulk modulus, the same code is then used to calculate three cases of water flows passing a cylinder at Re = 89,000, 67,000, and 44,000.

On the classification of scalar evolution equations with non-constant separant

NASA Astrophysics Data System (ADS)

Hümeyra Bilge, Ayşe; Mizrahi, Eti

2017-01-01

The ‘separant’ of the evolution equation u t   =  F, where F is some differentiable function of the derivatives of u up to order m, is the partial derivative \\partial F/\\partial {{u}m}, where {{u}m}={{\\partial}m}u/\\partial {{x}m} . As an integrability test, we use the formal symmetry method of Mikhailov-Shabat-Sokolov, which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives a sequence of conservation laws, called the ‘conserved densities’ {ρ(i)}, i=-1,1,2,3,\\ldots . We apply this method to the classification of scalar evolution equations of orders 3≤slant m≤slant 15 , for which {ρ(-1)}={≤ft[\\partial F/\\partial {{u}m}\\right]}-1/m} and {{ρ(1)} are non-trivial, i.e. they are not total derivatives and {ρ(-1)} is not linear in its highest order derivative. We obtain the ‘top level’ parts of these equations and their ‘top dependencies’ with respect to the ‘level grading’, that we defined in a previous paper, as a grading on the algebra of polynomials generated by the derivatives u b+i , over the ring of {{C}∞} functions of u,{{u}1},\\ldots,{{u}b} . In this setting b and i are called ‘base’ and ‘level’, respectively. We solve the conserved density conditions to show that if {ρ(-1)} depends on u,{{u}1},\\ldots,{{u}b}, then, these equations are level homogeneous polynomials in {{u}b+i},\\ldots,{{u}m} , i≥slant 1 . Furthermore, we prove that if {ρ(3)} is non-trivial, then {ρ(-1)}={≤ft(α ub2+β {{u}b}+γ \\right)}1/2} , with b≤slant 3 while if {{ρ(3)} is trivial, then {ρ(-1)}={≤ft(λ {{u}b}+μ \\right)}1/3} , where b≤slant 5 and α, β, γ, λ and μ are functions of u,\\ldots,{{u}b-1} . We show that the equations that we obtain form commuting flows and we construct their recursion operators that are respectively of orders 2 and 6 for non-trivial and trivial {{ρ(3)} respectively. Omitting lower order dependencies, we show that equations with non-trivial {ρ(3)} and b  =  3 are symmetries of the ‘essentially non-linear third order equation’ for trivial {ρ(3)} , the equations with b  =  5 are symmetries of a non-quasilinear fifth order equation obtained in previous work, while for b  =  3, 4 they are symmetries of quasilinear fifth order equations.

Finite grid radius and thickness effects on retarding potential analyzer measured suprathermal electron density and temperature

NASA Technical Reports Server (NTRS)

Knudsen, William C.

1992-01-01

The effect of finite grid radius and thickness on the electron current measured by planar retarding potential analyzers (RPAs) is analyzed numerically. Depending on the plasma environment, the current is significantly reduced below that which is calculated using a theoretical equation derived for an idealized RPA having grids with infinite radius and vanishingly small thickness. A correction factor to the idealized theoretical equation is derived for the Pioneer Venus (PV) orbiter RPA (ORPA) for electron gasses consisting of one or more components obeying Maxwell statistics. The error in density and temperature of Maxwellian electron distributions previously derived from ORPA data using the theoretical expression for the idealized ORPA is evaluated by comparing the densities and temperatures derived from a sample of PV ORPA data using the theoretical expression with and without the correction factor.

Metastable sound speed in gas-liquid mixtures

NASA Technical Reports Server (NTRS)

Bursik, J. W.; Hall, R. M.

1979-01-01

A new method of calculating speed of sound for two-phase flow is presented. The new equation assumes no phase change during the propagation of an acoustic disturbance and assumes that only the total entropy of the mixture remains constant during the process. The new equation predicts single-phase values for the speed of sound in the limit of all gas or all liquid and agrees with available two-phase, air-water sound speed data. Other expressions used in the two-phase flow literature for calculating two-phase, metastable sound speed are reviewed and discussed. Comparisons are made between the new expression and several of the previous expressions -- most notably a triply isentropic equation as used, a triply isentropic equation as used, among others, by Karplus and by Wallis. Appropriate differences are pointed out and a thermodynamic criterion is derived which must be satisfied in order for the triply isentropic expression to be thermodynamically consistent. This criterion is not satisfied for the cases examined, which included two-phase nitrogen, air-water, two-phase parahydrogen, and steam-water. Consequently, the new equation derived is found to be superior to the other equations reviewed.

Equations of motion of slung-load systems, including multilift systems

NASA Technical Reports Server (NTRS)

Cicolani, Luigi S.; Kanning, Gerd

1992-01-01

General simulation equations are derived for the rigid body motion of slung-load systems. This work is motivated by an interest in trajectory control for slung loads carried by two or more helicopters. An approximation of these systems consists of several rigid bodies connected by straight-line cables or links. The suspension can be assumed elastic or inelastic. Equations for the general system are obtained from the Newton-Euler rigid-body equations with the introduction of generalized velocity coordinates. Three forms are obtained: two generalize previous case-specific results for single-helicopter systems with elastic and inelastic suspensions, respectively; and the third is a new formulation for inelastic suspensions. The latter is derived from the elastic suspension equations by choosing the generalized coordinates so that motion induced by cable stretching is separated from motion with invariant cable lengths, and by then nulling the stretching coordinates to get a relation for the suspension forces. The result is computationally more efficient than the conventional formulation, is readily integrated with the elastic suspension formulation, and is easily applied to the complex dual-lift and multilift systems. Results are given for two-helicopter systems; three configurations are included and these can be integrated in a single simulation. Equations are also given for some single-helicopter systems, for comparison with the previous literature, and for a multilift system. Equations for degenerate-body approximations (point masses, rigid rods) are also formulated and results are given for dual-lift and multilift systems. Finally, linearlized equations of motion are given for general slung-load systems are presented along with results for the two-helicopter system with a spreader bar.

A low dimensional dynamical system for the wall layer

NASA Technical Reports Server (NTRS)

Aubry, N.; Keefe, L. R.

1987-01-01

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

Nucleophilic Participation in the Solvolyses of (Arylthio)methyl Chlorides and Derivatives: Application of Simple and Extended Forms of the Grunwald-Winstein Equations

PubMed Central

Kevill, Dennis N.; Park, Young Hoon; Park, Byoung-Chun; D’Souza, Malcolm J.

2012-01-01

The specific rates of solvolysis of chloromethyl phenyl sulfide [(phenylthio)methyl chloride] and its p-chloro-derivative have been determined at 0.0 °C in a wide range of hydroxylic solvents, including several containing a fluroalcohol. Treatment in terms of a two-term Grunwald-Winstein equation, incorporating terms based on solvent ionizing power (YCl) and solvent nucleophilicity (NT) suggest a mechanism similar to that for the solvolyses of tert-butyl chloride, involving in the rate-determining step a nucleophilic solvation of the incipient carbocation in an ionization process. A previous suggestion, that a third-term governed by the aromatic ring parameter (I) is required, is shown both for the new and for the previously studied related substrates to be an artifact, resulting from an appreciable degree of multicollinearity between I values and a linear combination of NT and YCl values. PMID:22711999

The symbolic computation of series solutions to ordinary differential equations using trees (extended abstract)

NASA Technical Reports Server (NTRS)

Grossman, Robert

1991-01-01

Algorithms previously developed by the author give formulas which can be used for the efficient symbolic computation of series expansions to solutions of nonlinear systems of ordinary differential equations. As a by product of this analysis, formulas are derived which relate to trees to the coefficients of the series expansions, similar to the work of Leroux and Viennot, and Lamnabhi, Leroux and Viennot.

Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium

NASA Astrophysics Data System (ADS)

Yurkin, Maxim A.; Mishchenko, Michael I.

2018-04-01

We present a general derivation of the frequency-domain volume integral equation (VIE) for the electric field inside a nonmagnetic scattering object from the differential Maxwell equations, transmission boundary conditions, radiation condition at infinity, and locally-finite-energy condition. The derivation applies to an arbitrary spatially finite group of particles made of isotropic materials and embedded in a passive host medium, including those with edges, corners, and intersecting internal interfaces. This is a substantially more general type of scatterer than in all previous derivations. We explicitly treat the strong singularity of the integral kernel, but keep the entire discussion accessible to the applied scattering community. We also consider the known results on the existence and uniqueness of VIE solution and conjecture a general sufficient condition for that. Finally, we discuss an alternative way of deriving the VIE for an arbitrary object by means of a continuous transformation of the everywhere smooth refractive-index function into a discontinuous one. Overall, the paper examines and pushes forward the state-of-the-art understanding of various analytical aspects of the VIE.

The dynamics and control of large-flexible space structures, part 10

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reddy, A. S. S. R.

1988-01-01

A mathematical model is developed to predict the dynamics of the proposed orbiting Spacecraft Control Laboratory Experiment (SCOLE) during the station keeping phase. The equations of motion are derived using a Newton-Euler formulation. The model includes the effects of gravity, flexibility, and orbital dynamics. The control is assumed to be provided to the system through the Shuttle's three torquers, and through six actuators located by pairs at two points on the mast and at the mass center of the reflector. The modal shape functions are derived using the fourth order beam equation. The generic mode equations are derived to account for the effects of the control forces on the modal shape and frequencies. The equations are linearized about a nominal equilibrium position. The linear regulator theory is used to derive control laws for both the linear model of the rigidized SCOLE as well as that of the actual SCOLE including the first four flexible modes. The control strategy previously derived for the linear model of the rigidized SCOLE is applied to the nonlinear model of the same configuration of the system and preliminary single axis slewing maneuvers conducted. The results obtained confirm the applicability of the intuitive and appealing two-stage control strategy which would slew the SCOLE system, as if rigid to its desired position and then concentrate on damping out the residual flexible motions.

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

PubMed

Kanagawa, Tetsuya

2015-05-01

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

Finite-volume spectra of the Lee-Yang model

NASA Astrophysics Data System (ADS)

Bajnok, Zoltan; el Deeb, Omar; Pearce, Paul A.

2015-04-01

We consider the non-unitary Lee-Yang minimal model in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels ( r, s) = (1 , 1) , (1 , 2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ 1,3 integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ1,3 integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A 4 RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of ( m, n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.

Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation

NASA Astrophysics Data System (ADS)

de la Rosa, R.; Gandarias, M. L.; Bruzón, M. S.

2016-11-01

In this paper we study the generalized variable-coefficient Gardner equations of the form ut + A(t) unux + C(t) u2nux + B(t) uxxx + Q(t) u = 0 . This class broadens out many other equations previously considered: Johnpillai and Khalique (2010), Molati and Ramollo (2012) and Vaneeva et al. (2015). The use of the equivalence group of this class allows us to perform an exhaustive study and a simple and clear formulation of the results. Some conservation laws are derived for the nonlinearly self-adjoint equations by using a general theorem on conservation laws. We also construct conservation laws by applying the multipliers method.

Resonance line polarization and the Hanle effect in optically thick media. I - Formulation for the two-level atom

NASA Astrophysics Data System (ADS)

Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S.

1990-08-01

A general formalism is presented to describe resonance line polarization for a two-level atom in an optically thick, three-dimensional medium embedded in an arbitrary varying magnetic field and irradiated by an arbitrary radiation field. The magnetic field is supposed sufficiently small to induce a Zeeman splitting much smaller than the typical line width. By neglecting atomic polarization in the lower level and stimulated emission, an integral equation is derived for the multipole moments of the density matrix of the upper level. This equation shows how the multipole moments at any assigned point of the medium are coupled to the multipole moments relative at a different point as a consequence of the propagation of polarized radiation between the two points. The equation also accounts for the effect of the magnetic field, described by a kernel locally connecting multipole moments of the same rank, and for the role of inelastic and elastic (or depolarizing) collisions. After having given its formal derivation for the general case, the integral equation is particularized to the one-dimensional and two-dimensional cases. For the one-dimensional case of a plane parallel atmosphere, neglecting both the magnetic field and depolarizing collisions, the equation here derived reduces to a previous one given by Rees (1978).

A new unified theory of electromagnetic and gravitational interactions

NASA Astrophysics Data System (ADS)

Li, Li-Xin

2016-12-01

In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the fivedimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: ∇a F ab - ξ R b a A a = -4π J b with ξ = -2, where F ab is the antisymmetric electromagnetic field tensor defined by the potential vector A a , R ab is the Ricci curvature tensor of the hypersurface, and J a is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term ξ R b a A a , whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza-Klein theory and its variants in which the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.

FEV1/FVC and FEV1 for the assessment of chronic airflow obstruction in prevalence studies: do prediction equations need revision?

PubMed

Roche, Nicolas; Dalmay, François; Perez, Thierry; Kuntz, Claude; Vergnenègre, Alain; Neukirch, Françoise; Giordanella, Jean-Pierre; Huchon, Gérard

2008-11-01

Little is known on the long-term validity of reference equations used in the calculation of FEV(1) and FEV(1)/FVC predicted values. This survey assessed the prevalence of chronic airflow obstruction in a population-based sample and how it is influenced by: (i) the definition of airflow obstruction; and (ii) equations used to calculate predicted values. Subjects aged 45 or more were recruited in health prevention centers, performed spirometry and fulfilled a standardized ECRHS-derived questionnaire. Previously diagnosed cases and risk factors were identified. Prevalence of airflow obstruction was calculated using: (i) ATS-GOLD definition (FEV(1)/FVC<0.70); and (ii) ERS definition (FEV(1)/FVC

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations

NASA Astrophysics Data System (ADS)

Mansfield, Christopher M.; Shoemaker, Christine A.

1999-05-01

This paper extends earlier work on derivative-based optimization for cost-effective remediation to unconfined aquifers, which have more complex, nonlinear flow dynamics than confined aquifers. Most previous derivative-based optimization of contaminant removal has been limited to consideration of confined aquifers; however, contamination is more common in unconfined aquifers. Exact derivative equations are presented, and two computationally efficient approximations, the quasi-confined (QC) and head independent from previous (HIP) unconfined-aquifer finite element equation derivative approximations, are presented and demonstrated to be highly accurate. The derivative approximations can be used with any nonlinear optimization method requiring derivatives for computation of either time-invariant or time-varying pumping rates. The QC and HIP approximations are combined with the nonlinear optimal control algorithm SALQR into the unconfined-aquifer algorithm, which is shown to compute solutions for unconfined aquifers in CPU times that were not significantly longer than those required by the confined-aquifer optimization model. Two of the three example unconfined-aquifer cases considered obtained pumping policies with substantially lower objective function values with the unconfined model than were obtained with the confined-aquifer optimization, even though the mean differences in hydraulic heads predicted by the unconfined- and confined-aquifer models were small (less than 0.1%). We suggest a possible geophysical index based on differences in drawdown predictions between unconfined- and confined-aquifer models to estimate which aquifers require unconfined-aquifer optimization and which can be adequately approximated by the simpler confined-aquifer analysis.

Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms

NASA Astrophysics Data System (ADS)

Mondal, Ritwik; Berritta, Marco; Oppeneer, Peter M.

2018-07-01

The phenomenological Landau–Lifshitz–Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term; the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy–Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.

Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms.

PubMed

Mondal, Ritwik; Berritta, Marco; Oppeneer, Peter M

2018-05-17

The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term; the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy-Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.

Bukhvostov-Lipatov model and quantum-classical duality

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Runov, Boris A.

2018-02-01

The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1 + 1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O (3) non-linear sigma model. In our previous work [arxiv:arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.

Analytical Energy Gradients for Excited-State Coupled-Cluster Methods

NASA Astrophysics Data System (ADS)

Wladyslawski, Mark; Nooijen, Marcel

The equation-of-motion coupled-cluster (EOM-CC) and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) methods have been firmly established as accurate and routinely applicable extensions of single-reference coupled-cluster theory to describe electronically excited states. An overview of these methods is provided, with emphasis on the many-body similarity transform concept that is the key to a rationalization of their accuracy. The main topic of the paper is the derivation of analytical energy gradients for such non-variational electronic structure approaches, with an ultimate focus on obtaining their detailed algebraic working equations. A general theoretical framework using Lagrange's method of undetermined multipliers is presented, and the method is applied to formulate the EOM-CC and STEOM-CC gradients in abstract operator terms, following the previous work in [P.G. Szalay, Int. J. Quantum Chem. 55 (1995) 151] and [S.R. Gwaltney, R.J. Bartlett, M. Nooijen, J. Chem. Phys. 111 (1999) 58]. Moreover, the systematics of the Lagrange multiplier approach is suitable for automation by computer, enabling the derivation of the detailed derivative equations through a standardized and direct procedure. To this end, we have developed the SMART (Symbolic Manipulation and Regrouping of Tensors) package of automated symbolic algebra routines, written in the Mathematica programming language. The SMART toolkit provides the means to expand, differentiate, and simplify equations by manipulation of the detailed algebraic tensor expressions directly. The Lagrangian multiplier formulation establishes a uniform strategy to perform the automated derivation in a standardized manner: A Lagrange multiplier functional is constructed from the explicit algebraic equations that define the energy in the electronic method; the energy functional is then made fully variational with respect to all of its parameters, and the symbolic differentiations directly yield the explicit equations for the wavefunction amplitudes, the Lagrange multipliers, and the analytical gradient via the perturbation-independent generalized Hellmann-Feynman effective density matrix. This systematic automated derivation procedure is applied to obtain the detailed gradient equations for the excitation energy (EE-), double ionization potential (DIP-), and double electron affinity (DEA-) similarity transformed equation-of-motion coupled-cluster singles-and-doubles (STEOM-CCSD) methods. In addition, the derivatives of the closed-shell-reference excitation energy (EE-), ionization potential (IP-), and electron affinity (EA-) equation-of-motion coupled-cluster singles-and-doubles (EOM-CCSD) methods are derived. Furthermore, the perturbative EOM-PT and STEOM-PT gradients are obtained. The algebraic derivative expressions for these dozen methods are all derived here uniformly through the automated Lagrange multiplier process and are expressed compactly in a chain-rule/intermediate-density formulation, which facilitates a unified modular implementation of analytic energy gradients for CCSD/PT-based electronic methods. The working equations for these analytical gradients are presented in full detail, and their factorization and implementation into an efficient computer code are discussed.

Modified cable equation incorporating transverse polarization of neuronal membranes for accurate coupling of electric fields.

PubMed

Wang, Boshuo; Aberra, Aman S; Grill, Warren M; Peterchev, Angel V

2018-04-01

We present a theory and computational methods to incorporate transverse polarization of neuronal membranes into the cable equation to account for the secondary electric field generated by the membrane in response to transverse electric fields. The effect of transverse polarization on nonlinear neuronal activation thresholds is quantified and discussed in the context of previous studies using linear membrane models. The response of neuronal membranes to applied electric fields is derived under two time scales and a unified solution of transverse polarization is given for spherical and cylindrical cell geometries. The solution is incorporated into the cable equation re-derived using an asymptotic model that separates the longitudinal and transverse dimensions. Two numerical methods are proposed to implement the modified cable equation. Several common neural stimulation scenarios are tested using two nonlinear membrane models to compare thresholds of the conventional and modified cable equations. The implementations of the modified cable equation incorporating transverse polarization are validated against previous results in the literature. The test cases show that transverse polarization has limited effect on activation thresholds. The transverse field only affects thresholds of unmyelinated axons for short pulses and in low-gradient field distributions, whereas myelinated axons are mostly unaffected. The modified cable equation captures the membrane's behavior on different time scales and models more accurately the coupling between electric fields and neurons. It addresses the limitations of the conventional cable equation and allows sound theoretical interpretations. The implementation provides simple methods that are compatible with current simulation approaches to study the effect of transverse polarization on nonlinear membranes. The minimal influence by transverse polarization on axonal activation thresholds for the nonlinear membrane models indicates that predictions of stronger effects in linear membrane models with a fixed activation threshold are inaccurate. Thus, the conventional cable equation works well for most neuroengineering applications, and the presented modeling approach is well suited to address the exceptions.

Autonomous Aerobraking: Thermal Analysis and Response Surface Development

NASA Technical Reports Server (NTRS)

Dec, John A.; Thornblom, Mark N.

2011-01-01

A high-fidelity thermal model of the Mars Reconnaissance Orbiter was developed for use in an autonomous aerobraking simulation study. Response surface equations were derived from the high-fidelity thermal model and integrated into the autonomous aerobraking simulation software. The high-fidelity thermal model was developed using the Thermal Desktop software and used in all phases of the analysis. The use of Thermal Desktop exclusively, represented a change from previously developed aerobraking thermal analysis methodologies. Comparisons were made between the Thermal Desktop solutions and those developed for the previous aerobraking thermal analyses performed on the Mars Reconnaissance Orbiter during aerobraking operations. A variable sensitivity screening study was performed to reduce the number of variables carried in the response surface equations. Thermal analysis and response surface equation development were performed for autonomous aerobraking missions at Mars and Venus.

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

Hwang, Jai-chan; Noh, Hyerim

Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.

Influence of Temperature, Relative Humidity, and Soil Properties on the Soil-Air Partitioning of Semivolatile Pesticides: Laboratory Measurements and Predictive Models.

PubMed

Davie-Martin, Cleo L; Hageman, Kimberly J; Chin, Yu-Ping; Rougé, Valentin; Fujita, Yuki

2015-09-01

Soil-air partition coefficient (Ksoil-air) values are often employed to investigate the fate of organic contaminants in soils; however, these values have not been measured for many compounds of interest, including semivolatile current-use pesticides. Moreover, predictive equations for estimating Ksoil-air values for pesticides (other than the organochlorine pesticides) have not been robustly developed, due to a lack of measured data. In this work, a solid-phase fugacity meter was used to measure the Ksoil-air values of 22 semivolatile current- and historic-use pesticides and their degradation products. Ksoil-air values were determined for two soils (semiarid and volcanic) under a range of environmentally relevant temperature (10-30 °C) and relative humidity (30-100%) conditions, such that 943 Ksoil-air measurements were made. Measured values were used to derive a predictive equation for pesticide Ksoil-air values based on temperature, relative humidity, soil organic carbon content, and pesticide-specific octanol-air partition coefficients. Pesticide volatilization losses from soil, calculated with the newly derived Ksoil-air predictive equation and a previously described pesticide volatilization model, were compared to previous results and showed that the choice of Ksoil-air predictive equation mainly affected the more-volatile pesticides and that the way in which relative humidity was accounted for was the most critical difference.

Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition

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

Jang, Seogjoo, E-mail: sjang@qc.cuny.edu

2016-06-07

This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functionalmore » but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.« less

Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition

NASA Astrophysics Data System (ADS)

Jang, Seogjoo

2016-06-01

This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.

Pauling's electronegativity equation and a new corollary accurately predict bond dissociation enthalpies and enhance current understanding of the nature of the chemical bond.

PubMed

Matsunaga, Nikita; Rogers, Donald W; Zavitsas, Andreas A

2003-04-18

Contrary to other recent reports, Pauling's original electronegativity equation, applied as Pauling specified, describes quite accurately homolytic bond dissociation enthalpies of common covalent bonds, including highly polar ones, with an average deviation of +/-1.5 kcal mol(-1) from literature values for 117 such bonds. Dissociation enthalpies are presented for more than 250 bonds, including 79 for which experimental values are not available. Some previous evaluations of accuracy gave misleadingly poor results by applying the equation to cases for which it was not derived and for which it should not reproduce experimental values. Properly interpreted, the results of the equation provide new and quantitative insights into many facets of chemistry such as radical stabilities, factors influencing reactivity in electrophilic aromatic substitutions, the magnitude of steric effects, conjugative stabilization in unsaturated systems, rotational barriers, molecular and electronic structure, and aspects of autoxidation. A new corollary of the original equation expands its applicability and provides a rationale for previously observed empirical correlations. The equation raises doubts about a new bonding theory. Hydrogen is unique in that its electronegativity is not constant.

Soliton Resolution for the Derivative Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine

2018-05-01

We study the derivative nonlinear Schrödinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the correction dispersive term. We use the nonlinear steepest descent method of Deift and Zhou (Commun Pure Appl Math 56:1029-1077, 2003) revisited by the {\\overline{partial}} -analysis of McLaughlin and Miller (IMRP Int Math Res Pap 48673:1-77, 2006) and Dieng and McLaughlin (Long-time asymptotics for the NLS equation via dbar methods. Preprint, arXiv:0805.2807, 2008), and complemented by the recent work of Borghese et al. (Ann Inst Henri Poincaré Anal Non Linéaire, https://doi.org/10.1016/j.anihpc.2017.08.006, 2017) on soliton resolution for the focusing nonlinear Schrödinger equation. Our results imply that N-soliton solutions of the derivative nonlinear Schrödinger equation are asymptotically stable.

Derivation of the RPA (Random Phase Approximation) Equation of ATDDFT (Adiabatic Time Dependent Density Functional Ground State Response Theory) from an Excited State Variational Approach Based on the Ground State Functional.

PubMed

Ziegler, Tom; Krykunov, Mykhaylo; Autschbach, Jochen

2014-09-09

The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation. ATDDFT is approximate in that it makes use of a frequency independent energy kernel derived from the ground state functional. It is shown in this study that one can derive the RPA equation of ATDDFT from a purely variational approach in which stationary states above the ground state are located using our constricted variational DFT (CV-DFT) method and the ground state functional. Thus, locating stationary states above the ground state due to one-electron excitations with a ground state functional is completely equivalent to solving the RPA equation of TDDFT employing the same functional. The present study is an extension of a previous work in which we demonstrated the equivalence between ATDDFT and CV-DFT within the Tamm-Dancoff approximation.

Two-Layer Viscous Shallow-Water Equations and Conservation Laws

NASA Astrophysics Data System (ADS)

Kanayama, Hiroshi; Dan, Hiroshi

In our previous papers, the two-layer viscous shallow-water equations were derived from the three-dimensional Navier-Stokes equations under the hydrostatic assumption. Also, it was noted that the combination of upper and lower equations in the two-layer model produces the classical one-layer equations if the density of each layer is the same. Then, the two-layer equations were approximated by a finite element method which followed our numerical scheme established for the one-layer model in 1978. Also, it was numerically demonstrated that the interfacial instability generated when the densities are the same can be eliminated by providing a sufficient density difference. In this paper, we newly show that conservation laws are still valid in the two-layer model. Also, we show results of a new physical experiment for the interfacial instability.

An Exactly Solvable Model for the Spread of Disease

ERIC Educational Resources Information Center

Mickens, Ronald E.

2012-01-01

We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.

Local Equation of State for Protons, and Implications for Proton Heating in the Solar Wind.

NASA Astrophysics Data System (ADS)

Zaslavsky, A.; Maksimovic, M.; Kasper, J. C.

2017-12-01

The solar wind protons temperature is observed to decrease with distance to the Sun at a slower rate than expected from an adiabatic expansion law: the protons are therefore said to be heated. This observation raises the question of the evaluation of the heating rate, and the question of the heat source.These questions have been investigated by previous authors by gathering proton data on various distances to the Sun, using spacecraft as Helios or Ulysses, and then computing the radial derivative of the proton temperature in order to obtain a heating rate from the internal energy equation. The problem of such an approach is the computation of the radial derivative of the temperature profile, for which uncertainties are very large, given the dispersion of the temperatures measured at a given distance.An alternative approach, that we develop in this paper, consists in looking for an equation of state that links locally the pressure (or temperature) to the mass density. If such a relation exists then one can evaluate the proton heating rate on a local basis, without having any space derivative to compute.Here we use several years of STEREO and WIND proton data to search for polytropic equation of state. We show that such relationships are indeed a good approximation in given solar wind's velocity intervals and deduce the associated protons heating rates as a function of solar wind's speed. The obtained heating rates are shown to scale from around 1 kW/kg in the slow wind to around 10 kW/kg in the fast wind, in remarkable agreement with the rate of energy observed by previous authors to cascade in solar wind's MHD turbulence at 1 AU. These results therefore support the idea of proton turbulent heating in the solar wind.

Local energy decay for linear wave equations with variable coefficients

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

2005-06-01

A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

Helicity evolution at small-x

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2016-01-13

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g1 structure function. These evolution equations resum powers of α s ln 2(1/x) in the polarization-dependent evolution along with the powers of α s ln(1/x) in the unpolarized evolution which includes saturation efects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-N c and large-N c & N f limits. As a cross-check,more » in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for g 1 structure function derived previously by Bartels, Ermolaev and Ryskin.« less

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

A time-dependent neutron transport method of characteristics formulation with time derivative propagation

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

Hoffman, Adam J., E-mail: adamhoff@umich.edu; Lee, John C., E-mail: jcl@umich.edu

2016-02-15

A new time-dependent Method of Characteristics (MOC) formulation for nuclear reactor kinetics was developed utilizing angular flux time-derivative propagation. This method avoids the requirement of storing the angular flux at previous points in time to represent a discretized time derivative; instead, an equation for the angular flux time derivative along 1D spatial characteristics is derived and solved concurrently with the 1D transport characteristic equation. This approach allows the angular flux time derivative to be recast principally in terms of the neutron source time derivatives, which are approximated to high-order accuracy using the backward differentiation formula (BDF). This approach, called Sourcemore » Derivative Propagation (SDP), drastically reduces the memory requirements of time-dependent MOC relative to methods that require storing the angular flux. An SDP method was developed for 2D and 3D applications and implemented in the computer code DeCART in 2D. DeCART was used to model two reactor transient benchmarks: a modified TWIGL problem and a C5G7 transient. The SDP method accurately and efficiently replicated the solution of the conventional time-dependent MOC method using two orders of magnitude less memory.« less

On the subsystem formulation of linear-response time-dependent DFT.

PubMed

Pavanello, Michele

2013-05-28

A new and thorough derivation of linear-response subsystem time-dependent density functional theory (TD-DFT) is presented and analyzed in detail. Two equivalent derivations are presented and naturally yield self-consistent subsystem TD-DFT equations. One reduces to the subsystem TD-DFT formalism of Neugebauer [J. Chem. Phys. 126, 134116 (2007)]. The other yields Dyson type equations involving three types of subsystem response functions: coupled, uncoupled, and Kohn-Sham. The Dyson type equations for subsystem TD-DFT are derived here for the first time. The response function formalism reveals previously hidden qualities and complications of subsystem TD-DFT compared with the regular TD-DFT of the supersystem. For example, analysis of the pole structure of the subsystem response functions shows that each function contains information about the electronic spectrum of the entire supersystem. In addition, comparison of the subsystem and supersystem response functions shows that, while the correlated response is subsystem additive, the Kohn-Sham response is not. Comparison with the non-subjective partition DFT theory shows that this non-additivity is largely an artifact introduced by the subjective nature of the density partitioning in subsystem DFT.

A new multiscale model to describe a modified Hall-Petch relation at different scales for nano and micro materials

NASA Astrophysics Data System (ADS)

Fadhil, Sadeem Abbas; Alrawi, Aoday Hashim; Azeez, Jazeel H.; Hassan, Mohsen A.

2018-04-01

In the present work, a multiscale model is presented and used to modify the Hall-Petch relation for different scales from nano to micro. The modified Hall-Petch relation is derived from a multiscale equation that determines the cohesive energy between the atoms and their neighboring grains. This brings with it a new term that was originally ignored even in the atomistic models. The new term makes it easy to combine all other effects to derive one modified equation for the Hall-Petch relation that works for all scales together, without the need to divide the scales into two scales, each scale with a different equation, as it is usually done in other works. Due to that, applying the new relation does not require a previous knowledge of the grain size distribution. This makes the new derived relation more consistent and easier to be applied for all scales. The new relation is used to fit the data for Copper and Nickel and it is applied well for the whole range of grain sizes from nano to micro scales.

Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

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

Azarnykh, Dmitrii, E-mail: d.azarnykh@tum.de; Litvinov, Sergey; Adams, Nikolaus A.

2016-06-01

A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker–Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solvedmore » by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau–Lifshitz Navier–Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.« less

Three-dimensional marginal separation

NASA Technical Reports Server (NTRS)

Duck, Peter W.

1988-01-01

The three dimensional marginal separation of a boundary layer along a line of symmetry is considered. The key equation governing the displacement function is derived, and found to be a nonlinear integral equation in two space variables. This is solved iteratively using a pseudo-spectral approach, based partly in double Fourier space, and partly in physical space. Qualitatively, the results are similar to previously reported two dimensional results (which are also computed to test the accuracy of the numerical scheme); however quantitatively the three dimensional results are much different.

Low-frequency Carbon Radio Recombination Lines. I. Calculations of Departure Coefficients

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

Salgado, F.; Morabito, L. K.; Oonk, J. B. R.

In the first paper of this series, we study the level population problem of recombining carbon ions. We focus our study on high quantum numbers, anticipating observations of carbon radio recombination lines to be carried out by the Low Frequency Array. We solve the level population equation including angular momentum levels with updated collision rates up to high principal quantum numbers. We derive departure coefficients by solving the level population equation in the hydrogenic approximation and including low-temperature dielectronic capture effects. Our results in the hydrogenic approximation agree well with those of previous works. When comparing our results including dielectronicmore » capture, we find differences that we ascribe to updates in the atomic physics (e.g., collision rates) and to the approximate solution method of the statistical equilibrium equations adopted in previous studies. A comparison with observations is discussed in an accompanying article, as radiative transfer effects need to be considered.« less

The fifth-order partial differential equation for the description of the α + β Fermi-Pasta-Ulam model

NASA Astrophysics Data System (ADS)

Kudryashov, Nikolay A.; Volkov, Alexandr K.

2017-01-01

We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.

Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Barati, Mohammad Reza; Dabbagh, Ali

2018-04-01

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton's principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.

Skinfold Prediction Equations Fail to Provide an Accurate Estimate of Body Composition in Elite Rugby Union Athletes of Caucasian and Polynesian Ethnicity.

PubMed

Zemski, Adam J; Broad, Elizabeth M; Slater, Gary J

2018-01-01

Body composition in elite rugby union athletes is routinely assessed using surface anthropometry, which can be utilized to provide estimates of absolute body composition using regression equations. This study aims to assess the ability of available skinfold equations to estimate body composition in elite rugby union athletes who have unique physique traits and divergent ethnicity. The development of sport-specific and ethnicity-sensitive equations was also pursued. Forty-three male international Australian rugby union athletes of Caucasian and Polynesian descent underwent surface anthropometry and dual-energy X-ray absorptiometry (DXA) assessment. Body fat percent (BF%) was estimated using five previously developed equations and compared to DXA measures. Novel sport and ethnicity-sensitive prediction equations were developed using forward selection multiple regression analysis. Existing skinfold equations provided unsatisfactory estimates of BF% in elite rugby union athletes, with all equations demonstrating a 95% prediction interval in excess of 5%. The equations tended to underestimate BF% at low levels of adiposity, whilst overestimating BF% at higher levels of adiposity, regardless of ethnicity. The novel equations created explained a similar amount of variance to those previously developed (Caucasians 75%, Polynesians 90%). The use of skinfold equations, including the created equations, cannot be supported to estimate absolute body composition. Until a population-specific equation is established that can be validated to precisely estimate body composition, it is advocated to use a proven method, such as DXA, when absolute measures of lean and fat mass are desired, and raw anthropometry data routinely to derive an estimate of body composition change.

Thermal equation of state of hcp-iron: Constraint on the density deficit of Earth's solid inner core: THERMAL EQUATION OF STATE OF HCP-IRON

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

Fei, Yingwei; Murphy, Caitlin; Shibazaki, Yuki

We conducted high-pressure experiments on hexagonal close packed iron (hcp-Fe) in MgO, NaCl, and Ne pressure-transmitting media and found general agreement among the experimental data at 300 K that yield the best fitted values of the bulk modulus K 0 = 172.7(±1.4) GPa and its pressure derivative K 0'= 4.79(±0.05) for hcp-Fe, using the third-order Birch-Murnaghan equation of state. Using the derived thermal pressures for hcp-Fe up to 100 GPa and 1800 K and previous shockwave Hugoniot data, we developed a thermal equation of state of hcp-Fe. The thermal equation of state of hcp-Fe is further used to calculate themore » densities of iron along adiabatic geotherms to define the density deficit of the inner core, which serves as the basis for developing quantitative composition models of the Earth's inner core. We determine the density deficit at the inner core boundary to be 3.6%, assuming an inner core boundary temperature of 6000 K.« less

Effective equations for the precession dynamics of electron spins and electron-impurity correlations in diluted magnetic semiconductors

NASA Astrophysics Data System (ADS)

Cygorek, M.; Axt, V. M.

2015-08-01

Starting from a quantum kinetic theory for the spin dynamics in diluted magnetic semiconductors, we derive simplified equations that effectively describe the spin transfer between carriers and magnetic impurities for an arbitrary initial impurity magnetization. Taking the Markov limit of these effective equations, we obtain good quantitative agreement with the full quantum kinetic theory for the spin dynamics in bulk systems at high magnetic doping. In contrast, the standard rate description where the carrier-dopant interaction is treated according to Fermi’s golden rule, which involves the assumption of a short memory as well as a perturbative argument, has been shown previously to fail if the impurity magnetization is non-zero. The Markov limit of the effective equations is derived, assuming only a short memory, while higher order terms are still accounted for. These higher order terms represent the precession of the carrier-dopant correlations in the effective magnetic field due to the impurity spins. Numerical calculations show that the Markov limit of our effective equations reproduces the results of the full quantum kinetic theory very well. Furthermore, this limit allows for analytical solutions and for a physically transparent interpretation.

Derivation and Validation of a New Cardiovascular Risk Score for People With Type 2 Diabetes

PubMed Central

Elley, C. Raina; Robinson, Elizabeth; Kenealy, Tim; Bramley, Dale; Drury, Paul L.

