A new approach to exact optical soliton solutions for the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Baleanu, Dumitru

2018-05-01

By using the modified homotopy analysis transform method, we construct the analytical solutions of the space-time generalized nonlinear Schrödinger equation involving a new fractional conformable derivative in the Liouville-Caputo sense and the fractional-order derivative with the Mittag-Leffler law. Employing theoretical parameters, we present some numerical simulations and compare the solutions obtained.

THEORETICAL BACKGROUND AND DERIVATION OF SELECTED EQUATIONS FROM THE REPORT STUDY OF BLAST EFFECTS IN SOIL

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

Ehlers, O.K.; Grum, A.F.

1959-03-27

An amplification and clarification of the report Study of Blast Effects in Soil by M. A. Chaszeyka and F. B. Porzel of the Armour Research Foundation is presented. The basic thermodynamic relationships that are essential to the understanding of the Armour Report are given, and the more complex equations of the Armour Report are derived. (auth)

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.

Minimum-variance Brownian motion control of an optically trapped probe.

PubMed

Huang, Yanan; Zhang, Zhipeng; Menq, Chia-Hsiang

2009-10-20

This paper presents a theoretical and experimental investigation of the Brownian motion control of an optically trapped probe. The Langevin equation is employed to describe the motion of the probe experiencing random thermal force and optical trapping force. Since active feedback control is applied to suppress the probe's Brownian motion, actuator dynamics and measurement delay are included in the equation. The equation of motion is simplified to a first-order linear differential equation and transformed to a discrete model for the purpose of controller design and data analysis. The derived model is experimentally verified by comparing the model prediction to the measured response of a 1.87 microm trapped probe subject to proportional control. It is then employed to design the optimal controller that minimizes the variance of the probe's Brownian motion. Theoretical analysis is derived to evaluate the control performance of a specific optical trap. Both experiment and simulation are used to validate the design as well as theoretical analysis, and to illustrate the performance envelope of the active control. Moreover, adaptive minimum variance control is implemented to maintain the optimal performance in the case in which the system is time varying when operating the actively controlled optical trap in a complex environment.

The theoretical tools of experimental gravitation

NASA Technical Reports Server (NTRS)

Will, C. M.

1972-01-01

Theoretical frameworks for testing relativistic gravity are presented in terms of a system for analyzing theories of gravity invented as alternatives to Einstein. The parametrized post-Newtonian (PPN) formalism, based on the Dicke framework and the Eotvos-Dicke-Braginsky experiment, is discussed in detail. The metric theories of gravity, and their post-Newtonian limits are reviewed, and PPN equations of motion are derived. These equations are used to analyze specific effects and experimental tests in the solar system.

Effective Elastic Modulus as a Function of Angular Leaf Span for Curved Leaves of Pyrolytic Boron Nitride

NASA Technical Reports Server (NTRS)

Kaforey, M. L.; Deeb, C. W.; Matthiesen, D. H.

1999-01-01

A theoretical equation was derived to predict the spring constant (load/deflection) for a simply supported cylindrical section with a line force applied at the center. Curved leaves of PBN were mechanically deformed and the force versus deflection data was recorded and compared to the derived theoretical equation to yield an effective modulus for each leaf. The effective modulus was found to vary from the pure shear modulus for a flat plate to a mixed mode for a half cylinder as a function of the sine of one half the angular leaf span. The spring constants of individual PBN leaves were usually predicted to within 30%.

Measuring the effects of heat wave episodes on the human body's thermal balance

NASA Astrophysics Data System (ADS)

Katavoutas, George; Theoharatos, George; Flocas, Helena A.; Asimakopoulos, Dimosthenis N.

2009-03-01

During the peak of an extensive heat wave episode on 23-25 July 2007, simultaneous thermophysiological measurements were made in two non-acclimated healthy adults of different sex in a suburban area of Greater Athens, Greece. Based on experimental measurements of mean skin temperature and metabolic heat production, heat fluxes to and from the human body were calculated, and the biometeorological index heat load (HL) produced was determined according to the heat balance equation. Comparing experimental values with those derived from theoretical estimates revealed a great heat stress for both individuals, especially the male, while theoretical values underestimated heat stress. The study also revealed that thermophysiological factors, such as mean skin temperature and metabolic heat production, play an important role in determining heat fluxes patterns in the heat balance equation. The theoretical values of mean skin temperature as derived from an empirical equation may not be appropriate to describe the changes that take place in a non-acclimated individual. Furthermore, the changes in metabolic heat production were significant even for standard activity.

Mode-coupling theory

NASA Astrophysics Data System (ADS)

Reichman, David R.; Charbonneau, Patrick

2005-05-01

In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the use the Mori Zwanzig projection operator technique. We also derive schematic mode-coupling equations of a similar form from a field-theoretic perspective. We review the successes and failures of mode-coupling theory, and discuss recent advances in the applications of the theory.

A three-dimensional kinematic model for the dissolution of crystals

NASA Astrophysics Data System (ADS)

Tellier, C. R.

1989-06-01

The two-dimensional kinematic theory developed by Frank is extended into three dimensions. It is shown that the theoretical equations for the propagation vector associated with the displacement of a moving surface element can be directly derived from the polar equation of the slowness surface.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

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.

Theoretical analysis for double-liquid variable focus lens

NASA Astrophysics Data System (ADS)

Peng, Runling; Chen, Jiabi; Zhuang, Songlin

2007-09-01

In this paper, various structures for double-liquid variable focus lens are introduced. And based on an energy minimization method, explicit calculations and detailed analyses upon an extended Young-type equation are given for double-liquid lenses with cylindrical electrode. Such an equation is especially applicable to liquid-liquid-solid tri-phase systems. It is a little different from the traditional Young equation that was derived according to vapor-liquid-solid triphase systems. The electrowetting effect caused by an external voltage changes the interface shape between two liquids as well as the focal length of the lens. Based on the extended Young-type equation, the relationship between the focal length and the external voltage can also be derived. Corresponding equations and simulation results are presented.

Charts for Estimating Tail-rotor Contribution to Helicopter Directional Stability and Control in Low-Speed Flight

NASA Technical Reports Server (NTRS)

Amer, Kenneth B; Gessow, Alfred

1955-01-01

Theoretically derived charts and equations are presented by which tail-rotor design studies of directional trim and control response at low forward speed can be conveniently made. The charts can also be used to obtain the main-rotor stability derivatives of thrust with respect to collective pitch and angle of attack at low forward speeds. The use of the charts and equations for tail-rotor design studies is illustrated. Comparisons between theoretical and experimental results are presented. The charts indicate, and flight tests confirm, that the region of vortex roughness which is familiar for the main rotor is also encountered by the tail rotor and that prolonged operation at the corresponding flight conditions would be difficult.

Conical Pendulum--Linearization Analyses

ERIC Educational Resources Information Center

Dean, Kevin; Mathew, Jyothi

2016-01-01

A theoretical analysis is presented, showing the derivations of seven different linearization equations for the conical pendulum period "T", as a function of radial and angular parameters. Experimental data obtained over a large range of fixed conical pendulum lengths (0.435 m-2.130 m) are plotted with the theoretical lines and…

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Multigrid Techniques for Highly Indefinite Equations

NASA Technical Reports Server (NTRS)

Shapira, Yair

1996-01-01

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

Theoretical Investigation of Thermo-Mechanical Behavior of Carbon Nanotube-Based Composites Using the Integral Transform Method

NASA Technical Reports Server (NTRS)

Pawloski, Janice S.

2001-01-01

This project uses the integral transform technique to model the problem of nanotube behavior as an axially symmetric system of shells. Assuming that the nanotube behavior can be described by the equations of elasticity, we seek a stress function x which satisfies the biharmonic equation: del(exp 4) chi = [partial deriv(r(exp 2)) + partial deriv(r) + partial deriv(z(exp 2))] chi = 0. The method of integral transformations is used to transform the differential equation. The symmetry with respect to the z-axis indicates that we only need to consider the sine transform of the stress function: X(bar)(r,zeta) = integral(from 0 to infinity) chi(r,z)sin(zeta,z) dz.

Experimental verification of theoretical equations for acoustic radiation force on compressible spherical particles in traveling waves.

PubMed

Johnson, Kennita A; Vormohr, Hannah R; Doinikov, Alexander A; Bouakaz, Ayache; Shields, C Wyatt; López, Gabriel P; Dayton, Paul A

2016-05-01

Acoustophoresis uses acoustic radiation force to remotely manipulate particles suspended in a host fluid for many scientific, technological, and medical applications, such as acoustic levitation, acoustic coagulation, contrast ultrasound imaging, ultrasound-assisted drug delivery, etc. To estimate the magnitude of acoustic radiation forces, equations derived for an inviscid host fluid are commonly used. However, there are theoretical predictions that, in the case of a traveling wave, viscous effects can dramatically change the magnitude of acoustic radiation forces, which make the equations obtained for an inviscid host fluid invalid for proper estimation of acoustic radiation forces. To date, experimental verification of these predictions has not been published. Experimental measurements of viscous effects on acoustic radiation forces in a traveling wave were conducted using a confocal optical and acoustic system and values were compared with available theories. Our results show that, even in a low-viscosity fluid such as water, the magnitude of acoustic radiation forces is increased manyfold by viscous effects in comparison with what follows from the equations derived for an inviscid fluid.

Experimental verification of theoretical equations for acoustic radiation force on compressible spherical particles in traveling waves

NASA Astrophysics Data System (ADS)

Johnson, Kennita A.; Vormohr, Hannah R.; Doinikov, Alexander A.; Bouakaz, Ayache; Shields, C. Wyatt; López, Gabriel P.; Dayton, Paul A.

2016-05-01

Acoustophoresis uses acoustic radiation force to remotely manipulate particles suspended in a host fluid for many scientific, technological, and medical applications, such as acoustic levitation, acoustic coagulation, contrast ultrasound imaging, ultrasound-assisted drug delivery, etc. To estimate the magnitude of acoustic radiation forces, equations derived for an inviscid host fluid are commonly used. However, there are theoretical predictions that, in the case of a traveling wave, viscous effects can dramatically change the magnitude of acoustic radiation forces, which make the equations obtained for an inviscid host fluid invalid for proper estimation of acoustic radiation forces. To date, experimental verification of these predictions has not been published. Experimental measurements of viscous effects on acoustic radiation forces in a traveling wave were conducted using a confocal optical and acoustic system and values were compared with available theories. Our results show that, even in a low-viscosity fluid such as water, the magnitude of acoustic radiation forces is increased manyfold by viscous effects in comparison with what follows from the equations derived for an inviscid fluid.

Phase-space methods for the spin dynamics in condensed matter systems

PubMed Central

Hurst, Jérôme; Manfredi, Giovanni

2017-01-01

Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin- fermions (typically, electrons) including the Zeeman effect and the spin–orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A simple closure relation is proposed to obtain a closed set of hydrodynamic equations. This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’. PMID:28320903

The discrete Toda equation revisited: dual β-Grothendieck polynomials, ultradiscretization, and static solitons

NASA Astrophysics Data System (ADS)

Iwao, Shinsuke; Nagai, Hidetomo

2018-04-01

This paper presents a study of the discrete Toda equation that was introduced in 1977. In this paper, it is proved that the determinantal solution of the discrete Toda equation, obtained via the Lax formalism, is naturally related to the dual Grothendieck polynomials, a K-theoretic generalization of the Schur polynomials. A tropical permanent solution to the ultradiscrete Toda equation is also derived. The proposed method gives a tropical algebraic representation of the static solitons. Lastly, a new cellular automaton realization of the ultradiscrete Toda equation is proposed.

Simple radiative transfer model for relationships between canopy biomass and reflectance

NASA Technical Reports Server (NTRS)

Park, J. K.; Deering, D. W.

1982-01-01

A modified Kubelka-Munk model has been utilized to derive useful equations for the analysis of apparent canopy reflectance. Based on the solution to the model simple working equations were formulated by employing reflectance characteristic parameters. The relationships derived show the asymptotic nature of reflectance data that is typically observed in remote sensing studies of plant biomass. They also establish the range of expected apparent canopy reflectance values for specific plant canopy types. The usefulness of the simplified equations was demonstrated by the exceptionally close fit of the theoretical curves to two separately acquired data sets for alfalfa and shortgrass prairie canopies.

Derivation of nonlinear wave equations for ultrasound beam in nonuniform bubbly liquids

NASA Astrophysics Data System (ADS)

Kanagawa, Tetsuya; Yano, Takeru; Kawahara, Junya; Kobayashi, Kazumichi; Watanabe, Masao; Fujikawa, Shigeo

2012-09-01

Weakly nonlinear propagation of diffracted ultrasound beams in a nonuniform bubbly liquid is theoretically studied based on the method of multiple scales with the set of scaling relations of some physical parameters. It is assumed that the spatial distribution of the number density of bubbles in an initial state at rest is a slowly varying function of space coordinates and the amplitude of its variation is small compared with a mean number density. As a result, a Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with dispersion and nonuniform effects for a low frequency case and a nonlinear Schrödinger (NLS) equation with dissipation, diffraction, and nonuniform effects for a high frequency case, are derived from the basic equations of bubbly flows.

Kinetic equation and nonequilibrium entropy for a quasi-two-dimensional gas.

PubMed

Brey, J Javier; Maynar, Pablo; García de Soria, M I

2016-10-01

A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle diameters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement on the particle collisions. A function S(t) is constructed by adding to the Boltzmann expression a confinement contribution. Then it is shown that for the solutions of the kinetic equation, S(t) increases monotonically in time, until the system reaches a stationary inhomogeneous state, when S becomes the equilibrium entropy of the confined system as derived from equilibrium statistical mechanics. From the entropy, other equilibrium properties are obtained, and molecular dynamics simulations are used to verify some of the theoretical predictions.

Video Measurement of the Muzzle Velocity of a Potato Gun

ERIC Educational Resources Information Center

Jasperson, Christopher; Pollman, Anthony

2011-01-01

Using first principles, a theoretical equation for the maximum and actual muzzle velocities for a pneumatic cannon was recently derived. For a fixed barrel length, this equation suggests that the muzzle velocity can be enhanced by maximizing the product of the initial pressure and the volume of the propellant gas and decreasing the projectile…

Density perturbations in general modified gravitational theories

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

De Felice, Antonio; Tsujikawa, Shinji; Mukohyama, Shinji

2010-07-15

We derive the equations of linear cosmological perturbations for the general Lagrangian density f(R,{phi},X)/2+L{sub c}, where R is a Ricci scalar, {phi} is a scalar field, and X=-{partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}/}2 is a field kinetic energy. We take into account a nonlinear self-interaction term L{sub c}={xi}({phi}) {open_square}{phi}({partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}}) recently studied in the context of ''Galileon'' cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasistatic approximation on subhorizon scales. We also derive conditions for the avoidance of ghosts and Laplacianmore » instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature; and thus it is convenient to test the viability of such models from both theoretical and observational points of view.« less

q-Gaussian distributions and multiplicative stochastic processes for analysis of multiple financial time series

NASA Astrophysics Data System (ADS)

Sato, Aki-Hiro

2010-12-01

This study considers q-Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a q-Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both mutually independent multiplicative and additive noises. By using the proposed stochastic differential equation a method to evaluate a default probability under a given risk buffer is proposed.

Consistent three-equation model for thin films

NASA Astrophysics Data System (ADS)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

The Equations of Oceanic Motions

NASA Astrophysics Data System (ADS)

Müller, Peter

2006-10-01

Modeling and prediction of oceanographic phenomena and climate is based on the integration of dynamic equations. The Equations of Oceanic Motions derives and systematically classifies the most common dynamic equations used in physical oceanography, from large scale thermohaline circulations to those governing small scale motions and turbulence. After establishing the basic dynamical equations that describe all oceanic motions, M|ller then derives approximate equations, emphasizing the assumptions made and physical processes eliminated. He distinguishes between geometric, thermodynamic and dynamic approximations and between the acoustic, gravity, vortical and temperature-salinity modes of motion. Basic concepts and formulae of equilibrium thermodynamics, vector and tensor calculus, curvilinear coordinate systems, and the kinematics of fluid motion and wave propagation are covered in appendices. Providing the basic theoretical background for graduate students and researchers of physical oceanography and climate science, this book will serve as both a comprehensive text and an essential reference.

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

Towards Mechanochemistry of Fracture and Cohesion: General Introduction and the Simplest Model of Velcro

DTIC Science & Technology

2010-09-01

reports. This project is aimed at a combined theoretical and experimental analysis of adhesives. The theoretical part of it is based on usage of... Theoretical Difficulties in the Thermodynamics of Heterogeneous Systems and Fracture 3 3. Thermodynamic Model of Velcro 7 3.1 Derivation of Equations 5 and 6...mechanochemical systems). Among those are fracture of solids , analysis of solid explosives , chemical reactions in solids , environmental stress corrosion and

An Improved Theoretical Aerodynamic Derivatives Computer Program for Sounding Rockets

NASA Technical Reports Server (NTRS)

Barrowman, J. S.; Fan, D. N.; Obosu, C. B.; Vira, N. R.; Yang, R. J.

1979-01-01

The paper outlines a Theoretical Aerodynamic Derivatives (TAD) computer program for computing the aerodynamics of sounding rockets. TAD outputs include normal force, pitching moment and rolling moment coefficient derivatives as well as center-of-pressure locations as a function of the flight Mach number. TAD is applicable to slender finned axisymmetric vehicles at small angles of attack in subsonic and supersonic flows. TAD improvement efforts include extending Mach number regions of applicability, improving accuracy, and replacement of some numerical integration algorithms with closed-form integrations. Key equations used in TAD are summarized and typical TAD outputs are illustrated for a second-stage Tomahawk configuration.

Transport equations for low-energy solar particles in evolving interplanetary magnetic fields

NASA Technical Reports Server (NTRS)

Ng, C. K.

1988-01-01

Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealized solution suggests that the 'invariant' anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.

A Structural Equation Model at the Individual and Group Level for Assessing Faking-Related Change

ERIC Educational Resources Information Center

Ferrando, Pere Joan; Anguiano-Carrasco, Cristina

2011-01-01

This article proposes a comprehensive approach based on structural equation modeling for assessing the amount of trait-level change derived from faking-motivating situations. The model is intended for a mixed 2-wave 2-group design, and assesses change at both the group and the individual level. Theoretically the model adopts an integrative…

Modeling ultrashort electromagnetic pulses with a generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Hofstrand, A.; Moloney, J. V.

2018-03-01

In this paper we derive a properly scaled model for the nonlinear propagation of intense, ultrashort, mid-infrared electromagnetic pulses (10-100 femtoseconds) through an arbitrary dispersive medium. The derivation results in a generalized Kadomtsev-Petviashvili (gKP) equation. In contrast to envelope-based models such as the Nonlinear Schrödinger (NLS) equation, the gKP equation describes the dynamics of the field's actual carrier wave. It is important to resolve these dynamics when modeling ultrashort pulses. We proceed by giving an original proof of sufficient conditions on the initial pulse for a singularity to form in the field after a finite propagation distance. The model is then numerically simulated in 2D using a spectral-solver with initial data and physical parameters highlighting our theoretical results.

Why history matters: Ab initio rederivation of Fresnel equations confirms microscopic theory of refractive index

NASA Astrophysics Data System (ADS)

Starke, R.; Schober, G. A. H.

2018-03-01

We provide a systematic theoretical, experimental, and historical critique of the standard derivation of Fresnel's equations, which shows in particular that these well-established equations actually contradict the traditional, macroscopic approach to electrodynamics in media. Subsequently, we give a rederivation of Fresnel's equations which is exclusively based on the microscopic Maxwell equations and hence in accordance with modern first-principles materials physics. In particular, as a main outcome of this analysis being of a more general interest, we propose the most general boundary conditions on electric and magnetic fields which are valid on the microscopic level.

Magnonic analog of relativistic Zitterbewegung in an antiferromagnetic spin chain

NASA Astrophysics Data System (ADS)

Wang, Weiwei; Gu, Chenjie; Zhou, Yan; Fangohr, Hans

2017-07-01

We theoretically investigate the spin-wave (magnon) excitations in a classical antiferromagnetic spin chain with easy-axis anisotropy. We obtain a Dirac-like equation by linearizing the Landau-Lifshitz-Gilbert equation in this antiferromagnetic system, in contrast to the ferromagnetic system in which a Schrödinger-type equation is derived. The Hamiltonian operator in the Dirac-like equation is a pseudo-Hermitian. We compute and demonstrate relativistic Zitterbewegung (trembling motion) in the antiferromagnetic spin chain by measuring the expectation values of the wave-packet position.

Analysis of stability for stochastic delay integro-differential equations.

PubMed

Zhang, Yu; Li, Longsuo

2018-01-01

In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

On the theory of drainage area for regular and non-regular points.

PubMed

Bonetti, S; Bragg, A D; Porporato, A

2018-03-01

The drainage area is an important, non-local property of a landscape, which controls surface and subsurface hydrological fluxes. Its role in numerous ecohydrological and geomorphological applications has given rise to several numerical methods for its computation. However, its theoretical analysis has lagged behind. Only recently, an analytical definition for the specific catchment area was proposed (Gallant & Hutchinson. 2011 Water Resour. Res. 47 , W05535. (doi:10.1029/2009WR008540)), with the derivation of a differential equation whose validity is limited to regular points of the watershed. Here, we show that such a differential equation can be derived from a continuity equation (Chen et al. 2014 Geomorphology 219 , 68-86. (doi:10.1016/j.geomorph.2014.04.037)) and extend the theory to critical and singular points both by applying Gauss's theorem and by means of a dynamical systems approach to define basins of attraction of local surface minima. Simple analytical examples as well as applications to more complex topographic surfaces are examined. The theoretical description of topographic features and properties, such as the drainage area, channel lines and watershed divides, can be broadly adopted to develop and test the numerical algorithms currently used in digital terrain analysis for the computation of the drainage area, as well as for the theoretical analysis of landscape evolution and stability.

On the theory of drainage area for regular and non-regular points

NASA Astrophysics Data System (ADS)

Bonetti, S.; Bragg, A. D.; Porporato, A.

2018-03-01

The drainage area is an important, non-local property of a landscape, which controls surface and subsurface hydrological fluxes. Its role in numerous ecohydrological and geomorphological applications has given rise to several numerical methods for its computation. However, its theoretical analysis has lagged behind. Only recently, an analytical definition for the specific catchment area was proposed (Gallant & Hutchinson. 2011 Water Resour. Res. 47, W05535. (doi:10.1029/2009WR008540)), with the derivation of a differential equation whose validity is limited to regular points of the watershed. Here, we show that such a differential equation can be derived from a continuity equation (Chen et al. 2014 Geomorphology 219, 68-86. (doi:10.1016/j.geomorph.2014.04.037)) and extend the theory to critical and singular points both by applying Gauss's theorem and by means of a dynamical systems approach to define basins of attraction of local surface minima. Simple analytical examples as well as applications to more complex topographic surfaces are examined. The theoretical description of topographic features and properties, such as the drainage area, channel lines and watershed divides, can be broadly adopted to develop and test the numerical algorithms currently used in digital terrain analysis for the computation of the drainage area, as well as for the theoretical analysis of landscape evolution and stability.

A Theoretical Analysis of the Influence of Electroosmosis on the Effective Ionic Mobility in Capillary Zone Electrophoresis

ERIC Educational Resources Information Center

Hijnen, Hens

2009-01-01

A theoretical description of the influence of electroosmosis on the effective mobility of simple ions in capillary zone electrophoresis is presented. The mathematical equations derived from the space-charge model contain the pK[subscript a] value and the density of the weak acid surface groups as parameters characterizing the capillary. It is…

The stability of the contact interface of cylindrical and spherical shock tubes

NASA Astrophysics Data System (ADS)

Crittenden, Paul E.; Balachandar, S.

2018-06-01

The stability of the contact interface for radial shock tubes is investigated as a model for explosive dispersal. The advection upstream splitting method with velocity and pressure diffusion (AUSM+-up) is used to solve for the radial base flow. To investigate the stability of the resulting contact interface, perturbed governing equations are derived assuming harmonic modes in the transverse directions. The perturbed harmonic flow is solved by assuming an initial disturbance and using a perturbed version of AUSM+-up derived in this paper. The intensity of the perturbation near the contact interface is computed and compared to theoretical results obtained by others. Despite the simplifying assumptions of the theoretical analysis, very good agreement is observed. Not only can the magnitude of the instability be predicted during the initial expansion, but also remarkably the agreement between the numerical and theoretical results can be maintained through the collision between the secondary shock and the contact interface. Since the theoretical results only depend upon the time evolution of the base flow, the stability of various modes could be quickly investigated without explicitly solving a system of partial differential equations for the perturbed flow.

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.

PubMed

Vorobev, Anatoliy

2010-11-01

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

The renormalization group and the implicit function theorem for amplitude equations

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

Kirkinis, Eleftherios

2008-07-15

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen et al., Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation formore » both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases.« less

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

Chen, Chuchu, E-mail: chenchuchu@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Zhang, Liying, E-mail: lyzhang@lsec.cc.ac.cn

Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the correspondingmore » discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.« less

Patterns induced by super cross-diffusion in a predator-prey system with Michaelis-Menten type harvesting.

PubMed

Liu, Biao; Wu, Ranchao; Chen, Liping

2018-04-01

Turing instability and pattern formation in a super cross-diffusion predator-prey system with Michaelis-Menten type predator harvesting are investigated. Stability of equilibrium points is first explored with or without super cross-diffusion. It is found that cross-diffusion could induce instability of equilibria. To further derive the conditions of Turing instability, the linear stability analysis is carried out. From theoretical analysis, note that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes by means of weakly nonlinear theory. Dynamical analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, the theoretical results are illustrated via numerical simulations. Copyright © 2018. Published by Elsevier Inc.

A theoretical derivation of the dilatancy equation for brittle rocks based on Maxwell model

NASA Astrophysics Data System (ADS)

Li, Jie; Huang, Houxu; Wang, Mingyang

2017-03-01

In this paper, the micro-cracks in the brittle rocks are assumed to be penny shaped and evenly distributed; the damage and dilatancy of the brittle rocks is attributed to the growth and expansion of numerous micro-cracks under the local tensile stress. A single crack's behaviour under the local tensile stress is generalized to all cracks based on the distributed damage mechanics. The relationship between the local tensile stress and the external loading is derived based on the Maxwell model. The damage factor corresponding to the external loading is represented using the p-alpha ( p- α) model. A dilatancy equation that can build up a link between the external loading and the rock dilatancy is established. A test of dilatancy of a brittle rock under triaxial compression is conducted; the comparison between experimental results and our theoretical results shows good consistency.

On the Divergence of the Velocity Vector in Real-Gas Flow

NASA Technical Reports Server (NTRS)

Bellan, Josette

2009-01-01

A theoretical study was performed addressing the degree of applicability or inapplicability, to a real gas, of the occasionally stated belief that for an ideal gas, incompressibility is synonymous with a zero or very low Mach number. The measure of compressibility used in this study is the magnitude of the divergence of the flow velocity vector [V(bar) (raised dot) u (where u is the flow velocity)]. The study involves a mathematical derivation that begins with the governing equations of flow and involves consideration of equations of state, thermodynamics, and fluxes of heat, mass, and the affected molecular species. The derivation leads to an equation for the volume integral of (V(bar) (raised dot) u)(sup 2) that indicates contributions of several thermodynamic, hydrodynamic, and species-flux effects to compressibility and reveals differences between real and ideal gases. An analysis of the equation leads to the conclusion that for a real gas, incompressibility is not synonymous with zero or very small Mach number. Therefore, it is further concluded, the contributions to compressibility revealed by the derived equation should be taken into account in simulations of real-gas flows.

An Equation for Moist Entropy in a Precipitating and Icy Atmosphere

NASA Technical Reports Server (NTRS)

Tao, Wei-Kuo; Simpson, Joanne; Zeng, Xiping

2003-01-01

Moist entropy is nearly conserved in adiabatic motion. It is redistributed rather than created by moist convection. Thus moist entropy and its equation, as a healthy direction, can be used to construct analytical and numerical models for the interaction between tropical convective clouds and large-scale circulations. Hence, an accurate equation of moist entropy is needed for the analysis and modeling of atmospheric convective clouds. On the basis of the consistency between the energy and the entropy equations, a complete equation of moist entropy is derived from the energy equation. The equation expresses explicitly the internal and external sources of moist entropy, including those in relation to the microphysics of clouds and precipitation. In addition, an accurate formula for the surface flux of moist entropy from the underlying surface into the air above is derived. Because moist entropy deals "easily" with the transition among three water phases, it will be used as a prognostic variable in the next generation of cloud-resolving models (e. g. a global cloud-resolving model) for low computational noise. Its equation that is derived in this paper is accurate and complete, providing a theoretical basis for using moist entropy as a prognostic variable in the long-term modeling of clouds and large-scale circulations.

Theoretical Prediction of Pressure Distributions on Nonlifting Airfoils at High Subsonic Speeds

NASA Technical Reports Server (NTRS)

Spreiter, John R; Alksne, Alberta

1955-01-01

Theoretical pressure distributions on nonlifting circular-arc airfoils in two-dimensional flows with high subsonic free-stream velocity are found by determining approximate solutions, through an iteration process, of an integral equation for transonic flow proposed by Oswatitsch. The integral equation stems directly from the small-disturbance theory for transonic flow. This method of analysis possesses the advantage of remaining in the physical, rather than the hodograph, variable and can be applied in airfoils having curved surfaces. After discussion of the derivation of the integral equation and qualitative aspects of the solution, results of calculations carried out for circular-arc airfoils in flows with free-stream Mach numbers up to unity are described. These results indicate most of the principal phenomena observed in experimental studies.

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Loh, Ching Y.; Povinelli, Louis A.

1994-01-01

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

A variational data assimilation system for the range dependent acoustic model using the representer method: Theoretical derivations.

PubMed

Ngodock, Hans; Carrier, Matthew; Fabre, Josette; Zingarelli, Robert; Souopgui, Innocent

2017-07-01

This study presents the theoretical framework for variational data assimilation of acoustic pressure observations into an acoustic propagation model, namely, the range dependent acoustic model (RAM). RAM uses the split-step Padé algorithm to solve the parabolic equation. The assimilation consists of minimizing a weighted least squares cost function that includes discrepancies between the model solution and the observations. The minimization process, which uses the principle of variations, requires the derivation of the tangent linear and adjoint models of the RAM. The mathematical derivations are presented here, and, for the sake of brevity, a companion study presents the numerical implementation and results from the assimilation simulated acoustic pressure observations.

Optimality conditions for the numerical solution of optimization problems with PDE constraints :

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

Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

2014-03-01

A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

Coupled 2-dimensional cascade theory for noise an d unsteady aerodynamics of blade row interaction in turbofans. Volume 2: Documentation for computer code CUP2D

NASA Technical Reports Server (NTRS)

Hanson, Donald B.

1994-01-01

A two dimensional linear aeroacoustic theory for rotor/stator interaction with unsteady coupling was derived and explored in Volume 1 of this report. Computer program CUP2D has been written in FORTRAN embodying the theoretical equations. This volume (Volume 2) describes the structure of the code, installation and running, preparation of the input file, and interpretation of the output. A sample case is provided with printouts of the input and output. The source code is included with comments linking it closely to the theoretical equations in Volume 1.

Slip Boundary Conditions for the Compressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Baranger, Céline; Hattori, Masanari; Kosuge, Shingo; Martalò, Giorgio; Mathiaud, Julien; Mieussens, Luc

2017-11-01

The slip boundary conditions for the compressible Navier-Stokes equations are derived systematically from the Boltzmann equation on the basis of the Chapman-Enskog solution of the Boltzmann equation and the analysis of the Knudsen layer adjacent to the boundary. The resulting formulas of the slip boundary conditions are summarized with explicit values of the slip coefficients for hard-sphere molecules as well as the Bhatnagar-Gross-Krook model. These formulas, which can be applied to specific problems immediately, help to prevent the use of often used slip boundary conditions that are either incorrect or without theoretical basis.

Using Theoretical Descriptions in Structure Activity Relations. 3. Electronic Descriptors

DTIC Science & Technology

1988-08-01

Activity Relationships (QSAR) have been used successfully in the past to develop predictive equations for several biological and physical properties...Linear Free Energy Relationships (,FF.3) and is based on work by Hammet in which he derived electronic descriptors for the dissociation of substituted...structure of a compound and its activity in a system. Several different structural descriptors have been used in QSAR equations . These range from

A simple analytical model for dynamics of time-varying target leverage ratios

NASA Astrophysics Data System (ADS)

Lo, C. F.; Hui, C. H.

2012-03-01

In this paper we have formulated a simple theoretical model for the dynamics of the time-varying target leverage ratio of a firm under some assumptions based upon empirical observations. In our theoretical model the time evolution of the target leverage ratio of a firm can be derived self-consistently from a set of coupled Ito's stochastic differential equations governing the leverage ratios of an ensemble of firms by the nonlinear Fokker-Planck equation approach. The theoretically derived time paths of the target leverage ratio bear great resemblance to those used in the time-dependent stationary-leverage (TDSL) model [Hui et al., Int. Rev. Financ. Analy. 15, 220 (2006)]. Thus, our simple model is able to provide a theoretical foundation for the selected time paths of the target leverage ratio in the TDSL model. We also examine how the pace of the adjustment of a firm's target ratio, the volatility of the leverage ratio and the current leverage ratio affect the dynamics of the time-varying target leverage ratio. Hence, with the proposed dynamics of the time-dependent target leverage ratio, the TDSL model can be readily applied to generate the default probabilities of individual firms and to assess the default risk of the firms.

Theoretical considerations for Reaction-Formed Silicon Carbide (RFSC) formation by molten silicon infiltration into slurry-derived preforms

NASA Technical Reports Server (NTRS)

Behrendt, D. R.; Singh, M.

1993-01-01

For reaction-formed silicon carbide (RFSC) ceramics produced by silicon melt infiltration of porous carbon preforms, equations are developed to relate the amount of residual silicon to the initial carbon density. Also, for a slurry derived preform containing both carbon and silicon powder, equations are derived which relate the amount of residual silicon in the RFSC to the relative density of the carbon in the preform and to the amount of silicon powder added to the slurry. For a porous carbon preform that does not have enough porosity to prevent choking-off of the silicon infiltration, these results show that complete silicon infiltration can occur by adding silicon powder to the slurry mixture used to produce these preforms.

Second-order variational equations for N-body simulations

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2016-07-01

First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.

METal matrix composite ANalyzer (METCAN): Theoretical manual

NASA Technical Reports Server (NTRS)

Murthy, P. L. N.; Chamis, C. C.

1993-01-01

This manuscript is intended to be a companion volume to the 'METCAN User's Manual' and the 'METAN Demonstration Manual.' The primary purpose of the manual is to give details pertaining to micromechanics and macromechanics equations of high temperature metal matrix composites that are programmed in the METCAN computer code. The subroutines which contain the programmed equations are also mentioned in order to facilitate any future changes or modifications that the user may intend to incorporate in the code. Assumptions and derivations leading to the micromechanics equations are briefly mentioned.

Gravitational waves — A review on the theoretical foundations of gravitational radiation

NASA Astrophysics Data System (ADS)

Dirkes, Alain

2018-05-01

In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating n-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.

Rate and time dependent behavior of structural adhesives. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Renieri, M. P.; Herakovich, C. T.; Brinson, H. F.

1976-01-01

Studies on two adhesives (Metlbond 1113 and 1113-2) identified as having applications in the bonding of composite materials are presented. Constitutive equations capable of describing changes in material behavior with strain rate are derived from various theoretical approaches. It is shown that certain unique relationships exist between these approaches. It is also shown that the constitutive equation derived from mechanical models can be used for creep and relaxation loading. A creep to failure phenomenon is shown to exist and is correlated with a delayed yield equation proposed by Crochet. Loading-unloading results are presented and are shown to correlate well with the proposed form of the loading-unloading equations for the modified Bingham model. Experimental results obtained for relaxation tests above and below the glass transition temperature are presented. It is shown that the adhesives obey the time-temperature superposition principle.

Closed form solutions of two time fractional nonlinear wave equations

NASA Astrophysics Data System (ADS)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

Theoretical predictions of latitude dependencies in the solar wind

NASA Technical Reports Server (NTRS)

Winge, C. R., Jr.; Coleman, P. J., Jr.

1974-01-01

Results are presented which were obtained with the Winge-Coleman model for theoretical predictions of latitudinal dependencies in the solar wind. A first-order expansion is described which allows analysis of first-order latitudinal variations in the coronal boundary conditions and results in a second-order partial differential equation for the perturbation stream function. Latitudinal dependencies are analytically separated out in the form of Legendre polynomials and their derivative, and are reduced to the solution of radial differential equations. This analysis is shown to supply an estimate of how large the coronal variation in latitude must be to produce an 11 km/sec/deg gradient in the radial velocity of the solar wind, assuming steady-state processes.

Active motion on curved surfaces

NASA Astrophysics Data System (ADS)

Castro-Villarreal, Pavel; Sevilla, Francisco J.

2018-05-01

A theoretical analysis of active motion on curved surfaces is presented in terms of a generalization of the telegrapher equation. Such a generalized equation is explicitly derived as the polar approximation of the hierarchy of equations obtained from the corresponding Fokker-Planck equation of active particles diffusing on curved surfaces. The general solution to the generalized telegrapher equation is given for a pulse with vanishing current as initial data. Expressions for the probability density and the mean squared geodesic displacement are given in the limit of weak curvature. As an explicit example of the formulated theory, the case of active motion on the sphere is presented, where oscillations observed in the mean squared geodesic displacement are explained.

The Designing of CALM (Computer Anxiety and Learning Measure): Validation of a Multidimensional Measure of Anxiety and Cognitions Relating to Adult Learning of Computing Skills Using Structural Equation Modeling.

ERIC Educational Resources Information Center

McInerney, Valentina; Marsh, Herbert W.; McInerney, Dennis M.

This paper discusses the process through which a powerful multidimensional measure of affect and cognition in relation to adult learning of computing skills was derived from its early theoretical stages to its validation using structural equation modeling. The discussion emphasizes the importance of ensuring a strong substantive base from which to…

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

NASA Technical Reports Server (NTRS)

Deutsch, Ivan H.; Garrison, John C.

1992-01-01

Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

Can a numerically stable subgrid-scale model for turbulent flow computation be ideally accurate?: a preliminary theoretical study for the Gaussian filtered Navier-Stokes equations.

PubMed

Ida, Masato; Taniguchi, Nobuyuki

2003-09-01

This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 < α , β ≤ 2 } based on the fractional derivative, has not been obtained, where α and β are time and space derivative orders. It is essential to derive a general PFG signal attenuation expression including the FGPW effect for PFG anisotropic anomalous diffusion research. In this paper, two recently developed modified-Bloch equations, the fractal differential modified-Bloch equation and the fractional integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

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

DOE PAGES

Gabitto, Jorge; Tsouris, Costas

2018-01-19

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

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

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

Gabitto, Jorge; Tsouris, Costas

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

A 1D-2D Shallow Water Equations solver for discontinuous porosity field based on a Generalized Riemann Problem

NASA Astrophysics Data System (ADS)

Ferrari, Alessia; Vacondio, Renato; Dazzi, Susanna; Mignosa, Paolo

2017-09-01

A novel augmented Riemann Solver capable of handling porosity discontinuities in 1D and 2D Shallow Water Equation (SWE) models is presented. With the aim of accurately approximating the porosity source term, a Generalized Riemann Problem is derived by adding an additional fictitious equation to the SWEs system and imposing mass and momentum conservation across the porosity discontinuity. The modified Shallow Water Equations are theoretically investigated, and the implementation of an augmented Roe Solver in a 1D Godunov-type finite volume scheme is presented. Robust treatment of transonic flows is ensured by introducing an entropy fix based on the wave pattern of the Generalized Riemann Problem. An Exact Riemann Solver is also derived in order to validate the numerical model. As an extension of the 1D scheme, an analogous 2D numerical model is also derived and validated through test cases with radial symmetry. The capability of the 1D and 2D numerical models to capture different wave patterns is assessed against several Riemann Problems with different wave patterns.

Brownian motion of a particle with arbitrary shape.

PubMed

Cichocki, Bogdan; Ekiel-Jeżewska, Maria L; Wajnryb, Eligiusz

2015-06-07

Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed.

Shock Waves in a Bose-Einstein Condensate

NASA Technical Reports Server (NTRS)

Kulikov, Igor; Zak, Michail

2005-01-01

A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders.

PubMed

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-30

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders

NASA Astrophysics Data System (ADS)

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-01

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Status of rates and rate equations for thermal leptogenesis

NASA Astrophysics Data System (ADS)

Biondini, S.; Bödeker, D.; Brambilla, N.; Garny, M.; Ghiglieri, J.; Hohenegger, A.; Laine, M.; Mendizabal, S.; Millington, P.; Salvio, A.; Vairo, A.

2018-02-01

In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma T exceeds the right-handed neutrino mass scale M is efficiently erased, and one can focus on the temperature window T ≪ M. We review recent progress in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number densities, their rigorous formulation and applicability are also discussed.

A study of the geographic coverage properties of a satellite borne Doppler lidar wind velocity measuring system

NASA Technical Reports Server (NTRS)

Pate, T. H.

1982-01-01

Geographic coverage frequency and geographic shot density for a satellite borne Doppler lidar wind velocity measuring system are measured. The equations of motion of the light path on the ground were derived and a computer program devised to compute shot density and coverage frequency by latitude-longitude sections. The equations for the coverage boundaries were derived and a computer program developed to plot these boundaries, thus making it possible, after an application of a map coloring algorithm, to actually see the areas of multiple coverage. A theoretical cross-swath shot density function that gives close approximations in certain cases was also derived. This information should aid in the design of an efficient data-processing system for the Doppler lidar.

Dynamics of osmosis in a porous medium.

