An improved two-dimensional depth-integrated flow equation for rough-walled fractures

NASA Astrophysics Data System (ADS)

Mallikamas, Wasin; Rajaram, Harihar

2010-08-01

We present the development of an improved 2-D flow equation for rough-walled fractures. Our improved equation accounts for the influence of midsurface tortuosity and the fact that the aperture normal to the midsurface is in general smaller than the vertical aperture. It thus improves upon the well-known Reynolds equation that is widely used for modeling flow in fractures. Unlike the Reynolds equation, our approach begins from the lubrication approximation applied in an inclined local coordinate system tangential to the fracture midsurface. The local flow equation thus obtained is rigorously transformed to an arbitrary global Cartesian coordinate system, invoking the concepts of covariant and contravariant transformations for vectors defined on surfaces. Unlike previously proposed improvements to the Reynolds equation, our improved flow equation accounts for tortuosity both along and perpendicular to a flow path. Our approach also leads to a well-defined anisotropic local transmissivity tensor relating the representations of the flux and head gradient vectors in a global Cartesian coordinate system. We show that the principal components of the transmissivity tensor and the orientation of its principal axes depend on the directional local midsurface slopes. In rough-walled fractures, the orientations of the principal axes of the local transmissivity tensor will vary from point to point. The local transmissivity tensor also incorporates the influence of the local normal aperture, which is uniquely defined at each point in the fracture. Our improved flow equation is a rigorous statement of mass conservation in any global Cartesian coordinate system. We present three examples of simple geometries to compare our flow equation to analytical solutions obtained using the exact Stokes equations: an inclined parallel plate, and circumferential and axial flows in an incomplete annulus. The effective transmissivities predicted by our flow equation agree very well with values obtained using the exact Stokes equations in all these cases. We discuss potential limitations of our depth-integrated equation, which include the neglect of convergence/divergence and the inaccuracies implicit in any depth-averaging process near sharp corners where the wall and midsurface curvatures are large.

Validating Reference Equations for Impulse Oscillometry in Healthy Mexican Children.

PubMed

Gochicoa-Rangel, Laura; Del Río-Hidalgo, Rodrigo; Hernández-Ruiz, Juana; Rodríguez-Moreno, Luis; Martínez-Briseño, David; Mora-Romero, Uri; Cid-Juárez, Silvia; García-Sancho, Cecilia; Torre-Bouscoulet, Luis

2017-09-01

The impulse oscillometry system (IOS) measures the impedance (Z) of the respiratory system, but proper interpretation of its results requires adequate reference values. The objectives of this work were: (1) to validate the reference equations for the IOS published previously by our group and (2) to compare the adjustment of new available reference equations for the IOS from different countries in a sample of healthy children. Subjects were healthy 4-15-y-old children from the metropolitan area of Mexico City, who performed an IOS test. The functional IOS parameters obtained were compared with the predicted values from 12 reference equations determined in studies of different ethnic groups. The validation methods applied were: analysis of the differences between measured and predicted values for each reference equation; correlation and concordance coefficients; adjustment by Z-score values; percentage of predicted value; and the percentage of patients below the lower limit of normality or above the upper limit of normality. Of the 224 participants, 117 (52.3%) were girls, and the mean age was 8.6 ± 2.3 y. The equations that showed the best adjustment for the different parameters were those from the studies by Nowowiejska et al (2008) and Gochicoa et al (2015). The equations proposed by Frei et al (2005), Hellinckx et al (1998), Kalhoff et al (2011), Klug and Bisgaard (1998), de Assumpção et al (2016), and Dencker et al (2006) overestimated the airway resistance of the children in our sample, whereas the equation of Amra et al (2008) underestimated it. In the analysis of the lower and upper limits of normality, Gochicoa et al equation was the closest, since 5% of subjects were below or above percentiles 5 and 95, respectively. The study found that, in general, all of the equations showed greater error at the extremes of the age distribution. Because of the robust adjustment of the present study reference equations for the IOS, it can be recommended for both clinical and research purposes in our population. The differential adjustment of other equations underlines the need to obtain local reference values. Copyright © 2017 by Daedalus Enterprises.

Analytical and Experimental Random Vibration of Nonlinear Aeroelastic Structures.

DTIC Science & Technology

1987-01-28

firstorder differential equations. In view of the system complexi- ty an attempt s made to close the infinite hierarchy by using a Gaussian scheme. This sc...year of this project-. When the first normal mode is externally excited by a band-limited random excitation, the system mean square response is found...governed mainly by the internal detuning parameter and the system damping ratios. The results are completely different when the second normal mode is

a Recursive Approach to Compute Normal Forms

NASA Astrophysics Data System (ADS)

HSU, L.; MIN, L. J.; FAVRETTO, L.

2001-06-01

Normal forms are instrumental in the analysis of dynamical systems described by ordinary differential equations, particularly when singularities close to a bifurcation are to be characterized. However, the computation of a normal form up to an arbitrary order is numerically hard. This paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms. A computer program to reduce the system to its normal form on a center manifold is developed using the Maple symbolic language. However, it should be stressed that the program relies essentially on recursive numerical computations, while symbolic calculations are used only for minor tasks. Some strategies are proposed to save computation time. Examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension.

Rigorous Combination of GNSS and VLBI: How it Improves Earth Orientation and Reference Frames

NASA Astrophysics Data System (ADS)

Lambert, S. B.; Richard, J. Y.; Bizouard, C.; Becker, O.

2017-12-01

Current reference series (C04) of the International Earth Rotation and Reference Systems Service (IERS) are produced by a weighted combination of Earth orientation parameters (EOP) time series built up by combination centers of each technique (VLBI, GNSS, Laser ranging, DORIS). In the future, we plan to derive EOP from a rigorous combination of the normal equation systems of the four techniques.We present here the results of a rigorous combination of VLBI and GNSS pre-reduced, constraint-free, normal equations with the DYNAMO geodetic analysis software package developed and maintained by the French GRGS (Groupe de Recherche en GeÌodeÌsie Spatiale). The used normal equations are those produced separately by the IVS and IGS combination centers to which we apply our own minimal constraints.We address the usefulness of such a method with respect to the classical, a posteriori, combination method, and we show whether EOP determinations are improved.Especially, we implement external validations of the EOP series based on comparison with geophysical excitation and examination of the covariance matrices. Finally, we address the potential of the technique for the next generation celestial reference frames, which are currently determined by VLBI only.

Nonalgebraic integrability of one reversible dynamical system of the Cremona type

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

1998-05-01

A reversible dynamical system (RDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions [the Chew-Low-type equations with crossing-symmetry matrix A(l,1)], are considered. This RDS is split into one- and two-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous three-point functional equation. Nonalgebraic integrability of RDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a nonresonant fixed point.

Sensitivity of Satellite Altimetry Data Assimilation on a Naval Anti-Submarine Warfare Weapon System

DTIC Science & Technology

2004-09-01

representing the actual ocean structure than static climatology databases (Fox et. al., 2002; Chu et. al., 2004). It is expected that this 2...pressure amplitude function and ( , )P P r z= is the phase function, or eikonal . Doing this and collecting real and imaginary terms yields an equation... eikonal equation, [ ]2 2P k∇ = , (13) from which differential equations for rays can be derived (Etter, 1991). The rays are the normals to surfaces

Local and global Hopf bifurcation analysis in a neutral-type neuron system with two delays

NASA Astrophysics Data System (ADS)

Lv, Qiuyu; Liao, Xiaofeng

2018-03-01

In recent years, neutral-type differential-difference equations have been applied extensively in the field of engineering, and their dynamical behaviors are more complex than that of the delay differential-difference equations. In this paper, the equations used to describe a neutral-type neural network system of differential difference equation with two delays are studied (i.e. neutral-type differential equations). Firstly, by selecting τ1, τ2 respectively as a parameter, we provide an analysis about the local stability of the zero equilibrium point of the equations, and sufficient conditions of asymptotic stability for the system are derived. Secondly, by using the theory of normal form and applying the theorem of center manifold introduced by Hassard et al., the Hopf bifurcation is found and some formulas for deciding the stability of periodic solutions and the direction of Hopf bifurcation are given. Moreover, by applying the theorem of global Hopf bifurcation, the existence of global periodic solution of the system is studied. Finally, an example is given, and some computer numerical simulations are taken to demonstrate and certify the correctness of the presented results.

Investigation of the Dirac Equation by Using the Conformable Fractional Derivative

NASA Astrophysics Data System (ADS)

Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.

2018-05-01

In this paper,the Dirac equation is constructed using the conformable fractional derivative so that in its limit for the fractional parameter, the normal version is recovered. Then, the Cornell potential is considered as the interaction of the system. In this case, the wave function and the energy eigenvalue equation are derived with the aim of the bi-confluent Heun functions. use of the conformable fractional derivative is proven to lead to a branching treatment for the energy of the system. Such a treatment is obvious for small values of the fractional parameter, and a united value as the fractional parameter approaches unity.

Self-consistent-field perturbation theory for the Schröautdinger equation

NASA Astrophysics Data System (ADS)

Goodson, David Z.

1997-06-01

A method is developed for using large-order perturbation theory to solve the systems of coupled differential equations that result from the variational solution of the Schröautdinger equation with wave functions of product form. This is a noniterative, computationally efficient way to solve self-consistent-field (SCF) equations. Possible applications include electronic structure calculations using products of functions of collective coordinates that include electron correlation, vibrational SCF calculations for coupled anharmonic oscillators with selective coupling of normal modes, and ab initio calculations of molecular vibration spectra without the Born-Oppenheimer approximation.

Fast Legendre moment computation for template matching

NASA Astrophysics Data System (ADS)

Li, Bing C.

2017-05-01

Normalized cross correlation (NCC) based template matching is insensitive to intensity changes and it has many applications in image processing, object detection, video tracking and pattern recognition. However, normalized cross correlation implementation is computationally expensive since it involves both correlation computation and normalization implementation. In this paper, we propose Legendre moment approach for fast normalized cross correlation implementation and show that the computational cost of this proposed approach is independent of template mask sizes which is significantly faster than traditional mask size dependent approaches, especially for large mask templates. Legendre polynomials have been widely used in solving Laplace equation in electrodynamics in spherical coordinate systems, and solving Schrodinger equation in quantum mechanics. In this paper, we extend Legendre polynomials from physics to computer vision and pattern recognition fields, and demonstrate that Legendre polynomials can help to reduce the computational cost of NCC based template matching significantly.

Construction of normal-regular decisions of Bessel typed special system

NASA Astrophysics Data System (ADS)

Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.

2017-09-01

Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.

Application of Power Geometry and Normal Form Methods to the Study of Nonlinear ODEs

NASA Astrophysics Data System (ADS)

Edneral, Victor

2018-02-01

This paper describes power transformations of degenerate autonomous polynomial systems of ordinary differential equations which reduce such systems to a non-degenerative form. Example of creating exact first integrals of motion of some planar degenerate system in a closed form is given.

The New Data Assimilation System at the Italian Air Force Weather Service: Design and Preliminary Results

DTIC Science & Technology

2002-09-01

weather conditions (1999 Christmas storm in Europe , January 2000 snow storm over the eastern coast of the US) can be attributed to the inaccuracies in...over the normal modes of a linearized version of the model equations. These 5 normal modes can be classified (at least for the extratropics ) based

Plasma Modes

NASA Astrophysics Data System (ADS)

Dubin, D. H. E.

This chapter explores several aspects of the linear electrostatic normal modes of oscillation for a single-species non-neutral plasma in a Penning trap. Linearized fluid equations of motion are developed, assuming the plasma is cold but collisionless, which allow derivation of the cold plasma dielectric tensor and the electrostatic wave equation. Upper hybrid and magnetized plasma waves in an infinite uniform plasma are described. The effect of the plasma surface in a bounded plasma system is considered, and the properties of surface plasma waves are characterized. The normal modes of a cylindrical plasma column are discussed, and finally, modes of spheroidal plasmas, and finite temperature effects on the modes, are briefly described.

EGSIEM: Combination of GRACE monthly gravity models on normal equation level

NASA Astrophysics Data System (ADS)

Meyer, Ulrich; Jean, Yoomin; Jäggi, Adrian; Mayer-Gürr, Torsten; Neumayer, Hans; Lemoine, Jean-Michel

2016-04-01

One of the three geodetic services to be realized in the frame of the EGSIEM project is a scientific combination service. Each associated processing center (AC) will follow a set of common processing standards but will apply its own, independent analysis method. Therefore the quality, robustness and reliability of the combined monthly gravity fields is expected to improve significantly compared to the individual solutions. The Monthly GRACE gravity fields of all ACs are combined on normal equation level. The individual normal equations are weighted depending on pairwise comparisons of the individual gravity field solutions. To derive these weights and for quality control of the individual contributions first a combination of the monthly gravity fields on solution level is performed. The concept of weighting and of the combination on normal equation level is introduced and the formats used for normal equation exchange and gravity field solutions is described. First results of the combination on normal equation level are presented and compared to the corresponding combinations on solution level. EGSIEM has an open data policy and all processing centers of GRACE gravity fields are invited to participate in the combination.

Interactive calculation procedure for supersonic flows. Ph.D. Thesis - Case Western Reserve Univ., 1976. Final Report

NASA Technical Reports Server (NTRS)

Tassa, Y.; Anderson, B. H.; Reshotko, E.