2010-01-01

OBJECTIVE To derive a 5-year cardiovascular disease (CVD) risk equation from usual-care data that is appropriate for people with type 2 diabetes from a wide range of ethnic groups, variable glycemic control, and high rates of albuminuria in New Zealand. RESEARCH DESIGN AND METHODS This prospective open-cohort study used primary-care data from 36,127 people with type 2 diabetes without previous CVD to derive a CVD equation using Cox proportional hazards regression models. Data from 12,626 people from a geographically different area were used for validation. Outcome measure was time to first fatal or nonfatal cardiovascular event, derived from national hospitalization and mortality records. Risk factors were age at diagnosis, diabetes duration, sex, systolic blood pressure, smoking status, total cholesterol–to–HDL ratio, ethnicity, glycated hemoglobin (A1C), and urine albumin-to-creatinine ratio. RESULTS Baseline median age was 59 years, 51% were women, 55% were of non-European ethnicity, and 33% had micro- or macroalbuminuria. Median follow-up was 3.9 years (141,169 person-years), including 10,030 individuals followed for at least 5 years. At total of 6,479 first cardiovascular events occurred during follow-up. The 5-year observed risk was 20.8% (95% CI 20.3–21.3). Risk increased with each 1% A1C (adjusted hazard ratio 1.06 [95% CI 1.05–1.08]), when macroalbuminuria was present (2.04 [1.89–2.21]), and in Indo-Asians (1.29 [1.14–1.46]) and Maori (1.23 [1.14–1.32]) compared with Europeans. The derived risk equations performed well on the validation cohort compared with other risk equations. CONCLUSIONS Renal function, ethnicity, and glycemic control contribute significantly to cardiovascular risk prediction. Population-appropriate risk equations can be derived from routinely collected data. PMID:20299482

Gauged BPS baby Skyrmions with quantized magnetic flux

NASA Astrophysics Data System (ADS)

Adam, C.; Wereszczynski, A.

2017-06-01

A new type of gauged BPS baby Skyrme model is presented, where the derivative term is just the Schroers current (i.e., gauge invariant and conserved version of the topological current) squared. This class of models has a topological bound saturated for solutions of the pertinent Bogomolnyi equations supplemented by a so-called superpotential equation. In contrast to the gauged BPS baby Skyrme models considered previously, the superpotential equation is linear and, hence, completely solvable. Furthermore, the magnetic flux is quantized in units of 2 π , which allows, in principle, to define this theory on a compact manifold without boundary, unlike all gauged baby Skyrme models considered so far.

Interface equation and viscosity contrast in Hele-Shaw flow

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

Casademunt, J.; Jasnow, D.; Hernandez-Machado, A.

1992-05-20

In this paper, the authors derive an integro-differential equation for the evolution of the interface separating two immiscible viscous fluids in a Hele-Shaw cell with a channel geometry, for arbitrary viscosity contrast. The authors' equation differs from a previous one obtained by a vortex-sheet formulation of the problem, in that the normal component of the interface velocity is formally decoupled from the gauge-dependent tangential part. The result is thus a closed integral equation for the normal velocity. The authors briefly comment on the advantages of such a formulation and implement an alternative computational algorithm based on it. Preliminary numerical resultsmore » confirm a highly inefficient finger competition in the zero viscosity contrast limit.« less

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

Ordinary differential equation for local accumulation time.

PubMed

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

On the effective field theory of heterotic vacua

NASA Astrophysics Data System (ADS)

McOrist, Jock

2018-04-01

The effective field theory of heterotic vacua that realise [InlineEquation not available: see fulltext.] preserving N{=}1 supersymmetry is studied. The vacua in question admit large radius limits taking the form [InlineEquation not available: see fulltext.], with [InlineEquation not available: see fulltext.] a smooth threefold with vanishing first Chern class and a stable holomorphic gauge bundle [InlineEquation not available: see fulltext.]. In a previous paper we calculated the kinetic terms for moduli, deducing the moduli metric and Kähler potential. In this paper, we compute the remaining couplings in the effective field theory, correct to first order in {α ^{\\backprime } }. In particular, we compute the contribution of the matter sector to the Kähler potential and derive the Yukawa couplings and other quadratic fermionic couplings. From this we write down a Kähler potential [InlineEquation not available: see fulltext.] and superpotential [InlineEquation not available: see fulltext.].

Misconceptions about an Expanding Universe

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

Samuel, Stuart; /SLAC /LBL, Berkeley

2005-12-14

Various results are obtained for a Friedmann-Robertson-Walker cosmology. We derive an exact equation that determines Hubble's law, clarify issues concerning the speeds of faraway objects and uncover a ''tail-light angle effect'' for distant luminous sources. The latter leads to a small, previously unnoticed correction to the parallax distance formula.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

Renormalization group methods for the Reynolds stress transport equations

NASA Technical Reports Server (NTRS)

Rubinstein, R.

1992-01-01

The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

Thermodynamic properties by Equation of state of liquid sodium under pressure

NASA Astrophysics Data System (ADS)

Li, Huaming; Sun, Yongli; Zhang, Xiaoxiao; Li, Mo

Isothermal bulk modulus, molar volume and speed of sound of molten sodium are calculated through an equation of state of a power law form within good precision as compared with the experimental data. The calculated internal energy data show the minimum along the isothermal lines as the previous result but with slightly larger values. The calculated values of isobaric heat capacity show the unexpected minimum in the isothermal compression. The temperature and pressure derivative of various thermodynamic quantities in liquid Sodium are derived. It is discussed about the contribution from entropy to the temperature and pressure derivative of isothermal bulk modulus. The expressions for acoustical parameter and nonlinearity parameter are obtained based on thermodynamic relations from the equation of state. Both parameters for liquid Sodium are calculated under high pressure along the isothermal lines by using the available thermodynamic data and numeric derivations. By comparison with the results from experimental measurements and quasi-thermodynamic theory, the calculated values are found to be very close at melting point at ambient condition. Furthermore, several other thermodynamic quantities are also presented. Scientific Research Starting Foundation from Taiyuan university of Technology, Shanxi Provincial government (``100-talents program''), China Scholarship Council and National Natural Science Foundation of China (NSFC) under Grant No. 11204200.

Nonlocal symmetries and Bäcklund transformations for the self-dual Yang-Mills system

NASA Astrophysics Data System (ADS)

Papachristou, C. J.; Harrison, B. Kent

1988-01-01

The observation is made that generalized evolutionary isovectors of the self-dual Yang-Mills equation, obtained by ``verticalization'' of the geometrical isovectors derived in a previous paper [J. Math. Phys. 28, 1261 (1987)], generate Bäcklund transformations for the self-dual system. In particular, new Bäcklund transformations are obtained by ``verticalizing'' the generators of point transformations on the solution manifold. A geometric ansatz for the derivation of such (generally nonlocal) symmetries is proposed.

A Sub-filter Scale Noise Equation far Hybrid LES Simulations

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.

2006-01-01

Hybrid LES/subscale modeling approaches have an important advantage over the current noise prediction methods in that they only involve modeling of the relatively universal subscale motion and not the configuration dependent larger scale turbulence . Previous hybrid approaches use approximate statistical techniques or extrapolation methods to obtain the requisite information about the sub-filter scale motion. An alternative approach would be to adopt the modeling techniques used in the current noise prediction methods and determine the unknown stresses from experimental data. The present paper derives an equation for predicting the sub scale sound from information that can be obtained with currently available experimental procedures. The resulting prediction method would then be intermediate between the current noise prediction codes and previously proposed hybrid techniques.

Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows.

PubMed

Liang, H; Shi, B C; Guo, Z L; Chai, Z H

2014-05-01

In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is proposed for incompressible multiphase flow systems. In this model, one distribution function is used to solve the Chan-Hilliard equation and the other is adopted to solve the Navier-Stokes equations. Unlike previous phase-field-based LB models, a proper source term is incorporated in the interfacial evolution equation such that the Chan-Hilliard equation can be derived exactly and also a pressure distribution is designed to recover the correct hydrodynamic equations. Furthermore, the pressure and velocity fields can be calculated explicitly. A series of numerical tests, including Zalesak's disk rotation, a single vortex, a deformation field, and a static droplet, have been performed to test the accuracy and stability of the present model. The results show that, compared with the previous models, the present model is more stable and achieves an overall improvement in the accuracy of the capturing interface. In addition, compared to the single-relaxation-time LB model, the present model can effectively reduce the spurious velocity and fluctuation of the kinetic energy. Finally, as an application, the Rayleigh-Taylor instability at high Reynolds numbers is investigated.

Statistical foundations of liquid-crystal theory: II: Macroscopic balance laws.

PubMed

Seguin, Brian; Fried, Eliot

2013-01-01

Working on a state space determined by considering a discrete system of rigid rods, we use nonequilibrium statistical mechanics to derive macroscopic balance laws for liquid crystals. A probability function that satisfies the Liouville equation serves as the starting point for deriving each macroscopic balance. The terms appearing in the derived balances are interpreted as expected values and explicit formulas for these terms are obtained. Among the list of derived balances appear two, the tensor moment of inertia balance and the mesofluctuation balance, that are not standard in previously proposed macroscopic theories for liquid crystals but which have precedents in other theories for structured media.

Statistical foundations of liquid-crystal theory

PubMed Central

Seguin, Brian; Fried, Eliot

2013-01-01

Working on a state space determined by considering a discrete system of rigid rods, we use nonequilibrium statistical mechanics to derive macroscopic balance laws for liquid crystals. A probability function that satisfies the Liouville equation serves as the starting point for deriving each macroscopic balance. The terms appearing in the derived balances are interpreted as expected values and explicit formulas for these terms are obtained. Among the list of derived balances appear two, the tensor moment of inertia balance and the mesofluctuation balance, that are not standard in previously proposed macroscopic theories for liquid crystals but which have precedents in other theories for structured media. PMID:23554513

MULTISCALE MODELS OF TAXIS-DRIVEN PATTERNING IN BACTERIAL POPULATIONS

PubMed Central

XUE, CHUAN; OTHMER, HANS G.

2009-01-01

Spatially-distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants. In the past decade a great deal has been learned about signal transduction, metabolism and movement in E. coli and other bacteria, but translating the individual-level behavior into population-level dynamics is still a challenging problem. However, this is a necessary step because it is computationally impractical to use a strictly cell-based model to understand patterning in growing populations, since the total number of cells may reach 1012 - 1014 in some experiments. In the past phenomenological equations such as the Patlak-Keller-Segel equations have been used in modeling the cell movement that is involved in the formation of such patterns, but the question remains as to how the microscopic behavior can be correctly described by a macroscopic equation. Significant progress has been made for bacterial species that employ a “run-and-tumble” strategy of movement, in that macroscopic equations based on simplified schemes for signal transduction and turning behavior have been derived [14, 15]. Here we extend previous work in a number of directions: (i) we allow for time-dependent signals, which extends the applicability of the equations to natural environments, (ii) we use a more general turning rate function that better describes the biological behavior, and (iii) we incorporate the effect of hydrodynamic forces that arise when cells swim in close proximity to a surface. We also develop a new approach to solving the moment equations derived from the transport equation that does not involve closure assumptions. Numerical examples show that the solution of the lowest-order macroscopic equation agrees well with the solution obtained from a Monte Carlo simulation of cell movement under a variety of temporal protocols for the signal. We also apply the method to derive equations of chemotactic movement that are governed by multiple chemotactic signals. PMID:19784399

On the three dimensional structure of stratospheric material transport associated with various types of waves

NASA Astrophysics Data System (ADS)

Kinoshita, T.; Sato, K.

2016-12-01

The Transformed Eulerian-Mean (TEM) equations were derived by Andrews and McIntyre (1976, 1978) and have been widely used to examine wave-mean flow interaction in the meridional cross section. According to previous studies, the Brewer-Dobson circulation in the stratosphere is driven by planetary waves, baroclinic waves, and inertia-gravity waves, and that the meridional circulation from the summer hemisphere to the winter hemisphere in the mesosphere is mainly driven by gravity waves (e.g., Garcia and Boville 1994; Plumb and Semeniuk 2003; Watanabe et al. 2008; Okamoto et al. 2011). However, the TEM equations do not provide the three-dimensional view of the transport, so that the three dimensional TEM equations have been formulated (Hoskins et al. 1983, Trenberth 1986, Plumb 1985, 1986, Takaya and Nakamura 1997, 2001, Miyahara 2006, Kinoshita et al. 2010, Noda 2010, Kinoshita and Sato 2013a, b, and Noda 2014). On the other hand, the TEM equations cannot properly treat the lower boundary and unstable waves. The Mass-weighted Isentropic Mean (MIM) equations derived by Iwasaki (1989, 1990) are the equations that overcome those problems and the formulation of three-dimensional MIM equations have been studied. The present study applies the three-dimensional TEM and MIM equations to the ERA-Interim reanalysis data and examines the climatological character of three-dimensional structure of Stratospheric Brewer-Dobson circulation. Next, we will discuss how to treat the flow associated with spatial structure of stationary waves.

Thermal equation of state of TiC: A synchrotron x-ray diffraction study

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

Yu Xiaohui; National Lab for Condensed Matter Physics, Institute of Physics, CAS, Beijing 100080; Department of Physics, University of Science and Technology of China, Hefei 230026

2010-06-15

The pressure-volume-temperature measurements were carried out for titanium carbide (TiC) at pressures and temperatures up to 8.1 GPa and 1273 K using energy-dispersive synchrotron x-ray diffraction. Thermoelastic parameters were derived for TiC based on a modified high-temperature Birch-Murnaghan equation of state and a thermal pressure approach. With the pressure derivative of the bulk modulus, K{sub 0}{sup '}, fixed at 4.0, we obtain: the ambient bulk modulus K{sub 0}=268(6) GPa, which is comparable to previously reported value; temperature derivative of bulk modulus at constant pressure ({partial_derivative}K{sub T}/{partial_derivative}T){sub P}=-0.026(9) GPa K{sup -1}, volumetric thermal expansivity {alpha}{sub T}(K{sup -1})=a+bT with a=1.62(12)x10{sup -5} K{supmore » -1} and b=1.07(17)x10{sup -8} K{sup -2}, pressure derivative of thermal expansion ({partial_derivative}{alpha}/{partial_derivative}P){sub T}=(-3.62{+-}1.14)x10{sup -7} GPa{sup -1} K{sup -1}, and temperature derivative of bulk modulus at constant volume ({partial_derivative}K{sub T}/{partial_derivative}T){sub V}=-0.015(8) GPa K{sup -1}. These results provide fundamental thermophysical properties for TiC for the first time and are important to theoretical and computational modeling of transition metal carbides.« less

Hydrodynamic Equations for Flocking Models without Velocity Alignment

NASA Astrophysics Data System (ADS)

Peruani, Fernando

2017-10-01

The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been shown recently that several flocking behaviors can emerge in the absence of velocity alignment and as a result of short-range, position-based, attractive forces that act inside a vision cone. Here, we derive the corresponding hydrodynamic equations of a microscopic position-based flocking model, reviewing and extending previous reported results. In particular, we show that three distinct macroscopic collective behaviors can be observed: i) the coarsening of aggregates with no orientational order, ii) the emergence of static, elongated nematic bands, and iii) the formation of moving, locally polar structures, which we call worms. The derived hydrodynamic equations indicate that active particles interacting via position-based interactions belong to a distinct class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems.

A Gaussian theory for fluctuations in simple liquids.

PubMed

Krüger, Matthias; Dean, David S

2017-04-07

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

A Gaussian theory for fluctuations in simple liquids

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Dean, David S.

2017-04-01

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Hölder Regularity of the 2D Dual Semigeostrophic Equations via Analysis of Linearized Monge-Ampère Equations

NASA Astrophysics Data System (ADS)

Le, Nam Q.

2018-05-01

We obtain the Hölder regularity of time derivative of solutions to the dual semigeostrophic equations in two dimensions when the initial potential density is bounded away from zero and infinity. Our main tool is an interior Hölder estimate in two dimensions for an inhomogeneous linearized Monge-Ampère equation with right hand side being the divergence of a bounded vector field. As a further application of our Hölder estimate, we prove the Hölder regularity of the polar factorization for time-dependent maps in two dimensions with densities bounded away from zero and infinity. Our applications improve previous work by G. Loeper who considered the cases of densities sufficiently close to a positive constant.

A deterministic particle method for one-dimensional reaction-diffusion equations

NASA Technical Reports Server (NTRS)

Mascagni, Michael

1995-01-01

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Equation of State for RX-08-EL and RX-08-EP

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

Lee, E.L.; Walton, J.

1985-05-07

JWL Equations of State (EOS's) have been estimated for RX-08-EL and RX-08-EP. The estimated JWL EOS parameters are listed. Previously, we derived a JWL EOS for RX-08-EN based on DYNA2D hydrodynamic code cylinder computations and comparisons with experimental cylinder test results are shown. The experimental cylinder shot results for RX-08-EL, shot K-473, were compared to the experimental cylinder shot results for RX-08-EN, shot K-463, as a reference. 10 figs., 6 tabs.

The stability of locus equation slopes across stop consonant voicing/aspiration

NASA Astrophysics Data System (ADS)

Sussman, Harvey M.; Modarresi, Golnaz

2004-05-01

The consistency of locus equation slopes as phonetic descriptors of stop place in CV sequences across voiced and voiceless aspirated stops was explored in the speech of five male speakers of American English and two male speakers of Persian. Using traditional locus equation measurement sites for F2 onsets, voiceless labial and coronal stops had significantly lower locus equation slopes relative to their voiced counterparts, whereas velars failed to show voicing differences. When locus equations were derived using F2 onsets for voiced stops that were measured closer to the stop release burst, comparable to the protocol for measuring voiceless aspirated stops, no significant effects of voicing/aspiration on locus equation slopes were observed. This methodological factor, rather than an underlying phonetic-based explanation, provides a reasonable account for the observed flatter locus equation slopes of voiceless labial and coronal stops relative to voiced cognates reported in previous studies [Molis et al., J. Acoust. Soc. Am. 95, 2925 (1994); O. Engstrand and B. Lindblom, PHONUM 4, 101-104]. [Work supported by NIH.

Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

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

Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.

2010-09-15

We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delaymore » time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.« less

Partition-free approach to open quantum systems in harmonic environments: An exact stochastic Liouville equation

NASA Astrophysics Data System (ADS)

McCaul, G. M. G.; Lorenz, C. D.; Kantorovich, L.

2017-03-01

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system, termed the extended stochastic Liouville-von Neumann equation. Our approach generalizes previous work based on Caldeira-Leggett models and a partitioned initial density matrix. This provides a simple, yet exact, closed-form description for the evolution of open systems from equilibriated initial conditions. The applicability of this model and the potential for numerical implementations are also discussed.

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Ragel, F. C.

2014-04-01

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

Asymptotics of a Class of Solutions to the Cylindrical Toda Equations

NASA Astrophysics Data System (ADS)

Tracy, Craig A.; Widom, Harold

The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, , have the representation where Kk$ are integral operators. This class includes the n-periodic cylindrical Toda equations. For n=2 our results reduce to the previously computed asymptotics of the 2D radial sinh-Gordon equation and for n=3 (and with an additional symmetry constraint) they reduce to earlier results for the radial Bullough-Dodd equation. Both of these special cases are examples of Painlevé III and have arisen in various applications. The asymptotics of are derived by computing the small t asymptotics where explicit formulas are given for the quantities ak and bk. The method consists of showing that the resolvent operator of Kk has an approximation in terms of resolvents of certain Wiener-Hopf operators, for which there are explicit integral formulas.

Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian

NASA Astrophysics Data System (ADS)

Zabrodin, A.; Zotov, A.

2018-02-01

We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable) glN Ruijsenaars-Schneider model. It is based on the first order equations in N + M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars-Schneider model. In the elliptic case it holds M = N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero-Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars-Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero-Moser models arise from ordinary intermediate long wave and Benjamin-Ono equations.

Toward Better Modeling of Supercritical Turbulent Mixing

NASA Technical Reports Server (NTRS)

Selle, Laurent; Okongo'o, Nora; Bellan, Josette; Harstad, Kenneth

2008-01-01

study was done as part of an effort to develop computational models representing turbulent mixing under thermodynamic supercritical (here, high pressure) conditions. The question was whether the large-eddy simulation (LES) approach, developed previously for atmospheric-pressure compressible-perfect-gas and incompressible flows, can be extended to real-gas non-ideal (including supercritical) fluid mixtures. [In LES, the governing equations are approximated such that the flow field is spatially filtered and subgrid-scale (SGS) phenomena are represented by models.] The study included analyses of results from direct numerical simulation (DNS) of several such mixing layers based on the Navier-Stokes, total-energy, and conservation- of-chemical-species governing equations. Comparison of LES and DNS results revealed the need to augment the atmospheric- pressure LES equations with additional SGS momentum and energy terms. These new terms are the direct result of high-density-gradient-magnitude regions found in the DNS and observed experimentally under fully turbulent flow conditions. A model has been derived for the new term in the momentum equation and was found to perform well at small filter size but to deteriorate with increasing filter size. Several alternative models were derived for the new SGS term in the energy equation that would need further investigations to determine if they are too computationally intensive in LES.

Physiology driven adaptivity for the numerical solution of the bidomain equations.

PubMed

Whiteley, Jonathan P

2007-09-01

Previous work [Whiteley, J. P. IEEE Trans. Biomed. Eng. 53:2139-2147, 2006] derived a stable, semi-implicit numerical scheme for solving the bidomain equations. This scheme allows the timestep used when solving the bidomain equations numerically to be chosen by accuracy considerations rather than stability considerations. In this study we modify this scheme to allow an adaptive numerical solution in both time and space. The spatial mesh size is determined by the gradient of the transmembrane and extracellular potentials while the timestep is determined by the values of: (i) the fast sodium current; and (ii) the calcium release from junctional sarcoplasmic reticulum to myoplasm current. For two-dimensional simulations presented here, combining the numerical algorithm in the paper cited above with the adaptive algorithm presented here leads to an increase in computational efficiency by a factor of around 250 over previous work, together with significantly less computational memory being required. The speedup for three-dimensional simulations is likely to be more impressive.

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

NASA Technical Reports Server (NTRS)

Hu, Fang; Pizzo, Michelle E.; Nark, Douglas M.

2017-01-01

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Thermo-magnetic field effects on the wave propagation behavior of smart magnetostrictive sandwich nanoplates

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Dabbagh, Ali

2018-03-01

In this paper, a three-variable plate model is utilized to explore the wave propagation problem of smart sandwich nanoplates made of a magnetostrictive core and ceramic face sheets while subjected to thermo-magnetic loading. Herein, the magnetostriction effect is considered and controlled via a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak elastic substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small-scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations are derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of the propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of the presented model are verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

Free energy models for ice VII and liquid water derived from pressure, entropy, and heat capacity relations

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

Myint, Philip C.; Benedict, Lorin X.; Belof, Jonathan L.

Here, we present equations of state relevant to conditions encountered in ramp and multiple-shock compression experiments of water. These experiments compress water from ambient conditions to pressures as high as about 14 GPa and temperatures of up to several hundreds of Kelvin. Water may freeze into ice VII during this process. Although there are several studies on the thermodynamic properties of ice VII, an accurate and analytic free energy model from which all other properties may be derived in a thermodynamically consistent manner has not been previously determined. We have developed such a free energy model for ice VII thatmore » is calibrated with pressure-volume-temperature measurements and melt curve data. Furthermore, we show that liquid water in the pressure and temperature range of interest is well-represented by a simple Mie-Grüneisen equation of state. Our liquid water and ice VII equations of state are validated by comparing to sound speed and Hugoniot data. Although they are targeted towards ramp and multiple-shock compression experiments, we demonstrate that our equations of state also behave reasonably well at pressures and temperatures that lie somewhat beyond those found in the experiments.« less

Free energy models for ice VII and liquid water derived from pressure, entropy, and heat capacity relations

DOE PAGES

Myint, Philip C.; Benedict, Lorin X.; Belof, Jonathan L.

2017-08-28

Here, we present equations of state relevant to conditions encountered in ramp and multiple-shock compression experiments of water. These experiments compress water from ambient conditions to pressures as high as about 14 GPa and temperatures of up to several hundreds of Kelvin. Water may freeze into ice VII during this process. Although there are several studies on the thermodynamic properties of ice VII, an accurate and analytic free energy model from which all other properties may be derived in a thermodynamically consistent manner has not been previously determined. We have developed such a free energy model for ice VII thatmore » is calibrated with pressure-volume-temperature measurements and melt curve data. Furthermore, we show that liquid water in the pressure and temperature range of interest is well-represented by a simple Mie-Grüneisen equation of state. Our liquid water and ice VII equations of state are validated by comparing to sound speed and Hugoniot data. Although they are targeted towards ramp and multiple-shock compression experiments, we demonstrate that our equations of state also behave reasonably well at pressures and temperatures that lie somewhat beyond those found in the experiments.« less

Two-component Superfluid Hydrodynamics of Neutron Star Cores

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

Kobyakov, D. N.; Pethick, C. J., E-mail: dmitry.kobyakov@appl.sci-nnov.ru, E-mail: pethick@nbi.dk

2017-02-20

We consider the hydrodynamics of the outer core of a neutron star under conditions when both neutrons and protons are superfluid. Starting from the equation of motion for the phases of the wave functions of the condensates of neutron pairs and proton pairs, we derive the generalization of the Euler equation for a one-component fluid. These equations are supplemented by the conditions for conservation of neutron number and proton number. Of particular interest is the effect of entrainment, the fact that the current of one nucleon species depends on the momenta per nucleon of both condensates. We find that themore » nonlinear terms in the Euler-like equation contain contributions that have not always been taken into account in previous applications of superfluid hydrodynamics. We apply the formalism to determine the frequency of oscillations about a state with stationary condensates and states with a spatially uniform counterflow of neutrons and protons. The velocities of the coupled sound-like modes of neutrons and protons are calculated from properties of uniform neutron star matter evaluated on the basis of chiral effective field theory. We also derive the condition for the two-stream instability to occur.« less

Thermodynamic Equations of State for Aqueous Solutions Applied to Deep Icy Satellite and Exoplanet Oceans

NASA Astrophysics Data System (ADS)

Vance, S.; Brown, J. M.; Bollengier, O.; Journaux, B.; Sotin, C.; Choukroun, M.; Barnes, R.

2014-12-01

Supporting life in icy world or exoplanet oceans may require global seafloor chemical reactions between water and rock. Such interactions have been regarded as limited in larger icy worlds such as Ganymede and Titan, where ocean depths approach 800 km and GPa pressures (>10katm). If the oceans are composed of pure water, such conditions are consistent with the presence of dense ice phases V and VI that cover the rocky seafloor. Exoplanets with oceans can obtain pressures sufficient to generate ices VII and VIII. We have previously demonstrated temperature gradients in such oceans on the order of 20 K or more, resulting from fluid compressibility in a deep adiabatic ocean based on our experimental work. Accounting for increases in density for highly saline oceans leads to the possibility of oceans perched under and between high pressure ices. Ammonia has the opposite effect, instead decreasing ocean density, as reported by others and confirmed by our laboratory measurements in the ammonia water system. Here we report on the completed equation of state for aqueous ammonia derived from our prior measurements and optimized global b-spline fitting methods We use recent diamond anvil cell measurements for water and ammonia to extend the equation of state to 400°C and beyond 2 GPa, temperatures and pressures applicable to icy worlds and exoplanets. Densities show much less temperature dependence but comparabe high-pressure derivatives to previously published ammonia-water properties derived for application to Titan (Croft et al. 1988). Thermal expansion is in better agreement with the more self-consistent equation of state of Tillner-Roth and Friend (1998). We also describe development of a planetary NaCl equation of state using recent measurements of phase boundaries and sound speeds. We examine implications of realistic ocean-ice thermodynamics for Titan and exoplanet interiors using the methodology recently applied to Ganymede for oceans dominated by MgSO4. High pressure ices should not be present on Titan if its ocean composition is Dead-Sea like, as recently inferred from tidal dissipation and topography, and if Titan's moment of inertia has the published value of C/MR2 = 0.3414.

Standard Errors of Equating for the Percentile Rank-Based Equipercentile Equating with Log-Linear Presmoothing

ERIC Educational Resources Information Center

Wang, Tianyou

2009-01-01

Holland and colleagues derived a formula for analytical standard error of equating using the delta-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank-based equipercentile equating with log-linear smoothing. This procedure is…

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

Célérier, Marie-Noëlle; Nottale, Laurent, E-mail: marie-noelle.celerier@obspm.fr, E-mail: laurent.nottale@obspm.fr

Owing to the non-differentiable nature of the theory of Scale Relativity, the emergence of complex wave functions, then of spinors and bi-spinors occurs naturally in its framework. The wave function is here a manifestation of the velocity field of geodesics of a continuous and non-differentiable (therefore fractal) space-time. In a first paper (Paper I), we have presented the general argument which leads to this result using an elaborate and more detailed derivation than previously displayed. We have therefore been able to show how the complex wave function emerges naturally from the doubling of the velocity field and to revisit themore » derivation of the non-relativistic Schrödinger equation of motion. In the present paper (Paper II), we deal with relativistic motion and detail the natural emergence of the bi-spinors from such first principles of the theory. Moreover, while Lorentz invariance has been up to now inferred from mathematical results obtained in stochastic mechanics, we display here a new and detailed derivation of the way one can obtain a Lorentz invariant expression for the expectation value of the product of two independent fractal fluctuation fields in the sole framework of the theory of Scale Relativity. These new results allow us to enhance the robustness of our derivation of the two main equations of motion of relativistic quantum mechanics (the Klein-Gordon and Dirac equations) which we revisit here at length.« less

Statistical thermodynamics foundation for photovoltaic and photothermal conversion. II. Application to photovoltaic conversion

NASA Astrophysics Data System (ADS)

Badescu, Viorel; Landsberg, Peter T.

1995-08-01

The general theory developed in part I was applied to build up two models of photovoltaic conversion. To this end two different systems were analyzed. The first system consists of the whole absorber (converter), for which the balance equations for energy and entropy are written and then used to derive an upper bound for solar energy conversion. The second system covers a part of the absorber (converter), namely the valence and conduction electronic bands. The balance of energy is used in this case to derive, under additional assumptions, another upper limit for the conversion efficiency. This second system deals with the real location where the power is generated. Both models take into consideration the radiation polarization and reflection, and the effects of concentration. The second model yields a more accurate upper bound for the conversion efficiency. A generalized solar cell equation is derived. It is proved that other previous theories are particular cases of the present more general formalism.

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.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Stability of flat spacetime in quantum gravity

NASA Astrophysics Data System (ADS)

Jordan, R. D.

1987-12-01

In a previous paper, a modified effective-action formalism was developed which produces equations satisfied by the expectation value of the field, rather than the usual in-out average. Here this formalism is applied to a quantized scalar field in a background which is a small perturbation from Minkowski spacetime. The one-loop effective field equation describes the back reaction of created particles on the gravitational field, and is calculated in this paper to linear order in the perturbation. In this way we rederive an equation first found by Horowitz using completely different methods. This equation possesses exponentially growing solutions, so we confirm Horowitz's conclusion that flat spacetime is unstable in this approximation to the theory. The new derivation shows that the field equation is just as useful as the one-loop approximation to the in-out equation, contrary to earlier arguments. However, the instability suggests that the one-loop approximation cannot be trusted for gravity. These results are compared with the corresponding situation in QED and QCD.

Errors in calculated oncotic pressure of dog plasma.

PubMed

Gabel, J C; Scott, R L; Adair, T H; Drake, R E; Traber, D L

1980-12-01

Several equations to calculate plasma oncotic pressure (pi) from the total protein concentration (C) have been previously described. These equations were derived empirically from samples with a wide range of C obtained by diluting or concentrating normal plasma samples. To test these equations over a range of naturally occurring C, we measured C and pi of plasma samples from 40 dogs. C ranged from 5.3 to 8.7 g/dl and averaged 6.5 +/- 0.1 (mean +/- SE) and pi averaged 17.9 +/- 0.3 mmHg. The regression equation was pi = 78.14 + 1.67 C (r = 0.74). pi increased with C much less than predicted with the commonly used equations. The albumin-to-globulin concentration ratios (A/G), determined in 27 of the dogs, decreased with increasing C (A/G = 1.56-0.128 C, r = 0.62). The lower A/G at the higher C's could cause the lower than predicted increase in pi with C, because the equations were developed from data in which A/G was constant.

Moment equations for chromatography using superficially porous spherical particles.

PubMed

Miyabe, Kanji

2011-01-01

New moment equations were developed for chromatography using superficially porous (shell-type) spherical particles, which have recently attracted much attention as one of separation media for fast separation with high efficiency. At first, the moment equations of the first absolute and second central moments in the real time domain were derived from the analytical solution in the Laplace domain of a set of basic equations of the general rate model of chromatography, which represent the mass balance, mass-transfer rate, and reaction kinetics in the column packed with shell-type particles. Then, the moment equations were used for analyzing the experimental data of chromatography of kallidin in a Halo column, which were published in a previous paper written by other researchers. It was tried to predict the chromatographic behavior of shell-type particles having different shell thicknesses. The new moment equations are useful for a detailed analysis of the chromatographic behavior of shell-type spherical particles. It is also concluded that they can be used for the preliminarily optimization of their structural characteristics.

Exact multisoliton solutions of general nonlinear Schrödinger equation with derivative.

PubMed

Li, Qi; Duan, Qiu-yuan; Zhang, Jian-bing

2014-01-01

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

Corrigendum: The creation, destruction, and transfer of multipole moments in electron- and proton-impact ionization of atoms and ions (2013 J. Phys. B: At. Mol. Opt. Phys. 46 245202)

DOE PAGES

Csanak, George; Inal, Mokhtar K; Fontes, Christopher John; ...

2015-04-15

The present corrigendum is dedicated to correcting unfortunate errors made in certain equations of our paper [1]. We should first stress the point that those errors have no serious consequences on the main results of the paper and most derived equations remain valid. This is a follow-up to the first corrigendum which was reported in reference [2] to correct errors of a similar nature in another previously reported work [3]. The source of all those errors resides in the treatment of charged-particle scattering and the subtle manipulations made to obtain some of the equations in both references [1, 3]. Allmore » equation numbers cited here correspond to those of [1] unless specified otherwise.« less

Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods.

PubMed

Bertin, Eric; Baskaran, Aparna; Chaté, Hugues; Marchetti, M Cristina

2015-10-01

Considering systems of self-propelled polar particles with nematic interactions ("rods"), we compare the continuum equations describing the evolution of polar and nematic order parameters, derived either from Smoluchowski or Boltzmann equations. Our main goal is to understand the discrepancies between the continuum equations obtained so far in both frameworks. We first show that, in the simple case of point-like particles with only alignment interactions, the continuum equations obtained have the same structure in both cases. We further study, in the Smoluchowski framework, the case where an interaction force is added on top of the aligning torque. This clarifies the origin of the additional terms obtained in previous works. Our observations lead us to emphasize the need for a more involved closure scheme than the standard normal form of the distribution when dealing with active systems.

Finite Element Analysis of Poroelastic Composites Undergoing Thermal and Gas Diffusion

NASA Technical Reports Server (NTRS)

Salamon, N. J. (Principal Investigator); Sullivan, Roy M.; Lee, Sunpyo

1995-01-01

A theory for time-dependent thermal and gas diffusion in mechanically time-rate-independent anisotropic poroelastic composites has been developed. This theory advances previous work by the latter two authors by providing for critical transverse shear through a three-dimensional axisymmetric formulation and using it in a new hypothesis for determining the Biot fluid pressure-solid stress coupling factor. The derived governing equations couple material deformation with temperature and internal pore pressure and more strongly couple gas diffusion and heat transfer than the previous theory. Hence the theory accounts for the interactions between conductive heat transfer in the porous body and convective heat carried by the mass flux through the pores. The Bubnov Galerkin finite element method is applied to the governing equations to transform them into a semidiscrete finite element system. A numerical procedure is developed to solve the coupled equations in the space and time domains. The method is used to simulate two high temperature tests involving thermal-chemical decomposition of carbon-phenolic composites. In comparison with measured data, the results are accurate. Moreover unlike previous work, for a single set of poroelastic parameters, they are consistent with two measurements in a restrained thermal growth test.

Thermal Equation of State of TiC: A Synchrotron X-ray Diffraction

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

Yu, X.; Lin, Z; Zhang, J

2010-01-01

The pressure-volume-temperature measurements were carried out for titanium carbide (TiC) at pressures and temperatures up to 8.1 GPa and 1273 K using energy-dispersive synchrotron x-ray diffraction. Thermoelastic parameters were derived for TiC based on a modified high-temperature Birch-Murnaghan equation of state and a thermal pressure approach. With the pressure derivative of the bulk modulus, K{prime}{sub 0}, fixed at 4.0, we obtain: the ambient bulk modulus K{sub 0} = 268(6) GPa, which is comparable to previously reported value; temperature derivative of bulk modulus at constant pressure ({partial_derivative}K{sub T}/{partial_derivative}T){sub P} = -0.026(9) GPa K{sup -1}, volumetric thermal expansivity {alpha}{sub T}(K{sup -1}) =more » a+b T with a = 1.62(12) x 10{sup -5} K{sup -1} and b = 1.07(17) x 10{sup -8}K{sup -2}, pressure derivative of thermal expansion ({partial_derivative}{sub {alpha}}/{partial_derivative}{sub P}){sub T} = (-3.62 {+-} 1.14) x 10{sup -7} GPa{sup -1} K{sup -1}, and temperature derivative of bulk modulus at constant volume ({partial_derivative}K{sub T}/{partial_derivative}T){sub V} = -0.015(8) GPa K{sup -1}. These results provide fundamental thermophysical properties for TiC for the first time and are important to theoretical and computational modeling of transition metal carbides.« less

On the Calculation of the Fe K-alpha Line Emissivity of Black Hole Accretion Disks

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

Krawczynski, H.; Beheshtipour, B., E-mail: krawcz@wustl.edu

Observations of the fluorescent Fe K α emission line from the inner accretion flows of stellar mass black holes in X-ray binaries and supermassive black holes in active galactic nuclei have become an important tool to study the magnitude and inclination of the black hole spin, and the structure of the accretion flow close to the event horizon of the black hole. Modeling spectral, timing, and soon also X-ray polarimetric observations of the Fe K α emission requires the calculation of the specific intensity in the rest frame of the emitting plasma. We revisit the derivation of the equation usedmore » for calculating the illumination of the accretion disk by the corona. We present an alternative derivation leading to a simpler equation, and discuss the relation to previously published results.« less

Solution of the one-dimensional consolidation theory equation with a pseudospectral method

USGS Publications Warehouse

Sepulveda, N.; ,

1991-01-01

The one-dimensional consolidation theory equation is solved for an aquifer system using a pseudospectral method. The spatial derivatives are computed using Fast Fourier Transforms and the time derivative is solved using a fourth-order Runge-Kutta scheme. The computer model calculates compaction based on the void ratio changes accumulated during the simulated periods of time. Compactions and expansions resulting from groundwater withdrawals and recharges are simulated for two observation wells in Santa Clara Valley and two in San Joaquin Valley, California. Field data previously published are used to obtain mean values for the soil grain density and the compression index and to generate depth-dependent profiles for hydraulic conductivity and initial void ratio. The water-level plots for the wells studied were digitized and used to obtain the time dependent profiles of effective stress.