PubMed

Cardoso, Silvana S S; Cartwright, Julyan H E

2014-11-01

We derive from kinetic theory, fluid mechanics and thermodynamics the minimal continuum-level equations governing the flow of a binary, non-electrolytic mixture in an isotropic porous medium with osmotic effects. For dilute mixtures, these equations are linear and in this limit provide a theoretical basis for the widely used semi-empirical relations of Kedem & Katchalsky (Kedem & Katchalsky 1958 Biochim. Biophys. Acta 27, 229-246 (doi:10.1016/0006-3002(58)90330-5), which have hitherto been validated experimentally but not theoretically. The above linearity between the fluxes and the driving forces breaks down for concentrated or non-ideal mixtures, for which our equations go beyond the Kedem-Katchalsky formulation. We show that the heretofore empirical solute permeability coefficient reflects the momentum transfer between the solute molecules that are rejected at a pore entrance and the solvent molecules entering the pore space; it can be related to the inefficiency of a Maxwellian demi-demon.

Sound transmission of cavity walls due to structure borne transmission via point and line connections.

PubMed

Davy, John L

2012-08-01

The author has published equations for predicting the air borne sound transmission of double leaf cavity walls due to the structure borne sound transmission across the air cavity via (possibly resilient) line connections, but has never published the full derivation of these equations. The author also derived equations for the case when the connections are rigid point connections but has never used them or published them or their derivations. This paper will present the full derivation of the author's theory of the air borne sound transmission of double leaf cavity walls due to the structure borne sound transmission across the air cavity via point or line connections which are modeled as four pole networks. The theoretical results will be compared with experimental results on wooden stud cavity walls from the National Research Council of Canada because the screw spacing is given for these results. This enables connections via studs and screws to be modeled as point connections and avoids the need to make any assumptions about the compliance of the equivalent point or line connections.

Theoretical investigations on plasma processes in the Kaufman thruster

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.

1973-01-01

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

The high pressure structure and equation of state of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) up to 20 GPa: X-ray diffraction measurements and first principles molecular dynamics simulations

DOE PAGES

Stavou, Elissaios; Manaa, M. Riad; Zaug, Joseph M.; ...

2015-10-14

Recent theoretical studies of 2,6-diamino-3,5-dinitropyrazine-1-oxide (C 4H 4N 6O 5 Lawrence Livermore Molecule No. 105, LLM-105) report unreacted high pressure equations of state that include several structural phase transitions, between 8 and 50 GPa, while one published experimental study reports equation of state (EOS) data up to a pressure of 6 GPa with no observed transition. Here we report the results of a synchrotron-based X-ray diffraction study and also ambient temperature isobaric-isothermal atomistic molecular dynamics simulations of LLM-105 up to 20 GPa. We find that the ambient pressure phase remains stable up to 20 GPa; there is no indication ofmore » a pressure induced phase transition. We do find a prominent decrease in b-axis compressibility starting at approximately 13 GPa and attribute the stiffening to a critical length where inter-sheet distance becomes similar to the intermolecular distance within individual sheets. The ambient temperature isothermal equation of state was determined through refinements of measured X-ray diffraction patterns. The pressure-volume data were fit using various EOS models to yield bulk moduli with corresponding pressure derivatives. As a result, we find very good agreement between the experimental and theoretically derived EOS.« less

Dark soliton pair of ultracold Fermi gases for a generalized Gross-Pitaevskii equation model.

PubMed

Wang, Ying; Zhou, Yu; Zhou, Shuyu; Zhang, Yongsheng

2016-07-01

We present the theoretical investigation of dark soliton pair solutions for one-dimensional as well as three-dimensional generalized Gross-Pitaevskii equation (GGPE) which models the ultracold Fermi gas during Bardeen-Cooper-Schrieffer-Bose-Einstein condensates crossover. Without introducing any integrability constraint and via the self-similar approach, the three-dimensional solution of GGPE is derived based on the one-dimensional dark soliton pair solution, which is obtained through a modified F-expansion method combined with a coupled modulus-phase transformation technique. We discovered the oscillatory behavior of the dark soliton pair from the theoretical results obtained for the three-dimensional case. The calculated period agrees very well with the corresponding reported experimental result [Weller et al., Phys. Rev. Lett. 101, 130401 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.130401], demonstrating the applicability of the theoretical treatment presented in this work.

Modeling the Capacitive Deionization Process in Dual-Porosity Electrodes

DOE PAGES

Gabitto, Jorge; Tsouris, Costas

2016-04-28

In many areas of the world, there is a need to increase water availability. Capacitive deionization (CDI) is an electrochemical water treatment process that can be a viable alternative for treating water and for saving energy. A model is presented to simulate the CDI process in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two steps volume averaging technique is used to derive the averaged transport equations in the limit of thin electrical double layers. A one-equationmore » model based on the principle of local equilibrium is derived. The constraints determining the range of application of the one-equation model are presented. The effective transport parameters for isotropic porous media are calculated solving the corresponding closure problems. The source terms that appear in the average equations are calculated using theoretical derivations. The global diffusivity is calculated by solving the closure problem.« less

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

PubMed

Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

2013-03-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

PubMed Central

Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

2013-01-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian. PMID:23772179

Demonstrating the Gas Laws.

ERIC Educational Resources Information Center

Holko, David A.

1982-01-01

Presents a complete computer program demonstrating the relationship between volume/pressure for Boyle's Law, volume/temperature for Charles' Law, and volume/moles of gas for Avagadro's Law. The programing reinforces students' application of gas laws and equates a simulated moving piston to theoretical values derived using the ideal gas law.…

Emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators.

PubMed

English, L Q; Mertens, David; Abdoulkary, Saidou; Fritz, C B; Skowronski, K; Kevrekidis, P G

2016-12-01

We derive the Kuramoto-Sakaguchi model from the basic circuit equations governing two coupled Wien-bridge oscillators. A Wien-bridge oscillator is a particular realization of a tunable autonomous oscillator that makes use of frequency filtering (via an RC bandpass filter) and positive feedback (via an operational amplifier). In the past few years, such oscillators have started to be utilized in synchronization studies. We first show that the Wien-bridge circuit equations can be cast in the form of a coupled pair of van der Pol equations. Subsequently, by applying the method of multiple time scales, we derive the differential equations that govern the slow evolution of the oscillator phases and amplitudes. These equations are directly reminiscent of the Kuramoto-Sakaguchi-type models for the study of synchronization. We analyze the resulting system in terms of the existence and stability of various coupled oscillator solutions and explain on that basis how their synchronization emerges. The phase-amplitude equations are also compared numerically to the original circuit equations and good agreement is found. Finally, we report on experimental measurements of two coupled Wien-bridge oscillators and relate the results to the theoretical predictions.

Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller.

PubMed

Gong, Shuqing; Yang, Shaofu; Guo, Zhenyuan; Huang, Tingwen

2018-06-01

The paper is concerned with the synchronization problem of inertial memristive neural networks with time-varying delay. First, by choosing a proper variable substitution, inertial memristive neural networks described by second-order differential equations can be transformed into first-order differential equations. Then, a novel controller with a linear diffusive term and discontinuous sign term is designed. By using the controller, the sufficient conditions for assuring the global exponential synchronization of the derive and response neural networks are derived based on Lyapunov stability theory and some inequality techniques. Finally, several numerical simulations are provided to substantiate the effectiveness of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Theoretical analysis of linearized acoustics and aerodynamics of advanced supersonic propellers

NASA Technical Reports Server (NTRS)

Farassat, F.

1985-01-01

The derivation of a formula for prediction of the noise of supersonic propellers using time domain analysis is presented. This formula is a solution of the Ffowcs Williams-Hawkings equation and does not have the Doppler singularity of some other formulations. The result presented involves some surface integrals over the blade and line integrals over the leading and trailing edges. The blade geometry, motion and surface pressure are needed for noise calculation. To obtain the blade surface pressure, the observer is moved onto the blade surface and a linear singular integral equation is derived which can be solved numerically. Two examples of acoustic calculations using a computer program are currently under development.

Modelling of piezoelectric actuator dynamics for active structural control

NASA Technical Reports Server (NTRS)

Hagood, Nesbitt W.; Chung, Walter H.; Von Flotow, Andreas

1990-01-01

The paper models the effects of dynamic coupling between a structure and an electrical network through the piezoelectric effect. The coupled equations of motion of an arbitrary elastic structure with piezoelectric elements and passive electronics are derived. State space models are developed for three important cases: direct voltage driven electrodes, direct charge driven electrodes, and an indirect drive case where the piezoelectric electrodes are connected to an arbitrary electrical circuit with embedded voltage and current sources. The equations are applied to the case of a cantilevered beam with surface mounted piezoceramics and indirect voltage and current drive. The theoretical derivations are validated experimentally on an actively controlled cantilevered beam test article with indirect voltage drive.

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.

Exact comprehensive equations for the photon management properties of silicon nanowire

PubMed Central

Li, Yingfeng; Li, Meicheng; Li, Ruike; Fu, Pengfei; Wang, Tai; Luo, Younan; Mbengue, Joseph Michel; Trevor, Mwenya

2016-01-01

Unique photon management (PM) properties of silicon nanowire (SiNW) make it an attractive building block for a host of nanowire photonic devices including photodetectors, chemical and gas sensors, waveguides, optical switches, solar cells, and lasers. However, the lack of efficient equations for the quantitative estimation of the SiNW’s PM properties limits the rational design of such devices. Herein, we establish comprehensive equations to evaluate several important performance features for the PM properties of SiNW, based on theoretical simulations. Firstly, the relationships between the resonant wavelengths (RW), where SiNW can harvest light most effectively, and the size of SiNW are formulized. Then, equations for the light-harvesting efficiency at RW, which determines the single-frequency performance limit of SiNW-based photonic devices, are established. Finally, equations for the light-harvesting efficiency of SiNW in full-spectrum, which are of great significance in photovoltaics, are established. Furthermore, using these equations, we have derived four extra formulas to estimate the optimal size of SiNW in light-harvesting. These equations can reproduce majority of the reported experimental and theoretical results with only ~5% error deviations. Our study fills up a gap in quantitatively predicting the SiNW’s PM properties, which will contribute significantly to its practical applications. PMID:27103087

Nonlinear waves of a nonlocal modified KdV equation in the atmospheric and oceanic dynamical system

NASA Astrophysics Data System (ADS)

Tang, Xiao-yan; Liang, Zu-feng; Hao, Xia-zhi

2018-07-01

A new general nonlocal modified KdV equation is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a β-plane. The nonlocal property is manifested in the shifted parity and delayed time reversal symmetries. Exact solutions of the nonlocal modified KdV equation are obtained including periodic waves, kink waves, solitary waves, kink- and/or anti-kink-cnoidal periodic wave interaction solutions, which can be utilized to describe various two-place and time-delayed correlated events. As an illustration, a special approximate solution is applied to theoretically capture the salient features of two correlated dipole blocking events in atmospheric dynamical systems.

Theoretical and Numerical Study of Anomalous Turbulent Transport in Plasmas

DTIC Science & Technology

1991-02-05

Balescu -Lenard equation in the classical limit. This result was presented at the APS Topical Conference on Plasma Astrophysics at Santa Fe in September...itself, which can be Incorporated as the effect of renormali- zation of the particle mass. 2 Tho derived equa- tion reduces to the Balescu -Lenard

Dispersion equation for electrostatic ion cyclotron instability under the effect of ionization in a dusty plasma

NASA Astrophysics Data System (ADS)

Singh, Sukhmander

2018-05-01

In the present paper we derive the plasma dispersion equation under the effect of ionization rate in a dust plasma to investigate the electrostatic ion cyclotron instability, where dust charge fluctuation is absent. It has one of the lowest threshold drift velocities among all the current-driven instabilities in isothermal plasma. The Electrostatic ion cyclotron instability in a dusty plasma containing electrons, light ions, and massive negatively charged dust grains which can be investigated both experimentally and theoretically.

Relationships between diffuse reflectance and vegetation canopy variables based on the radiative transfer theory

NASA Technical Reports Server (NTRS)

Park, J. K.; Deering, D. W.

1981-01-01

Out of the lengthy original expression of the diffuse reflectance formula, simple working equations were derived by employing characteristic parameters, which are independent of the canopy coverage and identifiable by field observations. The typical asymptotic nature of reflectance data that is usually observed in biomass studies was clearly explained. The usefulness of the simplified equations was demonstrated by the exceptionally close fit of the theoretical curves to two separately acquired data sets for alfalfa and shortgrass prairie canopies.

Multiscale techniques for parabolic equations.

PubMed

Målqvist, Axel; Persson, Anna

2018-01-01

We use the local orthogonal decomposition technique introduced in Målqvist and Peterseim (Math Comput 83(290):2583-2603, 2014) to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale coefficients. We consider nonsmooth initial data and a backward Euler scheme for the temporal discretization. Optimal order convergence rate, depending only on the contrast, but not on the variations of the coefficients, is proven in the [Formula: see text]-norm. We present numerical examples, which confirm our theoretical findings.

Implication of Tsallis entropy in the Thomas–Fermi model for self-gravitating fermions

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

Ourabah, Kamel; Tribeche, Mouloud, E-mail: mouloudtribeche@yahoo.fr

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q-statistics. Starting from the q-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy preserves a scaling property of this equation. The q-statistical approach to Jeans’ instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans’ wavenumber (or the Jeans length) on the parameter q is traced. It is found that the q-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length. -- Highlights: •Thomas–Fermi approach for self-gravitatingmore » fermions. •A generalized Thomas–Fermi equation is derived. •Nonextensivity preserves a scaling property of this equation. •Nonextensive approach to Jeans’ instability of self-gravitating fermions. •It is found that nonextensivity makes the Fermionic system unstable at shorter scales.« less

Relationships of models of the inner magnetosphere to the Rice Convection Model

NASA Astrophysics Data System (ADS)

Heinemann, M.; Wolf, R. A.

2001-08-01

Ideal magnetohydrodynamics is known to be inaccurate for the Earth's inner magnetosphere, where transport by gradient-curvature drift is nonnegligible compared to E×B drift. Most theoretical treatments of the inner plasma sheet and ring current, including the Rice Convection Model (RCM), treat the inner magnetospheric plasma in terms of guiding center drifts. The RCM assumes that the distribution function is isotropic, but particles with different energy invariants are treated as separate guiding center fluids. However, Peymirat and Fontaine [1994] developed a two-fluid picture of the inner magnetosphere, which utilizes modified forms of the conventional fluid equations, not guiding center drift equations. Heinemann [1999] argued theoretically that for inner magnetospheric conditions the fluid energy equation should include a heat flux term, which, in the case of Maxwellian plasma, was derived by Braginskii [1965]. We have now reconciled the Heinemann [1999] fluid approach with the RCM. The fluid equations, including the Braginskii heat flux, can be derived by taking appropriate moments of the RCM equations for the case of the Maxwellian distribution. The physical difference between the RCM formalism and the Heinemann [1999] fluid approach is that the RCM pretends that particles suffer elastic collisions that maintain the isotropy of the distribution function but do not change particle energies. The Heinemann [1999] fluid treatment makes a different physical approximation, namely that the collisions maintain local thermal equilibrium among the ions and separately among the electrons. For some simple cases, numerical results are presented that illustrate the differences in the predictions of the two formalisms, along with those of MHD, guiding center theory, and Peymirat and Fontaine [1994].

Interaction of non-radially symmetric camphor particles

NASA Astrophysics Data System (ADS)

Ei, Shin-Ichiro; Kitahata, Hiroyuki; Koyano, Yuki; Nagayama, Masaharu

2018-03-01

In this study, the interaction between two non-radially symmetric camphor particles is theoretically investigated and the equation describing the motion is derived as an ordinary differential system for the locations and the rotations. In particular, slightly modified non-radially symmetric cases from radial symmetry are extensively investigated and explicit motions are obtained. For example, it is theoretically shown that elliptically deformed camphor particles interact so as to be parallel with major axes. Such predicted motions are also checked by real experiments and numerical simulations.

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).

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution - Part 1: theoretical development

NASA Astrophysics Data System (ADS)

Dib, Alain; Kavvas, M. Levent

2018-03-01

The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian-Eulerian Fokker-Planck equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.

Solvation thermodynamics and the physical-chemical meaning of the constant in Abraham solvation equations.

PubMed

van Noort, Paul C M

2012-04-01

Abraham solvation equations find widespread use in environmental chemistry. Until now, the intercept in these equations was determined by fitting experimental data. To simplify the determination of the coefficients in Abraham solvation equations, this study derives theoretical expressions for the value of the intercept for various partition processes. To that end, a modification of the description of the Ben-Naim standard state into the van der Waals volume is proposed. Differences between predicted and fitted values of the Abraham solvation equation intercept for the enthalpy of solvation, the entropy of solvation, solvent-water partitioning, air-solvent partitioning, partitioning into micelles, partitioning into lipid membranes and lipids, and chromatographic retention indices are comparable to experimental uncertainties in these values. Copyright © 2011 Elsevier Ltd. All rights reserved.

Asymmetric information and macroeconomic dynamics

NASA Astrophysics Data System (ADS)

Hawkins, Raymond J.; Aoki, Masanao; Roy Frieden, B.

2010-09-01

We show how macroeconomic dynamics can be derived from asymmetric information. As an illustration of the utility of this approach we derive the equilibrium density, non-equilibrium densities and the equation of motion for the response to a demand shock for productivity in a simple economy. Novel consequences of this approach include a natural incorporation of time dependence into macroeconomics and a common information-theoretic basis for economics and other fields seeking to link micro-dynamics and macro-observables.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

Nonplanar KdV and KP equations for quantum electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Dutta, Debjit

2015-12-01

Nonlinear quantum ion-acoustic waves with the effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the standard reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation for ion-acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave are studied analytically. It is found that the dynamics of ion-acoustic solitary waves (IASWs) is governed by a three-dimensional cylindrical Kadomtsev-Petviashvili equation (CKPE). The results could help in a theoretical analysis of astrophysical and laser produced plasmas.

The General Fishbone Like Dispersion Relation

NASA Astrophysics Data System (ADS)

Zonca, Fulvio

2015-12-01

The following sections are included: * Introduction * Motivation and outline * Fundamental equations * The collisionless gyrokinetic equation * Vorticity equation * Quasi-neutrality condition * Perpendicular Ampère's law * Studying collective modes in burning plasmas * Ideal plasma equilibrium in the low-β limit * Approximations for the energetic population * Characteristic frequencies of particle motions * Alfvén wave frequency and wavelength orderings * Applications of the general theoretical framework * The general fishbone like dispersion relation * Properties of the fishbone like dispersion relation * Derivation of the fishbone like dispersion relation * Special cases of the fishbone like dispersion relation * Toroidal Alfvén Eigenmodes (TAE) * Alfvén Cascades * Summary and discussions * Acknowledgments * References

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

DOE PAGES

Su, Hongling; Li, Shengtai

2016-02-03

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

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

Su, Hongling; Li, Shengtai

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

Gradient-Induced Voltages on 12-Lead ECGs during High Duty-Cycle MRI Sequences and a Method for Their Removal considering Linear and Concomitant Gradient Terms

PubMed Central

Zhang, Shelley HuaLei; Ho Tse, Zion Tsz; Dumoulin, Charles L.; Kwong, Raymond Y.; Stevenson, William G.; Watkins, Ronald; Ward, Jay; Wang, Wei; Schmidt, Ehud J.

2015-01-01

Purpose To restore 12-lead ECG signal fidelity inside MRI by removing magnetic-field gradient induced-voltages during high gradient-duty-cycle sequences. Theory and Methods A theoretical equation was derived, providing first- and second-order electrical fields induced at individual ECG electrode as a function of gradient fields. Experiments were performed at 3T on healthy volunteers, using a customized acquisition system which captured full amplitude and frequency response of ECGs, or a commercial recording system. The 19 equation coefficients were derived by linear regression of data from accelerated sequences, and used to compute induced-voltages in real-time during full-resolution sequences to remove ECG artifacts. Restored traces were evaluated relative to ones acquired without imaging. Results Measured induced-voltages were 0.7V peak-to-peak during balanced Steady-State Free Precession (bSSFP) with heart at the isocenter. Applying the equation during gradient echo sequencing, three-dimensional fast spin echo and multi-slice bSSFP imaging restored nonsaturated traces and second-order concomitant terms showed larger contributions in electrodes farther from the magnet isocenter. Equation coefficients are evaluated with high repeatability (ρ = 0.996) and are subject, sequence, and slice-orientation dependent. Conclusion Close agreement between theoretical and measured gradient-induced voltages allowed for real-time removal. Prospective estimation of sequence-periods where large induced-voltages occur may allow hardware removal of these signals. PMID:26101951

Focal length hysteresis of a double-liquid lens based on electrowetting

NASA Astrophysics Data System (ADS)

Peng, Runling; Wang, Dazhen; Hu, Zhiwei; Chen, Jiabi; Zhuang, Songlin

2013-02-01

In this paper, an extended Young equation especially suited for an ideal cylindrical double-liquid variable-focus lens is derived by means of an energy minimization method. Based on the extended Young equation, a kind of focal length hysteresis effect is introduced into the double-liquid variable-focus lens. Such an effect can be explained theoretically by adding a force of friction to the tri-phase contact line. Theoretical analysis shows that the focal length at a particular voltage can be different depending on whether the applied voltage is increasing or decreasing, that is, there is a focal length hysteresis effect. Moreover, the focal length at a particular voltage must be larger when the voltage is rising than when it is dropping. These conclusions are also verified by experiments.

Theoretical model of droplet wettability on a low-surface-energy solid under the influence of gravity.

PubMed

Yonemoto, Yukihiro; Kunugi, Tomoaki

2014-01-01

The wettability of droplets on a low surface energy solid is evaluated experimentally and theoretically. Water-ethanol binary mixture drops of several volumes are used. In the experiment, the droplet radius, height, and contact angle are measured. Analytical equations are derived that incorporate the effect of gravity for the relationships between the droplet radius and height, radius and contact angle, and radius and liquid surface energy. All the analytical equations display good agreement with the experimental data. It is found that the fundamental wetting behavior of the droplet on the low surface energy solid can be predicted by our model which gives geometrical information of the droplet such as the contact angle, droplet radius, and height from physical values of liquid and solid.

Comparison of internal wave properties calculated by Boussinesq equations with/without rigid-lid assumption

NASA Astrophysics Data System (ADS)

Liu, C. M.

2017-12-01

Wave properties predicted by the rigid-lid and the free-surface Boussinesq equations for a two-fluid system are theoretically calculated and compared in this study. Boussinesq model is generally applied to numerically simulate surface waves in coastal regions to provide credible information for disaster prevention and breaker design. As for internal waves, Liu et al. (2008) and Liu (2016) respectively derived a free-surface model and a rigid-lid Boussinesq models for a two-fluid system. The former and the latter models respectively contain four and three key variables which may result in different results and efficiency while simulating. Therefore, present study shows the results theoretically measured by these two models to provide more detailed observation and useful information for motions of internal waves.

Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.

PubMed

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chen, Jie; Yin, Linmao; Chew, Jia Wei

2017-04-01

Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.

High Resolution Electro-Optical Aerosol Phase Function Database PFNDAT2006

DTIC Science & Technology

2006-08-01

snow models use the gamma distribution (equation 12) with m = 0. 3.4.1 Rain Model The most widely used analytical parameterization for raindrop size ...Uijlenhoet and Stricker (22), as the result of an analytical derivation based on a theoretical parameterization for the raindrop size distribution ...6 2.2 Particle Size Distribution Models

Mathematics in Marine Botany: Examples of the Modelling Process. Part II: Continuous Models.

ERIC Educational Resources Information Center

Nyman, Melvin A.; Brown, Murray T.

1996-01-01

Describes some continuous models for growth of the seaweed Macrocystis pyrifera. Uses observed growth rates over several months to derive first-order differential equations as models for growth rates of individual fronds. The nature of the solutions is analyzed and comparison between these theoretical results and documented characteristics of…

3-Dimensional stereo implementation of photoacoustic imaging based on a new image reconstruction algorithm without using discrete Fourier transform

NASA Astrophysics Data System (ADS)

Ham, Woonchul; Song, Chulgyu

2017-05-01

In this paper, we propose a new three-dimensional stereo image reconstruction algorithm for a photoacoustic medical imaging system. We also introduce and discuss a new theoretical algorithm by using the physical concept of Radon transform. The main key concept of proposed theoretical algorithm is to evaluate the existence possibility of the acoustic source within a searching region by using the geometric distance between each sensor element of acoustic detector and the corresponding searching region denoted by grid. We derive the mathematical equation for the magnitude of the existence possibility which can be used for implementing a new proposed algorithm. We handle and derive mathematical equations of proposed algorithm for the one-dimensional sensing array case as well as two dimensional sensing array case too. A mathematical k-wave simulation data are used for comparing the image quality of the proposed algorithm with that of general conventional algorithm in which the FFT should be necessarily used. From the k-wave Matlab simulation results, we can prove the effectiveness of the proposed reconstruction algorithm.

Equation of state of U2Mo up-to Mbar pressure range: Ab-initio study

NASA Astrophysics Data System (ADS)

Mukherjee, D.; Sahoo, B. D.; Joshi, K. D.; Kaushik, T. C.

2018-04-01

Experimentally, U2Mo is known to exist in tetragonal structure at ambient conditions. In contrast to experimental reports, the past theoretical studies carried out in this material do not find this phase to be stable structure at zero pressure. In order to examine this discrepancy between experiment and theory, we have performed ab-initio electronic band structure calculations on this material. In our theoretical study, we have attempted to search for lowest enthalpy structure at ambient as well at high pressure up to 200 GPa, employing evolutionary structure search algorithm in conjunction with ab-inito method. Our investigations suggest that a hexagonal structure with space group symmetry P6/mmm is the lowest enthalpy structure not only at ambient pressure but also up to pressure range of ˜200 GPa. To further, substantiate the results of these static lattice calculations the elastic and lattice dynamical stability has also been analysed. The theoretical isotherm derived from these calculations has been utilized to determine the Hugoniot of this material. Various physical properties such as zero pressure equilibrium volume, bulk modulus and its pressure derivative has also been derived from theoretical isotherm.

Homoclinic snaking in the discrete Swift-Hohenberg equation

NASA Astrophysics Data System (ADS)

Kusdiantara, R.; Susanto, H.

2017-12-01

We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization effect on the bifurcation behavior, where we identify three regions of the coupling parameter, i.e., strong, weak, and intermediate coupling. Within the regions, the discrete Swift-Hohenberg equation behaves either similarly or differently from the continuum limit. In the intermediate coupling region, multiple Maxwell points can occur for the periodic solutions and may cause irregular snaking and isolas. Numerical continuation is used to obtain and analyze localized and periodic solutions for each case. Theoretical analysis for the snaking and stability of the corresponding solutions is provided in the weak coupling region.

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

NASA Astrophysics Data System (ADS)

Walicka, A.; Walicki, E.; Jurczak, P.; Falicki, J.

2017-05-01

The present theoretical analysis is to investigate the effect of non-Newtonian lubricant modelled by a Rabinowitsch fluid on the performance of a curvilinear squeeze film bearing with one porous wall. The equations of motion of a Rabinowitsch fluid are used to derive the Reynolds equation. After general considerations on the flow in a bearing clearance and in a porous layer using the Morgan-Cameron approximation the modified Reynolds equation is obtained. The analytical solution of this equation for the case of a squeeze film bearing is presented. As a result one obtains the formulae expressing pressure distribution and load-carrying capacity. Thrust radial bearing and spherical bearing with a squeeze film are considered as numerical examples.

Theory and procedure for determining loads and motions in chine-immersed hydrodynamic impacts of prismatic bodies

NASA Technical Reports Server (NTRS)

Schnitzer, Emanuel

1953-01-01

A theoretical method is derived for the determination of the motions and loads during chine-immersed water landings of prismatic bodies. This method makes use of a variation of two-dimensional deflected water mass over the complete range of immersion, modified by a correction for three-dimensional flow. Equations are simplified through omission of the term proportional to the acceleration of the deflected mass for use in calculation of loads on hulls having moderate and heavy beam loading. The effects of water rise at the keel are included in these equations. In order to make a direct comparison of theory with experiment, a modification of the equations was made to include the effect of finite test-carriage mass. A simple method of computation which can be applied without reading the body of this report is presented as an appendix along with the required theoretical plots for determination of loads and motions in chine-immersed landings.

Theoretical analysis of exponential transversal method of lines for the diffusion equation

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

Salazar, A.; Raydan, M.; Campo, A.

1996-12-31

Recently a new approximate technique to solve the diffusion equation was proposed by Campo and Salazar. This new method is inspired on the Method of Lines (MOL) with some insight coming from the method of separation of variables. The proposed method, the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly good numerical results. In this paper, the authors study the theoretical properties of ETMOL in depth. In particular, consistency,more » stability and convergence are established in the framework of the heat/mass diffusion equation. In most practical applications the method presents a very reduced truncation error in time and its different versions are proven to be unconditionally stable in the Fourier sense. Convergence of the solutions is then established. The theory is corroborated by several analytical/numerical experiments.« less

Electrostatic forces in the Poisson-Boltzmann systems

NASA Astrophysics Data System (ADS)

Xiao, Li; Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2013-09-01

Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

Far-Field Lorenz-Mie Scattering in an Absorbing Host Medium: Theoretical Formalism and FORTRAN Program

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Yang, Ping

2018-01-01

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenzâ€"Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

Far-field Lorenz-Mie scattering in an absorbing host medium: Theoretical formalism and FORTRAN program

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Yang, Ping

2018-01-01

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenz-Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

A case study using kinematic quantities derived from a triangle of VHF Doppler wind profilers

NASA Technical Reports Server (NTRS)

Carlson, Catherine A.; Forbes, Gregory S.

1989-01-01

Horizontal divergence, relative vorticity, kinematic vertical velocity, and geostrophic and ageostrophic winds are computed from Colorado profiler network data to investigate an upslope snowstorm in northeastern Colorado. Horizontal divergence and relative vorticity are computed using the Gauss and Stokes theorems, respectively. Kinematic vertical velocities are obtained from the surface to 9 km by vertically integrating the continuity equation. The geostrophic and ageostrophic winds are computed by applying a finite differencing technique to evaluate the derivatives in the horizontal equations of motion. Comparison of the synoptic-scale data with the profiler network data reveals that the two datasets are generally consistent. Also, the profiler-derived quantities exhibit coherent vertical and temporal patterns consistent with conceptual and theoretical flow fields of various meteorological phenomena. It is suggested that the profiler-derived quantities are of potential use to weather forecasters in that they enable the dynamic and kinematic interpretation of weather system structure to be made and thus have nowcasting and short-term forecasting value.

Theoretical basis, experimental design, and computerized simulation of synergism and antagonism in drug combination studies.

PubMed

Chou, Ting-Chao

2006-09-01

The median-effect equation derived from the mass-action law principle at equilibrium-steady state via mathematical induction and deduction for different reaction sequences and mechanisms and different types of inhibition has been shown to be the unified theory for the Michaelis-Menten equation, Hill equation, Henderson-Hasselbalch equation, and Scatchard equation. It is shown that dose and effect are interchangeable via defined parameters. This general equation for the single drug effect has been extended to the multiple drug effect equation for n drugs. These equations provide the theoretical basis for the combination index (CI)-isobologram equation that allows quantitative determination of drug interactions, where CI < 1, = 1, and > 1 indicate synergism, additive effect, and antagonism, respectively. Based on these algorithms, computer software has been developed to allow automated simulation of synergism and antagonism at all dose or effect levels. It displays the dose-effect curve, median-effect plot, combination index plot, isobologram, dose-reduction index plot, and polygonogram for in vitro or in vivo studies. This theoretical development, experimental design, and computerized data analysis have facilitated dose-effect analysis for single drug evaluation or carcinogen and radiation risk assessment, as well as for drug or other entity combinations in a vast field of disciplines of biomedical sciences. In this review, selected examples of applications are given, and step-by-step examples of experimental designs and real data analysis are also illustrated. The merging of the mass-action law principle with mathematical induction-deduction has been proven to be a unique and effective scientific method for general theory development. The median-effect principle and its mass-action law based computer software are gaining increased applications in biomedical sciences, from how to effectively evaluate a single compound or entity to how to beneficially use multiple drugs or modalities in combination therapies.

Development of One-Group and Two-Group Interfacial Area Transport Equation

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

Ishii, M.; Kim, S.

A dynamic approach employing the interfacial area transport equation is presented to replace the static flow regime dependent correlations for the interfacial area concentration. The current study derives the transport equations for the bubble number, volume, and interfacial area concentration. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, both one-group and two-group interfacial area transport equations are developed along with the necessary constitutive relations. The framework for the complicated source and sink terms in the two-group transport equation is also presented by identifying the major intragroup and intergroup bubble interaction mechanisms. In view ofmore » evaluating the theoretical model, the one-group interfacial area transport equation is benchmarked based on the available data obtained in a wide range of air-water bubbly flow in round tubes of various diameters. In general, the results show good agreement within the measurement error of {+-}10%.« less

Modeling electro-magneto-hydrodynamic thermo-fluidic transport of biofluids with new trend of fractional derivative without singular kernel

NASA Astrophysics Data System (ADS)

Abdulhameed, M.; Vieru, D.; Roslan, R.

2017-10-01

This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo-Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo-Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo-Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo-Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological analysis and medical diagnosis.

Blade selection for a modern axial-flow compressor

NASA Technical Reports Server (NTRS)

Wright, L. C.

1974-01-01

The procedures leading to successful design of an axial flow compressor are discussed. The three related approaches to cascade selection are: (1) experimental approach which relies on the use of experimental results from identical cascades to satisfy the velocity diagrams calculated, (2) a purely analytical procedure whereby blade shapes are calculated from the theoretical cascade and viscous flow equations, and (3) a semiempirical procedure which used experimental data together with the theoretically derived functional relations to relate the cascade parameters. Diagrams of typical transonic blade sections with uncambered leading edges are presented.

Analysis of nonlinear internal waves observed by Landsat thematic mapper

NASA Astrophysics Data System (ADS)

Artale, V.; Levi, D.; Marullo, S.; Santoleri, R.

1990-09-01

In this work we test the compatibility between the theoretical parameters of a nonlinear wave model and the quantitative information that one can deduce from satellite-derived data. The theoretical parameters are obtained by applying an inverse problem to the solution of the Cauchy problem for the Korteweg-de Vries equation. Our results are applied to the case of internal wave patterns elaborated from two different satellite sensors at the south of Messina (the thematic mapper) and at the north of Messina (the synthetic aperture radar).

Earth's rotation in the framework of general relativity: rigid multipole moments

NASA Astrophysics Data System (ADS)

Klioner, S. A.; Soffel, M.; Xu, Ch.; Wu, X.

A set of equations describing the rotational motion of the Earth relative to the GCRS is formulated in the approximation of rigidly rotating multipoles. The external bodies are supposed to be mass monopoles. The derived set of formulas is supposed to form the theoretical basis for a practical post-Newtonian theory of Earth precession and nutation.

A Multiscale Model for Virus Capsid Dynamics

PubMed Central

Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei

2010-01-01

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. PMID:20224756

Procedures for experimental measurement and theoretical analysis of large plastic deformations

NASA Technical Reports Server (NTRS)

Morris, R. E.

1974-01-01

Theoretical equations are derived and analytical procedures are presented for the interpretation of experimental measurements of large plastic strains in the surface of a plate. Orthogonal gage lengths established on the metal surface are measured before and after deformation. The change in orthogonality after deformation is also measured. Equations yield the principal strains, deviatoric stresses in the absence of surface friction forces, true stresses if the stress normal to the surface is known, and the orientation angle between the deformed gage line and the principal stress-strain axes. Errors in the measurement of nominal strains greater than 3 percent are within engineering accuracy. Applications suggested for this strain measurement system include the large-strain-stress analysis of impact test models, burst tests of spherical or cylindrical pressure vessels, and to augment small-strain instrumentation tests where large strains are anticipated.

Lorentz violation and gravity

NASA Astrophysics Data System (ADS)

Bailey, Quentin G.

2007-08-01

This work explores the theoretical and experimental aspects of Lorentz violation in gravity. A set of modified Einstein field equations is derived from the general Lorentz-violating Standard-Model Extension (SME). Some general theoretical implications of these results are discussed. The experimental consequences for weak-field gravitating systems are explored in the Earth- laboratory setting, the solar system, and beyond. The role of spontaneous Lorentz-symmetry breaking is discussed in the context of the pure-gravity sector of the SME. To establish the low-energy effective Einstein field equations, it is necessary to take into account the dynamics of 20 coefficients for Lorentz violation. As an example, the results are compared with bumblebee models, which are general theories of vector fields with spontaneous Lorentz violation. The field equations are evaluated in the post- newtonian limit using a perfect fluid description of matter. The post-newtonian metric of the SME is derived and compared with some standard test models of gravity. The possible signals for Lorentz violation due to gravity-sector coefficients are studied. Several new effects are identified that have experimental implications for current and future tests. Among the unconventional effects are a new type of spin precession for a gyroscope in orbit and a modification to the local gravitational acceleration on the Earth's surface. These and other tests are expected to yield interesting sensitivities to dimensionless gravity- sector coefficients.

Scaling of mean inertia and theoretical basis for a log law in turbulent boundary layers

NASA Astrophysics Data System (ADS)

Philip, Jimmy; Morrill-Winter, Caleb; Klewicki, Joseph

2017-11-01

Log law in the mean streamwise velocity (U) for pipes/channels is well accepted based on the derivation from the mean momentum balance (MMB) equation and support from experimental data. For flat plate turbulent boundary layers (TBLs), however, there is only empirical evidence and a theoretical underpinning of the kind available for pipes/channels in lacking. The main difficultly is the mean inertia (MI) term in the MMB equation, which, unlike in pipes/channels, is not a constant in TBLs. We present results from our paper (JFM `` 2017, Vol 813, pp 594-617), where the MI term for TBL is transformed so as to render it invariant in the outer region, corroborated with high Re (δ+) data from Melbourne Wind Tunnel and New Hampshire Flow Physics Facility. The transformation is possible because the MI term in the TBL has a `shape' which becomes invariant with increasing δ+ and a `magnitude' which is proportional to 1 /δ+ . The transformed equation is then employed to derive a log law for U with κ an order one (von-Karman) constant. We also show that the log law begins at y+ =C1√{δ+} , and the peak location of the Reynolds shear stress, ym+ =C2√{δ+} , where, C1 3.6 and C2 2.17 are from high Re data. Australian Research Council and the US National Science Foundation.

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.

Hierarchical equations of motion method applied to nonequilibrium heat transport in model molecular junctions: Transient heat current and high-order moments of the current operator

NASA Astrophysics Data System (ADS)

Song, Linze; Shi, Qiang

2017-02-01

We present a theoretical approach to study nonequilibrium quantum heat transport in molecular junctions described by a spin-boson type model. Based on the Feynman-Vernon path integral influence functional formalism, expressions for the average value and high-order moments of the heat current operators are derived, which are further obtained directly from the auxiliary density operators (ADOs) in the hierarchical equations of motion (HEOM) method. Distribution of the heat current is then derived from the high-order moments. As the HEOM method is nonperturbative and capable of treating non-Markovian system-environment interactions, the method can be applied to various problems of nonequilibrium quantum heat transport beyond the weak coupling regime.

Propagation of mechanical waves through a stochastic medium with spherical symmetry

NASA Astrophysics Data System (ADS)

Avendaño, Carlos G.; Reyes, J. Adrián

2018-01-01

We theoretically analyze the propagation of outgoing mechanical waves through an infinite isotropic elastic medium possessing spherical symmetry whose Lamé coefficients and density are spatial random functions characterized by well-defined statistical parameters. We derive the differential equation that governs the average displacement for a system whose properties depend on the radial coordinate. We show that such an equation is an extended version of the well-known Bessel differential equation whose perturbative additional terms contain coefficients that depend directly on the squared noise intensities and the autocorrelation lengths in an exponential decay fashion. We numerically solve the second order differential equation for several values of noise intensities and autocorrelation lengths and compare the corresponding displacement profiles with that of the exact analytic solution for the case of absent inhomogeneities.

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

NASA Astrophysics Data System (ADS)

Sazonov, S. V.; Ustinov, N. V.

2017-02-01

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky-Vakhnenko equation. Different types of solutions of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.

Human body surface area: a theoretical approach.

PubMed

Wang, Jianfeng; Hihara, Eiji

2004-04-01

Knowledge of the human body surface area has important applications in medical practice, garment design, and other engineering sizing. Therefore, it is not surprising that several expressions correlating body surface area with direct measurements of body mass and length have been reported in the literature. In the present study, based on the assumption that the exterior shape of the human body is the result of convex and concave deformations from a basic cylinder, we derive a theoretical equation minimizing body surface area (BSA) at a fixed volume (V): BSA=(9pi VL)(0.5), where L is the reference length of the body. Assuming a body density value of 1,000 kg.m(-3), the equation becomes BSA=(BM.BH/35.37)(0.5), where BSA is in square meters, BM is the body mass in kilograms, and BH is the body height in meters. BSA values calculated by means of this equation fall within +/-7% of the values obtained by means of the equations available in the literature, in the range of BSA from children to adults. It is also suggested that the above equation, which is obtained by minimizing the outer body surface at a fixed volume, implies a fundamental relation set by the geometrical constraints governing the growth and the development of the human body.

Quantum-field-theoretical approach to phase-space techniques: Generalizing the positive-P representation

NASA Astrophysics Data System (ADS)

Plimak, L. I.; Fleischhauer, M.; Olsen, M. K.; Collett, M. J.