1977-01-01

An interactive procedure was developed for supersonic viscous flows that can be used for either two-dimensional or axisymmetric configurations. The procedure is directed to supersonic internal flows as well as those supersonic external flows that require consideration of mutual interaction between the outer flow and the boundary layer flow. The flow field is divided into two regions: an inner region which is highly viscous and mostly subsonic and an outer region where the flow is supersonic and in which viscous effects are small but not negligible. For the outer region a numerical solution is obtained by applying the method of characteristics to a system of equations which includes viscous and conduction transport terms only normal to the streamlines. The inner region is treated by a system of equations of the boundary layer type that includes higher order effects such as longitudinal and transverse curvature and normal pressure gradients. These equations are coupled and solved simultaneously in the physical coordinates by using an implicit finite difference scheme. This system can also be used to calculate laminar and turbulent boundary layers using a scalar eddy viscosity concept.

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.

Dynamics of localized structures in reaction-diffusion systems induced by delayed feedback

NASA Astrophysics Data System (ADS)

Gurevich, Svetlana V.

2013-05-01

We are interested in stability properties of a single localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to complex dynamical behavior of the system, including formation of target patterns, spontaneous motion, and spontaneous breathing as well as various complex structures, arising from combination of different oscillatory instabilities. In the case of spontaneous motion, we provide a bifurcation analysis of the delayed system and derive an order parameter equation for the position of the localized structure, explicitly describing its temporal evolution in the vicinity of the bifurcation point. This equation is a subject to a nonlinear delay differential equation, which can be transformed to the normal form of the pitchfork drift bifurcation.

On a Parabolic-Elliptic system with chemotaxis and logistic type growth

NASA Astrophysics Data System (ADS)

Galakhov, Evgeny; Salieva, Olga; Tello, J. Ignacio

2016-10-01

We consider a nonlinear PDEs system of two equations of Parabolic-Elliptic type with chemotactic terms. The system models the movement of a biological population ;u; towards a higher concentration of a chemical agent ;w; in a bounded and regular domain Ω ⊂RN for arbitrary N ∈ N. After normalization, the system is as follows

Modified Van der Waals equation and law of corresponding states

NASA Astrophysics Data System (ADS)

Zhong, Wei; Xiao, Changming; Zhu, Yongkai

2017-04-01

It is well known that the Van der Waals equation is a modification of the ideal gas law, yet it can be used to describe both gas and liquid, and some important messages can be obtained from this state equation. However, the Van der Waals equation is not a precise state equation, and it does not give a good description of the law of corresponding states. In this paper, we expand the Van der Waals equation into its Taylor's series form, and then modify the fourth order expansion by changing the constant Virial coefficients into their analogous ones. Via this way, a more precise result about the law of corresponding states has been obtained, and the law of corresponding states can then be expressed as: in terms of the reduced variables, all fluids should obey the same equation with the analogous Virial coefficients. In addition, the system of 3 He with quantum effects has also been taken into consideration with our modified Van der Waals equation, and it is found that, for a normal system without quantum effect, the modification on ideal gas law from the Van der Waals equation is more significant than the real case, however, for a system with quantum effect, this modification is less significant than the real case, thus a factor is introduced in this paper to weaken or strengthen the modification of the Van der Waals equation, respectively.

Similar solutions for the compressible laminar boundary layer with heat transfer and pressure gradient

NASA Technical Reports Server (NTRS)

Cohen, Clarence B; Reshotko, Eli

1956-01-01

Stewartson's transformation is applied to the laminar compressible boundary-layer equations and the requirement of similarity is introduced, resulting in a set of ordinary nonlinear differential equations previously quoted by Stewartson, but unsolved. The requirements of the system are Prandtl number of 1.0, linear viscosity-temperature relation across the boundary layer, an isothermal surface, and the particular distributions of free-stream velocity consistent with similar solutions. This system admits axial pressure gradients of arbitrary magnitude, heat flux normal to the surface, and arbitrary Mach numbers. The system of differential equations is transformed to integral system, with the velocity ratio as the independent variable. For this system, solutions are found by digital computation for pressure gradients varying from that causing separation to the infinitely favorable gradient and for wall temperatures from absolute zero to twice the free-stream stagnation temperature. Some solutions for separated flows are also presented.

Nonlinear normal modes in electrodynamic systems: A nonperturbative approach

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

Kudrin, A. V., E-mail: kud@rf.unn.ru; Kudrina, O. A.; Petrov, E. Yu.

2016-06-15

We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known tomore » hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.« less

Birkhoff Normal Form for Some Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Bambusi, Dario

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

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

PubMed

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

2015-10-01

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

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

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

Konor, Celal S.; Randall, David A.

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

Analyzing Axial Stress and Deformation of Tubular for Steam Injection Process in Deviated Wells Based on the Varied (T, P) Fields

PubMed Central

Liu, Yunqiang; Xu, Jiuping; Wang, Shize; Qi, Bin

2013-01-01

The axial stress and deformation of high temperature high pressure deviated gas wells are studied. A new model is multiple nonlinear equation systems by comprehensive consideration of axial load of tubular string, internal and external fluid pressure, normal pressure between the tubular and well wall, and friction and viscous friction of fluid flowing. The varied temperature and pressure fields were researched by the coupled differential equations concerning mass, momentum, and energy equations instead of traditional methods. The axial load, the normal pressure, the friction, and four deformation lengths of tubular string are got ten by means of the dimensionless iterative interpolation algorithm. The basic data of the X Well, 1300 meters deep, are used for case history calculations. The results and some useful conclusions can provide technical reliability in the process of designing well testing in oil or gas wells. PMID:24163623

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

DOE PAGES

Konor, Celal S.; Randall, David A.

2018-05-08

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

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

NASA Astrophysics Data System (ADS)

Konor, Celal S.; Randall, David A.

2018-05-01

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

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering Based on the Newly Developed Self-consistent RC/EMIC Waves Model by Khazanov et al. [2006

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gallagher, D. L.; Gamayunov, K.

2007-01-01

It is well known that the effects of EMIC waves on RC ion and RB electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. Therefore, realistic characteristics of EMIC waves should be properly determined by modeling the RC-EMIC waves evolution self-consistently. Such a selfconsistent model progressively has been developing by Khaznnov et al. [2002-2006]. It solves a system of two coupled kinetic equations: one equation describes the RC ion dynamics and another equation describes the energy density evolution of EMIC waves. Using this model, we present the effectiveness of relativistic electron scattering and compare our results with previous work in this area of research.

The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

NASA Astrophysics Data System (ADS)

Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran

2018-04-01

This paper investigates the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces, specifically RT0 for triangles and unmapped RT[0] for quadrilaterals. These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation. The method produces continuous normal fluxes and is locally mass-conservative, regardless of mesh quality, and has optimal order convergence in pressure, velocity, and normal flux, when the quadrilaterals are asymptotically parallelograms. Implementation is straightforward and results in symmetric positive-definite discrete linear systems. We present numerical experiments and comparisons with other existing methods.

Partial differential equations of 3D boundary layer and their numerical solutions in turbomachinery

NASA Astrophysics Data System (ADS)

Zhang, Guoqing; Hua, Yaonan; Wu, Chung-Hua

1991-08-01

This paper studies the 3D boundary layer equations (3DBLE) and their numerical solutions in turbomachinery: (1) the general form of 3DBLE in turbomachines with rotational and curvature effects are derived under the semiorthogonal coordinate system, in which the normal pressure gradient is not equal to zero; (2) the method of solution of the 3DBLE is discussed; (3) the 3D boundary layers on the rotating blade surface, IGV endwall, rotor endwall (with a relatively moving boundary) are numerically solved, and the predicted data correlates well with the measured data; and (4) the comparison is made between the numerical results of 3DBLE with and without normal pressure gradient.

Observability of nonlinear dynamics: normalized results and a time-series approach.

PubMed

Aguirre, Luis A; Bastos, Saulo B; Alves, Marcela A; Letellier, Christophe

2008-03-01

This paper investigates the observability of nonlinear dynamical systems. Two difficulties associated with previous studies are dealt with. First, a normalized degree observability is defined. This permits the comparison of different systems, which was not generally possible before. Second, a time-series approach is proposed based on omnidirectional nonlinear correlation functions to rank a set of time series of a system in terms of their potential use to reconstruct the original dynamics without requiring the knowledge of the system equations. The two approaches proposed in this paper and a former method were applied to five benchmark systems and an overall agreement of over 92% was found.

On Nonequivalence of Several Procedures of Structural Equation Modeling

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Chan, Wai

2005-01-01

The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure…

The Shock and Vibration Digest. Volume 16, Number 7

DTIC Science & Technology

1984-07-01

Brayton -Moser :,. existence of classical normal modes in various classes equations has been presented (32, 33]. Two methods of problems, the concept of...and Re- "Connections between the Generalized Hamil- strained Dynamical Systems," J. Appl. Mech., ton-Lagrange and Brayton -Moser Equations," Trans...committees within the division. Short Ccourses are also offered as a part of this conference, Walter Taylor described how he used a microcom- and the

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.

On locally and nonlocally related potential systems

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.; Bluman, George W.

2010-07-01

For any partial differential equation (PDE) system, a local conservation law yields potential equations in terms of some potential variable, which normally is a nonlocal variable. The current paper examines situations when such a potential variable is a local variable, i.e., is a function of the independent and dependent variables of a given PDE system, and their derivatives. In the case of two independent variables, a simple necessary and sufficient condition is presented for the locality of such a potential variable, and this is illustrated by several examples. As a particular example, two-dimensional reductions of equilibrium equations for fluid and plasma dynamics are considered. It is shown that such reductions with respect to helical, axial, and translational symmetries have conservation laws which yield local potential variables. This leads to showing that the well-known Johnson-Frieman-Kruskal-Oberman (JFKO) and Bragg-Hawthorne (Grad-Shafranov) equations are locally related to the corresponding helically and axially symmetric PDE systems of fluid/plasma dynamics. For the axially symmetric case, local symmetry classifications and arising invariant solutions are compared for the original PDE system and the Bragg-Hawthorne (potential) equation. The potential equation is shown to have additional symmetries, denoted as restricted symmetries. Restricted symmetries leave invariant a family of solutions of a given PDE system but not the whole solution manifold, and hence are not symmetries of the given PDE system. Corresponding reductions are shown to yield solutions, which are not obtained as invariant solutions from local symmetry reduction.

Purfication kinetics of beryllium during vacuum induction melting

NASA Technical Reports Server (NTRS)

Mukherjee, J. L.; Gupta, K. P.; Li, C. H.

1972-01-01

The kinetics of evaporation in binary alloys were quantitatively treated. The formalism so developed works well for several systems studied. The kinetics of purification of beryllium was studied through evaporation data actually acquired during vacuum induction melting. Normal evaporation equations are shown to be generally valid and useful for understanding the kinetics of beryllium purification. The normal evaporation analysis has been extended to cover cases of limited liquid diffusion. It was shown that under steady-state evaporation, the solute concentration near the surface may be up to six orders of magnitude different from the bulk concentration. Corrections for limited liquid diffusion are definitely needed for the highly evaporative solute elements, such as Zn, Mg, and Na, for which the computed evaporation times are improved by five orders of magnitude. The commonly observed logarithmic relation between evaporation time and final concentration further supports the validity of the normal evaporation equations.

Mode instability in one-dimensional anharmonic lattices: Variational equation approach

NASA Astrophysics Data System (ADS)

Yoshimura, K.

1999-03-01

The stability of normal mode oscillations has been studied in detail under the single-mode excitation condition for the Fermi-Pasta-Ulam-β lattice. Numerical experiments indicate that the mode stability depends strongly on k/N, where k is the wave number of the initially excited mode and N is the number of degrees of freedom in the system. It has been found that this feature does not change when N increases. We propose an average variational equation - approximate version of the variational equation - as a theoretical tool to facilitate a linear stability analysis. It is shown that this strong k/N dependence of the mode stability can be explained from the view point of the linear stability of the relevant orbits. We introduce a low-dimensional approximation of the average variational equation, which approximately describes the time evolution of variations in four normal mode amplitudes. The linear stability analysis based on this four-mode approximation demonstrates that the parametric instability mechanism plays a crucial role in the strong k/N dependence of the mode stability.

On the JWKB solution of the uniformly lengthening pendulum via change of independent variable in the Bessel's equation

NASA Astrophysics Data System (ADS)

Deniz, Coşkun

2017-01-01

Common recipe for the lengthening pendulum (LP) involves some change of variables to give a relationship with the Bessel's equation. In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel's equation into the normal form `via the suggested change of independent variable'. JWKB approximation of the first-order Bessel functions ( ν=1) of both types along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders ( ν=0 and 2) by the recursion relations. The required initial values are also being studied and a quantization rule regarding the experimental LP parameters is being determined. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is slow, JWKB solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined by the JWKB applicability criterion given in the literature. As a result, the semiclassical JWKB method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully.

Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form

NASA Astrophysics Data System (ADS)

Gituliar, Oleksandr; Magerya, Vitaly

2017-10-01

We present Fuchsia - an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂x J(x , ɛ) = A(x , ɛ) J(x , ɛ) finds a basis transformation T(x , ɛ) , i.e., J(x , ɛ) = T(x , ɛ) J‧(x , ɛ) , such that the system turns into the epsilon form : ∂xJ‧(x , ɛ) = ɛ S(x) J‧(x , ɛ) , where S(x) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ɛ. That makes the construction of the transformation T(x , ɛ) crucial for obtaining solutions of the initial system. In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals. Program Files doi:http://dx.doi.org/10.17632/zj6zn9vfkh.1 Licensing provisions: MIT Programming language:Python 2.7 Nature of problem: Feynman master integrals may be calculated from solutions of a linear system of differential equations with rational coefficients. Such a system can be easily solved as an ɛ-series when its epsilon form is known. Hence, a tool which is able to find the epsilon form transformations can be used to evaluate Feynman master integrals. Solution method: The solution method is based on the Lee algorithm (Lee, 2015) which consists of three main steps: fuchsification, normalization, and factorization. During the fuchsification step a given system of differential equations is transformed into the Fuchsian form with the help of the Moser method (Moser, 1959). Next, during the normalization step the system is transformed to the form where eigenvalues of all residues are proportional to the dimensional regulator ɛ. Finally, the system is factorized to the epsilon form by finding an unknown transformation which satisfies a system of linear equations. Additional comments including Restrictions and Unusual features: Systems of single-variable differential equations are considered. A system needs to be reducible to Fuchsian form and eigenvalues of its residues must be of the form n + m ɛ, where n is integer. Performance depends upon the input matrix, its size, number of singular points and their degrees. It takes around an hour to reduce an example 74 × 74 matrix with 20 singular points on a PC with a 1.7 GHz Intel Core i5 CPU. An additional slowdown is to be expected for matrices with complex and/or irrational singular point locations, as these are particularly difficult for symbolic algebra software to handle.

For operation of the Computer Software Management and Information Center (COSMIC)

NASA Technical Reports Server (NTRS)

Carmon, J. L.

1983-01-01

Computer programs for large systems of normal equations, an interactive digital signal process, structural analysis of cylindrical thrust chambers, swirling turbulent axisymmetric recirculating flows in practical isothermal combustor geometrics, computation of three dimensional combustor performance, a thermal radiation analysis system, transient response analysis, and a software design analysis are summarized.

Comments on compressible effects on Alfven normal modes in nonuniform plasmas

NASA Technical Reports Server (NTRS)

Mok, Y.; Einaudi, G.

1990-01-01

The paper discusses the regime of validity of the theory of dissipative Alfven normal modes presented by Mok and Einaudi (1985) and Einaudi and Mok (1985), which was based on the incompressible closure of the system of ideal MHD equations. Some simple extensions of the earlier results to the compressible case are described. In addition, certain misunderstandings of this work, which have appeared in other papers, are clarified.

A collocation--Galerkin finite element model of cardiac action potential propagation.

PubMed

Rogers, J M; McCulloch, A D

1994-08-01

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

Nonlocal Symmetries, Conservation Laws and Interaction Solutions of the Generalised Dispersive Modified Benjamin-Bona-Mahony Equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian

2018-05-01

We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.

The use of lidar for stratospheric measurements

NASA Technical Reports Server (NTRS)

Mccormick, M. P.

1977-01-01

Stratospheric measurements possible with ground-based, airborne, and satellite-borne lidar systems are reviewed. The instruments, basic equations, and formats normally used for various scattering and absorption phenomena measurements are presented including a discussion of elastic, resonance, Raman, and fluorescence scattering techniques.

Singularity-free dynamic equations of spacecraft-manipulator systems

NASA Astrophysics Data System (ADS)

From, Pål J.; Ytterstad Pettersen, Kristin; Gravdahl, Jan T.

2011-12-01

In this paper we derive the singularity-free dynamic equations of spacecraft-manipulator systems using a minimal representation. Spacecraft are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange's equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of a spacecraft is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of free-floating and free-flying spacecraft-manipulator systems and we show how to calculate the inertia and Coriolis matrices in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. This paper represents the first detailed study of modeling of spacecraft-manipulator systems with a focus on a singularity free formulation using the proposed framework.

NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations.

PubMed

Prague, Mélanie; Commenges, Daniel; Guedj, Jérémie; Drylewicz, Julia; Thiébaut, Rodolphe

2013-08-01

Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2015-01-01

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1993-01-01

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

Modified Chapman-Enskog moment approach to diffusive phonon heat transport.

PubMed

Banach, Zbigniew; Larecki, Wieslaw

2008-12-01

A detailed treatment of the Chapman-Enskog method for a phonon gas is given within the framework of an infinite system of moment equations obtained from Callaway's model of the Boltzmann-Peierls equation. Introducing no limitations on the magnitudes of the individual components of the drift velocity or the heat flux, this method is used to derive various systems of hydrodynamic equations for the energy density and the drift velocity. For one-dimensional flow problems, assuming that normal processes dominate over resistive ones, it is found that the first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) yield the equations of hydrodynamics which are linearly stable at all wavelengths. This result can be achieved either by examining the dispersion relations for linear plane waves or by constructing the explicit quadratic Lyapunov entropy functionals for the linear perturbation equations. The next order in the Chapman-Enskog expansion leads to equations which are unstable to some perturbations. Precisely speaking, the linearized equations of motion that describe the propagation of small disturbances in the flow have unstable plane-wave solutions in the short-wavelength limit of the dispersion relations. This poses no problem if the equations are used in their proper range of validity.

On the wall-normal velocity of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Pruett, C. David

1991-01-01

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

Velocity lag of solid particles in oscillating gases and in gases passing through normal shock waves

NASA Technical Reports Server (NTRS)

Maxwell, B. R.; Seasholtz, R. G.

1974-01-01

The velocity lag of micrometer size spherical particles is theoretically determined for gas particle mixtures passing through a stationary normal shock wave and also for particles embedded in an oscillating gas flow. The particle sizes and densities chosen are those considered important for laser Doppler velocimeter applications. The governing equations for each flow system are formulated. The deviation from Stokes flow caused by inertial, compressibility, and rarefaction effects is accounted for in both flow systems by use of an empirical drag coefficient. Graphical results are presented which characterize particle tracking as a function of system parameters.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Sex Discrimination as to Maternity Benefits

ERIC Educational Resources Information Center

Larson, Arthur

1975-01-01

A general survey of the state of the law at all points where maternity produces a claim of sex discrimination in employment and discussion of whether, under Geduldig v. Aiello, all private fringe benefit systems must equate normal pregnancy with temporary sickness and disability. (JT)

On the MAF solution of the uniformly lengthening pendulum via change of independent variable in the Bessel's equation

NASA Astrophysics Data System (ADS)

Deniz, Coşkun

Common recipe for the Lengthening Pendulum (LP) involves some change of variables to give a relationship with the Bessel's equation. In this work, semiclassical MAF (Modified Airy Function) solution of the LP is being obtained by first transforming the related Bessel's equation into the normal form via the suggested change of independent variable just as one of our recent work regarding the JWKB solution of the LP in (Deniz, 2017). MAF approximation of the first order Bessel Functions (ν = 1) of both type along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders (ν = 0 and 2) by the recursion relations. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is small, MAF solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined via the use of MAF applicability criterion given in the literature. As a result, the semiclassical MAF method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully just as our previous work regarding the JWKB solution of the LP. Interestingly, we have very accurate results in the entire domain except for x ≈ 0 .

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

NASA Astrophysics Data System (ADS)

Kwang-Hua, Chu Rainer

2018-05-01

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

Boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Panaras, Argyris G.

1987-01-01

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

A stockability equation for forest land in Siskiyou County, California.

Treesearch

Neil. McKay

1985-01-01

An equation is presented that estimates the relative stocking capacity of forest land in Siskiyou County, California, from the amount of precipitation and the presence of significant indicator plants. The equation is a toot for identifying sites incapable of supporting normal stocking. Estimated relative stocking capacity may be used to discount normal yields to levels...

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

Combined effects of magnetic field and partial slip on obliquely striking rheological fluid over a stretching surface

NASA Astrophysics Data System (ADS)

Nadeem, S.; Mehmood, Rashid; Akbar, Noreen Sher

2015-03-01

This study explores the collective effects of partial slip and transverse magnetic field on an oblique stagnation point flow of a rheological fluid. The prevailing momentum equations are designed by manipulating Casson fluid model. By applying the suitable similarity transformations, the governing system of equations is being transformed into coupled nonlinear ordinary differential equations. The resulting system is handled numerically through midpoint integration scheme together with Richardson's extrapolation. It is found that both normal and tangential velocity profiles decreases with an increase in magnetic field as well as slip parameter. Streamlines pattern are presented to study the actual impact of slip mechanism and magnetic field on the oblique flow. A suitable comparison with the previous literature is also provided to confirm the accuracy of present results for the limiting case.

Probability distributions for multimeric systems.

PubMed

Albert, Jaroslav; Rooman, Marianne

2016-01-01

We propose a fast and accurate method of obtaining the equilibrium mono-modal joint probability distributions for multimeric systems. The method necessitates only two assumptions: the copy number of all species of molecule may be treated as continuous; and, the probability density functions (pdf) are well-approximated by multivariate skew normal distributions (MSND). Starting from the master equation, we convert the problem into a set of equations for the statistical moments which are then expressed in terms of the parameters intrinsic to the MSND. Using an optimization package on Mathematica, we minimize a Euclidian distance function comprising of a sum of the squared difference between the left and the right hand sides of these equations. Comparison of results obtained via our method with those rendered by the Gillespie algorithm demonstrates our method to be highly accurate as well as efficient.

Causality Analysis: Identifying the Leading Element in a Coupled Dynamical System

PubMed Central

BozorgMagham, Amir E.; Motesharrei, Safa; Penny, Stephen G.; Kalnay, Eugenia

2015-01-01

Physical systems with time-varying internal couplings are abundant in nature. While the full governing equations of these systems are typically unknown due to insufficient understanding of their internal mechanisms, there is often interest in determining the leading element. Here, the leading element is defined as the sub-system with the largest coupling coefficient averaged over a selected time span. Previously, the Convergent Cross Mapping (CCM) method has been employed to determine causality and dominant component in weakly coupled systems with constant coupling coefficients. In this study, CCM is applied to a pair of coupled Lorenz systems with time-varying coupling coefficients, exhibiting switching between dominant sub-systems in different periods. Four sets of numerical experiments are carried out. The first three cases consist of different coupling coefficient schemes: I) Periodic–constant, II) Normal, and III) Mixed Normal/Non-normal. In case IV, numerical experiment of cases II and III are repeated with imposed temporal uncertainties as well as additive normal noise. Our results show that, through detecting directional interactions, CCM identifies the leading sub-system in all cases except when the average coupling coefficients are approximately equal, i.e., when the dominant sub-system is not well defined. PMID:26125157

A variational approach to dynamics of flexible multibody systems

NASA Technical Reports Server (NTRS)

Wu, Shih-Chin; Haug, Edward J.; Kim, Sung-Soo

1989-01-01

This paper presents a variational formulation of constrained dynamics of flexible multibody systems, using a vector-variational calculus approach. Body reference frames are used to define global position and orientation of individual bodies in the system, located and oriented by position of its origin and Euler parameters, respectively. Small strain linear elastic deformation of individual components, relative to their body references frames, is defined by linear combinations of deformation modes that are induced by constraint reaction forces and normal modes of vibration. A library of kinematic couplings between flexible and/or rigid bodies is defined and analyzed. Variational equations of motion for multibody systems are obtained and reduced to mixed differential-algebraic equations of motion. A space structure that must deform during deployment is analyzed, to illustrate use of the methods developed.

Closed system of coupling effects in generalized thermo-elastoplasticity

NASA Astrophysics Data System (ADS)

Śloderbach, Z.

2016-05-01

In this paper, the field equations of the generalized coupled thermoplasticity theory are derived using the postulates of classical thermodynamics of irreversible processses. Using the Legendre transformations two new thermodynamics potentials P and S depending upon internal thermodynamic forces Π are introduced. The most general form for all the thermodynamics potentials are assumed instead of the usually used additive form. Due to this assumption, it is possible to describe all the effects of thermomechanical couples and also the elastic-plastic coupling effects observed in such materials as rocks, soils, concretes and in some metalic materials. In this paper not only the usual postulate of existence of a dissipation qupotential (the Gyarmati postulate) is used to derive the velocity equation. The plastic flow constitutive equations have the character of non-associated flow laws even when the Gyarmati postulate is assumed. In general formulation, the plastic strain rate tensor is normal to the surface of the generalized function of plastic flow defined in the the space of internal thermodynamic forces Π but is not normal to the yield surface. However, in general formulation and after the use the Gyarmati postulate, the direction of the sum of the plastic strain rate tensor and the coupled elastic strain rate tensor is normal to the yield surface.

Standard Error of Linear Observed-Score Equating for the NEAT Design with Nonnormally Distributed Data

ERIC Educational Resources Information Center

Zu, Jiyun; Yuan, Ke-Hai

2012-01-01

In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed-score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the…

Modeling water vapor and heat transfer in the normal and the intubated airways.

PubMed

Tawhai, Merryn H; Hunter, Peter J

2004-04-01

Intubation of the artificially ventilated patient with an endotracheal tube bypasses the usual conditioning regions of the nose and mouth. In this situation any deficit in heat or moisture in the air is compensated for by evaporation and thermal transfer from the pulmonary airway walls. To study the dynamics of heat and water transport in the intubated airway, a coupled system of nonlinear equations is solved in airway models with symmetric geometry and anatomically based geometry. Radial distribution of heat, water vapor, and velocity in the airway are described by power-law equations. Solution of the time-dependent system of equations yields dynamic airstream and mucosal temperatures and air humidity. Comparison of model results with two independent experimental studies in the normal and intubated airway shows a close correlation over a wide range of minute ventilation. Using the anatomically based model a range of spatially distributed temperature paths is demonstrated, which highlights the model's ability to predict thermal behavior in airway regions currently inaccessible to measurement. Accurate representation of conducting airway geometry is shown to be necessary for simulating mouth-breathing at rates between 15 and 100 l x min(-1), but symmetric geometry is adequate for the low minute ventilation and warm inspired air conditions that are generally supplied to the intubated patient.