Modifying Taper-Derived Merchantable Height Estimates to Account for Tree Characteristics

Treesearch

James A. Westfall

2006-01-01

The U.S. Department of Agriculture Forest Service Northeastern Forest Inventory and Analysis program (NE-FIA) is developing regionwide tree-taper equations. Unlike most previous work on modeling tree form, this effort necessarily includes a wide array of tree species. For some species, branching patterns can produce undesirable tree form that reduces the merchantable...

Documenting the NASA Armstrong Flight Research Center Oblate Earth Simulation Equations of Motion and Integration Algorithm

NASA Technical Reports Server (NTRS)

Clarke, R.; Lintereur, L.; Bahm, C.

2016-01-01

A desire for more complete documentation of the National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center (AFRC), Edwards, California legacy code used in the core simulation has led to this e ort to fully document the oblate Earth six-degree-of-freedom equations of motion and integration algorithm. The authors of this report have taken much of the earlier work of the simulation engineering group and used it as a jumping-o point for this report. The largest addition this report makes is that each element of the equations of motion is traced back to first principles and at no point is the reader forced to take an equation on faith alone. There are no discoveries of previously unknown principles contained in this report; this report is a collection and presentation of textbook principles. The value of this report is that those textbook principles are herein documented in standard nomenclature that matches the form of the computer code DERIVC. Previous handwritten notes are much of the backbone of this work, however, in almost every area, derivations are explicitly shown to assure the reader that the equations which make up the oblate Earth version of the computer routine, DERIVC, are correct.

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

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

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

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

A framework for qualitative reasoning about solid objects

NASA Technical Reports Server (NTRS)

Davis, E.

1987-01-01

Predicting the behavior of a qualitatively described system of solid objects requires a combination of geometrical, temporal, and physical reasoning. Methods based upon formulating and solving differential equations are not adequate for robust prediction, since the behavior of a system over extended time may be much simpler than its behavior over local time. A first-order logic, in which one can state simple physical problems and derive their solution deductively, without recourse to solving the differential equations, is discussed. This logic is substantially more expressive and powerful than any previous AI representational system in this domain.

Generalized extended Lagrangian Born-Oppenheimer molecular dynamics

DOE PAGES

Niklasson, Anders M. N.; Cawkwell, Marc J.

2014-10-29

Extended Lagrangian Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are derived directly from the extended Lagrangian under the condition of an adiabatic separation between the nuclear and the electronic degrees of freedom. We show how this separation is automatically fulfilled and system independent. The generalized equations of motion require only one diagonalization per time step and are applicable to a broader range of materials with improved accuracy and stability compared to previous formulations.

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.

Heterogeneous nucleation in multi-component vapor on a partially wettable charged conducting particle. II. The generalized Laplace, Gibbs-Kelvin, and Young equations and application to nucleation.

PubMed

Noppel, M; Vehkamäki, H; Winkler, P M; Kulmala, M; Wagner, P E

2013-10-07

Based on the results of a previous paper [M. Noppel, H. Vehkamäki, P. M. Winkler, M. Kulmala, and P. E. Wagner, J. Chem. Phys. 139, 134107 (2013)], we derive a thermodynamically consistent expression for reversible or minimal work needed to form a dielectric liquid nucleus of a new phase on a charged insoluble conducting sphere within a uniform macroscopic one- or multicomponent mother phase. The currently available model for ion-induced nucleation assumes complete spherical symmetry of the system, implying that the seed ion is immediately surrounded by the condensing liquid from all sides. We take a step further and treat more realistic geometries, where a cap-shaped liquid cluster forms on the surface of the seed particle. We derive the equilibrium conditions for such a cluster. The equalities of chemical potentials of each species between the nucleus and the vapor represent the conditions of chemical equilibrium. The generalized Young equation that relates contact angle with surface tensions, surface excess polarizations, and line tension, also containing the electrical contribution from triple line excess polarization, expresses the condition of thermodynamic equilibrium at three-phase contact line. The generalized Laplace equation gives the condition of mechanical equilibrium at vapor-liquid dividing surface: it relates generalized pressures in neighboring bulk phases at an interface with surface tension, excess surface polarization, and dielectric displacements in neighboring phases with two principal radii of surface curvature and curvatures of equipotential surfaces in neighboring phases at that point. We also re-express the generalized Laplace equation as a partial differential equation, which, along with electrostatic Laplace equations for bulk phases, determines the shape of a nucleus. We derive expressions that are suitable for calculations of the size and composition of a critical nucleus (generalized version of the classical Kelvin-Thomson equation).

Cavity losses for the dissipative Jaynes Cummings Hamiltonian beyond rotating wave approximation

NASA Astrophysics Data System (ADS)

Scala, M.; Militello, B.; Messina, A.; Maniscalco, S.; Piilo, J.; Suominen, K.-A.

2007-11-01

A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows us to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis (Scala et al 2007 Phys. Rev. A 75 013811), where a microscopic derivation was given in the framework of the rotating wave approximation.

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

NASA Technical Reports Server (NTRS)

King, H. F.; Komornicki, A.

1986-01-01

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

NASA Astrophysics Data System (ADS)

Oskouie, M. Faraji; Ansari, R.; Rouhi, H.

2018-04-01

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

A simple method to derive bounds on the size and to train multilayer neural networks

NASA Technical Reports Server (NTRS)

Sartori, Michael A.; Antsaklis, Panos J.

1991-01-01

A new derivation is presented for the bounds on the size of a multilayer neural network to exactly implement an arbitrary training set; namely, the training set can be implemented with zero error with two layers and with the number of the hidden-layer neurons equal to no.1 is greater than p - 1. The derivation does not require the separation of the input space by particular hyperplanes, as in previous derivations. The weights for the hidden layer can be chosen almost arbitrarily, and the weights for the output layer can be found by solving no.1 + 1 linear equations. The method presented exactly solves (M), the multilayer neural network training problem, for any arbitrary training set.

Stability of Thin-Walled Tubes Under Torsion

NASA Technical Reports Server (NTRS)

Donnell, L H

1935-01-01

In this report a theoretical solution is developed for the torsion on a round thin-walled tube for which the walls become unstable. The results of this theory are given by a few simple formulas and curves which cover all cases. The differential equations of equilibrium are derived in a simpler form than previously found, it being shown that many items can be neglected.

On the ground state energy of the delta-function Fermi gas

NASA Astrophysics Data System (ADS)

Tracy, Craig A.; Widom, Harold

2016-10-01

The weak coupling asymptotics to order γ of the ground state energy of the delta-function Fermi gas, derived heuristically in the literature, is here made rigorous. Further asymptotics are in principle computable. The analysis applies to the Gaudin integral equation, a method previously used by one of the authors for the asymptotics of large Toeplitz matrices.

The Adoption of Blended E-Learning Technology in Vietnam Using a Revision of the Technology Acceptance Model

ERIC Educational Resources Information Center

Tran, Khanh Ngo Nhu

2016-01-01

This study examines factors that determine the attitudes of learners toward a blended e-learning system (BELS) using data collected by questionnaire from a sample of 396 students involved in a BELS environment in Vietnam. A theoretical model is derived from previous studies and is analyzed and developed using structural equation modeling…

Odds Ratio, Delta, ETS Classification, and Standardization Measures of DIF Magnitude for Binary Logistic Regression

ERIC Educational Resources Information Center

Monahan, Patrick O.; McHorney, Colleen A.; Stump, Timothy E.; Perkins, Anthony J.

2007-01-01

Previous methodological and applied studies that used binary logistic regression (LR) for detection of differential item functioning (DIF) in dichotomously scored items either did not report an effect size or did not employ several useful measures of DIF magnitude derived from the LR model. Equations are provided for these effect size indices.…

Thermal equation of state of (Mg 0.9Fe 0.1) 2SiO 4 olivine

NASA Astrophysics Data System (ADS)

Liu, Wei; Li, Baosheng

2006-08-01

In situ synchrotron X-ray diffraction measurements have been carried out on San Carlos olivine (Mg 0.9Fe 0.1) 2SiO 4 up to 8 GPa and 1073 K. Data analysis using the high-temperature Birch-Murnaghan (HTBM) equation of state (EoS) yields the temperature derivative of the bulk modulus (∂ KT/∂ T) P = -0.019 ± 0.002 GPa K -1. The thermal pressure (TH) approach gives αKT = 4.08 ± 0.10 × 10 -3 GPa K -1, from which (∂ KT/∂ T) P = -0.019 ± 0.001 GPa K -1 is derived. Fitting the present data to the Mie-Grüneisen-Debye (MGD) formalism, the Grüneisen parameter at ambient conditions γ0 is constrained to be 1.14 ± 0.02 with fixed volume dependence q = 1. Combining the present data with previous results on iron-bearing olivine and fitting to MGD EoS, we obtain γ0 = 1.11 ± 0.01 and q = 0.54 ± 0.36. In this study the thermoelastic parameters obtained from various approaches are in good agreement with one another and previous results.

Infinite order quantum-gravitational correlations

NASA Astrophysics Data System (ADS)

Knorr, Benjamin

2018-06-01

A new approximation scheme for nonperturbative renormalisation group equations for quantum gravity is introduced. Correlation functions of arbitrarily high order can be studied by resolving the full dependence of the renormalisation group equations on the fluctuation field (graviton). This is reminiscent of a local potential approximation in O(N)-symmetric field theories. As a first proof of principle, we derive the flow equation for the ‘graviton potential’ induced by a conformal fluctuation and corrections induced by a gravitational wave fluctuation. Indications are found that quantum gravity might be in a non-metric phase in the deep ultraviolet. The present setup significantly improves the quality of previous fluctuation vertex studies by including infinitely many couplings, thereby testing the reliability of schemes to identify different couplings to close the equations, and represents an important step towards the resolution of the Nielsen identity. The setup further allows one, in principle, to address the question of putative gravitational condensates.

Equations of state and stability of MgSiO 3 perovskite and post-perovskite phases from quantum Monte Carlo simulations

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

Lin, Yangzheng; Cohen, Ronald E.; Stackhouse, Stephen

2014-11-10

In this study, we have performed quantum Monte Carlo (QMC) simulations and density functional theory calculations to study the equations of state of MgSiO 3 perovskite (Pv, bridgmanite) and post-perovskite (PPv) up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground-state energies were derived using QMC simulations and the temperature-dependent Helmholtz free energies were calculated within the quasiharmonic approximation and density functional perturbation theory. The equations of state for both phases of MgSiO 3 agree well with experiments, and better than those from generalized gradient approximation calculations. The Pv-PPv phase boundary calculated from ourmore » QMC equations of state is also consistent with experiments, and better than previous local density approximation calculations. Lastly, we discuss the implications for double crossing of the Pv-PPv boundary in the Earth.« less

Comment on "Dynamics and properties of waves in a modified Noguchi electrical transmission line"

NASA Astrophysics Data System (ADS)

Kenmogne, Fabien; Yemélé, David; Marquié, Patrick

2016-09-01

A recent paper [Phys. Rev. E 91, 022925 (2015), 10.1103/PhysRevE.91.022925] presents the derivation of the nonlinear equation modeling envelope waves in a specific case of band passed filter discrete nonlinear electrical transmission line (NLTL), called "A modified Noguchi electrical transmission line" according to the authors. Using the reductive perturbation approach in the semidiscrete approximation, they showed that the modulated waves propagating in this NLTL are described by the ordinary nonlinear Schrödinger (NLS) equation. On the basis of their results, the authors claimed that all previous works on the band passed filter NLTL, which considered the vanishing of the dc component of the signal voltage, are incorrect, and this dc term is nonzero. As a consequence, the dispersion and nonlinearity coefficients of the NLS equation are strongly different from those usually obtained, and they found, according to the sign of the product P Q , the existence of one more region (compared to the work of Marquié et al. [Phys. Rev. E 49, 828 (1994)], 10.1103/PhysRevE.49.828) in the dispersion curve that allows the motion of envelope solitons of higher frequency in the system. In this Comment we provide sufficient theoretical and numerical evidence showing that the evidence obtained by the authors otherwise is due to certain terms missed in their mathematical developments when they derived the NLS equation. Our results also suggest that the previous work of Marquié and co-workers correctly predict the fact that the dc term of the signal voltage does not exist and there exist only two regions in the dispersion curve according to the sign of the product P Q .

Physical uniqueness of higher-order Korteweg-de Vries theory for continuously stratified fluids without background shear

NASA Astrophysics Data System (ADS)

Shimizu, Kenji

2017-10-01

The 2nd-order Korteweg-de Vries (KdV) equation and the Gardner (or extended KdV) equation are often used to investigate internal solitary waves, commonly observed in oceans and lakes. However, application of these KdV-type equations for continuously stratified fluids to geophysical problems is hindered by nonuniqueness of the higher-order coefficients and the associated correction functions to the wave fields. This study proposes to reduce arbitrariness of the higher-order KdV theory by considering its uniqueness in the following three physical senses: (i) consistency of the nonlinear higher-order coefficients and correction functions with the corresponding phase speeds, (ii) wavenumber-independence of the vertically integrated available potential energy, and (iii) its positive definiteness. The spectral (or generalized Fourier) approach based on vertical modes in the isopycnal coordinate is shown to enable an alternative derivation of the 2nd-order KdV equation, without encountering nonuniqueness. Comparison with previous theories shows that Parseval's theorem naturally yields a unique set of special conditions for (ii) and (iii). Hydrostatic fully nonlinear solutions, derived by combining the spectral approach and simple-wave analysis, reveal that both proposed and previous 2nd-order theories satisfy (i), provided that consistent definitions are used for the wave amplitude and the nonlinear correction. This condition reduces the arbitrariness when higher-order KdV-type theories are compared with observations or numerical simulations. The coefficients and correction functions that satisfy (i)-(iii) are given by explicit formulae to 2nd order and by algebraic recurrence relationships to arbitrary order for hydrostatic fully nonlinear and linear fully nonhydrostatic effects.

Dietary intakes assessed by 24-h recalls in peri-urban African adolescents: validity of energy intake compared with estimated energy expenditure.

PubMed

Rankin, D; Ellis, S M; Macintyre, U E; Hanekom, S M; Wright, H H

2011-08-01

The objective of this study is to determine the relative validity of reported energy intake (EI) derived from multiple 24-h recalls against estimated energy expenditure (EE(est)). Basal metabolic rate (BMR) equations and physical activity factors were incorporated to calculate EE(est). This analysis was nested in the multidisciplinary PhysicaL Activity in the Young study with a prospective study design. Peri-urban black South African adolescents were investigated in a subsample of 131 learners (87 girls and 44 boys) from the parent study sample of 369 (211 girls and 158 boys) who had all measurements taken. Pearson correlation coefficients and Bland-Altman plots were calculated to identify the most accurate published equations to estimate BMR (P<0.05 statistically significant). EE(est) was estimated using BMR equations and estimated physical activity factors derived from Previous Day Physical Activity Recall questionnaires. After calculation of EE(est), the relative validity of reported energy intake (EI(rep)) derived from multiple 24-h recalls was tested for three data subsets using Pearson correlation coefficients. Goldberg's formula identified cut points (CPs) for under and over reporting of EI. Pearson correlation coefficients between calculated BMRs ranged from 0.97 to 0.99. Bland-Altman analyses showed acceptable agreement (two equations for each gender). One equation for each gender was used to calculate EE(est). Pearson correlation coefficients between EI(rep) and EE(est) for three data sets were weak, indicating poor agreement. CPs for physical activity groups showed under reporting in 87% boys and 95% girls. The 24-h recalls measured at five measurements over 2 years offered poor validity between EI(rep) and EE(est).

Dynamics of 3D Timoshenko gyroelastic beams with large attitude changes for the gyros

NASA Astrophysics Data System (ADS)

Hassanpour, Soroosh; Heppler, G. R.

2016-01-01

This work is concerned with the theoretical development of dynamic equations for undamped gyroelastic beams which are dynamic systems with continuous inertia, elasticity, and gyricity. Assuming unrestricted or large attitude changes for the axes of the gyros and utilizing generalized Hooke's law, Duleau torsion theory, and Timoshenko bending theory, the energy expressions and equations of motion for the gyroelastic beams in three-dimensional space are derived. The so-obtained comprehensive gyroelastic beam model is compared against earlier gyroelastic beam models developed using Euler-Bernoulli beam models and is used to study the dynamics of gyroelastic beams through numerical examples. It is shown that there are significant differences between the developed unrestricted Timoshenko gyroelastic beam model and the previously derived zero-order restricted Euler-Bernoulli gyroelastic beam models. These differences are more pronounced in the short beam and transverse gyricity cases.

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

Casana, Rodolfo, E-mail: rodolfo.casana@gmail.com; Ferreira, Manoel M., E-mail: manojr.ufma@gmail.com; Mota, Alexsandro Lucena, E-mail: lucenalexster@gmail.com

We have studied the existence of topological self-dual configurations in a nonminimal CPT-odd and Lorentz-violating (LV) Maxwell–Higgs model, where the LV interaction is introduced by modifying the minimal covariant derivative. The Bogomol’nyi–Prasad–Sommerfield formalism has been implemented, revealing that the scalar self-interaction implying self-dual equations contains a derivative coupling. The CPT-odd self-dual equations describe electrically neutral configurations with finite total energy proportional to the total magnetic flux, which differ from the charged solutions of other CPT-odd and LV models previously studied. In particular, we have investigated the axially symmetrical self-dual vortex solutions altered by the LV parameter. For large distances, themore » profiles possess general behavior similar to the vortices of Abrikosov–Nielsen–Olesen. However, within the vortex core, the profiles of the magnetic field and energy can differ substantially from ones of the Maxwell–Higgs model depending if the LV parameter is negative or positive.« less

Suspension concentration distribution in turbulent flows: An analytical study using fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Kundu, Snehasis

2018-09-01

In this study vertical distribution of sediment particles in steady uniform turbulent open channel flow over erodible bed is investigated using fractional advection-diffusion equation (fADE). Unlike previous investigations on fADE to investigate the suspension distribution, in this study the modified Atangana-Baleanu-Caputo fractional derivative with a non-singular and non-local kernel is employed. The proposed fADE is solved and an analytical model for finding vertical suspension distribution is obtained. The model is validated against experimental as well as field measurements of Missouri River, Mississippi River and Rio Grande conveyance channel and is compared with the Rouse equation and other fractional model found in literature. A quantitative error analysis shows that the proposed model is able to predict the vertical distribution of particles more appropriately than previous models. The validation results shows that the fractional model can be equally applied to all size of particles with an appropriate choice of the order of the fractional derivative α. It is also found that besides particle diameter, parameter α depends on the mass density of particle and shear velocity of the flow. To predict this parameter, a multivariate regression is carried out and a relation is proposed for easy application of the model. From the results for sand and plastic particles, it is found that the parameter α is more sensitive to mass density than the particle diameter. The rationality of the dependence of α on particle and flow characteristics has been justified physically.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Revised techniques for estimating peak discharges from channel width in Montana

USGS Publications Warehouse

Parrett, Charles; Hull, J.A.; Omang, R.J.

1987-01-01

This study was conducted to develop new estimating equations based on channel width and the updated flood frequency curves of previous investigations. Simple regression equations for estimating peak discharges with recurrence intervals of 2, 5, 10 , 25, 50, and 100 years were developed for seven regions in Montana. The standard errors of estimates for the equations that use active channel width as the independent variables ranged from 30% to 87%. The standard errors of estimate for the equations that use bankfull width as the independent variable ranged from 34% to 92%. The smallest standard errors generally occurred in the prediction equations for the 2-yr flood, 5-yr flood, and 10-yr flood, and the largest standard errors occurred in the prediction equations for the 100-yr flood. The equations that use active channel width and the equations that use bankfull width were determined to be about equally reliable in five regions. In the West Region, the equations that use bankfull width were slightly more reliable than those based on active channel width, whereas in the East-Central Region the equations that use active channel width were slightly more reliable than those based on bankfull width. Compared with similar equations previously developed, the standard errors of estimate for the new equations are substantially smaller in three regions and substantially larger in two regions. Limitations on the use of the estimating equations include: (1) The equations are based on stable conditions of channel geometry and prevailing water and sediment discharge; (2) The measurement of channel width requires a site visit, preferably by a person with experience in the method, and involves appreciable measurement errors; (3) Reliability of results from the equations for channel widths beyond the range of definition is unknown. In spite of the limitations, the estimating equations derived in this study are considered to be as reliable as estimating equations based on basin and climatic variables. Because the two types of estimating equations are independent, results from each can be weighted inversely proportional to their variances, and averaged. The weighted average estimate has a variance less than either individual estimate. (Author 's abstract)

Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

NASA Astrophysics Data System (ADS)

Yasuhiko Igarashi,; Masafumi Oizumi,; Masato Okada,

2010-08-01

We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing-state variable and a synaptic variable. In these equations, the average product of thesevariables is decoupled as the product of their averages because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight Jij is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady-state equations for a network with uniform connections and for a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady-state solutions. An oscillatory uniform state was observed in the network with uniform connections owing to a Hopf instability. For the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading to two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previously unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.

Further Development of a New, Flux-Conserving Newton Scheme for the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Scott, James R.

1996-01-01

This paper is one of a series of papers describing the development of a new numerical approach for solving the steady Navier-Stokes equations. The key features in the current development are (1) the discrete representation of the dependent variables by way of high order polynomial expansions, (2) the retention of all derivatives in the expansions as unknowns to be explicitly solved for, (3) the automatic balancing of fluxes at cell interfaces, and (4) the discrete simulation of both the integral and differential forms of the governing equations. The main purpose of this paper is, first, to provide a systematic and rigorous derivation of the conditions that are used to simulate the differential form of the Navier-Stokes equations, and second, to extend our previously-presented internal flow scheme to external flows and nonuniform grids. Numerical results are presented for high Reynolds number flow (Re = 100,000) around a finite flat plate, and detailed comparisons are made with the Blasius flat plate solution and Goldstein wake solution. It is shown that the error in the streamwise velocity decreases like r(sup alpha)(Delta)y(exp 2), where alpha approx. 0.25 and r = delta(y)/delta(x) is the grid aspect ratio.

High-dynamic range imaging techniques based on both color-separation algorithms used in conventional graphic arts and the human visual perception modeling

NASA Astrophysics Data System (ADS)

Lo, Mei-Chun; Hsieh, Tsung-Hsien; Perng, Ruey-Kuen; Chen, Jiong-Qiao

2010-01-01

The aim of this research is to derive illuminant-independent type of HDR imaging modules which can optimally multispectrally reconstruct of every color concerned in high-dynamic-range of original images for preferable cross-media color reproduction applications. Each module, based on either of broadband and multispectral approach, would be incorporated models of perceptual HDR tone-mapping, device characterization. In this study, an xvYCC format of HDR digital camera was used to capture HDR scene images for test. A tone-mapping module was derived based on a multiscale representation of the human visual system and used equations similar to a photoreceptor adaptation equation, proposed by Michaelis-Menten. Additionally, an adaptive bilateral type of gamut mapping algorithm, using approach of a multiple conversing-points (previously derived), was incorporated with or without adaptive Un-sharp Masking (USM) to carry out the optimization of HDR image rendering. An LCD with standard color space of Adobe RGB (D65) was used as a soft-proofing platform to display/represent HDR original RGB images, and also evaluate both renditionquality and prediction-performance of modules derived. Also, another LCD with standard color space of sRGB was used to test gamut-mapping algorithms, used to be integrated with tone-mapping module derived.

Helicity evolution at small x : Flavor singlet and nonsinglet observables

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2017-01-30

We extend our earlier results for the quark helicity evolution at small x to derive the small-x asymptotics of the flavor singlet and flavor nonsinglet quark helicity TMDs and PDFs and of the g 1 structure function. In the flavor singlet case we rederive the evolution equations obtained in our previous paper on the subject, performing additional cross-checks of our results. In the flavor nonsinglet case we construct new small-x evolution equations by employing the large-N c limit. Here, all evolution equations resum double-logarithmic powers of α sln 2(1/x) in the polarization-dependent evolution along with the single-logarithmic powers of αmore » sln(1/x) in the unpolarized evolution which includes saturation effects.« less

Helicity evolution at small x : Flavor singlet and nonsinglet observables

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

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

We extend our earlier results for the quark helicity evolution at small x to derive the small-x asymptotics of the flavor singlet and flavor nonsinglet quark helicity TMDs and PDFs and of the g 1 structure function. In the flavor singlet case we rederive the evolution equations obtained in our previous paper on the subject, performing additional cross-checks of our results. In the flavor nonsinglet case we construct new small-x evolution equations by employing the large-N c limit. Here, all evolution equations resum double-logarithmic powers of α sln 2(1/x) in the polarization-dependent evolution along with the single-logarithmic powers of αmore » sln(1/x) in the unpolarized evolution which includes saturation effects.« less

A FORTRAN program for interpretation of relative permeability from unsteady-state displacements with capillary pressure included

USGS Publications Warehouse

Udegbunam, E.O.

1991-01-01

This paper presents a FORTRAN program for the determination of two-phase relative permeabilities from unsteady-state displacement data with capillary pressure terms included. The interpretative model employed in this program combines the simultaneous solution of a variant of the fractional flow equation which includes a capillary pressure term and an integro-differential equation derived from Darcy's law without assuming the simplified Buckley-Leverett flow. The incorporation of capillary pressure in the governing equations dispenses with the high flowrate experimental requirements normally employed to overcome capillarity effects. An illustrative example is presented herein which implements this program for the determination of oil/water relative permeabilities from a sandstone core sample. Results obtained compares favorably with results previously given in the literature. ?? 1991.

A Note on the Wave Action Density of a Viscous Instability Mode on a Laminar Free-shear Flow

NASA Technical Reports Server (NTRS)

Balsa, Thomas F.

1994-01-01

Using the assumptions of an incompressible and viscous flow at large Reynolds number, we derive the evolution equation for the wave action density of an instability wave traveling on top of a laminar free-shear flow. The instability is considered to be viscous; the purpose of the present work is to include the cumulative effect of the (locally) small viscous correction to the wave, over length and time scales on which the underlying base flow appears inhomogeneous owing to its viscous diffusion. As such, we generalize our previous work for inviscid waves. This generalization appears as an additional (but usually non-negligible) term in the equation for the wave action. The basic structure of the equation remains unaltered.

Multiloop functional renormalization group for general models

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-02-01

We present multiloop flow equations in the functional renormalization group (fRG) framework for the four-point vertex and self-energy, formulated for a general fermionic many-body problem. This generalizes the previously introduced vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403 (2018), 10.1103/PhysRevLett.120.057403] and provides the necessary corrections to the self-energy flow in order to complete the derivative of all diagrams involved in the truncated fRG flow. Due to its iterative one-loop structure, the multiloop flow is well suited for numerical algorithms, enabling improvement of many fRG computations. We demonstrate its equivalence to a solution of the (first-order) parquet equations in conjunction with the Schwinger-Dyson equation for the self-energy.

Generation of long subharmonic internal waves by surface waves

NASA Astrophysics Data System (ADS)

Tahvildari, Navid; Kaihatu, James M.; Saric, William S.

2016-10-01

A new set of Boussinesq equations is derived to study the nonlinear interactions between long waves in a two-layer fluid. The fluid layers are assumed to be homogeneous, inviscid, incompressible, and immiscible. Based on the Boussinesq equations, an analytical model is developed using a second-order perturbation theory and applied to examine the transient evolution of a resonant triad composed of a surface wave and two oblique subharmonic internal waves. Wave damping due to weak viscosity in both layers is considered. The Boussinesq equations and the analytical model are verified. In contrast to previous studies which focus on short internal waves, we examine long waves and investigate some previously unexplored characteristics of this class of triad interaction. In viscous fluids, surface wave amplitudes must be larger than a threshold to overcome viscous damping and trigger internal waves. The dependency of this critical amplitude as well as the growth and damping rates of internal waves on important parameters in a two-fluid system, namely the directional angle of the internal waves, depth, density, and viscosity ratio of the fluid layers, and surface wave amplitude and frequency is investigated.

New Equations for the Sublimation Pressure and Melting Pressure of H2O Ice Ih

NASA Astrophysics Data System (ADS)

Wagner, Wolfgang; Riethmann, Thomas; Feistel, Rainer; Harvey, Allan H.

2011-12-01

New reference equations, adopted by the International Association for the Properties of Water and Steam (IAPWS), are presented for the sublimation pressure and melting pressure of ice Ih as a function of temperature. These equations are based on input values derived from the phase-equilibrium condition between the IAPWS-95 scientific standard for thermodynamic properties of fluid H2O and the equation of state of H2O ice Ih adopted by IAPWS in 2006, making them thermodynamically consistent with the bulk-phase properties. Compared to the previous IAPWS formulations, which were empirical fits to experimental data, the new equations have significantly less uncertainty. The sublimation-pressure equation covers the temperature range from 50 K to the vapor-liquid-solid triple point at 273.16 K. The ice Ih melting-pressure equation describes the entire melting curve from 273.16 K to the ice Ih-ice III-liquid triple point at 251.165 K. For completeness, we also give the IAPWS melting-pressure equation for ice III, which is slightly adjusted to agree with the ice Ih melting-pressure equation at the corresponding triple point, and the unchanged IAPWS melting-pressure equations for ice V, ice VI, and ice VII.

In vivo estimates of NO and CO conductance for haemoglobin and for lung transfer in humans.

PubMed

Guénard, Hervé Jean-Pierre; Martinot, Jean-Benoit; Martin, Sebastien; Maury, Bertrand; Lalande, Sophie; Kays, Christian

2016-07-01

Membrane conductance (Dm) and capillary lung volume (Vc) derived from NO and CO lung transfer measurements in humans depend on the blood conductance (θ) values of both gases. Many θ values have been proposed in the literature. In the present study, measurements of CO and NO transfer while breathing 15% or 21% O2 allowed the estimation of θNO and the calculation of the optimal equation relating 1/θCO to pulmonary capillary oxygen pressure (PcapO2). In 10 healthy subjects, the mean calculated θNO value was similar to the θNO value previously reported in the literature (4.5mmHgmin(-1)) provided that one among three θCO equations from the literature was chosen. Setting 1/θCO=a·PcapO2+b, optimal values of a and b could be chosen using two methods: 1) by minimizing the difference between Dm/Vc ratios for any PcapO2, 2) by establishing a linear equation relating a and b. Using these methods, we are proposing the equation 1/θCO=0.0062·PcapO2+1.16, which is similar to two equations previously reported in the literature. With this set of θ values, DmCO reached the morphometric range. Copyright © 2016 Elsevier B.V. All rights reserved.

About Tidal Evolution of Quasi-Periodic Orbits of Satellites

NASA Astrophysics Data System (ADS)

Ershkov, Sergey V.

2017-06-01

Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. The modern ansatz in the theory of tidal dissipation in Saturn was developed previously by the international team of scientists from various countries in the field of celestial mechanics. Our applying to the theory of tidal dissipation concerns the investigating of the system of ODE-equations (ordinary differential equations) that govern the orbital evolution of the satellites; such an extremely non-linear system of 2 ordinary differential equations describes the mutual internal dynamics for the eccentricity of the orbit along with involving the semi-major axis of the proper satellite into such a monstrous equations. In our derivation, we have presented the elegant analytical solutions to the system above; so, the motivation of our ansatz is to transform the previously presented system of equations to the convenient form, in which the minimum of numerical calculations are required to obtain the final solutions. Preferably, it should be the analytical solutions; we have presented the solution as a set of quasi- periodic cycles via re-inversing of the proper ultra- elliptical integral. It means a quasi-periodic character of the evolution of the eccentricity, of the semi-major axis for the satellite orbit as well as of the quasi-periodic character of the tidal dissipation in the Planet.

Radiation-reaction force on a small charged body to second order

NASA Astrophysics Data System (ADS)

Moxon, Jordan; Flanagan, Éanna

2018-05-01

In classical electrodynamics, an accelerating charged body emits radiation and experiences a corresponding radiation-reaction force, or self-force. We extend to higher order in the total charge a previous rigorous derivation of the electromagnetic self-force in flat spacetime by Gralla, Harte, and Wald. The method introduced by Gralla, Harte, and Wald computes the self-force from the Maxwell field equations and conservation of stress-energy in a limit where the charge, size, and mass of the body go to zero, and it does not require regularization of a singular self-field. For our higher-order computation, an adjustment of the definition of the mass of the body is necessary to avoid including self-energy from the electromagnetic field sourced by the body in the distant past. We derive the evolution equations for the mass, spin, and center-of-mass position of the body through second order. We derive, for the first time, the second-order acceleration dependence of the evolution of the spin (self-torque), as well as a mixing between the extended body effects and the acceleration-dependent effects on the overall body motion.

Derivation of regularized Grad's moment system from kinetic equations: modes, ghosts and non-Markov fluxes

NASA Astrophysics Data System (ADS)

Karlin, Ilya

2018-04-01

Derivation of the dynamic correction to Grad's moment system from kinetic equations (regularized Grad's 13 moment system, or R13) is revisited. The R13 distribution function is found as a superposition of eight modes. Three primary modes, known from the previous derivation (Karlin et al. 1998 Phys. Rev. E 57, 1668-1672. (doi:10.1103/PhysRevE.57.1668)), are extended into the nonlinear parameter domain. Three essentially nonlinear modes are identified, and two ghost modes which do not contribute to the R13 fluxes are revealed. The eight-mode structure of the R13 distribution function implies partition of R13 fluxes into two types of contributions: dissipative fluxes (both linear and nonlinear) and nonlinear streamline convective fluxes. Physical interpretation of the latter non-dissipative and non-local in time effect is discussed. A non-perturbative R13-type solution is demonstrated for a simple Lorentz scattering kinetic model. The results of this study clarify the intrinsic structure of the R13 system. This article is part of the theme issue `Hilbert's sixth problem'.

The varying cosmological constant: a new approximation to the Friedmann equations and universe model

NASA Astrophysics Data System (ADS)

Öztaş, Ahmet M.; Dil, Emre; Smith, Michael L.

2018-05-01

We investigate the time-dependent nature of the cosmological constant, Λ, of the Einstein Field Equation (EFE). Beginning with the Einstein-Hilbert action as our fundamental principle we develop a modified version of the EFE allowing the value of Λ to vary as a function of time, Λ(t), indirectly, for an expanding universe. We follow the evolving Λ presuming four-dimensional space-time and a flat universe geometry and present derivations of Λ(t) as functions of the Hubble constant, matter density, and volume changes which can be traced back to the radiation epoch. The models are more detailed descriptions of the Λ dependence on cosmological factors than previous, allowing calculations of the important parameters, Ωm and Ωr, to deep lookback times. Since we derive these without the need for extra dimensions or other special conditions our derivations are useful for model evaluation with astronomical data. This should aid resolution of several difficult problems of astronomy such as the best value for the Hubble constant at present and at recombination.

Thermodynamic aspect in using modified Boltzmann model as an acoustic probe for URu2Si2

NASA Astrophysics Data System (ADS)

Kwang-Hua, Chu Rainer

2018-05-01

The approximate system of equations describing ultrasonic attenuation propagating in many electrons of the heavy-fermion materials URu2Si2 under high magnetic fields were firstly derived and then calculated based on the modified Boltzmann model considering the microscopic contributions due to electronic fluids. A system of nonlinear partial differential coupled with integral equations were linearized firstly and approximately solved considering the perturbed thermodynamic equilibrium states. Our numerical data were compared with previous measurements using non-dimensional or normalized physical values. The rather good fit of our numerical calculations with experimental measurements confirms our present approach.

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

Song, Kai; Song, Linze; Shi, Qiang, E-mail: qshi@iccas.ac.cn

Based on the path integral approach, we derive a new realization of the exact non-Markovian stochastic Schrödinger equation (SSE). The main difference from the previous non-Markovian quantum state diffusion (NMQSD) method is that the complex Gaussian stochastic process used for the forward propagation of the wave function is correlated, which may be used to reduce the amplitude of the non-Markovian memory term at high temperatures. The new SSE is then written into the recently developed hierarchy of pure states scheme, in a form that is more closely related to the hierarchical equation of motion approach. Numerical simulations are then performedmore » to demonstrate the efficiency of the new method.« less

Nonequilibrium itinerant-electron magnetism: A time-dependent mean-field theory

NASA Astrophysics Data System (ADS)

Secchi, A.; Lichtenstein, A. I.; Katsnelson, M. I.

2016-08-01

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation that is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the nonequilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of nonequilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of nonequilibrium single-electron Green's functions and self-energies. In the particular case of equilibrium, we recover previously known results.

General-relativistic celestial mechanics. 4: Theory of satellite motion

NASA Astrophysics Data System (ADS)

Damour, T.; Soffel, M.; Xu, C.

1993-09-01

The basic equations needed for developing a complete relativistic theory of artificial Earth satellites are explicitly written down. These equations are given both in a local, geocentric frame and in the global, barycentric one. They are derived within our recently introduced general-relativistic celestial mechanics framework. Our approach is more satisfactory than previous ones, especially with regard to its consistency, completeness, and flexibility. In particular, the problem of representing the relativistic gravitational effects associated with the quadrupole and higher multipole moments of the moving Earth, which caused difficulties in several other approaches, is easily dealth with in our approach, thanks to the use of previously developed tools: definition of relativistic multipole moments and transformation theory between reference frames. With this last paper in a series, we hope to indicate the way of using our formalism in specific problems in applied celestial mechanics and astrometry.