2003-01-01

We present an introduction to phase-space techniques (PST) based on a quantum-field-theoretical (QFT) approach. In addition to bridging the gap between PST and QFT, our approach results in a number of generalizations of the PST. First, for problems where the usual PST do not result in a genuine Fokker-Planck equation (even after phase-space doubling) and hence fail to produce a stochastic differential equation (SDE), we show how the system in question may be approximated via stochastic difference equations (SΔE). Second, we show that introducing sources into the SDE’s (or SΔE’s) generalizes them to a full quantum nonlinear stochastic response problem (thus generalizing Kubo’s linear reaction theory to a quantum nonlinear stochastic response theory). Third, we establish general relations linking quantum response properties of the system in question to averages of operator products ordered in a way different from time normal. This extends PST to a much wider assemblage of operator products than are usually considered in phase-space approaches. In all cases, our approach yields a very simple and straightforward way of deriving stochastic equations in phase space.

Salient features of solitary waves in dusty plasma under the influence of Coriolis force

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

Das, G. C.; Nag, Apratim; Department of Physics, G. C. College, Silchar-788004

The main interest is to study the nonlinear acoustic wave in rotating dusty plasma augmented through the derivation of a modified Sagdeev potential equation. Small rotation causes the interaction of Coriolis force in the dynamical system, and leads to the complexity in the derivation of the nonlinear wave equation. As a result, the finding of solitary wave propagation in dusty plasma ought to be of merit. However, the nonlinear wave equation has been successfully solved by the use of the hyperbolic method. Main emphasis has been given to the changes on the evolution and propagation of soliton, and the variationmore » caused by the dusty plasma constituents as well as by the Coriolis force have been highlighted. Some interesting nonlinear wave behavior has been found which can be elaborately studied for the interest of laboratory and space plasmas. Further, to support the theoretical investigations, numeric plasma parameters have been taken for finding the inherent features of solitons.« less

Discontinuous Galerkin Methods for NonLinear Differential Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy; Mansour, Nagi (Technical Monitor)

2001-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

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.

Theoretical study of turbulent channel flow - Bulk properties, pressure fluctuations, and propagation of electromagnetic waves

NASA Technical Reports Server (NTRS)

Canuto, V. M.; Hartke, G. J.; Battaglia, A.; Chasnov, J.; Albrecht, G. F.

1990-01-01

In this paper, we apply two theoretical turbulence models, DIA and the recent GISS model, to study properties of a turbulent channel flow. Both models provide a turbulent kinetic energy spectral function E(k) as the solution of a non-linear equation; the two models employ the same source function but different closures. The source function is characterized by a rate n sub s (k) which is derived from the complex eigenvalues of the Orr-Sommerfeld (OS) equation in which the basic flow is taken to be of a Poiseuille type. The O-S equation is solved for a variety of Reynolds numbers corresponding to available experimental data. A physical argument is presented whereby the central line velocity characterizing the basic flow, U0 sup L, is not to be identified with the U0 appearing in the experimental Reynolds number. The theoretical results are compared with two types of experimental data: (1) turbulence bulk properties, and (2) properties that depend strongly on the structure of the turbulence spectrum at low wave numbers. The only existing analytical expression for Pi (k) cannot be used in the present case because it applies to the case of a flat plate, not a finite channel.

A Comparison of Experimental and Theoretical Results for Labyrinth Gas Seals. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Scharrer, Joseph Kirk

1987-01-01

The basic equations are derived for a two control volume model for compressible flow in a labyrinth seal. The flow is assumed to be completely turbulent and isoenergetic. The wall friction factors are determined using the Blasius formula. Jet flow theory is used for the calculation of the recirculation velocity in the cavity. Linearized zeroth and first order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth order pressure distribution is found by satisfying the leakage equation. The circumferential velocity distribution is determined by satisfying the momentum equations. The first order equations are solved by a separation of variable solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are compared to experimental test results.

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.

A structurally based analytic model of growth and biomass dynamics in single species stands of conifers

Treesearch

Robin J. Tausch

2015-01-01

A theoretically based analytic model of plant growth in single species conifer communities based on the species fully occupying a site and fully using the site resources is introduced. Model derivations result in a single equation simultaneously describes changes over both, different site conditions (or resources available), and over time for each variable for each...

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…

Some Recent Developments in the Endochronic Theory with Application to Cyclic Histories

NASA Technical Reports Server (NTRS)

Valanis, K. C.; Lee, C. F.

1983-01-01

Constitutive equations with only two easily determined material constants predict the stress (strain) response of normalized mild steel to a variety of general strain (stress) histories, without a need for special unloading-reloading rules. The equations are derived from the endochronic theory of plasticity of isotropic materials with an intrinsic time scale defined in the plastic strain space. Agreement between theoretical predictions and experiments are are excellent quantitatively in cases of various uniaxial constant amplitude histories, variable uniaxial strain amplitude histories and cyclic relaxation. The cyclic ratcheting phenomenon is predicted by the present theory.

On magnetoelectric coupling at equilibrium in continua with microstructure

NASA Astrophysics Data System (ADS)

Romeo, Maurizio

2017-10-01

A theory of micromorphic continua, applied to electromagnetic solids, is exploited to study magnetoelectric effects at equilibrium. Microcurrents are modeled by the microgyration tensor of stationary micromotions, compatibly with the balance equations for null microdeformation. The equilibrium of the continuum subject to electric and magnetic fields is reformulated accounting for electric multipoles which are related to microdeformation by evolution equations. Polarization and magnetization are derived for uniform fields under the micropolar reduction in terms of microstrain and octupole structural parameters. Nonlinear dependance on the electromagnetic fields is evidenced, compatibly with known theoretical and experimental results on magnetoelectric coupling.

A NOTE ON THE UNIFIED FIRST LAW IN f(R) GRAVITY THEORY

NASA Astrophysics Data System (ADS)

Zhang, Yi; Gong, Yungui; Zhu, Zong-Hong

2012-04-01

Because of the dynamical equivalence between the f(R) gravity and the Brans-Dicke theory, the dynamical equation in the f(R) gravity is suggested to be derived from a view point of thermodynamics here. By a conformal transformation, the Brans-Dicke theory in the Jordan frame could be expressed as a minimal coupling scalar field theory in Einstein frame. Using the entropy-area relation d˜ {S} = d˜ {A}/4 G, the correct Friedmann equations could be gotten in both frames. Furthermore, we also discuss the corresponding generalized Misner-Sharp energies for theoretical consistence.

Photon emission from quark-gluon plasma out of equilibrium

NASA Astrophysics Data System (ADS)

Hauksson, Sigtryggur; Jeon, Sangyong; Gale, Charles

2018-01-01

The photon emission from a nonequilibrium quark-gluon plasma is analyzed. We derive an integral equation that describes photon production through quark-antiquark annihilation and quark bremsstrahlung. It includes coherence between different scattering sites, also known as the Landau-Pomeranchuk-Migdal effect. These leading-order processes are studied for the first time together in an out-of-equilibrium field theoretical treatment that enables the inclusion of viscous corrections to the calculation of electromagnetic emission rates. In the special case of an isotropic, viscous, plasma the integral equation only depends on three constants, which capture the nonequilibrium nature of the medium.

Asymmetrical booster ascent guidance and control system design study. Volume 5: Space shuttle powered explicit guidance. [space shuttle development

NASA Technical Reports Server (NTRS)

Jaggers, R. F.

1974-01-01

An optimum powered explicit guidance algorithm capable of handling all space shuttle exoatospheric maneuvers is presented. The theoretical and practical basis for the currently baselined space shuttle powered flight guidance equations and logic is documented. Detailed flow diagrams for implementing the steering computations for all shuttle phases, including powered return to launch site (RTLS) abort, are also presented. Derivation of the powered RTLS algorithm is provided, as well as detailed flow diagrams for implementing the option. The flow diagrams and equations are compatible with the current powered flight documentation.

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.

Derivation of an applied nonlinear Schroedinger equation

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

Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens

We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release

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

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

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

Yu, Xiaohui; Lin, Zhijun; Zhang, Jianzhong

2009-01-01

The pressure (P)-volume (V)-temperature (T) measurements were carried out for titanium carbide 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}, fixed at 4.0, we obtain: the ambient bulk modulus K{sub 0} = 268(6) GPa, 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 a{sub T}(K{sup -1}) = a + bT with a =more » 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}a/{partial_derivative}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 thermo physical properties for TiC and are important to theoretical and computational modeling of transition metal carbides.« less

A theoretical model for investigating the effect of vacuum fluctuations on the electromechanical stability of nanotweezers

NASA Astrophysics Data System (ADS)

Farrokhabadi, A.; Mokhtari, J.; Koochi, A.; Abadyan, M.

2015-06-01

In this paper, the impact of the Casimir attraction on the electromechanical stability of nanowire-fabricated nanotweezers is investigated using a theoretical continuum mechanics model. The Dirichlet mode is considered and an asymptotic solution, based on path integral approach, is applied to consider the effect of vacuum fluctuations in the model. The Euler-Bernoulli beam theory is employed to derive the nonlinear governing equation of the nanotweezers. The governing equations are solved by three different approaches, i.e. the modified variation iteration method, generalized differential quadrature method and using a lumped parameter model. Various perspectives of the problem, including the comparison with the van der Waals force regime, the variation of instability parameters and effects of geometry are addressed in present paper. The proposed approach is beneficial for the precise determination of the electrostatic response of the nanotweezers in the presence of Casimir force.

Electron acoustic solitary waves in a magnetized plasma with nonthermal electrons and an electron beam

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

Singh, S. V., E-mail: satyavir@iigs.iigm.res.in; Lakhina, G. S., E-mail: lakhina@iigs.iigm.res.in; University of the Western Cape, Belville

2016-08-15

A theoretical investigation is carried out to study the obliquely propagating electron acoustic solitary waves having nonthermal hot electrons, cold and beam electrons, and ions in a magnetized plasma. We have employed reductive perturbation theory to derive the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation describing the nonlinear evolution of these waves. The two-dimensional plane wave solution of KdV-ZK equation is analyzed to study the effects of nonthermal and beam electrons on the characteristics of the solitons. Theoretical results predict negative potential solitary structures. We emphasize that the inclusion of finite temperature effects reduces the soliton amplitudes and the width of the solitons increasesmore » by an increase in the obliquity of the wave propagation. The numerical analysis is presented for the parameters corresponding to the observations of “burst a” event by Viking satellite on the auroral field lines.« less

Statistical Mechanical Model for Adsorption Coupled with SAFT-VR Mie Equation of State.

PubMed

Franco, Luís F M; Economou, Ioannis G; Castier, Marcelo

2017-10-24

We extend the SAFT-VR Mie equation of state to calculate adsorption isotherms by considering explicitly the residual energy due to the confinement effect. Assuming a square-well potential for the fluid-solid interactions, the structure imposed by the fluid-solid interface is calculated using two different approaches: an empirical expression proposed by Travalloni et al. ( Chem. Eng. Sci. 65 , 3088 - 3099 , 2010 ), and a new theoretical expression derived by applying the mean value theorem. Adopting the SAFT-VR Mie ( Lafitte et al. J. Chem. Phys. , 139 , 154504 , 2013 ) equation of state to describe the fluid-fluid interactions, and solving the phase equilibrium criteria, we calculate adsorption isotherms for light hydrocarbons adsorbed in a carbon molecular sieve and for carbon dioxide, nitrogen, and water adsorbed in a zeolite. Good results are obtained from the model using either approach. Nonetheless, the theoretical expression seems to correlate better the experimental data than the empirical one, possibly implying that a more reliable way to describe the structure ensures a better description of the thermodynamic behavior.

Theoretical Analysis on Mechanical Deformation of Membrane-Based Photomask Blanks

NASA Astrophysics Data System (ADS)

Marumoto, Kenji; Aya, Sunao; Yabe, Hedeki; Okada, Tatsunori; Sumitani, Hiroaki

2012-04-01

Membrane-based photomask is used in proximity X-ray lithography including that in LIGA (Lithographie, Galvanoformung und Abformung) process, and near-field photolithography. In this article, out-of-plane deformation (OPD) and in-plane displacement (IPD) of membrane-based photomask blanks are theoretically analyzed to obtain the mask blanks with flat front surface and low stress absorber film. First, we derived the equations of OPD and IPD for the processing steps of membrane-based photomask such as film deposition, back-etching and bonding, using a theory of symmetrical bending of circular plates with a coaxial circular hole and that of deformation of cylinder under hydrostatic pressure. The validity of the equations was proved by comparing the calculation results with experimental ones. Using these equations, we investigated the relation between the geometry of the mask blanks and the distortions generally, and gave the criterion to attain the flat front surface. Moreover, the absorber stress-bias required to obtain zero-stress on finished mask blanks was also calculated and it has been found that only little stress-bias was required for adequate hole size of support plate.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves.

PubMed

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-11-08

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

PubMed Central

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-01-01

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water. PMID:25383023

Analytical and numerical solution for wave reflection from a porous wave absorber

NASA Astrophysics Data System (ADS)

Magdalena, Ikha; Roque, Marian P.

2018-03-01

In this paper, wave reflection from a porous wave absorber is investigated theoretically and numerically. The equations that we used are based on shallow water type model. Modification of motion inside the absorber is by including linearized friction term in momentum equation and introducing a filtered velocity. Here, an analytical solution for wave reflection coefficient from a porous wave absorber over a flat bottom is derived. Numerically, we solve the equations using the finite volume method on a staggered grid. To validate our numerical model, comparison of the numerical reflection coefficient is made against the analytical solution. Further, we implement our numerical scheme to study the evolution of surface waves pass through a porous absorber over varied bottom topography.

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

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

Sazonov, S. V., E-mail: sazonov.sergey@gmail.com; Ustinov, N. V., E-mail: n-ustinov@mail.ru

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky–Vakhnenko equation. Different types of solutionsmore » of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.« less

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

On some nonlinear effects in ultrasonic fields

PubMed

Tjotta

2000-03-01

Nonlinear effects associated with intense sound fields in fluids are considered theoretically. Special attention is directed to the study of higher effects that cannot be described within the standard propagation models of nonlinear acoustics (the KZK and Burgers equations). The analysis is based on the fundamental equations of motion for a thermoviscous fluid, for which thermal equations of state exist. Model equations are derived and used to analyze nonlinear sources for generation of flow and heat, and other changes in the ambient state of the fluid. Fluctuations in the coefficients of viscosity and thermal conductivity caused by the sound field, are accounted for. Also considered are nonlinear effects induced in the fluid by flexural vibrations. The intensity and absorption of finite amplitude sound waves are calculated, and related to the sources for generation of higher order effects.

A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Zhang, Guoyu; Huang, Chengming; Li, Meng

2018-04-01

We consider the numerical simulation of the coupled nonlinear space fractional Schrödinger equations. Based on the Galerkin finite element method in space and the Crank-Nicolson (CN) difference method in time, a fully discrete scheme is constructed. Firstly, we focus on a rigorous analysis of conservation laws for the discrete system. The definitions of discrete mass and energy here correspond with the original ones in physics. Then, we prove that the fully discrete system is uniquely solvable. Moreover, we consider the unconditionally convergent properties (that is to say, we complete the error estimates without any mesh ratio restriction). We derive L2-norm error estimates for the nonlinear equations and L^{∞}-norm error estimates for the linear equations. Finally, some numerical experiments are included showing results in agreement with the theoretical predictions.

Equation of state and critical point behavior of hard-core double-Yukawa fluids.

PubMed

Montes, J; Robles, M; López de Haro, M

2016-02-28

A theoretical study on the equation of state and the critical point behavior of hard-core double-Yukawa fluids is presented. Thermodynamic perturbation theory, restricted to first order in the inverse temperature and having the hard-sphere fluid as the reference system, is used to derive a relatively simple analytical equation of state of hard-core multi-Yukawa fluids. Using such an equation of state, the compressibility factor and phase behavior of six representative hard-core double-Yukawa fluids are examined and compared with available simulation results. The effect of varying the parameters of the hard-core double-Yukawa intermolecular potential on the location of the critical point is also analyzed using different perspectives. The relevance of this analysis for fluids whose molecules interact with realistic potentials is also pointed out.

Rotating non-Boussinesq convection: oscillating hexagons

NASA Astrophysics Data System (ADS)

Moroz, Vadim; Riecke, Hermann; Pesch, Werner

2000-11-01

Within weakly nonlinear theory hexagon patterns are expected to undergo a Hopf bifurcation to oscillating hexagons when the chiral symmetry of the system is broken. Quite generally, the oscillating hexagons are expected to exhibit bistability of spatio-temporal defect chaos and periodic dynamics. This regime is described by the complex Ginzburg-Landau equation, which has been investigated theoretically in great detail. Its complex dynamics have, however, not been observed in experiments. Starting from the Navier-Stokes equations with realistic boundary conditions, we derive the three coupled real Ginzburg-Landau equations describing hexagons in rotating non-Boussinesq convection. We use them to provide quantitative results for the wavenumber range of stability of the stationary hexagons as well as the range of existence and stability of the oscillating hexagons. Our investigation is complemented by direct numerical simulations of the Navier-Stokes equations.

Theoretical Fluid Mechanics

NASA Astrophysics Data System (ADS)

Fitzpatrick, Richard

2017-12-01

'Theoretical Fluid Mechanics' has been written to aid physics students who wish to pursue a course of self-study in fluid mechanics. It is a comprehensive, completely self-contained text with equations of fluid mechanics derived from first principles, and any required advanced mathematics is either fully explained in the text, or in an appendix. It is accompanied by about 180 exercises with completely worked out solutions. It also includes extensive sections on the application of fluid mechanics to topics of importance in astrophysics and geophysics. These topics include the equilibrium of rotating, self-gravitating, fluid masses; tidal bores; terrestrial ocean tides; and the Eddington solar model.

Propagation of Ion Solitary Pulses in Dense Astrophysical Electron-Positron-Ion Magnetoplasmas

NASA Astrophysics Data System (ADS)

Ata-Ur-Rahman; A. Khan, S.; Qamar, A.

2015-12-01

In this paper, we theoretically investigate the existence and propagation of low amplitude nonlinear ion waves in a dense plasma under the influence of a strong magnetic field. The plasma consists of ultra-relativistic and degenerate electrons and positrons and non-degenerate cold ions. Firstly, the appearance of two distinct linear modes and their evolution is studied by deriving a dispersion equation with the aid of Fourier analysis. Secondly, the dynamics of low amplitude ion solitary structures is investigated via a Korteweg-de Vries equation derived by employing a reductive perturbation method. The effects of various plasma parameters like positron concentration, strength of magnetic field, obliqueness of field, etc., are discussed in detail. At the end, analytical results are supplemented through numerical analysis by using typical representative parameters consistent with degenerate and ultra-relativistic magnetoplasmas of astrophysical regimes.

Anomalous diffusion and scaling in coupled stochastic processes

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

Bel, Golan; Nemenman, Ilya

2009-01-01

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the Pocker-Planck the friction coefficient of the first depends on the state of the second. Integrating out the latter, we derive the Focker-Planck equation for the probability distribution of the former. This has the fonn of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well. Themore » diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standandard, diffusive Langevin descritpion.« less

Efficient field-theoretic simulation of polymer solutions

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

Villet, Michael C.; Fredrickson, Glenn H., E-mail: ghf@mrl.ucsb.edu; Department of Materials, University of California, Santa Barbara, California 93106

2014-12-14

We present several developments that facilitate the efficient field-theoretic simulation of polymers by complex Langevin sampling. A regularization scheme using finite Gaussian excluded volume interactions is used to derive a polymer solution model that appears free of ultraviolet divergences and hence is well-suited for lattice-discretized field theoretic simulation. We show that such models can exhibit ultraviolet sensitivity, a numerical pathology that dramatically increases sampling error in the continuum lattice limit, and further show that this pathology can be eliminated by appropriate model reformulation by variable transformation. We present an exponential time differencing algorithm for integrating complex Langevin equations for fieldmore » theoretic simulation, and show that the algorithm exhibits excellent accuracy and stability properties for our regularized polymer model. These developments collectively enable substantially more efficient field-theoretic simulation of polymers, and illustrate the importance of simultaneously addressing analytical and numerical pathologies when implementing such computations.« less

A higher order numerical method for time fractional partial differential equations with nonsmooth data

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

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

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

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation formore » the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.« less

Electron impact polarization of atomic spectral lines. I - A general theoretical scheme

NASA Technical Reports Server (NTRS)

Fineschi, Silvano; Degl'innocenti, Egidio L.

1992-01-01

A suitable theoretical scheme able to describe, in a wide variety of astrophysical situations, the phenomenon of atomic line polarization by electron impact is developed. Starting from the general principles of quantum mechanics and assuming the Born approximation, the rate equations for the density matrix elements of a multilevel atomic system, interacting with a nonrelativistic electron beam having any kind of angular distribution, are derived in full generality. The resulting theory generalizes the previous ones by accounting for the collisional rates and the cross sections concerning both inelastic and superelastic collisions (in any geometrical situation), and, moreover, by taking into account the coherences among Zeeman sublevels split by a magnetic field. As an example of particular relevance, the general formulas derived in the first sections of the paper are subsequently particularized to the case of the electric dipole interaction.

Differential Geometry Based Multiscale Models

PubMed Central

Wei, Guo-Wei

2010-01-01

Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that are coupled to generalized Navier–Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation. PMID:20169418

A well-posed and stable stochastic Galerkin formulation of the incompressible Navier–Stokes equations with random data

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

Pettersson, Per, E-mail: per.pettersson@uib.no; Nordström, Jan, E-mail: jan.nordstrom@liu.se; Doostan, Alireza, E-mail: alireza.doostan@colorado.edu

2016-02-01

We present a well-posed stochastic Galerkin formulation of the incompressible Navier–Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimatemore » for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.« less

Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics.

PubMed

Yang, Mino

2007-06-07

Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.

Theoretical evaluation of the vapor compression cycle with a liquid-line/suction-line heat exchanger, economizer, and ejector

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

Domanski, P.A.

1995-03-01

The report presents a theoretical analysis of three vapor compression cycles which are derived from the Rankine cycle by incorporating a liquid-line/suction-line heat exchanger, economizer, or ejector. These addendums to the basic cycle reduce throttling losses using different principles, and they require different mechanical hardware of different complexity and cost. The theoretical merits of the three modified cycles were evaluated in relation to the reversed Carnot and Rankine cycle. Thirty-eight fluids were included in the study using the Carnahan-Starling-DeSantis equation of state. In general, the benefit of these addendums increases with the amount of the throttling losses realized by themore » refrigerant in the Rankine cycle.« less

Experimental determination of neutron lifetimes through macroscopic neutron noise in the IPEN/MB-01 reactor

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

Gonnelli, Eduardo; Diniz, Ricardo

2013-05-06

The neutron lifetimes of the core, reflector, and global were experimentally obtained through macroscopic neutron noise in the IPEN/MB-01 reactor for five levels of subcriticality. The theoretical Auto Power Spectral Densities were derived by point kinetic equations taking the reflector effect into account, and one of the approaches consider an additional group of delayed neutrons.

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.

Effects of mean flow on transmission loss of orthogonally rib-stiffened aeroelastic plates.

PubMed

Xin, F X; Lu, T J

2013-06-01

This paper investigates the sound transmission loss (STL) of aeroelastic plates reinforced by two sets of orthogonal rib-stiffeners in the presence of external mean flow. Built upon the periodicity of the structure, a comprehensive theoretical model is developed by considering the convection effect of mean flow. The rib-stiffeners are modeled by employing the Bernoulli-Euler beam theory and the torsional wave equation. While the solution for the transmission loss of the structure based on plate displacement and acoustic pressures is given in the form of space-harmonic series, the corresponding coefficients are obtained from the solution of a system of linear equations derived from the plate-beam coupling vibration governing equation and Helmholtz equation. The model predictions are validated by comparing with existing theoretical and experimental results in the absence of mean flow. A parametric study is subsequently performed to quantify the effects of mean flow as well as structure geometrical parameters upon the transmission loss. It is demonstrated that the transmission loss of periodically rib-stiffened structure is increased significantly with increasing Mach number of mean flow over a wide frequency range. The STL value for the case of sound wave incident downstream is pronouncedly larger than that associated with sound wave incident upstream.

Principles and equations for measuring and interpreting protein stability: From monomer to tetramer.

PubMed

Bedouelle, Hugues

2016-02-01

The ability to measure the thermodynamic stability of proteins with precision is important for both academic and applied research. Such measurements rely on mathematical models of the protein denaturation profile, i.e. the relation between a global protein signal, corresponding to the folding states in equilibrium, and the variable value of a denaturing agent, either heat or a chemical molecule, e.g. urea or guanidinium hydrochloride. In turn, such models rely on a handful of physical laws: the laws of mass action and conservation, the law that relates the protein signal and concentration, and the one that relates stability and denaturant value. So far, equations have been derived mainly for the denaturation profiles of homomeric proteins. Here, we review the underlying basic physical laws and show in detail how to derive model equations for the unfolding equilibria of homomeric or heteromeric proteins up to trimers and potentially tetramers, with or without folding intermediates, and give full demonstrations. We show that such equations cannot be derived for pentamers or higher oligomers except in special degenerate cases. We expand the method to signals that do not correspond to extensive protein properties. We review and expand methods for uncovering hidden intermediates of unfolding. Finally, we review methods for comparing and interpreting the thermodynamic parameters that derive from stability measurements for cognate wild-type and mutant proteins. This work should provide a robust theoretical basis for measuring the stability of complex proteins. Copyright © 2015 Elsevier B.V. and Société Française de Biochimie et Biologie Moléculaire (SFBBM). All rights reserved.

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

Venkatesan, R.C., E-mail: ravi@systemsresearchcorp.com; Plastino, A., E-mail: plastino@fisica.unlp.edu.ar

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS linkmore » and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided. - Highlights: • Legendre transform structure for the RFI is obtained with the Hellmann–Feynman theorem. • Inference of the energy-eigenvalues of the SWE-like equation for the RFI is accomplished. • Basis for reconstruction of the RFI framework from the FIM-case is established. • Substantial qualitative and quantitative distinctions with prior studies are discussed.« less

Theoretical Treatment of Ion Transfers in Two Polarizable Interface Systems When the Analyte Has Access to Both Interfaces.

PubMed

Olmos, José Manuel; Molina, Ángela; Laborda, Eduardo; Millán-Barrios, Enrique; Ortuño, Joaquín Ángel

2018-02-06

A new theory is presented to tackle the study of transfer processes of hydrophilic ions in two polarizable interface systems when the analyte is initially present in both aqueous phases. The treatment is applied to macrointerfaces (linear diffusion) and microholes (highly convergent diffusion), obtaining analytical equations for the current response in any voltammetric technique. The novel equations predict two signals in the current-potential curves that are symmetric when the compositions of the aqueous phases are identical while asymmetries appear otherwise. The theoretical results show good agreement with the experimental behavior of the "double transfer voltammograms" reported by Dryfe et al. in cyclic voltammetry (CV) ( Anal. Chem. 2014 , 86 , 435 - 442 ) as well as with cyclic square wave voltammetry (cSWV) experiments performed in the current work. The theoretical treatment is also extended to the situation where the target ion is lipophilic and initially present in the organic phase. The theory predicts an opposite effect of the lipophilicity of the ion on the shape of the voltammograms, which is validated experimentally via both CV and cSWV. For the above two cases, simple and manageable expressions and diagnosis criteria are derived for the qualitative and quantitative study of ion lipophilicity. The ion-transfer potentials can be easily quantified from the separation between the two signals making use of explicit analytical equations.

Stellar Mass Function of Active and Quiescent Galaxies via the Continuity Equation

NASA Astrophysics Data System (ADS)

Lapi, A.; Mancuso, C.; Bressan, A.; Danese, L.

2017-09-01

The continuity equation is developed for the stellar mass content of galaxies and exploited to derive the stellar mass function of active and quiescent galaxies over the redshift range z˜ 0{--}8. The continuity equation requires two specific inputs gauged from observations: (I) the star formation rate functions determined on the basis of the latest UV+far-IR/submillimeter/radio measurements and (II) average star formation histories for individual galaxies, with different prescriptions for disks and spheroids. The continuity equation also includes a source term taking into account (dry) mergers, based on recent numerical simulations and consistent with observations. The stellar mass function derived from the continuity equation is coupled with the halo mass function and with the SFR functions to derive the star formation efficiency and the main sequence of star-forming galaxies via the abundance-matching technique. A remarkable agreement of the resulting stellar mass functions for active and quiescent galaxies of the galaxy main sequence, and of the star formation efficiency with current observations is found; the comparison with data also allows the characteristic timescales for star formation and quiescence of massive galaxies, the star formation history of their progenitors, and the amount of stellar mass added by in situ star formation versus that contributed by external merger events to be robustly constrained. The continuity equation is shown to yield quantitative outcomes that detailed physical models must comply with, that can provide a basis for improving the (subgrid) physical recipes implemented in theoretical approaches and numerical simulations, and that can offer a benchmark for forecasts on future observations with multiband coverage, as will become routinely achievable in the era of JWST.

Application of ANNs approach for wave-like and heat-like equations

NASA Astrophysics Data System (ADS)

Jafarian, Ahmad; Baleanu, Dumitru

2017-12-01

Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

Accuracy of least-squares methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bochev, Pavel B.; Gunzburger, Max D.

1993-01-01

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Equation of state for technetium from X-ray diffraction and first-principle calculations

NASA Astrophysics Data System (ADS)

Mast, Daniel S.; Kim, Eunja; Siska, Emily M.; Poineau, Frederic; Czerwinski, Kenneth R.; Lavina, Barbara; Forster, Paul M.

2016-08-01

The ambient temperature equation of state (EoS) of technetium metal has been measured by X-ray diffraction. The metal was compressed using a diamond anvil cell and using a 4:1 methanol-ethanol pressure transmitting medium. The maximum pressure achieved, as determined from the gold pressureEquation of state for technetium from X-ray diffraction and first-principle calculations scale, was 67 GPa. The compression data shows that the HCP phase of technetium is stable up to 67 GPa. The compression curve of technetium was also calculated using first-principles total-energy calculations. Utilizing a number of fitting strategies to compare the experimental and theoretical data it is determined that the Vinet equation of state with an ambient isothermal bulk modulus of B0T=288 GPa and a first pressure derivative of B‧=5.9(2) best represent the compression behavior of technetium metal.

Molecular, metabolic, and genetic control: An introduction

NASA Astrophysics Data System (ADS)

Tyson, John J.; Mackey, Michael C.

2001-03-01

The living cell is a miniature, self-reproducing, biochemical machine. Like all machines, it has a power supply, a set of working components that carry out its necessary tasks, and control systems that ensure the proper coordination of these tasks. In this Special Issue, we focus on the molecular regulatory systems that control cell metabolism, gene expression, environmental responses, development, and reproduction. As for the control systems in human-engineered machines, these regulatory networks can be described by nonlinear dynamical equations, for example, ordinary differential equations, reaction-diffusion equations, stochastic differential equations, or cellular automata. The articles collected here illustrate (i) a range of theoretical problems presented by modern concepts of cellular regulation, (ii) some strategies for converting molecular mechanisms into dynamical systems, (iii) some useful mathematical tools for analyzing and simulating these systems, and (iv) the sort of results that derive from serious interplay between theory and experiment.

Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers.

PubMed

Tuan, P H; Wen, C P; Chiang, P Y; Yu, Y T; Liang, H C; Huang, K F; Chen, Y F

2015-04-01

The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the inhomogeneous Helmholtz equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

Communication: Nanoscale electrostatic theory of epistructural fields at the protein-water interface

NASA Astrophysics Data System (ADS)

Fernández, Ariel

2012-12-01

Nanoscale solvent confinement at the protein-water interface promotes dipole orientations that are not aligned with the internal electrostatic field of a protein, yielding what we term epistructural polarization. To quantify this effect, an equation is derived from first principles relating epistructural polarization with the magnitude of local distortions in water coordination causative of interfacial tension. The equation defines a nanoscale electrostatic model of water and enables an estimation of protein denaturation free energies and the inference of hot spots for protein associations. The theoretical results are validated vis-à-vis calorimetric data, revealing the destabilizing effect of epistructural polarization and its molecular origin.

Communication: Nanoscale electrostatic theory of epistructural fields at the protein-water interface.

PubMed

Fernández, Ariel

2012-12-21

Nanoscale solvent confinement at the protein-water interface promotes dipole orientations that are not aligned with the internal electrostatic field of a protein, yielding what we term epistructural polarization. To quantify this effect, an equation is derived from first principles relating epistructural polarization with the magnitude of local distortions in water coordination causative of interfacial tension. The equation defines a nanoscale electrostatic model of water and enables an estimation of protein denaturation free energies and the inference of hot spots for protein associations. The theoretical results are validated vis-à-vis calorimetric data, revealing the destabilizing effect of epistructural polarization and its molecular origin.

The polarized Debye sheath effect on Kadomtsev-Petviashvili electrostatic structures in strongly coupled dusty plasma

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

Shahmansouri, M.; Alinejad, H.

2015-04-15

We give a theoretical investigation on the dynamics of nonlinear electrostatic waves in a strongly coupled dusty plasma with strong electrostatic interaction between dust grains in the presence of the polarization force (i.e., the force due to the polarized Debye sheath). Adopting a reductive perturbation method, we derived a three-dimensional Kadomtsev-Petviashvili equation that describes the evolution of weakly nonlinear electrostatic localized waves. The energy integral equation is used to study the existence domains of the localized structures. The analysis provides the localized structure existence region, in terms of the effects of strong interaction between the dust particles and polarization force.

Theoretical study of the ionospheric G factor

NASA Technical Reports Server (NTRS)

Hagenbuch, K. M.

1972-01-01

A derivation from kinetic theory of the energy balance equation used in wave interaction work is reviewed. Then G is defined and two models for G are presented: one, a model based on Gerjuoy-Stein cross sections for both O2 and N2; the other based on a more recent model for O2 cross sections. The two models differ considerably in their temperature dependence. The limits of applicability of the useful energy balance equation (hence of the concept of G) are discussed and it is found that no difficulty arises unless the transmitter power is more than 1000 times that now employed at the present operating frequency.

Zakharov equations for viscous flow and their use in the blood clot formation

NASA Astrophysics Data System (ADS)

Zhou, Ai-Ping; Li, Xiao-Qing

2017-12-01

For theoretical study, blood can be regarded as a viscous electrically conducting fluid of negative ions and protons. Zakharov equations including viscosity are relevant for describing the behaviour of blood plasma. The dispersion formula is derived from the perturbation method and is solved numerically. It turns out that the imaginary part of one root of the perturbation frequency is greater than zero, and modulation instability occurs. This would lead to the formation of blood clot. The viscous force can suppress the occurrence of instability and prevent thrombosis. One can find that the chaotic state of blood signals human health.

Analytical Characterization on Pulse Propagation in a Semiconductor Optical Amplifier Based on Homotopy Analysis Method

NASA Astrophysics Data System (ADS)

Jia, Xiaofei

2018-06-01

Starting from the basic equations describing the evolution of the carriers and photons inside a semiconductor optical amplifier (SOA), the equation governing pulse propagation in the SOA is derived. By employing homotopy analysis method (HAM), a series solution for the output pulse by the SOA is obtained, which can effectively characterize the temporal features of the nonlinear process during the pulse propagation inside the SOA. Moreover, the analytical solution is compared with numerical simulations with a good agreement. The theoretical results will benefit the future analysis of other problems related to the pulse propagation in the SOA.

Optimal control strategy for an impulsive stochastic competition system with time delays and jumps

NASA Astrophysics Data System (ADS)

Liu, Lidan; Meng, Xinzhu; Zhang, Tonghua

2017-07-01

Driven by both white and jump noises, a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of two species are established. In addition, we obtain that the system is asymptotically stable in distribution by using ergodic method. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of differential equations. Finally, some numerical simulations are provided to illustrate the theoretical results.

Minimization of deviations of gear real tooth surfaces determined by coordinate measurements

NASA Technical Reports Server (NTRS)

Litvin, F. L.; Kuan, C.; Wang, J.-C.; Handschuh, R. F.; Masseth, J.; Maruyama, N.

1992-01-01

The deviations of a gear's real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method was developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine-tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

Analysis of the discontinuous Galerkin method applied to the European option pricing problem

NASA Astrophysics Data System (ADS)

Hozman, J.

2013-12-01

In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.

Fractional vector calculus and fluid mechanics

NASA Astrophysics Data System (ADS)

Lazopoulos, Konstantinos A.; Lazopoulos, Anastasios K.

2017-04-01

Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85-104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy's flow in porous media is studied.

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.

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.

Study of a Car Body Tilting System Using a Variable Link Mechanism: Fundamental Characteristics of Pendulum Motion and Strategy for Perfect Tilting

NASA Astrophysics Data System (ADS)

Yoshida, Hidehisa; Nagai, Masao

This paper analyzes the fundamental dynamic characteristics of a tilting railway vehicle using a variable link mechanism for compensating both the lateral acceleration experienced by passengers and the wheel load imbalance between the inner and outer rails. The geometric relations between the center of rotation, the center of gravity, and the positions of all four links of the tilting system are analyzed. Then, equations of the pendulum motions of the railway vehicle body with a four-link mechanism are derived. A theoretically discussion is given on the geometrical shapes employed in the link mechanism that can simultaneously provide zero lateral acceleration and zero wheel load fluctuation. Then, the perfect tilting condition, which is the control target of the feedforward tilting control, is derived from the linear equation of tilting motion.

Size Effect on Specific Energy Distribution in Particle Comminution

NASA Astrophysics Data System (ADS)

Xu, Yongfu; Wang, Yidong

A theoretical study is made to derive an energy distribution equation for the size reduction process from the fractal model for the particle comminution. Fractal model is employed as a valid measure of the self-similar size distribution of comminution daughter products. The tensile strength of particles varies with particle size in the manner of a power function law. The energy consumption for comminuting single particle is found to be proportional to the 5(D-3)/3rd order of the particle size, D being the fractal dimension of particle comminution daughter. The Weibull statistics is applied to describe the relationship between the breakage probability and specific energy of particle comminution. A simple equation is derived for the breakage probability of particles in view of the dependence of fracture energy on particle size. The calculated exponents and Weibull coefficients are generally in conformity with published data for fracture of particles.

Nonlinear density wave investigation for an extended car-following model considering driver’s memory and jerk

NASA Astrophysics Data System (ADS)

Jin, Zhizhan; Li, Zhipeng; Cheng, Rongjun; Ge, Hongxia

2018-01-01

Based on the two velocity difference model (TVDM), an extended car-following model is developed to investigate the effect of driver’s memory and jerk on traffic flow in this paper. By using linear stability analysis, the stability conditions are derived. And through nonlinear analysis, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are obtained, respectively. The mKdV equation is constructed to describe the traffic behavior near the critical point. The evolution of traffic congestion and the corresponding energy consumption are discussed. Numerical simulations show that the improved model is found not only to enhance the stability of traffic flow, but also to depress the energy consumption, which are consistent with the theoretical analysis.

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

Dynamic field theory and equations of motion in cosmology

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

Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu; Petrov, Alexander N., E-mail: alex.petrov55@gmail.com

2014-11-15

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equationsmore » in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress–energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.« less

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Dynamic modelling of a double-pendulum gantry crane system incorporating payload

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

Ismail, R. M. T. Raja; Ahmad, M. A.; Ramli, M. S.

The natural sway of crane payloads is detrimental to safe and efficient operation. Under certain conditions, the problem is complicated when the payloads create a double pendulum effect. This paper presents dynamic modelling of a double-pendulum gantry crane system based on closed-form equations of motion. The Lagrangian method is used to derive the dynamic model of the system. A dynamic model of the system incorporating payload is developed and the effects of payload on the response of the system are discussed. Extensive results that validate the theoretical derivation are presented in the time and frequency domains.

Modeling and analysis of circular flexural-vibration-mode piezoelectric transformer.

PubMed

Huang, Yihua; Huang, Wei

2010-12-01

We propose a circular flexural-vibration-mode piezoelectric transformer and perform a theoretical analysis of the transformer. An equivalent circuit is derived from the equations of piezoelectricity and the Hamilton's principle. With this equivalent circuit, the voltage gain ratio, input impedance, and the efficiency of the circular flexural-vibration-mode piezoelectric transformer can be determined. The basic behavior of the transformer is shown by numerical results.

A comparison between two powder compaction parameters of plasticity: the effective medium A parameter and the Heckel 1/K parameter.

PubMed

Mahmoodi, Foad; Klevan, Ingvild; Nordström, Josefina; Alderborn, Göran; Frenning, Göran

2013-09-10

The purpose of the research was to introduce a procedure to derive a powder compression parameter (EM A) representing particle yield stress using an effective medium equation and to compare the EM A parameter with the Heckel compression parameter (1/K). 16 pharmaceutical powders, including drugs and excipients, were compressed in a materials testing instrument and powder compression profiles were derived using the EM and Heckel equations. The compression profiles thus obtained could be sub-divided into regions among which one region was approximately linear and from this region, the compression parameters EM A and 1/K were calculated. A linear relationship between the EM A parameter and the 1/K parameter was obtained with a strong correlation. The slope of the plot was close to 1 (0.84) and the intercept of the plot was small in comparison to the range of parameter values obtained. The relationship between the theoretical EM A parameter and the 1/K parameter supports the interpretation of the empirical Heckel parameter as being a measure of yield stress. It is concluded that the combination of Heckel and EM equations represents a suitable procedure to derive a value of particle plasticity from powder compression data. Copyright © 2013 Elsevier B.V. All rights reserved.

Form of the manifestly covariant Lagrangian

NASA Astrophysics Data System (ADS)

Johns, Oliver Davis

1985-10-01

The preferred form for the manifestly covariant Lagrangian function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' Lagrangian and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant Lagrangian theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' Lagrangian, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives Lagrangian theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' Lagrangian is a completely adequate basis for covariant Lagrangian theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the Lagrangian and other four-vector equations.

Unprecedented homotopy perturbation method for solving nonlinear equations in the enzymatic reaction of glucose in a spherical matrix.