An improved algorithm for the determination of the system paramters of a visual binary by least squares

NASA Astrophysics Data System (ADS)

Xu, Yu-Lin

The problem of computing the orbit of a visual binary from a set of observed positions is reconsidered. It is a least squares adjustment problem, if the observational errors follow a bias-free multivariate Gaussian distribution and the covariance matrix of the observations is assumed to be known. The condition equations are constructed to satisfy both the conic section equation and the area theorem, which are nonlinear in both the observations and the adjustment parameters. The traditional least squares algorithm, which employs condition equations that are solved with respect to the uncorrelated observations and either linear in the adjustment parameters or linearized by developing them in Taylor series by first-order approximation, is inadequate in our orbit problem. D.C. Brown proposed an algorithm solving a more general least squares adjustment problem in which the scalar residual function, however, is still constructed by first-order approximation. Not long ago, a completely general solution was published by W.H Jefferys, who proposed a rigorous adjustment algorithm for models in which the observations appear nonlinearly in the condition equations and may be correlated, and in which construction of the normal equations and the residual function involves no approximation. This method was successfully applied in our problem. The normal equations were first solved by Newton's scheme. Practical examples show that this converges fast if the observational errors are sufficiently small and the initial approximate solution is sufficiently accurate, and that it fails otherwise. Newton's method was modified to yield a definitive solution in the case the normal approach fails, by combination with the method of steepest descent and other sophisticated algorithms. Practical examples show that the modified Newton scheme can always lead to a final solution. The weighting of observations, the orthogonal parameters and the efficiency of a set of adjustment parameters are also considered. The definition of efficiency is revised.

Kinetic Equation for an Unstable Plasma

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

Balescu, R.

1963-01-01

A kinetic equation is derived for the description of the evolution in time of the distribution of velocities in a spatially homogeneous ionized gas that, at the initial time, is able to sustain exponentially growing oscillations. This equation is expressed in terms of a functional of the distribution finction that obeys the same integral equation as in the stable case. Although the method of solution used in the stable case breaks down, the equation can still be solved in closed form under unstable conditions, and hence an explicit form of the kinetic equation is obtained. The latter contains the normalmore » collision term and a new additional term describing the stabilization of the plasma. The latter acts through friction and diffusion and brings the plasma into a state of neutral stability. From there on the system evolves toward thermal equilibrium under the action of the normal collision term as well as of an additional Fokker-Planck- like term with timedependent coefficients, which however becomes less and less efficient as the plasma approaches equilibrium.« less

Dark and antidark solitons in the modified nonlinear Schrödinger equation accounting for the self-steepening effect.

PubMed

Li, Min; Tian, Bo; Liu, Wen-Jun; Zhang, Hai-Qiang; Wang, Pan

2010-04-01

In this paper, the modified nonlinear Schrödinger equation is investigated, which describes the femtosecond optical pulse propagation in a monomodal optical fiber. Based on the Wadati-Konno-Ichikawa system, another type of Lax pair and infinitely many conservation laws are derived. Dark and antidark soliton solutions in the normal dispersion regime are obtained by means of the Hirota method. Parametric regions for the existence of the dark and antidark soliton solutions are given. Asymptotic analysis of the two-soliton solution shows that collisions between two solitons (two antidark solitons, two dark solitons, and dark and antidark solitons) are elastic. In addition, collision between dark and antidark solitons reveals that dark and antidark solitons can co-exist on the same background in the normal dispersion regime.

Fractional calculus and morphogen gradient formation

NASA Astrophysics Data System (ADS)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

Rotor dynamic simulation and system identification methods for application to vacuum whirl data

NASA Technical Reports Server (NTRS)

Berman, A.; Giansante, N.; Flannelly, W. G.

1980-01-01

Methods of using rotor vacuum whirl data to improve the ability to model helicopter rotors were developed. The work consisted of the formulation of the equations of motion of elastic blades on a hub using a Galerkin method; the development of a general computer program for simulation of these equations; the study and implementation of a procedure for determining physical parameters based on measured data; and the application of a method for computing the normal modes and natural frequencies based on test data.

A finite element solution algorithm for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.

Second- and third-order upwind difference schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Yang, J. Y.

1984-01-01

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

Correlation of embryonic skeletal muscle myotube physical characteristics with contractile force generation on an atomic force microscope-based bio-microelectromechanical systems device

NASA Astrophysics Data System (ADS)

Pirozzi, K. L.; Long, C. J.; McAleer, C. W.; Smith, A. S. T.; Hickman, J. J.

2013-08-01

Rigorous analysis of muscle function in in vitro systems is needed for both acute and chronic biomedical applications. Forces generated by skeletal myotubes on bio-microelectromechanical cantilevers were calculated using a modified version of Stoney's thin-film equation and finite element analysis (FEA), then analyzed for regression to physical parameters. The Stoney's equation results closely matched the more intensive FEA and the force correlated to cross-sectional area (CSA). Normalizing force to measured CSA significantly improved the statistical sensitivity and now allows for close comparison of in vitro data to in vivo measurements for applications in exercise physiology, robotics, and modeling neuromuscular diseases.

Hand-held monitor of sympathetic nervous system using salivary amylase activity and its validation by driver fatigue assessment.

PubMed

Yamaguchi, Masaki; Deguchi, Mitsuo; Wakasugi, Junichi; Ono, Shin; Takai, Noriyasu; Higashi, Tomoyuki; Mizuno, Yasufumi

2006-01-15

In order to realize a hand-held monitor of the sympathetic nervous system, we fabricated a completely automated analytical system for salivary amylase activity using a dry-chemistry system. This was made possible by the fabrication of a disposable test-strip equipped with built-in collecting and reagent papers and an automatic saliva transfer device. In order to cancel out the effects of variations in environmental temperature and pH of saliva, temperature- and pH-adjusted equations were experimentally determined, and each theoretical value was input into the memory of the hand-held monitor. Within a range of salivary amylase activity between 10 and 140 kU/l, the calibration curve for the hand-held monitor showed a coefficient with R(2)=0.97. Accordingly, it was demonstrated that the hand-held monitor enabled a user to automatically measure the salivary amylase activity with high accuracy with only 30 microl sample of saliva within a minute from collection to completion of the measurement. In order to make individual variations of salivary amylase activity negligible during driver fatigue assessment, a normalized equation was proposed. The normalized salivary amylase activity correlated with the mental and physical fatigue states. Thus, this study demonstrated that an excellent hand-held monitor with an algorithm for normalization of individuals' differences in salivary amylase activity, which could be easily and quickly used for evaluating the activity of the sympathetic nervous system at any time. Furthermore, it is suggested that the salivary amylase activity might be used as a better index for psychological research.

Derivation of a generalized Schrödinger equation from the theory of scale relativity

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2017-06-01

Using Nottale's theory of scale relativity relying on a fractal space-time, we derive a generalized Schrödinger equation taking into account the interaction of the system with the external environment. This equation describes the irreversible evolution of the system towards a static quantum state. We first interpret the scale-covariant equation of dynamics stemming from Nottale's theory as a hydrodynamic viscous Burgers equation for a potential flow involving a complex velocity field and an imaginary viscosity. We show that the Schrödinger equation can be directly obtained from this equation by performing a Cole-Hopf transformation equivalent to the WKB transformation. We then introduce a friction force proportional and opposite to the complex velocity in the scale-covariant equation of dynamics in a way that preserves the local conservation of the normalization condition. We find that the resulting generalized Schrödinger equation, or the corresponding fluid equations obtained from the Madelung transformation, involve not only a damping term but also an effective thermal term. The friction coefficient and the temperature are related to the real and imaginary parts of the complex friction coefficient in the scale-covariant equation of dynamics. This may be viewed as a form of fluctuation-dissipation theorem. We show that our generalized Schrödinger equation satisfies an H-theorem for the quantum Boltzmann free energy. As a result, the probability distribution relaxes towards an equilibrium state which can be viewed as a Boltzmann distribution including a quantum potential. We propose to apply this generalized Schrödinger equation to dark matter halos in the Universe, possibly made of self-gravitating Bose-Einstein condensates.

Weighted triangulation adjustment

USGS Publications Warehouse

Anderson, Walter L.

1969-01-01

The variation of coordinates method is employed to perform a weighted least squares adjustment of horizontal survey networks. Geodetic coordinates are required for each fixed and adjustable station. A preliminary inverse geodetic position computation is made for each observed line. Weights associated with each observed equation for direction, azimuth, and distance are applied in the formation of the normal equations in-the least squares adjustment. The number of normal equations that may be solved is twice the number of new stations and less than 150. When the normal equations are solved, shifts are produced at adjustable stations. Previously computed correction factors are applied to the shifts and a most probable geodetic position is found for each adjustable station. Pinal azimuths and distances are computed. These may be written onto magnetic tape for subsequent computation of state plane or grid coordinates. Input consists of punch cards containing project identification, program options, and position and observation information. Results listed include preliminary and final positions, residuals, observation equations, solution of the normal equations showing magnitudes of shifts, and a plot of each adjusted and fixed station. During processing, data sets containing irrecoverable errors are rejected and the type of error is listed. The computer resumes processing of additional data sets.. Other conditions cause warning-errors to be issued, and processing continues with the current data set.

Experimental observation of different soliton types in a net-normal group-dispersion fiber laser.

PubMed

Feng, Zhongyao; Rong, Qiangzhou; Qiao, Xueguang; Shao, Zhihua; Su, Dan

2014-09-20

Different soliton types are observed in a net-normal group-dispersion fiber laser based on nonlinear polarization rotation for passive mode locking. The proposed laser can deliver a dispersion-managed soliton, typical dissipation solitons, and a quasi-harmonic mode-locked pulse, a soliton bundle, and especially a dark pulse by only appropriately adjusting the linear cavity phase delay bias using one polarization controller at the fixed pump power. These nonlinear waves show different features, including the spectral shapes and time traces. The experimental observations show that the five soliton types could exist in the same laser cavity, which implies that integrable systems, dissipative systems, and dark pulse regimes can transfer and be switched in a passively mode-locked laser. Our studies not only verify the numeral simulation of the different soliton-types formation in a net-normal group-dispersion operation but also provide insight into Ginzburg-Landau equation systems.

Projecting diffusion along the normal bundle of a plane curve

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

Valero-Valdés, Carlos; Herrera-Guzmán, Rafael

2014-05-15

The purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized Fick-Jacob's equation obtained by projecting the two-dimensional diffusion equation along the normal directions of an arbitrary curve on the plane.

Wind velocity-change (gust rise) criteria for wind turbine design

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

Cliff, W.C.; Fichtl, G.H.

1978-07-01

A closed-form equation is derived for root mean square (rms) value of velocity change (gust rise) that occurs over the swept area of wind turbine rotor systems and an equation for rms value of velocity change that occurs at a single point in space. These formulas confirm the intuitive assumption that a large system will encounter a less severe environment than a small system when both are placed at the same location. Assuming a normal probability density function for the velocity differences, an equation is given for calculating the expected number of velocity differences that will occur in 1 hrmore » and will be larger than an arbitrary value. A formula is presented that gives the expected number of velocity differences larger than an arbitrary value that will be encountered during the design life of a wind turbine. In addition, a method for calculating the largest velocity difference expected during the life of a turbine and a formula for estimating the risk of exceeding a given velocity difference during the life of the structure are given. The equations presented are based upon general atmospheric boundary-layer conditions and do not include information regarding events such as tornados, hurricanes, etc.« less

Cross-Validation of a Recently Published Equation Predicting Energy Expenditure to Run or Walk a Mile in Normal-Weight and Overweight Adults

ERIC Educational Resources Information Center

Morris, Cody E.; Owens, Scott G.; Waddell, Dwight E.; Bass, Martha A.; Bentley, John P.; Loftin, Mark

2014-01-01

An equation published by Loftin, Waddell, Robinson, and Owens (2010) was cross-validated using ten normal-weight walkers, ten overweight walkers, and ten distance runners. Energy expenditure was measured at preferred walking (normal-weight walker and overweight walkers) or running pace (distance runners) for 5 min and corrected to a mile. Energy…

Relating constrained motion to force through Newton's second law

NASA Astrophysics Data System (ADS)

Roithmayr, Carlos M.

When a mechanical system is subject to constraints its motion is in some way restricted. In accordance with Newton's second law, motion is a direct result of forces acting on a system; hence, constraint is inextricably linked to force. The presence of a constraint implies the application of particular forces needed to compel motion in accordance with the constraint; absence of a constraint implies the absence of such forces. The objective of this thesis is to formulate a comprehensive, consistent, and concise method for identifying a set of forces needed to constrain the behavior of a mechanical system modeled as a set of particles and rigid bodies. The goal is accomplished in large part by expressing constraint equations in vector form rather than entirely in terms of scalars. The method developed here can be applied whenever constraints can be described at the acceleration level by a set of independent equations that are linear in acceleration. Hence, the range of applicability extends to servo-constraints or program constraints described at the velocity level with relationships that are nonlinear in velocity. All configuration constraints, and an important class of classical motion constraints, can be expressed at the velocity level by using equations that are linear in velocity; therefore, the associated constraint equations are linear in acceleration when written at the acceleration level. Two new approaches are presented for deriving equations governing motion of a system subject to constraints expressed at the velocity level with equations that are nonlinear in velocity. By using partial accelerations instead of the partial velocities normally employed with Kane's method, it is possible to form dynamical equations that either do or do not contain evidence of the constraint forces, depending on the analyst's interests.