Coupled rotor and fuselage equations of motion

NASA Technical Reports Server (NTRS)

Warmbrodt, W.

1979-01-01

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which are used to study coupled rotor/fuselage dynamics in forward flight. Rotor/fuselage coupling is documented and the importance of an ordering scheme in deriving nonlinear equations of motion is reviewed. The nature of the final equations and the use of multiblade coordinates are discussed.

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America

A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions. Appendix A

NASA Technical Reports Server (NTRS)

Constantinescu, George S.; Lele, S. K.

2001-01-01

Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius (1). Extension of the method described here for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical or spherical coordinates with finite-differences schemes of various level of accuracy is immediate.

Derivation of Inviscid Quasi-geostrophic Equation from Rotational Compressible Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam; Lin, Ying-Chieh; Su, Cheng-Fang

2018-04-01

In this paper, we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the rotational compressible magnetohydrodynamic flows with the well-prepared initial data. It is a first derivation of quasi-geostrophic equation governed by the magnetic field, and the tool is based on the relative entropy method. This paper covers two results: the existence of the unique local strong solution of quasi-geostrophic equation with the good regularity and the derivation of a quasi-geostrophic equation.

On the nature of liquid junction and membrane potentials.

PubMed

Perram, John W; Stiles, Peter J

2006-09-28

Whenever a spatially inhomogeneous electrolyte, composed of ions with different mobilities, is allowed to diffuse, charge separation and an electric potential difference is created. Such potential differences across very thin membranes (e.g. biomembranes) are often interpreted using the steady state Goldman equation, which is usually derived by assuming a spatially constant electric field. Through the fundamental Poisson equation of electrostatics, this implies the absence of free charge density that must provide the source of any such field. A similarly paradoxical situation is encountered for thick membranes (e.g. in ion-selective electrodes) for which the diffusion potential is normally interpreted using the Henderson equation. Standard derivations of the Henderson equation appeal to local electroneutrality, which is also incompatible with sources of electric fields, as these require separated charges. We analyse self-consistent solutions of the Nernst-Planck-Poisson equations for a 1 : 1-univalent electrolyte to show that the Goldman and Henderson steady-state membrane potentials are artefacts of extraneous charges created in the reservoirs of electrolyte solution on either side of the membrane, due to the unphysical nature of the usual (Dirichlet) boundary conditions assumed to apply at the membrane-electrolyte interfaces. We also show, with the aid of numerical simulations, that a transient electric potential difference develops in any confined, but initially non-uniform, electrolyte solution. This potential difference ultimately decays to zero in the real steady state of the electrolyte, which corresponds to thermodynamic equilibrium. We explain the surprising fact that such transient potential differences are well described by the Henderson equation by using a computer algebra system to extend previous steady-state singular perturbation theories to the time-dependent case. Our work therefore accounts for the success of the Henderson equation in analysing experimental liquid-junction potentials.

Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2014-03-14

The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneouslymore » integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.« less

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)

1996-01-01

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Generalized analytical solutions to sequentially coupled multi-species advective-dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Liu, Chen-Wuing; Liang, Ching-Ping; Lai, Keng-Hsin

2012-08-01

SummaryMulti-species advective-dispersive transport equations sequentially coupled with first-order decay reactions are widely used to describe the transport and fate of the decay chain contaminants such as radionuclide, chlorinated solvents, and nitrogen. Although researchers attempted to present various types of methods for analytically solving this transport equation system, the currently available solutions are mostly limited to an infinite or a semi-infinite domain. A generalized analytical solution for the coupled multi-species transport problem in a finite domain associated with an arbitrary time-dependent source boundary is not available in the published literature. In this study, we first derive generalized analytical solutions for this transport problem in a finite domain involving arbitrary number of species subject to an arbitrary time-dependent source boundary. Subsequently, we adopt these derived generalized analytical solutions to obtain explicit analytical solutions for a special-case transport scenario involving an exponentially decaying Bateman type time-dependent source boundary. We test the derived special-case solutions against the previously published coupled 4-species transport solution and the corresponding numerical solution with coupled 10-species transport to conduct the solution verification. Finally, we compare the new analytical solutions derived for a finite domain against the published analytical solutions derived for a semi-infinite domain to illustrate the effect of the exit boundary condition on coupled multi-species transport with an exponential decaying source boundary. The results show noticeable discrepancies between the breakthrough curves of all the species in the immediate vicinity of the exit boundary obtained from the analytical solutions for a finite domain and a semi-infinite domain for the dispersion-dominated condition.

On hydrostatic flows in isentropic coordinates

NASA Astrophysics Data System (ADS)

Bokhove, Onno

2000-01-01

The hydrostatic primitive equations of motion which have been used in large-scale weather prediction and climate modelling over the last few decades are analysed with variational methods in an isentropic Eulerian framework. The use of material isentropic coordinates for the Eulerian hydrostatic equations is known to have distinct conceptual advantages since fluid motion is, under inviscid and statically stable circumstances, confined to take place on quasi-horizontal isentropic surfaces. First, an Eulerian isentropic Hamilton's principle, expressed in terms of fluid parcel variables, is therefore derived by transformation of a Lagrangian Hamilton's principle to an Eulerian one. This Eulerian principle explicitly describes the boundary dynamics of the time-dependent domain in terms of advection of boundary isentropes sB; these are the values the isentropes have at their intersection with the (lower) boundary. A partial Legendre transform for only the interior variables yields an Eulerian ‘action’ principle. Secondly, Noether's theorem is used to derive energy and potential vorticity conservation from the Eulerian Hamilton's principle. Thirdly, these conservation laws are used to derive a wave-activity invariant which is second-order in terms of small-amplitude disturbances relative to a resting or moving basic state. Linear stability criteria are derived but only for resting basic states. In mid-latitudes a time- scale separation between gravity and vortical modes occurs. Finally, this time-scale separation suggests that conservative geostrophic and ageostrophic approximations can be made to the Eulerian action principle for hydrostatic flows. Approximations to Eulerian variational principles may be more advantageous than approximations to Lagrangian ones because non-dimensionalization and scaling tend to be based on Eulerian estimates of the characteristic scales involved. These approximations to the stratified hydrostatic formulation extend previous approximations to the shallow- water equations. An explicit variational derivation is given of an isentropic version of Hoskins & Bretherton's model for atmospheric fronts.

Simple Derivation of the Lindblad Equation

ERIC Educational Resources Information Center

Pearle, Philip

2012-01-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

Evaluation of the National Research Council (2001) dairy model and derivation of new prediction equations. 1. Digestibility of fiber, fat, protein, and nonfiber carbohydrate.

PubMed

White, R R; Roman-Garcia, Y; Firkins, J L; VandeHaar, M J; Armentano, L E; Weiss, W P; McGill, T; Garnett, R; Hanigan, M D

2017-05-01

Evaluation of ration balancing systems such as the National Research Council (NRC) Nutrient Requirements series is important for improving predictions of animal nutrient requirements and advancing feeding strategies. This work used a literature data set (n = 550) to evaluate predictions of total-tract digested neutral detergent fiber (NDF), fatty acid (FA), crude protein (CP), and nonfiber carbohydrate (NFC) estimated by the NRC (2001) dairy model. Mean biases suggested that the NRC (2001) lactating cow model overestimated true FA and CP digestibility by 26 and 7%, respectively, and under-predicted NDF digestibility by 16%. All NRC (2001) estimates had notable mean and slope biases and large root mean squared prediction error (RMSPE), and concordance (CCC) ranged from poor to good. Predicting NDF digestibility with independent equations for legumes, corn silage, other forages, and nonforage feeds improved CCC (0.85 vs. 0.76) compared with the re-derived NRC (2001) equation form (NRC equation with parameter estimates re-derived against this data set). Separate FA digestion coefficients were derived for different fat supplements (animal fats, oils, and other fat types) and for the basal diet. This equation returned improved (from 0.76 to 0.94) CCC compared with the re-derived NRC (2001) equation form. Unique CP digestibility equations were derived for forages, animal protein feeds, plant protein feeds, and other feeds, which improved CCC compared with the re-derived NRC (2001) equation form (0.74 to 0.85). New NFC digestibility coefficients were derived for grain-specific starch digestibilities, with residual organic matter assumed to be 98% digestible. A Monte Carlo cross-validation was performed to evaluate repeatability of model fit. In this procedure, data were randomly subsetted 500 times into derivation (60%) and evaluation (40%) data sets, and equations were derived using the derivation data and then evaluated against the independent evaluation data. Models derived with random study effects demonstrated poor repeatability of fit in independent evaluation. Similar equations derived without random study effects showed improved fit against independent data and little evidence of biased parameter estimates associated with failure to include study effects. The equations derived in this analysis provide interesting insight into how NDF, starch, FA, and CP digestibilities are affected by intake, feed type, and diet composition. The Authors. Published by the Federation of Animal Science Societies and Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Malay; Jayannavar, A. M.

2017-10-01

In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

The general Lie group and similarity solutions for the one-dimensional Vlasov-Maxwell equations

NASA Technical Reports Server (NTRS)

Roberts, D.

1985-01-01

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multispecies case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution for a one-species, one-dimensional plasma is one of the general similarity solutions.

Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

NASA Astrophysics Data System (ADS)

Zhang, Dong; Kushibiki, Junichi; Zou, Wei

2006-10-01

We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO2/specimen/SiO2 multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33-96 MHz. Regarding two different ultrasonic devices, the accuracies of the measurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.

The rigidity and mobility of screw dislocations in a thin film

NASA Astrophysics Data System (ADS)

Wang, Fei

2018-07-01

An equation of screw dislocations in a thin film is derived for arbitrary boundary conditions. The boundary conditions can be the free surface, the fixed surface or the gradient loading imposed on the surface. The new equation makes it possible to study changes in the dislocation structure under various gradient stress applied to the surface. The rigidity and mobility of screw dislocations in a thin film are explored by using the equation. It is found that the screw dislocation core in a thin film is like a Hookean body with a specific shear stress applied to the surface. Free-surface effects on the Peierls stress are investigated and compared with previous studies. An abnormal behavior of the Peierls stress of screw dislocations in a soft-inclusion film between two rigid films is predicted theoretically.

A second-order closure analysis of turbulent diffusion flames. [combustion physics

NASA Technical Reports Server (NTRS)

Varma, A. K.; Fishburne, E. S.; Beddini, R. A.

1977-01-01

A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.

High Reynolds number turbulence model of rotating shear flows

NASA Astrophysics Data System (ADS)

Masuda, S.; Ariga, I.; Koyama, H. S.

1983-09-01

A Reynolds stress closure model for rotating turbulent shear flows is developed. Special attention is paid to keeping the model constants independent of rotation. First, general forms of the model of a Reynolds stress equation and a dissipation rate equation are derived, the only restrictions of which are high Reynolds number and incompressibility. The model equations are then applied to two-dimensional equilibrium boundary layers and the effects of Coriolis acceleration on turbulence structures are discussed. Comparisons with the experimental data and with previous results in other external force fields show that there exists a very close analogy between centrifugal, buoyancy and Coriolis force fields. Finally, the model is applied to predict the two-dimensional boundary layers on rotating plane walls. Comparisons with existing data confirmed its capability of predicting mean and turbulent quantities without employing any empirical relations in rotating fields.

Stellar Equilibrium in Semiclassical Gravity.

PubMed

Carballo-Rubio, Raúl

2018-02-09

The phenomenon of quantum vacuum polarization in the presence of a gravitational field is well understood and is expected to have a physical reality, but studies of its backreaction on the dynamics of spacetime are practically nonexistent outside of the specific context of homogeneous cosmologies. Building on previous results of quantum field theory in curved spacetimes, in this Letter we first derive the semiclassical equations of stellar equilibrium in the s-wave Polyakov approximation. It is highlighted that incorporating the polarization of the quantum vacuum leads to a generalization of the classical Tolman-Oppenheimer-Volkoff equation. Despite the complexity of the resulting field equations, it is possible to find exact solutions. Aside from being the first known exact solutions that describe relativistic stars including the nonperturbative backreaction of semiclassical effects, these are identified as a nontrivial combination of the black star and gravastar proposals.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions

NASA Astrophysics Data System (ADS)

Qiao, Yu; Liu, Xuejiao; Chen, Minxin; Lu, Benzhuo

2016-04-01

The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al. in Phys Rev Lett 79:435-438, 1997; Kilic et al. in Phys Rev E 75:021502, 2007; Lu and Zhou in Biophys J 100:2475-2485, 2011; Liu and Eisenberg in J Chem Phys 141:22D532, 2014) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both LHSPNP and SMPNP models the stratification of one counterion species can be observed under certain bulk concentrations.

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

Unseren, M.A.

The report reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restricts the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for themore » closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.« less

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

Unseren, M.A.

The paper reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restrict the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for themore » closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.« less

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

Vacuum-bag-only processing of composites

NASA Astrophysics Data System (ADS)

Thomas, Shad

Ultrasonic imaging in the C-scan mode in conjunction with the amplitude of the reflected signal was used to measure flow rates of an epoxy resin film penetrating through the thickness of single layers of woven carbon fabric. Assemblies, comprised of a single layer of fabric and film, were vacuum-bagged and ultrasonically scanned in a water tank during impregnation at 50°C, 60°C, 70°C, and 80°C. Measured flow rates were plotted versus inverse viscosity to determine the permeability in the thin film, non-saturated system. The results demonstrated that ultrasonic imaging in the C-scan mode is an effective method of measuring z-direction resin flow through a single layer of fabric. The permeability values determined in this work were consistent with permeability values reported in the literature. Capillary flow was not observed at the temperatures and times required for pressurized flow to occur. The flow rate at 65°C was predicted from the linear plot of flow rate versus inverse viscosity. The effects of fabric architecture on through-thickness flow rates during impregnation of an epoxy resin film were measured by ultrasonic imaging. Multilayered laminates comprised of woven carbon fabrics and epoxy films (prepregs) were fabricated by vacuum-bagging. Ultrasonic imaging was performed in a heated water tank (65°C) during impregnation. Impregnation rates showed a strong dependence on fabric architecture, despite similar areal densities. Impregnation rates are directly affected by inter-tow spacing and tow nesting, which depend on fabric architecture, and are indirectly affected by areal densities. A new method of predicting resin infusion rates in prepreg and resin film infusion processes was proposed. The Stokes equation was used to derive an equation to predict the impregnation rate of laminates as a function of fabric architecture. Flow rate data previously measured by ultrasound was analyzed with the new equation and the Kozeny-Carman equation. A fiber interaction parameter was determined as a function of fabric architecture. The derived equation is straight-forward to use, unlike the Kozeny-Carman equation. The results demonstrated that the newly derived equation can be used to predict the resin infusion rate of multilayer laminates.

Quasi-linear theory of electron density and temperature fluctuations with application to MHD generators and MPD arc thrusters

NASA Technical Reports Server (NTRS)

Smith, M.

1972-01-01

Fluctuations in electron density and temperature coupled through Ohm's law are studied for an ionizable medium. The nonlinear effects are considered in the limit of a third order quasi-linear treatment. Equations are derived for the amplitude of the fluctuation. Conditions under which a steady state can exist in the presence of the fluctuation are examined and effective transport properties are determined. A comparison is made to previously considered second order theory. The effect of third order terms indicates the possibility of fluctuations existing in regions predicted stable by previous analysis.

Exact solutions for Hele-Shaw flows with surface tension: The Schwarz-function approach

NASA Astrophysics Data System (ADS)

Vasconcelos, Giovani L.

1993-08-01

An alternative derivation of the two-parameter family of solutions for a Hele-Shaw flow with surface tension reported previously by Vasconcelos and Kadanoff [Phys. Rev. A 44, 6490 (1991)] is presented. The method of solution given here is based on the formalism of the Schwarz function: an ordinary differential equation for the Schwarz function of the moving interface is obtained and then solved.

Generalized Spencer-Lewis equation

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

Filippone, W.L.

The Spencer-Lewis equation, which describes electron transport in homogeneous media when continuous slowing down theory is valid, is derived from the Boltzmann equation. Also derived is a time-dependent generalized Spencer-Lewis equation valid for inhomogeneous media. An independent verification of this last equation is obtained for the one-dimensional case using particle balance considerations.

Improvements to photometry. Part 1: Better estimation of derivatives in extinction and transformation equations

NASA Technical Reports Server (NTRS)

Young, Andrew T.

1988-01-01

Atmospheric extinction in wideband photometry is examined both analytically and through numerical simulations. If the derivatives that appear in the Stromgren-King theory are estimated carefully, it appears that wideband measurements can be transformed to outside the atmosphere with errors no greater than a millimagnitude. A numerical analysis approach is used to estimate derivatives of both the stellar and atmospheric extinction spectra, avoiding previous assumptions that the extinction follows a power law. However, it is essential to satify the requirements of the sampling theorem to keep aliasing errors small. Typically, this means that band separations cannot exceed half of the full width at half-peak response. Further work is needed to examine higher order effects, which may well be significant.

Effects of dynamic heterogeneity and density scaling of molecular dynamics on the relationship among thermodynamic coefficients at the glass transition

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

Koperwas, K., E-mail: kkoperwas@us.edu.pl; Grzybowski, A.; Grzybowska, K.

2015-07-14

In this paper, we define and experimentally verify thermodynamic characteristics of the liquid-glass transition, taking into account a kinetic origin of the process. Using the density scaling law and the four-point measure of the dynamic heterogeneity of molecular dynamics of glass forming liquids, we investigate contributions of enthalpy, temperature, and density fluctuations to spatially heterogeneous molecular dynamics at the liquid-glass transition, finding an equation for the pressure coefficient of the glass transition temperature, dTg/dp. This equation combined with our previous formula for dTg/dp, derived solely from the density scaling criterion, implies a relationship among thermodynamic coefficients at Tg. Since thismore » relationship and both the equations for dTg/dp are very well validated using experimental data at Tg, they are promising alternatives to the classical Prigogine-Defay ratio and both the Ehrenfest equations in case of the liquid-glass transition.« less

2-3D nonlocal transport model in magnetized laser plasmas.

NASA Astrophysics Data System (ADS)

Nicolaï, Philippe; Feugeas, Jean-Luc; Schurtz, Guy

2004-11-01

We present a model of nonlocal transport for multidimensional radiation magneto-hydrodynamics codes. This model, based on simplified Fokker-Planck equations, aims at extending the formulae of G Schurtz,Ph.Nicolaï and M. Busquet [Phys. Plasmas,7,4238 (2000)] to magnetized plasmas.The improvements concern various points as the electric field effects on nonlocal transport or conversely the kinetic effects on E field. However the main purpose of this work is to generalize the previous model by including magnetic field effects. A complete system of nonlocal equations is derived from kinetic equations with self-consistent E and B fields. These equations are analyzed and simplified in order to be implemented into large laser fusion codes and coupled to other relevent physics. Finally, our model allows to obtain the deformation of the electron distribution function due to nonlocal effects. This deformation leads to a non-maxwellian function which could be used to compute the influence on other physical processes.

On stability and turbulence of fluid flows

NASA Technical Reports Server (NTRS)

Heisenberg, Werner

1951-01-01

This investigation is divided into two parts, the treatment of the stability problem of fluid flows on the one hand, and that of the turbulent motion on the other. The first part summarizes all previous investigations under a unified point of view, that is, sets up as generally as possible the conditions under which a profile possesses unstable or stable characteristics, and indicates the methods for solution of the stability equation for any arbitrary velocity profile and for calculation of the critical Reynolds number for unstable profiles. In the second part, under certain greatly idealizing assumptions, differential equations for the turbulent motions are derived and from them qualitative information about several properties of the turbulent velocity distribution is obtained.

A Novel Approach to Solve Linearized Stellar Pulsation Equations

NASA Astrophysics Data System (ADS)

Bard, Christopher; Teitler, S.

2011-01-01

We present a new approach to modeling linearized, non-radial pulsations in differentially rotating, massive stars. As a first step in this direction, we consider adiabatic pulsations and adopt the Cowling approximation that perturbations of the gravitational potential and its radial derivative are negligible. The angular dependence of the pulsation modes is expressed as a series expansion of associated Legendre polynomials; the resulting coupled system of differential equations is then solved by finding the eigenfrequencies at which the determinant of a characteristic matrix vanishes. Our method improves on previous treatments by removing the requirement that an arbitrary normalization be applied to the eigenfunctions; this brings the benefit of improved numerical robustness.

Direct coordinate-free derivation of the compatibility equation for finite strains

NASA Astrophysics Data System (ADS)

Ryzhak, E. I.

2014-07-01

The compatibility equation for the Cauchy-Green tensor field (squared tensor of pure extensionwith respect to the reference configuration) is directly derived from the well-known relation expressing this tensor via the vector field determining the mapping (transformation) of the reference configuration into the actual one. The derivation is based on the use of the apparatus of coordinatefree tensor calculus and does not apply any notions and relations of Riemannian geometry at all. The method is illustrated by deriving the well-known compatibility equation for small strains. It is shown that when the obtained compatibility equation for finite strains is linearized, it becomes the compatibility equation for small strains which indirectly confirms its correctness.

The mu-derivative and its applications to finding exact solutions of the Cahn-Hilliard, Korteveg-de Vries, and Burgers equations.

PubMed

Mitlin, Vlad

2005-10-15

A new transformation termed the mu-derivative is introduced. Applying it to the Cahn-Hilliard equation yields dynamical exact solutions. It is shown that the mu-transformed Cahn-Hilliard equation can be presented in a separable form. This transformation also yields dynamical exact solutions and separable forms for other nonlinear models such as the modified Korteveg-de Vries and the Burgers equations. The general structure of a nonlinear partial differential equation that becomes separable upon applying the mu-derivative is described.

Discrete Painlevé equations for a class of PVI τ-functions given as U(N) averages

NASA Astrophysics Data System (ADS)

Forrester, P. J.; Witte, N. S.

2005-09-01

In a recent work, difference equations (Laguerre-Freud equations) for the bi-orthogonal polynomials and related quantities corresponding to the weight on the unit circle w(z)=\\prod^m_{j=1}(z-z_j(t))^{\\rho_j} were derived. It is shown here that in the case m = 3, these difference equations, when applied to the calculation of the underlying U(N) average, reduce to a coupled system identifiable with that obtained by Adler and van Moerbeke, using the methods of the Toeplitz lattice and Virasoro constraints. Moreover, it is shown that this coupled system can be reduced to yield the discrete fifth Painlevé equation dPV as it occurs in the theory of the sixth Painlevé system. Methods based on affine Weyl group symmetries of Bäcklund transformations have previously yielded the dPV equation, but with different parameters for the same problem. We find an explicit mapping between the two forms. Applications of our results are made to give recurrences for the gap probabilities and moments in the circular unitary ensemble of random matrices, and to the diagonal spin-spin correlation function of the square lattice Ising model.

Direct Effects on the Membrane Potential due to "Pumps" that Transfer No Net Charge

PubMed Central

Schwartz, Tobias L.

1971-01-01

The effects of active ionic transport are included in the derivation of a general expression for the zero current membrane potential. It is demonstrated that an active transport system that transfers no net charge (nonrheogenic) may, nevertheless, directly alter the membrane potential. This effect depends upon the exchange of matter within the membrane between the active and passive diffusion regimes. Furthermore, in the presence of such exchange, the transmembrane active fluxes measured by the usual techniques and the local pumped fluxes are not identical. Several common uses of the term “electrogenic pump” are thus shown to be inconsistent with each other. These inconsistencies persist when the derivation is extended to produce a Goldman equation modified to account for active transport; however, that equation is shown to be limited by less narrow constraints on membrane heterogeneity and internal electric field than those previously required. In particular, it is applicable to idealized mosaic membranes limited by these requirements. PMID:5113004

Langevin modelling of high-frequency Hang-Seng index data

NASA Astrophysics Data System (ADS)

Tang, Lei-Han

2003-06-01

Accurate statistical characterization of financial time series, such as compound stock indices, foreign currency exchange rates, etc., is fundamental to investment risk management, pricing of derivative products and financial decision making. Traditionally, such data were analyzed and modeled from a purely statistics point of view, with little concern on the specifics of financial markets. Increasingly, however, attention has been paid to the underlying economic forces and the collective behavior of investors. Here we summarize a novel approach to the statistical modeling of a major stock index (the Hang Seng index). Based on mathematical results previously derived in the fluid turbulence literature, we show that a Langevin equation with a variable noise amplitude correctly reproduces the ubiquitous fat tails in the probability distribution of intra-day price moves. The form of the Langevin equation suggests that, despite the extremely complex nature of financial concerns and investment strategies at the individual's level, there exist simple universal rules governing the high-frequency price move in a stock market.

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

NASA Astrophysics Data System (ADS)

Laurie, Jason; L'Vov, Victor S.; Nazarenko, Sergey; Rudenko, Oleksii

2010-03-01

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.

Open Group Transformations Within the Sp(2)-Formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

Previously we have shown that open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of the nilpotent BFV-BRST charge operator. Here we show that they may also be quantized within an Sp(2)-frame in which there are two odd anticommuting operators called Sp(2)-charges. Previous results for finite open group transformations are generalized to the Sp(2)-formalism. We show that in order to define open group transformations on the whole ghost extended space we need Sp(2)-charges in the nonminimal sector which contains dynamical Lagrange multipliers. We give an Sp(2)-version of the quantum master equation with extended Sp(2)-charges and a master charge of a more involved form, which is proposed to represent the integrability conditions of defining operators of connection operators and which therefore should encode the generalized quantum Maurer-Cartan equations for arbitrary open groups. General solutions of this master equation are given in explicit form. A further extended Sp(2)-formalism is proposed in which the group parameters are quadrupled to a supersymmetric set and from which all results may be derived.

Quantum ratchet effect in a time non-uniform double-kicked model

NASA Astrophysics Data System (ADS)

Chen, Lei; Wang, Zhen-Yu; Hui, Wu; Chu, Cheng-Yu; Chai, Ji-Min; Xiao, Jin; Zhao, Yu; Ma, Jin-Xiang

2017-07-01

The quantum ratchet effect means that the directed transport emerges in a quantum system without a net force. The delta-kicked model is a quantum Hamiltonian model for the quantum ratchet effect. This paper investigates the quantum ratchet effect based on a time non-uniform double-kicked model, in which two flashing potentials alternately act on a particle with a homogeneous initial state of zero momentum, while the intervals between adjacent actions are not equal. The evolution equation of the state of the particle is derived from its Schrödinger equation, and the numerical method to solve the evolution equation is pointed out. The results show that quantum resonances can induce the ratchet effect in this time non-uniform double-kicked model under certain conditions; some quantum resonances, which cannot induce the ratchet effect in previous models, can induce the ratchet effect in this model, and the strengths of the ratchet effect in this model are stronger than those in previous models under certain conditions. These results enrich people’s understanding of the delta-kicked model, and provides a new optional scheme to control the quantum transport of cold atoms in experiment.

Estimating Aeroheating of a 3D Body Using a 2D Flow Solver

NASA Technical Reports Server (NTRS)

Scott, Carl D.; Brykina, Irina G.

2005-01-01

A method for rapidly estimating the aeroheating, shear stress, and other properties of hypersonic flow about a three-dimensional (3D) blunt body has been devised. First, the geometry of the body is specified in Cartesian coordinates. The surface of the body is then described by its derivatives, coordinates, and principal curvatures. Next, previously relatively simple equations are used to find, for each desired combination of angle of attack and meridional angle, a scaling factor and the shape of an equivalent axisymmetric body. These factors and equivalent shapes are entered as inputs into a previously developed computer program that solves the two-dimensional (2D) equations of flow in a non-equilibrium viscous shock layer (VSL) about an axisymmetric body. The coordinates in the output of the VSL code are transformed back to the Cartesian coordinates of the 3D body, so that computed flow quantities can be registered with locations in the 3D flow field of interest. In tests in which the 3D bodies were elliptic paraboloids, the estimates obtained by use of this method were found to agree well with solutions of 3D, finite-rate-chemistry, thin-VSL equations for a catalytic body.

Torsional oscillations of magnetized relativistic stars

NASA Astrophysics Data System (ADS)

Messios, Neophytos; Papadopoulos, Demetrios B.; Stergioulas, Nikolaos

2001-12-01

Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental l=2 torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.

Compression behavior of WC and WC-6%Co up to 50 GPa determined by synchrotron x-ray diffraction and ultrasonic techniques

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

Amulele, George M.; Manghnani, Murli H.; Marriappan, Sekar

2008-07-23

The equations of state (pressure-volume relations) for WC and WC-6%Co have been determined by synchrotron x-ray diffraction measurements on polycrystalline powder samples loaded in a diamond anvil cell as well as by ultrasonic measurements on hot-pressed polycrystalline, cylindrical samples loaded in a multianvil high-pressure apparatus. The third-order Birch-Murnaghan equation of state fitted to the x-ray diffraction pressure-density sets of data, collected up to 50 GPa, yields ambient pressure isothermal bulk moduli of K{sub oT} = 411.8{+-}12.1 GPa and K{sub oT} = 402.4{+-}14.1 GPa, with pressure derivatives of K{sub oT}' = 5.45{+-}0.73 and K{sub oT}' = 7.50{+-}0.86 for WC and WC-6%Co,more » respectively. The ultrasonic measurements, conducted up to 14 GPa, enabled the determination of the pressure dependences of both bulk and shear moduli. Using Eulerian finite strain equations to fit the ultrasonic data, we obtain for WC an ambient pressure adiabatic bulk modulus of K{sub os} = 383.8{+-}0.8 GPa, and K{sub os}' = 2.61{+-}0.07 for its pressure derivative, while values of G{sub os} = 304.0{+-}0.3 GPa and G{sub os}' = 1.50{+-}0.09 were determined for the shear modulus and its pressure derivative, respectively. Meanwhile, for WC-6%Co, we obtain K{sub os} = 357.5{+-}1.0 GPa, K{sub os}' = 5.18{+-}0.14, G{sub os} = 253.5{+-}0.3 GPa, and G{sub os}' = 1.09{+-}0.09. The equations of state derived from the ultrasonic data are in good agreement with extrapolated results reported previously by Day and Ruoff [J. Appl. Phys. 44, 2447 (1973)] and Gerlich and Kennedy [J. Appl. Phys. 50, 3331 (1978)] who carried out measurements up to 0.2 and 1.0 GPa, respectively.« less

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

PubMed

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

Performance comparison of the Prophecy (forecasting) Algorithm in FFT form for unseen feature and time-series prediction

NASA Astrophysics Data System (ADS)

Jaenisch, Holger; Handley, James

2013-06-01

We introduce a generalized numerical prediction and forecasting algorithm. We have previously published it for malware byte sequence feature prediction and generalized distribution modeling for disparate test article analysis. We show how non-trivial non-periodic extrapolation of a numerical sequence (forecast and backcast) from the starting data is possible. Our ancestor-progeny prediction can yield new options for evolutionary programming. Our equations enable analytical integrals and derivatives to any order. Interpolation is controllable from smooth continuous to fractal structure estimation. We show how our generalized trigonometric polynomial can be derived using a Fourier transform.

Derivation and correction of the Tsu-Esaki tunneling current formula

NASA Astrophysics Data System (ADS)

Bandara, K. M. S. V.; Coon, D. D.

1989-07-01

The theoretical basis of the Tsu-Esaki tunneling current formula [Appl. Phys. Lett. 22, 562 (1973)] is examined in detail and corrections are found. The starting point is an independent particle picture with fully antisymmetrized N-electron wave functions. Unitarity is used to resolve an orthonormality issue raised in earlier work. A new set of mutually consistent equations is derived for bias voltage, tunneling current, and electron densities in the emitter and collector. Corrections include a previously noted kinematic factor and a modification of emitter and collector Fermi levels. The magnitude of the corrections is illustrated numerically for the case of a resonant tunneling current-voltage characteristic.

Vapor Transport Within the Thermal Diffusion Cloud Chamber

NASA Technical Reports Server (NTRS)

Ferguson, Frank T.; Heist, Richard H.; Nuth, Joseph A., III

2000-01-01

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

Analytical approach for the fractional differential equations by using the extended tanh method

NASA Astrophysics Data System (ADS)

Pandir, Yusuf; Yildirim, Ayse

2018-07-01

In this study, we consider analytical solutions of space-time fractional derivative foam drainage equation, the nonlinear Korteweg-de Vries equation with time and space-fractional derivatives and time-fractional reaction-diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.

Harmonic Chain with Velocity Flips: Thermalization and Kinetic Theory

NASA Astrophysics Data System (ADS)

Lukkarinen, Jani; Marcozzi, Matteo; Nota, Alessia

2016-12-01

We consider the detailed structure of correlations in harmonic chains with pinning and a bulk velocity flip noise during the heat relaxation phase which occurs on diffusive time scales, for t=O(L^2) where L is the chain length. It has been shown earlier that for non-degenerate harmonic interactions these systems thermalize, and the dominant part of the correlations is given by local thermal equilibrium determined by a temperature profile which satisfies a linear heat equation. Here we are concerned with two new aspects about the thermalization process: the first order corrections in 1 / L to the local equilibrium correlations and the applicability of kinetic theory to study the relaxation process. Employing previously derived explicit uniform estimates for the temperature profile, we first derive an explicit form for the first order corrections to the particle position-momentum correlations. By suitably revising the definition of the Wigner transform and the kinetic scaling limit we derive a phonon Boltzmann equation whose predictions agree with the explicit computation. Comparing the two results, the corrections can be understood as arising from two different sources: a current-related term and a correction to the position-position correlations related to spatial changes in the phonon eigenbasis.

Conservative 3 + 1 general relativistic variable Eddington tensor radiation transport equations

DOE PAGES

Cardall, Christian Y.; Endeve, Eirik; Mezzacappa, Anthony

2013-05-07

We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These equations are intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are the lab frame coordinate basis spacetime position coordinates and the particle energy measured in the comoving frame. With an eye towards astrophysical applications—such as core-collapse supernovae and compact object mergers—in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles aremore » neutrinos, we pay special attention to the consistency of four-momentum and lepton number exchange between neutrinos and the fluid, showing the term-by-term cancellations that must occur for this consistency to be achieved.« less

Equations for obtaining melting points for the ternary system ethylene glycol/sodium chloride/water and their application to cryopreservation.

PubMed

Woods, E J; Zieger, M A; Gao, D Y; Critser, J K

1999-06-01

The present study describes the H(2)O-NaCl-ethylene glycol ternary system by using a differential scanning calorimeter to measure melting points (T(m)) of four different ratios (R) of ethylene glycol to NaCl and then devising equations to fit the experimental measurements. Ultimately an equation is derived which characterizes the liquidus surface above the eutectic for any R value in the system. This study focuses on ethylene glycol in part because of recent evidence indicating it may be less toxic to pancreatic islets than Me(2)SO, which is currently used routinely for islet cryopreservation. The resulting physical data and previously determined information regarding the osmotic characteristics of canine pancreatic islets are combined in a mathematical model to describe the volumetric response to equilibrium-rate freezing in varying initial concentrations of ethylene glycol. Copyright 1999 Academic Press.

An EBIC equation for solar cells. [Electron Beam Induced Current

NASA Technical Reports Server (NTRS)

Luke, K. L.; Von Roos, O.

1983-01-01

When an electron beam of a scanning electron microscope (SEM) impinges on an N-P junction, the generation of electron-hole pairs by impact ionization causes a characteristic short circuit current I(sc) to flow. The I(sc), i.e., EBIC (electron beam induced current) depends strongly on the configuration used to investigate the cell's response. In this paper the case where the plane of the junction is perpendicular to the surface is considered. An EBIC equation amenable to numerical computations is derived as a function of cell thickness, source depth, surface recombination velocity, diffusion length, and distance of the junction to the beam-cell interaction point for a cell with an ohmic contact at its back surface. It is shown that the EBIC equation presented here is more general and easier to use than those previously reported. The effects of source depth, ohmic contact, and diffusion length on the normalized EBIC characteristic are discussed.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes

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

Konor, Celal S.; Randall, David A.

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity modes on a midlatitude f plane.The results of our normal-modemore » analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.« less

Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model.

PubMed

Paninski, Liam; Haith, Adrian; Szirtes, Gabor

2008-02-01

We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods.

Improved computational treatment of transonic flow about swept wings

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Bailey, F. R.; Frick, J.

1976-01-01

Relaxation solutions to classical three-dimensional small-disturbance (CSD) theory for transonic flow about lifting swept wings are reported. For such wings, the CSD theory was found to be a poor approximation to the full potential equation in regions of the flow field that are essentially two-dimensional in a plane normal to the sweep direction. The effect of this deficiency on the capture of embedded shock waves in terms of (1) the conditions under which shock waves can exist and (2) the relations they must satisfy when they do exist is emphasized. A modified small-disturbance (MSD) equation, derived by retaining two previously neglected terms, was proposed and shown to be a consistent approximation to the full potential equation over a wider range of sweep angles. The effect of these extra terms is demonstrated by comparing CSD, MSD, and experimental wing surface pressures.

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

PubMed

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

Estimating unknown input parameters when implementing the NGA ground-motion prediction equations in engineering practice

USGS Publications Warehouse

Kaklamanos, James; Baise, Laurie G.; Boore, David M.

2011-01-01

The ground-motion prediction equations (GMPEs) developed as part of the Next Generation Attenuation of Ground Motions (NGA-West) project in 2008 are becoming widely used in seismic hazard analyses. However, these new models are considerably more complicated than previous GMPEs, and they require several more input parameters. When employing the NGA models, users routinely face situations in which some of the required input parameters are unknown. In this paper, we present a framework for estimating the unknown source, path, and site parameters when implementing the NGA models in engineering practice, and we derive geometrically-based equations relating the three distance measures found in the NGA models. Our intent is for the content of this paper not only to make the NGA models more accessible, but also to help with the implementation of other present or future GMPEs.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes

DOE PAGES

Konor, Celal S.; Randall, David A.