PubMed

Saranya, K; Mohan, V; Kizek, R; Fernandez, C; Rajendran, L

2018-02-01

The theory of glucose-responsive composite membranes for the planar diffusion and reaction process is extended to a microsphere membrane. The theoretical model of glucose oxidation and hydrogen peroxide production in the chitosan-aliginate microsphere has been discussed in this manuscript for the first time. We have successfully reported an analytical derived methodology utilizing homotopy perturbation to perform the numerical simulation. The influence and sensitive analysis of various parameters on the concentrations of gluconic acid and hydrogen peroxide are also discussed. The theoretical results enable to predict and optimize the performance of enzyme kinetics.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Viscous regularization of the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations

DOE PAGES

Delchini, Marc O.; Ragusa, Jean C.; Ferguson, Jim

2017-02-17

A viscous regularization technique, based on the local entropy residual, was proposed by Delchini et al. (2015) to stabilize the nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, Delchini et al. (2015) only based their work on the hyperbolic parts of the Grey Radiation-Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here in this paper, we extend the theoretical grounds for the method and derive an entropy minimum principlemore » for the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation-hydrodynamic shock simulations. Radiative shock calculations using constant and temperature-dependent opacities are compared against semi-analytical reference solutions, and we present a procedure to perform spatial convergence studies of such simulations.« less

Amplitude and polarization asymmetries in a ring laser

NASA Technical Reports Server (NTRS)

Campbell, L. L.; Buholz, N. E.

1971-01-01

Asymmetric amplitude effects between the oppositely directed traveling waves in a He-Ne ring laser are analyzed both theoretically and experimentally. These effects make it possible to detect angular orientations of an inner-cavity bar with respect to the plane of the ring cavity. The amplitude asymmetries occur when a birefringent bar is placed in the three-mirror ring cavity, and an axial magnetic field is applied to the active medium. A simplified theoretical analysis is performed by using a first order perturbation theory to derive an expression for the polarization of the active medium, and a set of self-consistent equations are derived to predict threshold conditions. Polarization asymmetries between the oppositely directed waves are also predicted. Amplitude asymmetries similar in nature to those predicted at threshold occur when the laser is operating in 12-15 free-running modes, and polarization asymmetry occurs simultaneously.

Stability and synchronization analysis of inertial memristive neural networks with time delays.

PubMed

Rakkiyappan, R; Premalatha, S; Chandrasekar, A; Cao, Jinde

2016-10-01

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.

Theoretical and Experimental Investigation of the Translational Diffusion of Proteins in the Vicinity of Temperature-Induced Unfolding Transition.

PubMed

Molchanov, Stanislav; Faizullin, Dzhigangir A; Nesmelova, Irina V

2016-10-06

Translational diffusion is the most fundamental form of transport in chemical and biological systems. The diffusion coefficient is highly sensitive to changes in the size of the diffusing species; hence, it provides important information on the variety of macromolecular processes, such as self-assembly or folding-unfolding. Here, we investigate the behavior of the diffusion coefficient of a macromolecule in the vicinity of heat-induced transition from folded to unfolded state. We derive the equation that describes the diffusion coefficient of the macromolecule in the vicinity of the transition and use it to fit the experimental data from pulsed-field-gradient nuclear magnetic resonance (PFG NMR) experiments acquired for two globular proteins, lysozyme and RNase A, undergoing temperature-induced unfolding. A very good qualitative agreement between the theoretically derived diffusion coefficient and experimental data is observed.

Theoretical analysis of heat flow in horizontal ribbon growth from a melt. [silicon metal

NASA Technical Reports Server (NTRS)

Zoutendyk, J. A.

1978-01-01

A theoretical heat flow analysis for horizontalribbon growth is presented. Equations are derived relating pull speed, ribbon thickness, thermal gradient in the melt, and melt temperature for limiting cases of heat removal by radiation only and isothermal heat removal from the solid surface over the melt. Geometrical cross sections of the growth zone are shown to be triangular and nearly parabolic for the two respective cases. Theoretical pull speed for silicon ribbon 0.01 cm thick, where the loss of latent heat of fusion is by radiation to ambient temperature (300 K) only, is shown to be 1 cm/sec for horizontal growth extending 2 cm over the melt and with no heat conduction either to or from the melt. Further enhancement of ribbon growth rate by placing cooling blocks adjacent to the top surface is shown to be theoretically possible.

Linear and nonlinear analysis of fluid slosh dampers

NASA Astrophysics Data System (ADS)

Sayar, B. A.; Baumgarten, J. R.

1982-11-01

A vibrating structure and a container partially filled with fluid are considered coupled in a free vibration mode. To simplify the mathematical analysis, a pendulum model to duplicate the fluid motion and a mass-spring dashpot representing the vibrating structure are used. The equations of motion are derived by Lagrange's energy approach and expressed in parametric form. For a wide range of parametric values the logarithmic decrements of the main system are calculated from theoretical and experimental response curves in the linear analysis. However, for the nonlinear analysis the theoretical and experimental response curves of the main system are compared. Theoretical predictions are justified by experimental observations with excellent agreement. It is concluded finally that for a proper selection of design parameters, containers partially filled with viscous fluids serve as good vibration dampers.

Rate equations for nitrogen molecules in ultrashort and intense x-ray pulses

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

Liu, Ji -Cai; Berrah, Nora; Cederbaum, Lorenz S.

Here, we study theoretically the quantum dynamics of nitrogen molecules (N2) exposed to intense and ultrafast x-rays at a wavelength ofmore » $$1.1\\;{\\rm{nm}}$$ ($$1100\\;{\\rm{eV}}$$ photon energy) from the Linac Coherent Light Source (LCLS) free electron laser. Molecular rate equations are derived to describe the intertwined photoionization, decay, and dissociation processes occurring for N2. This model complements our earlier phenomenological approaches, the single-atom, symmetric-sharing, and fragmentation-matrix models of 2012 (J. Chem. Phys. 136 214310). Our rate-equations are used to obtain the effective pulse energy at the sample and the time scale for the dissociation of the metastable dication $${{\\rm{N}}}_{2}^{2+}$$. This leads to a very good agreement between the theoretically and experimentally determined ion yields and, consequently, the average charge states. The effective pulse energy is found to decrease with shortening pulse duration. This variation together with a change in the molecular fragmentation pattern and frustrated absorption—an effect that reduces absorption of x-rays due to (double) core hole formation—are the causes for the drop of the average charge state with shortening LCLS pulse duration discovered previously.« less

Rate equations for nitrogen molecules in ultrashort and intense x-ray pulses

DOE PAGES

Liu, Ji -Cai; Berrah, Nora; Cederbaum, Lorenz S.; ...

2016-03-16

Here, we study theoretically the quantum dynamics of nitrogen molecules (N2) exposed to intense and ultrafast x-rays at a wavelength ofmore » $$1.1\\;{\\rm{nm}}$$ ($$1100\\;{\\rm{eV}}$$ photon energy) from the Linac Coherent Light Source (LCLS) free electron laser. Molecular rate equations are derived to describe the intertwined photoionization, decay, and dissociation processes occurring for N2. This model complements our earlier phenomenological approaches, the single-atom, symmetric-sharing, and fragmentation-matrix models of 2012 (J. Chem. Phys. 136 214310). Our rate-equations are used to obtain the effective pulse energy at the sample and the time scale for the dissociation of the metastable dication $${{\\rm{N}}}_{2}^{2+}$$. This leads to a very good agreement between the theoretically and experimentally determined ion yields and, consequently, the average charge states. The effective pulse energy is found to decrease with shortening pulse duration. This variation together with a change in the molecular fragmentation pattern and frustrated absorption—an effect that reduces absorption of x-rays due to (double) core hole formation—are the causes for the drop of the average charge state with shortening LCLS pulse duration discovered previously.« less

Contact angle and local wetting at contact line.

PubMed

Li, Ri; Shan, Yanguang

2012-11-06

This theoretical study was motivated by recent experiments and theoretical work that had suggested the dependence of the static contact angle on the local wetting at the triple-phase contact line. We revisit this topic because the static contact angle as a local wetting parameter is still not widely understood and clearly known. To further clarify the relationship of the static contact angle with wetting, two approaches are applied to derive a general equation for the static contact angle of a droplet on a composite surface composed of heterogeneous components. A global approach based on the free surface energy of a thermodynamic system containing the droplet and solid surface shows the static contact angle as a function of local surface chemistry and local wetting state at the contact line. A local approach, in which only local forces acting on the contact line are considered, results in the same equation. The fact that the local approach agrees with the global approach further demonstrates the static contact angle as a local wetting parameter. Additionally, the study also suggests that the wetting described by the Wenzel and Cassie equations is also the local wetting of the contact line rather than the global wetting of the droplet.

Miscible gravitational instability of initially stable horizontal interface in a porous medium: Non-monotonic density profiles

NASA Astrophysics Data System (ADS)

Kim, Min Chan

2014-11-01

To simulate a CO2 sequestration process, some researchers employed a water/propylene glycol (PPG) system which shows a non-monotonic density profile. Motivated by this fact, the stability of the diffusion layer of two miscible fluids saturated in a porous medium is analyzed. For a non-monotonic density profile system, linear stability equations are derived in a global domain, and then transformed into a system of ordinary differential equations in an infinite domain. Initial growth rate analysis is conducted without the quasi-steady state approximation (QSSA) and shows that initially the system is unconditionally stable for the least stable disturbance. For the time evolving case, the ordinary differential equations are solved applying the eigen-analysis and numerical shooting scheme with and without the QSSA. To support these theoretical results, direct numerical simulations are conducted using the Fourier spectral method. The results of theoretical linear stability analyses and numerical simulations validate one another. The present linear and nonlinear analyses show that the water/PPG system is more unstable than the CO2/brine one, and the flow characteristics of these two systems are quite different from each other.

Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential

NASA Astrophysics Data System (ADS)

Kengne, E.; Lakhssassi, A.; Liu, W. M.

2017-08-01

A lossless nonlinear L C transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear L C transmission networks.

Entropy-based separation of yeast cells using a microfluidic system of conjoined spheres

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

Huang, Kai-Jian; Qin, S.-J., E-mail: shuijie.qin@gmail.com; Bai, Zhong-Chen

2013-11-21

A physical model is derived to create a biological cell separator that is based on controlling the entropy in a microfluidic system having conjoined spherical structures. A one-dimensional simplified model of this three-dimensional problem in terms of the corresponding effects of entropy on the Brownian motion of particles is presented. This dynamic mechanism is based on the Langevin equation from statistical thermodynamics and takes advantage of the characteristics of the Fokker-Planck equation. This mechanism can be applied to manipulate biological particles inside a microfluidic system with identical, conjoined, spherical compartments. This theoretical analysis is verified by performing a rapid andmore » a simple technique for separating yeast cells in these conjoined, spherical microfluidic structures. The experimental results basically match with our theoretical model and we further analyze the parameters which can be used to control this separation mechanism. Both numerical simulations and experimental results show that the motion of the particles depends on the geometrical boundary conditions of the microfluidic system and the initial concentration of the diffusing material. This theoretical model can be implemented in future biophysics devices for the optimized design of passive cell sorters.« less

A High Efficiency Boost Converter with MPPT Scheme for Low Voltage Thermoelectric Energy Harvesting

NASA Astrophysics Data System (ADS)

Guan, Mingjie; Wang, Kunpeng; Zhu, Qingyuan; Liao, Wei-Hsin

2016-11-01

Using thermoelectric elements to harvest energy from heat has been of great interest during the last decade. This paper presents a direct current-direct current (DC-DC) boost converter with a maximum power point tracking (MPPT) scheme for low input voltage thermoelectric energy harvesting applications. Zero current switch technique is applied in the proposed MPPT scheme. Theoretical analysis on the converter circuits is explored to derive the equations for parameters needed in the design of the boost converter. Simulations and experiments are carried out to verify the theoretical analysis and equations. A prototype of the designed converter is built using discrete components and a low-power microcontroller. The results show that the designed converter can achieve a high efficiency at low input voltage. The experimental efficiency of the designed converter is compared with a commercial converter solution. It is shown that the designed converter has a higher efficiency than the commercial solution in the considered voltage range.

On the generation and evolution of internal gravity waves

NASA Technical Reports Server (NTRS)

Lansing, F. S.; Maxworthy, T.

1984-01-01

The tidal generation and evolution of internal gravity waves is investigated experimentally and theoretically using a two-dimensional two-layer model. Time-dependent flow is created by moving a profile of maximum submerged depth 7.7 cm through a total stroke of 29 cm in water above a freon-kerosene mixture in an 8.6-m-long 30-cm-deep 20-cm-wide transparent channel, and the deformation of the fluid interface is recorded photographically. A theoretical model of the interface as a set of discrete vortices is constructed numerically; the rigid structures are represented by a source distribution; governing equations in Lagrangian form are obtained; and two integrodifferential equations relating baroclinic vorticity generation and source-density generation are derived. The experimental and computed results are shown in photographs and graphs, respectively, and found to be in good agreement at small Froude numbers. The reasons for small discrepancies in the position of the maximum interface displacement at large Froude numbers are examined.

Study of discrete-particle effects in a one-dimensional plasma simulation with the Krook type collision model

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

Lai, Po-Yen; Chen, Liu; Institute for Fusion Theory and Simulation, Zhejiang University, 310027 Hangzhou

2015-09-15

The thermal relaxation time of a one-dimensional plasma has been demonstrated to scale with N{sub D}{sup 2} due to discrete particle effects by collisionless particle-in-cell (PIC) simulations, where N{sub D} is the particle number in a Debye length. The N{sub D}{sup 2} scaling is consistent with the theoretical analysis based on the Balescu-Lenard-Landau kinetic equation. However, it was found that the thermal relaxation time is anomalously shortened to scale with N{sub D} while externally introducing the Krook type collision model in the one-dimensional electrostatic PIC simulation. In order to understand the discrete particle effects enhanced by the Krook type collisionmore » model, the superposition principle of dressed test particles was applied to derive the modified Balescu-Lenard-Landau kinetic equation. The theoretical results are shown to be in good agreement with the simulation results when the collisional effects dominate the plasma system.« less

Instabilities and patterns in an active nematic film

NASA Astrophysics Data System (ADS)

Srivastava, Pragya; Marchetti, Cristina

2015-03-01

Experiments on microtubule bundles confined to an oil-water interface have motivated extensive theoretical studies of two-dimensional active nematics. Theoretical models taking into account the interplay between activity, flow and order have remarkably reproduced several experimentally observed features of the defect-dynamics in these ``living'' nematics. Here, we derive minimal description of a two-dimensional active nematic film confined between walls. At high friction, we eliminate the flow to obtain closed equations for the nematic order parameter, with renormalized Frank elastic constants. Active processes can render the ``Frank'' constants negative, resulting in the instability of the uniformly ordered nematic state. The minimal model yields emergent patterns of growing complexity with increasing activity, including bands and turbulent dynamics with a steady density of topological defects, as obtained with the full hydrodynamic equations. We report on the scaling of the length scales of these patterns and of the steady state number of defects with activity and system size. National Science Foundation grant DMR-1305184 and Syracuse Soft Matter Program.

The Zero-Point Field and the NASA Challenge to Create the Space Drive

NASA Technical Reports Server (NTRS)

Haisch, Bernhard; Rueda, Alfonso

1999-01-01

This NASA Breakthrough Propulsion Physics Workshop seeks to explore concepts that could someday enable interstellar travel. The effective superluminal motion proposed by Alcubierre (1994) to be a possibility owing to theoretically allowed space-time metric distortions within general relativity has since been shown by Pfenning and Ford (1997) to be physically unattainable. A number of other hypothetical possibilities have been summarized by Millis (1997). We present herein an overview of a concept that has implications for radically new propulsion possibilities and has a basis in theoretical physics: the hypothesis that the inertia and gravitation of matter originate in electromagnetic interactions between the zero-point field (ZPF) and the quarks and electrons constituting atoms. A new derivation of the connection between the ZPF and inertia has been carried through that is properly co-variant, yielding the relativistic equation of motion from Maxwell's equations. This opens new possibilities, but also rules out the basis of one hypothetical propulsion mechanism: Bondi's "negative inertial mass," appears to be an impossibility.

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2004-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

Vibration signal models for fault diagnosis of planet bearings

NASA Astrophysics Data System (ADS)

Feng, Zhipeng; Ma, Haoqun; Zuo, Ming J.

2016-05-01

Rolling element bearings are key components of planetary gearboxes. Among them, the motion of planet bearings is very complex, encompassing spinning and revolution. Therefore, planet bearing vibrations are highly intricate and their fault characteristics are completely different from those of fixed-axis case, making planet bearing fault diagnosis a difficult topic. In order to address this issue, we derive the explicit equations for calculating the characteristic frequency of outer race, rolling element and inner race fault, considering the complex motion of planet bearings. We also develop the planet bearing vibration signal model for each fault case, considering the modulation effects of load zone passing, time-varying angle between the gear pair mesh and fault induced impact force, as well as the time-varying vibration transfer path. Based on the developed signal models, we derive the explicit equations of Fourier spectrum in each fault case, and summarize the vibration spectral characteristics respectively. The theoretical derivations are illustrated by numerical simulation, and further validated experimentally and all the three fault cases (i.e. outer race, rolling element and inner race localized fault) are diagnosed.

Kinematics of Hooke universal joint robot wrists

NASA Technical Reports Server (NTRS)

Mckinney, William S., Jr.

1988-01-01

The singularity problem associated with wrist mechanisms commonly found on industrial manipulators can be alleviated by redesigning the wrist so that it functions as a three-axis gimbal system. This paper discussess the kinematics of gimbal robot wrists made of one and two Hooke universal joints. Derivations of the resolved rate motion control equations for the single and double Hooke universal joint wrists are presented using the three-axis gimbal system as a theoretical wrist model.

E=mc2 in theory and in practice

NASA Astrophysics Data System (ADS)

Friedlander, Michael W.

2009-02-01

Einstein and Oppenheimer are forever linked by that famous equation. Einstein derived it and Oppenheimer oversaw its terrible application. The Meaning of Genius is the subtitle that Silvan Schweber has chosen for his study of these two very different giants. Schweber is a theoretical physicist whose years at the Institute for Advanced Study in Princeton overlapped with those of Einstein and Oppenheimer, for whom he provides a perceptive comparison in his book's introductory chapter.

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.

Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments

DOE PAGES

Nishawala, Vinesh V.; Ostoja-Starzewski, Martin; Leamy, Michael J.; ...

2015-09-10

Peridynamics is a non-local continuum mechanics formulation that can handle spatial discontinuities as the governing equations are integro-differential equations which do not involve gradients such as strains and deformation rates. This paper employs bond-based peridynamics. Cellular Automata is a local computational method which, in its rectangular variant on interior domains, is mathematically equivalent to the central difference finite difference method. However, cellular automata does not require the derivation of the governing partial differential equations and provides for common boundary conditions based on physical reasoning. Both methodologies are used to solve a half-space subjected to a normal load, known as Lamb’smore » Problem. The results are compared with theoretical solution from classical elasticity and experimental results. Furthermore, this paper is used to validate our implementation of these methods.« less

Understanding sport continuation: an integration of the theories of planned behaviour and basic psychological needs.

PubMed

Gucciardi, Daniel F; Jackson, Ben

2015-01-01

Fostering individuals' long-term participation in activities that promote positive development such as organised sport is an important agenda for research and practice. We integrated the theories of planned behaviour (TPB) and basic psychological needs (BPN) to identify factors associated with young adults' continuation in organised sport over a 12-month period. Prospective study, including an online psycho-social assessment at Time 1 and an assessment of continuation in sport approximately 12 months later. Participants (N=292) aged between 17 and 21 years (M=18.03; SD=1.29) completed an online survey assessing the theories of planned behaviour and basic psychological needs constructs. Bayesian structural equation modelling (BSEM) was employed to test the hypothesised theoretical sequence, using informative priors for structural relations based on empirical and theoretical expectations. The analyses revealed support for the robustness of the hypothesised theoretical model in terms of the pattern of relations as well as the direction and strength of associations among the constructs derived from quantitative summaries of existing research and theoretical expectations. The satisfaction of basic psychological needs was associated with more positive attitudes, higher levels of perceived behavioural control, and more favourable subjective norms; positive attitudes and perceived behavioural control were associated with higher behavioural intentions; and both intentions and perceived behavioural control predicted sport continuation. This study demonstrated the utility of Bayesian structural equation modelling for testing the robustness of an integrated theoretical model, which is informed by empirical evidence from meta-analyses and theoretical expectations, for understanding sport continuation. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

Theoretical and numerical study of axisymmetric lattice Boltzmann models

NASA Astrophysics Data System (ADS)

Huang, Haibo; Lu, Xi-Yun

2009-07-01

The forcing term in the lattice Boltzmann equation (LBE) is usually used to mimic Navier-Stokes equations with a body force. To derive axisymmetric model, forcing terms are incorporated into the two-dimensional (2D) LBE to mimic the additional axisymmetric contributions in 2D Navier-Stokes equations in cylindrical coordinates. Many axisymmetric lattice Boltzmann D2Q9 models were obtained through the Chapman-Enskog expansion to recover the 2D Navier-Stokes equations in cylindrical coordinates [I. Halliday , Phys. Rev. E 64, 011208 (2001); K. N. Premnath and J. Abraham, Phys. Rev. E 71, 056706 (2005); T. S. Lee, H. Huang, and C. Shu, Int. J. Mod. Phys. C 17, 645 (2006); T. Reis and T. N. Phillips, Phys. Rev. E 75, 056703 (2007); J. G. Zhou, Phys. Rev. E 78, 036701 (2008)]. The theoretical differences between them are discussed in detail. Numerical studies were also carried out by simulating two different flows to make a comparison on these models’ accuracy and τ sensitivity. It is found all these models are able to obtain accurate results and have the second-order spatial accuracy. However, the model C [J. G. Zhou, Phys. Rev. E 78, 036701 (2008)] is the most stable one in terms of τ sensitivity. It is also found that if density of fluid is defined in its usual way and not directly relevant to source terms, the lattice Boltzmann model seems more stable.

Gravity discharge vessel revisited: An explicit Lambert W function solution

NASA Astrophysics Data System (ADS)

Digilov, Rafael M.

2017-07-01

Based on the generalized Poiseuille equation modified by a kinetic energy correction, an explicit solution for the time evolution of a liquid column draining under gravity through an exit capillary tube is derived in terms of the Lambert W function. In contrast to the conventional exponential behavior, as implied by the Poiseuille law, a new analytical solution gives a full account for the volumetric flow rate of a fluid through a capillary of any length and improves the precision of viscosity determination. The theoretical consideration may be of interest to students as an example of how implicit equations in the field of physics can be solved analytically using the Lambert function.

Numerical stability of an explicit finite difference scheme for the solution of transient conduction in composite media

NASA Technical Reports Server (NTRS)

Campbell, W.

1981-01-01

A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.

Novel models on fluid's variable thermo-physical properties for extensive study on convection heat and mass transfer

NASA Astrophysics Data System (ADS)

Shang, De-Yi; Zhong, Liang-Cai

2017-01-01

Our novel models for fluid's variable physical properties are improved and reported systematically in this work for enhancement of theoretical and practical value on study of convection heat and mass transfer. It consists of three models, namely (1) temperature parameter model, (2) polynomial model, and (3) weighted-sum model, respectively for treatment of temperature-dependent physical properties of gases, temperature-dependent physical properties of liquids, and concentration- and temperature-dependent physical properties of vapour-gas mixture. Two related components are proposed, and involved in each model for fluid's variable physical properties. They are basic physic property equations and theoretical similarity equations on physical property factors. The former, as the foundation of the latter, is based on the typical experimental data and physical analysis. The latter is built up by similarity analysis and mathematical derivation based on the former basic physical properties equations. These models are available for smooth simulation and treatment of fluid's variable physical properties for assurance of theoretical and practical value of study on convection of heat and mass transfer. Especially, so far, there has been lack of available study on heat and mass transfer of film condensation convection of vapour-gas mixture, and the wrong heat transfer results existed in widespread studies on the related research topics, due to ignorance of proper consideration of the concentration- and temperature-dependent physical properties of vapour-gas mixture. For resolving such difficult issues, the present novel physical property models have their special advantages.

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

NASA Astrophysics Data System (ADS)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

Propagation of intense short laser pulses in the atmosphere.

PubMed

Sprangle, P; Peñano, J R; Hafizi, B

2002-10-01

The propagation of short, intense laser pulses in the atmosphere is investigated theoretically and numerically. A set of three-dimensional (3D), nonlinear propagation equations is derived, which includes the effects of dispersion, nonlinear self-focusing, stimulated molecular Raman scattering, multiphoton and tunneling ionization, energy depletion due to ionization, relativistic focusing, and ponderomotively excited plasma wakefields. The instantaneous frequency spread along a laser pulse in air, which develops due to various nonlinear effects, is analyzed and discussed. Coupled equations for the power, spot size, and electron density are derived for an intense ionizing laser pulse. From these equations we obtain an equilibrium for a single optical-plasma filament, which involves a balancing between diffraction, nonlinear self-focusing, and plasma defocusing. The equilibrium is shown to require a specific distribution of power along the filament. It is found that in the presence of ionization a self-guided optical filament is not realizable. A method for generating a remote spark in the atmosphere is proposed, which utilizes the dispersive and nonlinear properties of air to cause a low-intensity chirped laser pulse to compress both longitudinally and transversely. For optimally chosen parameters, we find that the transverse and longitudinal focal lengths can be made to coincide, resulting in rapid intensity increase, ionization, and white light generation in a localized region far from the source. Coupled equations for the laser spot size and pulse duration are derived, which can describe the focusing and compression process in the low-intensity regime. More general examples involving beam focusing, compression, ionization, and white light generation near the focal region are studied by numerically solving the full set of 3D, nonlinear propagation equations.

Modeling NAPL dissolution from pendular rings in idealized porous media

NASA Astrophysics Data System (ADS)

Huang, Junqi; Christ, John A.; Goltz, Mark N.; Demond, Avery H.

2015-10-01

The dissolution rate of nonaqueous phase liquid (NAPL) often governs the remediation time frame at subsurface hazardous waste sites. Most formulations for estimating this rate are empirical and assume that the NAPL is the nonwetting fluid. However, field evidence suggests that some waste sites might be organic wet. Thus, formulations that assume the NAPL is nonwetting may be inappropriate for estimating the rates of NAPL dissolution. An exact solution to the Young-Laplace equation, assuming NAPL resides as pendular rings around the contact points of porous media idealized as spherical particles in a hexagonal close packing arrangement, is presented in this work to provide a theoretical prediction for NAPL-water interfacial area. This analytic expression for interfacial area is then coupled with an exact solution to the advection-diffusion equation in a capillary tube assuming Hagen-Poiseuille flow to provide a theoretical means of calculating the mass transfer rate coefficient for dissolution at the NAPL-water interface in an organic-wet system. A comparison of the predictions from this theoretical model with predictions from empirically derived formulations from the literature for water-wet systems showed a consistent range of values for the mass transfer rate coefficient, despite the significant differences in model foundations (water wetting versus NAPL wetting, theoretical versus empirical). This finding implies that, under these system conditions, the important parameter is interfacial area, with a lesser role played by NAPL configuration.

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.

Subsonic and Supersonic Effects in Bose-Einstein Condensate

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A paper presents a theoretical investigation of subsonic and supersonic effects in a Bose-Einstein condensate (BEC). The BEC is represented by a time-dependent, nonlinear Schroedinger equation that includes terms for an external confining potential term and a weak interatomic repulsive potential proportional to the number density of atoms. From this model are derived Madelung equations, which relate the quantum phase with the number density, and which are used to represent excitations propagating through the BEC. These equations are shown to be analogous to the classical equations of flow of an inviscid, compressible fluid characterized by a speed of sound (g/Po)1/2, where g is the coefficient of the repulsive potential and Po is the unperturbed mass density of the BEC. The equations are used to study the effects of a region of perturbation moving through the BEC. The excitations created by a perturbation moving at subsonic speed are found to be described by a Laplace equation and to propagate at infinite speed. For a supersonically moving perturbation, the excitations are found to be described by a wave equation and to propagate at finite speed inside a Mach cone.

Theoretical study of the kinetics of chlorine atom abstraction from chloromethanes by atomic chlorine.

PubMed

Brudnik, Katarzyna; Twarda, Maria; Sarzyński, Dariusz; Jodkowski, Jerzy T

2013-10-01

Ab initio calculations at the G3 level were used in a theoretical description of the kinetics and mechanism of the chlorine abstraction reactions from mono-, di-, tri- and tetra-chloromethane by chlorine atoms. The calculated profiles of the potential energy surface of the reaction systems show that the mechanism of the studied reactions is complex and the Cl-abstraction proceeds via the formation of intermediate complexes. The multi-step reaction mechanism consists of two elementary steps in the case of CCl4 + Cl, and three for the other reactions. Rate constants were calculated using the theoretical method based on the RRKM theory and the simplified version of the statistical adiabatic channel model. The temperature dependencies of the calculated rate constants can be expressed, in temperature range of 200-3,000 K as [Formula: see text]. The rate constants for the reverse reactions CH3/CH2Cl/CHCl2/CCl3 + Cl2 were calculated via the equilibrium constants derived theoretically. The kinetic equations [Formula: see text] allow a very good description of the reaction kinetics. The derived expressions are a substantial supplement to the kinetic data necessary to describe and model the complex gas-phase reactions of importance in combustion and atmospheric chemistry.

Breakdown of a gas on a metallic surface by CO2 laser pulses of 10-1000 microsec duration

NASA Astrophysics Data System (ADS)

Kovalev, A. S.; Popov, A. M.; Rakhimov, A. T.; Seleznev, B. V.; Khropov, S. M.

1985-04-01

The formation of a plasma on the surface of a metal target under direct exposure to a CO2 laser is studied theoretically. A classical kinetic equation is derived to calculate the critical radiation intensity of several metallic target materials. Experimental measurements of the time to the development of optical breakdown are found to agree with the theoretical results. It is shown that the breakdown discontinuity of the target shifts to the front of the laser pulse if the temperature of the radiation exceeds the critical temperature. No relation was found between the breakdown discontinuity and the boiling point of the metallic target materials.

Spreading of a granular droplet.

PubMed

Sánchez, Iván; Raynaud, Franck; Lanuza, José; Andreotti, Bruno; Clément, Eric; Aranson, Igor S

2007-12-01

The influence of controlled vibrations on the granular rheology is investigated in a specifically designed experiment in which a granular film spreads under the action of horizontal vibrations. A nonlinear diffusion equation is derived theoretically that describes the evolution of the deposit shape. A self-similar parabolic shape (the "granular droplet") and a spreading dynamics are predicted that both agree quantitatively with the experimental results. The theoretical analysis is used to extract effective friction coefficients between the base and the granular layer under sustained and controlled vibrations. A shear thickening regime characteristic of dense granular flows is evidenced at low vibration energy, both for glass beads and natural sand. Conversely, shear thinning is observed at high agitation.

Long-range spin-singlet proximity effect for a Josephson system with a single-crystal ferromagnet due to its band-structure features

NASA Astrophysics Data System (ADS)

Avdeev, M. V.; Proshin, Yu. N.

2018-03-01

A possible explanation for the long-range proximity effect observed in single-crystalline cobalt nanowires sandwiched between two tungsten superconducting electrodes [Nat. Phys. 6, 389 (2010), 10.1038/nphys1621] is proposed. The theoretical model uses properties of a ferromagnet band structure. Specifically, to connect the exchange field with the momentum of quasiparticles the distinction between the effective masses in majority and minority spin subbands and the Fermi-surface anisotropy are considered. The derived Eilenberger-like equations allowed us to obtain a renormalized exchange interaction that is completely compensated for some crystallographic directions under certain conditions. The proposed theoretical model is compared with previous approaches.

Spreading of a granular droplet

NASA Astrophysics Data System (ADS)

Clement, Eric; Sanchez, Ivan; Raynaud, Franck; Lanuza, Jose; Andreotti, Bruno; Aranson, Igor

2008-03-01

The influence of controlled vibrations on the granular rheology is investigated in a specifically designed experiment in which a granular film spreads under the action of horizontal vibrations. A nonlinear diffusion equation is derived theoretically that describes the evolution of the deposit shape. A self-similar parabolic shape (the``granular droplet'') and a spreading dynamics are predicted that both agree quantitatively with the experimental results. The theoretical analysis is used to extract effective friction coefficients between the base and the granular layer under sustained and controlled vibrations. A shear thickening regime characteristic of dense granular flows is evidenced at low vibration energy, both for glass beads and natural sand. Conversely, shear thinning is observed at high agitation.

Spreading of a granular droplet

NASA Astrophysics Data System (ADS)

Sánchez, Iván; Raynaud, Franck; Lanuza, José; Andreotti, Bruno; Clément, Eric; Aranson, Igor S.

2007-12-01

The influence of controlled vibrations on the granular rheology is investigated in a specifically designed experiment in which a granular film spreads under the action of horizontal vibrations. A nonlinear diffusion equation is derived theoretically that describes the evolution of the deposit shape. A self-similar parabolic shape (the“granular droplet”) and a spreading dynamics are predicted that both agree quantitatively with the experimental results. The theoretical analysis is used to extract effective friction coefficients between the base and the granular layer under sustained and controlled vibrations. A shear thickening regime characteristic of dense granular flows is evidenced at low vibration energy, both for glass beads and natural sand. Conversely, shear thinning is observed at high agitation.

A novel frequency tuned wireless actuator with snake-like motion

NASA Astrophysics Data System (ADS)

Zhang, Kewei; Zhu, Qianke; Chai, Yuesheng

2016-07-01

In this work, we propose a novel wireless actuator which is composed of magnetostrictive material/copper bi-layer film. The actuator can be controlled to move like a snake bi-directionally along a pipe by tuning the frequency of external magnetic field near its first order resonant frequency. The governing equation for the actuator is established and the vibration mode shape function is derived. Theoretical analysis shows that motion of the actuator is achieved by asymmetric vibration mode shape, specific vibration bending deformation, and effective net total impacting force. The simulation and experimental results well confirm the theoretical analysis. This work provides contribution to the development of wireless micro robots and autonomous magnetostrictive sensors.

Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems

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

Deumens, E.; Diz, A.; Longo, R.

1994-07-01

An overview is presented of methods for time-dependent treatments of molecules as systems of electrons and nuclei. The theoretical details of these methods are reviewed and contrasted in the light of a recently developed time-dependent method called electron-nuclear dynamics. Electron-nuclear dynamics (END) is a formulation of the complete dynamics of electrons and nuclei of a molecular system that eliminates the necessity of constructing potential-energy surfaces. Because of its general formulation, it encompasses many aspects found in other formulations and can serve as a didactic device for clarifying many of the principles and approximations relevant in time-dependent treatments of molecular systems.more » The END equations are derived from the time-dependent variational principle applied to a chosen family of efficiently parametrized approximate state vectors. A detailed analysis of the END equations is given for the case of a single-determinantal state for the electrons and a classical treatment of the nuclei. The approach leads to a simple formulation of the fully nonlinear time-dependent Hartree-Fock theory including nuclear dynamics. The nonlinear END equations with the [ital ab] [ital initio] Coulomb Hamiltonian have been implemented at this level of theory in a computer program, ENDyne, and have been shown feasible for the study of small molecular systems. Implementation of the Austin Model 1 semiempirical Hamiltonian is discussed as a route to large molecular systems. The linearized END equations at this level of theory are shown to lead to the random-phase approximation for the coupled system of electrons and nuclei. The qualitative features of the general nonlinear solution are analyzed using the results of the linearized equations as a first approximation. Some specific applications of END are presented, and the comparison with experiment and other theoretical approaches is discussed.« less

Remote sensing of earth terrain

NASA Technical Reports Server (NTRS)

Yueh, Herng-Aung; Kong, Jin AU

1991-01-01

In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.

Out-of-equilibrium dynamical mean-field equations for the perceptron model

NASA Astrophysics Data System (ADS)

Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco

2018-02-01

Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.

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

Half-cell potentials of semiconductive simple binary sulphides in aqueous solution

USGS Publications Warehouse

Sato, M.

1966-01-01

Theoretical consideration of the charge-transfer mechanism operative in cells with an electrode of a semiconductive binary compound leads to the conclusion that the half-cell potential of such a compound is not only a function of ionic activities in the electrolytic solution, but also a function of the activities of the component elements in the compound phase. The most general form of the electrode equation derived for such a compound with a formula MiXj which dissociates into Mj+ and Xi- ions in aqueous solution is. EMiXj = EMiXj0 + R T 2 ij ln [ (sua Mj+)aqi ?? (suaX)jMiXj/ (suaXi-)aqj ?? (suaM)iMiXj],. where. EMiXj0 = 1 2(EM,Mj+0 + EXi-,X). The equation can be modified to other forms. When applied to semiconductive simple binary sulphides, these equations appear to give better descriptions of the observed electrode potentials of such sulphides than any other proposed equations. ?? 1966.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

The development of methods for the prediction of primary creep behavior in metals

NASA Technical Reports Server (NTRS)

Zerwekh, R. P.

1978-01-01

The applicability of a thermodynamic constitutive theory of deformation to the prediction of primary creep and creep strain relaxation behavior in metals is examined. Constitutive equations derived from the theory are subjected to a parametric analysis in order to determine the influence of several parameters on the curve forms generated by the equations. A computer program is developed which enables the solution of a generalized constitutive equation using experimental data as input. Several metals were tested to form a data base of primary creep and relaxation behavior. The extent to which these materials conformed to the constitutive equation showed wide variability, with the alloy Ti-6Al-4V exhibiting the most consistent results. Accordingly, most of the analysis is concentrated upon data from that alloy, although creep and relaxation data from all the materials tested are presented. Experimental methods are outlined as well as some variations in methods of analysis. Various theoretical and practical implications of the work are discussed.

Use of source distributions for evaluating theoretical aerodynamics of thin finite wings at supersonic speeds

NASA Technical Reports Server (NTRS)

Evvard, John C

1950-01-01

A series of publications on the source-distribution methods for evaluating the aerodynamics of thin wings at supersonic speeds is summarized, extended, and unified. Included in the first part are the deviations of: (a) the linearized partial-differential equation for unsteady flow at a substantially constant Mach number. b) The source-distribution solution for the perturbation-velocity potential that satisfies the boundary conditions of tangential flow at the surface and in the plane of the wing; and (c) the integral equation for determining the strength and the location of sources to describe the interaction effects (as represented by upwash) of the bottom and top wing surfaces through the region between the finite wing boundary and the foremost Mach wave. The second part deals with steady-state thin-wing problems. The third part of the report approximates the integral equation for unsteady upwash and includes a solution of approximate equation. Expressions are then derived to evaluate the load distributions for time-dependent finite-wing motions.

Temperature lowering program for homogeneous doping in flux growth

NASA Astrophysics Data System (ADS)

Qiwei, Wang; Shouquan, Jia

1989-10-01

Based on the mass conservation law and the Burton-Prim-Slichter equation, the temperature program for homogeneous doping in flux growth by slow cooling was derived. The effect of various factors, such as initial supersaturation, solution volume, growth kinetic coefficient and degree of mixing in the solution on growth rate, crystal size and temperature program is discussed in detail. Theoretical analysis shows that there is a critical crystal size above which homogeneous doping is impossible.

Bounds on the performance of a class of digital communication systems

NASA Technical Reports Server (NTRS)

Polk, D. R.; Gupta, S. C.; Cohn, D. L.

1973-01-01

Bounds on the capacity of a class of digital communication channels are derived. Equating the bounds on capacity to rate-distortion functions of (typical) sources in turn produces bounds on the performance of a class of digital communication systems. For ratios of squared quantization level to noise variance much less than one, the power requirements for this class of digital communication systems are shown to be within approximately 3 dB of the theoretical optimum.

Global hot-star wind models for stars from Magellanic Clouds

NASA Astrophysics Data System (ADS)

Krtička, J.; Kubát, J.

2018-04-01

We provide mass-loss rate predictions for O stars from Large and Small Magellanic Clouds. We calculate global (unified, hydrodynamic) model atmospheres of main sequence, giant, and supergiant stars for chemical composition corresponding to Magellanic Clouds. The models solve radiative transfer equation in comoving frame, kinetic equilibrium equations (also known as NLTE equations), and hydrodynamical equations from (quasi-)hydrostatic atmosphere to expanding stellar wind. The models allow us to predict wind density, velocity, and temperature (consequently also the terminal wind velocity and the mass-loss rate) just from basic global stellar parameters. As a result of their lower metallicity, the line radiative driving is weaker leading to lower wind mass-loss rates with respect to the Galactic stars. We provide a formula that fits the mass-loss rate predicted by our models as a function of stellar luminosity and metallicity. On average, the mass-loss rate scales with metallicity as Ṁ Z0.59. The predicted mass-loss rates are lower than mass-loss rates derived from Hα diagnostics and can be reconciled with observational results assuming clumping factor Cc = 9. On the other hand, the predicted mass-loss rates either agree or are slightly higher than the mass-loss rates derived from ultraviolet wind line profiles. The calculated P V ionization fractions also agree with values derived from observations for LMC stars with Teff ≤ 40 000 K. Taken together, our theoretical predictions provide reasonable models with consistent mass-loss rate determination, which can be used for quantitative study of stars from Magellanic Clouds.

Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows.

PubMed

Abel, I G; Plunk, G G; Wang, E; Barnes, M; Cowley, S C; Dorland, W; Schekochihin, A A

2013-11-01

This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ε = ρi/α of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad-Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the 'high-flow' gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.