Determination of Earth rotation by the combination of data from different space geodetic systems

NASA Technical Reports Server (NTRS)

Archinal, Brent Allen

1987-01-01

Formerly, Earth Rotation Parameters (ERP), i.e., polar motion and UTI-UTC values, have been determined using data from only one observational system at a time, or by the combination of parameters previously obtained in such determinations. The question arises as to whether a simultaneous solution using data from several sources would provide an improved determination of such parameters. To pursue this reasoning, fifteen days of observations have been simulated using realistic networks of Lunar Laser Ranging (LLR), Satellite Laser Ranging (SLR) to Lageos, and Very Long Baseline Interferometry (VLBI) stations. A comparison has been done of the accuracy and precision of the ERP obtained from: (1) the individual system solutions, (2) the weighted means of those values, (3) all of the data by means of the combination of the normal equations obtained in 1, and (4) a grand solution with all the data. These simulations show that solutions done by the normal equation combination and grand solution methods provide the best or nearly the best ERP for all the periods considered, but that weighted mean solutions provide nearly the same accuracy and precision. VLBI solutions also provide similar accuracies.

An analytical study of the dual mass mechanical system stability

NASA Astrophysics Data System (ADS)

Nikolov, Svetoslav; Sinapov, Petko; Kralov, Ivan; Ignatov, Ignat

2011-12-01

In this paper an autonomous, nonlinear model of five ordinary differential equations modeling the motion of a dual mass mechanical system with universal joint is studied. The model is investigated qualitatively. On the base of the stability analysis performed, we obtain that the system is: i) in an equilibrium state, or ii) in a structurally unstable behavior when equilibrium states disappear. In case (i) the system is in a normal technical condition and in case (ii) hard break-downs take place.

Normal evaporation of binary alloys

NASA Technical Reports Server (NTRS)

Li, C. H.

1972-01-01

In the study of normal evaporation, it is assumed that the evaporating alloy is homogeneous, that the vapor is instantly removed, and that the alloy follows Raoult's law. The differential equation of normal evaporation relating the evaporating time to the final solute concentration is given and solved for several important special cases. Uses of the derived equations are exemplified with a Ni-Al alloy and some binary iron alloys. The accuracy of the predicted results are checked by analyses of actual experimental data on Fe-Ni and Ni-Cr alloys evaporated at 1600 C, and also on the vacuum purification of beryllium. These analyses suggest that the normal evaporation equations presented here give satisfactory results that are accurate to within an order of magnitude of the correct values, even for some highly concentrated solutions. Limited diffusion and the resultant surface solute depletion or enrichment appear important in the extension of this normal evaporation approach.

Requirements for CEC POP Machine Protection System

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

Pinayev, I.

2015-02-18

The requirements of CEC POP machine protection system are meant to prevent damage to a vacuum chamber by a missteered electron beam. In this example, beam energy = 22 MeV, Maximal bunch charge = 5 nC, Maximal repetition rate = 78 kHz, Normalized emittance = 5 mm mrad, Minimal β-function = 1 m. From this information the requirements of the protection system can be calculated by factoring the information into equations to find beam densities and temperature excursions.

Relation of Different Type Love-Shida Numbers Determined with the Use of Time-Varying Incremental Gravitational Potential

NASA Astrophysics Data System (ADS)

Varga, Peter; Grafarend, Erik; Engels, Johannes

2017-03-01

There are different equations to describe relations between different classes of Love-Shida numbers. In this study with the use of the time-varying gravitational potential an integral relation was obtained which connects tidal Love-Shida numbers (h, l, k), load numbers (h', l', k'), potential free Love-Shida numbers generated by normal (h″, l″, k″) and horizontal (h‴, l‴, k‴) stresses. The equations obtained in frame of present study is the only one which - holds for every type of Love-Shida numbers, - describes a relationship not between different, but the same type of Love-Shida numbers, - does not follow from the sixth-order differential equation system of motion usually applied to calculate the Love-Shida numbers.

Analysis of a diffuse interface model of multispecies tumor growth

NASA Astrophysics Data System (ADS)

Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E.

2017-04-01

We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity \\mathbf{u} satisfies \\mathbf{u}\\centerdot ν >0 , where ν is the outer normal to the boundary of the domain.

Extraction of skin-friction fields from surface flow visualizations as an inverse problem

NASA Astrophysics Data System (ADS)

Liu, Tianshu

2013-12-01

Extraction of high-resolution skin-friction fields from surface flow visualization images as an inverse problem is discussed from a unified perspective. The surface flow visualizations used in this study are luminescent oil-film visualization and heat-transfer and mass-transfer visualizations with temperature- and pressure-sensitive paints (TSPs and PSPs). The theoretical foundations of these global methods are the thin-oil-film equation and the limiting forms of the energy- and mass-transport equations at a wall, which are projected onto the image plane to provide the relationships between a skin-friction field and the relevant quantities measured by using an imaging system. Since these equations can be re-cast in the same mathematical form as the optical flow equation, they can be solved by using the variational method in the image plane to extract relative or normalized skin-friction fields from images. Furthermore, in terms of instrumentation, essentially the same imaging system for measurements of luminescence can be used in these surface flow visualizations. Examples are given to demonstrate the applications of these methods in global skin-friction diagnostics of complex flows.

An Experimental and Computational Study on Soot Formation in a Coflow Jet Flame Under Microgravity and Normal Gravity

NASA Technical Reports Server (NTRS)

Ma, Bin; Cao, Su; Giassi, Davide; Stocker, Dennis P.; Takahashi, Fumiaki; Bennett, Beth Anne V.; Smooke, Mitchell D.; Long, Marshall B.

2014-01-01

Upon the completion of the Structure and Liftoff in Combustion Experiment (SLICE) in March 2012, a comprehensive and unique set of microgravity coflow diffusion flame data was obtained. This data covers a range of conditions from weak flames near extinction to strong, highly sooting flames, and enabled the study of gravitational effects on phenomena such as liftoff, blowout and soot formation. The microgravity experiment was carried out in the Microgravity Science Glovebox (MSG) on board the International Space Station (ISS), while the normal gravity experiment was performed at Yale utilizing a copy of the flight hardware. Computational simulations of microgravity and normal gravity flames were also carried out to facilitate understanding of the experimental observations. This paper focuses on the different sooting behaviors of CH4 coflow jet flames in microgravity and normal gravity. The unique set of data serves as an excellent test case for developing more accurate computational models.Experimentally, the flame shape and size, lift-off height, and soot temperature were determined from line-of-sight flame emission images taken with a color digital camera. Soot volume fraction was determined by performing an absolute light calibration using the incandescence from a flame-heated thermocouple. Computationally, the MC-Smooth vorticity-velocity formulation was employed to describe the chemically reacting flow, and the soot evolution was modeled by the sectional aerosol equations. The governing equations and boundary conditions were discretized on an axisymmetric computational domain by finite differences, and the resulting system of fully coupled, highly nonlinear equations was solved by a damped, modified Newtons method. The microgravity sooting flames were found to have lower soot temperatures and higher volume fraction than their normal gravity counterparts. The soot distribution tends to shift from the centerline of the flame to the wings from normal gravity to microgravity.

Angular motion equations for a satellite with hinged flexible solar panel

NASA Astrophysics Data System (ADS)

Ovchinnikov, M. Yu.; Tkachev, S. S.; Roldugin, D. S.; Nuralieva, A. B.; Mashtakov, Y. V.

2016-11-01

Non-linear mathematical model for the satellite with hinged flexible solar panel is presented. Normal modes of flexible elements are used for motion description. Motion equations are derived using virtual work principle. A comparison of normal modes calculation between finite element method and developed model is presented.

Stability of the accelerated expansion in nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Sharif, M.; Mumtaz, Saadia

2017-02-01

This paper is devoted to the phase space analysis of an isotropic and homogeneous model of the universe by taking a noninteracting mixture of the electromagnetic and viscous radiating fluids whose viscous pressure satisfies a nonlinear version of the Israel-Stewart transport equation. We establish an autonomous system of equations by introducing normalized dimensionless variables. In order to analyze the stability of the system, we find corresponding critical points for different values of the parameters. We also evaluate the power-law scale factor whose behavior indicates different phases of the universe in this model. It is concluded that the bulk viscosity as well as electromagnetic field enhances the stability of the accelerated expansion of the isotropic and homogeneous model of the universe.

Progressive wave expansions and open boundary problems

NASA Technical Reports Server (NTRS)

Hagstrom, T.; Hariharan, S. I.

1995-01-01

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

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

Online gaming for learning optimal team strategies in real time

NASA Astrophysics Data System (ADS)

Hudas, Gregory; Lewis, F. L.; Vamvoudakis, K. G.

2010-04-01

This paper first presents an overall view for dynamical decision-making in teams, both cooperative and competitive. Strategies for team decision problems, including optimal control, zero-sum 2-player games (H-infinity control) and so on are normally solved for off-line by solving associated matrix equations such as the Riccati equation. However, using that approach, players cannot change their objectives online in real time without calling for a completely new off-line solution for the new strategies. Therefore, in this paper we give a method for learning optimal team strategies online in real time as team dynamical play unfolds. In the linear quadratic regulator case, for instance, the method learns the Riccati equation solution online without ever solving the Riccati equation. This allows for truly dynamical team decisions where objective functions can change in real time and the system dynamics can be time-varying.

KAM Tori for 1D Nonlinear Wave Equationswith Periodic Boundary Conditions

NASA Astrophysics Data System (ADS)

Chierchia, Luigi; You, Jiangong

In this paper, one-dimensional (1D) nonlinear wave equations with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function vanishing together with its derivative at u≡0. It is proved that for ``most'' potentials V(x), the above equation admits small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theorem which allows for multiple normal frequencies.

Effect of electron beam on the properties of electron-acoustic rogue waves

NASA Astrophysics Data System (ADS)

El-Shewy, E. K.; Elwakil, S. A.; El-Hanbaly, A. M.; Kassem, A. I.

2015-04-01

The properties of nonlinear electron-acoustic rogue waves have been investigated in an unmagnetized collisionless four-component plasma system consisting of a cold electron fluid, Maxwellian hot electrons, an electron beam and stationary ions. It is found that the basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of rogue wave profiles and the associated electric field on the carrier wave number, normalized density of hot electron and electron beam, relative cold electron temperature and relative beam temperature are discussed. The results of the present investigation may be applicable in auroral zone plasma.

The Pauli Objection

NASA Astrophysics Data System (ADS)

Leon, Juan; Maccone, Lorenzo

2017-12-01

Schrödinger's equation says that the Hamiltonian is the generator of time translations. This seems to imply that any reasonable definition of time operator must be conjugate to the Hamiltonian. Then both time and energy must have the same spectrum since conjugate operators are unitarily equivalent. Clearly this is not always true: normal Hamiltonians have lower bounded spectrum and often only have discrete eigenvalues, whereas we typically desire that time can take any real value. Pauli concluded that constructing a general a time operator is impossible (although clearly it can be done in specific cases). Here we show how the Pauli argument fails when one uses an external system (a "clock") to track time, so that time arises as correlations between the system and the clock (conditional probability amplitudes framework). In this case, the time operator is conjugate to the clock Hamiltonian and not to the system Hamiltonian, but its eigenvalues still satisfy the Schrödinger equation for arbitrary system Hamiltonians.

The use of normal forms for analysing nonlinear mechanical vibrations

PubMed Central

Neild, Simon A.; Champneys, Alan R.; Wagg, David J.; Hill, Thomas L.; Cammarano, Andrea

2015-01-01

A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations. PMID:26303917

The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1984-01-01

The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner.

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

NASA Technical Reports Server (NTRS)

Friedrich, R.; Drewelow, W.

1978-01-01

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

Solving nonlinear equilibrium equations of deformable systems by method of embedded polygons

NASA Astrophysics Data System (ADS)

Razdolsky, A. G.

2017-09-01

Solving of nonlinear algebraic equations is an obligatory stage of studying the equilibrium paths of nonlinear deformable systems. The iterative method for solving a system of nonlinear algebraic equations stated in an explicit or implicit form is developed in the present work. The method consists of constructing a sequence of polygons in Euclidean space that converge into a single point that displays the solution of the system. Polygon vertices are determined on the assumption that individual equations of the system are independent from each other and each of them is a function of only one variable. Initial positions of vertices for each subsequent polygon are specified at the midpoints of certain straight segments determined at the previous iteration. The present algorithm is applied for analytical investigation of the behavior of biaxially compressed nonlinear-elastic beam-column with an open thin-walled cross-section. Numerical examples are made for the I-beam-column on the assumption that its material follows a bilinear stress-strain diagram. A computer program based on the shooting method is developed for solving the problem. The method is reduced to numerical integration of a system of differential equations and to the solution of a system of nonlinear algebraic equations between the boundary values of displacements at the ends of the beam-column. A stress distribution at the beam-column cross-sections is determined by subdividing the cross-section area into many small cells. The equilibrium path for the twisting angle and the lateral displacements tend to the stationary point when the load is increased. Configuration of the path curves reveals that the ultimate load is reached shortly once the maximal normal stresses at the beam-column fall outside the limit of the elastic region. The beam-column has a unique equilibrium state for each value of the load, that is, there are no equilibrium states once the maximum load is reached.

Thermodynamics of an Attractive 2D Fermi Gas

NASA Astrophysics Data System (ADS)

Fenech, K.; Dyke, P.; Peppler, T.; Lingham, M. G.; Hoinka, S.; Hu, H.; Vale, C. J.

2016-01-01

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density, and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behavior.