2018-05-08

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity modes on a midlatitude f plane.The results of our normal-modemore » analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.« less

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations - Part 2: Quasi-geostrophic Rossby modes

NASA Astrophysics Data System (ADS)

Konor, Celal S.; Randall, David A.

2018-05-01

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia-gravity modes on a midlatitude f plane.The results of our normal-mode analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.

Diffusion of test particles in stochastic magnetic fields for small Kubo numbers.

PubMed

Neuer, Marcus; Spatschek, Karl H

2006-02-01

Motion of charged particles in a collisional plasma with stochastic magnetic field lines is investigated on the basis of the so-called A-Langevin equation. Compared to the previously used A-Langevin model, here finite Larmor radius effects are taken into account. The A-Langevin equation is solved under the assumption that the Lagrangian correlation function for the magnetic field fluctuations is related to the Eulerian correlation function (in Gaussian form) via the Corrsin approximation. The latter is justified for small Kubo numbers. The velocity correlation function, being averaged with respect to the stochastic variables including collisions, leads to an implicit differential equation for the mean square displacement. From the latter, different transport regimes, including the well-known Rechester-Rosenbluth diffusion coefficient, are derived. Finite Larmor radius contributions show a decrease of the diffusion coefficient compared to the guiding center limit. The case of small (or vanishing) mean fields is also discussed.

A Lagrangian meshfree method applied to linear and nonlinear elasticity

PubMed Central

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code. PMID:29045443

Finding the Equation for a Vibrating Car Antenna.

ERIC Educational Resources Information Center

Newburgh, Ronald; Newburgh, G. Alexander

2000-01-01

Presents the physical assumptions and mathematical expressions necessary to derive a fourth-order differential equation that describes the vibration of a particular car antenna. Contends that while students may not be able to derive or use the equation, they should be able to appreciate a guided derivation as an example of how physics is done.…

Minimal area surfaces dual to Wilson loops and the Mathieu equation

DOE PAGES

Huang, Changyu; He, Yifei; Kruczenski, Martin

2016-08-11

The AdS/CFT correspondence relates Wilson loops in N=4 SYM to minimal area surfaces in AdS 5 × S 5 space. Recently, a new approach to study minimal area surfaces in AdS 3 c AdS 5 was discussed based on a Schroedinger equation with a periodic potential determined by the Schwarzian derivative of the shape of the Wilson loop. Here we use the Mathieu equation, a standard example of a periodic potential, to obtain a class of Wilson loops such that the area of the dual minimal area surface can be computed analytically in terms of eigenvalues of such equation. Asmore » opposed to previous examples, these minimal surfaces have an umbilical point (where the principal curvatures are equal) and are invariant under λ-deformations. In various limits they reduce to the single and multiple wound circular Wilson loop and to the regular light-like polygons studied by Alday and Maldacena. In this last limit, the periodic potential becomes a series of deep wells each related to a light-like segment. Small corrections are described by a tight-binding approximation. In the circular limit they are well approximated by an expansion developed by A. Dekel. In the particular case of no umbilical points they reduce to a previous solution proposed by J. Toledo. The construction works both in Euclidean and Minkowski signature of AdS 3.« less

The rate of bubble growth in a superheated liquid in pool boiling

NASA Astrophysics Data System (ADS)

Abdollahi, Mohammad Reza; Jafarian, Mehdi; Jamialahmadi, Mohammad

2017-12-01

A semi-empirical model for the estimation of the rate of bubble growth in nucleate pool boiling is presented, considering a new equation to estimate the temperature history of the bubble in the bulk of liquid. The conservation equations of energy, mass and momentum have been firstly derived and solved analytically. The present analytical model of the bubble growth predicts that the radius of the bubble grows as a function of √{t}.{\\operatorname{erf}}( N√{t}) , while so far the bubble growth rate has been mainly correlated to √{t} in the previous studies. In the next step, the analytical solutions were used to develop a new semi-empirical equation. To achieve this, firstly the analytical solution were non-dimensionalised and then the experimental data, available in the literature, were applied to tune the dimensionless coefficients appeared in the dimensionless equation. Finally, the reliability of the proposed semi-empirical model was assessed through comparison of the model predictions with the available experimental data in the literature, which were not applied in the tuning of the dimensionless parameters of the model. The comparison of the model predictions with other proposed models in the literature was also performed. These comparisons show that this model enables more accurate predictions than previously proposed models with a deviation of less than 10% in a wide range of operating conditions.

A massive Feynman integral and some reduction relations for Appell functions

NASA Astrophysics Data System (ADS)

Shpot, M. A.

2007-12-01

New explicit expressions are derived for the one-loop two-point Feynman integral with arbitrary external momentum and masses m12 and m22 in D dimensions. The results are given in terms of Appell functions, manifestly symmetric with respect to the masses mi2. Equating our expressions with previously known results in terms of Gauss hypergeometric functions yields reduction relations for the involved Appell functions that are apparently new mathematical results.

On the 4D generalized Proca action for an Abelian vector field

NASA Astrophysics Data System (ADS)

Allys, Erwan; Beltrán Almeida, Juan P.; Peter, Patrick; Rodríguez, Yeinzon

2016-09-01

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 05 (2014) 015 and Phys. Lett. B 757 (2016) 405 and complements those of JCAP 02 (2016) 004. We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field Aμ, the Faraday tensor Fμν and its Hodge dual tilde Fμν.

Species abundance distribution and population dynamics in a two-community model of neutral ecology

NASA Astrophysics Data System (ADS)

Vallade, M.; Houchmandzadeh, B.

2006-11-01

Explicit formulas for the steady-state distribution of species in two interconnected communities of arbitrary sizes are derived in the framework of Hubbell’s neutral model of biodiversity. Migrations of seeds from both communities as well as mutations in both of them are taken into account. These results generalize those previously obtained for the “island-continent” model and they allow an analysis of the influence of the ratio of the sizes of the two communities on the dominance/diversity equilibrium. Exact expressions for species abundance distributions are deduced from a master equation for the joint probability distribution of species in the two communities. Moreover, an approximate self-consistent solution is derived. It corresponds to a generalization of previous results and it proves to be accurate over a broad range of parameters. The dynamical correlations between the abundances of a species in both communities are also discussed.

Head-on collisions of localized pressure excitations in derivative cubic relaxing media: dynamical structure survey

NASA Astrophysics Data System (ADS)

Youssoufa, Saliou; Kamgang Kuetche, Victor; Crepin Kofane, Timoleon

2015-02-01

In the wake of the recent derivation of the new cubic nonlinear evolution equation of high-frequency pressure perturbations of a barothropic medium under relaxation (Kuetche V K et al 2014 J. Math. Phys. 55 052702), we closely investigate the head-on collisions of some typical localized waveguide excitations, which are solutions to the previous system. From the viewpoint of Hirota's formalism, we delve into the structural scattering features of the interacting waves mentioned above. As a result, we find that there might exist some ‘characteristic’ amplitude ratio of the interacting waves at which the scattering changes its features. Accordingly, we provide an illustration of the previous result within the depiction of the interactions between three single soliton solutions alongside the phase-shift of each particle. Following these depictions, we address some physical implications of the results as well as the different potential applications.

A micromorphic model for steel fiber reinforced concrete.

PubMed

Oliver, J; Mora, D F; Huespe, A E; Weyler, R

2012-10-15

A new formulation to model the mechanical behavior of high performance fiber reinforced cement composites with arbitrarily oriented short fibers is presented. The formulation can be considered as a two scale approach, in which the macroscopic model, at the structural level, takes into account the mesostructural phenomenon associated with the fiber-matrix interface bond/slip process. This phenomenon is contemplated by including, in the macroscopic description, a micromorphic field representing the relative fiber-cement displacement. Then, the theoretical framework, from which the governing equations of the problem are derived, can be assimilated to a specific case of the material multifield theory. The balance equation derived for this model, connecting the micro stresses with the micromorphic forces, has a physical meaning related with the fiber-matrix bond slip mechanism. Differently to previous procedures in the literature, addressed to model fiber reinforced composites, where this equation has been added as an additional independent ingredient of the methodology, in the present approach it arises as a natural result derived from the multifield theory. Every component of the composite is defined with a specific free energy and constitutive relation. The mixture theory is adopted to define the overall free energy of the composite, which is assumed to be homogeneously constituted, in the sense that every infinitesimal volume is occupied by all the components in a proportion given by the corresponding volume fraction. The numerical model is assessed by means of a selected set of experiments that prove the viability of the present approach.

Estimating earthquake magnitudes from reported intensities in the central and eastern United States

USGS Publications Warehouse

Boyd, Oliver; Cramer, Chris H.

2014-01-01

A new macroseismic intensity prediction equation is derived for the central and eastern United States and is used to estimate the magnitudes of the 1811–1812 New Madrid, Missouri, and 1886 Charleston, South Carolina, earthquakes. This work improves upon previous derivations of intensity prediction equations by including additional intensity data, correcting magnitudes in the intensity datasets to moment magnitude, and accounting for the spatial and temporal population distributions. The new relation leads to moment magnitude estimates for the New Madrid earthquakes that are toward the lower range of previous studies. Depending on the intensity dataset to which the new macroseismic intensity prediction equation is applied, mean estimates for the 16 December 1811, 23 January 1812, and 7 February 1812 mainshocks, and 16 December 1811 dawn aftershock range from 6.9 to 7.1, 6.8 to 7.1, 7.3 to 7.6, and 6.3 to 6.5, respectively. One‐sigma uncertainties on any given estimate could be as high as 0.3–0.4 magnitude units. We also estimate a magnitude of 6.9±0.3 for the 1886 Charleston, South Carolina, earthquake. We find a greater range of magnitude estimates when also accounting for multiple macroseismic intensity prediction equations. The inability to accurately and precisely ascertain magnitude from intensities increases the uncertainty of the central United States earthquake hazard by nearly a factor of two. Relative to the 2008 national seismic hazard maps, our range of possible 1811–1812 New Madrid earthquake magnitudes increases the coefficient of variation of seismic hazard estimates for Memphis, Tennessee, by 35%–42% for ground motions expected to be exceeded with a 2% probability in 50 years and by 27%–35% for ground motions expected to be exceeded with a 10% probability in 50 years.

Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Rui, Wenjuan; Zhang, Xiangzhi

2016-05-01

This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

Progressive wave expansions and open boundary problems

NASA Technical Reports Server (NTRS)

Hagstrom, T.; Hariharan, S. I.

1995-01-01

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory.

Masses from an inhomogeneous partial difference equation with higher-order isospin contributions

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

Masson, P.J.; Jaenecke, J.

In the present work, a mass equation obtained as the solution of an inhomogeneous partial difference equation is used to predict masses of unknown neutron-rich and proton-rich nuclei. The inhomogeneous source terms contain shell-dependent symmetry energy expressions (quadratic in isospin), and include, as well, an independently derived shell-model Coulomb energy equation which describes all known Coulomb displacement energies with a standarad deviation of sigma/sub c/ = 41 keV. Perturbations of higher order in isospin, previously recognized as a cause of systematic effects in long-range mass extrapolations, are also incorporated. The most general solutions of the inhomogeneous difference equation have beenmore » deduced from a chi/sup 2/-minimization procedure based on the recent atomic mass adjustment of Wapstra, Audi, and Hoekstra. Subjecting the solutions further to the condition of charge symmetry preserves the accuracy of Coulomb energies and allows mass predictions for nuclei with both Ngreater than or equal toZ and Z>N. The solutions correspond to a mass equation with 470 parameters. Using this equation, 4385 mass values have been calculated for nuclei with Agreater than or equal to16 (except N = Z = odd for A<40), with a standard deviation of sigma/sub m/ = 194 keV from the experimental masses. copyright 1988 Academic Press, Inc.« less

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

PubMed

Eu, Byung Chan

2008-09-07

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny-Lin equation

NASA Astrophysics Data System (ADS)

Rashidi, Saeede; Hejazi, S. Reza

This paper investigates the invariance properties of the time fractional Benny-Lin equation with Riemann-Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto-Sivashinsky equation and Navier-Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny-Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler Equations

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Tiwari, S. N.; Smith, R. E.

1997-01-01

Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

The general dispersion relation of induced streaming instabilities in quantum outflow systems

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

Mehdian, H., E-mail: mehdian@khu.ac.ir; Hajisharifi, K.; Hasanbeigi, A.

2015-11-15

In this manuscript the dispersion relations of streaming instabilities, by using the unique property (neutralized in charge and current by default) of plasma shells colliding, have been generalized and studied. This interesting property for interpenetrating beams enables one to find the general dispersion relations without any restrictions used in the previous works in this area. In our previous work [H. Mehdian et al., ApJ. 801, 89 (2015)], employing the plasma shell concept and boost frame method, the general dispersion relation for filamentation instability has been derived in the relativistic classical regime. But in this paper, using the above mentioned concepts,more » the general dispersion relations (for each of streaming instabilities, filamentation, two-stream and multi-stream) in the non-relativistic quantum regime have been derived by employing the quantum fluid equations together with Maxwell equations. The derived dispersion relations enable to describe any arbitrary system of interacting two and three beams, justified neutralization condition, by choosing the inertial reference frame embedded on the one of the beams. Furthermore, by the numerical and analytical study of these dispersion relations, many new features of streaming instabilities (E.g. their cut-off wave numbers and growth rates) in terms of all involved parameters have been illustrated. The obtained results in this paper can be used to describe many astrophysical systems and laboratory astrophysics setting, such as collision of non-parallel plasma shells over a background plasma or the collision of three neutralized plasma slabs, and justifying the many plasma phenomena such as particle accelerations and induced fields.« less

The general dispersion relation of induced streaming instabilities in quantum outflow systems

NASA Astrophysics Data System (ADS)

Mehdian, H.; Hajisharifi, K.; Hasanbeigi, A.

2015-11-01

In this manuscript the dispersion relations of streaming instabilities, by using the unique property (neutralized in charge and current by default) of plasma shells colliding, have been generalized and studied. This interesting property for interpenetrating beams enables one to find the general dispersion relations without any restrictions used in the previous works in this area. In our previous work [H. Mehdian et al., ApJ. 801, 89 (2015)], employing the plasma shell concept and boost frame method, the general dispersion relation for filamentation instability has been derived in the relativistic classical regime. But in this paper, using the above mentioned concepts, the general dispersion relations (for each of streaming instabilities, filamentation, two-stream and multi-stream) in the non-relativistic quantum regime have been derived by employing the quantum fluid equations together with Maxwell equations. The derived dispersion relations enable to describe any arbitrary system of interacting two and three beams, justified neutralization condition, by choosing the inertial reference frame embedded on the one of the beams. Furthermore, by the numerical and analytical study of these dispersion relations, many new features of streaming instabilities (E.g. their cut-off wave numbers and growth rates) in terms of all involved parameters have been illustrated. The obtained results in this paper can be used to describe many astrophysical systems and laboratory astrophysics setting, such as collision of non-parallel plasma shells over a background plasma or the collision of three neutralized plasma slabs, and justifying the many plasma phenomena such as particle accelerations and induced fields.

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Generalization of the van der Pauw relationship derived from electrostatics

NASA Astrophysics Data System (ADS)

Weiss, Jonathan D.

2011-08-01

In an earlier paper, this author, along with two others Weiss et al. (2008) [1], demonstrated that the original van der Pauw relationship could be derived from three-dimensional electrostatics, as opposed to van der Pauw's use of conformal mapping. The earlier derivation was done for a conducting material of rectangular cross section with contacts placed at the corners. Presented here is a generalization of the previous work involving a square sample and a square array of electrodes that are not confined to the corners, since this measurement configuration could be a more convenient one. As in the previous work, the effects of non-zero sample thickness and contact size have been investigated. Buehler and Thurber derived a similar relationship using an infinite series of current images on a large and thin conducting sheet to satisfy the conditions at the boundary of the sample. The results presented here agree with theirs numerically, but analytic agreement could not be shown using any of the perused mathematical literature. By simply equating the two solutions, it appears that, as a byproduct of this work, a new mathematical relationship has been uncovered. Finally, the application of this methodology to the Hall Effect is discussed.

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation. Volume 2, Part 2: Appendixes B, C, D and E

NASA Technical Reports Server (NTRS)

Lowrie, J. W.; Fermelia, A. J.; Haley, D. C.; Gremban, K. D.; Vanbaalen, J.; Walsh, R. W.

1982-01-01

The derivation of the equations is presented, the rate control algorithm described, and simulation methodologies summarized. A set of dynamics equations that can be used recursively to calculate forces and torques acting at the joints of an n link manipulator given the manipulator joint rates are derived. The equations are valid for any n link manipulator system with any kind of joints connected in any sequence. The equations of motion for the class of manipulators consisting of n rigid links interconnected by rotary joints are derived. A technique is outlined for reducing the system of equations to eliminate contraint torques. The linearized dynamics equations for an n link manipulator system are derived. The general n link linearized equations are then applied to a two link configuration. The coordinated rate control algorithm used to compute individual joint rates when given end effector rates is described. A short discussion of simulation methodologies is presented.

Investigation of Damping Physics and CFD Tool Validation for Simulation of Baffled Tanks at Variable Slosh Amplitude

NASA Technical Reports Server (NTRS)

Yang, H. Q.; West, Jeffrey

2016-01-01

To meet the flight control damping requirement, baffles of various configurations have been devised to increase the natural viscous damping and decrease the magnitude of the slosh forces and torques. In the design of slosh baffles, the most widely used damping equation is the one derived by Miles, which is based on the experiments of Keulegan and Carpenter. This equation has been used in predicting damping of the baffled tanks in different diameters ranging from 12 to 112 inches. The analytical expression of Miles equation is easy to use, especially in the design of complex baffle system. Previous investigations revealed that some experiments had shown good agreements with the prediction method of Miles, whereas other experiments have shown significant deviations. For example, damping from Miles equation differs from experimental measurements by as much as 100 percent over a range of tank diameters from 12 to 112 inches, oscillation amplitudes from 0.1 to 1.5 baffle widths, and baffle depths of 0.3 to 0.5 tank radius. Previously, much of this difference has been attributed to experimental scatter. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between Miles equation and experimental measurement, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use CFD technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. A well validated CFD solver, developed at NASA MSFC, Loci-STREAM-VOF, is applied to study vorticity field around the baffle and around the fluid interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data are then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (h/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Macroscopic constitutive equations of thermo-poroviscoelasticity derived using eigenstrains

NASA Astrophysics Data System (ADS)

Suvorov, A. P.; Selvadurai, A. P. S.

2010-10-01

Macroscopic constitutive equations for thermo-viscoelastic processes in a fully saturated porous medium are re-derived from basic principles of micromechanics applicable to solid multi-phase materials such as composites. Simple derivations of the constitutive relations and the void occupancy relationship are presented. The derivations use the notion of eigenstrain or, equivalently, eigenstress applied to the separate phases of a porous medium. Governing coupled equations for the displacement components and the fluid pressure are also obtained.

Algebro-geometric Solutions for the Derivative Burgers Hierarchy

NASA Astrophysics Data System (ADS)

Hou, Yu; Fan, Engui; Qiao, Zhijun; Wang, Zhong

2015-02-01

Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyperelliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we study algebro-geometric solutions for the derivative Burgers (DB) equation, which is derived by Qiao and Li (2004) as a short wave model of the DP equation with the help of functional gradient and a pair of Lenard operators. Based on the characteristic polynomial of a Lax matrix for the DB equation, we introduce a third order algebraic curve with genus , from which the associated Baker-Akhiezer functions, meromorphic function, and Dubrovin-type equations are constructed. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker-Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DB hierarchy.

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Dissolution of solid dosage form. II. Equations for the dissolution of nondisintegrating tablet under the sink condition.

PubMed

Yonezawa, Y; Shirakura, K; Otsuka, A; Sunada, H

1991-03-01

An equation for dissolution from the whole surface of a nondisintegrating single component tablet under the sink condition was derived. Also, equations for several dissolution manners of the tablet under the sink condition were derived in the postulation of the dominant dissolution rate constant which determines the dissolution manner. The applicability or validity of these equations were examined by the dissolution measurements with nondisintegrating single component tablets. About one-tenth the amount of the amount needed to saturate the solution was used to prepare a tablet, and dissolution measurements were carried out with the tablet whose flat or side surface was masked with an adhesive tape in accordance with the conditions for derivation of equations. Among the derived equations, dissolution from the whole surface of a tablet was expressed by a form similar to the cube root law equation for particles. Hence, a single component tablet compressed by the use of a suitable amount was thought to behave like a single crystal. Also, equations derived for several dissolution manners were thought to be applicable for the dissolution of a nonspherical particle and crystal concerning the crystal's habit and its dissolution property, and the extended applicability was examined by converting the crystal into a simplified or idealized form, i.e., rectangle or plate.

Generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains

NASA Astrophysics Data System (ADS)

Angstmann, C. N.; Henry, B. I.; McGann, A. V.

2017-10-01

The ubiquity of subdiffusive transport in physical and biological systems has led to intensive efforts to provide robust theoretical models for this phenomena. These models often involve fractional derivatives. The important physical extension of this work to processes occurring in growing materials has proven highly nontrivial. Here we derive evolution equations for modeling subdiffusive transport in a growing medium. The derivation is based on a continuous-time random walk. The concise formulation of these evolution equations requires the introduction of a new, comoving, fractional derivative. The implementation of the evolution equation is illustrated with a simple model of subdiffusing proteins in a growing membrane.

Body composition estimation from selected slices: equations computed from a new semi-automatic thresholding method developed on whole-body CT scans

PubMed Central

Villa, Chiara; Brůžek, Jaroslav

2017-01-01

Background Estimating volumes and masses of total body components is important for the study and treatment monitoring of nutrition and nutrition-related disorders, cancer, joint replacement, energy-expenditure and exercise physiology. While several equations have been offered for estimating total body components from MRI slices, no reliable and tested method exists for CT scans. For the first time, body composition data was derived from 41 high-resolution whole-body CT scans. From these data, we defined equations for estimating volumes and masses of total body AT and LT from corresponding tissue areas measured in selected CT scan slices. Methods We present a new semi-automatic approach to defining the density cutoff between adipose tissue (AT) and lean tissue (LT) in such material. An intra-class correlation coefficient (ICC) was used to validate the method. The equations for estimating the whole-body composition volume and mass from areas measured in selected slices were modeled with ordinary least squares (OLS) linear regressions and support vector machine regression (SVMR). Results and Discussion The best predictive equation for total body AT volume was based on the AT area of a single slice located between the 4th and 5th lumbar vertebrae (L4-L5) and produced lower prediction errors (|PE| = 1.86 liters, %PE = 8.77) than previous equations also based on CT scans. The LT area of the mid-thigh provided the lowest prediction errors (|PE| = 2.52 liters, %PE = 7.08) for estimating whole-body LT volume. We also present equations to predict total body AT and LT masses from a slice located at L4-L5 that resulted in reduced error compared with the previously published equations based on CT scans. The multislice SVMR predictor gave the theoretical upper limit for prediction precision of volumes and cross-validated the results. PMID:28533960

Body composition estimation from selected slices: equations computed from a new semi-automatic thresholding method developed on whole-body CT scans.

PubMed

Lacoste Jeanson, Alizé; Dupej, Ján; Villa, Chiara; Brůžek, Jaroslav

2017-01-01

Estimating volumes and masses of total body components is important for the study and treatment monitoring of nutrition and nutrition-related disorders, cancer, joint replacement, energy-expenditure and exercise physiology. While several equations have been offered for estimating total body components from MRI slices, no reliable and tested method exists for CT scans. For the first time, body composition data was derived from 41 high-resolution whole-body CT scans. From these data, we defined equations for estimating volumes and masses of total body AT and LT from corresponding tissue areas measured in selected CT scan slices. We present a new semi-automatic approach to defining the density cutoff between adipose tissue (AT) and lean tissue (LT) in such material. An intra-class correlation coefficient (ICC) was used to validate the method. The equations for estimating the whole-body composition volume and mass from areas measured in selected slices were modeled with ordinary least squares (OLS) linear regressions and support vector machine regression (SVMR). The best predictive equation for total body AT volume was based on the AT area of a single slice located between the 4th and 5th lumbar vertebrae (L4-L5) and produced lower prediction errors (|PE| = 1.86 liters, %PE = 8.77) than previous equations also based on CT scans. The LT area of the mid-thigh provided the lowest prediction errors (|PE| = 2.52 liters, %PE = 7.08) for estimating whole-body LT volume. We also present equations to predict total body AT and LT masses from a slice located at L4-L5 that resulted in reduced error compared with the previously published equations based on CT scans. The multislice SVMR predictor gave the theoretical upper limit for prediction precision of volumes and cross-validated the results.

MEASURING THE MASS OF 4UO900-40 DYNAMICALLY

NASA Technical Reports Server (NTRS)

Dolan, J. F.; Etzel, Paul B.; Boyd, Patricia T.

2006-01-01

Accurate measurements of neutron star masses are needed to constrain the equation of state of neutron star matter - of importance to both particle physics and the astrophysics of neutron stars - and to identify the evolutionary track of the progenitor stars that form neutron stars. The best measured values of the mass of 4UO900-40 (= Vela XR-l), 1.86 +/- 0.16 Msun (Barziv et al. 2001) and 1.93 +/- 0.20 Msun (Abubekerov et al. 2004), make it a leading candidate for the most massive neutron star known. The direct relationship between the maximum mass of neutron stars and the equation of state of ultra-dense matter makes 4UO900-40 an important neutron star mass to determine accurately. The confidence interval on previous mass estimates, obtained from observations that include parameters determined by non-dynamical methods, are not small enough to significantly restrict possible equations of state. We describe here a purely dynamical method for determining the mass of 4UO900-40, an X-ray pulsar, using the reprocessed UV pulses emitted by its BO.5Ib companion. One can derive the instantaneous radial velocity of each component by simultaneous X-ray and UV observations at the two quadratures of the system. The Doppler shift caused by the primary's rotational velocity and the illumination pattern of the X-rays on the primary, two of the three principal contributors to the uncertainty on the derived mass of the neutron star, almost exactly cancel by symmetry in this method. A heuristic measurement of the mass of 4UO900-40 using observations obtained previously with the High Speed Photometer on HST is given in Appendix A.

Annual regression-based estimates of evapotranspiration for the contiguous United States based on climate, remote sensing, and stream gage data

NASA Astrophysics Data System (ADS)

Reitz, M. D.; Sanford, W. E.; Senay, G. B.; Cazenas, J.

2015-12-01

Evapotranspiration (ET) is a key quantity in the hydrologic cycle, accounting for ~70% of precipitation across the contiguous United States (CONUS). However, it is a challenge to estimate, due to difficulty in making direct measurements and gaps in our theoretical understanding. Here we present a new data-driven, ~1km2 resolution map of long-term average actual evapotranspiration rates across the CONUS. The new ET map is a function of the USGS Landsat-derived National Land Cover Database (NLCD), precipitation, temperature, and daily average temperature range (from the PRISM climate dataset), and is calibrated to long-term water balance data from 679 watersheds. It is unique from previously presented ET maps in that (1) it was co-developed with estimates of runoff and recharge; (2) the regression equation was chosen from among many tested, previously published and newly proposed functional forms for its optimal description of long-term water balance ET data; (3) it has values over open-water areas that are derived from separate mass-transfer and humidity equations; and (4) the data include additional precipitation representing amounts converted from 2005 USGS water-use census irrigation data. The regression equation is calibrated using data from 2000-2013, but can also be applied to individual years with their corresponding input datasets. Comparisons among this new map, the more detailed remote-sensing-based estimates of MOD16 and SSEBop, and AmeriFlux ET tower measurements shows encouraging consistency, and indicates that the empirical ET estimate approach presented here produces closer agreement with independent flux tower data for annual average actual ET than other more complex remote sensing approaches.

Interacting dark sector and precision cosmology

NASA Astrophysics Data System (ADS)

Buen-Abad, Manuel A.; Schmaltz, Martin; Lesgourgues, Julien; Brinckmann, Thejs

2018-01-01

We consider a recently proposed model in which dark matter interacts with a thermal background of dark radiation. Dark radiation consists of relativistic degrees of freedom which allow larger values of the expansion rate of the universe today to be consistent with CMB data (H0-problem). Scattering between dark matter and radiation suppresses the matter power spectrum at small scales and can explain the apparent discrepancies between ΛCDM predictions of the matter power spectrum and direct measurements of Large Scale Structure LSS (σ8-problem). We go beyond previous work in two ways: 1. we enlarge the parameter space of our previous model and allow for an arbitrary fraction of the dark matter to be interacting and 2. we update the data sets used in our fits, most importantly we include LSS data with full k-dependence to explore the sensitivity of current data to the shape of the matter power spectrum. We find that LSS data prefer models with overall suppressed matter clustering due to dark matter - dark radiation interactions over ΛCDM at 3–4 σ. However recent weak lensing measurements of the power spectrum are not yet precise enough to clearly distinguish two limits of the model with different predicted shapes for the linear matter power spectrum. In two appendices we give a derivation of the coupled dark matter and dark radiation perturbation equations from the Boltzmann equation in order to clarify a confusion in the recent literature, and we derive analytic approximations to the solutions of the perturbation equations in the two physically interesting limits of all dark matter weakly interacting or a small fraction of dark matter strongly interacting.

Stochastic model of financial markets reproducing scaling and memory in volatility return intervals

NASA Astrophysics Data System (ADS)

Gontis, V.; Havlin, S.; Kononovicius, A.; Podobnik, B.; Stanley, H. E.

2016-11-01

We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive macroscopic equations based on the microscopic herding interactions of agents and find that they are able to reproduce various stylized facts of different markets and different assets with the same set of model parameters. We show that the power-law properties and the scaling of return intervals and other financial variables have a similar origin and could be a result of a general class of non-linear stochastic differential equations derived from a master equation of an agent system that is coupled by herding interactions. Specifically, we find that this approach enables us to recover the volatility return interval statistics as well as volatility probability and spectral densities for the NYSE and FOREX markets, for different assets, and for different time-scales. We find also that the historical S&P500 monthly series exhibits the same volatility return interval properties recovered by our proposed model. Our statistical results suggest that human herding is so strong that it persists even when other evolving fluctuations perturbate the financial system.

The discovery of indicator variables for QSAR using inductive logic programming

NASA Astrophysics Data System (ADS)

King, Ross D.; Srinivasan, Ashwin

1997-11-01

A central problem in forming accurate regression equations in QSAR studies isthe selection of appropriate descriptors for the compounds under study. Wedescribe a novel procedure for using inductive logic programming (ILP) todiscover new indicator variables (attributes) for QSAR problems, and show thatthese improve the accuracy of the derived regression equations. ILP techniqueshave previously been shown to work well on drug design problems where thereis a large structural component or where clear comprehensible rules arerequired. However, ILP techniques have had the disadvantage of only being ableto make qualitative predictions (e.g. active, inactive) and not to predictreal numbers (regression). We unify ILP and linear regression techniques togive a QSAR method that has the strength of ILP at describing stericstructure, with the familiarity and power of linear regression. We evaluatedthe utility of this new QSAR technique by examining the prediction ofbiological activity with and without the addition of new structural indicatorvariables formed by ILP. In three out of five datasets examined the additionof ILP variables produced statistically better results (P < 0.01) over theoriginal description. The new ILP variables did not increase the overallcomplexity of the derived QSAR equations and added insight into possiblemechanisms of action. We conclude that ILP can aid in the process of drugdesign.

The prediction of the noise of supersonic propellers in time domain - New theoretical results

NASA Technical Reports Server (NTRS)

Farassat, F.

1983-01-01

In this paper, a new formula for the prediction of the noise of supersonic propellers is derived in the time domain which is superior to the previous formulations in several respects. The governing equation is based on the Ffowcs Williams-Hawkings (FW-H) equation with the thickness source term replaced by an equivalent loading source term derived by Isom (1975). Using some results of generalized function theory and simple four-dimensional space-time geometry, the formal solution of the governing equation is manipulated to a form requiring only the knowledge of blade surface pressure data and geometry. The final form of the main result of this paper consists of some surface and line integrals. The surface integrals depend on the surface pressure, time rate of change of surface pressure, and surface pressure gradient. These integrals also involve blade surface curvatures. The line integrals which depend on local surface pressure are along the trailing edge, the shock traces on the blade, and the perimeter of the airfoil section at the inner radius of the blade. The new formulation is for the full blade surface and does not involve any numerical observer time differentiation. The method of implementation on a computer for numerical work is also discussed.

SPH modeling and simulation of spherical particles interacting in a viscoelastic matrix

NASA Astrophysics Data System (ADS)

Vázquez-Quesada, A.; Ellero, M.

2017-12-01

In this work, we extend the three-dimensional Smoothed Particle Hydrodynamics (SPH) non-colloidal particulate model previously developed for Newtonian suspending media in Vázquez-Quesada and Ellero ["Rheology and microstructure of non-colloidal suspensions under shear studied with smoothed particle hydrodynamics," J. Non-Newtonian Fluid Mech. 233, 37-47 (2016)] to viscoelastic matrices. For the solvent medium, the coarse-grained SPH viscoelastic formulation proposed in Vázquez-Quesada, Ellero, and Español ["Smoothed particle hydrodynamic model for viscoelastic fluids with thermal fluctuations," Phys. Rev. E 79, 056707 (2009)] is adopted. The property of this particular set of equations is that they are entirely derived within the general equation for non-equilibrium reversible-irreversible coupling formalism and therefore enjoy automatically thermodynamic consistency. The viscoelastic model is derived through a physical specification of a conformation-tensor-dependent entropy function for the fluid particles. In the simple case of suspended Hookean dumbbells, this delivers a specific SPH discretization of the Oldroyd-B constitutive equation. We validate the suspended particle model by studying the dynamics of single and mutually interacting "noncolloidal" rigid spheres under shear flow and in the presence of confinement. Numerical results agree well with available numerical and experimental data. It is straightforward to extend the particulate model to Brownian conditions and to more complex viscoelastic solvents.

Linear force and moment equations for an annular smooth shaft seal perturbed both angularly and laterally

NASA Technical Reports Server (NTRS)

Fenwick, J.; Dijulio, R.; Ek, M. C.; Ehrgott, R.

1982-01-01

Coefficients are derived for equations expressing the lateral force and pitching moments associated with both planar translation and angular perturbations from a nominally centered rotating shaft with respect to a stationary seal. The coefficients for the lowest order and first derivative terms emerge as being significant and are of approximately the same order of magnitude as the fundamental coefficients derived by means of Black's equations. Second derivative, shear perturbation, and entrance coefficient variation effects are adjudged to be small.

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

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

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

Updated observational constraints on quintessence dark energy models

NASA Astrophysics Data System (ADS)

Durrive, Jean-Baptiste; Ooba, Junpei; Ichiki, Kiyotomo; Sugiyama, Naoshi

2018-02-01

The recent GW170817 measurement favors the simplest dark energy models, such as a single scalar field. Quintessence models can be classified in two classes, freezing and thawing, depending on whether the equation of state decreases towards -1 or departs from it. In this paper, we put observational constraints on the parameters governing the equations of state of tracking freezing, scaling freezing, and thawing models using updated data, from the Planck 2015 release, joint light-curve analysis, and baryonic acoustic oscillations. Because of the current tensions on the value of the Hubble parameter H0, unlike previous authors, we let this parameter vary, which modifies significantly the results. Finally, we also derive constraints on neutrino masses in each of these scenarios.

Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2 + 1)-dimensional Breaking Soliton equation

NASA Astrophysics Data System (ADS)

Hossen, Md. Belal; Roshid, Harun-Or; Ali, M. Zulfikar

2018-05-01

Under inquisition in this paper is a (2 + 1)-dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering.

An intrinsic approach in the curved n-body problem: The negative curvature case

NASA Astrophysics Data System (ADS)

Diacu, Florin; Pérez-Chavela, Ernesto; Reyes Victoria, J. Guadalupe

We consider the motion of n point particles of positive masses that interact gravitationally on the 2-dimensional hyperbolic sphere, which has negative constant Gaussian curvature. Using the stereographic projection, we derive the equations of motion of this curved n-body problem in the Poincaré disk, where we study the elliptic relative equilibria. Then we obtain the equations of motion in the Poincaré upper half plane in order to analyze the hyperbolic and parabolic relative equilibria. Using techniques of Riemannian geometry, we characterize each of the above classes of periodic orbits. For n=2 and n=3 we recover some previously known results and find new qualitative results about relative equilibria that were not apparent in an extrinsic setting.

Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization

NASA Technical Reports Server (NTRS)

Arian, Eyal; Salas, Manuel D.

1997-01-01

We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

A theoretical analysis of fluid flow and energy transport in hydrothermal systems

USGS Publications Warehouse

Faust, Charles R.; Mercer, James W.

1977-01-01

A mathematical derivation for fluid flow and energy transport in hydrothermal systems is presented. Specifically, the mathematical model describes the three-dimensional flow of both single- and two-phase, single-component water and the transport of heat in porous media. The derivation begins with the point balance equations for mass, momentum, and energy. These equations are then averaged over a finite volume to obtain the macroscopic balance equations for a porous medium. The macroscopic equations are combined by appropriate constitutive relationships to form two similified partial differential equations posed in terms of fluid pressure and enthalpy. A two-dimensional formulation of the simplified equations is also derived by partial integration in the vertical dimension. (Woodard-USGS)

An isotherm-based thermodynamic model of multicomponent aqueous solutions, applicable over the entire concentration range.