A theoretical investigation of the rolling oscillations of an airplane with ailerons free

NASA Technical Reports Server (NTRS)

Cohen, Doris

1944-01-01

An analysis is made of the stability of an airplane with ailerons free, with particular attention to the motions when the ailerons have a tendency to float against the wind. The present analysis supersedes the aileron investigation contained in NACA Technical Report no. 709. The equations of motion are first written to include yawing and sideslipping, and it is demonstrated that the principal effects of freeing the ailerons can be determined without regard to these motions. If the ailerons tend to float against the wind and have a high degree of aerodynamic balance, rolling oscillations, in addition to the normal lateral oscillations, are likely to occur. On the basis of the equations including only the rolling motion and the aileron deflection, formulas derived for the stability and damping of the rolling oscillations in terms of the hinge-moment derivatives are also presented showing the oscillatory regions and stability boundaries for a fictitious airplane of conventional proportion. The effects of friction in the control system are investigated and discussed.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Radon exhalation rates from building materials using electret ion chamber radon monitors in accumulators.

PubMed

Kotrappa, Payasada; Stieff, Frederick

2009-08-01

An electret ion chamber (EIC) radon monitor in a sealed accumulator measures the integrated average radon concentration at the end of the accumulation duration. Theoretical equations have been derived to relate such radon concentrations (Bq m(-3) ) to the radon emanation rate (Bq d(-1)) from building materials enclosed in the accumulator. As an illustration, a 4-L sealable glass jar has been used as an accumulator to calculate the radon emanation rate from different granite samples. The radon emanation rate was converted into radon flux (Bq mm(-2) d(-1)) by dividing the emanation rate by surface area of the sample. Fluxes measured on typical, commercially available granites ranged from 20-30 Bq m(-2) d(-1). These results are similar to the results reported in the literature. The lower limit of detection for a 2-d measurement works out to be 7 Bq m(-2) d(-1). Equations derived can also be used for other sealable accumulators and other integrating detectors, such as alpha track detectors.

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

Akdoğan, Ender, E-mail: ender.akdogan@tpe.gov.tr; Çiftçi, Muharrem, E-mail: muharrem-ciftci@windowslive.com

This article is based on the master thesis [4] related to our invention which was published in World Intellectual Property Organization (WO/2011/048506) as a microwave water heater. In the project, a prototype was produced to use microwave in industrial heating. In order to produce the prototype, the most appropriate material kind for microwave-water experiments was determined by a new energy loss rate calculation technique. This new energy loss calculation is a determinative factor for material permeability at microwave frequency band (1-100 GHz). This experimental series aim to investigate the rationality of using microwave in heating industry. Theoretically, heating water by microwavemore » (with steady frequency 2.45 GHz) is analyzed from sub-molecular to Classical Mechanic results of heating. In the study, we examined Quantum Mechanical base of heating water by microwave experiments. As a result, we derived a Semi-Quantum Mechanical equation for microwave-water interactions and thus, Wien displacement law can be derived to verify experimental observations by this equation.« less

SVBRDF-Invariant Shape and Reflectance Estimation from a Light-Field Camera.

PubMed

Wang, Ting-Chun; Chandraker, Manmohan; Efros, Alexei A; Ramamoorthi, Ravi

2018-03-01

Light-field cameras have recently emerged as a powerful tool for one-shot passive 3D shape capture. However, obtaining the shape of glossy objects like metals or plastics remains challenging, since standard Lambertian cues like photo-consistency cannot be easily applied. In this paper, we derive a spatially-varying (SV)BRDF-invariant theory for recovering 3D shape and reflectance from light-field cameras. Our key theoretical insight is a novel analysis of diffuse plus single-lobe SVBRDFs under a light-field setup. We show that, although direct shape recovery is not possible, an equation relating depths and normals can still be derived. Using this equation, we then propose using a polynomial (quadratic) shape prior to resolve the shape ambiguity. Once shape is estimated, we also recover the reflectance. We present extensive synthetic data on the entire MERL BRDF dataset, as well as a number of real examples to validate the theory, where we simultaneously recover shape and BRDFs from a single image taken with a Lytro Illum camera.

The compressibility and the capacitance coefficient of helium-oxygen atmospheres.

PubMed

Imbert, G; Dejours, P; Hildwein, G

1982-12-01

The capacitance coefficient beta of an ideal gas mixture depends only on its temperature T, and its value is derived from the ideal gas law (i.e., beta = 1/RT, R being the ideal gas constant). But real gases behave as ideal gases only at low pressures, and this would not be the case in deep diving. High pressures of helium-oxygen are used in human and animal experimental dives (up to 7 or 12 MPa or more, respectively). At such pressures deviations from the ideal gas law cannot be neglected in hyperbaric atmospheres with respect to current accuracy of measuring instruments. As shown both theoretically and experimentally by this study, the non-ideal nature of helium-oxygen has a significant effect on the capacitance coefficient of hyperbaric atmospheres. The theoretical study is based on interaction energy in either homogeneous (He-He and O2-O2) or heterogeneous (He-O2) molecular pairs, and on the virial equation of state for gas mixtures. The experimental study is based on weight determination of samples of known volume of binary helium-oxygen mixtures, which are prepared in well-controlled pressure and temperature conditions. Our experimental results are in good agreement with theoretical predictions. 1) The helium compressibility factor ZHe increases linearly with pressure [ZHe = 1 + 0.0045 P (in MPa) at 30 degrees C]; and 2) in same temperature and pressure conditions (T = 303 K and P = 0.1 to 15 MPa), the same value for Z is valid for a helium-oxygen binary mixture and for pure helium. As derived from the equation of state of real gases, the capacitance coefficient is inversely related to Z (beta = 1/ZRT); therefore, for helium-oxygen mixtures, this coefficient would decrease with increasing pressure. A table is given for theoretical values of helium-oxygen capacitance coefficient, at pressures ranging from 0.1 to 15.0 MPa and at temperatures ranging from 25 degrees C to 37 degrees C.

Electron energy distribution function in the positive column of a neon glow discharge using the black wall approximation

NASA Astrophysics Data System (ADS)

Al-Hawat, Sh; Naddaf, M.

2005-04-01

The electron energy distribution function (EEDF) was determined from the second derivative of the I-V Langmuir probe characteristics and, thereafter, theoretically calculated by solving the plasma kinetic equation, using the black wall (BW) approximation, in the positive column of a neon glow discharge. The pressure has been varied from 0.5 to 4 Torr and the current from 10 to 30 mA. The measured electron temperature, density and electric field strength were used as input data for solving the kinetic equation. Comparisons were made between the EEDFs obtained from experiment, the BW approach, the Maxwellian distribution and the Rutcher solution of the kinetic equation in the elastic energy range. The best conditions for the BW approach are found to be under the discharge conditions: current density jd = 4.45 mA cm-2 and normalized electric field strength E/p = 1.88 V cm-1 Torr-1.

Equation of state for technetium from X-ray diffraction and first-principle calculations

DOE PAGES

Mast, Daniel S.; Kim, Eunja; Siska, Emily M.; ...

2016-03-20

Here, the ambient temperature equation of state (EoS) of technetium metal has been measured by X-ray diffraction. The metal was compressed using a diamond anvil cell and using a 4:1 methanol-ethanol pressure transmitting medium. The maximum pressure achieved, as determined from the gold pressure scale, was 67 GPa. The compression data shows that the HCP phase of technetium is stable up to 67 GPa. The compression curve of technetium was also calculated using first-principles total-energy calculations. Utilizing a number of fitting strategies to compare the experimental and theoretical data it is determined that the Vinet equation of state with anmore » ambient isothermal bulk modulus of B 0T = 288 GPa and a first pressure derivative of B' = 5.9(2) best represent the compression behavior of technetium metal.« less

Consistent transport coefficients in astrophysics

NASA Technical Reports Server (NTRS)

Fontenla, Juan M.; Rovira, M.; Ferrofontan, C.

1986-01-01

A consistent theory for dealing with transport phenomena in stellar atmospheres starting with the kinetic equations and introducing three cases (LTE, partial LTE, and non-LTE) was developed. The consistent hydrodynamical equations were presented for partial-LTE, the transport coefficients defined, and a method shown to calculate them. The method is based on the numerical solution of kinetic equations considering Landau, Boltzmann, and Focker-Planck collision terms. Finally a set of results for the transport coefficients derived for a partially ionized hydrogen gas with radiation was shown, considering ionization and recombination as well as elastic collisions. The results obtained imply major changes is some types of theoretical model calculations and can resolve some important current problems concerning energy and mass balance in the solar atmosphere. It is shown that energy balance in the lower solar transition region can be fully explained by means of radiation losses and conductive flux.

Solitary Potential in a Space Plasma Containing Dynamical Heavy Ions and Bi-Kappa Distributed Electrons of Two Distinct Temperatures

NASA Astrophysics Data System (ADS)

Sarker, M.; Hosen, B.; Hossen, M. R.; Mamun, A. A.

2018-01-01

The heavy ion-acoustic solitary waves (HIASWs) in a magnetized, collisionless, space plasma system (containing dynamical heavy ions and bi-kappa distributed electrons of two distinct temperatures) have been theoretically investigated. The Korteweg-de Vries (K-dV), modified K-dV (MK-dV), and higher-order MK-dV (HMK-dV) equations are derived by employing the reductive perturbation method. The basic features of HIASWs (viz. speed, polarity, amplitude, width, etc.) are found to be significantly modified by the effects of number density and temperature of different plasma species, and external magnetic field (obliqueness). The K-dV and HM-KdV equations give rise to both compressive and rarefactive solitary structures, whereas the MK-dV equation supports only the compressive solitary structures. The implication of our results in some space and laboratory plasma situations are briefly discussed.

Temporal cross-correlation asymmetry and departure from equilibrium in a bistable chemical system.

PubMed

Bianca, C; Lemarchand, A

2014-06-14

This paper aims at determining sustained reaction fluxes in a nonlinear chemical system driven in a nonequilibrium steady state. The method relies on the computation of cross-correlation functions for the internal fluctuations of chemical species concentrations. By employing Langevin-type equations, we derive approximate analytical formulas for the cross-correlation functions associated with nonlinear dynamics. Kinetic Monte Carlo simulations of the chemical master equation are performed in order to check the validity of the Langevin equations for a bistable chemical system. The two approaches are found in excellent agreement, except for critical parameter values where the bifurcation between monostability and bistability occurs. From the theoretical point of view, the results imply that the behavior of cross-correlation functions cannot be exploited to measure sustained reaction fluxes in a specific nonlinear system without the prior knowledge of the associated chemical mechanism and the rate constants.

Theoretical Evaluation of the Maximum Work of Free-Piston Engine Generators

NASA Astrophysics Data System (ADS)

Kojima, Shinji

2017-01-01

Utilizing the adjoint equations that originate from the calculus of variations, we have calculated the maximum thermal efficiency that is theoretically attainable by free-piston engine generators considering the work loss due to friction and Joule heat. Based on the adjoint equations with seven dimensionless parameters, the trajectory of the piston, the histories of the electric current, the work done, and the two kinds of losses have been derived in analytic forms. Using these we have conducted parametric studies for the optimized Otto and Brayton cycles. The smallness of the pressure ratio of the Brayton cycle makes the net work done negative even when the duration of heat addition is optimized to give the maximum amount of heat addition. For the Otto cycle, the net work done is positive, and both types of losses relative to the gross work done become smaller with the larger compression ratio. Another remarkable feature of the optimized Brayton cycle is that the piston trajectory of the heat addition/disposal process is expressed by the same equation as that of an adiabatic process. The maximum thermal efficiency of any combination of isochoric and isobaric heat addition/disposal processes, such as the Sabathe cycle, may be deduced by applying the methods described here.

A piecewise mass-spring-damper model of the human breast.

PubMed

Cai, Yiqing; Chen, Lihua; Yu, Winnie; Zhou, Jie; Wan, Frances; Suh, Minyoung; Chow, Daniel Hung-Kay

2018-01-23

Previous models to predict breast movement whilst performing physical activities have, erroneously, assumed uniform elasticity within the breast. Consequently, the predicted displacements have not yet been satisfactorily validated. In this study, real time motion capture of the natural vibrations of a breast that followed, after raising and allowing it to fall freely, revealed an obvious difference in the vibration characteristics above and below the static equilibrium position. This implied that the elastic and viscous damping properties of a breast could vary under extension or compression. Therefore, a new piecewise mass-spring-damper model of a breast was developed with theoretical equations to derive values for its spring constants and damping coefficients from free-falling breast experiments. The effective breast mass was estimated from the breast volume extracted from a 3D body scanned image. The derived spring constant (k a  = 73.5 N m -1 ) above the static equilibrium position was significantly smaller than that below it (k b  = 658 N m -1 ), whereas the respective damping coefficients were similar (c a  = 1.83 N s m -1 , c b  = 2.07 N s m -1 ). These values were used to predict the nipple displacement during bare-breasted running for validation. The predicted and experimental results had a 2.6% or less root-mean-square-error of the theoretical and experimental amplitudes, so the piecewise mass-spring-damper model and equations were considered to have been successfully validated. This provides a theoretical basis for further research into the dynamic, nonlinear viscoelastic properties of different breasts and the prediction of external forces for the necessary breast support during different sports activities. Copyright © 2017 Elsevier Ltd. All rights reserved.

Theoretical study of the kinetics of reactions of the monohalogenated methanes with atomic chlorine.

PubMed

Brudnik, Katarzyna; Twarda, Maria; Sarzyński, Dariusz; Jodkowski, Jerzy T

2013-04-01

Ab initio calculations at the G2 level were used in a theoretical description of the kinetics and mechanism of the hydrogen abstraction reactions from fluoro-, chloro- and bromomethane by chlorine atoms. The profiles of the potential energy surfaces show that mechanism of the reactions under investigation is complex and consists of two - in the case of CH3F+Cl - and of three elementary steps for CH3Cl+Cl and CH3Br+Cl. The heights of the energy barrier related to the H-abstraction are of 8-10 kJ mol(-1), the lowest value corresponds to CH3Cl+Cl and the highest one to CH3F+Cl. The rate constants were calculated using the theoretical method based on the RRKM theory and the simplified version of the statistical adiabatic channel model. The kinetic equations derived in this study[Formula: see text]and[Formula: see text]allow a description of the kinetics of the reactions under investigation in the temperature range of 200-3000 K. The kinetics of reactions of the entirely deuterated reactants were also included in the kinetic analysis. Results of ab initio calculations show that D-abstraction process is related with the energy barrier of 5 kJ mol(-1) higher than the H-abstraction from the corresponding non-deuterated reactant molecule. The derived analytical equations for the reactions, CD3X+Cl, CH2X+HCl and CD2X+DCl (X = F, Cl and Br) are a substantial supplement of the kinetic data necessary for the description and modeling of the processes of importance in the atmospheric chemistry.

Analysis of the electromechanical characteristics of a piezoelectric multilayered structure for in-air ultrasound radiation

NASA Astrophysics Data System (ADS)

Shim, Hayeong; Roh, Yongrae

2018-07-01

Ultrasonic sensors in air are used to measure distances from obstacles in household appliances, automobiles, and other areas. Among these ultrasonic sensors in air, sensors using disk-shaped piezoelectric ceramics are composed of a multilayered structure having a vibrational plate, a piezoelectric ceramic disk, and a backing layer. In this study, we derived theoretical equations that can accurately analyze the acoustic characteristics of the piezoelectric multilayered structure, and then analyzed the performance of the ultrasonic sensor according to the geometrical change of the multilayered structure. The characteristics analyzed were the resonant frequency and the radiated sound pressure at a far field of the sensor. The validity of the theoretical analysis was verified by comparing the results with those obtained from the finite element analysis of the same structure. The exact functional forms of the resonant frequency of and the radiated sound pressure from the piezoelectric multilayered structure derived in this study can be directly utilized to maximize the performance of various ultrasonic sensors in air.

Theoretical analysis of shock induced depolarization and current generation in ferroelectrics

NASA Astrophysics Data System (ADS)

Agrawal, Vinamra; Bhattacharya, Kaushik

Ferroelectric generators are used to generate large magnitude current pulse by impacting a polarized ferroelectric material. The impact causes depolarization of the material and at high impact speeds, dielectric breakdown. Depending on the loading conditions and the electromechanical boundary conditions, the current or voltage profiles obtained vary. In this study, we explore the large deformation dynamic response of a ferroelectric material. Using the Maxwell's equations, conservation laws and the second law of thermodynamics, we derive the governing equations for the phase boundary propagation as well as the driving force acting on it. We allow for the phase boundary to contain surface charges which introduces the contribution of curvature of phase boundary in the governing equations and the driving force. This type of analysis accounts for the dielectric breakdown and resulting conduction in the material. Next, we implement the equations derived to solve a one dimensional impact problem on a ferroelectric material under different electrical boundary conditions. The constitutive law is chosen to be piecewise quadratic in polarization and quadratic in the strain. We solve for the current profile generated in short circuit case and for voltage profile in open circuited case. This work was made possible by the financial support of the US Air Force Office of Scientific Research through the Center of Excellence in High Rate Deformation Physics of Heterogeneous Materials (Grant: FA 9550-12-1-0091).

Improving traditional balancing methods for high-speed rotors

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

Ling, J.; Cao, Y.

1996-01-01

This paper introduces frequency response functions, analyzes the relationships between the frequency response functions and influence coefficients theoretically, and derives corresponding mathematical equations for high-speed rotor balancing. The relationships between the imbalance masses on the rotor and frequency response functions are also analyzed based upon the modal balancing method, and the equations related to the static and dynamic imbalance masses and the frequency response function are obtained. Experiments on a high-speed rotor balancing rig were performed to verify the theory, and the experimental data agree satisfactorily with the analytical solutions. The improvement on the traditional balancing method proposed in thismore » paper will substantially reduce the number of rotor startups required during the balancing process of rotating machinery.« less

Nonlinear analysis of composite thin-walled helicopter blades

NASA Astrophysics Data System (ADS)

Kalfon, J. P.; Rand, O.

Nonlinear theoretical modeling of laminated thin-walled composite helicopter rotor blades is presented. The derivation is based on nonlinear geometry with a detailed treatment of the body loads in the axial direction which are induced by the rotation. While the in-plane warping is neglected, a three-dimensional generic out-of-plane warping distribution is included. The formulation may also handle varying thicknesses and mass distribution along the cross-sectional walls. The problem is solved by successive iterations in which a system of equations is constructed and solved for each cross-section. In this method, the differential equations in the spanwise directions are formulated and solved using a finite-differences scheme which allows simple adaptation of the spanwise discretization mesh during iterations.

Modelling and Computation in the Valuation of Carbon Derivatives with Stochastic Convenience Yields

PubMed Central

Chang, Shuhua; Wang, Xinyu

2015-01-01

The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results. PMID:26010900

Modelling and computation in the valuation of carbon derivatives with stochastic convenience yields.

PubMed

Chang, Shuhua; Wang, Xinyu

2015-01-01

The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results.

A Digital Program for Calculating the Interaction Between Flexible Structures, Unsteady Aerodynamics and Active Controls

NASA Technical Reports Server (NTRS)

Peele, E. L.; Adams, W. M., Jr.

1979-01-01

A computer program, ISAC, is described which calculates the stability and response of a flexible airplane equipped with active controls. The equations of motion relative to a fixed inertial coordinate system are formulated in terms of the airplane's rigid body motion and its unrestrained normal vibration modes. Unsteady aerodynamic forces are derived from a doublet lattice lifting surface theory. The theoretical basis for the program is briefly explained together with a description of input data and output results.

Power formula for open-channel flow resistance

USGS Publications Warehouse

Chen, Cheng-lung

1988-01-01

This paper evaluates various power formulas for flow resistance in open channels. Unlike the logarithmic resistance equation that can be theoretically derived either from Prandtl's mixing-length hypothesis or von Karman's similarity hypothesis, the power formula has long had an appearance of empiricism. Nevertheless, the simplicity in the form of the power formula has made it popular among the many possible forms of flow resistance formulas. This paper reexamines the concept and rationale of the power formulation, thereby addressing some critical issues in the modeling of flow resistance.

Dissipative ion-cyclotron oscillitons in a form of solitons with chirp in Earth's low-altitude ionosphere

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

Kovaleva, I. Kh.

2012-10-15

In this paper, we consider theoretically nonlinear ion-cyclotron gradient-drift dissipative structures (oscillitons) in low ionospheric plasmas. Similar to Nonlinear Optics and Condensed Matter Physics, the Ginzburg-Landau equation for the envelope of electric wave fields is derived, and solutions for oscillitons in the form of solitons with chirp are examined. The whole dissipative structure constitutes a soliton with a moving charge-neutral density hump. Conditions for excitation and properties of the structures are considered.

Dynamics of multi-frequency oscillator ensembles with resonant coupling

NASA Astrophysics Data System (ADS)

Lück, S.; Pikovsky, A.

2011-07-01

We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two interacting subpopulations are in relation 2:1. Depending on the parameter of coupling, ensembles can demonstrate fully synchronous clusters, partial synchrony (only one subpopulation synchronizes), or asynchrony in both subpopulations. Theoretical description of the dynamics based on the Watanabe-Strogatz approach is developed.

User's guide for a computer program to analyze the LRC 16 ft transonic dynamics tunnel cable mount system

NASA Technical Reports Server (NTRS)

Barbero, P.; Chin, J.

1973-01-01

The theoretical derivation of the set of equations is discussed which is applicable to modeling the dynamic characteristics of aeroelastically-scaled models flown on the two-cable mount system in a 16 ft transonic dynamics tunnel. The computer program provided for the analysis is also described. The program calculates model trim conditions as well as 3 DOF longitudinal and lateral/directional dynamic conditions for various flying cable and snubber cable configurations. Sample input and output are included.

Effect of epidemic spreading on species coexistence in spatial rock-paper-scissors games.

PubMed

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2010-04-01

A fundamental question in nonlinear science and evolutionary biology is how epidemic spreading may affect coexistence. We address this question in the framework of mobile species under cyclic competitions by investigating the roles of both intra- and interspecies spreading. A surprising finding is that intraspecies infection can strongly promote coexistence while interspecies spreading cannot. These results are quantified and a theoretical paradigm based on nonlinear partial differential equations is derived to explain the numerical results.

Dynamics of essential collective motions in proteins: Theory

NASA Astrophysics Data System (ADS)

Stepanova, Maria

2007-11-01

A general theoretical background is introduced for characterization of conformational motions in protein molecules, and for building reduced coarse-grained models of proteins, based on the statistical analysis of their phase trajectories. Using the projection operator technique, a system of coupled generalized Langevin equations is derived for essential collective coordinates, which are generated by principal component analysis of molecular dynamic trajectories. The number of essential degrees of freedom is not limited in the theory. An explicit analytic relation is established between the generalized Langevin equation for essential collective coordinates and that for the all-atom phase trajectory projected onto the subspace of essential collective degrees of freedom. The theory introduced is applied to identify correlated dynamic domains in a macromolecule and to construct coarse-grained models representing the conformational motions in a protein through a few interacting domains embedded in a dissipative medium. A rigorous theoretical background is provided for identification of dynamic correlated domains in a macromolecule. Examples of domain identification in protein G are given and employed to interpret NMR experiments. Challenges and potential outcomes of the theory are discussed.

Part-2: Analytical Expressions of Concentrations of Glucose, Oxygen, and Gluconic Acid in a Composite Membrane for Closed-Loop Insulin Delivery for the Non-steady State Conditions.

PubMed

Mehala, N; Rajendran, L; Meena, V

2017-02-01

A mathematical model developed by Abdekhodaie and Wu (J Membr Sci 335:21-31, 2009), which describes a dynamic process involving an enzymatic reaction and diffusion of reactants and product inside glucose-sensitive composite membrane has been discussed. This theoretical model depicts a system of non-linear non-steady state reaction diffusion equations. These equations have been solved using new approach of homotopy perturbation method and analytical solutions pertaining to the concentrations of glucose, oxygen, and gluconic acid are derived. These analytical results are compared with the numerical results, and limiting case results for steady state conditions and a good agreement is observed. The influence of various kinetic parameters involved in the model has been presented graphically. Theoretical evaluation of the kinetic parameters like the maximal reaction velocity (V max ) and Michaelis-Menten constants for glucose and oxygen (K g and K ox ) is also reported. This predicted model is very much useful for designing the glucose-responsive composite membranes for closed-loop insulin delivery.

A bias correction for covariance estimators to improve inference with generalized estimating equations that use an unstructured correlation matrix.

PubMed

Westgate, Philip M

2013-07-20

Generalized estimating equations (GEEs) are routinely used for the marginal analysis of correlated data. The efficiency of GEE depends on how closely the working covariance structure resembles the true structure, and therefore accurate modeling of the working correlation of the data is important. A popular approach is the use of an unstructured working correlation matrix, as it is not as restrictive as simpler structures such as exchangeable and AR-1 and thus can theoretically improve efficiency. However, because of the potential for having to estimate a large number of correlation parameters, variances of regression parameter estimates can be larger than theoretically expected when utilizing the unstructured working correlation matrix. Therefore, standard error estimates can be negatively biased. To account for this additional finite-sample variability, we derive a bias correction that can be applied to typical estimators of the covariance matrix of parameter estimates. Via simulation and in application to a longitudinal study, we show that our proposed correction improves standard error estimation and statistical inference. Copyright © 2012 John Wiley & Sons, Ltd.

Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Lv, Yu; Dolatabadi, Ali; Ihme, Matthias

2014-11-01

The instability dynamics of inviscid liquid jets issuing from elliptical orifices is studied, and effects of the surrounding gas and the liquid surface tension on the stability behavior are investigated. A dispersion relation for the zeroth azimuthal (axisymmetric) instability mode is derived. Consistency of the analysis is confirmed by demonstrating that these equations reduce to the well-known dispersion equations for the limiting cases of round and planar jets. It is shown that the effect of the ellipticity is to increase the growth rate over a large range of wavenumbers in comparison to those of a circular jet. For higher Weber numbers, at which capillary forces have a stabilizing effect, the growth rate decreases with increasing ellipticity. Similar to circular and planar jets, increasing the density ratio between gas and liquid increases the growth of disturbances significantly. These theoretical investigations are complemented by experiments to validate the local linear stability results. Comparisons of predicted growth rates with measurements over a range of jet ellipticities confirm that the theoretical model provides a quantitatively accurate description of the instability dynamics in the Rayleigh and first wind-induced regimes.

Photon diffusion coefficient in scattering and absorbing media.

PubMed

Pierrat, Romain; Greffet, Jean-Jacques; Carminati, Rémi

2006-05-01

We present a unified derivation of the photon diffusion coefficient for both steady-state and time-dependent transport in disordered absorbing media. The derivation is based on a modal analysis of the time-dependent radiative transfer equation. This approach confirms that the dynamic diffusion coefficient is given by the random-walk result D = cl(*)/3, where l(*) is the transport mean free path and c is the energy velocity, independent of the level of absorption. It also shows that the diffusion coefficient for steady-state transport, often used in biomedical optics, depends on absorption, in agreement with recent theoretical and experimental works. These two results resolve a recurrent controversy in light propagation and imaging in scattering media.

Arbitrary electron acoustic waves in degenerate dense plasmas

NASA Astrophysics Data System (ADS)

Rahman, Ata-ur; Mushtaq, A.; Qamar, A.; Neelam, S.

2017-05-01

A theoretical investigation is carried out of the nonlinear dynamics of electron-acoustic waves in a collisionless and unmagnetized plasma whose constituents are non-degenerate cold electrons, ultra-relativistic degenerate electrons, and stationary ions. A dispersion relation is derived for linear EAWs. An energy integral equation involving the Sagdeev potential is derived, and basic properties of the large amplitude solitary structures are investigated in such a degenerate dense plasma. It is shown that only negative large amplitude EA solitary waves can exist in such a plasma system. The present analysis may be important to understand the collective interactions in degenerate dense plasmas, occurring in dense astrophysical environments as well as in laser-solid density plasma interaction experiments.

Damping factor estimation using spin wave attenuation in permalloy film

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

Manago, Takashi, E-mail: manago@fukuoka-u.ac.jp; Yamanoi, Kazuto; Kasai, Shinya

2015-05-07

Damping factor of a Permalloy (Py) thin film is estimated by using the magnetostatic spin wave propagation. The attenuation lengths are obtained by the dependence of the transmission intensity on the antenna distance, and decrease with increasing magnetic fields. The relationship between the attenuation length, damping factor, and external magnetic field is derived theoretically, and the damping factor was determined to be 0.0063 by fitting the magnetic field dependence of the attenuation length, using the derived equation. The obtained value is in good agreement with the general value of Py. Thus, this estimation method of the damping factor using spinmore » waves attenuation can be useful tool for ferromagnetic thin films.« less

DFT calculation of pKa’s for dimethoxypyrimidinylsalicylic based herbicides

NASA Astrophysics Data System (ADS)

Delgado, Eduardo J.

2009-03-01

Dimethoxypyrimidinylsalicylic derived compounds show potent herbicidal activity as a result of the inhibition of acetohydroxyacid synthase, the first common enzyme in the biosynthetic pathway of the branched-chain aminoacids (valine, leucine and isoleucine) in plants, bacteria and fungi. Despite its practical importance, this family of compounds have been poorly characterized from a physico-chemical point of view. Thus for instance, their pK a's have not been reported earlier neither experimentally nor theoretically. In this study, the acid-dissociation constants of 39 dimethoxypyrimidinylsalicylic derived herbicides are calculated by DFT methods at B3LYP/6-31G(d,p) level of theory. The calculated values are validated by two checking tests based on the Hammett equation.

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.

Electron-beam-induced potentials in semiconductors: calculation and measurement with an SEM/SPM hybrid system

NASA Astrophysics Data System (ADS)

Thomas, Ch; Joachimsthaler, I.; Heiderhoff, R.; Balk, L. J.

2004-10-01

In this work electron-beam-induced potentials are analysed theoretically and experimentally for semiconductors. A theoretical model is developed to describe the surface potential distribution produced by an electron beam. The distribution of generated carriers is calculated using semiconductor equations. This distribution causes a local change in surface potential, which is derived with the help of quasi-Fermi energies. The potential distribution is simulated using the model developed and measured with a scanning probe microscope (SPM) built inside a scanning electron microscope (SEM), for different samples, for different beam excitations and for different cantilever voltages of SPM. In the end, some fields of application are shown where material properties can be determined using an SEM/SPM hybrid system.

Transport properties of partially ionized and unmagnetized plasmas.

PubMed

Magin, Thierry E; Degrez, Gérard

2004-10-01

This work is a comprehensive and theoretical study of transport phenomena in partially ionized and unmagnetized plasmas by means of kinetic theory. The pros and cons of different models encountered in the literature are presented. A dimensional analysis of the Boltzmann equation deals with the disparity of mass between electrons and heavy particles and yields the epochal relaxation concept. First, electrons and heavy particles exhibit distinct kinetic time scales and may have different translational temperatures. The hydrodynamic velocity is assumed to be identical for both types of species. Second, at the hydrodynamic time scale the energy exchanged between electrons and heavy particles tends to equalize both temperatures. Global and species macroscopic fluid conservation equations are given. New constrained integral equations are derived from a modified Chapman-Enskog perturbative method. Adequate bracket integrals are introduced to treat thermal nonequilibrium. A symmetric mathematical formalism is preferred for physical and numerical standpoints. A Laguerre-Sonine polynomial expansion allows for systems of transport to be derived. Momentum, mass, and energy fluxes are associated to shear viscosity, diffusion coefficients, thermal diffusion coefficients, and thermal conductivities. A Goldstein expansion of the perturbation function provides explicit expressions of the thermal diffusion ratios and measurable thermal conductivities. Thermal diffusion terms already found in the Russian literature ensure the exact mass conservation. A generalized Stefan-Maxwell equation is derived following the method of Kolesnikov and Tirskiy. The bracket integral reduction in terms of transport collision integrals is presented in Appendix for the thermal nonequilibrium case. A simple Eucken correction is proposed to deal with the internal degrees of freedom of atoms and polyatomic molecules, neglecting inelastic collisions. The authors believe that the final expressions are readily usable for practical applications in fluid dynamics.

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.

Optimal preconditioning of lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

Izquierdo, Salvador; Fueyo, Norberto

2009-09-01

A preconditioning technique to accelerate the simulation of steady-state problems using the single-relaxation-time (SRT) lattice Boltzmann (LB) method was first proposed by Guo et al. [Z. Guo, T. Zhao, Y. Shi, Preconditioned lattice-Boltzmann method for steady flows, Phys. Rev. E 70 (2004) 066706-1]. The key idea in this preconditioner is to modify the equilibrium distribution function in such a way that, by means of a Chapman-Enskog expansion, a time-derivative preconditioner of the Navier-Stokes (NS) equations is obtained. In the present contribution, the optimal values for the free parameter γ of this preconditioner are searched both numerically and theoretically; the later with the aid of linear-stability analysis and with the condition number of the system of NS equations. The influence of the collision operator, single- versus multiple-relaxation-times (MRT), is also studied. Three steady-state laminar test cases are used for validation, namely: the two-dimensional lid-driven cavity, a two-dimensional microchannel and the three-dimensional backward-facing step. Finally, guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the Reynolds and Mach numbers. The new optimally preconditioned MRT method derived is shown to improve, simultaneously, the rate of convergence, the stability and the accuracy of the lattice Boltzmann simulations, when compared to the non-preconditioned methods and to the optimally preconditioned SRT one. Additionally, direct time-derivative preconditioning of the LB equation is also studied.

Kinetic theory molecular dynamics and hot dense matter: theoretical foundations.

PubMed

Graziani, F R; Bauer, J D; Murillo, M S

2014-09-01

Electrons are weakly coupled in hot, dense matter that is created in high-energy-density experiments. They are also mildly quantum mechanical and the ions associated with them are classical and may be strongly coupled. In addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory is an ideal tool for treating the electrons but it is not adequate for treating the ions. Molecular dynamics is perfectly suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines a Wigner kinetic treatment of the electrons with classical molecular dynamics for the ions. We refer to this hybrid method as "kinetic theory molecular dynamics," or KTMD. The purpose of this paper is to derive KTMD from first principles and place it on a firm theoretical foundation. The framework that KTMD provides for simulating plasmas in the hot, dense regime is particularly useful since current computational methods are generally limited by their inability to treat the dynamical quantum evolution of the electronic component. Using the N-body von Neumann equation for the electron-proton plasma, three variations of KTMD are obtained. Each variant is determined by the physical state of the plasma (e.g., collisional versus collisionless). The first variant of KTMD yields a closed set of equations consisting of a mean-field quantum kinetic equation for the electron one-particle distribution function coupled to a classical Liouville equation for the protons. The latter equation includes both proton-proton Coulombic interactions and an effective electron-proton interaction that involves the convolution of the electron density with the electron-proton Coulomb potential. The mean-field approach is then extended to incorporate equilibrium electron-proton correlations through the Singwi-Tosi-Land-Sjolander (STLS) ansatz. This is the second variant of KTMD. The STLS contribution produces an effective electron-proton interaction that involves the electron-proton structure factor, thereby extending the usual mean-field theory to correlated but near equilibrium systems. Finally, a third variant of KTMD is derived. It includes dynamical electrons and their correlations coupled to a MD description for the ions. A set of coupled equations for the one-particle electron Wigner function and the electron-electron and electron-proton correlation functions are coupled to a classical Liouville equation for the protons. This latter variation has both time and momentum dependent correlations.

New insights in permafrost modelling

NASA Astrophysics Data System (ADS)

Tubini, Niccolò; Serafin, Francesco; Gruber, Stephan; Casulli, Vincenzo; Rigon, Riccardo

2017-04-01

Simulating freezing soil has ignored for long time in mainstream surface hydrology. However, it has indubitably a large influence on soil infiltrability and an even larger influence on the soil energy budget, and, over large spatial scales, a considerable feedback on climate. The topic is difficult because it involves concepts of disequilibrium Thermodynamics and also because, once solved the theoretical problem, integration of the resulting partial differential equations in a robust manner, is not trivial at all. In this abstract, we are presenting a new algorithm to estimate the water and energy budget in freezing soils. The first step is a derivation of a new equation for freezing soil mass budget (called generalized Richards equation) based on the freezing equals drying hypothesis (Miller 1965). The second step is the re-derivation of the energy budget. Finally there is the application of new techniques based on the double nested Newton algorithm (Casulli and Zanolli, 2010) to integrate the coupled equations. Some examples of the freezing dynamics and comparison with the Dall'Amico et al. (2011) algorithm are also shown. References Casulli, V., & Zanolli,P. (2010). A nested newton-type algorithm for finite colume methods solving Richards' equation in mixed form. SIAM J. SCI. Comput., 32(4), 2225-2273. Dall'Amico, M., Endrizzi, S., Gruber, S., & Rigon, R. (2011). A robust and energy-conserving model of freezing variably-saturated soil. The Cryosphere, 5(2), 469-484. http://doi.org/10.5194/tc-5-469-2011 Miller, R.: Phase equilibria and soil freezing, in: Permafrost: Proceedings of the Second International Conference. Washington DC: National Academy of Science-National Research Council, 287, 193-197, 1965.

Thomas Young's investigations in gradient-index optics.

PubMed

Atchison, David A; Charman, W Neil

2011-05-01

James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some 50 years earlier, Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young's contributions. We attempted to derive Young's equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. We did not confirm Young's equation for the axial gradient to provide aberration-free optics but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index toward the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Young's theoretical work in gradient-index optics received no acknowledgment from either his contemporaries or later authors. Although his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young's work deserves wider recognition.

A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

1997-12-01

The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic volatility is reviewed starting from the first principles of finance. The equation of Merton and Garman is then recast using the path integration technique of theoretical physics. The price of the stock option is shown to be the analogue of the Schrödinger wavefunction of quantum mechanics and the exact Hamiltonian and Lagrangian of the system is obtained. The results of Hull and White are generalized to the case when stock price and volatility have non-zero correlation. Some exact results for pricing stock options for the general correlated case are derived.

Controlling Contagion Processes in Activity Driven Networks

NASA Astrophysics Data System (ADS)

Liu, Suyu; Perra, Nicola; Karsai, Márton; Vespignani, Alessandro

2014-03-01

The vast majority of strategies aimed at controlling contagion processes on networks consider the connectivity pattern of the system either quenched or annealed. However, in the real world, many networks are highly dynamical and evolve, in time, concurrently with the contagion process. Here, we derive an analytical framework for the study of control strategies specifically devised for a class of time-varying networks, namely activity-driven networks. We develop a block variable mean-field approach that allows the derivation of the equations describing the coevolution of the contagion process and the network dynamic. We derive the critical immunization threshold and assess the effectiveness of three different control strategies. Finally, we validate the theoretical picture by simulating numerically the spreading process and control strategies in both synthetic networks and a large-scale, real-world, mobile telephone call data set.

Generic picture of the emission properties of III-nitride polariton laser diodes: Steady state and current modulation response

NASA Astrophysics Data System (ADS)

Iorsh, Ivan; Glauser, Marlene; Rossbach, Georg; Levrat, Jacques; Cobet, Munise; Butté, Raphaël; Grandjean, Nicolas; Kaliteevski, Mikhail A.; Abram, Richard A.; Kavokin, Alexey V.

2012-09-01

The main emission characteristics of electrically driven polariton lasers based on planar GaN microcavities with embedded InGaN quantum wells are studied theoretically. The polariton emission dependence on pump current density is first modeled using a set of semiclassical Boltzmann equations for the exciton polaritons that are coupled to the rate equation describing the electron-hole plasma population. Two experimentally relevant pumping geometries are considered, namely the direct injection of electrons and holes into the strongly coupled microcavity region and intracavity optical pumping via an embedded light-emitting diode. The theoretical framework allows the determination of the minimum threshold current density Jthr,min as a function of lattice temperature and exciton-cavity photon detuning for the two pumping schemes. A Jthr,min value of 5 and 6 A cm-2 is derived for the direct injection scheme and for the intracavity optical pumping one, respectively, at room temperature at the optimum detuning. Then an approximate quasianalytical model is introduced to derive solutions for both the steady-state and high-speed current modulation. This analysis makes it possible to show that the exciton population, which acts as a reservoir for the stimulated relaxation process, gets clamped once the condensation threshold is crossed, a behavior analogous to what happens in conventional laser diodes with the carrier density above threshold. Finally, the modulation transfer function is calculated for both pumping geometries and the corresponding cutoff frequency is determined.

The Poynting-Stokes Tensor And Radiative Transfer In Turbid Media: The Microphysical Paradigm

NASA Astrophysics Data System (ADS)

Mishchenko, M. I.

2010-12-01

This paper solves the long-standing problem of establishing the fundamental physical link between the radiative transfer theory and macroscopic electromagnetics in the case of elastic scattering by a sparse discrete random medium. The radiative transfer equation (RTE) is derived directly from the macroscopic Maxwell equations by computing theoretically the appropriately defined so-called Poynting-Stokes tensor carrying informa-tion on both the direction, magnitude, and polarization characteristics of lo-cal electromagnetic energy flow. Our derivation from first principles shows that to compute the local Poynting vector averaged over a sufficiently long period of time, one can solve the RTE for the direction-dependent specific intensity column vector and then integrate the direction-weighted specific intensity over all directions. Furthermore, we demonstrate that the specific intensity (or specific intensity column vector) can be measured with a well-collimated radiometer (photopolarimeter), which provides the ultimate physical justification for the use of such instruments in radiation-budget and particle-characterization applications. However, the specific intensity cannot be interpreted in phenomenological terms as signifying the amount of elec-tromagnetic energy transported in a given direction per unit area normal to this direction per unit time per unit solid angle. Also, in the case of a densely packed scattering medium the relation of the measurement with a well-collimated radiometer to the time-averaged local Poynting vector re-mains uncertain, and the theoretical modeling of this measurement is likely to require a much more complicated approach than solving an RTE.