APL-UW Deep Water Propagation 2015-2017: Philippine Sea Data Analysis

DTIC Science & Technology

independent Monte Carlo parabolic equation simulations . The autospectrum of normalized intensity had an excellent match to that of a time-dependent Monte...ambient noise; systems along the Aleutian chain have either no significant trendor a slight increasing trend; systems in the central Pacific Ocean...At the end of the grant, it was determined that the Kauai cable had suffered a break in the shallow near-shore region. Additional contractual

Comparison of anthropometric-based equations for estimation of body fat percentage in a normal-weight and overweight female cohort: validation via air-displacement plethysmography.

PubMed

Temple, Derry; Denis, Romain; Walsh, Marianne C; Dicker, Patrick; Byrne, Annette T

2015-02-01

To evaluate the accuracy of the most commonly used anthropometric-based equations in the estimation of percentage body fat (%BF) in both normal-weight and overweight women using air-displacement plethysmography (ADP) as the criterion measure. A comparative study in which the equations of Durnin and Womersley (1974; DW) and Jackson, Pollock and Ward (1980) at three, four and seven sites (JPW₃, JPW₄ and JPW₇) were validated against ADP in three groups. Group 1 included all participants, group 2 included participants with a BMI <25·0 kg/m² and group 3 included participants with a BMI ≥25·0 kg/m². Human Performance Laboratory, Institute for Sport and Health, University College Dublin, Republic of Ireland. Forty-three female participants aged between 18 and 55 years. In all three groups, the %BF values estimated from the DW equation were closer to the criterion measure (i.e. ADP) than those estimated from the other equations. Of the three JPW equations, JPW₃ provided the most accurate estimation of %BF when compared with ADP in all three groups. In comparison to ADP, these findings suggest that the DW equation is the most accurate anthropometric method for the estimation of %BF in both normal-weight and overweight females.

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

NASA Technical Reports Server (NTRS)

Mintz, Y.; Walker, G. K.

1993-01-01

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

Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood versus Robust Methods

ERIC Educational Resources Information Center

Zhong, Xiaoling; Yuan, Ke-Hai

2011-01-01

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

Reconstruction of normal forms by learning informed observation geometries from data.

PubMed

Yair, Or; Talmon, Ronen; Coifman, Ronald R; Kevrekidis, Ioannis G

2017-09-19

The discovery of physical laws consistent with empirical observations is at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters; dynamical systems theory provides, through the appropriate normal forms, an "intrinsic" prototypical characterization of the types of dynamical regimes accessible to a given model. Using an implementation of data-informed geometry learning, we directly reconstruct the relevant "normal forms": a quantitative mapping from empirical observations to prototypical realizations of the underlying dynamics. Interestingly, the state variables and the parameters of these realizations are inferred from the empirical observations; without prior knowledge or understanding, they parametrize the dynamics intrinsically without explicit reference to fundamental physical quantities.

A quantitative description of normal AV nodal conduction curve in man.

PubMed

Teague, S; Collins, S; Wu, D; Denes, P; Rosen, K; Arzbaecher, R

1976-01-01

The AV nodal conduction curve generated by the atrial extrastimulus technique has been described only qualitatively in man, making clinical comparison of known normal curves with those of suspected AV nodal dysfunction difficult. Also, the effects of physiological and pharmacological interventions have not been quantifiable. In 50 patients with normal AV conduction as defined by normal AH (less than 130 ms), normal AV nodal effective and functional refractory periods (less than 380 and less than 500 ms), and absence of demonstrable dual AV nodal pathways, we found that conduction curves (at sinus rhythm or longest paced cycle length) can be described by an exponential equation of the form delta = Ae-Bx. In this equation, delta is the increase in AV nodal conduction time of an extrastimulus compared to that of a regular beat and x is extrastimulus interval. The natural logarithm of this equation is linear in the semilogarithmic plane, thus permitting the constants A and B to be easily determined by a least-squares regression analysis with a hand calculator.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Greengard, Leslie F; Waag, Robert C

2010-02-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators

PubMed Central

Hesford, Andrew J.; Astheimer, Jeffrey P.; Greengard, Leslie F.; Waag, Robert C.

2010-01-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method. PMID:20136208

A normalized plot as a novel and time-saving tool in complex enzyme kinetic analysis.

PubMed

Bravo, I G; Busto, F; De Arriaga, D; Ferrero, M A; Rodríguez-Aparicio, L B; Martínez-Blanco, H; Reglero, A

2001-09-15

A new data treatment is described for designing kinetic experiments and analysing kinetic results for multi-substrate enzymes. Normalized velocities are plotted against normalized substrate concentrations. Data are grouped into n + 1 families across the range of substrate or product tested, n being the number of substrates plus products assayed. It has the following advantages over traditional methods: (1) it reduces to less than a half the amount of data necessary for a proper description of the system; (2) it introduces a self-consistency checking parameter that ensures the 'scientific reliability' of the mathematical output; (3) it eliminates the need for a prior knowledge of Vmax; (4) the normalization of data allows the use of robust and fuzzy methods suitable for managing really 'noisy' data; (5) it is appropriate for analysing complex systems, as the complete general equation is used, and the actual influence of effectors can be typified; (6) it is amenable to being implemented as a software that incorporates testing and electing among rival kinetic models.

Applicability of the Old European Respiratory Society/European Community for Steel and Coal reference equations for spirometry interpretation in Tunisian adult population.

PubMed

El Attar, Mohamed Nour; Hadj Mabrouk, Khaoula; Ben Abdelaziz, Ahmed; Abdelghani, Ahmed; Bousarssar, Mohamed; Limam, Khélifa; Maatoug, Chiraz; Bouslah, Hmida; Charrada, Ameur; Rouatbi, Sonia; Ben Saad, Helmi

2014-01-01

Tunisian pulmonary functional laboratories accept the default settings for reference equations (European Respiratory Society/European Community for Steel and Coal (ERS/ECSC1983) offered by the manufacturer even though adult Tunisian reference equations (Tunisian1995) are available. To compare the spirometric profile of Tunisian subjects, according to the two reference equations. Spirometric data were recorded from 1192 consecutive spirometry procedures in adults aged 18-60 years. Reference values and lower limits of normality (LLN) were calculated using the two reference equations. Applied definitions: large airway obstructive ventilatory defect (LAOVD): ratio between the 1st second expiratory volume and forced vital capacity (FEV1/FVC) < LLN. Small AOVD (SAOVD): FEV1/FVC > LLN and FVC > LLN and maximal midexpiratory flow < LLN. Tendency through a restrictive ventilatory defect (TRVD): FEV1 and FVC < LLN. The spirometric profile, according the two reference equations, was determined. Using Tunisian1995 reference equations, 34%, 7%, 37% and 19% of spirometry records were interpreted as normal, and as having, LAOVD, SAOVD and TRVD, respectively. Using ERS/ECSC1983 reference equations, 85%, 3%, 9% and 2% of spirometry records were interpreted as normal, and as having, LAOVD, SAOVD and TRVD, respectively. Using the ERS/ECSC1983 reference equations, misclassification was worse for LAOVD, for SAOVD and for TRVD, respectively, 68%, 94% and 89%. Our results showed that the use of the old Caucasian reference equations resulted in misinterpretation of spirometry data in a significant proportion of subjects. This could result in inappropriate diagnosis and/or management.

System diagnostics using qualitative analysis and component functional classification

DOEpatents

Reifman, J.; Wei, T.Y.C.

1993-11-23

A method for detecting and identifying faulty component candidates during off-normal operations of nuclear power plants involves the qualitative analysis of macroscopic imbalances in the conservation equations of mass, energy and momentum in thermal-hydraulic control volumes associated with one or more plant components and the functional classification of components. The qualitative analysis of mass and energy is performed through the associated equations of state, while imbalances in momentum are obtained by tracking mass flow rates which are incorporated into a first knowledge base. The plant components are functionally classified, according to their type, as sources or sinks of mass, energy and momentum, depending upon which of the three balance equations is most strongly affected by a faulty component which is incorporated into a second knowledge base. Information describing the connections among the components of the system forms a third knowledge base. The method is particularly adapted for use in a diagnostic expert system to detect and identify faulty component candidates in the presence of component failures and is not limited to use in a nuclear power plant, but may be used with virtually any type of thermal-hydraulic operating system. 5 figures.

System diagnostics using qualitative analysis and component functional classification

DOEpatents

Reifman, Jaques; Wei, Thomas Y. C.

1993-01-01

A method for detecting and identifying faulty component candidates during off-normal operations of nuclear power plants involves the qualitative analysis of macroscopic imbalances in the conservation equations of mass, energy and momentum in thermal-hydraulic control volumes associated with one or more plant components and the functional classification of components. The qualitative analysis of mass and energy is performed through the associated equations of state, while imbalances in momentum are obtained by tracking mass flow rates which are incorporated into a first knowledge base. The plant components are functionally classified, according to their type, as sources or sinks of mass, energy and momentum, depending upon which of the three balance equations is most strongly affected by a faulty component which is incorporated into a second knowledge base. Information describing the connections among the components of the system forms a third knowledge base. The method is particularly adapted for use in a diagnostic expert system to detect and identify faulty component candidates in the presence of component failures and is not limited to use in a nuclear power plant, but may be used with virtually any type of thermal-hydraulic operating system.

Volume-preserving normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2013-10-01

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Free geometric adjustment of the SECOR Equatorial Network (Solution SECOR-27)

NASA Technical Reports Server (NTRS)

Mueller, I. I.; Kumar, M.; Soler, T.

1973-01-01

The basic purpose of this experiment is to compute reduced normal equations from the observational data of the SECOR Equatorial Network obtained from DMA/Topographic Center, D/Geodesy, Geosciences Div. Washington, D.C. These reduced normal equations are to be combined with reduced normal equations of other satellite networks of the National Geodetic Satellite Program to provide station coordinates from a single least square adjustment. An individual SECOR solution was also obtained and is presented in this report, using direction constraints computed from BC-4 optical data from stations collocated with SECOR stations. Due to the critical configuration present in the range observations, weighted height constraints were also applied in order to break the near coplanarity of the observing stations.

Exponential model normalization for electrical capacitance tomography with external electrodes under gap permittivity conditions

NASA Astrophysics Data System (ADS)

Baidillah, Marlin R.; Takei, Masahiro

2017-06-01

A nonlinear normalization model which is called exponential model for electrical capacitance tomography (ECT) with external electrodes under gap permittivity conditions has been developed. The exponential model normalization is proposed based on the inherently nonlinear relationship characteristic between the mixture permittivity and the measured capacitance due to the gap permittivity of inner wall. The parameters of exponential equation are derived by using an exponential fitting curve based on the simulation and a scaling function is added to adjust the experiment system condition. The exponential model normalization was applied to two dimensional low and high contrast dielectric distribution phantoms by using simulation and experimental studies. The proposed normalization model has been compared with other normalization models i.e. Parallel, Series, Maxwell and Böttcher models. Based on the comparison of image reconstruction results, the exponential model is reliable to predict the nonlinear normalization of measured capacitance in term of low and high contrast dielectric distribution.

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

NASA Astrophysics Data System (ADS)

Karpathopoulos, L.; Basilakos, S.; Leon, G.; Paliathanasis, A.; Tsamparlis, M.

2018-07-01

In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization.

Analytic integrable systems: Analytic normalization and embedding flows

NASA Astrophysics Data System (ADS)

Zhang, Xiang

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

Normal mode study of the earth's rigid body motions

NASA Technical Reports Server (NTRS)

Chao, B. F.

1983-01-01

In this paper it is shown that the earth's rigid body (rb) motions can be represented by an analytical set of eigensolutions to the equation of motion for elastic-gravitational free oscillations. Thus each degree of freedom in the rb motion is associated with a rb normal mode. Cases of both nonrotating and rotating earth models are studied, and it is shown that the rb modes do incorporate neatly into the earth's system of normal modes of free oscillation. The excitation formula for the rb modes are also obtained, based on normal mode theory. Physical implications of the results are summarized and the fundamental differences between rb modes and seismic modes are emphasized. In particular, it is ascertained that the Chandler wobble, being one of the rb modes belonging to the rotating earth, can be studied using the established theory of normal modes.

Normalization in Lie algebras via mould calculus and applications

NASA Astrophysics Data System (ADS)

Paul, Thierry; Sauzin, David

2017-11-01

We establish Écalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincaré-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging procedure for vector fields with fast angular variables (Hamiltonian or not), or the construction of Birkhoff normal forms both in classical and quantum situations. As a by-product we obtain, in the case of harmonic oscillators, the convergence of the quantum Birkhoff form to the classical one, without any Diophantine hypothesis on the frequencies of the unperturbed Hamiltonians.

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.

Helical localized wave solutions of the scalar wave equation.

PubMed

Overfelt, P L

2001-08-01

A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch.

Dynamo Effects in Magnetized Ideal Plasma Cosmologies

NASA Astrophysics Data System (ADS)

Kleidis, Kostas; Kuiroukidis, Apostolos; Papadopoulos, Demetrios; Vlahos, Loukas

The excitation of cosmological perturbations in an anisotropic cosmological model and in the presence of a homogeneous magnetic field has been studied, using the ideal magnetohydrodynamic (MHD) equations. In this case, the system of partial differential equations which governs the evolution of the magnetized cosmological perturbations can be solved analytically. Our results verify that fast-magnetosonic modes propagating normal to the magnetic field, are excited. But, what is most important, is that, at late times, the magnetic-induction contrast (δB/B) grows, resulting in the enhancement of the ambient magnetic field. This process can be particularly favored by condensations, formed within the plasma fluid due to gravitational instabilities.

Strongly coupled stress waves in heterogeneous plates.