PubMed

Dutcher, Cari S; Ge, Xinlei; Wexler, Anthony S; Clegg, Simon L

2013-04-18

In previous studies (Dutcher et al. J. Phys. Chem. C 2011, 115, 16474-16487; 2012, 116, 1850-1864), we derived equations for the Gibbs energy, solvent and solute activities, and solute concentrations in multicomponent liquid mixtures, based upon expressions for adsorption isotherms that include arbitrary numbers of hydration layers on each solute. In this work, the long-range electrostatic interactions that dominate in dilute solutions are added to the Gibbs energy expression, thus extending the range of concentrations for which the model can be used from pure liquid solute(s) to infinite dilution in the solvent, water. An equation for the conversion of the reference state for solute activity coefficients to infinite dilution in water has been derived. A number of simplifications are identified, notably the equivalence of the sorption site parameters r and the stoichiometric coefficients of the solutes, resulting in a reduction in the number of model parameters. Solute concentrations in mixtures conform to a modified Zdanovskii-Stokes-Robinson mixing rule, and solute activity coefficients to a modified McKay-Perring relation, when the effects of the long-range (Debye-Hückel) term in the equations are taken into account. Practical applications of the equations to osmotic and activity coefficients of pure aqueous electrolyte solutions and mixtures show both satisfactory accuracy from low to high concentrations, together with a thermodynamically reasonable extrapolation (beyond the range of measurements) to extreme concentration and to the pure liquid solute(s).

Effect of three-body interactions on the zero-temperature equation of state of HCP solid 4He

NASA Astrophysics Data System (ADS)

Barnes, Ashleigh L.; Hinde, Robert J.

2017-03-01

Previous studies have pointed to the importance of three-body interactions in high density 4He solids. However the computational cost often makes it unfeasible to incorporate these interactions into the simulation of large systems. We report the implementation and evaluation of a computationally efficient perturbative treatment of three-body interactions in hexagonal close packed solid 4He utilizing the recently developed nonadditive three-body potential of Cencek et al. This study represents the first application of the Cencek three-body potential to condensed phase 4He systems. Ground state energies from quantum Monte Carlo simulations, with either fully incorporated or perturbatively treated three-body interactions, are calculated in systems with molar volumes ranging from 21.3 cm3/mol down to 2.5 cm3/mol. These energies are used to derive the zero-temperature equation of state for comparison against existing experimental and theoretical data. The equations of state derived from both perturbative and fully incorporated three-body interactions are found to be in very good agreement with one another, and reproduce the experimental pressure-volume data with significantly better accuracy than is obtained when only two-body interactions are considered. At molar volumes below approximately 4.0 cm3/mol, neither two-body nor three-body equations of state are able to accurately reproduce the experimental pressure-volume data, suggesting that below this molar volume four-body and higher many-body interactions are becoming important.

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

1981-01-01

An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507

Finite difference schemes for long-time integration

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1993-01-01

Finite difference schemes for the evaluation of first and second derivatives are presented. These second order compact schemes were designed for long-time integration of evolution equations by solving a quadratic constrained minimization problem. The quadratic cost function measures the global truncation error while taking into account the initial data. The resulting schemes are applicable for integration times fourfold, or more, longer than similar previously studied schemes. A similar approach was used to obtain improved integration schemes.

Equations of motion for the variable mass flow-variable exhaust velocity rocket

NASA Technical Reports Server (NTRS)

Tempelman, W. H.

1972-01-01

An equation of motion for a one dimensional rocket is derived as a function of the mass flow rate into the acceleration chamber and the velocity distribution along the chamber, thereby including the transient flow changes in the chamber. The derivation of the mass density requires the introduction of the special time coordinate. The equation of motion is derived from both classical force and momentum approaches and is shown to be consistent with the standard equation expressed in terms of flow parameters at the exit to the acceleration chamber.

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Simbanefayi, Innocent; Khalique, Chaudry Masood

2018-03-01

In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

Computation of the stability derivatives via CFD and the sensitivity equations

NASA Astrophysics Data System (ADS)

Lei, Guo-Dong; Ren, Yu-Xin

2011-04-01

The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is extended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agreement with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows.

Real-ear-to-coupler difference predictions as a function of age for two coupling procedures.

PubMed

Bagatto, Marlene P; Scollie, Susan D; Seewald, Richard C; Moodie, K Shane; Hoover, Brenda M

2002-09-01

The predicted real-ear-to-coupler difference (RECD) values currently used in pediatric hearing instrument prescription methods are based on 12-month age range categories and were derived from measures using standard acoustic immittance probe tips. Consequently, the purpose of this study was to develop normative RECD predicted values for foam/acoustic immittance tips and custom earmolds across the age continuum. To this end, RECD data were collected on 392 infants and children (141 with acoustic immittance tips, 251 with earmolds) to develop normative regression equations for use in deriving continuous age predictions of RECDs for foam/acoustic immittance tips and earmolds. Owing to the substantial between-subject variability observed in the data, the predictive equations of RECDs by age (in months) resulted in only gross estimates of RECD values (i.e., within +/- 4.4 dB for 95% of acoustic immittance tip measures; within +/- 5.4 dB in 95% of measures with custom earmolds) across frequency. Thus, it is concluded that the estimates derived from this study should not be used to replace the more precise individual RECD measurements. Relative to previously available normative RECD values for infants and young children, however, the estimates derived through this study provide somewhat more accurate predicted values for use under those circumstances for which individual RECD measurements cannot be made.

Estimation of diastolic intraventricular pressure gradients by Doppler M-mode echocardiography

NASA Technical Reports Server (NTRS)

Greenberg, N. L.; Vandervoort, P. M.; Firstenberg, M. S.; Garcia, M. J.; Thomas, J. D.

2001-01-01

Previous studies have shown that small intraventricular pressure gradients (IVPG) are important for efficient filling of the left ventricle (LV) and as a sensitive marker for ischemia. Unfortunately, there has previously been no way of measuring these noninvasively, severely limiting their research and clinical utility. Color Doppler M-mode (CMM) echocardiography provides a spatiotemporal velocity distribution along the inflow tract throughout diastole, which we hypothesized would allow direct estimation of IVPG by using the Euler equation. Digital CMM images, obtained simultaneously with intracardiac pressure waveforms in six dogs, were processed by numerical differentiation for the Euler equation, then integrated to estimate IVPG and the total (left atrial to left ventricular apex) pressure drop. CMM-derived estimates agreed well with invasive measurements (IVPG: y = 0.87x + 0.22, r = 0.96, P < 0.001, standard error of the estimate = 0.35 mmHg). Quantitative processing of CMM data allows accurate estimation of IVPG and tracking of changes induced by beta-adrenergic stimulation. This novel approach provides unique information on LV filling dynamics in an entirely noninvasive way that has previously not been available for assessment of diastolic filling and function.

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.

Quantum cluster variational method and message passing algorithms revisited

NASA Astrophysics Data System (ADS)

Domínguez, E.; Mulet, Roberto

2018-02-01

We present a general framework to study quantum disordered systems in the context of the Kikuchi's cluster variational method (CVM). The method relies in the solution of message passing-like equations for single instances or in the iterative solution of complex population dynamic algorithms for an average case scenario. We first show how a standard application of the Kikuchi's CVM can be easily translated to message passing equations for specific instances of the disordered system. We then present an "ad hoc" extension of these equations to a population dynamic algorithm representing an average case scenario. At the Bethe level, these equations are equivalent to the dynamic population equations that can be derived from a proper cavity ansatz. However, at the plaquette approximation, the interpretation is more subtle and we discuss it taking also into account previous results in classical disordered models. Moreover, we develop a formalism to properly deal with the average case scenario using a replica-symmetric ansatz within this CVM for quantum disordered systems. Finally, we present and discuss numerical solutions of the different approximations for the quantum transverse Ising model and the quantum random field Ising model in two-dimensional lattices.

The S factor--a new derived hemodynamic oxygenation parameter--a useful tool for simplified mathematical modeling of global problems of oxygen transport.

PubMed

Farrell, K; Wasser, T

1997-01-01

We describe a new derived hemodynamic oxygenation parameter, the S factor (S). The factor is based on oxygen delivery and oxygen consumption and can range from -3 to 1. It allows simplified mathematical modeling of clinical problems of oxygen transport and can be applied to many clinical situations. A new hemodynamic oxygenation parameter, the S factor (S), is introduced as an aid to mathematical modeling. It is defined as follows: [formula: see text] (DO2 = oxygen delivery, VO2 = oxygen consumption) S can theoretically vary from -3 (DO2 = VO2) to +1 (VO2 = 0). When DO2/VO2 = 4 (ie. OER = 0.25), S = 0. An S < 0 implies utilization of reserve oxygen transport capacity. An S > 0 implies increased oxygen delivery in relation to oxygen consumption (ie. "shunted oxygen delivery"). By algebraic manipulation and substitution of the components of DO2 into Equation 1: DO2 = Q x Ca x 10 DO2 = Q [(Hb)(Sat)(1.36) + PaO2(.0031)] 10 (2) the following equations can be derived: [formula: see text] [formula: see text] Ca - Cv (Ca = arterial content, Cv = venous content) can be determined by substituting components of oxygen consumption: VO2 = Q (Ca - Cv) x 10 (5) into equation 1 and solving for Ca - Cv. [formula: see text] Equation 6 can be simplified to: [formula: see text] A previously defined relationship between mixed venous PO2 (PvO2) and DO2/VO2 (where calculated P50 is 26.6 +/- 1.0) can be used to modify S in a clinically relevant manner. PvO2 = 5.44D O2/VO2 + 18.16 (8) The relationship between S and PvO2 can be defined by substituting Equation 4 into Equation 1 and solving for PvO2 PvO2 = [21.76/(1-S)] + 18.16 (9) As an example, at a PvO2 of 28 torr (anaerobic threshold), S = -1.2. The relationship between PvO2 and S is shown in Figure 1. S, which can also be defined as 1-4(VO2/DO2) or 1-4(OER), is a useful tool for mathematical modeling of global problems of oxygen transport because the previously derived equations with the S value allow the components of oxygen transport to be interrelated in a clinically relevant manner. Additional advantages of using S in mathematical modeling are: 1. Conceptually it 'fits' in that in regards to the sign (+ or -), as a -S implies utilization of reserve oxygen transport capacity and a +S implies wasted or excess oxygen delivery (shunted). 2. These concepts are easily quantified using the S factor. 3. It 'spreads out' the difference between values for parameters (OER or S) integrating components of oxygen transport, ie. in the 'normal state' regarding oxygen transport, OER = 0.25 and S = 0. At the anaerobic threshold (PvO2 = 28 torr), OER = 0.55 and S = -1.2. Thus, the change in OER from 'normal state' to anaerobic threshold is 0.3 (0.55-0.25) and the change in S is 1.2. This represents a four-fold increase. Four examples of mathematical modeling of global problems of oxygen transport using the S factor are described below.

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

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

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

DOE PAGES

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris; ...

2018-04-23

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Analyzing the uncertainties in use of forest-derived biomass equations for open-grown trees in agricultural land

Treesearch

Xinhua Zhou; Michele M. Schoeneberger; James R. Brandle; Tala N. Awada; Jianmin Chu; Derrel L. Martin; Jihong Li; Yuqiang Li; Carl W. Mize

2014-01-01

Quantifying carbon in agroforestry trees requires biomass equations that capture the growth differences (e.g., tree specific gravity and architecture) created in the more open canopies of agroforestry plantings compared with those generally encountered in forests. Whereas forest-derived equations are available, equations for open-grown trees are not. Data from...

The living Drake equation of the Tau Zero Foundation

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2011-03-01

The living Drake equation is our statistical generalization of the Drake equation such that it can take into account any number of factors. This new result opens up the possibility to enrich the equation by inserting more new factors as long as the scientific learning increases. The adjective "Living" refers just to this continuous enrichment of the Drake equation and is the goal of a new research project that the Tau Zero Foundation has entrusted to this author as the discoverer of the statistical Drake equation described hereafter. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be arbitrarily distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov form of the CLT, or the Lindeberg form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the lognormal distribution. Then, the mean value, standard deviation, mode, median and all the moments of this lognormal N can be derived from the means and standard deviations of the seven input random variables. In fact, the seven factors in the ordinary Drake equation now become seven independent positive random variables. The probability distribution of each random variable may be arbitrary. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) distance between any two neighbouring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, this distance now becomes a new random variable. We derive the relevant probability density function, apparently previously unknown (dubbed "Maccone distribution" by Paul Davies). Data Enrichment Principle. It should be noticed that any positive number of random variables in the statistical Drake equation is compatible with the CLT. So, our generalization allows for many more factors to be added in the future as long as more refined scientific knowledge about each factor will be known to the scientists. This capability to make room for more future factors in the statistical Drake equation we call the "Data Enrichment Principle", and regard as the key to more profound, future results in Astrobiology and SETI.

Direct S -matrix calculation for diffractive structures and metasurfaces

NASA Astrophysics Data System (ADS)

Shcherbakov, Alexey A.; Stebunov, Yury V.; Baidin, Denis F.; Kämpfe, Thomas; Jourlin, Yves

2018-06-01

The paper presents a derivation of analytical components of S matrices for arbitrary planar diffractive structures and metasurfaces in the Fourier domain. The attained general formulas for S -matrix components can be applied within both formulations in the Cartesian and curvilinear metric. A numerical method based on these results can benefit from all previous improvements of the Fourier domain methods. In addition, we provide expressions for S -matrix calculation in the case of periodically corrugated layers of two-dimensional materials, which are valid for arbitrary corrugation depth-to-period ratios. As an example, the derived equations are used to simulate resonant grating excitation of graphene plasmons and the impact of a silica interlayer on corresponding reflection curves.

Sound velocity measurement in liquid water up to 25 GPa and 900 K: Implications for densities of water at lower mantle conditions

NASA Astrophysics Data System (ADS)

Asahara, Yuki; Murakami, Motohiko; Ohishi, Yasuo; Hirao, Naohisa; Hirose, Kei

2010-01-01

We extended the pressure range of sound velocity measurements for liquid water to 25 GPa and 900 K along the melting curve using a laser heated diamond anvil cell with a combined system of Brillouin scattering and synchrotron X-ray diffraction. Experimental pressure and temperature were obtained by solving simultaneous equations: the melting curve of ice and the equation of state for gold. The sound velocities obtained in liquid water at high pressures and melting temperatures were converted to density using Murnaghan's equation of state by fitting a parameter of the pressure derivative of bulk modulus at 1 GPa. The results are in good agreement with the values predicted by a previously reported equation of state for water based on sound velocity measurements. The equation of state for water obtained in this study could be applicable to water released by dehydration reactions of dense hydrous magnesium silicate phases in cold subducting slabs at lower mantle conditions, although the validity of Murnaghan's equation of state for water should be evaluated in a wider pressure and temperature ranges. The present velocity data provides the basis for future improvement of the accurate thermodynamic model for water at high pressures.

Comments on gravitoelectromagnetism of Ummarino and Gallerati in "Superconductor in a weak static gravitational field" vs other versions

NASA Astrophysics Data System (ADS)

Behera, Harihar

2017-12-01

Recently reported [Eur. Phys. J. C., 77, 549 (2017). https://doi.org/10.1140/epjc/s10052-017-5116-y] gravitoelectromagnetic equations of Ummarino and Gallerati (UG) in their linearized version of general relativity (GR) are shown to match with (a) our previously reported special relativistic Maxwellian Gravity equations in the non-relativistic limit and with (b) the non-relativistic equations derived here, when the speed of gravity c_g (an undetermined parameter of the theory here) is set equal to c (the speed of light in vacuum). Seen in the light of our new results, the UG equations satisfy the Correspondence Principle (cp), while many other versions of linearized GR equations that are being (or may be) used to interpret the experimental data defy the cp. Such new findings assume significance and relevance in the contexts of recent detection of gravitational waves and the gravitomagnetic field of the spinning earth and their interpretations. Being well-founded and self-consistent, the equations may be of interest and useful to researchers exploring the phenomenology of gravitomagnetism, gravitational waves and the novel interplay of gravity with different states of matter in flat space-time like UG's interesting work on superconductors in weak gravitational fields.

Global fields of soil moisture and land surface evapotranspiration derived from observed precipitation and surface air temperature

NASA Technical Reports Server (NTRS)

Mintz, Y.; Walker, G. K.

1993-01-01

The global fields of normal monthly soil moisture and land surface evapotranspiration are derived with a simple water budget model that has precipitation and potential evapotranspiration as inputs. The precipitation is observed and the potential evapotranspiration is derived from the observed surface air temperature with the empirical regression equation of Thornthwaite (1954). It is shown that at locations where the net surface radiation flux has been measured, the potential evapotranspiration given by the Thornthwaite equation is in good agreement with those obtained with the radiation-based formulations of Priestley and Taylor (1972), Penman (1948), and Budyko (1956-1974), and this provides the justification for the use of the Thornthwaite equation. After deriving the global fields of soil moisture and evapotranspiration, the assumption is made that the potential evapotranspiration given by the Thornthwaite equation and by the Priestley-Taylor equation will everywhere be about the same; the inverse of the Priestley-Taylor equation is used to obtain the normal monthly global fields of net surface radiation flux minus ground heat storage. This and the derived evapotranspiration are then used in the equation for energy conservation at the surface of the earth to obtain the global fields of normal monthly sensible heat flux from the land surface to the atmosphere.

Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

NASA Astrophysics Data System (ADS)

Grigor'ev, Yu. N.; Ershov, I. V.

2017-01-01

An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models

NASA Technical Reports Server (NTRS)

Smith, L. M.; Reynolds, W. C.

1992-01-01

An independent, comprehensive, critical review of the 'renormalization group' (RNG) theory of turbulence developed by Yakhot and Orszag (1986) is provided. Their basic theory for the Navier-Stokes equations is confirmed, and approximations in the scale removal procedure are discussed. The YO derivations of the velocity-derivative skewness and the transport equation for the energy dissipation rate are examined. An algebraic error in the derivation of the skewness is corrected. The corrected RNG skewness value of -0.59 is in agreement with experiments at moderate Reynolds numbers. Several problems are identified in the derivation of the energy dissipation rate equations which suggest that the derivation should be reformulated.

Dynamics and Control of Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Part I

NASA Astrophysics Data System (ADS)

Amengonu, Yawo H.; Kakad, Yogendra P.

2014-07-01

Quasivelocity techniques such as Maggi's and Boltzmann-Hamel's equations eliminate Lagrange multipliers from the beginning as opposed to the Euler-Lagrange method where one has to solve for the n configuration variables and the multipliers as functions of time when there are m nonholonomic constraints. Maggi's equation produces n second-order differential equations of which (n-m) are derived using (n-m) independent quasivelocities and the time derivative of the m kinematic constraints which add the remaining m second order differential equations. This technique is applied to derive the dynamics of a differential mobile robot and a controller which takes into account these dynamics is developed.

Determination of lateral-stability derivatives and transfer-function coefficients from frequency-response data for lateral motions

NASA Technical Reports Server (NTRS)

Donegan, James J; Robinson, Samuel W , Jr; Gates, Ordway, B , jr

1955-01-01

A method is presented for determining the lateral-stability derivatives, transfer-function coefficients, and the modes for lateral motion from frequency-response data for a rigid aircraft. The method is based on the application of the vector technique to the equations of lateral motion, so that the three equations of lateral motion can be separated into six equations. The method of least squares is then applied to the data for each of these equations to yield the coefficients of the equations of lateral motion from which the lateral-stability derivatives and lateral transfer-function coefficients are computed. Two numerical examples are given to demonstrate the use of the method.

A finite-volume Eulerian-Lagrangian Localized Adjoint Method for solution of the advection-dispersion equation

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1993-01-01

A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.

Kinetic theory of pattern formation in mixtures of microtubules and molecular motors

NASA Astrophysics Data System (ADS)

Maryshev, Ivan; Marenduzzo, Davide; Goryachev, Andrew B.; Morozov, Alexander

2018-02-01

In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson and Tsimring [Phys. Rev. E 74, 031915 (2006), 10.1103/PhysRevE.74.031915] we model the motor-induced reorientation of microtubules as collision rules, and devise a semianalytical method to calculate the corresponding interaction integrals. This procedure yields an infinite hierarchy of kinetic equations that we terminate by employing a well-established closure strategy, developed in the pattern-formation community and based on a power-counting argument. We thus arrive at a closed set of coupled equations for slowly varying local density and orientation of the microtubules, and study its behavior by performing a linear stability analysis and direct numerical simulations. By comparing our method with the work of Aranson and Tsimring, we assess the validity of the assumptions required to derive their and our theories. We demonstrate that our approximation-free evaluation of the interaction integrals and our choice of a systematic closure strategy result in a rather different dynamical behavior than was previously reported. Based on our theory, we discuss the ensuing phase diagram and the patterns observed.

Higuchi equation: derivation, applications, use and misuse.

PubMed

Siepmann, Juergen; Peppas, Nicholas A

2011-10-10

Fifty years ago, the legendary Professor Takeru Higuchi published the derivation of an equation that allowed for the quantification of drug release from thin ointment films, containing finely dispersed drug into a perfect sink. This became the famous Higuchi equation whose fiftieth anniversary we celebrate this year. Despite the complexity of the involved mass transport processes, Higuchi derived a very simple equation, which is easy to use. Based on a pseudo-steady-state approach, a direct proportionality between the cumulative amount of drug released and the square root of time can be demonstrated. In contrast to various other "square root of time" release kinetics, the constant of proportionality in the classical Higuchi equation has a specific, physically realistic meaning. The major benefits of this equation include the possibility to: (i) facilitate device optimization, and (ii) to better understand the underlying drug release mechanisms. The equation can also be applied to other types of drug delivery systems than thin ointment films, e.g., controlled release transdermal patches or films for oral controlled drug delivery. Later, the equation was extended to other geometries and related theories have been proposed. The aim of this review is to highlight the assumptions the derivation of the classical Higuchi equation is based on and to give an overview on the use and potential misuse of this equation as well as of related theories. Copyright © 2011 Elsevier B.V. All rights reserved.

Evaluation of the magnitude and frequency of floods in urban watersheds in Phoenix and Tucson, Arizona

USGS Publications Warehouse

Kennedy, Jeffrey R.; Paretti, Nicholas V.

2014-01-01

Flooding in urban areas routinely causes severe damage to property and often results in loss of life. To investigate the effect of urbanization on the magnitude and frequency of flood peaks, a flood frequency analysis was carried out using data from urbanized streamgaging stations in Phoenix and Tucson, Arizona. Flood peaks at each station were predicted using the log-Pearson Type III distribution, fitted using the expected moments algorithm and the multiple Grubbs-Beck low outlier test. The station estimates were then compared to flood peaks estimated by rural-regression equations for Arizona, and to flood peaks adjusted for urbanization using a previously developed procedure for adjusting U.S. Geological Survey rural regression peak discharges in an urban setting. Only smaller, more common flood peaks at the 50-, 20-, 10-, and 4-percent annual exceedance probabilities (AEPs) demonstrate any increase in magnitude as a result of urbanization; the 1-, 0.5-, and 0.2-percent AEP flood estimates are predicted without bias by the rural-regression equations. Percent imperviousness was determined not to account for the difference in estimated flood peaks between stations, either when adjusting the rural-regression equations or when deriving urban-regression equations to predict flood peaks directly from basin characteristics. Comparison with urban adjustment equations indicates that flood peaks are systematically overestimated if the rural-regression-estimated flood peaks are adjusted upward to account for urbanization. At nearly every streamgaging station in the analysis, adjusted rural-regression estimates were greater than the estimates derived using station data. One likely reason for the lack of increase in flood peaks with urbanization is the presence of significant stormwater retention and detention structures within the watershed used in the study.

A tensor formulation of the equation of transfer for spherically symmetric flows. [radiative transfer in seven dimensional Riemannian space

NASA Technical Reports Server (NTRS)

Haisch, B. M.

1976-01-01

A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.

PubMed

Lehtonen, Jussi

2018-01-01

A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.

Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory

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

Denicol, G. S.; Koide, T.; Rischke, D. H.

2010-10-15

We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.

Alternative Regression Equations for Estimation of Annual Peak-Streamflow Frequency for Undeveloped Watersheds in Texas using PRESS Minimization

USGS Publications Warehouse

Asquith, William H.; Thompson, David B.

2008-01-01

The U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, investigated a refinement of the regional regression method and developed alternative equations for estimation of peak-streamflow frequency for undeveloped watersheds in Texas. A common model for estimation of peak-streamflow frequency is based on the regional regression method. The current (2008) regional regression equations for 11 regions of Texas are based on log10 transformations of all regression variables (drainage area, main-channel slope, and watershed shape). Exclusive use of log10-transformation does not fully linearize the relations between the variables. As a result, some systematic bias remains in the current equations. The bias results in overestimation of peak streamflow for both the smallest and largest watersheds. The bias increases with increasing recurrence interval. The primary source of the bias is the discernible curvilinear relation in log10 space between peak streamflow and drainage area. Bias is demonstrated by selected residual plots with superimposed LOWESS trend lines. To address the bias, a statistical framework based on minimization of the PRESS statistic through power transformation of drainage area is described and implemented, and the resulting regression equations are reported. Compared to log10-exclusive equations, the equations derived from PRESS minimization have PRESS statistics and residual standard errors less than the log10 exclusive equations. Selected residual plots for the PRESS-minimized equations are presented to demonstrate that systematic bias in regional regression equations for peak-streamflow frequency estimation in Texas can be reduced. Because the overall error is similar to the error associated with previous equations and because the bias is reduced, the PRESS-minimized equations reported here provide alternative equations for peak-streamflow frequency estimation.

Motion of particles in solar and galactic systems by using Neumann boundary condition

NASA Astrophysics Data System (ADS)

Shenavar, Hossein

2016-12-01

A new equation of motion, which is derived previously by imposing Neumann boundary condition on cosmological perturbation equations (Shenavar in Astrophys. Space Sci., 2016a, doi: 10.1007/s10509-016-2676-5), is investigated. By studying the precession of perihelion, it is shown that the new equation of motion suggests a small, though detectable, correction in orbits of solar system objects. Then a system of particles is surveyed to have a better understanding of galactic structures. Also the general form of the force law is introduced by which the rotation curve and mass discrepancy of axisymmetric disks of stars are derived. In addition, it is suggested that the mass discrepancy as a function of centripetal acceleration becomes significant near a constant acceleration 2c1a0 where c1 is the Neumann constant and a0 = 6.59 ×10^{-10} m/s2 is a fundamental acceleration. Furthermore, it is shown that a critical surface density equal to σ0=a0/G, in which G is the Newton gravitational constant, has a significant role in rotation curve and mass discrepancy plots. Also, the specific form of NFW mass density profile at small radii, ρ∝1/r, is explained too. Finally, the present model will be tested by using a sample of 39 LSB galaxies for which we will show that the rotation curve fittings are generally acceptable. The derived mass to light ratios too are found within the plausible bound except for the galaxy F571-8.

Comparison of formulas for resonant interactions between energetic electrons and oblique whistler-mode waves

NASA Astrophysics Data System (ADS)

Li, Jinxing; Bortnik, Jacob; Xie, Lun; Pu, Zuyin; Chen, Lunjin; Ni, Binbin; Tao, Xin; Thorne, Richard M.; Fu, Suiyan; Yao, Zhonghua; Guo, Ruilong

2015-05-01

Test particle simulation is a useful method for studying both linear and nonlinear wave-particle interactions in the magnetosphere. The gyro-averaged equations of particle motion for first-order and other cyclotron harmonic resonances with oblique whistler-mode waves were first derived by Bell [J. Geophys. Res. 89, 905 (1984)] and the most recent relativistic form was given by Ginet and Albert [Phys. Fluids B 3, 2994 (1991)], and Bortnik [Ph.D. thesis (Stanford University, 2004), p. 40]. However, recently we found there was a ( - 1 ) l - 1 term difference between their formulas of perpendicular motion for the lth-order resonance. This article presents the detailed derivation process of the generalized resonance formulas, and suggests a check of the signs for self-consistency, which is independent of the choice of conventions, that is, the energy variation equation resulting from the momentum equations should not contain any wave magnetic components, simply because the magnetic field does not contribute to changes of particle energy. In addition, we show that the wave centripetal force, which was considered small and was neglect in previous studies of nonlinear interactions, has a profound time derivative and can significantly enhance electron phase trapping especially in high frequency waves. This force can also bounce the low pitch angle particles out of the loss cone. We justify both the sign problem and the missing wave centripetal force by demonstrating wave-particle interaction examples, and comparing the gyro-averaged particle motion to the full particle motion under the Lorentz force.

An Economical Analytical Equation for the Integrated Vertical Overlap of Cumulus and Stratus

NASA Astrophysics Data System (ADS)

Park, Sungsu

2018-03-01

By extending the previously proposed heuristic parameterization, the author derived an analytical equation computing the overlap areas between the precipitation (or radiation) areas and the cloud areas in a cloud system consisting of cumulus and stratus. The new analytical equation is accurate and much more efficient than the previous heuristic equation, which suffers from the truncation error in association with the digitalization of the overlap areas. Global test simulations with the new analytical formula in an offline mode showed that the maximum cumulus overlap simulates more surface precipitation flux than the random cumulus overlap. On the other hand, the maximum stratus overlap simulates less surface precipitation flux than random stratus overlap, which is due to the increase in the evaporation rate of convective precipitation from the random to maximum stratus overlap. The independent precipitation approximation (IPA) marginally decreases the surface precipitation flux, implying that IPA works well with other parameterizations. In contrast to the net production rate of precipitation and surface precipitation flux that increase when the cumulus and stratus are maximally and randomly overlapped, respectively, the global mean net radiative cooling and longwave cloud radiative forcing (LWCF) increase when the cumulus and stratus are randomly overlapped. On the global average, the vertical cloud overlap exerts larger impacts on the precipitation flux than on the radiation flux. The radiation scheme taking the subgrid variability of water vapor between the cloud and clear portions into account substantially increases the global mean LWCF in tropical deep convection and midlatitude storm track regions.

Moss bags as sentinels for human safety in mercury-polluted groundwaters.

PubMed

Cesa, Mattia; Nimis, Pier Luigi; Buora, Clara; Lorenzonetto, Alberta; Pozzobon, Alessandro; Raris, Marina; Rosa, Maria; Salvadori, Michela

2014-05-01

An equation to estimate Hg concentrations of <4 μg/L in groundwaters of a polluted area in NE Italy was set out by using transplants of the aquatic moss Rhynchostegium riparioides as trace element bioaccumulators. The equation is derived from a previous mathematical model which was implemented under laboratory conditions. The work aimed at (1) checking the compliance of the uptake kinetics with the model, (2) improving/adapting the model for groundwater monitoring, (3) comparing the performances of two populations of moss collected from different sites, and (4) assessing the environmental impact of Hg contamination on a small river. The main factors affecting Hg uptake in the field were-as expected-water concentration and time of exposure, even though the uptake kinetics in the field were slightly different from those which were previously observed in the lab, since the redox environmental conditions influence the solubility of cationic Fe, which is a negative competitor of Hg(2+). The equation was improved by including the variable 'dissolved oxygen concentration'. A numerical parameter depending on the moss collection site was also provided, since the differences in uptake efficiency were observed between the two populations tested. Predicted Hg concentrations well fitted the values measured in situ (approximately ±50%), while a notable underestimation was observed when the equation was used to predict Hg concentration in a neighbouring river (-96%), probably due to the organic pollution which hampers metal uptake by mosses.

Eigenvalue sensitivity analysis of planar frames with variable joint and support locations

NASA Technical Reports Server (NTRS)

Chuang, Ching H.; Hou, Gene J. W.

1991-01-01

Two sensitivity equations are derived in this study based upon the continuum approach for eigenvalue sensitivity analysis of planar frame structures with variable joint and support locations. A variational form of an eigenvalue equation is first derived in which all of the quantities are expressed in the local coordinate system attached to each member. Material derivative of this variational equation is then sought to account for changes in member's length and orientation resulting form the perturbation of joint and support locations. Finally, eigenvalue sensitivity equations are formulated in either domain quantities (by the domain method) or boundary quantities (by the boundary method). It is concluded that the sensitivity equation derived by the boundary method is more efficient in computation but less accurate than that of the domain method. Nevertheless, both of them in terms of computational efficiency are superior to the conventional direct differentiation method and the finite difference method.

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.

PubMed

Khusnutdinova, K R; Klein, C; Matveev, V B; Smirnov, A O

2013-03-01

There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

NASA Astrophysics Data System (ADS)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

Adiabatic bulk modulus of elasticity for 2D liquid dusty plasmas

NASA Astrophysics Data System (ADS)

Feng, Yan; Huang, Dong; Li, Wei

2018-05-01

From the recently obtained equation of state (EOS) for two-dimensional (2D) liquid dusty plasmas, their various physical quantities have been derived analytically, such as the specific heat CV, the Grüneisen parameter, the bulk modulus of elasticity, and the isothermal compressibility. Here, the coefficient of volumetric thermal expansion αV and the relative pressure coefficient αP of 2D liquid dusty plasmas are derived from their EOS. Using the obtained CV, αV, and αP, the analytical expression of their heat capacity under constant-pressure conditions CP is obtained. Thus, the heat capacity ratio, expressed as CP/CV , is analytically achieved. Then the adiabatic bulk modulus of elasticity is derived, so that the adiabatic sound speeds are obtained. These obtained results are compared with previous findings using a different approach.

Spirometric Reference Equations for Elderly Chinese in Jinan Aged 60–84 Years

PubMed Central

Tian, Xin-Yu; Liu, Chun-Hong; Wang, De-Xiang; Ji, Xiu-Li; Shi, Hui; Zheng, Chun-Yan; Xie, Meng-Shuang; Xiao, Wei

2018-01-01

Background: The interpretation of spirometry varies on different reference values. Older people are usually underrepresented in published predictive values. This study aimed at developing spirometric reference equations for elderly Chinese in Jinan aged 60–84 years and to compare them to previous equations. Methods: The project covered all of Jinan city, and the recruitment period lasted 9 months from January 1, 2017 to September 30, 2017, 434 healthy people aged 60–84 years who had never smoked (226 females and 208 males) were recruited to undergo spirometry. Vital capacity (VC), forced VC (FVC), forced expiratory volume in 1 s (FEV1), FEV1/FVC, FEV1/VC, FEV6, peak expiratory flow, and forced expiratory flow at 25%, 50%, 75%, and 25–75% of FVC exhaled (FEF25%, FEF50%, FEF75%, and FEF25–75%) were analyzed. Reference equations for mean and the lower limit of normal (LLN) were derived using the lambda-mu-sigma method. Comparisons between new and previous equations were performed by paired t-test. Results: New reference equations were developed from the sample. The LLN of FEV1/FVC, FEF25–75% computed using the 2012-Global Lung Function Initiative (GLI) and 2006-Hong Kong equations were both lower than the new equations. The biggest degree of difference for FEV1/FVC was 19% (70.46% vs. 59.29%, t = 33.954, P < 0.01) and for maximal midexpiratory flow (MMEF, equals to FEF25–75%) was 22% (0.82 vs. 0.67, t = 21.303, P < 0.01). The 1990-North China and 2009-North China equations predicted higher mean values of FEV1/FVC and FEF25–75% than the present model. The biggest degrees of difference were −4% (78.31% vs. 81.27%, t = −85.359, P < 0.01) and −60% (2.11 vs. 4.68, t = −170.287, P < 0.01), respectively. Conclusions: The newly developed spirometric reference equations are applicable to elderly Chinese in Jinan. The 2012-GLI and 2006-Hong Kong equations may lead to missed diagnoses of obstructive ventilatory defects and the small airway dysfunction, while traditional linear equations for all ages may lead to overdiagnosis. PMID:29553052

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

QSAR, QSPR and QSRR in Terms of 3-D-MoRSE Descriptors for In Silico Screening of Clofibric Acid Analogues.

PubMed

Di Tullio, Maurizio; Maccallini, Cristina; Ammazzalorso, Alessandra; Giampietro, Letizia; Amoroso, Rosa; De Filippis, Barbara; Fantacuzzi, Marialuigia; Wiczling, Paweł; Kaliszan, Roman

2012-07-01

A series of 27 analogues of clofibric acid, mostly heteroarylalkanoic derivatives, have been analyzed by a novel high-throughput reversed-phase HPLC method employing combined gradient of eluent's pH and organic modifier content. The such determined hydrophobicity (lipophilicity) parameters, log kw , and acidity constants, pKa , were subjected to multiple regression analysis to get a QSRR (Quantitative StructureRetention Relationships) and a QSPR (Quantitative Structure-Property Relationships) equation, respectively, describing these pharmacokinetics-determining physicochemical parameters in terms of the calculation chemistry derived structural descriptors. The previously determined in vitro log EC50 values - transactivation activity towards PPARα (human Peroxisome Proliferator-Activated Receptor α) - have also been described in a QSAR (Quantitative StructureActivity Relationships) equation in terms of the 3-D-MoRSE descriptors (3D-Molecule Representation of Structures based on Electron diffraction descriptors). The QSAR model derived can serve for an a priori prediction of bioactivity in vitro of any designed analogue, whereas the QSRR and the QSPR models can be used to evaluate lipophilicity and acidity, respectively, of the compounds, and hence to rational guide selection of structures of proper pharmacokinetics. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Constrained low-rank matrix estimation: phase transitions, approximate message passing and applications

NASA Astrophysics Data System (ADS)

Lesieur, Thibault; Krzakala, Florent; Zdeborová, Lenka

2017-07-01

This article is an extended version of previous work of Lesieur et al (2015 IEEE Int. Symp. on Information Theory Proc. pp 1635-9 and 2015 53rd Annual Allerton Conf. on Communication, Control and Computing (IEEE) pp 680-7) on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic methods used in data analysis for unsupervised learning of relevant features and other types of dimensionality reduction. We present a framework to study the constrained low-rank matrix estimation for a general prior on the factors, and a general output channel through which the matrix is observed. We draw a parallel with the study of vector-spin glass models—presenting a unifying way to study a number of problems considered previously in separate statistical physics works. We present a number of applications for the problem in data analysis. We derive in detail a general form of the low-rank approximate message passing (Low-RAMP) algorithm, that is known in statistical physics as the TAP equations. We thus unify the derivation of the TAP equations for models as different as the Sherrington-Kirkpatrick model, the restricted Boltzmann machine, the Hopfield model or vector (xy, Heisenberg and other) spin glasses. The state evolution of the Low-RAMP algorithm is also derived, and is equivalent to the replica symmetric solution for the large class of vector-spin glass models. In the section devoted to result we study in detail phase diagrams and phase transitions for the Bayes-optimal inference in low-rank matrix estimation. We present a typology of phase transitions and their relation to performance of algorithms such as the Low-RAMP or commonly used spectral methods.