Coevolutionary dynamics in large, but finite populations

NASA Astrophysics Data System (ADS)

Traulsen, Arne; Claussen, Jens Christian; Hauert, Christoph

2006-07-01

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form of a Fokker-Planck equation was derived for frequency-dependent selection with two strategies in finite populations based on microscopic processes [A. Traulsen, J. C. Claussen, and C. Hauert, Phys. Rev. Lett. 95, 238701 (2005)]. Here we generalize this approach in a twofold way: First, we extend the framework to an arbitrary number of strategies and second, we allow for mutations in the evolutionary process. The deterministic limit of infinite population size of the frequency-dependent Moran process yields the adjusted replicator-mutator equation, which describes the combined effect of selection and mutation. For finite populations, we provide an extension taking random drift into account. In the limit of neutral selection, i.e., whenever the process is determined by random drift and mutations, the stationary strategy distribution is derived. This distribution forms the background for the coevolutionary process. In particular, a critical mutation rate uc is obtained separating two scenarios: above uc the population predominantly consists of a mixture of strategies whereas below uc the population tends to be in homogeneous states. For one of the fundamental problems in evolutionary biology, the evolution of cooperation under Darwinian selection, we demonstrate that the analytical framework provides excellent approximations to individual based simulations even for rather small population sizes. This approach complements simulation results and provides a deeper, systematic understanding of coevolutionary dynamics.

General slip regime permeability model for gas flow through porous media

NASA Astrophysics Data System (ADS)

Zhou, Bo; Jiang, Peixue; Xu, Ruina; Ouyang, Xiaolong

2016-07-01

A theoretical effective gas permeability model was developed for rarefied gas flow in porous media, which holds over the entire slip regime with the permeability derived as a function of the Knudsen number. This general slip regime model (GSR model) is derived from the pore-scale Navier-Stokes equations subject to the first-order wall slip boundary condition using the volume-averaging method. The local closure problem for the volume-averaged equations is studied analytically and numerically using a periodic sphere array geometry. The GSR model includes a rational fraction function of the Knudsen number which leads to a limit effective permeability as the Knudsen number increases. The mechanism for this behavior is the viscous fluid inner friction caused by converging-diverging flow channels in porous media. A linearization of the GSR model leads to the Klinkenberg equation for slightly rarefied gas flows. Finite element simulations show that the Klinkenberg model overestimates the effective permeability by as much as 33% when a flow approaches the transition regime. The GSR model reduces to the unified permeability model [F. Civan, "Effective correlation of apparent gas permeability in tight porous media," Transp. Porous Media 82, 375 (2010)] for the flow in the slip regime and clarifies the physical significance of the empirical parameter b in the unified model.

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.

Hot super-dense compact object with particular EoS

NASA Astrophysics Data System (ADS)

Tito, E. P.; Pavlov, V. I.

2018-03-01

We show the possibility of existence of a self-gravitating spherically-symmetric equilibrium configuration for a neutral matter with neutron-like density, small mass M ≪ M_{⊙}, and small radius R ≪ R_{⊙}. We incorporate the effects of both the special and general theories of relativity. Such object may be formed in a cosmic cataclysm, perhaps an exotic one. Since the base equations of hydrostatic equilibrium are completed by the equation of state (EoS) for the matter of the object, we offer a novel, interpolating experimental data from high-energy physics, EoS which permits the existence of such compact system of finite radius. This EoS model possesses a critical state characterized by density ρc and temperature Tc. For such an object, we derive a radial distribution for the super-dense matter in "liquid" phase using Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium. We demonstrate that a stable configuration is indeed possible (only) for temperatures smaller than the critical one. We derive the mass-radius relation (adjusted for relativistic corrections) for such small (M ≪ M_{⊙}) super-dense compact objects. The results are within the constraints established by both heavy-ion collision experiments and theoretical studies of neutron-rich matter.

Backpropagation and ordered derivatives in the time scales calculus.

PubMed

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1986-01-01

The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

PubMed

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-04-08

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

PubMed Central

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-01-01

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719

Applying transfer matrix method to the estimation of the modal characteristics of the NASA Mini-Mass Truss

NASA Technical Reports Server (NTRS)

Shen, Ji-Yao; Taylor, Lawrence W., Jr.

1994-01-01

It is beneficial to use a distributed parameter model for large space structures because the approach minimizes the number of model parameters. Holzer's transfer matrix method provides a useful means to simplify and standardize the procedure for solving the system of partial differential equations. Any large space structures can be broken down into sub-structures with simple elastic and dynamical properties. For each single element, such as beam, tether, or rigid body, we can derive the corresponding transfer matrix. Combining these elements' matrices enables the solution of the global system equations. The characteristics equation can then be formed by satisfying the appropriate boundary conditions. Then natural frequencies and mode shapes can be determined by searching the roots of the characteristic equation at frequencies within the range of interest. This paper applies this methodology, and the maximum likelihood estimation method, to refine the modal characteristics of the NASA Mini-Mast Truss by successively matching the theoretical response to the test data of the truss. The method is being applied to more complex configurations.

Electroosmotic flow in capillary channels filled with nonconstant viscosity electrolytes: exact solution of the Navier-Stokes equation.

PubMed

Otevrel, Marek; Klepárník, Karel

2002-10-01

The partial differential equation describing unsteady velocity profile of electroosmotic flow (EOF) in a cylindrical capillary filled with a nonconstant viscosity electrolyte was derived. Analytical solution, based on the general Navier-Stokes equation, was found for constant viscosity electrolytes using the separation of variables (Fourier method). For the case of a nonconstant viscosity electrolyte, the steady-state velocity profile was calculated assuming that the viscosity decreases exponentially in the direction from the wall to the capillary center. Since the respective equations with nonconstant viscosity term are not solvable in general, the method of continuous binding conditions was used to solve this problem. In this method, an arbitrary viscosity profile can be modeled. The theoretical conclusions show that the relaxation times at which an EOF approaches the steady state are too short to have an impact on a separation process in any real systems. A viscous layer at the wall affects EOF significantly, if it is thicker than the Debye length of the electric double layer. The presented description of the EOF dynamics is applicable to any microfluidic systems.

Electrical and mechanical fully coupled theory and experimental verification of Rosen-type piezoelectric transformers.

PubMed

Hsu, Yu-Hsiang; Lee, Chih-Kung; Hsiao, Wen-Hsin

2005-10-01

A piezoelectric transformer is a power transfer device that converts its input and output voltage as well as current by effectively using electrical and mechanical coupling effects of piezoelectric materials. Equivalent-circuit models, which are traditionally used to analyze piezoelectric transformers, merge each mechanical resonance effect into a series of ordinary differential equations. Because of using ordinary differential equations, equivalent circuit models are insufficient to reflect the mechanical behavior of piezoelectric plates. Electromechanically, fully coupled governing equations of Rosen-type piezoelectric transformers, which are partial differential equations in nature, can be derived to address the deficiencies of the equivalent circuit models. It can be shown that the modal actuator concept can be adopted to optimize the electromechanical coupling effect of the driving section once the added spatial domain design parameters are taken into account, which are three-dimensional spatial dependencies of electromechanical properties. The maximum power transfer condition for a Rosen-type piezoelectric transformer is detailed. Experimental results, which lead us to a series of new design rules, also are presented to prove the validity and effectiveness of the theoretical predictions.

Non-Markovian electron dynamics in nanostructures coupled to dissipative contacts

NASA Astrophysics Data System (ADS)

Novakovic, B.; Knezevic, I.

2013-02-01

In quasiballistic semiconductor nanostructures, carrier exchange between the active region and dissipative contacts is the mechanism that governs relaxation. In this paper, we present a theoretical treatment of transient quantum transport in quasiballistic semiconductor nanostructures, which is based on the open system theory and valid on timescales much longer than the characteristic relaxation time in the contacts. The approach relies on a model interaction between the current-limiting active region and the contacts, given in the scattering-state basis. We derive a non-Markovian master equation for the irreversible evolution of the active region's many-body statistical operator by coarse-graining the exact dynamical map over the contact relaxation time. In order to obtain the response quantities of a nanostructure under bias, such as the potential and the charge and current densities, the non-Markovian master equation must be solved numerically together with the Schr\\"{o}dinger, Poisson, and continuity equations. We discuss how to numerically solve this coupled system of equations and illustrate the approach on the example of a silicon nin diode.

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Analytical and experimental study of the vibration of bonded beams with a lap joint

NASA Technical Reports Server (NTRS)

Rao, M. D.; Crocker, M. J.

1990-01-01

A theoretical model to study the flexural vibration of a bonded lap joint system is described in this paper. First, equations of motion at the joint region are derived using a differential element approach. The transverse displacements of the upper and lower beam are considered to be different. The adhesive is assumed to be linearly viscoelastic and the widely used Kelvin-Voight model is used to represent the viscoelastic behavior of the adhesive. The shear force at the interface between the adhesive and the beam is obtained from the simple bending motion equations of the two beams. The resulting equations of motion are combined with the equations of transverse vibration of the beams in the unjointed regions. These are later solved as a boundary value problem to obtain the eigenvalues and eigenvectors of the system. The model can be used to predict the natural frequencies, modal damping ratios, and mode shapes of the system for free vibration. Good agreement between numerical and experimental results was obtained for a system of graphite epoxy beams lap-jointed by an epoxy adhesive.

Nonlinear evolution equations for surface plasmons for nano-focusing at a Kerr/metallic interface and tapered waveguide

NASA Astrophysics Data System (ADS)

Crutcher, Sihon H.; Osei, Albert; Biswas, Anjan

2012-06-01

Maxwell's equations for a metallic and nonlinear Kerr interface waveguide at the nanoscale can be approximated to a (1+1) D Nonlinear Schrodinger type model equation (NLSE) with appropriate assumptions and approximations. Theoretically, without losses or perturbations spatial plasmon solitons profiles are easily produced. However, with losses, the amplitude or beam profile is no longer stationary and adiabatic parameters have to be considered to understand propagation. For this model, adiabatic parameters are calculated considering losses resulting in linear differential coupled integral equations with constant definite integral coefficients not dependent on the transverse and longitudinal coordinates. Furthermore, by considering another configuration, a waveguide that is an M-NL-M (metal-nonlinear Kerr-metal) that tapers, the tapering can balance the loss experienced at a non-tapered metal/nonlinear Kerr interface causing attenuation of the beam profile, so these spatial plasmon solitons can be produced. In this paper taking into consideration the (1+1)D NLSE model for a tapered waveguide, we derive a one soliton solution based on He's Semi-Inverse Variational Principle (HPV).

An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1980-01-01

A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.

Earth-moon system: Dynamics and parameter estimation

NASA Technical Reports Server (NTRS)

Breedlove, W. J., Jr.

1975-01-01

A theoretical development of the equations of motion governing the earth-moon system is presented. The earth and moon were treated as finite rigid bodies and a mutual potential was utilized. The sun and remaining planets were treated as particles. Relativistic, non-rigid, and dissipative effects were not included. The translational and rotational motion of the earth and moon were derived in a fully coupled set of equations. Euler parameters were used to model the rotational motions. The mathematical model is intended for use with data analysis software to estimate physical parameters of the earth-moon system using primarily LURE type data. Two program listings are included. Program ANEAMO computes the translational/rotational motion of the earth and moon from analytical solutions. Program RIGEM numerically integrates the fully coupled motions as described above.

Thermo-solutal growth of an anisotropic dendrite with six-fold symmetry

NASA Astrophysics Data System (ADS)

Alexandrov, D. V.; Galenko, P. K.

2018-03-01

A stable growth of dendritic crystal with the six-fold crystalline anisotropy is analyzed in a binary nonisothermal mixture. A selection criterion representing a relationship between the dendrite tip velocity and its tip diameter is derived on the basis of morphological stability analysis and solvability theory. A complete set of nonlinear equations, consisting of the selection criterion and undercooling balance condition, which determines implicit dependencies of the dendrite tip velocity and tip diameter as functions of the total undercooling, is formulated. Exact analytical solutions of these nonlinear equations are found in a parametric form. Asymptotic solutions describing the crystal growth at small Péclet numbers are determined. Theoretical predictions are compared with experimental data obtained for ice dendrites growing in binary water-ethylenglycol solutions as well as in pure water.

Adapting the Euler-Lagrange equation to study one-dimensional motions under the action of a constant force

NASA Astrophysics Data System (ADS)

Dias, Clenilda F.; Araújo, Maria A. S.; Carvalho-Santos, Vagson L.

2018-01-01

The Euler-Lagrange equations (ELE) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of ELE to study one-dimensional motions under the action of a constant force. From the use of the definition of partial derivative, we have proposed two operators, here called mean delta operators, which may be used to solve the ELE in a simplest way. We have applied this simplification to solve three simple mechanical problems in which the particle is under the action of the gravitational field: a free fall body, the Atwood’s machine and the inclined plan. The proposed simplification can be used to introduce the lagrangian formalism in teaching classical mechanics in introductory physics courses.

Modeling and analysis on ring-type piezoelectric transformers.

PubMed

Ho, Shine-Tzong

2007-11-01

This paper presents an electromechanical model for a ring-type piezoelectric transformer (PT). To establish this model, vibration characteristics of the piezoelectric ring with free boundary conditions are analyzed in advance. Based on the vibration analysis of the piezoelectric ring, the operating frequency and vibration mode of the PT are chosen. Then, electromechanical equations of motion for the PT are derived based on Hamilton's principle, which can be used to simulate the coupled electromechanical system for the transformer. Such as voltage stepup ratio, input impedance, output impedance, input power, output power, and efficiency are calculated by the equations. The optimal load resistance and the maximum efficiency for the PT will be presented in this paper. Experiments also were conducted to verify the theoretical analysis, and a good agreement was obtained.

Hierarchy of models: From qualitative to quantitative analysis of circadian rhythms in cyanobacteria

NASA Astrophysics Data System (ADS)

Chaves, M.; Preto, M.

2013-06-01

A hierarchy of models, ranging from high to lower levels of abstraction, is proposed to construct "minimal" but predictive and explanatory models of biological systems. Three hierarchical levels will be considered: Boolean networks, piecewise affine differential (PWA) equations, and a class of continuous, ordinary, differential equations' models derived from the PWA model. This hierarchy provides different levels of approximation of the biological system and, crucially, allows the use of theoretical tools to more exactly analyze and understand the mechanisms of the system. The Kai ABC oscillator, which is at the core of the cyanobacterial circadian rhythm, is analyzed as a case study, showing how several fundamental properties—order of oscillations, synchronization when mixing oscillating samples, structural robustness, and entrainment by external cues—can be obtained from basic mechanisms.

Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models

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

Felice, Antonio De; Tsujikawa, Shinji, E-mail: antoniod@nu.ac.th, E-mail: shinji@rs.kagu.tus.ac.jp

2012-02-01

In the Horndeski's most general scalar-tensor theories with second-order field equations, we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar, tensor, and vector perturbations in the presence of two perfect fluids on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) background. Our general results are useful for the construction of theoretically consistent models of dark energy. We apply our formulas to extended Galileon models in which a tracker solution with an equation of state smaller than -1 is present. We clarify the allowed parameter space in which the ghosts and Laplacian instabilities are absent and we numerically confirmmore » that such models are indeed cosmologically viable.« less

Aeroelastic Studies of a Rectangular Wing with a Hole: Correlation of Theory and Experiment

NASA Technical Reports Server (NTRS)

Conyers, Howard J.; Dowell, Earl H.; Hall, Kenneth C.

2010-01-01

Two rectangular wing models with a hole have been designed and tested in the Duke University wind tunnel to better understand the effects of damage. A rectangular hole is used to simulate damage. The wing with a hole is modeled structurally as a thin elastic plate using the finite element method. The unsteady aerodynamics of the plate-like wing with a hole is modeled using the doublet lattice method. The aeroelastic equations of motion are derived using Lagrange's equation. The flutter boundary is found using the V-g method. The hole's location effects the wing's mass, stiffness, aerodynamics and therefore the aeroelastic behavior. Linear theoretical models were shown to be capable of predicting the critical flutter velocity and frequency as verified by wind tunnel tests.

Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description

NASA Astrophysics Data System (ADS)

Alber, Mark; Chen, Nan; Glimm, Tilmann; Lushnikov, Pavel M.

2006-05-01

The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.

Study of flutter related computational procedures for minimum weight structural sizing of advanced aircraft, supplemental data

NASA Technical Reports Server (NTRS)

Oconnell, R. F.; Hassig, H. J.; Radovcich, N. A.

1975-01-01

Computational aspects of (1) flutter optimization (minimization of structural mass subject to specified flutter requirements), (2) methods for solving the flutter equation, and (3) efficient methods for computing generalized aerodynamic force coefficients in the repetitive analysis environment of computer-aided structural design are discussed. Specific areas included: a two-dimensional Regula Falsi approach to solving the generalized flutter equation; method of incremented flutter analysis and its applications; the use of velocity potential influence coefficients in a five-matrix product formulation of the generalized aerodynamic force coefficients; options for computational operations required to generate generalized aerodynamic force coefficients; theoretical considerations related to optimization with one or more flutter constraints; and expressions for derivatives of flutter-related quantities with respect to design variables.

Modelling nonlinearity in piezoceramic transducers: From equations to nonlinear equivalent circuits.

PubMed

Parenthoine, D; Tran-Huu-Hue, L-P; Haumesser, L; Vander Meulen, F; Lematre, M; Lethiecq, M

2011-02-01

Quadratic nonlinear equations of a piezoelectric element under the assumptions of 1D vibration and weak nonlinearity are derived by the perturbation theory. It is shown that the nonlinear response can be represented by controlled sources that are added to the classical hexapole used to model piezoelectric ultrasonic transducers. As a consequence, equivalent electrical circuits can be used to predict the nonlinear response of a transducer taking into account the acoustic loads on the rear and front faces. A generalisation of nonlinear equivalent electrical circuits to cases including passive layers and propagation media is then proposed. Experimental results, in terms of second harmonic generation, on a coupled resonator are compared to theoretical calculations from the proposed model. Copyright © 2010 Elsevier B.V. All rights reserved.

Building a USGS National Crustal Model: Theoretical foundation, inputs, and calibration for the Western United States

NASA Astrophysics Data System (ADS)

Shah, A. K.; Boyd, O. S.; Sowers, T.; Thompson, E.

2017-12-01

Seismic hazard assessments depend on an accurate prediction of ground motion, which in turn depends on a base knowledge of three-dimensional variations in density, seismic velocity, and attenuation. We are building a National Crustal Model (NCM) using a physical theoretical foundation, 3-D geologic model, and measured data for calibration. An initial version of the NCM for the western U.S. is planned to be available in mid-2018 and for the remainder of the U.S. in 2019. The theoretical foundation of the NCM couples Biot-Gassmann theory for the porous composite with mineral physics calculations for the solid mineral matrix. The 3-D geologic model is defined through integration of results from a range of previous studies including maps of surficial porosity, surface and subsurface lithology, and the depths to bedrock and crystalline basement or seismic equivalent. The depths to bedrock and basement are estimated using well, seismic, and gravity data; in many cases these data are compiled by combining previous studies. Two parameters controlling how porosity changes with depth are assumed to be a function of lithology and calibrated using measured shear- and compressional-wave velocity and density profiles. Uncertainties in parameters derived from the model increase with depth and are dependent on the quantity and quality of input data sets. An interface to the model provides parameters needed for ground motion prediction equations in the Western U.S., including, for example, the time-averaged shear-wave velocity in the upper 30 meters (VS30) and the depths to 1.0 and 2.5 km/s shear-wave speeds (Z1.0 and Z2.5), which have a very rough correlation to the depths to bedrock and basement, as well as interpolated 3D models for use with various Urban Hazard Mapping strategies. We compare parameters needed for ground motion prediction equations including VS30, Z1.0, and Z2.5 between those derived from existing models, for example, 3-D velocity models for southern California available from the Southern California Earthquake Center, and those derived from the NCM and assess their ability to reduce the variance of observed ground motions.

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.

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

Boundary conditions for a one-sided numerical model of evaporative instabilities in sessile drops of ethanol on heated substrates

NASA Astrophysics Data System (ADS)

Semenov, Sergey; Carle, Florian; Medale, Marc; Brutin, David

2017-12-01

The work is focused on obtaining boundary conditions for a one-sided numerical model of thermoconvective instabilities in evaporating pinned sessile droplets of ethanol on heated substrates. In the one-sided model, appropriate boundary conditions for heat and mass transfer equations are required at the droplet surface. Such boundary conditions are obtained in the present work based on a derived semiempirical theoretical formula for the total droplet's evaporation rate, and on a two-parametric nonisothermal approximation of the local evaporation flux. The main purpose of these boundary conditions is to be applied in future three-dimensional (3D) one-sided numerical models in order to save a lot of computational time and resources by solving equations only in the droplet domain. Two parameters, needed for the nonisothermal approximation of the local evaporation flux, are obtained by fitting computational results of a 2D two-sided numerical model. Such model is validated here against parabolic flight experiments and the theoretical value of the total evaporation rate. This study combines theoretical, experimental, and computational approaches in convective evaporation of sessile droplets. The influence of the gravity level on evaporation rate and contributions of different mechanisms of vapor transport (diffusion, Stefan flow, natural convection) are shown. The qualitative difference (in terms of developing thermoconvective instabilities) between steady-state and unsteady numerical approaches is demonstrated.

Analysis of dynamic capacity of low-contact-ratio spur gears using Lundberg-Palmgren theory

NASA Technical Reports Server (NTRS)

Coy, J. J.

1975-01-01

A concise mathematical model is developed for surface fatigue life of low-contact-ratio spur gears. The expected fatigue life of the pinion, gear, or gear sets may be calculated from the model. An equation for the dynamic capacity of the gear set was also derived in terms of the transmitted tangential tooth load which will give a 10-percent fatigue life of one million pinion revolutions. The theoretical life was compared with experimental data for a set of VAR AISI 9310 gears operating at a Hertz stress of 1.71X10 to the 9th power newtons per square meter (248,000 psi) and 10 000 revolutions per minute. Good agreement was obtained between the experimental and theoretical surface fatigue life of the gears.

Creation of second-order nonlinear optical effects by photoisomerization of polar azo dyes in polymeric films: theoretical study of steady-state and transient properties

NASA Astrophysics Data System (ADS)

Sekkat, Zouheir; Knoll, Wolfgang

1995-10-01

It was shown recently that the application of a dc field across a polymer film containing polar azo dye chromophores at a temperature far below that of its glass transition leads to an appreciable polar order when the azo dyes undergo cis \\left-right-double-arrow trans isomerization. We present a detailed theoretical study of this phenomenon based on the enhanced mobility of the azo chromophores during the isomerization process. The equations representing this phenomenological theory are solved by recurrence relations of Legendre polynomials, and both the steady state and the dynamics are investigated. Analytical expressions are derived for the photoinduced polar order and its related anisotropy for both cis and trans molecular distributions.

Analysis on spectra of hydroacoustic field in sonar cavity of the sandwich elastic wall structure

NASA Astrophysics Data System (ADS)

Xuetao, W.; Rui, H.; Weike, W.

2017-09-01

In this paper, the characteristics of the mechanical self - noise in sonar array cavity are studied by using the elastic flatbed - filled rectangular cavity parameterization model. Firstly, the analytic derivation of the vibration differential equation of the single layer, sandwich elastic wall plate structure and internal fluid coupling is carried out, and the modal method is used to solve it. Finally, the spectral characteristics of the acoustic field of rectangular cavity of different elastic wallboard materials are simulated and analyzed, which provides a theoretical reference for the prediction and control of sonar mechanical self-noise. In this paper, the sandwich board as control inside the dome background noise of a potential means were discussed, the dome background noise of qualitative prediction analysis and control has important theoretical significance.

Optimization of post-column reactor radius in capillary high performance liquid chromatography Effect of chromatographic column diameter and particle diameter

PubMed Central

Xu, Hongjuan; Weber, Stephen G.

2006-01-01

A post-column reactor consisting of a simple open tube (Capillary Taylor Reactor) affects the performance of a capillary LC in two ways: stealing pressure from the column and adding band spreading. The former is a problem for very small radius reactors, while the latter shows itself for large reactor diameters. We derived an equation that defines the observed number of theoretical plates (Nobs) taking into account the two effects stated above. Making some assumptions and asserting certain conditions led to a final equation with a limited number of variables, namely chromatographic column radius, reactor radius and chromatographic particle diameter. The assumptions and conditions are that the van Deemter equation applies, the mass transfer limitation is for intraparticle diffusion in spherical particles, the velocity is at the optimum, the analyte’s retention factor, k′, is zero, the post-column reactor is only long enough to allow complete mixing of reagents and analytes and the maximum operating pressure of the pumping system is used. Optimal ranges of the reactor radius (ar) are obtained by comparing the number of observed theoretical plates (and theoretical plates per time) with and without a reactor. Results show that the acceptable reactor radii depend on column diameter, particle diameter, and maximum available pressure. Optimal ranges of ar become narrower as column diameter increases, particle diameter decreases or the maximum pressure is decreased. When the available pressure is 4000 psi, a Capillary Taylor Reactor with 12 μm radius is suitable for all columns smaller than 150 μm (radius) packed with 2–5 μm particles. For 1 μm packing particles, only columns smaller than 42.5 μm (radius) can be used and the reactor radius needs to be 5 μm. PMID:16494886

A Proposal for a Subcritical Reactivity Meter based on Gandini and Salvatores' point kinetics equations for Multiplying Subcritical Systems

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

Pinto, Leticia N.; Dos Santos, Adimir

2015-07-01

Multiplying Subcritical Systems were for a long time poorly studied and its theoretical description remains with plenty open questions. Great interest on such systems arose partly due to the improvement of hybrid concepts, such as the Accelerator-Driven Systems (ADS). Along with the need for new technologies to be developed, further study and understanding of subcritical systems are essential also in more practical situations, such as in the case of a PWR criticalization in their physical startup tests. Point kinetics equations are fundamental to continuously monitor the reactivity behavior to a possible variation of external sources intensity. In this case, quicklymore » and accurately predicting power transients and reactivity becomes crucial. It is known that conventional Reactivity Meters cannot operate in subcritical levels nor describe the dynamics of multiplying systems in these conditions, by the very structure of the classical kinetic equations. Several theoretical models have been proposed to characterize the kinetics of such systems with special regard to the reactivity, as the one developed by Gandini and Salvatores among others. This work presents a discussion about the derivation of point kinetics equations for subcritical systems and the importance of considering the external source. From the point of view of the Gandini and Salvatores' point kinetics model and based on the experimental results provided by Lee and dos Santos, it was possible to develop an innovative approach. This article proposes an algorithm that describes the subcritical reactivity with external source, contributing to the advancement of studies in the field. (authors)« less

Phase reduction of a limit cycle oscillator perturbed by a strong amplitude-modulated high-frequency force.

PubMed

Pyragas, Kestutis; Novičenko, Viktor

2015-07-01

The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show that if the effective phase response curve is everywhere positive (negative), then an entrainment of the oscillator to an envelope frequency is possible only when this frequency is higher (lower) than the natural frequency of the oscillator. Also, by using the Pontryagin maximum principle, we have derived an optimal waveform of the perturbation that ensures an entrainment of the oscillator with minimal power. The theoretical results are demonstrated with the Stuart-Landau oscillator and model neurons.

Poroelastic theory of consolidation in unsaturated soils incorporating gravitational body forces

NASA Astrophysics Data System (ADS)

Lo, Wei-Cheng; Chao, Nan-Chieh; Chen, Chu-Hui; Lee, Jhe-Wei

2017-08-01

The generalization of the poroelasticity theory of consolidation in unsaturated soils to well represent gravitational body forces is presented in the current study. Three partial differential equations featuring the displacement vector of the solid phase, along with the excess pore water and air pressures as dependent variables are derived, with coupling that occurs in the first-order temporal- and spatial- derivative terms. The former arises from viscous drag between solid and fluid, whereas the latter is attributed to the presence of gravity. Given the physically-consistent initial and boundary conditions, these coupled equations are numerically solved under uniaxial strain as a representative example. Our results reveal that variations in the excess pore water pressure due to the existence of gravitational forces increase with soil depth, but these variations are not significant if the soil layer is not sufficiently long. A dimensionless parameter is defined theoretically to quantify the impact of those forces on the final total settlement. This impact is shown to become greater as the soil layer is less stiff and has more length, and bears an inversely-proportional trend with initial water saturation.

Does space-time torsion determine the minimum mass of gravitating particles?

NASA Astrophysics Data System (ADS)

Böhmer, Christian G.; Burikham, Piyabut; Harko, Tiberiu; Lake, Matthew J.

2018-03-01

We derive upper and lower limits for the mass-radius ratio of spin-fluid spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically symmetric interior geometry, we obtain the generalized continuity and Tolman-Oppenheimer-Volkoff equations for a Weyssenhoff spin fluid in hydrostatic equilibrium, expressed in terms of the effective mass, density and pressure, all of which contain additional contributions from the spin. The generalized Buchdahl inequality, which remains valid at any point in the interior, is obtained, and general theoretical limits for the maximum and minimum mass-radius ratios are derived. As an application of our results we obtain gravitational red shift bounds for compact spin-fluid objects, which may (in principle) be used for observational tests of Einstein-Cartan theory in an astrophysical context. We also briefly consider applications of the torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass.

Temperature effects on the universal equation of state of solids

NASA Technical Reports Server (NTRS)

Vinet, P.; Ferrante, J.; Smith, J. R.; Rose, J. H.

1986-01-01

Recently it has been argued based on theoretical calculations and experimental data that there is a universal form for the equation of state of solids. This observation was restricted to the range of temperatures and pressures such that there are no phase transitions. The use of this universal relation to estimate pressure-volume relations (i.e., isotherms) required three input parameters at each fixed temperature. It is shown that for many solids the input data needed to predict high temperature thermodynamical properties can be dramatically reduced. In particular, only four numbers are needed: (1) the zero pressure (P=0) isothermal bulk modulus; (2)it P=0 pressure derivative; (3) the P=0 volume; and (4) the P=0 thermal expansion; all evaluated at a single (reference) temperature. Explicit predictions are made for the high temperature isotherms, the thermal expansion as a function of temperature, and the temperature variation of the isothermal bulk modulus and its pressure derivative. These predictions are tested using experimental data for three representative solids: gold, sodium chloride, and xenon. Good agreement between theory and experiment is found.

Temperature effects on the universal equation of state of solids

NASA Technical Reports Server (NTRS)

Vinet, Pascal; Ferrante, John; Smith, John R.; Rose, James H.

1987-01-01

Recently it has been argued based on theoretical calculations and experimental data that there is a universal form for the equation of state of solids. This observation was restricted to the range of temperatures and pressures such that there are no phase transitions. The use of this universal relation to estimate pressure-volume relations (i.e., isotherms) required three input parameters at each fixed temperature. It is shown that for many solids the input data needed to predict high temperature thermodynamical properties can be dramatically reduced. In particular, only four numbers are needed: (1) the zero pressure (P = 0) isothermal bulk modulus; (2) its P = 0 pressure derivative; (3) the P = 0 volume; and (4) the P = 0 thermal expansion; all evaluated at a single (reference) temperature. Explicit predictions are made for the high temperature isotherms, the thermal expansion as a function of temperature, and the temperature variation of the isothermal bulk modulus and its pressure derivative. These predictions are tested using experimental data for three representative solids: gold, sodium chloride, and xenon. Good agreement between theory and experiment is found.

Concentration Dependence of Solution Shear Viscosity and Solute Mass Diffusivity in Crystal Growth from Solutions

NASA Technical Reports Server (NTRS)

Izmailov, Alexander F.; Myerson, Allan S.

1995-01-01

The physical properties of a supersaturated binary solution such as its density rho, shear viscosity eta, and solute mass diffusivity D are dependent on the solute concentration c: rho = rho(c), eta = eta(c), and D = D(c). The diffusion boundary layer equations related to crystal growth from solution are derived for the case of natural convection with a solution density, a shear viscosity, and a solute diffusivity that are all depen- dent on solute concentration. The solution of these equations has demonstrated the following. (1) At the vicinity of the saturation concentration c(sub s) the solution shear viscosity eta depends on rho as eta(sub s) = eta(rho(sub s))varies as square root of rho(c(sub s)). This theoretically derived result has been verified in experiments with several aqueous solutions of inorganic and organic salts. (2) The maximum solute mass transfer towards the growing crystal surface can be achieved for values of c where the ratio of d ln(D(c)/dc) to d ln(eta(c)/dc) is a maximum.

Does space-time torsion determine the minimum mass of gravitating particles?

PubMed

Böhmer, Christian G; Burikham, Piyabut; Harko, Tiberiu; Lake, Matthew J

2018-01-01

We derive upper and lower limits for the mass-radius ratio of spin-fluid spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically symmetric interior geometry, we obtain the generalized continuity and Tolman-Oppenheimer-Volkoff equations for a Weyssenhoff spin fluid in hydrostatic equilibrium, expressed in terms of the effective mass, density and pressure, all of which contain additional contributions from the spin. The generalized Buchdahl inequality, which remains valid at any point in the interior, is obtained, and general theoretical limits for the maximum and minimum mass-radius ratios are derived. As an application of our results we obtain gravitational red shift bounds for compact spin-fluid objects, which may (in principle) be used for observational tests of Einstein-Cartan theory in an astrophysical context. We also briefly consider applications of the torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass.

An extended GS method for dense linear systems

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

2009-09-01

Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

On the tesseral-harmonics resonance problem in artificial-satellite theory

NASA Technical Reports Server (NTRS)

Romanowicz, B. A.

1975-01-01

The longitude-dependent part of the geopotential usually gives rise only to short-period effects in the motion of an artificial satellite. However, when the motion of the satellite is commensurable with that of the earth, the path of the satellite repeats itself relative to the earth and perturbations build up at each passage of the satellite in the same spot, so that there can be important long-period effects. In order to take these effects into account in deriving a theoretical solution to the equations of motion of an artificial satellite, it is necessary to select terms in the longitude-dependent part of the geopotential that will contribute significantly to the perturbations. Attempts made to obtain a selection that is valid in a general case, regardless of the initial eccentricity of the orbit and of the order of the resonance, are reported. The solution to the equations of motion of an artificial satellite, in a geopotential thus determined, is then derived by using Hori's method by Lie series, which, by its properties regarding canonical invariance, has proved advantageous in the classical theory.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

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

Wintermeyer, Niklas; Winters, Andrew R., E-mail: awinters@math.uni-koeln.de; Gassner, Gregor J.

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving schememore » we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.« less

Theoretically Investigating the Nature of Spacetime- A grand definition of what clocks measure

NASA Astrophysics Data System (ADS)

Egie, Meru

Einstein's special theory of relativity established time as a dimension of reality, explaining physically the mathematical stipulations of Lorentz transformation equations that are required to keep the validity of Maxwell's equations of light and explain the null result of Michelson-Morley experiment. Our current understanding of time is relativistic, that is time is not absolute but runs differently depending on the frame of reference, yet this description uncovers so little about the fundamental reality of time. Using mathematical arguments derived from a simple thought experiment, both Lorentz transformation equations and Einstein's far reaching conclusions of his 1905 paper on the electrodynamics of moving bodies are obtained with arguments that suggest no prior knowledge of both Einstein and Lorentz works. This work attempts uncovering the fundamental nature of what clocks measure and a major implication of this is that the fourth dimension could just be a persistent illusion caused by the existence of space. Gratitude to Mr. Jon Egie for his support and Aghogo Rita for her listening ears.

Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shear

NASA Astrophysics Data System (ADS)

Niu, Ben; Zhang, Jiaming; Wei, Junjie

2018-05-01

In this paper, time delay effect and distributed shear are considered in the Kuramoto model. On the Ott-Antonsen's manifold, through analyzing the associated characteristic equation of the reduced functional differential equation, the stability boundary of the incoherent state is derived in multiple-parameter space. Moreover, very rich dynamical behavior such as stability switches inducing synchronization switches can occur in this equation. With the loss of stability, Hopf bifurcating coherent states arise, and the criticality of Hopf bifurcations is determined by applying the normal form theory and the center manifold theorem. On one hand, theoretical analysis indicates that the width of shear distribution and time delay can both eliminate the synchronization then lead the Kuramoto model to incoherence. On the other, time delay can induce several coexisting coherent states. Finally, some numerical simulations are given to support the obtained results where several bifurcation diagrams are drawn, and the effect of time delay and shear is discussed.

Entropy production and energy dissipation in symmetric redox supercapacitors

NASA Astrophysics Data System (ADS)

Palma-Aramburu, N.; Santamaría-Holek, I.

2017-08-01

In this work we propose a theoretical model that accounts for the main features of the loading-unloading process of a symmetric redox MnO2-based supercapacitor dominated by fast electrochemical reactions at the electrodes. The model is formulated on the basis of nonequilibrium thermodynamics from which we are able to deduce generalized expressions for the electrochemical affinity, the load-voltage and the current-voltage equations that constitute generalizations of the current-overpotential and Butler-Volmer equations, and that are used to describe experimental voltagram data with good agreement. These equations allowed us to derive the behavior of the energy dissipated per cycle showing that it has a nonmonotonic behavior and that in the operation regime it follows a power-law behavior as a function of the frequency. The existence of a maximum for the energy dissipated as a function of the frequency suggests the that the corresponding optimal operation frequency should be similar in value to ωmax.

QSTR of the toxicity of some organophosphorus compounds by using the quantum chemical and topological descriptors.

PubMed

Senior, Samir A; Madbouly, Magdy D; El massry, Abdel-Moneim

2011-09-01

Quantum chemical and topological descriptors of some organophosphorus compounds (OP) were correlated with their toxicity LD(50) as a dermal. The quantum chemical parameters were obtained using B3LYP/LANL2DZdp-ECP optimization. Using linear regression analysis, equations were derived to calculate the theoretical LD(50) of the studied compounds. The inclusion of quantum parameters, having both charge indices and topological indices, affects the toxicity of the studied compounds resulting in high correlation coefficient factors for the obtained equations. Two of the new four firstly supposed descriptors give higher correlation coefficients namely the Heteroatom Corrected Extended Connectivity Randic index ((1)X(HCEC)) and the Density Randic index ((1)X(Den)). The obtained linear equations were applied to predict the toxicity of some related structures. It was found that the sulfur atoms in these compounds must be replaced by oxygen atoms to achieve improved toxicity. Copyright © 2011 Elsevier Ltd. All rights reserved.

Theoretical study of the design of a catalyst for para to ortho hydrogen conversion

NASA Technical Reports Server (NTRS)

Coffman, Robert E.

1992-01-01

The theory of Petzinger and Scalapino (1973) was thoroughly reviewed, and all of the basic equations for paramagnetic para to ortho hydrogen catalysis re-derived. There are only a few minor phase errors and errors of omission in the description of the theory. Three models (described by Petzinger and Scalapino) for the rate of para to ortho H2 catalysis were worked out, and uniform agreement obtained to within a constant factor of 2 pi. The analytical methods developed in the course of this study were then extended to two new models, which more adequately describe the process of surface catalysis including transfer of hydrogen molecules onto and off of the surface. All five equations for the para to ortho catalytic rate of conversion are described. The two new equations describe the catalytic rate for these models: H2 on the surface is a 2-D gas with lifetime tau; and H2 on the surface is a 2-D liquid undergoing Brownian motion (diffusion) with surface lifetime tau.

Dynamic Analysis and Control of Lightweight Manipulators with Flexible Parallel Link Mechanisms. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lee, Jeh Won

1990-01-01

The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.

Relativistic laser-plasma interactions in the quantum regime.

PubMed

Eliasson, Bengt; Shukla, P K

2011-04-01

We consider nonlinear interactions between a relativistically strong laser beam and a plasma in the quantum regime. The collective behavior of electrons is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the electromagnetic wave through the Maxwell and Poisson equations. This allows us to study nonlinear interactions between arbitrarily large-amplitude electromagnetic waves and a quantum plasma. We have used our system of nonlinear equations to study theoretically the parametric instabilities involving stimulated Raman scattering and modulational instabilities. A model for quasi-steady-state propagating electromagnetic wave packets is also derived, and which shows possibility of localized solitary structures in a quantum plasma. Numerical simulations demonstrate collapse and acceleration of electrons in the nonlinear stage of the modulational instability, as well as possibility of the wake-field acceleration of electrons to relativistic speeds by short laser pulses at nanometer length scales. Our study is relevant for understanding the localization of intense electromagnetic pulses in a quantum plasma with extremely high electron densities and relatively low temperature.

Dynamic density functional theory with hydrodynamic interactions: theoretical development and application in the study of phase separation in gas-liquid systems.

PubMed

Kikkinides, E S; Monson, P A

2015-03-07

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van der Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.

Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems

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

Kikkinides, E. S.; Monson, P. A.

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van dermore » Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.« less

Study on Predicting Axial Load Capacity of CFST Columns

NASA Astrophysics Data System (ADS)

Ravi Kumar, H.; Muthu, K. U.; Kumar, N. S.

2017-11-01

This work presents an analytical study and experimental study on the behaviour and ultimate load carrying capacity of axially compressed self-compacting concrete-filled steel tubular columns. Results of tests conducted by various researchers on 213 samples concrete-filled steel tubular columns are reported and present authors experimental data are reported. Two theoretical equations were derived for the prediction of the ultimate axial load strength of concrete-filled steel tubular columns. The results from prediction were compared with the experimental data. Validation to the experimental results was made.

Physical implications of the eclipsing binary pulsar

NASA Technical Reports Server (NTRS)

Wasserman, Ira; Cordes, James M.

1988-01-01

The observed characteristics of the msec pulsar P1957+20, discovered in an eclipsing binary by Fruchter et al. (1988), are considered theoretically. Model equations for the stellar wind and optical emission are derived and used to estimate the effective temperature and optical luminosity associated with wind excitation; then the energy levels required to generate such winds are investigated. The color temperature of the pulsar-heated stellar surface calculated under the assumption of adiabatic expansion is 1000-10,000 K, in good agreement with the observational estimate of 5500 K.

Random walks with random velocities.