NASA Technical Reports Server (NTRS)

Wang, A. S. D.; Chou, P. C.; Rose, J. L.

1972-01-01

Consideration of coupled stress waves generated by an impulsive load applied at one end of a semiinfinite plate. For the field equations governing the one-dimensional coupled waves a hyperbolic system of equations is obtained in which a strong coupling in the second derivatives exists. The method of characteristics described by Chou and Mortimer (1967) is extended to cover the case of strong coupling, and a study is made of the transient stress waves in a semiinfinite plate subjected to an initial step input. Coupled discontinuity fronts are found to propagate at different velocities. The normal plate stress and the bending moment at different time regimes are illustrated by graphs.

Estimating varying coefficients for partial differential equation models.

PubMed

Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J

2017-09-01

Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.

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.

Reconstructing the vibro-acoustic quantities on a highly non-spherical surface using the Helmholtz equation least squares method.

PubMed

Natarajan, Logesh Kumar; Wu, Sean F

2012-06-01

This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.

The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells.

PubMed

Levine, M W

1991-01-01

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity.(ABSTRACT TRUNCATED AT 250 WORDS)

Conic Sections and the Discovery of a Novel Curve Using Differential Equations

ERIC Educational Resources Information Center

de Alwis, Amal

2013-01-01

We began by observing a variety of properties related to the tangent and normal lines of three conic sections: a parabola, an ellipse, and a hyperbola. Some of these properties include specific relationships between the x- and y-intercepts of the tangent and normal lines. Using these properties, we were able to form several differential equations.…

From shunting inhibition to dynamic normalization: Attentional selection and decision-making in brief visual displays.

PubMed

Smith, Philip L; Sewell, David K; Lilburn, Simon D

2015-11-01

Normalization models of visual sensitivity assume that the response of a visual mechanism is scaled divisively by the sum of the activity in the excitatory and inhibitory mechanisms in its neighborhood. Normalization models of attention assume that the weighting of excitatory and inhibitory mechanisms is modulated by attention. Such models have provided explanations of the effects of attention in both behavioral and single-cell recording studies. We show how normalization models can be obtained as the asymptotic solutions of shunting differential equations, in which stimulus inputs and the activity in the mechanism control growth rates multiplicatively rather than additively. The value of the shunting equation approach is that it characterizes the entire time course of the response, not just its asymptotic strength. We describe two models of attention based on shunting dynamics, the integrated system model of Smith and Ratcliff (2009) and the competitive interaction theory of Smith and Sewell (2013). These models assume that attention, stimulus salience, and the observer's strategy for the task jointly determine the selection of stimuli into visual short-term memory (VSTM) and the way in which stimulus representations are weighted. The quality of the VSTM representation determines the speed and accuracy of the decision. The models provide a unified account of a variety of attentional phenomena found in psychophysical tasks using single-element and multi-element displays. Our results show the generality and utility of the normalization approach to modeling attention. Copyright © 2014 Elsevier B.V. All rights reserved.

Calculation of Thermally-Induced Displacements in Spherically Domed Ion Engine Grids

NASA Technical Reports Server (NTRS)

Soulas, George C.

2006-01-01

An analytical method for predicting the thermally-induced normal and tangential displacements of spherically domed ion optics grids under an axisymmetric thermal loading is presented. A fixed edge support that could be thermally expanded is used for this analysis. Equations for the displacements both normal and tangential to the surface of the spherical shell are derived. A simplified equation for the displacement at the center of the spherical dome is also derived. The effects of plate perforation on displacements and stresses are determined by modeling the perforated plate as an equivalent solid plate with modified, or effective, material properties. Analytical model results are compared to the results from a finite element model. For the solid shell, comparisons showed that the analytical model produces results that closely match the finite element model results. The simplified equation for the normal displacement of the spherical dome center is also found to accurately predict this displacement. For the perforated shells, the analytical solution and simplified equation produce accurate results for materials with low thermal expansion coefficients.

Metastable states and energy flow pathway in square graphene resonators

NASA Astrophysics Data System (ADS)

Wang, Yisen; Zhu, Zhigang; Zhang, Yong; Huang, Liang

2018-01-01

Nonlinear interaction between flexural modes is critical to heat conductivity and mechanical vibration of two-dimensional materials such as graphene. Much effort has been devoted to understand the underlying mechanism. In this paper, we examine solely the out-of-plane flexural modes and identify their energy flow pathway during thermalization process. The key is the development of a universal scheme that numerically characterizes the strength of nonlinear interactions between normal modes. In particular, for our square graphene system, the modes are grouped into four classes by their distinct symmetries. The couplings are significantly larger within a class than between classes. As a result, the equations for the normal modes in the same class as the initially excited one can be approximated by driven harmonic oscillators, therefore, they get energy almost instantaneously. Because of the hierarchical organization of the mode coupling, the energy distribution among the modes will arrive at a stable profile, where most of the energy is localized on a few modes, leading to the formation of "natural package" and metastable states. The dynamics for modes in other symmetry classes follows a Mathieu type of equation, thus, interclass energy flow, when the initial excitation energy is small, starts typically when there is a mode that lies in the unstable region in the parameter space of Mathieu equation. Due to strong coupling of the modes inside the class, the whole class will get energy and be lifted up by the unstable mode. This characterizes the energy flow pathway of the system. These results bring fundamental understandings to the Fermi-Pasta-Ulam problem in two-dimensional systems with complex potentials, and reveal clearly the physical picture of dynamical interactions between the flexural modes, which will be crucial to the understanding of their abnormal contribution to heat conduction and nonlinear mechanical vibrations.

Resonant-state expansion for open optical systems: generalization to magnetic, chiral, and bi-anisotropic materials

NASA Astrophysics Data System (ADS)

Muljarov, E. A.; Weiss, T.

2018-05-01

The resonant-state expansion, a recently developed powerful method in electrodynamics, is generalized here for open optical systems containing magnetic, chiral, or bi-anisotropic materials. It is shown that the key matrix eigenvalue equation of the method remains the same, but the matrix elements of the perturbation now contain variations of the permittivity, permeability, and bi-anisotropy tensors. A general normalization of resonant states in terms of the electric and magnetic fields is presented.

Hopf-Pitchfork Bifurcation in a Symmetrically Conservative Two-Mass System with Delay

NASA Astrophysics Data System (ADS)

Sun, Ye; Zhang, Chunrui; Cai, Yuting

2018-06-01

A symmetrically conservative two-mass system with time delay is considered here. We analyse the influence of interaction coefficient and time delay on the Hopf-pitchfork bifurcation. The bifurcation diagrams and phase portraits are then obtained by computing the normal forms for the system in which, particularly, the unfolding form for case III is seldom given in delayed differential equations. Furthermore, we also find some interesting dynamical behaviours of the original system, such as the coexistence of two stable non-trivial equilibria and a pair of stable periodic orbits, which are verified both theoretically and numerically.

GPU computing with Kaczmarz’s and other iterative algorithms for linear systems

PubMed Central

Elble, Joseph M.; Sahinidis, Nikolaos V.; Vouzis, Panagiotis

2009-01-01

The graphics processing unit (GPU) is used to solve large linear systems derived from partial differential equations. The differential equations studied are strongly convection-dominated, of various sizes, and common to many fields, including computational fluid dynamics, heat transfer, and structural mechanics. The paper presents comparisons between GPU and CPU implementations of several well-known iterative methods, including Kaczmarz’s, Cimmino’s, component averaging, conjugate gradient normal residual (CGNR), symmetric successive overrelaxation-preconditioned conjugate gradient, and conjugate-gradient-accelerated component-averaged row projections (CARP-CG). Computations are preformed with dense as well as general banded systems. The results demonstrate that our GPU implementation outperforms CPU implementations of these algorithms, as well as previously studied parallel implementations on Linux clusters and shared memory systems. While the CGNR method had begun to fall out of favor for solving such problems, for the problems studied in this paper, the CGNR method implemented on the GPU performed better than the other methods, including a cluster implementation of the CARP-CG method. PMID:20526446

Discrete dynamical system modelling for gene regulatory networks of 5-hydroxymethylfurfural tolerance for ethanologenic yeast.

PubMed

Song, M; Ouyang, Z; Liu, Z L

2009-05-01

Composed of linear difference equations, a discrete dynamical system (DDS) model was designed to reconstruct transcriptional regulations in gene regulatory networks (GRNs) for ethanologenic yeast Saccharomyces cerevisiae in response to 5-hydroxymethylfurfural (HMF), a bioethanol conversion inhibitor. The modelling aims at identification of a system of linear difference equations to represent temporal interactions among significantly expressed genes. Power stability is imposed on a system model under the normal condition in the absence of the inhibitor. Non-uniform sampling, typical in a time-course experimental design, is addressed by a log-time domain interpolation. A statistically significant DDS model of the yeast GRN derived from time-course gene expression measurements by exposure to HMF, revealed several verified transcriptional regulation events. These events implicate Yap1 and Pdr3, transcription factors consistently known for their regulatory roles by other studies or postulated by independent sequence motif analysis, suggesting their involvement in yeast tolerance and detoxification of the inhibitor.

Interface equation and viscosity contrast in Hele-Shaw flow

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

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

1992-05-20

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

Compact Representations of Extended Causal Models

DTIC Science & Technology

2012-10-01

get a yet more compact representation by assuming that, by default , it is typical for the variables to obey the structural equations. Finally, in...Halpern and Hitchcock (2011), is to incorporate considerations about about defaults , typicality, and normality. “Normality” and its cognates (“normal...atypical to violate it. 17 Variables typically obey the structural equations. Thus, it is often far more efficient to assume this holds by default

Predictive equations for total lung capacity and residual volume calculated from radiographs in a random sample of the Michigan population.

PubMed Central

Kilburn, K H; Warshaw, R H; Thornton, J C; Thornton, K; Miller, A

1992-01-01

BACKGROUND: Published predicted values for total lung capacity and residual volume are often based on a small number of subjects and derive from different populations from predicted spirometric values. Equations from the only two large studies gave smaller predicted values for total lung capacity than the smaller studies. A large number of subjects have been studied from a population which has already provided predicted values for spirometry and transfer factor for carbon monoxide. METHODS: Total lung capacity was measured from standard posteroanterior and lateral chest radiographs and forced vital capacity by spirometry in a population sample of 771 subjects. Prediction equations were developed for total lung capacity (TLC), residual volume (RV) and RV/TLC in two groups--normal and total. Subjects with signs or symptoms of cardiopulmonary disease were combined with the normal subjects and equations for all subjects were also modelled. RESULTS: Prediction equations for TLC and RV in non-smoking normal men and women were square root transformations which included height and weight but not age. They included a coefficient for duration of smoking in current smokers. The predictive equation for RV/TLC included weight, age, age and duration of smoking for current smokers and ex-smokers of both sexes. For the total population the equations took the same form but the height coefficients and constants were slightly different. CONCLUSION: These population based prediction equations for TLC, RV and RV/TLC provide reference standards in a population that has provided reference standards for spirometry and single breath transfer factor for carbon monoxide. PMID:1412094

Anisotropic elliptic optical fibers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kang, Soon Ahm

1991-01-01

The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.

Thin-film Faraday patterns in three dimensions

NASA Astrophysics Data System (ADS)

Richter, Sebastian; Bestehorn, Michael

2017-04-01

We investigate the long time evolution of a thin fluid layer in three spatial dimensions located on a horizontal planar substrate. The substrate is subjected to time-periodic external vibrations in normal and in tangential direction with respect to the plane surface. The governing partial differential equation system of our model is obtained from the incompressible Navier-Stokes equations considering the limit of a thin fluid geometry and using the long wave lubrication approximation. It includes inertia and viscous friction. Numerical simulations evince the existence of persistent spatially complex surface patterns (periodic and quasiperiodic) for certain superpositions of two vertical excitations and initial conditions. Additional harmonic lateral excitations cause deformations but retain the basic structure of the patterns. Horizontal ratchet-shaped forces lead to a controllable lateral movement of the fluid. A Floquet analysis is used to determine the stability of the linearized system.

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

Basic research and data analysis for the National Geodetic Satellite program and for the Earth Surveys program

NASA Technical Reports Server (NTRS)

1972-01-01

Current research is reported on precise and accurate descriptions of the earth's surface and gravitational field and on time variations of geophysical parameters. A new computer program was written in connection with the adjustment of the BC-4 worldwide geometric satellite triangulation net. The possibility that an increment to accuracy could be transferred from a super-control net to the basic geodetic (first-order triangulation) was investigated. Coordinates of the NA9 solution were computed and were transformed to the NAD datum, based on GEOS 1 observations. Normal equations from observational data of several different systems and constraint equations were added and a single solution was obtained for the combined systems. Transformation parameters with constraints were determined, and the impact of computers on surveying and mapping is discussed.