The chemical (not mechanical) paradigm of thermodynamics of colloid and interface science.

PubMed

Kaptay, George

2018-06-01

In the most influential monograph on colloid and interfacial science by Adamson three fundamental equations of "physical chemistry of surfaces" are identified: the Laplace equation, the Kelvin equation and the Gibbs adsorption equation, with a mechanical definition of surface tension by Young as a starting point. Three of them (Young, Laplace and Kelvin) are called here the "mechanical paradigm". In contrary it is shown here that there is only one fundamental equation of the thermodynamics of colloid and interface science and all the above (and other) equations of this field follow as its derivatives. This equation is due to chemical thermodynamics of Gibbs, called here the "chemical paradigm", leading to the definition of surface tension and to 5 rows of equations (see Graphical abstract). The first row is the general equation for interfacial forces, leading to the Young equation, to the Bakker equation and to the Laplace equation, etc. Although the principally wrong extension of the Laplace equation formally leads to the Kelvin equation, using the chemical paradigm it becomes clear that the Kelvin equation is generally incorrect, although it provides right results in special cases. The second row of equations provides equilibrium shapes and positions of phases, including sessile drops of Young, crystals of Wulff, liquids in capillaries, etc. The third row of equations leads to the size-dependent equations of molar Gibbs energies of nano-phases and chemical potentials of their components; from here the corrected versions of the Kelvin equation and its derivatives (the Gibbs-Thomson equation and the Freundlich-Ostwald equation) are derived, including equations for more complex problems. The fourth row of equations is the nucleation theory of Gibbs, also contradicting the Kelvin equation. The fifth row of equations is the adsorption equation of Gibbs, and also the definition of the partial surface tension, leading to the Butler equation and to its derivatives, including the Langmuir equation and the Szyszkowski equation. Positioning the single fundamental equation of Gibbs into the thermodynamic origin of colloid and interface science leads to a coherent set of correct equations of this field. The same provides the chemical (not mechanical) foundation of the chemical (not mechanical) discipline of colloid and interface science. Copyright © 2018 Elsevier B.V. All rights reserved.

Solutions of the heat conduction equation in multilayers for photothermal deflection experiments

NASA Technical Reports Server (NTRS)

Mcgahan, William A.; Cole, K. D.

1992-01-01

Analytical expressions for temperature and laser beam deflection in multilayer medium is derived using Green function techniques. The approach is based on calculation of the normal component of heat fluxes across the boundaries, from which either the beam deflections or the temperature anywhere in space can be found. A general expression for the measured signals for the case of four-quadrant detection is also presented and compared with previous calculations of detector response for finite probe beams.

Wafer Scale Distributed Radio

DTIC Science & Technology

2009-07-01

equation, we can derive: ∆ flock = f0 2Q Ain j A (5.34) with Ain j and A , the relative amplitude of the injecting signal and the oscillator signal, both...center of the line (Ain j = A ), then the locking range is equal to 1250MHz for a 10GHz oscillation frequency. With the architecture previously described...resonator in 90nm CMOS. In 2008 IEEE MTT-S International Microwave Symposium Digest (2008), pp. 775–778. [27] MCLEAN, J . A re-examination of the fundamental

On the Mo-Papas equation

NASA Astrophysics Data System (ADS)

Aguirregabiria, J. M.; Chamorro, A.; Valle, M. A.

1982-05-01

A new heuristic derivation of the Mo-Papas equation for charged particles is given. It is shown that this equation cannot be derived for a point particle by closely following Dirac's classical treatment of the problem. The Mo-Papas theory and the Bonnor-Rowe-Marx variable mass dynamics are not compatible.

Simplified Relativistic Force Transformation Equation.

ERIC Educational Resources Information Center

Stewart, Benjamin U.

1979-01-01

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic forces on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and relate it to Coulomb's law.…

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations

DOE PAGES

Shao, Xuan-Min

2016-04-12

The fundamental electromagnetic equations used by lightning researchers were introduced in a seminal paper by Uman, McLain, and Krider in 1975. However, these equations were derived for an infinitely thin, one-dimensional source current, and not for a general three-dimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a three-dimensional, time-dependent current density distribution based on Jefimenko's original electric and magnetic equations. To do this, we derive the Jefimenko electric field equation into a new form that depends only on the time-dependent current density similar to that of Uman, McLain, and Krider,more » rather than on both the charge and current densities in its original form. The original Jefimenko magnetic field equation depends only on current, so no further derivation is needed. We show that the equations of Uman, McLain, and Krider can be readily obtained from the generalized equations if a one-dimensional source current is considered. For the purpose of practical applications, we discuss computational implementation of the new equations and present electric field calculations for a three-dimensional, conical-shape discharge.« less

Approach to first-order exact solutions of the Ablowitz-Ladik equation.

PubMed

Ankiewicz, Adrian; Akhmediev, Nail; Lederer, Falk

2011-05-01

We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schrödinger equation (NLSE). © 2011 American Physical Society

Einstein-Cartan Theory of Gravitation: Kinematical Parameters and Maxwell Equations

NASA Astrophysics Data System (ADS)

Katkar, L. N.

2015-03-01

In the space-time manifold of Einstein-Cartan Theory (ECT) of gravitation, the expressions for the time-like kinematical parameters are derived and the propagation equation for expansion is obtained.It has been observed that when the spin tensor is u-orthogonal the spin of the gravitating matter has no influence on the propagation equation of expansion while it has influence when it is not u-orthogonal. The usual formula for the curl of gradient of a scalar function is not zero in ECT. So is the case with the divergence of the curl of a vector.Their expressions on the space-time manifold of ECT are derived. A new derivative operator d ∗ is introduced to develop the calculus on space-time manifold of ECT. It is obtained by taking the covariant derivative of an associated tensor of a form with respect to an asymmetric connections. We have used this differential operator to obtain the form of the Maxwell's equations in the ECT of gravitation. Cartan's equations of structure are also derived through the new derivative operator. It has been shown that unlike the consequences of exterior derivative in Einstein space-time, the repetition of d ∗ on a form of any degree is not zero.

The elastic theory of shells using geometric algebra

PubMed Central

Lasenby, J.; Agarwal, A.

2017-01-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible. PMID:28405404

The elastic theory of shells using geometric algebra.

PubMed

Gregory, A L; Lasenby, J; Agarwal, A

2017-03-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.

Non-classical and potential symmetry analysis of Richard's equation for moisture flow in soil

NASA Astrophysics Data System (ADS)

Wiltshire, Ron; El-Kafri, Manal

2004-01-01

This paper focuses upon the derivation of the non-classical symmetries of Bluman and Cole as they apply to Richard's equation for water flow in an unsaturated uniform soil. It is shown that the determining equations for the non-classical case lead to four highly non-linear equations which have been solved in five particular cases. In each case the corresponding similarity ansatz has been derived and Richard's equation is reduced to an ordinary differential equation. Explicit solutions are produced when possible. Richard's equation is also expressed as a potential system and in reviewing the classical Lie solutions a new symmetry is derived together with its similarity ansatz. Determining equations are then produced for the potential system using the non-classical algorithm. This results in an under-determined set of equations and an example symmetry that reveals a missing classical case is presented. An example of a classical and a non-classical symmetry reduction applied to the infiltration of moisture in soil is presented. The condition for surface invariance is used to demonstrate the equivalence of a classical Lie and a potential symmetry.

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

PubMed

Cammi, R

2009-10-28

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

The application of the principles of invariance to the radiative transfer equation in plant canopies

NASA Technical Reports Server (NTRS)

Ganapol, B. D.; Myneni, R. B.

1992-01-01

Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.

Exact example of backreaction of small scale inhomogeneities in cosmology

NASA Astrophysics Data System (ADS)

Green, Stephen; Wald, Robert

2013-04-01

We construct a one-parameter family of polarized vacuum Gowdy spacetimes on a torus. In the limit as the parameter N goes to infinity, the metric uniformly approaches a smooth ``background metric.'' However, spacetime derivatives of the metric do not approach a limit. As a result, we find that the background metric itself is not a solution of the vacuum Einstein equation. Rather, it is a solution of the Einstein equation with an ``effective stress-energy tensor,'' which is traceless and satisfies the weak energy condition. This is an explicit example of backreaction due to small scale inhomogeneities. We comment on the non-vacuum case, where we have proven in previous work that, provided the matter stress-energy tensor satisfies the weak energy condition, no additional backreaction is possible.

Isaac Newton and the astronomical refraction.

PubMed

Lehn, Waldemar H

2008-12-01

In a short interval toward the end of 1694, Isaac Newton developed two mathematical models for the theory of the astronomical refraction and calculated two refraction tables, but did not publish his theory. Much effort has been expended, starting with Biot in 1836, in the attempt to identify the methods and equations that Newton used. In contrast to previous work, a closed form solution is identified for the refraction integral that reproduces the table for his first model (in which density decays linearly with elevation). The parameters of his second model, which includes the exponential variation of pressure in an isothermal atmosphere, have also been identified by reproducing his results. The implication is clear that in each case Newton had derived exactly the correct equations for the astronomical refraction; furthermore, he was the first to do so.

Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.

PubMed

Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko

2014-04-01

The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials.

Solving the Hamilton-Jacobi equation for general relativity

NASA Astrophysics Data System (ADS)

Parry, J.; Salopek, D. S.; Stewart, J. M.

1994-03-01

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates (``gauge invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.

Enthalpy measurement of coal-derived liquids. Final report, April 1981-September 1983. [517 to 10342 kPa; 340 to 664 K

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

Kidnay, A.J.; Yesavage, V.F.

This report summarizes the results of experimental measurements of enthalpies for quinoline using a freon boil-off flow calorimeter, and an investigation of the applicability of cubic equations of state to correlating the enthalpy of coal-liquids. In Part A the compound quinoline is discussed. Process flow in the flow calorimeter, operational problems, and equipment modifications are described. Procedural modifications, including a new sample purification procedure, are described. Part B discusses the correlational effort. This includes a discussion of past correlational work and the difficulties associated with a general correlation for coal liquid enthalpy. In addition experimental data and computer generated predictionsmore » are presented. Three equations of state were used to predict vapor pressures and enthalpies for ten pure component systems previously studied in the lab. In general, the results were encouraging. All three equations were found to be effective in predicting both enthalpies and vapor pressures. In addition, the equations worked well when fit to mixture enthalpies. The Modified SRK equation was found to be superior to the other equations and modeled all properties for both associating and nonassociating systems well. The Modified SRK equation did have a drawback in that it was not readily generalized since it required two parameters which must be fit to data for best results. In sum, it was shown that a four parameter equation of state could be used successfully to correlate the enthalpy of coal-liquid model compounds.« less

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

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

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

Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations.

PubMed

Meffin, Hamish; Tahayori, Bahman; Grayden, David B; Burkitt, Anthony N

2012-12-01

Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

PubMed

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Brans-Dicke Galileon and the variational principle

NASA Astrophysics Data System (ADS)

Quiros, Israel; García-Salcedo, Ricardo; Gonzalez, Tame; Horta-Rangel, F. Antonio; Saavedra, Joel

2016-09-01

This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with cubic self-interaction. This is a modification of the Brans-Dicke theory by the addition of a term in the Lagrangian which is non-linear in the derivatives of the scalar field: it contains second-order derivatives. This is the basis of the so-called Brans-Dicke Galileon. We pay special attention to the variational principle and to the algebraic details of the derivation. It is shown how higher order derivatives of the fields appearing in the intermediate computations cancel out leading to second order motion equations. The reader will find useful tips for the derivation of the field equations of modifications of general relativity such as the scalar-tensor theories and f(R) theories, by means of the (stationary action) variational principle. The content of this paper is particularly recommended to those graduate and postgraduate students who are interested in the study of the mentioned modifications of general relativity.

Complex-valued derivative propagation method with approximate Bohmian trajectories: Application to electronic nonadiabatic dynamics

NASA Astrophysics Data System (ADS)

Wang, Yu; Chou, Chia-Chun

2018-05-01

The coupled complex quantum Hamilton-Jacobi equations for electronic nonadiabatic transitions are approximately solved by propagating individual quantum trajectories in real space. Equations of motion are derived through use of the derivative propagation method for the complex actions and their spatial derivatives for wave packets moving on each of the coupled electronic potential surfaces. These equations for two surfaces are converted into the moving frame with the same grid point velocities. Excellent wave functions can be obtained by making use of the superposition principle even when nodes develop in wave packet scattering.

Partially ionized hydrogen plasma in strong magnetic fields.

PubMed

Potekhin, A Y; Chabrier, G; Shibanov, Y A

1999-08-01

We study the thermodynamic properties of a partially ionized hydrogen plasma in strong magnetic fields, B approximately 10(12)-10(13) G, typical of neutron stars. The properties of the plasma depend significantly on the quantum-mechanical sizes and binding energies of the atoms, which are strongly modified by thermal motion across the field. We use new fitting formulas for the atomic binding energies and sizes, based on accurate numerical calculations and valid for any state of motion of the atom. In particular, we take into account decentered atomic states, neglected in previous studies of thermodynamics of magnetized plasmas. We also employ analytic fits for the thermodynamic functions of nonideal fully ionized electron-ion Coulomb plasmas. This enables us to construct an analytic model of the free energy. An ionization equilibrium equation is derived, taking into account the strong magnetic field effects and the nonideality effects. This equation is solved by an iteration technique. Ionization degrees, occupancies, and the equation of state are calculated.

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.

1984-01-01

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Liu, Di

2015-01-01

In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure

NASA Astrophysics Data System (ADS)

Be'er, Shay; Assaf, Michael; Meerson, Baruch

2015-06-01

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We circumvent this difficulty by deriving an exact zero-flux solution of the master equation and matching it with an approximate nonzero-flux solution of the pertinent Fokker-Planck equation in a small region around the critical population size. This procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization, for a wide range of immigration rates. At sufficiently high immigration rates our results agree with WKB results obtained previously. At low immigration rates the results can be very different.

Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure.

PubMed

Be'er, Shay; Assaf, Michael; Meerson, Baruch

2015-06-01

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We circumvent this difficulty by deriving an exact zero-flux solution of the master equation and matching it with an approximate nonzero-flux solution of the pertinent Fokker-Planck equation in a small region around the critical population size. This procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization, for a wide range of immigration rates. At sufficiently high immigration rates our results agree with WKB results obtained previously. At low immigration rates the results can be very different.

Analytic solutions for Long's equation and its generalization

NASA Astrophysics Data System (ADS)

Humi, Mayer

2017-12-01

Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

NASA Astrophysics Data System (ADS)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-11-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.

Gender disparity in BMD conversion: a comparison between Lunar and Hologic densitometers.

PubMed

Ganda, Kirtan; Nguyen, Tuan V; Pocock, Nicholas

2014-01-01

Female-derived inter-conversion and standardised BMD equations at the lumbar spine and hip have not been validated in men. This study of 110 male subjects scanned on Hologic and Lunar densitometers demonstrates that published equations may not applicable to men at the lumbar spine. Male inter-conversion equations have also been derived. Currently, available equations for inter-manufacturer conversion of bone mineral density (BMD) and calculation of standardised BMD (sBMD) are used in both males and females, despite being derived and validated only in women. Our aim was to test the validity of the published equations in men. One hundred ten men underwent lumbar spine (L2-4), femoral neck (FN) and total hip (TH) dual X-ray absorptiometry (DXA) using Hologic and Lunar scanners. Hologic BMD was converted to Lunar using published equations derived from women for L2-4 and FN. Actual Lunar BMD (A-Lunar) was compared to converted (Lunar equivalent) Hologic BMD values (H-Lunar). sBMD was calculated separately using Hologic (sBMD-H) and Lunar BMD (sBMD-L) at L2-4, FN and TH. Conversion equations in men for Hologic to Lunar BMD were derived using Deming regression analysis. There was a strong linear correlation between Lunar and Hologic BMD at all skeletal sites. A-Lunar BMD was however significantly higher than derived H-Lunar BMD (p < 0.001) at L2-L4 (mean difference, 0.07 g/cm(2)). There was no significant difference at the FN (mean difference, 0.01 g/cm(2)). sBMD-L at the spine was significantly higher than sBMD-H (mean difference, 0.06 g/cm(2), p < 0.001), whilst there was little difference at the FN and TH (mean difference, 0.01 g/cm(2)). Published conversion equations for Lunar BMD to Hologic BMD, and formulae for lumbar spine sBMD, derived in women may not be applicable to men.

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Maneuverability Estimation of High-Speed Craft

DTIC Science & Technology

2015-06-01

derived based on equations by Lewandowski and Denny- Hubble in order to find the fundamental maneuvering characteristics. The model is developed in...characteristic of high- speed craft. A mathematical model is derived based on equations by Lewandowski and Denny- Hubble in order to find the fundamental...33 C. EQUATIONS BY DENNY AND HUBBLE ................................................43 D. NOMOTO

The Empirical Derivation of Equations for Predicting Subjective Textual Information. Final Report.

ERIC Educational Resources Information Center

Kauffman, Dan; And Others

A study was made to derive an equation for predicting the "subjective" textual information contained in a text of material written in the English language. Specifically, this investigation describes, by a mathematical equation, the relationship between the "subjective" information content of written textual material and the relative number of…

Equations for the Filled Inelastic Membrane: A More General Derivation

ERIC Educational Resources Information Center

Deakin, Michael A. B.

2011-01-01

An earlier paper discussed the case of a flexible but inextensible membrane filled to capacity with incompressible fluid. It was found that the resulting shape satisfies a set of three simultaneous partial differential equations. This article gives a more general derivation of these equations and shows their form in an interesting special case.

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.

A Comprehensive Review on the Predictive Performance of the Sheiner-Tozer and Derivative Equations for the Correction of Phenytoin Concentrations.

PubMed

Kiang, Tony K L; Ensom, Mary H H

2016-04-01

In settings where free phenytoin concentrations are not available, the Sheiner-Tozer equation-Corrected total phenytoin concentration = Observed total phenytoin concentration/[(0.2 × Albumin) + 0.1]; phenytoin in µg/mL, albumin in g/dL-and its derivative equations are commonly used to correct for altered phenytoin binding to albumin. The objective of this article was to provide a comprehensive and updated review on the predictive performance of these equations in various patient populations. A literature search of PubMed, EMBASE, and Google Scholar was conducted using combinations of the following terms: Sheiner-Tozer, Winter-Tozer, phenytoin, predictive equation, precision, bias, free fraction. All English-language articles up to November 2015 (excluding abstracts) were evaluated. This review shows the Sheiner-Tozer equation to be biased and imprecise in various critical care, head trauma, and general neurology patient populations. Factors contributing to bias and imprecision include the following: albumin concentration, free phenytoin assay temperature, experimental conditions (eg, timing of concentration sampling, steady-state dosing conditions), renal function, age, concomitant medications, and patient type. Although derivative equations using varying albumin coefficients have improved accuracy (without much improvement in precision) in intensive care and elderly patients, these equations still require further validation. Further experiments are also needed to yield derivative equations with good predictive performance in all populations as well as to validate the equations' impact on actual patient efficacy and toxicity outcomes. More complex, multivariate predictive equations may be required to capture all variables that can potentially affect phenytoin pharmacokinetics and clinical therapeutic outcomes. © The Author(s) 2016.

Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar

NASA Technical Reports Server (NTRS)

Jacobsen, Richard T.; Stewart, Richard B.

1973-01-01

Tables of thermodynamic properties of nitrogen are presented for the liquid and vapor phases for temperatures from the freezing line to 2000K and pressures to 10,000 bar. The tables include values of density, internal energy, enthalpy, entropy, isochoric heat capacity, isobaric heat capacity velocity of sound, the isotherm derivative, and the isochor derivative. The thermodynamic property tables are based on an equation of state, P=P (p,T), which accurately represents liquid and gaseous nitrogen for the range of pressures and temperatures covered by the tables. Comparisons of property values calculated from the equation of state with measured values for P-p-T, heat capacity, enthalpy, latent heat, and velocity of sound are included to illustrate the agreement between the experimental data and the tables of properties presented here. The coefficients of the equation of state were determined by a weighted least squares fit to selected P-p-T data and, simultaneously, to isochoric heat capacity data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and the saturated vapor. The vapor pressure equation, melting curve equation, and an equation to represent the ideal gas heat capacity are also presented. Estimates of the accuracy of the equation of state, the vapor pressure equation, and the ideal gas heat capacity equation are given. The equation of state, derivatives of the equation, and the integral functions for calculating derived thermodynamic properties are included.

Acoustic impact on the laminated plates placed between barriers

NASA Astrophysics Data System (ADS)

Paimushin, V. N.; Gazizullin, R. K.; Fedotenkov, G. V.

2016-11-01

On the basis of previously derived equations, analytical solutions are established on the forced vibrations of two-layer and three-layers rectangular plates hinged in an opening of absolutely rigid walls during the transmission of monoharmonic sound waves. It is assumed that the partition wall is situated between two absolutely rigid barriers, one of them by harmonic oscillation with a given displacements amplitude on the plate forms the incident sound wave, and the other is stationary and has a coating of deformable energy absorbing material with high damping properties. The behavior of acoustic environments in the spaces between the deformable plate and the barriers described by classical wave equation based on the ideal compressible fluid model. To describe the process of dynamic deformation of the energy absorbing coating of fixed barrier, two-dimensional equations of motion based on the use of models transversely soft layer are derived with a linear approximation of the displacement field in the thickness direction of the coating and taking into account the damping properties of the material and the hysteresis model for it. The influence of the physical and mechanical properties of the concerned mechanical system and the frequency of the incident sound wave on the parameters of its insulation properties of the plate, as well as on the parameters of the stress-strain state of the plate has been analyzed.

Running interfacial waves in a two-layer fluid system subject to longitudinal vibrations.

PubMed

Goldobin, D S; Pimenova, A V; Kovalevskaya, K V; Lyubimov, D V; Lyubimova, T P

2015-05-01

We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of quasistationary states of free interface in fluid dynamical systems subject to vibrations, revealed the existence of standing periodic waves and solitons in this system. However, this approach does not provide regular means for dealing with evolutionary problems: neither stability problems nor ones associated with propagating waves. In this work, we rigorously derive the evolution equations for long waves in the system, which turn out to be identical to the plus (or good) Boussinesq equation. With these equations one can find all the time-independent-profile solitary waves (standing solitons are a specific case of these propagating waves), which exist below the linear instability threshold; the standing and slow solitons are always unstable while fast solitons are stable. Depending on initial perturbations, unstable solitons either grow in an explosive manner, which means layer rupture in a finite time, or falls apart into stable solitons. The results are derived within the long-wave approximation as the linear stability analysis for the flat-interface state [D.V. Lyubimov and A.A. Cherepanov, Fluid Dynamics 21, 849 (1986)] reveals the instabilities of thin layers to be long wavelength.

Finite Temperature Densities via the S-Function Method with Application to Electron Screening in Plasmas

NASA Astrophysics Data System (ADS)

Watrous, Mitchell James

1997-12-01

A new approach to the Green's-function method for the calculation of equilibrium densities within the finite temperature, Kohn-Sham formulation of density functional theory is presented, which extends the method to all temperatures. The contour of integration in the complex energy plane is chosen such that the density is given by a sum of Green's function differences evaluated at the Matsubara frequencies, rather than by the calculation and summation of Kohn-Sham single-particle wave functions. The Green's functions are written in terms of their spectral representation and are calculated as the solutions of their defining differential equations. These differential equations are boundary value problems as opposed to the standard eigenvalue problems. For large values of the complex energy, the differential equations are further simplified from second to first-order by writing the Green's functions in terms of logarithmic derivatives. An asymptotic expression for the Green's functions is derived, which allows the sum over Matsubara poles to be approximated. The method is applied to the screening of nuclei by electrons in finite temperature plasmas. To demonstrate the method's utility, and to illustrate its advantages, the results of previous wave function type calculations for protons and neon nuclei are reproduced. The method is also used to formulate a new screening model for fusion reactions in the solar core, and the predicted reaction rate enhancements factors are compared with existing models.

Macroscopic constitutive equations of thermo-poroelasticity derived using eigenstrain-eigenstress approaches

NASA Astrophysics Data System (ADS)

Suvorov, Alexander P.; Selvadurai, A. P. S.

2011-06-01

Macroscopic constitutive equations for thermoelastic processes in a fluid-saturated porous medium are re-derived using the notion of eigenstrain or, equivalently, eigenstress. The eigenstrain-stress approach is frequently used in micromechanics of solid multi-phase materials, such as composites. Simple derivations of the stress-strain constitutive relations and the void occupancy relationship are presented for both fully saturated and partially saturated porous media. Governing coupled equations for the displacement components and the fluid pressure are also obtained.

Equivalence of quantum Boltzmann equation and Kubo formula for dc conductivity

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

Su, Z.B.; Chen, L.Y.

1990-02-01

This paper presents a derivation of the quantum Boltzmann equation for linear dc transport with a correction term to Mahan-Hansch's equations and derive a formal solution to it. Based on this formal solution, the authors find the electric conductivity can be expressed as the retarded current-current correlation. Therefore, the authors explicitly demonstrate the equivalence of the two most important theoretical methods: quantum Boltzmann equation and Kubo formula.

Momentum Maps and Stochastic Clebsch Action Principles

NASA Astrophysics Data System (ADS)

Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.

2018-01-01

We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.

Alternative stable qP wave equations in TTI media with their applications for reverse time migration

NASA Astrophysics Data System (ADS)

Zhou, Yang; Wang, Huazhong; Liu, Wenqing

2015-10-01

Numerical instabilities may arise if the spatial variation of symmetry axis is handled improperly when implementing P-wave modeling and reverse time migration in heterogeneous tilted transversely isotropic (TTI) media, especially in the cases where fast changes exist in TTI symmetry axis’ directions. Based on the pseudo-acoustic approximation to anisotropic elastic wave equations in Cartesian coordinates, alternative second order qP (quasi-P) wave equations in TTI media are derived in this paper. Compared with conventional stable qP wave equations, the proposed equations written in stress components contain only spatial derivatives of wavefield variables (stress components) and are free from spatial derivatives involving media parameters. These lead to an easy and efficient implementation for stable P-wave modeling and imaging. Numerical experiments demonstrate the stability and computational efficiency of the presented equations in complex TTI media.

Mechanical modeling for magnetorheological elastomer isolators based on constitutive equations and electromagnetic analysis

NASA Astrophysics Data System (ADS)

Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping

2018-06-01

As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.

Gradients and Non-Adiabatic Derivative Coupling Terms for Spin-Orbit Wavefunctions

DTIC Science & Technology

2011-06-01

derivative, symmetric to the first time derivative. Solutions to the Dirac equation simultaneously satisfy the simple relativistic wave equation, the...For Pooki vi Acknowledgments I would like to thank the members of my committee for their time and...Theorem..............................................................................191 Appendix J. The Symmetric Group

A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows.

PubMed

Daivis, Peter J; Todd, B D

2006-05-21

We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.

General Tricomi-Rassias problem and oblique derivative problem for generalized Chaplygin equations

NASA Astrophysics Data System (ADS)

Wen, Guochun; Chen, Dechang; Cheng, Xiuzhen

2007-09-01

Many authors have discussed the Tricomi problem for some second order equations of mixed type, which has important applications in gas dynamics. In particular, Bers proposed the Tricomi problem for Chaplygin equations in multiply connected domains [L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958]. And Rassias proposed the exterior Tricomi problem for mixed equations in a doubly connected domain and proved the uniqueness of solutions for the problem [J.M. Rassias, Lecture Notes on Mixed Type Partial Differential Equations, World Scientific, Singapore, 1990]. In the present paper, we discuss the general Tricomi-Rassias problem for generalized Chaplygin equations. This is one general oblique derivative problem that includes the exterior Tricomi problem as a special case. We first give the representation of solutions of the general Tricomi-Rassias problem, and then prove the uniqueness and existence of solutions for the problem by a new method. In this paper, we shall also discuss another general oblique derivative problem for generalized Chaplygin equations.

Cardiovascular risk prediction tools for populations in Asia.

PubMed

Barzi, F; Patel, A; Gu, D; Sritara, P; Lam, T H; Rodgers, A; Woodward, M

2007-02-01

Cardiovascular risk equations are traditionally derived from the Framingham Study. The accuracy of this approach in Asian populations, where resources for risk factor measurement may be limited, is unclear. To compare "low-information" equations (derived using only age, systolic blood pressure, total cholesterol and smoking status) derived from the Framingham Study with those derived from the Asian cohorts, on the accuracy of cardiovascular risk prediction. Separate equations to predict the 8-year risk of a cardiovascular event were derived from Asian and Framingham cohorts. The performance of these equations, and a subsequently "recalibrated" Framingham equation, were evaluated among participants from independent Chinese cohorts. Six cohort studies from Japan, Korea and Singapore (Asian cohorts); six cohort studies from China; the Framingham Study from the US. 172,077 participants from the Asian cohorts; 25,682 participants from Chinese cohorts and 6053 participants from the Framingham Study. In the Chinese cohorts, 542 cardiovascular events occurred during 8 years of follow-up. Both the Asian cohorts and the Framingham equations discriminated cardiovascular risk well in the Chinese cohorts; the area under the receiver-operator characteristic curve was at least 0.75 for men and women. However, the Framingham risk equation systematically overestimated risk in the Chinese cohorts by an average of 276% among men and 102% among women. The corresponding average overestimation using the Asian cohorts equation was 11% and 10%, respectively. Recalibrating the Framingham risk equation using cardiovascular disease incidence from the non-Chinese Asian cohorts led to an overestimation of risk by an average of 4% in women and underestimation of risk by an average of 2% in men. A low-information Framingham cardiovascular risk prediction tool, which, when recalibrated with contemporary data, is likely to estimate future cardiovascular risk with similar accuracy in Asian populations as tools developed from data on local cohorts.

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

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.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham-Broer-Kaup-Like Equations

NASA Astrophysics Data System (ADS)

Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian

2017-03-01

In this article, a generalised Whitham-Broer-Kaup-Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham-Broer-Kaup-Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

Multicomponent lattice Boltzmann model from continuum kinetic theory.

PubMed

Shan, Xiaowen

2010-04-01

We derive from the continuum kinetic theory a multicomponent lattice Boltzmann model with intermolecular interaction. The resulting model is found to be consistent with the model previously derived from a lattice-gas cellular automaton [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] but applies in a much broader domain. A number of important insights are gained from the kinetic theory perspective. First, it is shown that even in the isothermal case, the energy equipartition principle dictates the form of the equilibrium distribution function. Second, thermal diffusion is shown to exist and the corresponding diffusivities are given in terms of macroscopic parameters. Third, the ordinary diffusion is shown to satisfy the Maxwell-Stefan equation at the ideal-gas limit.

Expanded solutions of force-free electrodynamics on general Kerr black holes

NASA Astrophysics Data System (ADS)

Li, Huiquan; Wang, Jiancheng

2017-07-01

In this work, expanded solutions of force-free magnetospheres on general Kerr black holes are derived through a radial distance expansion method. From the regular conditions both at the horizon and at spatial infinity, two previously known asymptotical solutions (one of them is actually an exact solution) are identified as the only solutions that satisfy the same conditions at the two boundaries. Taking them as initial conditions at the boundaries, expanded solutions up to the first few orders are derived by solving the stream equation order by order. It is shown that our extension of the exact solution can (partially) cure the problems of the solution: it leads to magnetic domination and a mostly timelike current for restricted parameters.

Control of flexible beams using a free-free active truss

NASA Technical Reports Server (NTRS)

Clark, W. W.; Kimiavi, B.; Robertshaw, H. H.

1989-01-01

An analytical and experimental study involving controlling flexible beams using a free-free active truss is presented. This work extends previous work in controlling flexible continua with active trusses which were configured with fixed-free boundary conditions. The following describes the Lagrangian approach used to derive the equations of motion for the active truss and the beams attached to it. A partial-state feedback control law is derived for this system based on a full-state feedback Linear Quadratic Regulator method. The analytical model is examined via numerical simulations and the results are compared to a similar experimental apparatus described herein. The results show that control of a flexible continua is possible with a free-free active truss.

Analytic theory of photoacoustic wave generation from a spheroidal droplet.

PubMed

Li, Yong; Fang, Hui; Min, Changjun; Yuan, Xiaocong

2014-08-25

In this paper, we develop an analytic theory for describing the photoacoustic wave generation from a spheroidal droplet and derive the first complete analytic solution. Our derivation is based on solving the photoacoustic Helmholtz equation in spheroidal coordinates with the separation-of-variables method. As the verification, besides carrying out the asymptotic analyses which recover the standard solutions for a sphere, an infinite cylinder and an infinite layer, we also confirm that the partial transmission and reflection model previously demonstrated for these three geometries still stands. We expect that this analytic solution will find broad practical uses in interpreting experiment results, considering that its building blocks, the spheroidal wave functions (SWFs), can be numerically calculated by the existing computer programs.

Macroscopic neural mass model constructed from a current-based network model of spiking neurons.

PubMed

Umehara, Hiroaki; Okada, Masato; Teramae, Jun-Nosuke; Naruse, Yasushi

2017-02-01

Neural mass models (NMMs) are efficient frameworks for describing macroscopic cortical dynamics including electroencephalogram and magnetoencephalogram signals. Originally, these models were formulated on an empirical basis of synaptic dynamics with relatively long time constants. By clarifying the relations between NMMs and the dynamics of microscopic structures such as neurons and synapses, we can better understand cortical and neural mechanisms from a multi-scale perspective. In a previous study, the NMMs were analytically derived by averaging the equations of synaptic dynamics over the neurons in the population and further averaging the equations of the membrane-potential dynamics. However, the averaging of synaptic current assumes that the neuron membrane potentials are nearly time invariant and that they remain at sub-threshold levels to retain the conductance-based model. This approximation limits the NMM to the non-firing state. In the present study, we newly propose a derivation of a NMM by alternatively approximating the synaptic current which is assumed to be independent of the membrane potential, thus adopting a current-based model. Our proposed model releases the constraint of the nearly constant membrane potential. We confirm that the obtained model is reducible to the previous model in the non-firing situation and that it reproduces the temporal mean values and relative power spectrum densities of the average membrane potentials for the spiking neurons. It is further ensured that the existing NMM properly models the averaged dynamics over individual neurons even if they are spiking in the populations.

Analysis of nonlocal neural fields for both general and gamma-distributed connectivities

NASA Astrophysics Data System (ADS)

Hutt, Axel; Atay, Fatihcan M.

2005-04-01

This work studies the stability of equilibria in spatially extended neuronal ensembles. We first derive the model equation from statistical properties of the neuron population. The obtained integro-differential equation includes synaptic and space-dependent transmission delay for both general and gamma-distributed synaptic connectivities. The latter connectivity type reveals infinite, finite, and vanishing self-connectivities. The work derives conditions for stationary and nonstationary instabilities for both kernel types. In addition, a nonlinear analysis for general kernels yields the order parameter equation of the Turing instability. To compare the results to findings for partial differential equations (PDEs), two typical PDE-types are derived from the examined model equation, namely the general reaction-diffusion equation and the Swift-Hohenberg equation. Hence, the discussed integro-differential equation generalizes these PDEs. In the case of the gamma-distributed kernels, the stability conditions are formulated in terms of the mean excitatory and inhibitory interaction ranges. As a novel finding, we obtain Turing instabilities in fields with local inhibition-lateral excitation, while wave instabilities occur in fields with local excitation and lateral inhibition. Numerical simulations support the analytical results.

Morphing Continuum Theory: A First Order Approximation to the Balance Laws

NASA Astrophysics Data System (ADS)

Wonnell, Louis; Cheikh, Mohamad Ibrahim; Chen, James

2017-11-01

Morphing Continuum Theory is constructed under the framework of Rational Continuum Mechanics (RCM) for fluid flows with inner structure. This multiscale theory has been successfully emplyed to model turbulent flows. The framework of RCM ensures the mathematical rigor of MCT, but contains new material constants related to the inner structure. The physical meanings of these material constants have yet to be determined. Here, a linear deviation from the zeroth-order Boltzmann-Curtiss distribution function is derived. When applied to the Boltzmann-Curtiss equation, a first-order approximation of the MCT governing equations is obtained. The integral equations are then related to the appropriate material constants found in the heat flux, Cauchy stress, and moment stress terms in the governing equations. These new material properties associated with the inner structure of the fluid are compared with the corresponding integrals, and a clearer physical interpretation of these coefficients emerges. The physical meanings of these material properties is determined by analyzing previous results obtained from numerical simulations of MCT for compressible and incompressible flows. The implications for the physics underlying the MCT governing equations will also be discussed. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-17-1-0154.

Explicit integration of Friedmann's equation with nonlinear equations of state

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

Chen, Shouxin; Gibbons, Gary W.; Yang, Yisong, E-mail: chensx@henu.edu.cn, E-mail: gwg1@damtp.cam.ac.uk, E-mail: yisongyang@nyu.edu

2015-05-01

In this paper we study the integrability of the Friedmann equations, when the equation of state for the perfect-fluid universe is nonlinear, in the light of the Chebyshev theorem. A series of important, yet not previously touched, problems will be worked out which include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born-Infeld, two-fluid models, and Chern-Simons modified gravity theory models. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution which may also offer clues to a profound understanding of the problems in generalmore » settings. For example, in the Chaplygin gas universe, a few integrable cases lead us to derive a universal formula for the asymptotic exponential growth rate of the scale factor, of an explicit form, whether the Friedmann equation is integrable or not, which reveals the coupled roles played by various physical sectors and it is seen that, as far as there is a tiny presence of nonlinear matter, conventional linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics not directly related to cosmology. We provide some examples ranging from geometric optics and central orbits to soap films and the shape of glaciated valleys to which our results may be applied.« less

Investigation of the Dirac Equation by Using the Conformable Fractional Derivative

NASA Astrophysics Data System (ADS)

Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.