PubMed

Zaburdaev, Vasily; Schmiedeberg, Michael; Stark, Holger

2008-07-01

We consider a random walk model that takes into account the velocity distribution of random walkers. Random motion with alternating velocities is inherent to various physical and biological systems. Moreover, the velocity distribution is often the first characteristic that is experimentally accessible. Here, we derive transport equations describing the dispersal process in the model and solve them analytically. The asymptotic properties of solutions are presented in the form of a phase diagram that shows all possible scaling regimes, including superdiffusive, ballistic, and superballistic motion. The theoretical results of this work are in excellent agreement with accompanying numerical simulations.

Post Kalman progress

NASA Technical Reports Server (NTRS)

Sonnabend, David

1995-01-01

In a paper here last year, an idea was put forward that much greater performance could be obtained from an observer, relative to a Kalman filter if more general performance indices were adopted, and the full power spectra of all the noises were employed. The considerable progress since then is reported here. Included are an extension of the theory to regulators, direct calculation of the theory's fundamental quantities - the noise effect integrals - for several theoretical spectra, and direct derivations of the Riccati equations of LQG (Linear-Quadratic-Gaussian) and Kalman theory yielding new insights.

Stress, deformation, conservation, and rheology: a survey of key concepts in continuum mechanics

USGS Publications Warehouse

Major, J.J.

2013-01-01

This chapter provides a brief survey of key concepts in continuum mechanics. It focuses on the fundamental physical concepts that underlie derivations of the mathematical formulations of stress, strain, hydraulic head, pore-fluid pressure, and conservation equations. It then shows how stresses are linked to strain and rates of distortion through some special cases of idealized material behaviors. The goal is to equip the reader with a physical understanding of key mathematical formulations that anchor continuum mechanics in order to better understand theoretical studies published in geomorphology.

Statistical Analysis and Storm Sampling Approach for Lakes Michigan and St. Clair, Great Lakes Coastal Flood Study, 2012 Federal Inter-Agency Initiative

DTIC Science & Technology

2012-09-01

Originally, Resio and Vincent (1977) used theoretical results derived from Cardone (1969) to develop curves relating overland to overlake wind speeds...Later, Schwab (1978) proposed the following equation as an approximation to the Cardone curves: ERDC/CHL TR-12-19 13 /Δ. Δ . ΔW L L TTU U U T...1992), the CEM (USACE 2002), and in Smith (1991); Schwab and Morton (1984); Donelan (1980); Schwab (1978); Resio and Vincent (1977); and Cardone

Transient Combustion in Granular Propellant Beds. Part I. Theoretical Modeling and Numerical Solution of Transient Combustion Processes in Mobile Granular Propellant Beds

DTIC Science & Technology

1977-08-01

TR~ANSIENT COMBUSTION PROCESSES IN MOBILE GRANULAR PROPELLANT BEDS Prqprid by The Pennsylvania Stats UnIversiV 197 Dopartme of Nmchanica! EngwineerIng...the ignition and flame spreadinb prc-eases by assuming that the granular propillents are fixed in space; and 3) modeling cf mobile granular beds so...through an aggrtgate of mobile "’actin&, partic~vi. The diffevewsoa Wi derivation of conservation equa~tions betvewu our approacit md this -f a Aivorain

Blinking fluorescence of single donor-acceptor pairs: important role of "dark'' states in resonance energy transfer via singlet levels.

PubMed

Osad'ko, I S; Shchukina, A L

2012-06-01

The influence of triplet levels on Förster resonance energy transfer via singlet levels in donor-acceptor (D-A) pairs is studied. Four types of D-A pair are considered: (i) two-level donor and two-level acceptor, (ii) three-level donor and two-level acceptor, (iii) two-level donor and three-level acceptor, and (iv) three-level donor and three-level acceptor. If singlet-triplet transitions in a three-level acceptor molecule are ineffective, the energy transfer efficiency E=I_{A}/(I_{A}+I_{D}), where I_{D} and I_{A} are the average intensities of donor and acceptor fluorescence, can be described by the simple theoretical equation E(F)=FT_{D}/(1+FT_{D}). Here F is the rate of energy transfer, and T_{D} is the donor fluorescence lifetime. In accordance with the last equation, 100% of the donor electronic energy can be transferred to an acceptor molecule at FT_{D}≫1. However, if singlet-triplet transitions in a three-level acceptor molecule are effective, the energy transfer efficiency is described by another theoretical equation, E(F)=F[over ¯](F)T_{D}/[1+F[over ¯](F)T_{D}]. Here F[over ¯](F) is a function of F depending on singlet-triplet transitions in both donor and acceptor molecules. Expressions for the functions F[over ¯](F) are derived. In this case the energy transfer efficiency will be far from 100% even at FT_{D}≫1. The character of the intensity fluctuations of donor and acceptor fluorescence indicates which of the two equations for E(F) should be used to find the value of the rate F. Therefore, random time instants of photon emission in both donor and acceptor fluorescence are calculated by the Monte Carlo method for all four types of D-A pair. Theoretical expressions for start-stop correlators (waiting time distributions) in donor and acceptor fluorescence are derived. The probabilities w_{N}^{D}(t) and w_{N}^{A}(t) of finding N photons of donor and acceptor fluorescence in the time interval t are calculated for various values of the energy transfer rate F and for all four types of D-A pair. Comparison of the calculated D and A fluorescence trajectories with those measured by Weiss and co-workers proves the important role of triplet levels in energy transfer via singlet levels.

Theoretical and computational analyses of LNG evaporator

NASA Astrophysics Data System (ADS)

Chidambaram, Palani Kumar; Jo, Yang Myung; Kim, Heuy Dong

2017-04-01

Theoretical and numerical analysis on the fluid flow and heat transfer inside a LNG evaporator is conducted in this work. Methane is used instead of LNG as the operating fluid. This is because; methane constitutes over 80% of natural gas. The analytical calculations are performed using simple mass and energy balance equations. The analytical calculations are made to assess the pressure and temperature variations in the steam tube. Multiphase numerical simulations are performed by solving the governing equations (basic flow equations of continuity, momentum and energy equations) in a portion of the evaporator domain consisting of a single steam pipe. The flow equations are solved along with equations of species transport. Multiphase modeling is incorporated using VOF method. Liquid methane is the primary phase. It vaporizes into the secondary phase gaseous methane. Steam is another secondary phase which flows through the heating coils. Turbulence is modeled by a two equation turbulence model. Both the theoretical and numerical predictions are seen to match well with each other. Further parametric studies are planned based on the current research.

The physics behind Van der Burgh's empirical equation, providing a new predictive equation for salinity intrusion in estuaries

NASA Astrophysics Data System (ADS)

Zhang, Zhilin; Savenije, Hubert H. G.

2017-07-01

The practical value of the surprisingly simple Van der Burgh equation in predicting saline water intrusion in alluvial estuaries is well documented, but the physical foundation of the equation is still weak. In this paper we provide a connection between the empirical equation and the theoretical literature, leading to a theoretical range of Van der Burgh's coefficient of 1/2 < K < 2/3 for density-driven mixing which falls within the feasible range of 0 < K < 1. In addition, we developed a one-dimensional predictive equation for the dispersion of salinity as a function of local hydraulic parameters that can vary along the estuary axis, including mixing due to tide-driven residual circulation. This type of mixing is relevant in the wider part of alluvial estuaries where preferential ebb and flood channels appear. Subsequently, this dispersion equation is combined with the salt balance equation to obtain a new predictive analytical equation for the longitudinal salinity distribution. Finally, the new equation was tested and applied to a large database of observations in alluvial estuaries, whereby the calibrated K values appeared to correspond well to the theoretical range.

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…

Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions

NASA Astrophysics Data System (ADS)

Barré, J.; Carrillo, J. A.; Degond, P.; Peurichard, D.; Zatorska, E.

2018-02-01

We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation-diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.

Development and validation of a short-lag spatial coherence theory for photoacoustic imaging

NASA Astrophysics Data System (ADS)

Graham, Michelle T.; Lediju Bell, Muyinatu A.

2018-02-01

We previously derived spatial coherence theory to be implemented for studying theoretical properties of ShortLag Spatial Coherence (SLSC) beamforming applied to photoacoustic images. In this paper, our newly derived theoretical equation is evaluated to generate SLSC images of a point target and a 1.2 mm diameter target and corresponding lateral profiles. We compared SLSC images simulated solely based on our theory to SLSC images created after beamforming acoustic channel data from k-Wave simulations of 1.2 mm-diameter disc target. This process was repeated for a point target and the full width at half the maximum signal amplitudes were measured to estimate the resolution of each imaging system. Resolution as a function of lag was comparable for the first 10% of the receive aperture (i.e., the short-lag region), after which resolution measurements diverged by a maximum of 1 mm between the two types of simulated images. These results indicate the potential for both simulation methods to be utilized as independent resources to study coherence-based photoacoustic beamformers when imaging point-like targets.

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

NASA Astrophysics Data System (ADS)

Yi, Dake; Wang, TzuChiang

2018-06-01

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J( z), the stress intensity factor K( z) and the tri-axial stress constraint level T z ( z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J( z) and T z ( z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions.

PubMed

Barré, J; Carrillo, J A; Degond, P; Peurichard, D; Zatorska, E

2018-01-01

We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation-diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.

The concept of entropy in landscape evolution

USGS Publications Warehouse

Leopold, Luna Bergere; Langbein, Walter Basil

1962-01-01

The concept of entropy is expressed in terms of probability of various states. Entropy treats of the distribution of energy. The principle is introduced that the most probable condition exists when energy in a river system is as uniformly distributed as may be permitted by physical constraints. From these general considerations equations for the longitudinal profiles of rivers are derived that are mathematically comparable to those observed in the field. The most probable river profiles approach the condition in which the downstream rate of production of entropy per unit mass is constant. Hydraulic equations are insufficient to determine the velocity, depths, and slopes of rivers that are themselves authors of their own hydraulic geometries. A solution becomes possible by introducing the concept that the distribution of energy tends toward the most probable. This solution leads to a theoretical definition of the hydraulic geometry of river channels that agrees closely with field observations. The most probable state for certain physical systems can also be illustrated by random-walk models. Average longitudinal profiles and drainage networks were so derived and these have the properties implied by the theory. The drainage networks derived from random walks have some of the principal properties demonstrated by the Horton analysis; specifically, the logarithms of stream length and stream numbers are proportional to stream order.

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.

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

NASA Astrophysics Data System (ADS)

Chen, Jing-Bo

2014-06-01

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

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.

Spreading of blood drops over dry porous substrate: complete wetting case.

PubMed

Chao, Tzu Chieh; Arjmandi-Tash, Omid; Das, Diganta B; Starov, Victor M

2015-05-15

The process of dried blood spot sampling involves simultaneous spreading and penetration of blood into a porous filter paper with subsequent evaporation and drying. Spreading of small drops of blood, which is a non-Newtonian liquid, over a dry porous layer is investigated from both theoretical and experimental points of view. A system of two differential equations is derived, which describes the time evolution of radii of both the drop base and the wetted region inside the porous medium. The system of equations does not include any fitting parameters. The predicted time evolutions of both radii are compared with experimental data published earlier. For a given power law dependency of viscosity of blood with different hematocrit level, radii of both drop base and wetted region, and contact angle fell on three universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and the wetted region inside the porous layer and dynamic contact angle on dimensionless time. The predicted theoretical relationships are three universal curves accounting satisfactorily for the experimental data. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Modeling and dynamic properties of dual-chamber solid and liquid mixture vibration isolator

NASA Astrophysics Data System (ADS)

Li, F. S.; Chen, Q.; Zhou, J. H.

2016-07-01

The dual-chamber solid and liquid mixture (SALiM) vibration isolator, mainly proposed for vibration isolation of heavy machines with low frequency, consists of four principle parts: SALiM working media including elastic elements and incompressible oil, multi-layers bellows container, rigid reservoir and the oil tube connecting the two vessels. The isolation system under study is governed by a two-degrees-of-freedom (2-DOF) nonlinear equation including quadratic damping. Simplifying the nonlinear damping into viscous damping, the equivalent stiffness and damping model is derived from the equation for the response amplitude. Theoretical analysis and numerical simulation reveal that the isolator's stiffness and damping have multiple properties with different parameters, among which the effects of exciting frequency, vibrating amplitude, quadratic damping coefficient and equivalent stiffness of the two chambers on the isolator's dynamics are discussed in depth. Based on the boundary characteristics of stiffness and damping and the main causes for stiffness hardening effect, improvement strategies are proposed to obtain better dynamic properties. At last, experiments were implemented and the test results were generally consistent with the theoretical ones, which verified the reliability of the nonlinear dynamic model.

Theoretical Foundation of Zisman's Empirical Equation for Wetting of Liquids on Solid Surfaces

ERIC Educational Resources Information Center

Zhu, Ruzeng; Cui, Shuwen; Wang, Xiaosong

2010-01-01

Theories of wetting of liquids on solid surfaces under the condition that van der Waals force is dominant are briefly reviewed. We show theoretically that Zisman's empirical equation for wetting of liquids on solid surfaces is a linear approximation of the Young-van der Waals equation in the wetting region, and we express the two parameters in…

Full analytical solution of the bloch equation when using a hyperbolic-secant driving function.

PubMed

Zhang, Jinjin; Garwood, Michael; Park, Jang-Yeon

2017-04-01

The frequency-swept pulse known as the hyperbolic-secant (HS) pulse is popular in NMR for achieving adiabatic spin inversion. The HS pulse has also shown utility for achieving excitation and refocusing in gradient-echo and spin-echo sequences, including new ultrashort echo-time imaging (e.g., Sweep Imaging with Fourier Transform, SWIFT) and B 1 mapping techniques. To facilitate the analysis of these techniques, the complete theoretical solution of the Bloch equation, as driven by the HS pulse, was derived for an arbitrary state of initial magnetization. The solution of the Bloch-Riccati equation for transverse and longitudinal magnetization for an arbitrary initial state was derived analytically in terms of HS pulse parameters. The analytical solution was compared with the solutions using both the Runge-Kutta method and the small-tip approximation. The analytical solution was demonstrated on different initial states at different frequency offsets with/without a combination of HS pulses. Evolution of the transverse magnetization was influenced significantly by the choice of HS pulse parameters. The deviation of the magnitude of the transverse magnetization, as obtained by comparing the small-tip approximation to the analytical solution, was < 5% for flip angles < 30 °, but > 10% for the flip angles > 40 °. The derived analytical solution provides insights into the influence of HS pulse parameters on the magnetization evolution. Magn Reson Med 77:1630-1638, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

A theoretical investigation on the parametric instability excited by X-mode polarized electromagnetic wave at Tromsø

NASA Astrophysics Data System (ADS)

Wang, Xiang; Cannon, Patrick; Zhou, Chen; Honary, Farideh; Ni, Binbin; Zhao, Zhengyu

2016-04-01

Recent ionospheric modification experiments performed at Tromsø, Norway, have indicated that X-mode pump wave is capable of stimulating high-frequency enhanced plasma lines, which manifests the excitation of parametric instability. This paper investigates theoretically how the observation can be explained by the excitation of parametric instability driven by X-mode pump wave. The threshold of the parametric instability has been calculated for several recent experimental observations at Tromsø, illustrating that our derived equations for the excitation of parametric instability for X-mode heating can explain the experimental observations. According to our theoretical calculation, a minimum fraction of pump wave electric field needs to be directed along the geomagnetic field direction in order for the parametric instability threshold to be met. A full-wave finite difference time domain simulation has been performed to demonstrate that a small parallel component of pump wave electric field can be achieved during X-mode heating in the presence of inhomogeneous plasma.

New circuit theory of multiconductor transmission lines resulting from a new practice of noise reduction.

PubMed

Toki, Hiroshi; Sato, Kenji

2014-01-01

In modern life, we are surrounded by and filled with electromagnetic noise caused by the dominant use of energy in the form of electricity. This situation is brought about by the fact that the noise is not understood theoretically. A new practice of noise reduction was introduced for the construction of Heavy Ion Medical Accelerator in Chiba (HIMAC). The key concept is a symmetric three-line circuit that arranges power supplies, noise filters and magnets around a third central ground line. A continuous theoretical effort forced us to find a new circuit theory involving a multiconductor transmission-line system starting from Maxwell's equations without any approximation. We discuss the essence of all of these experimental and theoretical developments with the hope to remove unnecessary electromagnetic noise not only from power supplies, but also from all electric devices. The newly derived circuit theory of multiconductor transmission lines is universal, and establishes the validity of the practice of noise reduction.

New circuit theory of multiconductor transmission lines resulting from a new practice of noise reduction

PubMed Central

TOKI, Hiroshi; SATO, Kenji

2014-01-01

In modern life, we are surrounded by and filled with electromagnetic noise caused by the dominant use of energy in the form of electricity. This situation is brought about by the fact that the noise is not understood theoretically. A new practice of noise reduction was introduced for the construction of Heavy Ion Medical Accelerator in Chiba (HIMAC). The key concept is a symmetric three-line circuit that arranges power supplies, noise filters and magnets around a third central ground line. A continuous theoretical effort forced us to find a new circuit theory involving a multiconductor transmission-line system starting from Maxwell’s equations without any approximation. We discuss the essence of all of these experimental and theoretical developments with the hope to remove unnecessary electromagnetic noise not only from power supplies, but also from all electric devices. The newly derived circuit theory of multiconductor transmission lines is universal, and establishes the validity of the practice of noise reduction. PMID:24522153

Analysis of Drop Oscillations Excited by an Electrical Point Force in AC EWOD

NASA Astrophysics Data System (ADS)

Oh, Jung Min; Ko, Sung Hee; Kang, Kwan Hyoung

2008-03-01

Recently, a few researchers have reported the oscillation of a sessile drop in AC EWOD (electrowetting on dielectrics), and some of its consequences. The drop oscillation problem in AC EWOD is associated with various applications based on electrowetting such as LOC (lab-on-a-chip), liquid lens, and electronic display. However, no theoretical analysis of the problem has been attempted yet. In the present paper, we propose a theoretical model to analyze the oscillation by applying the conventional method to analyze the drop oscillation. The domain perturbation method is used to derive the shape mode equations under the assumptions of weak viscous flow and small deformation. The Maxwell stress is exerted on the three-phase contact line of the droplet like a point force. The force is regarded as a delta function, and is decomposed into the driving forces of each shape mode. The theoretical results on the shape and the frequency responses are compared with experiments, which shows a qualitative agreement.

Theoretical foundations for quantitative paleogenetics. III - The molecular divergence of nucleic acids and proteins for the case of genetic events of unequal probability

NASA Technical Reports Server (NTRS)

Holmquist, R.; Pearl, D.

1980-01-01

Theoretical equations are derived for molecular divergence with respect to gene and protein structure in the presence of genetic events with unequal probabilities: amino acid and base compositions, the frequencies of nucleotide replacements, the usage of degenerate codons, the distribution of fixed base replacements within codons and the distribution of fixed base replacements among codons. Results are presented in the form of tables relating the probabilities of given numbers of codon base changes with respect to the original codon for the alpha hemoglobin, beta hemoglobin, myoglobin, cytochrome c and parvalbumin group gene families. Application of the calculations to the rabbit alpha and beta hemoglobin mRNAs and proteins indicates that the genes are separated by about 425 fixed based replacements distributed over 114 codon sites, which is a factor of two greater than previous estimates. The theoretical results also suggest that many more base replacements are required to effect a given gene or protein structural change than previously believed.

Derivative free Davidon-Fletcher-Powell (DFP) for solving symmetric systems of nonlinear equations

NASA Astrophysics Data System (ADS)

Mamat, M.; Dauda, M. K.; Mohamed, M. A. bin; Waziri, M. Y.; Mohamad, F. S.; Abdullah, H.

2018-03-01

Research from the work of engineers, economist, modelling, industry, computing, and scientist are mostly nonlinear equations in nature. Numerical solution to such systems is widely applied in those areas of mathematics. Over the years, there has been significant theoretical study to develop methods for solving such systems, despite these efforts, unfortunately the methods developed do have deficiency. In a contribution to solve systems of the form F(x) = 0, x ∈ Rn , a derivative free method via the classical Davidon-Fletcher-Powell (DFP) update is presented. This is achieved by simply approximating the inverse Hessian matrix with {Q}k+1-1 to θkI. The modified method satisfied the descent condition and possess local superlinear convergence properties. Interestingly, without computing any derivative, the proposed method never fail to converge throughout the numerical experiments. The output is based on number of iterations and CPU time, different initial starting points were used on a solve 40 benchmark test problems. With the aid of the squared norm merit function and derivative-free line search technique, the approach yield a method of solving symmetric systems of nonlinear equations that is capable of significantly reducing the CPU time and number of iteration, as compared to its counterparts. A comparison between the proposed method and classical DFP update were made and found that the proposed methodis the top performer and outperformed the existing method in almost all the cases. In terms of number of iterations, out of the 40 problems solved, the proposed method solved 38 successfully, (95%) while classical DFP solved 2 problems (i.e. 05%). In terms of CPU time, the proposed method solved 29 out of the 40 problems given, (i.e.72.5%) successfully whereas classical DFP solves 11 (27.5%). The method is valid in terms of derivation, reliable in terms of number of iterations and accurate in terms of CPU time. Thus, suitable and achived the objective.

The Dependence of Water Permeability in Quartz Sand on Gas Hydrate Saturation in the Pore Space

NASA Astrophysics Data System (ADS)

Kossel, E.; Deusner, C.; Bigalke, N.; Haeckel, M.

2018-02-01

Transport of fluids in gas hydrate bearing sediments is largely defined by the reduction of the permeability due to gas hydrate crystals in the pore space. Although the exact knowledge of the permeability behavior as a function of gas hydrate saturation is of crucial importance, state-of-the-art simulation codes for gas production scenarios use theoretically derived permeability equations that are hardly backed by experimental data. The reason for the insufficient validation of the model equations is the difficulty to create gas hydrate bearing sediments that have undergone formation mechanisms equivalent to the natural process and that have well-defined gas hydrate saturations. We formed methane hydrates in quartz sand from a methane-saturated aqueous solution and used magnetic resonance imaging to obtain time-resolved, three-dimensional maps of the gas hydrate saturation distribution. These maps were fed into 3-D finite element method simulations of the water flow. In our simulations, we tested the five most well-known permeability equations. All of the suitable permeability equations include the term (1-SH)n, where SH is the gas hydrate saturation and n is a parameter that needs to be constrained. The most basic equation describing the permeability behavior of water flow through gas hydrate bearing sand is k = k0 (1-SH)n. In our experiments, n was determined to be 11.4 (±0.3). Results from this study can be directly applied to bulk flow analysis under the assumption of homogeneous gas hydrate saturation and can be further used to derive effective permeability models for heterogeneous gas hydrate distributions at different scales.

Sensitivity of the model error parameter specification in weak-constraint four-dimensional variational data assimilation

NASA Astrophysics Data System (ADS)

Shaw, Jeremy A.; Daescu, Dacian N.

2017-08-01

This article presents the mathematical framework to evaluate the sensitivity of a forecast error aspect to the input parameters of a weak-constraint four-dimensional variational data assimilation system (w4D-Var DAS), extending the established theory from strong-constraint 4D-Var. Emphasis is placed on the derivation of the equations for evaluating the forecast sensitivity to parameters in the DAS representation of the model error statistics, including bias, standard deviation, and correlation structure. A novel adjoint-based procedure for adaptive tuning of the specified model error covariance matrix is introduced. Results from numerical convergence tests establish the validity of the model error sensitivity equations. Preliminary experiments providing a proof-of-concept are performed using the Lorenz multi-scale model to illustrate the theoretical concepts and potential benefits for practical applications.

A Thermo-Optic Propagation Modeling Capability.

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

Schrader, Karl; Akau, Ron

2014-10-01

A new theoretical basis is derived for tracing optical rays within a finite-element (FE) volume. The ray-trajectory equations are cast into the local element coordinate frame and the full finite-element interpolation is used to determine instantaneous index gradient for the ray-path integral equation. The FE methodology (FEM) is also used to interpolate local surface deformations and the surface normal vector for computing the refraction angle when launching rays into the volume, and again when rays exit the medium. The method is implemented in the Matlab(TM) environment and compared to closed- form gradient index models. A software architecture is also developedmore » for implementing the algorithms in the Zemax(TM) commercial ray-trace application. A controlled thermal environment was constructed in the laboratory, and measured data was collected to validate the structural, thermal, and optical modeling methods.« less

Hypervelocity impact on shielded plates

NASA Technical Reports Server (NTRS)

Smith, James P.

1993-01-01

A ballistic limit equation for hypervelocity impact on thin plates is derived analytically. This equation applies to cases of impulsive impact on a plate that is protected by a multi-shock shield, and it is valid in the range of velocity above 6 km/s. Experimental tests were conducted at the NASA Johnson Space Center on square aluminum plates. Comparing the center deflections of these plates with the theoretical deflections of a rigid-plastic plate subjected to a blast load, one determines the dynamic yield strength of the plate material. The analysis is based on a theory for the expansion of the fragmented projectile and on a simple failure criterion. Curves are presented for the critical projectile radius versus the projectile velocity, and for the critical plate thickness versus the velocity. These curves are in good agreement with curves that have been generated empirically.

Dynamic Modelling of the DEP Controlled Boiling in a Microchannel

NASA Astrophysics Data System (ADS)

Lackowski, Marcin; Kwidzinski, Roman

2018-04-01

The paper presents theoretical analysis of flow dynamics in a heated microchannel in which flow rate may be controlled by dielectrophoretic (DEP) forces. Proposed model equations were derived in terms of lumped parameters characterising the system comprising of DEP controller and the microchannel. In result, an equation for liquid height of rise in the controller was obtained from momentum balances in the two elements of the considered system. In the model, the boiling process in the heated section of microchannel is taken into account through a pressure drop, which is a function of flow rate and uniform heat flux. Presented calculation results show that the DEP forces influence mainly the flow rate in the microchannel. In this way, by proper modulation of voltage applied to the DEP controller, it is possible to lower the frequency of Ledinegg instabilities.

Parametric decay of an extraordinary electromagnetic wave in relativistic plasma

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

Dorofeenko, V. G.; Krasovitskiy, V. B., E-mail: krasovit@mail.ru; Turikov, V. A.

2015-03-15

Parametric instability of an extraordinary electromagnetic wave in plasma preheated to a relativistic temperature is considered. A set of self-similar nonlinear differential equations taking into account the electron “thermal” mass is derived and investigated. Small perturbations of the parameters of the heated plasma are analyzed in the linear approximation by using the dispersion relation determining the phase velocities of the fast and slow extraordinary waves. In contrast to cold plasma, the evanescence zone in the frequency range above the electron upper hybrid frequency vanishes and the asymptotes of both branches converge. Theoretical analysis of the set of nonlinear equations showsmore » that the growth rate of decay instability increases with increasing initial temperature of plasma electrons. This result is qualitatively confirmed by numerical simulations of plasma heating by a laser pulse injected from vacuum.« less

Stability and diversity in collective adaptation

NASA Astrophysics Data System (ADS)

Sato, Yuzuru; Akiyama, Eizo; Crutchfield, James P.

2005-10-01

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in collective adaptation. We also analyze the adaptation dynamics from an information-theoretic viewpoint and discuss self-organization induced by the dynamics of uncertainty, giving a novel view of collective adaptation.

The role and behavior of spin in gravitational physics

NASA Technical Reports Server (NTRS)

Ray, John R.

1987-01-01

A self-consistent method of introducing spin into any Lagrangian based theory of gravitation was developed. The metric variation of the Lagrangian in the theory leads to an improved energy-momentum tensor which represents the source term in the gravitational field equations. The goal of the research is the construction of a theory general enough to be used to investigate spin effects in astrophysical objects and cosmology, and also to serve as a basis for discussion of the theoretical ideas tested by the NASA Gyroscope Experiment (aboard Gravity Probe B). Specific accomplishments in the following areas are summarized: the inclusion of electromagnetism into the variational principle for spinning matter, formulation of a self-consistent theory for the case of a fluid in which particle production processes occur, and the derivation of the Raychaudhuri equation in the case of spinning matter.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

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.

Self-focusing skyrmion racetracks in ferrimagnets

NASA Astrophysics Data System (ADS)

Kim, Se Kwon; Lee, Kyung-Jin; Tserkovnyak, Yaroslav

2017-04-01

We theoretically study the dynamics of ferrimagnetic skyrmions in inhomogeneous metallic films close to the angular momentum compensation point. In particular, it is shown that the line of the vanishing angular momentum can be utilized as a self-focusing racetrack for skyrmions. To that end, we begin by deriving the equations of motion for the dynamics of collinear ferrimagnets in the presence of a charge current. The obtained equations of motion reduce to those of ferromagnets and antiferromagnets at two special limits. In the collective coordinate approach, a skyrmion behaves as a massive charged particle moving in a viscous medium subjected to a magnetic field. Analogous to the snake orbits of electrons in a nonuniform magnetic field, we show that a ferrimagnet with nonuniform angular momentum density can exhibit the snake trajectories of skyrmions, which can be utilized as racetracks for skyrmions.

Interface waves in multilayered plates.

PubMed

Li, Bing; Li, Ming-Hang; Lu, Tong

2018-04-01

In this paper, the characteristic equation of interface waves in multilayered plates is derived. With a reasonable assumption undertaken for the potential functions of longitudinal and shear waves in the nth layer medium, the characteristic equation of interface waves in the N-layered plate is derived and presented in a determinant form. The particle displacement and stress components are further presented in explicit forms. The dispersion curves and wave structures of interface waves in both a three-layered Al-Steel-Ti and a four-layered Steel-Al-Steel-Ti plate are displayed subsequently. It is observed in dispersion curves that obvious dispersion occurs on the low frequency band, whereas the phase velocities converge to the corresponding true Stoneley wave mode velocities at high frequency, and the number of interface wave modes equals the number of interfaces in multilayered plates (if all individual interfaces satisfy the existence condition of Stoneley waves). The wave structures reveal that the displacement components of interface waves are relatively high at interfaces, and the amplitude distribution varies from frequency to frequency. In the end, a similarly structured three-layered Al-Steel-Ti plate is tested. In this experiment, theoretical group velocity and experimental group velocity are compared. According to the discussion and comparison, the predicted group velocities are in good agreement with the experimental results. Thus, the theory of interface wave in multilayered plates is proved. As a result, the proposed theoretical approach represents a leap forward in the understanding of how to promote the characteristic study and practical applications of interface waves in multilayered structures.

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.

Theoretical Analysis of Fas Ligand-Induced Apoptosis with an Ordinary Differential Equation Model.

PubMed

Shi, Zhimin; Li, Yan; Liu, Zhihai; Mi, Jun; Wang, Renxiao

2012-12-01

Upon the treatment of Fas ligand, different types of cells exhibit different apoptotic mechanisms, which are determined by a complex network of biological pathways. In order to derive a quantitative interpretation of the cell sensitivity and apoptosis pathways, we have developed an ordinary differential equation model. Our model is intended to include all of the known major components in apoptosis pathways mediated by Fas receptor. It is composed of 29 equations using a total of 49 rate constants and 13 protein concentrations. All parameters used in our model were derived through nonlinear fitting to experimentally measured concentrations of four selected proteins in Jurkat T-cells, including caspase-3, caspase-8, caspase-9, and Bid. Our model is able to correctly interpret the role of kinetic parameters and protein concentrations in cell sensitivity to FasL. It reveals the possible reasons for the transition between type-I and type-II pathways and also provides some interesting predictions, such as the more decisive role of Fas over Bax in apoptosis pathway and a possible feedback mechanism between type-I and type-II pathways. But our model failed in predicting FasL-induced apoptotic mechanism of NCI-60 cells from their gene-expression levels. Limitations in our model are also discussed. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Some New Lidar Equations for Laser Pulses Scattered Back from Optically Thick Media Such as Clouds, Dense Aerosol Plumes, Sea Ice, Snow, and Turbid Coastal Waters

NASA Technical Reports Server (NTRS)

Davis, Anthony B.

2013-01-01

I survey the theoretical foundations of the slowly-but-surely emerging field of multiple scattering lidar, which has already found applications in atmospheric and cryospheric optics that I also discuss. In multiple scattering lidar, returned pulses are stretched far beyond recognition, and there is no longer a one-to-one connection between range and return-trip timing. Moreover, one can exploit the radial profile of the diffuse radiance field excited by the laser source that, by its very nature, is highly concentrated in space and collimated in direction. One needs, however, a new class of lidar equations to explore this new phenomenology. A very useful set is derived from radiative diffusion theory, which is found at the opposite asymptotic limit of radiative transfer theory than the conventional (single-scattering) limit used to derive the standard lidar equation. In particular, one can use it to show that, even if the simple time-of-flight-to-range connection is irretrievably lost, multiply-scattered lidar light can be used to restore a unique profiling capability with coarser resolution but much deeper penetration into a wide variety of optical thick media in nature. Several new applications are proposed, including a laser bathymetry technique that should work for highly turbid coastal waters.

Revisiting Wiedemann-Franz law through Boltzmann transport equations and ab-initio density functional theory

NASA Astrophysics Data System (ADS)

Nag, Abhinav; Kumari, Anuja; Kumar, Jagdish

2018-05-01

We have investigated structural, electronic and transport properties of the alkali metals using ab-initio density functional theory. The electron energy dispersions are found parabolic free electron like which is expected for alkali metals. The lattice constants for all the studied metals are also in good agreement within 98% with experiments. We have further computed their transport properties using semi-classical Boltzmann transport equations with special focus on electrical and thermal conductivity. Our objective was to obtain Wiedemann-Franz law and hence Lorenz number. The motivation to do these calculations is to see that how the incorporation of different interactions such as electron-lattice, electron-electron interaction affect the Wiedeman-Franz law. By solving Boltzmann transport equations, we have obtained electrical conductivity (σ/τ) and thermal conductivity (κ0 /τ) at different temperatures and then calculated Lorenz number using L = κ0 /(σT). The obtained value of Lorenz number has been found to match with value derived for free electron Fermi gas 2.44× 10-8 WΩK-2. Our results prove that the Wiedemann-Franz law as derived for free electron gas does not change much for alkali metals, even when one incorporates interaction of electrons with atomic nuclei and other electrons. However, at lower temperatures, the Lorenz number, was found to be deviating from its theoretical value.

Dynamics of Phase Transitions in a Snow Mass Containing Water-Soluble Salt Particles

NASA Astrophysics Data System (ADS)

Zelenko, V. L.; Heifets, L. I.; Orlov, Yu. N.; Voskresenskiy, N. M.

2018-07-01

A macrokinetic approach is used to describe the dynamics of phase transitions in a snow mass containing water-soluble salt particles. Equations are derived that describe the rate of salt granule dissolution and the change in the phase composition and temperature of a snow mass under the conditions of heat transfer with an isothermal surface. An experimental setup that models the change in the state of a snow mass placed on an isothermal surface is created to verify theoretical conclusions. Experimental observations of the change in temperature of the snow mass are compared to theoretical calculations. The mathematical model that is developed can be used to predict the state of a snow mass on roads treated with a deicing agent, or to analyze the state of snow masses containing water-soluble salt inclusions and resting on mountain slopes.

An interval precise integration method for transient unbalance response analysis of rotor system with uncertainty

NASA Astrophysics Data System (ADS)

Fu, Chao; Ren, Xingmin; Yang, Yongfeng; Xia, Yebao; Deng, Wangqun

2018-07-01

A non-intrusive interval precise integration method (IPIM) is proposed in this paper to analyze the transient unbalance response of uncertain rotor systems. The transfer matrix method (TMM) is used to derive the deterministic equations of motion of a hollow-shaft overhung rotor. The uncertain transient dynamic problem is solved by combing the Chebyshev approximation theory with the modified precise integration method (PIM). Transient response bounds are calculated by interval arithmetic of the expansion coefficients. Theoretical error analysis of the proposed method is provided briefly, and its accuracy is further validated by comparing with the scanning method in simulations. Numerical results show that the IPIM can keep good accuracy in vibration prediction of the start-up transient process. Furthermore, the proposed method can also provide theoretical guidance to other transient dynamic mechanical systems with uncertainties.

Theoretical Evaluation of the Transient Response of Constant Head and Constant Flow-Rate Permeability Tests

USGS Publications Warehouse

Zhang, M.; Takahashi, M.; Morin, R.H.; Esaki, T.

1998-01-01

A theoretical analysis is presented that compares the response characteristics of the constant head and the constant flowrate (flow pump) laboratory techniques for quantifying the hydraulic properties of geologic materials having permeabilities less than 10-10 m/s. Rigorous analytical solutions that describe the transient distributions of hydraulic gradient within a specimen are developed, and equations are derived for each method. Expressions simulating the inflow and outflow rates across the specimen boundaries during a constant-head permeability test are also presented. These solutions illustrate the advantages and disadvantages of each method, including insights into measurement accuracy and the validity of using Darcy's law under certain conditions. The resulting observations offer practical considerations in the selection of an appropriate laboratory test method for the reliable measurement of permeability in low-permeability geologic materials.

Unmagnetized diffusion for azimuthally symmetric wave and particle distributions

NASA Technical Reports Server (NTRS)

Dusenbery, P. B.; Lyons, L. R.

1988-01-01

The quasi-linear diffusion of particles from resonant interactions with a spectrum of electrostatic waves is investigated theoretically, extending results obtained for no magnetic field and for strong magnetic fields to cases where the ambient magnetic field which organizes azimuthally symmetric wave and particle distributions does not have to be taken into consideration in evaluating the local interaction. The derivation of the governing equations is explained, and numerical results are presented in extensive graphs and characterized in detail. Slow-mode ion-acoustic waves are shown to be unstable under the plasma conditions studied, and the dependence of resonant-ion diffusion rates with pitch angle, speed, and the distribution of wave energy in wavenumber space is explored. The implications of the present findings for theoretical models of the earth bow shock and plasma-sheet boundary layer are indicated.

A Study on Water Surface Profiles of Rivers with Constriction

NASA Astrophysics Data System (ADS)

Qian, Chaochao; Yamada, Tadashi

2013-04-01

Water surface profile of rivers with constrictions is precious in both classic hydraulics and river management practice. This study was conducted to clarify the essences of the water surface profiles. 3 cases of experiments and 1D numerical calculations with different discharges were made in the study and analysis solutions of the non-linear basic equation of surface profile in varied flow without considering friction were derived. The manning's number was kept in the same in each case by using crosspiece roughness. We found a new type of water surface profile of varied flow from the results of 1D numerical calculation and that of experiments and named it as Mc curve because of its mild condition with constriction segment. This kind of curves appears as a nature phenomenon ubiquitously. The process of water surface forming is dynamic and bore occurs at the upper side of constriction during increasing discharge before the surface profile formed. As a theoretical work, 3 analysis solutions were derived included 2 physical-meaning solutions in the study by using Man-Machine system. One of the derived physical-meaning solutions was confirmed that it is validity by comparing to the results of 1D numerical calculation and that of experiments. The solution represents a flow profile from under critical condition at the upper side to super critical condition at the down side of constriction segment. The other derived physical-meaning solution represents a flow profile from super critical condition at the upper side to under critical condition at the down side of constriction segment. These two kinds of flow profiles exist in the nature but no theoretical solution can express the phenomenon. We find the depth distribution only concerned with unit width discharge distribution and critical depth under a constant discharge from the derived solutions. Therefor, the profile can be gained simply and precisely by using the theoretical solutions instead of numerical calculation even in practice.

Heavy use of equations impedes communication among biologists.

PubMed

Fawcett, Tim W; Higginson, Andrew D

2012-07-17

Most research in biology is empirical, yet empirical studies rely fundamentally on theoretical work for generating testable predictions and interpreting observations. Despite this interdependence, many empirical studies build largely on other empirical studies with little direct reference to relevant theory, suggesting a failure of communication that may hinder scientific progress. To investigate the extent of this problem, we analyzed how the use of mathematical equations affects the scientific impact of studies in ecology and evolution. The density of equations in an article has a significant negative impact on citation rates, with papers receiving 28% fewer citations overall for each additional equation per page in the main text. Long, equation-dense papers tend to be more frequently cited by other theoretical papers, but this increase is outweighed by a sharp drop in citations from nontheoretical papers (35% fewer citations for each additional equation per page in the main text). In contrast, equations presented in an accompanying appendix do not lessen a paper's impact. Our analysis suggests possible strategies for enhancing the presentation of mathematical models to facilitate progress in disciplines that rely on the tight integration of theoretical and empirical work.

The influence of continuous historical velocity difference information on micro-cooperative driving stability

NASA Astrophysics Data System (ADS)

Yang, Liang-Yi; Sun, Di-Hua; Zhao, Min; Cheng, Sen-Lin; Zhang, Geng; Liu, Hui

2018-03-01

In this paper, a new micro-cooperative driving car-following model is proposed to investigate the effect of continuous historical velocity difference information on traffic stability. The linear stability criterion of the new model is derived with linear stability theory and the results show that the unstable region in the headway-sensitivity space will be shrunk by taking the continuous historical velocity difference information into account. Through nonlinear analysis, the mKdV equation is derived to describe the traffic evolution behavior of the new model near the critical point. Via numerical simulations, the theoretical analysis results are verified and the results indicate that the continuous historical velocity difference information can enhance the stability of traffic flow in the micro-cooperative driving process.

Extrapolation methods for vector sequences

NASA Technical Reports Server (NTRS)

Smith, David A.; Ford, William F.; Sidi, Avram

1987-01-01

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

Acoustic plane waves incident on an oblique clamped panel in a rectangular duct

NASA Technical Reports Server (NTRS)

Unz, H.; Roskam, J.

1980-01-01

The theory of acoustic plane waves incident on an oblique clamped panel in a rectangular duct was developed from basic theoretical concepts. The coupling theory between the elastic vibrations of the panel (plate) and the oblique incident acoustic plane wave in infinite space was considered in detail, and was used for the oblique clamped panel in the rectangular duct. The partial differential equation which governs the vibrations of the clamped panel (plate) was modified by adding to it stiffness (spring) forces and damping forces. The Transmission Loss coefficient and the Noise Reduction coefficient for oblique incidence were defined and derived in detail. The resonance frequencies excited by the free vibrations of the oblique finite clamped panel (plate) were derived and calculated in detail for the present case.

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Algebraic aspects of the driven dynamics in the density operator and correlation functions calculation for multi-level open quantum systems

NASA Astrophysics Data System (ADS)

Bogolubov, Nikolai N.; Soldatov, Andrey V.

2017-12-01

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can be simplified significantly if the free Hamiltonian driven dynamics of an arbitrary quantum multi-level system under the influence of the external driving fields as well as its Markovian and non-Markovian evolution, stipulated by the interaction with the environment, are described in terms of the SU(N) algebra representation. As a consequence, efficient numerical methods can be developed and employed to analyze these master equations for real problems in various fields of theoretical and applied physics. It was also shown that literally the same master equations hold not only for the reduced density operator but also for arbitrary nonequilibrium multi-time correlation functions as well under the only assumption that the system and the environment are uncorrelated at some initial moment of time. A calculational scheme was proposed to account for these lost correlations in a regular perturbative way, thus providing additional computable terms to the correspondent master equations for the correlation functions.

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.

How to derive biological information from the value of the normalization constant in allometric equations.

PubMed

Kaitaniemi, Pekka

2008-04-09

Allometric equations are widely used in many branches of biological science. The potential information content of the normalization constant b in allometric equations of the form Y = bX(a) has, however, remained largely neglected. To demonstrate the potential for utilizing this information, I generated a large number of artificial datasets that resembled those that are frequently encountered in biological studies, i.e., relatively small samples including measurement error or uncontrolled variation. The value of X was allowed to vary randomly within the limits describing different data ranges, and a was set to a fixed theoretical value. The constant b was set to a range of values describing the effect of a continuous environmental variable. In addition, a normally distributed random error was added to the values of both X and Y. Two different approaches were then used to model the data. The traditional approach estimated both a and b using a regression model, whereas an alternative approach set the exponent a at its theoretical value and only estimated the value of b. Both approaches produced virtually the same model fit with less than 0.3% difference in the coefficient of determination. Only the alternative approach was able to precisely reproduce the effect of the environmental variable, which was largely lost among noise variation when using the traditional approach. The results show how the value of b can be used as a source of valuable biological information if an appropriate regression model is selected.

[Relationships between suicide attitudes and perception of life purpose and meaning of life in college students].

PubMed

Xie, Xingli; Zou, Bing; Huang, Zhongyan

2012-10-01

To investigate the suicide attitudes of college students and analyze the impact of the perception of life purpose and meaning of life on their suicide attitudes using structural equation modeling. A total of 1050 college students were tested by Suicide Attitude Questionnaire (QSA), Purpose in Life test (PIL) and Chinese version of Meaning of Life questionnaire (C-MLQ). A theoretical model was established for confirming the influence of the purpose in life and meaning in life on suicide attitudes of the college students. The college students had generally a negative attitude towards suicide. The female students tended to show more objective attitudes towards suicide and the students from rural areas had a stronger attitude against euthanasia.The meanings and purposes in life were closely correlated with the attitudes towards suicide, and the structural equation modeling well fitted the data (Χ(2)/df=1.924, GFI=0.936, AGFI=0.915, NFI=0.937, CFI=0.940, and RMSEA=0.045). The perception of meaning and purposes in life had a direct predictive value on the suicide attitude of the college students, and the presumptions derived from the theoretical model were strongly supported by structural equation modeling. The perceptions in meanings in life and purposes in livelihood have important influence on the suicide attitudes of college students, and intervention with effective life education should be administered to guide the suicide attitude of the college students.

Variables and potential models for the bleaching of luminescence signals in fluvial environments

USGS Publications Warehouse

Gray, Harrison J.; Mahan, Shannon

2015-01-01

Luminescence dating of fluvial sediments rests on the assumption that sufficient sunlight is available to remove a previously obtained signal in a process deemed bleaching. However, luminescence signals obtained from sediment in the active channels of rivers often contain residual signals. This paper explores and attempts to build theoretical models for the bleaching of luminescence signals in fluvial settings. We present two models, one for sediment transported in an episodic manner, such as flood-driven washes in arid environments, and one for sediment transported in a continuous manner, such as in large continental scale rivers. The episodic flow model assumes that the majority of sediment is bleached while exposed to sunlight at the near surface between flood events and predicts a power-law decay in luminescence signal with downstream transport distance. The continuous flow model is developed by combining the Beer–Lambert law for the attenuation of light through a water column with a general-order kinetics equation to produce an equation with the form of a double negative exponential. The inflection point of this equation is compared with the sediment concentration from a Rouse profile to derive a non-dimensional number capable of assessing the likely extent of bleaching for a given set of luminescence and fluvial parameters. Although these models are theoretically based and not yet necessarily applicable to real-world fluvial systems, we introduce these ideas to stimulate discussion and encourage the development of comprehensive bleaching models with predictive power.

Synchronization of two homodromy rotors installed on a double vibro-body in a coupling vibration system.

PubMed

Fang, Pan; Hou, Yongjun; Nan, Yanghai

2015-01-01

A new mechanism is proposed to implement synchronization of the two unbalanced rotors in a vibration system, which consists of a double vibro-body, two induction motors and spring foundations. The coupling relationship between the vibro-bodies is ascertained with the Laplace transformation method for the dynamics equation of the system obtained with the Lagrange's equation. An analytical approach, the average method of modified small parameters, is employed to study the synchronization characteristics between the two unbalanced rotors, which is converted into that of existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters. By assuming the disturbance parameters that infinitely approach to zero, the synchronization condition for the two rotors is obtained. It indicated that the absolute value of the residual torque between the two motors should be equal to or less than the maximum of their coupling torques. Meanwhile, the stability criterion of synchronization is derived with the Routh-Hurwitz method, and the region of the stable phase difference is confirmed. At last, computer simulations are preformed to verify the correctness of the approximate solution of the theoretical computation for the stable phase difference between the two unbalanced rotors, and the results of theoretical computation is in accordance with that of computer simulations. To sum up, only the parameters of the vibration system satisfy the synchronization condition and the stability criterion of the synchronization, the two unbalanced rotors can implement the synchronization operation.

Synchronization of Two Homodromy Rotors Installed on a Double Vibro-Body in a Coupling Vibration System

PubMed Central

Fang, Pan; Hou, Yongjun; Nan, Yanghai

2015-01-01

A new mechanism is proposed to implement synchronization of the two unbalanced rotors in a vibration system, which consists of a double vibro-body, two induction motors and spring foundations. The coupling relationship between the vibro-bodies is ascertained with the Laplace transformation method for the dynamics equation of the system obtained with the Lagrange’s equation. An analytical approach, the average method of modified small parameters, is employed to study the synchronization characteristics between the two unbalanced rotors, which is converted into that of existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters. By assuming the disturbance parameters that infinitely approach to zero, the synchronization condition for the two rotors is obtained. It indicated that the absolute value of the residual torque between the two motors should be equal to or less than the maximum of their coupling torques. Meanwhile, the stability criterion of synchronization is derived with the Routh-Hurwitz method, and the region of the stable phase difference is confirmed. At last, computer simulations are preformed to verify the correctness of the approximate solution of the theoretical computation for the stable phase difference between the two unbalanced rotors, and the results of theoretical computation is in accordance with that of computer simulations. To sum up, only the parameters of the vibration system satisfy the synchronization condition and the stability criterion of the synchronization, the two unbalanced rotors can implement the synchronization operation. PMID:25993472

Planar isotropy of passive scalar turbulent mixing with a mean perpendicular gradient.

PubMed

Danaila, L; Dusek, J; Le Gal, P; Anselmet, F; Brun, C; Pumir, A

1999-08-01

A recently proposed evolution equation [Vaienti et al., Physica D 85, 405 (1994)] for the probability density functions (PDF's) of turbulent passive scalar increments obtained under the assumptions of fully three-dimensional homogeneity and isotropy is submitted to validation using direct numerical simulation (DNS) results of the mixing of a passive scalar with a nonzero mean gradient by a homogeneous and isotropic turbulent velocity field. It is shown that this approach leads to a quantitatively correct balance between the different terms of the equation, in a plane perpendicular to the mean gradient, at small scales and at large Péclet number. A weaker assumption of homogeneity and isotropy restricted to the plane normal to the mean gradient is then considered to derive an equation describing the evolution of the PDF's as a function of the spatial scale and the scalar increments. A very good agreement between the theory and the DNS data is obtained at all scales. As a particular case of the theory, we derive a generalized form for the well-known Yaglom equation (the isotropic relation between the second-order moments for temperature increments and the third-order velocity-temperature mixed moments). This approach allows us to determine quantitatively how the integral scale properties influence the properties of mixing throughout the whole range of scales. In the simple configuration considered here, the PDF's of the scalar increments perpendicular to the mean gradient can be theoretically described once the sources of inhomogeneity and anisotropy at large scales are correctly taken into account.

Theoretical Conversions of Different Hardness and Tensile Strength for Ductile Materials Based on Stress-Strain Curves

NASA Astrophysics Data System (ADS)

Chen, Hui; Cai, Li-Xun

2018-04-01

Based on the power-law stress-strain relation and equivalent energy principle, theoretical equations for converting between Brinell hardness (HB), Rockwell hardness (HR), and Vickers hardness (HV) were established. Combining the pre-existing relation between the tensile strength ( σ b ) and Hollomon parameters ( K, N), theoretical conversions between hardness (HB/HR/HV) and tensile strength ( σ b ) were obtained as well. In addition, to confirm the pre-existing σ b -( K, N) relation, a large number of uniaxial tensile tests were conducted in various ductile materials. Finally, to verify the theoretical conversions, plenty of statistical data listed in ASTM and ISO standards were adopted to test the robustness of the converting equations with various hardness and tensile strength. The results show that both hardness conversions and hardness-strength conversions calculated from the theoretical equations accord well with the standard data.

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…

Instability of surface electron cyclotron TM-modes influenced by non-monochromatic alternating electric field

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

Girka, I. O., E-mail: igorgirka@karazin.ua; Girka, V. O.; Sydora, R. D.

2016-06-15

The influence of non-monochromaticity of an external alternating electric field on excitation of TM eigenmodes at harmonics of the electron cyclotron frequency is considered here. These TM-modes propagate along the plasma interface in a metal waveguide. An external static constant magnetic field is oriented perpendicularly to the plasma interface. The problem is solved theoretically using the kinetic Vlasov-Boltzmann equation for description of plasma particles motion and the Maxwell equations for description of the electromagnetic mode fields. The external alternating electric field is supposed to be a superposition of two waves, whose amplitudes are different and their frequencies correlate as 2:1.more » An infinite set of equations for electric field harmonics of these modes is derived with the aid of nonlinear boundary conditions. This set is solved using the wave packet approach consisting of the main harmonic frequency and two nearest satellite temporal harmonics. Analytical studies of the obtained set of equations allow one to find two different regimes of parametric instability, namely, enhancement and suppression of the instability. Numerical analysis of the instability is carried out for the three first electron cyclotron harmonics.« less

Numerical solution of a logistic growth model for a population with Allee effect considering fuzzy initial values and fuzzy parameters

NASA Astrophysics Data System (ADS)

Amarti, Z.; Nurkholipah, N. S.; Anggriani, N.; Supriatna, A. K.

2018-03-01

Predicting the future of population number is among the important factors that affect the consideration in preparing a good management for the population. This has been done by various known method, one among them is by developing a mathematical model describing the growth of the population. The model usually takes form in a differential equation or a system of differential equations, depending on the complexity of the underlying properties of the population. The most widely used growth models currently are those having a sigmoid solution of time series, including the Verhulst logistic equation and the Gompertz equation. In this paper we consider the Allee effect of the Verhulst’s logistic population model. The Allee effect is a phenomenon in biology showing a high correlation between population size or density and the mean individual fitness of the population. The method used to derive the solution is the Runge-Kutta numerical scheme, since it is in general regarded as one among the good numerical scheme which is relatively easy to implement. Further exploration is done via the fuzzy theoretical approach to accommodate the impreciseness of the initial values and parameters in the model.

Dynamical modeling and experiment for an intra-cavity optical parametric oscillator pumped by a Q-switched self-mode-locking laser

NASA Astrophysics Data System (ADS)

Wang, Jing; Liu, Nianqiao; Song, Peng; Zhang, Haikun

2016-11-01

The rate-equation-based model for the Q-switched mode-locking (QML) intra-cavity OPO (IOPO) is developed, which includes the behavior of the fundamental laser. The intensity fluctuation mechanism of the fundamental laser is first introduced into the dynamics of a mode-locking OPO. In the derived model, the OPO nonlinear conversion is considered as a loss for the fundamental laser and thus the QML signal profile originates from the QML fundamental laser. The rate equations are solved by a digital computer for the case of an IOPO pumped by an electro-optic (EO) Q-switched self-mode-locking fundamental laser. The simulated results for the temporal shape with 20 kHz EO repetition and 11.25 W pump power, the signal average power, the Q-switched pulsewidth and the Q-switched pulse energy are obtained from the rate equations. The signal trace and output power from an EO QML Nd3+: GdVO4/KTA IOPO are experimentally measured. The theoretical values from the rate equations agree with the experimental results well. The developed model explains the behavior, which is helpful to system optimization.

Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics

NASA Astrophysics Data System (ADS)

Drogoul, Audric; Veltz, Romain

2017-02-01

In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.

Flow regimes for fluid injection into a confined porous medium

DOE PAGES

Zheng, Zhong; Guo, Bo; Christov, Ivan C.; ...

2015-02-24

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governingmore » equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less

A Model for the Oxidation of C/SiC Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2003-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of C/SiC composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. Within the mathematical formulation, two diffusion mechanisms are possible: (1) the relative diffusion of one species with respect to the mixture, which is concentration gradient driven and (2) the diffusion associated with the average velocity of the gas mixture, which is total gas pressure gradient driven. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations must be solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of space and time. The local rate of carbon oxidation is determined as a function of space and time using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The end result is a numerical scheme capable of determining the variation of the local carbon oxidation rates as a function of space and time for any arbitrary C/SiC composite structures.

High-order fractional partial differential equation transform for molecular surface construction.

PubMed

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

Consistent Pl Analysis of Aqueous Uranium-235 Critical Assemblies

NASA Technical Reports Server (NTRS)

Fieno, Daniel

1961-01-01

The lethargy-dependent equations of the consistent Pl approximation to the Boltzmann transport equation for slowing down neutrons have been used as the basis of an IBM 704 computer program. Some of the effects included are (1) linearly anisotropic center of mass elastic scattering, (2) heavy element inelastic scattering based on the evaporation model of the nucleus, and (3) optional variation of the buckling with lethargy. The microscopic cross-section data developed for this program covered 473 lethargy points from lethargy u = 0 (10 Mev) to u = 19.8 (0.025 ev). The value of the fission neutron age in water calculated here is 26.5 square centimeters; this value is to be compared with the recent experimental value given as 27.86 square centimeters. The Fourier transform of the slowing-down kernel for water to indium resonance energy calculated here compared well with the Fourier transform of the kernel for water as measured by Hill, Roberts, and Fitch. This method of calculation has been applied to uranyl fluoride - water solution critical assemblies. Theoretical results established for both unreflected and fully reflected critical assemblies have been compared with available experimental data. The theoretical buckling curve derived as a function of the hydrogen to uranium-235 atom concentration for an energy-independent extrapolation distance was successful in predicting the critical heights of various unreflected cylindrical assemblies. The critical dimensions of fully water-reflected cylindrical assemblies were reasonably well predicted using the theoretical buckling curve and reflector savings for equivalent spherical assemblies.

Isometric Non-Rigid Shape-from-Motion with Riemannian Geometry Solved in Linear Time.

PubMed

Parashar, Shaifali; Pizarro, Daniel; Bartoli, Adrien

2017-10-06

We study Isometric Non-Rigid Shape-from-Motion (Iso-NRSfM): given multiple intrinsically calibrated monocular images, we want to reconstruct the time-varying 3D shape of a thin-shell object undergoing isometric deformations. We show that Iso-NRSfM is solvable from local warps, the inter-image geometric transformations. We propose a new theoretical framework based on the Riemmanian manifold to represent the unknown 3D surfaces as embeddings of the camera's retinal plane. This allows us to use the manifold's metric tensor and Christoffel Symbol (CS) fields. These are expressed in terms of the first and second order derivatives of the inverse-depth of the 3D surfaces, which are the unknowns for Iso-NRSfM. We prove that the metric tensor and the CS are related across images by simple rules depending only on the warps. This forms a set of important theoretical results. We show that current solvers cannot solve for the first and second order derivatives of the inverse-depth simultaneously. We thus propose an iterative solution in two steps. 1) We solve for the first order derivatives assuming that the second order derivatives are known. We initialise the second order derivatives to zero, which is an infinitesimal planarity assumption. We derive a system of two cubics in two variables for each image pair. The sum-of-squares of these polynomials is independent of the number of images and can be solved globally, forming a well-posed problem for N ≥ 3 images. 2) We solve for the second order derivatives by initialising the first order derivatives from the previous step. We solve a linear system of 4N-4 equations in three variables. We iterate until the first order derivatives converge. The solution for the first order derivatives gives the surfaces' normal fields which we integrate to recover the 3D surfaces. The proposed method outperforms existing work in terms of accuracy and computation cost on synthetic and real datasets.

[Theoretical modeling and experimental research on direct compaction characteristics of multi-component pharmaceutical powders based on the Kawakita equation].

PubMed

Si, Guo-Ning; Chen, Lan; Li, Bao-Guo

2014-04-01

Base on the Kawakita powder compression equation, a general theoretical model for predicting the compression characteristics of multi-components pharmaceutical powders with different mass ratios was developed. The uniaxial flat-face compression tests of powder lactose, starch and microcrystalline cellulose were carried out, separately. Therefore, the Kawakita equation parameters of the powder materials were obtained. The uniaxial flat-face compression tests of the powder mixtures of lactose, starch, microcrystalline cellulose and sodium stearyl fumarate with five mass ratios were conducted, through which, the correlation between mixture density and loading pressure and the Kawakita equation curves were obtained. Finally, the theoretical prediction values were compared with experimental results. The analysis showed that the errors in predicting mixture densities were less than 5.0% and the errors of Kawakita vertical coordinate were within 4.6%, which indicated that the theoretical model could be used to predict the direct compaction characteristics of multi-component pharmaceutical powders.

Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series

NASA Astrophysics Data System (ADS)

Luce, C.; Tonina, D.; Gariglio, F. P.; Applebee, R.

2012-12-01

Differences in the diurnal variations of temperature at different depths in streambed sediments are commonly used for estimating vertical fluxes of water in the streambed. We applied spatial and temporal rescaling of the advection-diffusion equation to derive two new relationships that greatly extend the kinds of information that can be derived from streambed temperature measurements. The first equation provides a direct estimate of the Peclet number from the amplitude decay and phase delay information. The analytical equation is explicit (e.g. no numerical root-finding is necessary), and invertable. The thermal front velocity can be estimated from the Peclet number when the thermal diffusivity is known. The second equation allows for an independent estimate of the thermal diffusivity directly from the amplitude decay and phase delay information. Several improvements are available with the new information. The first equation uses a ratio of the amplitude decay and phase delay information; thus Peclet number calculations are independent of depth. The explicit form also makes it somewhat faster and easier to calculate estimates from a large number of sensors or multiple positions along one sensor. Where current practice requires a priori estimation of streambed thermal diffusivity, the new approach allows an independent calculation, improving precision of estimates. Furthermore, when many measurements are made over space and time, expectations of the spatial correlation and temporal invariance of thermal diffusivity are valuable for validation of measurements. Finally, the closed-form explicit solution allows for direct calculation of propagation of uncertainties in error measurements and parameter estimates, providing insight about error expectations for sensors placed at different depths in different environments as a function of surface temperature variation amplitudes. The improvements are expected to increase the utility of temperature measurement methods for studying groundwater-surface water interactions across space and time scales. We discuss the theoretical implications of the new solutions supported by examples with data for illustration and validation.

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.

Arrayed waveguide Sagnac interferometer.

PubMed

Capmany, José; Muñoz, Pascual; Sales, Salvador; Pastor, Daniel; Ortega, Beatriz; Martinez, Alfonso

2003-02-01

We present a novel device, an arrayed waveguide Sagnac interferometer, that combines the flexibility of arrayed waveguides and the wide application range of fiber or integrated optics Sagnac loops. We form the device by closing an array of wavelength-selective light paths provided by two arrayed waveguides with a single 2 x 2 coupler in a Sagnac configuration. The equations that describe the device's operation in general conditions are derived. A preliminary experimental demonstration is provided of a fiber prototype in passive operation that shows good agreement with the expected theoretical performance. Potential applications of the device in nonlinear operation are outlined and discussed.

Novel approach to investigation of semiconductor MOCVD by microreactor technology

NASA Astrophysics Data System (ADS)

Konakov, S. A.; Krzhizhanovskaya, V. V.

2017-11-01

Metal-Organic Chemical Vapour Deposition is a very complex technology that requires further investigation and optimization. We propose to apply microreactors to (1) replace multiple expensive time-consuming macroscale experiments by just one microreactor deposition with many points on one substrate; (2) to derive chemical reaction rates from individual deposition profiles using theoretical analytical solution. In this paper we also present the analytical solution of a simplified equation describing the deposition rate dependency on temperature. It allows to solve an inverse problem and to obtain detailed information about chemical reaction mechanism of MOCVD process.

Surfing surface gravity waves

NASA Astrophysics Data System (ADS)

Pizzo, Nick

2017-11-01

A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497-503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.

Scattering General Analysis; ANALISIS GENERAL DE LA DISPERSION

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

Tixaire, A.G.

1962-01-01

A definition of scattering states is given. It is shown that such states must belong to the absolutely continuous part of the spectrum of the total hamiltonian whenever scattering systems are considered. Such embedding may be proper unless the quantum system is physically admissible. The Moller wave operators are analyzed using Abel- and Cesaro-limit theoretical arguments. Von Neumann s ergodic theorem is partially generalized. A rigorous derivation of the Gell-Mann and Goldberger and Lippmann and Schwinger equations is obtained by making use of results on spectral theory, wave function, and eigendifferential concepts contained. (auth)

Structural and electronic properties of GaAs and GaP semiconductors

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

Rani, Anita; Kumar, Ranjan

2015-05-15

The Structural and Electronic properties of Zinc Blende phase of GaAs and GaP compounds are studied using self consistent SIESTA-code, pseudopotentials and Density Functional Theory (DFT) in Local Density Approximation (LDA). The Lattice Constant, Equillibrium Volume, Cohesive Energy per pair, Compressibility and Band Gap are calculated. The band gaps calcultated with DFT using LDA is smaller than the experimental values. The P-V data fitted to third order Birch Murnaghan equation of state provide the Bulk Modulus and its pressure derivatives. Our Structural and Electronic properties estimations are in agreement with available experimental and theoretical data.

Numerical solution of the time fractional reaction-diffusion equation with a moving boundary

NASA Astrophysics Data System (ADS)

Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J.

2017-06-01

A fractional reaction-diffusion model with a moving boundary is presented in this paper. An efficient numerical method is constructed to solve this moving boundary problem. Our method makes use of a finite difference approximation for the temporal discretization, and spectral approximation for the spatial discretization. The stability and convergence of the method is studied, and the errors of both the semi-discrete and fully-discrete schemes are derived. Numerical examples, motivated by problems from developmental biology, show a good agreement with the theoretical analysis and illustrate the efficiency of our method.

Complex methyl group and hydrogen-bonded proton motions in terms of the Arrhenius and Schrödinger equations.

PubMed

Latanowicz, L

2008-01-01

Equations for the temperature dependence of the spectral densities J(is)(m)(momega(I) +/-omega(T)), where m=1, 2, omega(I) and omega(T) are the resonance and tunnel splitting angular frequencies, in the presence of a complex motion, have been derived. The spin pairs of the protons or deuterons of the methyl group perform a complex motion consisting of three component motions. Two of them involve mass transportation over the barrier and through the barrier. They are characterized by k((H)) (Arrhenius) and k((T)) (Schrödinger) rate constants, respectively. The third motion causes fluctuations of the frequencies (nomega(I)+/-omega(T)) and it is related to the lifetime of the methyl spin at the energy level influenced by the rotor-bath interactions. These interactions induce rapid transitions, changing the symmetry of the torsional sublevels either from A to E or from E(a) to E(b). The correlation function for this third motion (k((omega)) rate constant) has been proposed by Müller-Warmuth et al. The spectral densities of the methyl group hindered rotation (k((H)), k((T)) and k((omega)) rate constants) differ from the spectral densities of the proton transfer (k((H)) and k((T)) rate constants) because three compound motions contribute to the complex motion of the methyl group. The recently derived equation [Formula: see text] , where [Formula: see text] and [Formula: see text] are the fraction and energy of particles with energies from zero to E(H), is taken into account in the calculations of the spectral densities. This equation follows from Maxwell's distribution of thermal energy. The spectral densities derived are applied to analyse the experimental temperature dependencies of proton and deuteron spin-lattice relaxation rate in solids containing the methyl group. A wide range of temperatures from zero Kelvin up to the melting point is considered. It has been established that the motion characterized by k((omega)) influences the spin-lattice relaxation up to the temperature T(tun) only. This temperature is directly determined by the equation C(p)T=E(H) (thermal energy=activation energy), where C(p) is the molar heat capacity. Probably the cessation of the third motion is a result of the de Broglie wavelength related to this motion becoming too short. As shown recently, the potential barrier can be an obstacle for the de Broglie wave. The theoretical equations derived in this paper are compared to those known in the literature.

Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

PubMed

Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

2015-11-01

The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

Theoretical Modelling of Sound Radiation from Plate

NASA Astrophysics Data System (ADS)

Zaman, I.; Rozlan, S. A. M.; Yusoff, A.; Madlan, M. A.; Chan, S. W.

2017-01-01

Recently the development of aerospace, automotive and building industries demands the use of lightweight materials such as thin plates. However, the plates can possibly add to significant vibration and sound radiation, which eventually lead to increased noise in the community. So, in this study, the fundamental concept of sound pressure radiated from a simply-supported thin plate (SSP) was analyzed using the derivation of mathematical equations and numerical simulation of ANSYS®. The solution to mathematical equations of sound radiated from a SSP was visualized using MATLAB®. The responses of sound pressure level were measured at far field as well as near field in the frequency range of 0-200 Hz. Result shows that there are four resonance frequencies; 12 Hz, 60 Hz, 106 Hz and 158 Hz were identified which represented by the total number of the peaks in the frequency response function graph. The outcome also indicates that the mathematical derivation correlated well with the simulation model of ANSYS® in which the error found is less than 10%. It can be concluded that the obtained model is reliable and can be applied for further analysis such as to reduce noise emitted from a vibrating thin plate.

Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion.

PubMed

Tricoli, Ugo; Macdonald, Callum M; Durduran, Turgut; Da Silva, Anabela; Markel, Vadim A

2018-02-01

Diffuse correlation tomography (DCT) uses the electric-field temporal autocorrelation function to measure the mean-square displacement of light-scattering particles in a turbid medium over a given exposure time. The movement of blood particles is here estimated through a Brownian-motion-like model in contrast to ordered motion as in blood flow. The sensitivity kernel relating the measurable field correlation function to the mean-square displacement of the particles can be derived by applying a perturbative analysis to the correlation transport equation (CTE). We derive an analytical expression for the CTE sensitivity kernel in terms of the Green's function of the radiative transport equation, which describes the propagation of the intensity. We then evaluate the kernel numerically. The simulations demonstrate that, in the transport regime, the sensitivity kernel provides sharper spatial information about the medium as compared with the correlation diffusion approximation. Also, the use of the CTE allows one to explore some additional degrees of freedom in the data such as the collimation direction of sources and detectors. Our results can be used to improve the spatial resolution of DCT, in particular, with applications to blood flow imaging in regions where the Brownian motion is dominant.

Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion

NASA Astrophysics Data System (ADS)

Tricoli, Ugo; Macdonald, Callum M.; Durduran, Turgut; Da Silva, Anabela; Markel, Vadim A.

2018-02-01

Diffuse correlation tomography (DCT) uses the electric-field temporal autocorrelation function to measure the mean-square displacement of light-scattering particles in a turbid medium over a given exposure time. The movement of blood particles is here estimated through a Brownian-motion-like model in contrast to ordered motion as in blood flow. The sensitivity kernel relating the measurable field correlation function to the mean-square displacement of the particles can be derived by applying a perturbative analysis to the correlation transport equation (CTE). We derive an analytical expression for the CTE sensitivity kernel in terms of the Green's function of the radiative transport equation, which describes the propagation of the intensity. We then evaluate the kernel numerically. The simulations demonstrate that, in the transport regime, the sensitivity kernel provides sharper spatial information about the medium as compared with the correlation diffusion approximation. Also, the use of the CTE allows one to explore some additional degrees of freedom in the data such as the collimation direction of sources and detectors. Our results can be used to improve the spatial resolution of DCT, in particular, with applications to blood flow imaging in regions where the Brownian motion is dominant.

Electron collisions with small esters: A joint experimental-theoretical investigation

NASA Astrophysics Data System (ADS)

de Souza, G. L. C.; da Silva, L. A.; de Sousa, W. J. C.; Sugohara, R. T.; Iga, I.; dos Santos, A. S.; Machado, L. E.; Homem, M. G. P.; Brescansin, L. M.; Lucchese, R. R.; Lee, M.-T.

2016-03-01

A theoretical and experimental investigation on elastic electron scattering by two small esters, namely, methyl formate and ethyl acetate, is reported. Experimental differential, integral, and momentum-transfer cross sections are given in the 30-1000 eV and 10∘-120∘ ranges. The relative-flow technique was used to determine such quantities. Particularly for methyl formate, a theoretical study was also carried out in the 1-500 eV range. A complex optical potential derived from a Hartree-Fock molecular wave function was used to represent the collision dynamics, whereas the Padé approximation was used to solve the scattering equations. In addition, calculations based on the framework of the independent-atom model (IAM) were also performed for both targets. In general, there is good agreement between our experimental data and the present theoretical results calculated using the Padé approximation. The theoretical results using the IAM also agree well with the experimental data at 200 eV and above. Moreover, for methyl formate, our calculations reveal a 2A'' (π*) resonance at about 3.0 eV and a σ*-type resonance centered at about 8.0 eV in the 2A' scattering channel. The π* resonance is also seen in other targets containing a carbonyl group.

Theoretical investigations of plasma processes in the ion bombardment thruster

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.

1975-01-01

A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.

Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

PubMed

Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L

2013-12-01

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.

Assessing Chaos in Sickle Cell Anemia Crises

NASA Astrophysics Data System (ADS)

Harris, Wesley; Le Floch, Francois

2006-11-01

Recent developments in sickle cell research and blood flow modeling allow for new interpretations of the sickle cell crises. With an appropriate set of theoretical and empirical equations describing the dynamics of the red cells in their environment, and the response of the capillaries to major changes in the rheology, a complete mathematical system has been derived. This system of equations is believed to be of major importance to provide new and significant insight into the causes of the disease and related crises. With simulations, it has been proven that the system transition from a periodic solution to a chaotic one, which illustrates the onset of crises from a regular blood flow synchronized with the heart beat. Moreover, the analysis of the effects of various physiological parameters exposes the potential to control chaotic solutions, which, in turn, could lead to the creation of new and more effective treatments for sickle cell anemia. .

Average value of the shape and direction factor in the equation of refractive index

NASA Astrophysics Data System (ADS)

Zhang, Tao

2017-10-01

The theoretical calculation of the refractive indices is of great significance for the developments of new optical materials. The calculation method of refractive index, which was deduced from the electron-cloud-conductor model, contains the shape and direction factor 〈g〉. 〈g〉 affects the electromagnetic-induction energy absorbed by the electron clouds, thereby influencing the refractive indices. It is not yet known how to calculate 〈g〉 value of non-spherical electron clouds. In this paper, 〈g〉 value is derived by imaginatively dividing the electron cloud into numerous little volume elements and then regrouping them. This paper proves that 〈g〉 = 2/3 when molecules’ spatial orientations distribute randomly. The calculations of the refractive indices of several substances validate this equation. This result will help to promote the application of the calculation method of refractive index.

Flow and Force Equations for a Body Revolving in a Fluid

NASA Technical Reports Server (NTRS)

Zahm, A. F.

1979-01-01

A general method for finding the steady flow velocity relative to a body in plane curvilinear motion, whence the pressure is found by Bernoulli's energy principle is described. Integration of the pressure supplies basic formulas for the zonal forces and moments on the revolving body. The application of the steady flow method for calculating the velocity and pressure at all points of the flow inside and outside an ellipsoid and some of its limiting forms is presented and graphs those quantities for the latter forms. In some useful cases experimental pressures are plotted for comparison with theoretical. The pressure, and thence the zonal force and moment, on hulls in plane curvilinear flight are calculated. General equations for the resultant fluid forces and moments on trisymmetrical bodies moving through a perfect fluid are derived. Formulas for potential coefficients and inertia coefficients for an ellipsoid and its limiting forms are presented.

Rate equation modeling of the frequency noise and the intrinsic spectral linewidth in quantum cascade lasers.

PubMed

Wang, Xing-Guang; Grillot, Frédéric; Wang, Cheng

2018-02-05

This work theoretically investigates the frequency noise (FN) characteristics of quantum cascade lasers (QCLs) through a three-level rate equation model, which takes into account both the carrier noise and the spontaneous emission noise through the Langevin approach. It is found that the power spectral density of the FN exhibits a broad peak due to the carrier noise induced carrier variation in the upper laser level, which is enhanced by the stimulated emission process. The peak amplitude is strongly dependent on the gain stage number and the linewidth broadening factor. In addition, an analytical formula of the intrinsic spectral linewidth of QCLs is derived based on the FN analysis. It is demonstrated that the laser linewidth can be narrowed by reducing the gain coefficient and/or accelerating the carrier scattering rates of the upper and the lower laser levels.

In-plane free vibration analysis of cable arch structure

NASA Astrophysics Data System (ADS)

Zhao, Yueyu; Kang, Houjun

2008-05-01

Cable-stayed arch bridge is a new type of composite bridge, which utilizes the mechanical characters of cable and arch. Based on the supporting members of cable-stayed arch bridge and of erection of arch bridge using of the cantilever construction method with tiebacks, we propose a novel mechanical model of cable-arch structure. In this model, the equations governing vibrations of the cable-arch are derived according to Hamilton's principle for dynamic problems in elastic body under equilibrium state. Then, the program of solving the dynamic governing equations is ultimately established by the transfer matrix method for free vibration of uniform and variable cross-section, and the internal characteristics of the cable-arch are investigated. After analyzing step by step, the research results approve that the program is accurate; meanwhile, the mechanical model and method are both valuable and significant not only in theoretical research and calculation but also in design of engineering.

Local sensitivity of per-recruit fishing mortality reference points.

PubMed

Cadigan, N G; Wang, S

2016-12-01

We study the sensitivity of fishery management per-recruit harvest rates which may be part of a quantitative harvest strategy designed to achieve some objective for catch or population size. We use a local influence sensitivity analysis to derive equations that describe how these reference harvest rates are affected by perturbations to productivity processes. These equations give a basic theoretical understanding of sensitivity that can be used to predict what the likely impacts of future changes in productivity will be. Our results indicate that per-recruit reference harvest rates are more sensitive to perturbations when the equilibrium catch or population size per recruit, as functions of the harvest rate, have less curvature near the reference point. Overall our results suggest that per recruit reference points will, with some exceptions, usually increase if (1) growth rates increase, (2) natural mortality rates increase, or (3) fishery selectivity increases to an older age.

Robust fast controller design via nonlinear fractional differential equations.

PubMed

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Kinetic description of electron beams in the solar chromosphere

NASA Technical Reports Server (NTRS)

Gomez, Daniel O.; Mauas, Pablo J.

1992-01-01

We formulate the relativistic Fokker-Plank equation for a beam of accelerated electrons interacting with a partially ionized plasma. In our derivation we conserved those terms contributing to velocity diffusion and found that this effect cannot be neglected a priori. We compute the terms accounting for elastic and inelastic collisions with neutral hydrogen and helium. Collisions with neutral hydrogen are found to be dominant throughout the chromosphere, except at the uppermost layers close to the transition region. As an application, we compute the loss of energy and momentum for a power-law beam impinging on the solar chromosphere, for a particular case in which the Fokker-Planck equation can be integrated analytically. We find that most of the beam energy is deposited in a relatively thin region of the chromosphere, a result which is largely insensitive to the theoretical method employed to compute the energy deposition rate.

Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence

NASA Astrophysics Data System (ADS)

Tarpin, Malo; Canet, Léonie; Wschebor, Nicolás

2018-05-01

In this paper, we present theoretical results on the statistical properties of stationary, homogeneous, and isotropic turbulence in incompressible flows in three dimensions. Within the framework of the non-perturbative renormalization group, we derive a closed renormalization flow equation for a generic n-point correlation (and response) function for large wave-numbers with respect to the inverse integral scale. The closure is obtained from a controlled expansion and relies on extended symmetries of the Navier-Stokes field theory. It yields the exact leading behavior of the flow equation at large wave-numbers |p→ i| and for arbitrary time differences ti in the stationary state. Furthermore, we obtain the form of the general solution of the corresponding fixed point equation, which yields the analytical form of the leading wave-number and time dependence of n-point correlation functions, for large wave-numbers and both for small ti and in the limit ti → ∞. At small ti, the leading contribution at large wave-numbers is logarithmically equivalent to -α (ɛL ) 2 /3|∑tip→ i|2, where α is a non-universal constant, L is the integral scale, and ɛ is the mean energy injection rate. For the 2-point function, the (tp)2 dependence is known to originate from the sweeping effect. The derived formula embodies the generalization of the effect of sweeping to n-point correlation functions. At large wave-numbers and large ti, we show that the ti2 dependence in the leading order contribution crosses over to a |ti| dependence. The expression of the correlation functions in this regime was not derived before, even for the 2-point function. Both predictions can be tested in direct numerical simulations and in experiments.

Derivation of Zagarola-Smits scaling in zero-pressure-gradient turbulent boundary layers

NASA Astrophysics Data System (ADS)

Wei, Tie; Maciel, Yvan

2018-01-01

This Rapid Communication derives the Zagarola-Smits scaling directly from the governing equations for zero-pressure-gradient turbulent boundary layers (ZPG TBLs). It has long been observed that the scaling of the mean streamwise velocity in turbulent boundary layer flows differs in the near surface region and in the outer layer. In the inner region of small-velocity-defect boundary layers, it is generally accepted that the proper velocity scale is the friction velocity, uτ, and the proper length scale is the viscous length scale, ν /uτ . In the outer region, the most generally used length scale is the boundary layer thickness, δ . However, there is no consensus on velocity scales in the outer layer. Zagarola and Smits [ASME Paper No. FEDSM98-4950 (1998)] proposed a velocity scale, U ZS=(δ1/δ ) U∞ , where δ1 is the displacement thickness and U∞ is the freestream velocity. However, there are some concerns about Zagarola-Smits scaling due to the lack of a theoretical base. In this paper, the Zagarola-Smits scaling is derived directly from a combination of integral, similarity, and order-of-magnitude analysis of the mean continuity equation. The analysis also reveals that V∞, the mean wall-normal velocity at the edge of the boundary layer, is a proper scale for the mean wall-normal velocity V . Extending the analysis to the streamwise mean momentum equation, we find that the Reynolds shear stress in ZPG TBLs scales as U∞V∞ in the outer region. This paper also provides a detailed analysis of the mass and mean momentum balance in the outer region of ZPG TBLs.

Oblique Propagation of Electrostatic Waves in a Magnetized Electron-Positron-Ion Plasma in the Presence of Heavy Particles

NASA Astrophysics Data System (ADS)

Sarker, M.; Hossen, M. R.; Shah, M. G.; Hosen, B.; Mamun, A. A.

2018-06-01

A theoretical investigation is carried out to understand the basic features of nonlinear propagation of heavy ion-acoustic (HIA) waves subjected to an external magnetic field in an electron-positron-ion plasma that consists of cold magnetized positively charged heavy ion fluids and superthermal distributed electrons and positrons. In the nonlinear regime, the Korteweg-de Vries (K-dV) and modified K-dV (mK-dV) equations describing the propagation of HIA waves are derived. The latter admits a solitary wave solution with both positive and negative potentials (for K-dV equation) and only positive potential (for mK-dV equation) in the weak amplitude limit. It is observed that the effects of external magnetic field (obliqueness), superthermal electrons and positrons, different plasma species concentration, heavy ion dynamics, and temperature ratio significantly modify the basic features of HIA solitary waves. The application of the results in a magnetized EPI plasma, which occurs in many astrophysical objects (e.g. pulsars, cluster explosions, and active galactic nuclei) is briefly discussed.

Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection.

PubMed

Sabelnikov, V A; Lipatnikov, A N

2014-09-01

The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

Frequency-dependent hydrodynamic interaction between two solid spheres

NASA Astrophysics Data System (ADS)

Jung, Gerhard; Schmid, Friederike

2017-12-01

Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions between finite-sized particles in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that at high frequencies, the compressibility of the fluid has a significant impact on the frequency-dependent pair interactions. The predictions of hydrodynamic theory are compared to molecular dynamics simulations of two nanocolloids in a Lennard-Jones fluid. For this system, we reconstruct memory functions by extending the inverse Volterra technique. The simulation data agree very well with the theory, therefore, the theory can be used to implement dynamically consistent hydrodynamic interactions in the increasingly popular field of non-Markovian modeling.