2018-05-01

In this paper,the Dirac equation is constructed using the conformable fractional derivative so that in its limit for the fractional parameter, the normal version is recovered. Then, the Cornell potential is considered as the interaction of the system. In this case, the wave function and the energy eigenvalue equation are derived with the aim of the bi-confluent Heun functions. use of the conformable fractional derivative is proven to lead to a branching treatment for the energy of the system. Such a treatment is obvious for small values of the fractional parameter, and a united value as the fractional parameter approaches unity.

Efficient computation of the Grünwald-Letnikov fractional diffusion derivative using adaptive time step memory

NASA Astrophysics Data System (ADS)

MacDonald, Christopher L.; Bhattacharya, Nirupama; Sprouse, Brian P.; Silva, Gabriel A.

2015-09-01

Computing numerical solutions to fractional differential equations can be computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In general, numerical approaches that depend on truncating part of the system history while efficient, can suffer from high degrees of error and inaccuracy. Here we present an adaptive time step memory method for smooth functions applied to the Grünwald-Letnikov fractional diffusion derivative. This method is computationally efficient and results in smaller errors during numerical simulations. Sampled points along the system's history at progressively longer intervals are assumed to reflect the values of neighboring time points. By including progressively fewer points backward in time, a temporally 'weighted' history is computed that includes contributions from the entire past of the system, maintaining accuracy, but with fewer points actually calculated, greatly improving computational efficiency.

Optimal Variable-Structure Control Tracking of Spacecraft Maneuvers

NASA Technical Reports Server (NTRS)

Crassidis, John L.; Vadali, Srinivas R.; Markley, F. Landis

1999-01-01

An optimal control approach using variable-structure (sliding-mode) tracking for large angle spacecraft maneuvers is presented. The approach expands upon a previously derived regulation result using a quaternion parameterization for the kinematic equations of motion. This parameterization is used since it is free of singularities. The main contribution of this paper is the utilization of a simple term in the control law that produces a maneuver to the reference attitude trajectory in the shortest distance. Also, a multiplicative error quaternion between the desired and actual attitude is used to derive the control law. Sliding-mode switching surfaces are derived using an optimal-control analysis. Control laws are given using either external torque commands or reaction wheel commands. Global asymptotic stability is shown for both cases using a Lyapunov analysis. Simulation results are shown which use the new control strategy to stabilize the motion of the Microwave Anisotropy Probe spacecraft.

Reconstructing signals from noisy data with unknown signal and noise covariance.

PubMed

Oppermann, Niels; Robbers, Georg; Ensslin, Torsten A

2011-10-01

We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle of minimum Gibbs free energy, which was previously used to derive a signal reconstruction algorithm handling uncertainties in the signal covariance. We extend this algorithm to simultaneously uncertain noise and signal covariances using the same principles in the derivation. The resulting equations are general enough to be applied in many different contexts. We demonstrate the performance of the algorithm by applying it to specific example situations and compare it to algorithms not allowing for uncertainties in the noise covariance. The results show that the method we suggest performs very well under a variety of circumstances and is indeed qualitatively superior to the other methods in cases where uncertainty in the noise covariance is present.

Power-law spatial dispersion from fractional Liouville equation

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

Tarasov, Vasily E.

2013-10-15

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

1/f Noise from nonlinear stochastic differential equations.

PubMed

Ruseckas, J; Kaulakys, B

2010-03-01

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fbeta noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fbeta noise, and provides further insights into the origin of 1/fbeta noise.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

How to Obtain the Covariant Form of Maxwell's Equations from the Continuity Equation

ERIC Educational Resources Information Center

Heras, Jose A.

2009-01-01

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

Estimating aspen crown fuels in northeastern Minnesota.

Treesearch

Robert M. Loomis; Peter J. Roussopoulos

1978-01-01

An application section presents tables for estimating foliage and branchwood (wood plus bark) of aspen tree crowns; the branchwood is subdivided by (1) living and dead material and by (2) living material alone into diameter size groups. A documentation section describes the derivation of equations and compares the equations derived with those derived by other...

Estimating Dynamical Systems: Derivative Estimation Hints From Sir Ronald A. Fisher.

PubMed

Deboeck, Pascal R

2010-08-06

The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common approach for estimating derivatives, Local Linear Approximation (LLA), produces estimates with correlated errors. Depending on the specific differential equation model used, such correlated errors can lead to severely biased estimates of differential equation model parameters. This article shows that the fitting of dynamical systems can be improved by estimating derivatives in a manner similar to that used to fit orthogonal polynomials. Two applications using simulated data compare the proposed method and a generalized form of LLA when used to estimate derivatives and when used to estimate differential equation model parameters. A third application estimates the frequency of oscillation in observations of the monthly deaths from bronchitis, emphysema, and asthma in the United Kingdom. These data are publicly available in the statistical program R, and functions in R for the method presented are provided.

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Lorenzo, C. F.

1979-01-01

Lumped volume dynamic equations are derived using an energy state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Lorenzo, C. F.

1979-01-01

Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

A unified Fourier theory for time-of-flight PET data

PubMed Central

Li, Yusheng; Matej, Samuel; Metzler, Scott D

2016-01-01

Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D X-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions—the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations are necessary and sufficient for 3D X-ray transform with TOF measurement. Finally, we give numerical examples of inverse rebinning for a 3D TOF PET and Fourier-based rebinning for a 2D TOF PET using the FORCEs to show the efficacy of the unified Fourier solutions. PMID:26689836

A unified Fourier theory for time-of-flight PET data.

PubMed

Li, Yusheng; Matej, Samuel; Metzler, Scott D

2016-01-21

Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D x-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions--the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations are necessary and sufficient for 3D x-ray transform with TOF measurement. Finally, we give numerical examples of inverse rebinning for a 3D TOF PET and Fourier-based rebinning for a 2D TOF PET using the FORCEs to show the efficacy of the unified Fourier solutions.

Mathematics of the total alkalinity-pH equation - pathway to robust and universal solution algorithms: the SolveSAPHE package v1.0.1

NASA Astrophysics Data System (ADS)

Munhoven, G.

2013-08-01

The total alkalinity-pH equation, which relates total alkalinity and pH for a given set of total concentrations of the acid-base systems that contribute to total alkalinity in a given water sample, is reviewed and its mathematical properties established. We prove that the equation function is strictly monotone and always has exactly one positive root. Different commonly used approximations are discussed and compared. An original method to derive appropriate initial values for the iterative solution of the cubic polynomial equation based upon carbonate-borate-alkalinity is presented. We then review different methods that have been used to solve the total alkalinity-pH equation, with a main focus on biogeochemical models. The shortcomings and limitations of these methods are made out and discussed. We then present two variants of a new, robust and universally convergent algorithm to solve the total alkalinity-pH equation. This algorithm does not require any a priori knowledge of the solution. SolveSAPHE (Solver Suite for Alkalinity-PH Equations) provides reference implementations of several variants of the new algorithm in Fortran 90, together with new implementations of other, previously published solvers. The new iterative procedure is shown to converge from any starting value to the physical solution. The extra computational cost for the convergence security is only 10-15% compared to the fastest algorithm in our test series.

Equation of state of pyrite to 80 GPa and 2400 K

DOE PAGES

Thompson, Elizabeth C.; Chidester, Bethany A.; Fischer, Rebecca A.; ...

2016-05-02

The high-cosmic abundance of sulfur is not reflected in the terrestrial crust, implying it is either sequestered in the Earth’s interior or was volatilized during accretion. As it has widely been suggested that sulfur could be one of the contributing light elements leading to the density deficit of Earth’s core, a robust thermal equation of state of iron sulfide is useful for understanding the evolution and properties of Earth’s interior. We performed X-ray diffraction measurements on FeS 2 achieving pressures from 15 to 80 GPa and temperatures up to 2400 K using laser-heated diamond-anvil cells. No phase transitions were observedmore » in the pyrite structure over the pressure and temperature ranges investigated. Combining our new P-V-T data with previously published room-temperature compression and thermochemical data, we fit a Debye temperature of 624(14) K and determined a Mie-Grüneisen equation of state for pyrite having bulk modulus K T = 141.2(18) GPa, pressure derivative K' T = 5.56(24), Grüneisen parameter γ 0 = 1.41, anharmonic coefficient A 2 = 2.53(27) × 10 –3 J/(K 2·mol), and q = 2.06(27). These findings are compared to previously published equation of state parameters for pyrite from static compression, shock compression, and ab initio studies. This revised equation of state for pyrite is consistent with an outer core density deficit satisfied by 11.4(10) wt% sulfur, yet matching the bulk sound speed of PREM requires an outer core composition of 4.8(19) wt% S. Here, this discrepancy suggests that sulfur alone cannot satisfy both seismological constraints simultaneously and cannot be the only light element within Earth’s core, and so the sulfur content needed to satisfy density constraints using our FeS 2 equation of state should be considered an upper bound for sulfur in the Earth’s core.« less

The thermodynamic and transport properties of GdCl3 in molten eutectic LiCl-KCl derived from the analysis of cyclic voltammetry signals

NASA Astrophysics Data System (ADS)

Samin, Adib; Wu, Evan; Zhang, Jinsuo

2017-02-01

Pyroprocessing technology is a promising tool for recycling nuclear fuel and producing high purity gadolinium for industrial applications. An efficient implementation of pyroprocessing entails a careful characterization of the electrochemical and transport properties of lanthanides in high temperature molten salts. In this work, the cyclic voltammetry signals of Gd in molten LiCl-KCl salt were recorded for a combination of three temperatures (723 K, 773 K, and 823 K) and three concentration levels (3 wt. %, 6 wt. %, and 9 wt. %) including concentration levels higher than previously reported and relevant for a realistic application of pyroprocessing for molten salt recycle, and the concentration effects were investigated. Four scan rates (200 mV/s to 500 mV/s) were used for each condition, and the signals were examined using conventional Cyclic Voltammetry (CV) analysis equations and by utilizing a two-plate Brunauer, Emmett, and Teller (BET) model accounting for mass diffusion, kinetics, adsorption, and the evolution of electrode morphology via a nonlinear least squares procedure for fitting the model to the experimental signals. It was determined that the redox process is quasi-reversible for the scan rates being used. Furthermore, the applicability of the conventional equations for CV analysis was shown to be problematic for the conditions used, and this is thought to be due to the fact that these equations were derived under the assumption of reversible conditions. The model-derived values for diffusivity are consistent with the literature and are shown to decrease with increasing concentration. This may be due to increased interactions at higher concentration levels. It was also shown that the formal redox potential increased with a concentration and was slightly more positive on the covered electrode.

Gravitational radiation from compact binary systems: Gravitational waveforms and energy loss to second post-Newtonian order

NASA Astrophysics Data System (ADS)

Will, Clifford M.; Wiseman, Alan G.

1996-10-01

We derive the gravitational waveform and gravitational-wave energy flux generated by a binary star system of compact objects (neutron stars or black holes), accurate through second post-Newtonian order (O[(v/c)4]=O[(Gm/rc2)2]) beyond the lowest-order quadrupole approximation. We cast the Einstein equations into the form of a flat-spacetime wave equation together with a harmonic gauge condition, and solve it formally as a retarded integral over the past null cone of the chosen field point. The part of this integral that involves the matter sources and the near-zone gravitational field is evaluated in terms of multipole moments using standard techniques; the remainder of the retarded integral, extending over the radiation zone, is evaluated in a novel way. The result is a manifestly convergent and finite procedure for calculating gravitational radiation to arbitrary orders in a post-Newtonian expansion. Through second post-Newtonian order, the radiation is also shown to propagate toward the observer along true null rays of the asymptotically Schwarzschild spacetime, despite having been derived using flat-spacetime wave equations. The method cures defects that plagued previous ``brute-force'' slow-motion approaches to the generation of gravitational radiation, and yields results that agree perfectly with those recently obtained by a mixed post-Minkowskian post-Newtonian method. We display explicit formulas for the gravitational waveform and the energy flux for two-body systems, both in arbitrary orbits and in circular orbits. In an appendix, we extend the formalism to bodies with finite spatial extent, and derive the spin corrections to the waveform and energy loss.

Chiral dynamos and magnetogenesis induced by torsionful Maxwell-Chern Simons electrodynamics

NASA Astrophysics Data System (ADS)

de Andrade, L. C. Garcia

2018-03-01

Recently chiral anomalous currents have been investigated by Boyarsky et al. and Brandenburg et al. with respect to applications to the early universe. In this paper we show that these magnetic field anomalies, which can give rise to dynamo magnetic field amplification can also be linked to spacetime torsion through the use of a chemical potential and Maxwell electrodynamics with torsion firstly proposed by de Sabbata and Gasperini. When the axial torsion is constant this electrodynamics acquires the form of a Maxwell-Chern-Simmons (MCS) equations where the chiral current appears naturally and the zero component of torsion plays the role of a chemical potential, while the other components play the role of anisotropic conductivity. The chiral dynamo equation in torsionful spacetime is derived here from MSC electrodynamics. Here we have used a recently derived a torsion LV bound of T0˜ {10^{-26}} GeV and the constraint that this chiral magnetic field is a seed for galactic dynamo. This estimate is weaker than the one obtained from the chiral battery seed of ˜ {10^{30}} G without making use of Cartan torsion. The torsion obtained here was derived at 500 pc coherence scale. When a chiral MF is forced to seed a galactic dynamo one obtains a yet weaker MF, of the order of B˜ {10^{12}} G, which is the value of a MF at nucleosynthesis. By the use of chiral dynamo equations from parity-violating torsion one obtains a seed field of B˜ {10^{27}} G, which is a much stronger MF closer to the one obtained by making use of chiral batteries. Chiral vortical currents in non-Riemannian spacetimes derived in Riemannian spaces previously by Flaschi and Fukushima are extended to include minimal coupling with torsion. The present universe yields B˜ {10^{-24}} G, still sufficient to seed galactic dynamos.

Nonlinear Equations of Motion for Cantilever Rotor Blades in Hover with Pitch Link Flexibility, Twist, Precone, Droop, Sweep, Torque Offset, and Blade Root Offset

NASA Technical Reports Server (NTRS)

Hodges, D. H.

1976-01-01

Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.

Effective Size of Nonrandom Mating Populations

PubMed Central

Caballero, A.; Hill, W. G.

1992-01-01

Nonrandom mating whereby parents are related is expected to cause a reduction in effective population size because their gene frequencies are correlated and this will increase the genetic drift. The published equation for the variance effective size, N(e), which includes the possibility of nonrandom mating, does not take into account such a correlation, however. Further, previous equations to predict effective sizes in populations with partial sib mating are shown to be different, but also incorrect. In this paper, a corrected form of these equations is derived and checked by stochastic simulation. For the case of stable census number, N, and equal progeny distributions for each sex, the equation is & where S(k)(2) is the variance of family size and α is the departure from Hardy-Weinberg proportions. For a Poisson distribution of family size (S(k)(2) = 2), it reduces to N(e) = N/(1 + α), as when inbreeding is due to selfing. When nonrandom mating occurs because there is a specified system of partial inbreeding every generation, α can be substituted by Wright's F(IS) statistic, to give the effective size as a function of the proportion of inbred mates. PMID:1582565

A new approach to spherically symmetric junction surfaces and the matching of FLRW regions

NASA Astrophysics Data System (ADS)

Kirchner, U.

2004-08-01

We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann Lemaître Robertson Walker (FLRW) models. We discuss 'vacuum bubbles' and closed open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time.

Prediction of unsteady transonic flow around missile configurations

NASA Technical Reports Server (NTRS)

Nixon, D.; Reisenthel, P. H.; Torres, T. O.; Klopfer, G. H.

1990-01-01

This paper describes the preliminary development of a method for predicting the unsteady transonic flow around missiles at transonic and supersonic speeds, with the final goal of developing a computer code for use in aeroelastic calculations or during maneuvers. The basic equations derived for this method are an extension of those derived by Klopfer and Nixon (1989) for steady flow and are a subset of the Euler equations. In this approach, the five Euler equations are reduced to an equation similar to the three-dimensional unsteady potential equation, and a two-dimensional Poisson equation. In addition, one of the equations in this method is almost identical to the potential equation for which there are well tested computer codes, allowing the development of a prediction method based in part on proved technology.

Use of digital land-cover data from the Landsat satellite in estimating streamflow characteristics in the Cumberland Plateau of Tennessee

USGS Publications Warehouse

Hollyday, E.F.; Hansen, G.R.

1983-01-01

Streamflow may be estimated with regression equations that relate streamflow characteristics to characteristics of the drainage basin. A statistical experiment was performed to compare the accuracy of equations using basin characteristics derived from maps and climatological records (control group equations) with the accuracy of equations using basin characteristics derived from Landsat data as well as maps and climatological records (experimental group equations). Results show that when the equations in both groups are arranged into six flow categories, there is no substantial difference in accuracy between control group equations and experimental group equations for this particular site where drainage area accounts for more than 90 percent of the variance in all streamflow characteristics (except low flows and most annual peak logarithms). (USGS)

General solution of the Bagley-Torvik equation with fractional-order derivative

NASA Astrophysics Data System (ADS)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

The Liouville equation for flavour evolution of neutrinos and neutrino wave packets

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

Hansen, Rasmus Sloth Lundkvist; Smirnov, Alexei Yu., E-mail: rasmus@mpi-hd.mpg.de, E-mail: smirnov@mpi-hd.mpg.de

We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over amore » trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.« less

Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems.

PubMed

Wang, Xiang-Sheng; He, Dongdong; Wylie, Jonathan J; Huang, Huaxiong

2014-02-01

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

Deriving Biomass Estimation Equations for Seven Plantation Hardwood Species

Treesearch

Bryce E. Schlaegel; Harvey E. Kennedy

1986-01-01

Trees of seven species sampled from a plantation over 7 years were used to derive weight equations to predict primary tree components. The seven species required the use of five different model forms to insure the greatest precision. Regardless of model form, all equations include variables for tree diameter, tree height, age, and number of trees planted. The most...

Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Zhang, Kai

2018-06-01

In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise C α, C 1,α and C 2,α regularity. As byproducts, we also prove the A-B-P maximum principle, Harnack inequality, uniqueness and solvability of the equations.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

An improved 2D MoF method by using high order derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2017-11-01

The MoF (Moment of Fluid) method is one of the most accurate approaches among various interface reconstruction algorithms. Alike other second order methods, the MoF method needs to solve an implicit optimization problem to obtain the optimal approximate interface, so an iteration process is inevitable under most circumstances. In order to solve the optimization efficiently, the properties of the objective function are worthy of studying. In 2D problems, the first order derivative has been deduced and applied in the previous researches. In this paper, the high order derivatives of the objective function are deduced on the convex polygon. We show that the nth (n ≥ 2) order derivatives are discontinuous, and the number of the discontinuous points is two times the number of the polygon edge. A rotation algorithm is proposed to successively calculate these discontinuous points, thus the target interval where the optimal solution is located can be determined. Since the high order derivatives of the objective function are continuous in the target interval, the iteration schemes based on high order derivatives can be used to improve the convergence rate. Moreover, when iterating in the target interval, the value of objective function and its derivatives can be directly updated without explicitly solving the volume conservation equation. The direct update makes a further improvement of the efficiency especially when the number of edges of the polygon is increasing. The Halley's method, which is based on the first three order derivatives, is applied as the iteration scheme in this paper and the numerical results indicate that the CPU time is about half of the previous method on the quadrilateral cell and is about one sixth on the decagon cell.

A note on the evolution equations from the area fraction and the thickness of a floating ice cover

NASA Astrophysics Data System (ADS)

Schulkes, R. M. S. M.

1995-03-01

In this paper, two sets of evolution equations for the area fraction and the ice thickness are investigated. First of all, a simplified alternative derivation of the evolution equations as presented by Gray and Morland (1994) is given. In addition, it is shown that with proper identification of ridging functions, there is a close connection between the derived equations and the thickness distribution model introduced by Thorndike et al. (1975).

Stability analysis solutions and optical solitons in extended nonlinear Schrödinger equation with higher-order odd and even terms

NASA Astrophysics Data System (ADS)

Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

2018-01-01

In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.

Third-order dissipative hydrodynamics from the entropy principle

NASA Astrophysics Data System (ADS)

El, Andrej; Xu, Zhe; Greiner, Carsten

2010-06-01

We review the entropy based derivation of third-order hydrodynamic equations and compare their solutions in one-dimensional boost-invariant geometry with calculations by the partonic cascade BAMPS. We demonstrate that Grad's approximation, which underlies the derivation of both Israel-Stewart and third-order equations, describes the transverse spectra from BAMPS with high accuracy. At the same time solutions of third-order equations are much closer to BAMPS results than solutions of Israel-Stewart equations. Introducing a resummation scheme for all higher-oder corrections to one-dimensional hydrodynamic equation we demonstrate the importance of higher-order terms if the Knudsen number is large.

The KP Approximation Under a Weak Coriolis Forcing

NASA Astrophysics Data System (ADS)

Melinand, Benjamin

2018-02-01

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

Equations of condition for high order Runge-Kutta-Nystrom formulae

NASA Technical Reports Server (NTRS)

Bettis, D. G.

1974-01-01

Derivation of the equations of condition of order eight for a general system of second-order differential equations approximated by the basic Runge-Kutta-Nystrom algorithm. For this general case, the number of equations of condition is considerably larger than for the special case where the first derivative is not present. Specifically, it is shown that, for orders two through eight, the number of equations for each order is 1, 1, 1, 2, 3, 5, and 9 for the special case and is 1, 1, 2, 5, 13, 34, and 95 for the general case.

Simple derivation of the Lindblad equation

NASA Astrophysics Data System (ADS)

Pearle, Philip

2012-07-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is ‘simple’ in that all it uses is the expression of a Hermitian matrix in terms of its orthonormal eigenvectors and real eigenvalues. Thus, it is appropriate for students who have learned the algebra of quantum theory. Where helpful, arguments are first given in a two-dimensional Hilbert space.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

An updated model of induced airflow in the unsaturated zone

USGS Publications Warehouse

Baehr, Arthur L.; Joss, Craig J.

1995-01-01

Simulation of induced movement of air in the unsaturated zone provides a method to determine permeability and to design vapor extraction remediation systems. A previously published solution to the airflow equation for the case in which the unsaturated zone is separated from the atmosphere by a layer of lower permeability (such as a clay layer) has been superseded. The new solution simulates airflow through the layer of lower permeability more rigorously by defining the leakage in terms of the upper boundary condition rather than by adding a leakage term to the governing airflow equation. This note presents the derivation of the new solution. Formulas for steady state pressure, specific discharge, and mass flow in the domain are obtained for the new model and for the case in which the unsaturated zone is in direct contact with the atmosphere.

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.

2009-01-01

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

Conservation Laws for Gyrokinetic Equations for Large Perturbations and Flows

NASA Astrophysics Data System (ADS)

Dimits, Andris

2017-10-01

Gyrokinetic theory has proved to be very useful for the understanding of magnetized plasmas, both to simplify analytical treatments and as a basis for efficient numerical simulations. Gyrokinetic theories were previously developed in two extended orderings that are applicable to large fluctuations and flows as may arise in the tokamak edge and scrapeoff layer. In the present work, we cast the resulting equations in a field-theoretical variational form, and derive, up to second order in the respective orderings, the associated global and local energy and (linear and toroidal) momentum conservation relations that result from Noether's theorem. The consequences of these for the various possible choices of numerical discretization used in gyrokinetic simulations are considered. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and supported by the U.S. DOE, OFES.

Influence of nonlinear interactions on the development of instability in hydrodynamic wave systems

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

Romanova, N. N.; Chkhetiani, O. G., E-mail: ochkheti@mx.iki.rssi.ru, E-mail: ochkheti@gmail.ru; Yakushkin, I. G.

2016-05-15

The problem of the development of shear instability in a three-layer medium simulating the flow of a stratified incompressible fluid is considered. The hydrodynamic equations are solved by expanding the Hamiltonian in a small parameter. The equations for three interacting waves, one of which is unstable, have been derived and solved numerically. The three-wave interaction is shown to stabilize the instability. Various regimes of the system’s dynamics, including the stochastic ones dependent on one of the invariants in the problem, can arise in this case. It is pointed out that the instability development scenario considered differs from the previously consideredmore » scenario of a different type, where the three-wave interaction does not stabilize the instability. The interaction of wave packets is considered briefly.« less

Practical aspects of modeling aircraft dynamics from flight data

NASA Technical Reports Server (NTRS)

Iliff, K. W.; Maine, R. E.

1984-01-01

The purpose of parameter estimation, a subset of system identification, is to estimate the coefficients (such as stability and control derivatives) of the aircraft differential equations of motion from sampled measured dynamic responses. In the past, the primary reason for estimating stability and control derivatives from flight tests was to make comparisons with wind tunnel estimates. As aircraft became more complex, and as flight envelopes were expanded to include flight regimes that were not well understood, new requirements for the derivative estimates evolved. For many years, the flight determined derivatives were used in simulations to aid in flight planning and in pilot training. The simulations were particularly important in research flight test programs in which an envelope expansion into new flight regimes was required. Parameter estimation techniques for estimating stability and control derivatives from flight data became more sophisticated to support the flight test programs. As knowledge of these new flight regimes increased, more complex aircraft were flown. Much of this increased complexity was in sophisticated flight control systems. The design and refinement of the control system required higher fidelity simulations than were previously required.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Development of Semi-Empirical Damping Equation for Baffled Tank with Oblate Spheroidal Dome

NASA Technical Reports Server (NTRS)

Yang, H. Q.; West, Jeff; Brodnick, Jacob; Eberhart, Chad

2016-01-01

Propellant slosh is a potential source of disturbance that can significantly impact the stability of space vehicles. The slosh dynamics are typically represented by a mechanical model of a spring-mass-damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. The typical parameters required by the mechanical model include natural frequency of the slosh, slosh mass, slosh mass center location, and the critical damping ratio. A fundamental study has been undertaken at NASA MSFC to understand the fluid damping physics from a ring baffle in the barrel section of a propellant tank. An asymptotic damping equation and CFD blended equation have been derived by NASA MSFC team to complement the popularly used Miles equation at different flow regimes. The new development has found success in providing a nonlinear damping model for the Space Launch System. The purpose of this study is to further extend the semi-empirical damping equations into the oblate spheroidal dome section of the propellant tanks. First, previous experimental data from the spherical baffled tank are collected and analyzed. Several methods of taking the dome curvature effect, including a generalized Miles equation, area projection method, and equalized fill height method, are assessed. CFD simulation is used to shed light on the interaction of vorticity around the baffle with the locally curved wall and liquid-gas interface. The final damping equation will be validated by a recent subscale test with an oblate spheroidal dome conducted at NASA MSFC.

Turbulent fluid motion 3: Basic continuum equations

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1991-01-01

A derivation of the continuum equations used for the analysis of turbulence is given. These equations include the continuity equation, the Navier-Stokes equations, and the heat transfer or energy equation. An experimental justification for using a continuum approach for the study of turbulence is given.

Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential

PubMed Central

Wang, Ying; Zhou, Yu; Zhou, Shuyu

2016-01-01

We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study. PMID:27922129

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection at large Rayleigh numbers

NASA Astrophysics Data System (ADS)

Kozitskiy, Sergey

2018-06-01

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.

On singlet s-wave electron-hydrogen scattering.

NASA Technical Reports Server (NTRS)

Madan, R. N.

1973-01-01

Discussion of various zeroth-order approximations to s-wave scattering of electrons by hydrogen atoms below the first excitation threshold. The formalism previously developed by the author (1967, 1968) is applied to Feshbach operators to derive integro-differential equations, with the optical-potential set equal to zero, for the singlet and triplet cases. Phase shifts of s-wave scattering are computed in the zeroth-order approximation of the Feshbach operator method and in the static-exchange approximation. It is found that the convergence of numerical computations is faster in the former approximation than in the latter.

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection at large Rayleigh numbers

NASA Astrophysics Data System (ADS)

Kozitskiy, Sergey

2018-05-01

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.

Oxygen concentration dependence of silicon oxide dynamical properties

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Prediction of fat-free body mass from bioelectrical impedance and anthropometry among 3-year-old children using DXA

PubMed Central

Ejlerskov, Katrine T.; Jensen, Signe M.; Christensen, Line B.; Ritz, Christian; Michaelsen, Kim F.; Mølgaard, Christian

2014-01-01

For 3-year-old children suitable methods to estimate body composition are sparse. We aimed to develop predictive equations for estimating fat-free mass (FFM) from bioelectrical impedance (BIA) and anthropometry using dual-energy X-ray absorptiometry (DXA) as reference method using data from 99 healthy 3-year-old Danish children. Predictive equations were derived from two multiple linear regression models, a comprehensive model (height2/resistance (RI), six anthropometric measurements) and a simple model (RI, height, weight). Their uncertainty was quantified by means of 10-fold cross-validation approach. Prediction error of FFM was 3.0% for both equations (root mean square error: 360 and 356 g, respectively). The derived equations produced BIA-based prediction of FFM and FM near DXA scan results. We suggest that the predictive equations can be applied in similar population samples aged 2–4 years. The derived equations may prove useful for studies linking body composition to early risk factors and early onset of obesity. PMID:24463487

Prediction of fat-free body mass from bioelectrical impedance and anthropometry among 3-year-old children using DXA.

PubMed

Ejlerskov, Katrine T; Jensen, Signe M; Christensen, Line B; Ritz, Christian; Michaelsen, Kim F; Mølgaard, Christian

2014-01-27

For 3-year-old children suitable methods to estimate body composition are sparse. We aimed to develop predictive equations for estimating fat-free mass (FFM) from bioelectrical impedance (BIA) and anthropometry using dual-energy X-ray absorptiometry (DXA) as reference method using data from 99 healthy 3-year-old Danish children. Predictive equations were derived from two multiple linear regression models, a comprehensive model (height(2)/resistance (RI), six anthropometric measurements) and a simple model (RI, height, weight). Their uncertainty was quantified by means of 10-fold cross-validation approach. Prediction error of FFM was 3.0% for both equations (root mean square error: 360 and 356 g, respectively). The derived equations produced BIA-based prediction of FFM and FM near DXA scan results. We suggest that the predictive equations can be applied in similar population samples aged 2-4 years. The derived equations may prove useful for studies linking body composition to early risk factors and early onset of obesity.

Gyrokinetic equations and full f solution method based on Dirac's constrained Hamiltonian and inverse Kruskal iteration

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

Heikkinen, J. A.; Nora, M.

2011-02-15

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J= as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allowsmore » direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.« less

The Enskog Equation for Confined Elastic Hard Spheres

NASA Astrophysics Data System (ADS)

Maynar, P.; García de Soria, M. I.; Brey, J. Javier

2018-03-01

A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, H[f], is identified. For any solution of the kinetic equation, H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a density field consistent with equilibrium statistical mechanics.

A de Sitter tachyon thick braneworld

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

Germán, Gabriel; Herrera-Aguilar, Alfredo; Malagón-Morejón, Dagoberto

2013-02-01

Among the multiple 5D thick braneworld models that have been proposed in the last years, in order to address several open problems in modern physics, there is a specific one involving a tachyonic bulk scalar field. Delving into this framework, a thick braneworld with a cosmological background induced on the brane is here investigated. The respective field equations — derived from the model with a warped 5D geometry — are highly non-linear equations, admitting a non-trivial solution for the warp factor and the tachyon scalar field as well, in a de Sitter 4D cosmological background. Moreover, the non-linear tachyonic scalarmore » field, that generates the brane in complicity with warped gravity, has the form of a kink-like configuration. Notwithstanding, the non-linear field equations restricting character does not allow one to easily find thick brane solutions with a decaying warp factor which leads to the localization of 4D gravity and other matter fields. We derive such a thick brane configuration altogether in this tachyon-gravity setup. When analyzing the spectrum of gravity fluctuations in the transverse traceless sector, the 4D gravity is shown to be localized due to the presence of a single zero mode bound state, separated by a continuum of massive Kaluza-Klein (KK) modes by a mass gap. It contrasts with previous results, where there is a KK massive bound excitation providing no clear physical interpretation. The mass gap is determined by the scale of the metric parameter H. Finally, the corrections to Newton's law in this model are computed and shown to decay exponentially. It is in full compliance to corrections reported in previous results (up to a constant factor) within similar braneworlds with induced 4D de Sitter metric, despite the fact that the warp factor and the massive modes have a different form.« less

BHR equations re-derived with immiscible particle effects

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

Schwarzkopf, John Dennis; Horwitz, Jeremy A.

2015-05-01

Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied tomore » the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.« less

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

NASA Astrophysics Data System (ADS)

Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

2018-02-01

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

Wind laws for shockless initialization. [numerical forecasting model

NASA Technical Reports Server (NTRS)

Ghil, M.; Shkoller, B.

1976-01-01

A system of diagnostic equations for the velocity field, or wind laws, was derived for each of a number of models of large-scale atmospheric flow. The derivation in each case is mathematically exact and does not involve any physical assumptions not already present in the prognostic equations, such as nondivergence or vanishing of derivatives of the divergence. Therefore, initial states computed by solving these diagnostic equations should be compatible with the type of motion described by the prognostic equations of the model and should not generate initialization shocks when inserted into the model. Numerical solutions of the diagnostic system corresponding to a barotropic model are exhibited. Some problems concerning the possibility of implementing such a system in operational numerical weather prediction are discussed.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

LETTER TO THE EDITOR: Bicomplexes and conservation laws in non-Abelian Toda models

NASA Astrophysics Data System (ADS)

Gueuvoghlanian, E. P.

2001-08-01

A bicomplex structure is associated with the Leznov-Saveliev equation of integrable models. The linear problem associated with the zero-curvature condition is derived in terms of the bicomplex linear equation. The explicit example of a non-Abelian conformal affine Toda model is discussed in detail and its conservation laws are derived from the zero-curvature representation of its equation of motion.

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

NASA Technical Reports Server (NTRS)

Grove, R. D.; Bowles, R. L.; Mayhew, S. C.

1972-01-01

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Hamiltonian derivation of the nonhydrostatic pressure-coordinate model

NASA Astrophysics Data System (ADS)

Salmon, Rick; Smith, Leslie M.

1994-07-01

In 1989, the Miller-Pearce (MP) model for nonhydrostatic fluid motion governed by equations written in pressure coordinates was extended by removing the prescribed reference temperature, T(sub s)(p), while retaining the conservation laws and other desirable properties. It was speculated that this extension of the MP model had a Hamiltonian structure and that a slick derivation of the Ertel property could be constructed if the relevant Hamiltonian were known. In this note, the extended equations are derived using Hamilton's principle. The potential vorticity law arises from the usual particle-relabeling symmetry of the Lagrangian, and even the absence of sound waves is anticipated from the fact that the pressure inside the free energy G(p, theta) in the derived equation is hydrostatic and thus G is insensitive to local pressure fluctuations. The model extension is analogous to the semigeostrophic equations for nearly geostrophic flow, which do not incorporate a prescribed reference state, while the earlier MP model is analogous to the quasigeostrophic equations, which become highly inaccurate when the flow wanders from a prescribed state with nearly flat isothermal surfaces.

Evaluating the generalizability of GEP models for estimating reference evapotranspiration in distant humid and arid locations

NASA Astrophysics Data System (ADS)

Kiafar, Hamed; Babazadeh, Hosssien; Marti, Pau; Kisi, Ozgur; Landeras, Gorka; Karimi, Sepideh; Shiri, Jalal

2017-10-01

Evapotranspiration estimation is of crucial importance in arid and hyper-arid regions, which suffer from water shortage, increasing dryness and heat. A modeling study is reported here to cross-station assessment between hyper-arid and humid conditions. The derived equations estimate ET0 values based on temperature-, radiation-, and mass transfer-based configurations. Using data from two meteorological stations in a hyper-arid region of Iran and two meteorological stations in a humid region of Spain, different local and cross-station approaches are applied for developing and validating the derived equations. The comparison of the gene expression programming (GEP)-based-derived equations with corresponding empirical-semi empirical ET0 estimation equations reveals the superiority of new formulas in comparison with the corresponding empirical equations. Therefore, the derived models can be successfully applied in these hyper-arid and humid regions as well as similar climatic contexts especially in data-lack situations. The results also show that when relying on proper input configurations, cross-station might be a promising alternative for locally trained models for the stations with data scarcity.

A wide angle and high Mach number parabolic equation.

PubMed

Lingevitch, Joseph F; Collins, Michael D; Dacol, Dalcio K; Drob, Douglas P; Rogers, Joel C W; Siegmann, William L

2002-02-01

Various parabolic equations for advected acoustic waves have been derived based on the assumptions of small Mach number and narrow propagation angles, which are of limited validity in atmospheric acoustics. A parabolic equation solution that does not require these assumptions is derived in the weak shear limit, which is appropriate for frequencies of about 0.1 Hz and above for atmospheric acoustics. When the variables are scaled appropriately in this limit, terms involving derivatives of the sound speed, density, and wind speed are small but can have significant cumulative effects. To obtain a solution that is valid at large distances from the source, it is necessary to account for linear terms in the first derivatives of these quantities [A. D. Pierce, J. Acoust. Soc. Am. 87, 2292-2299 (1990)]. This approach is used to obtain a scalar wave equation for advected waves. Since this equation contains two depth operators that do not commute with each other, it does not readily factor into outgoing and incoming solutions. An approximate factorization is obtained that is correct to first order in the commutator of the depth operators.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

Lagrangian averaging, nonlinear waves, and shock regularization

NASA Astrophysics Data System (ADS)

Bhat, Harish S.

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the Lagrangian averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given Lagrangian flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out numerical experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity, solutions of the PDE converge strongly to weak solutions of the inviscid Burgers equation. We provide numerical evidence that this limit satisfies an entropy inequality for the inviscid Burgers equation. We demonstrate a Hamiltonian structure for the PDE.

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.

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

Feynman-Kac formula for stochastic hybrid systems.

PubMed

Bressloff, Paul C

2017-01-01

We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.

Analytic theory of orbit contraction

NASA Technical Reports Server (NTRS)

Vinh, N. X.; Longuski, J. M.; Busemann, A.; Culp, R. D.

1977-01-01

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.