Topographies and dynamics on multidimensional potential energy surfaces

NASA Astrophysics Data System (ADS)

Ball, Keith Douglas

The stochastic master equation is a valuable tool for elucidating potential energy surface (PES) details that govern structural relaxation in clusters, bulk systems, and protein folding. This work develops a comprehensive framework for studying non-equilibrium relaxation dynamics using the master equation. Since our master equations depend upon accurate partition function models for use in Rice-Ramsperger-Kassel-Marcus (RRK(M) transition state theory, this work introduces several such models employing various harmonic and anharmonic approximations and compares their predicted equilibrium population distributions with those determined from molecular dynamics. This comparison is performed for the fully-delineated surfaces (KCl)5 and Ar9 to evaluate model performance for potential surfaces with long- and short-range interactions, respectively. For each system, several models perform better than a simple harmonic approximation. While no model gives acceptable results for all minima, and optimal modeling strategies differ for (KCl)5 and Ar9, a particular one-parameter model gives the best agreement with simulation for both systems. We then construct master equations from these models and compare their isothermal relaxation predictions for (KCl)5 and Ar9 with molecular dynamics simulations. This is the first comprehensive test of the kinetic performance of partition function models of its kind. Our results show that accurate modeling of transition-state partition functions is more important for (KCl)5 than for Ar9 in reproducing simulation results, due to a marked stiffening anharmonicity in the transition-state normal modes of (KCl)5. For both systems, several models yield qualitative agreement with simulation over a large temperature range. To examine the robustness of the master equation when applied to larger systems, for which full topographical descriptions would be either impossible or infeasible, we compute relaxation predictions for Ar11 using a master equation constructed from data representing the full PES, and compare these predictions to those of reduced master equations based on statistical samples of the full PES. We introduce a sampling method which generates random, Boltzmann-weighted, energetically 'downhill' sequences. The study reveals that, at moderate temperatures, the slowest relaxation timescale converges as the number of sequences in a sample grows to ~1000. Furthermore, the asymptotic timescale is comparable to the full-PES value.

A theory of fine structure image models with an application to detection and classification of dementia.

PubMed

O'Neill, William; Penn, Richard; Werner, Michael; Thomas, Justin

2015-06-01

Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible.

Behavior of respiratory muscle strength in morbidly obese women by using different predictive equations.

PubMed

Pazzianotto-Forti, Eli M; Peixoto-Souza, Fabiana S; Piconi-Mendes, Camila; Rasera-Junior, Irineu; Barbalho-Moulim, Marcela

2012-01-01

Studies on the behavior of respiratory muscle strength (RMS) in morbidly obese patients have found conflicting results. To evaluate RMS in morbidly obese women and to compare the results by using different predictive equations. This is a cross-sectional study that recruited 30 morbidly obese women and a control group of 30 normal-weight women. The subjects underwent anthropometric and maximal respiratory pressure measurement. Visual inspection of the Bland-Altman plots was performed to evaluate the correlation between the different equations, with a p value lower than 0.05 considered as statistically significant. The obese women showed a significant increase in maximal inspiratory pressure (MIP) values (-87.83±21.40 cmH(2)O) compared with normal-weight women (-72±15.23 cmH(2)O) and a significant reduction of MIP (-87.83±21.40 cmH(2)O) according to the values predicted by the EHarik equation (-130.71±11.98 cmH(2)O). Regarding the obtained maximal expiratory pressure (MEP), there were no between-group differences (p>0.05), and no agreeement was observed between obtained and predicted values of MEP and the ENeder and ECosta equations. Inspiratory muscle strength was greater in the morbidly obese subjects. The most appropriate equation for calculating the predicted MIP values for the morbidly obese seems to be Harik-Khan equation. There seem to be similarities between the respiratory muscle strength behavior of morbidly obese and normal-weight women, however, these findings are still inconclusive.

Coordinates of features on the Galilean satellites

NASA Technical Reports Server (NTRS)

Davies, M. E.; Katayama, F. Y.

1980-01-01

The coordinate systems of each of the Galilean satellites are defined and coordinates of features seen in the Voyager pictures of these satellites are presented. The control nets of the satellites were computed by means of single block analytical triangulations. The normal equations were solved by the conjugate iterative method which is convenient and which converges rapidly as the initial estimates of the parameters are very good.

Reference Values of Impulse Oscillometric Lung Function Indices in Adults of Advanced Age

PubMed Central

Schulz, Holger; Flexeder, Claudia; Behr, Jürgen; Heier, Margit; Holle, Rolf; Huber, Rudolf M.; Jörres, Rudolf A.; Nowak, Dennis; Peters, Annette; Wichmann, H.-Erich; Heinrich, Joachim; Karrasch, Stefan

2013-01-01

Background Impulse oscillometry (IOS) is a non-demanding lung function test. Its diagnostic use may be particularly useful in patients of advanced age with physical or mental limitations unable to perform spirometry. Only few reference equations are available for Caucasians, none of them covering the old age. Here, we provide reference equations up to advanced age and compare them with currently available equations. Methods IOS was performed in a population-based sample of 1990 subjects, aged 45–91 years, from KORA cohorts (Augsburg, Germany). From those, 397 never-smoking, lung healthy subjects with normal spirometry were identified and sex-specific quantile regression models with age, height and body weight as predictors for respiratory system impedance, resistance, reactance, and other parameters of IOS applied. Results Women (n = 243) showed higher resistance values than men (n = 154), while reactance at low frequencies (up to 20 Hz) was lower (p<0.05). A significant age dependency was observed for the difference between resistance values at 5 Hz and 20 Hz (R5–R20), the integrated area of low-frequency reactance (AX), and resonant frequency (Fres) in both sexes whereas reactance at 5 Hz (X5) was age dependent only in females. In the healthy subjects (n = 397), mean differences between observed values and predictions for resistance (5 Hz and 20 Hz) and reactance (5 Hz) ranged between −1% and 5% when using the present model. In contrast, differences based on the currently applied equations (Vogel & Smidt 1994) ranged between −34% and 76%. Regarding our equations the indices were beyond the limits of normal in 8.1% to 18.6% of the entire KORA cohort (n = 1990), and in 0.7% to 9.4% with the currently applied equations. Conclusions Our study provides up-to-date reference equations for IOS in Caucasians aged 45 to 85 years. We suggest the use of the present equations particularly in advanced age in order to detect airway dysfunction. PMID:23691036

Thin film flow along a periodically-stretched elastic beam

NASA Astrophysics Data System (ADS)

Boamah Mensah, Chris; Chini, Greg; Jensen, Oliver

2017-11-01

Motivated by an application to pulmonary alveolar micro-mechanics, a system of partial differential equations is derived that governs the motion of a thin liquid film lining both sides of an inertia-less elastic substrate. The evolution of the film mass distribution is described by invoking the usual lubrication approximation while the displacement of the substrate is determined by employing a kinematically nonlinear Euler-Bernoulli beam formulation. In the parameter regime of interest, the axial strain can be readily shown to be a linear function of arc-length specified completely by the motion of ends of the substrate. In contrast, the normal force balance on the beam yields an equation for the substrate curvature that is fully coupled to the time-dependent lubrication equation. Linear analyses of both a stationary and periodically-stretched flat substrate confirm the potential for buckling instabilities and reveal an upper bound on the dimensionless axial stiffness for which the coupled thin-film/inertial-less-beam model is well-posed. Numerical simulations of the coupled system are used to explore the nonlinear development of the buckling instabilities.

Meson properties in asymmetric matter

NASA Astrophysics Data System (ADS)

Mammarella, Andrea; Mannarelli, Massimo

2018-03-01

In this work we study dynamic and thermodynamic (at T = 0) properties of mesons in asymmetric matter in the framework of Chiral Perturbation Theory. We consider a system at vanishing temperature with nonzero isospin chemical potential and strangeness chemical potential; meson masses and mixing in the normal phase, the pion condensation phase and the kaon condensation phase are described. We find differences with previous works, but the results presented here are supported by both theory group analysis and by direct calculations. Some pion decay channels in the normal and the pion condensation phases are studied, finding a nonmonotonic behavior of the decay width as a function of µ I . Furthermore, pressure, density and equation of state of the system at T = 0 are studied, finding remarkable agreement with analogue studies performed by lattice calculations.

A Novel Approach to Solve Linearized Stellar Pulsation Equations

NASA Astrophysics Data System (ADS)

Bard, Christopher; Teitler, S.

2011-01-01

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

Mathematical model with autoregressive process for electrocardiogram signals

NASA Astrophysics Data System (ADS)

Evaristo, Ronaldo M.; Batista, Antonio M.; Viana, Ricardo L.; Iarosz, Kelly C.; Szezech, José D., Jr.; Godoy, Moacir F. de

2018-04-01

The cardiovascular system is composed of the heart, blood and blood vessels. Regarding the heart, cardiac conditions are determined by the electrocardiogram, that is a noninvasive medical procedure. In this work, we propose autoregressive process in a mathematical model based on coupled differential equations in order to obtain the tachograms and the electrocardiogram signals of young adults with normal heartbeats. Our results are compared with experimental tachogram by means of Poincaré plot and dentrended fluctuation analysis. We verify that the results from the model with autoregressive process show good agreement with experimental measures from tachogram generated by electrical activity of the heartbeat. With the tachogram we build the electrocardiogram by means of coupled differential equations.

Elementary diagrams in nuclear and neutron matter

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

Wiringa, R.B.

1995-08-01

Variational calculations of nuclear and neutron matter are currently performed using a diagrammatic cluster expansion with the aid of nonlinear integral equations for evaluating expectation values. These are the Fermi hypernetted chain (FHNC) and single-operator chain (SOC) equations, which are a way of doing partial diagram summations to infinite order. A more complete summation can be made by adding elementary diagrams to the procedure. The simplest elementary diagrams appear at the four-body cluster level; there is one such E{sub 4} diagram in Bose systems, but 35 diagrams in Fermi systems, which gives a level of approximation called FHNC/4. We developedmore » a novel technique for evaluating these diagrams, by computing and storing 6 three-point functions, S{sub xyz}(r{sub 12}, r{sub 13}, r{sub 23}), where xyz (= ccd, cce, ddd, dde, dee, or eee) denotes the exchange character at the vertices 1, 2, and 3. All 35 Fermi E{sub 4} diagrams can be constructed from these 6 functions and other two-point functions that are already calculated. The elementary diagrams are known to be important in some systems like liquid {sup 3}He. We expect them to be small in nuclear matter at normal density, but they might become significant at higher densities appropriate for neutron star calculations. This year we programmed the FHNC/4 contributions to the energy and tested them in a number of simple model cases, including liquid {sup 3}He and Bethe`s homework problem. We get reasonable, but not exact agreement with earlier published work. In nuclear and neutron matter with the Argonne v{sub 14} interaction these contributions are indeed small corrections at normal density and grow to only 5-10 MeV/nucleon at 5 times normal density.« less

On two parabolic systems: Convergence and blowup

NASA Astrophysics Data System (ADS)

Huang, Yamin

1998-12-01

This dissertation studies two parabolic systems. It consists of two parts. In part one (chapter one), we prove a convergence result, namely, the solution (AK,/ BK) of a system of chemical diffusion-reaction equations (with reaction rate K) converges to the solution (A, B) of a diffusion- instantaneous-reaction equation. To prove our main result, we use some L1 and L2 'energy' estimates and a compactness result due to Aubin (1). As a by-product we also prove that as K approaches infinity, the limit solution exhibits phase separation between A and B. In part two (chapter two), we study the blowup rate for a system of heat equations ut=/Delta u,/ vt=/Delta v in a bounded domain Ωtimes(0,T) coupled in the nonlinear Neumann boundary conditions [/partial u/over/partial n]=vp,/ [/partial v/over/partial n]=uq on ∂Omega×[ 0,T), where p>0,/ q>0,/ pq>1 and n is the exterior normal vector on ∂Omega. Under certain assumptions, we establish exact blowup rate which generalizes the corresponding results of some authors' recent work including Deng (2), Deng-Fila-Levine (3) and Hu-Yin (4). ftn (1) J. P. A scUBIN, Un theoreme de compacite, C. R. Acad. Sci., 256(1963), pp. 5042-5044. (2) K. D scENG, Blow-up rates for parabolic systems, Z. Angew. Math. Phys., 47(1996), No. 1, pp. 132-143. (3) K. D scENG, M. F scILA AND H. A. L scEVINE, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenian. (N.S.), 36(1994), No. 2, pp. 169-192. (4) B. H scU scAND H. M. Y scIN, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 346(1994), pp. 117-135.

An analytic method to account for drag in the Vinti Satellite theory

NASA Technical Reports Server (NTRS)

Watson, J. S.; Mistretta, G. D.; Bonavito, N. L.

1974-01-01

To retain separability in the Vinti theory of earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all altitudes and simultaneously reduced the variational equations to indefinite integrals with closed form evaluations. The values of the limits for any arbitrary time interval are obtained from the Vinti program.

Diffusion length measurements in bulk and epitaxially grown 3-5 semiconductors using charge collection microscopy

NASA Technical Reports Server (NTRS)

Leon, R. P.

1987-01-01

Diffusion lengths and surface recombination velocities were measured in GaAs diodes and InP finished solar cells. The basic techniques used was charge collection microscopy also known as electron beam induced current (EBIC). The normalized currents and distances from the pn junction were read directly from the calibrated curves obtained while using the line scan mode in an SEM. These values were then equated to integral and infinite series expressions resulting from the solution of the diffusion equation with both extended generation and point generation functions. This expands previous work by examining both thin and thick samples. The surface recombination velocity was either treated as an unknown in a system of two equations, or measured directly using low e(-) beam accelerating voltages. These techniques give accurate results by accounting for the effects of surface recombination and the finite size of the generation volume.

Kinematic equations for resolved-rate control of an industrial robot arm

NASA Technical Reports Server (NTRS)

Barker, L. K.

1983-01-01

An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.

Spin effects induced by thermal perturbation in a normal metal/magnetic insulator system

NASA Astrophysics Data System (ADS)

Lyapilin, I. I.; Okorokov, M. S.; Ustinov, V. V.

2015-05-01

Using one of the methods of quantum nonequilibrium statistical physics, we have investigated the spin transport transverse to the normal metal/ferromagnetic insulator interface in hybrid nanostructures. An approximation of the effective parameters, when each of the interacting subsystems (electron spin, magnon, and phonon) is characterized by its own effective temperature, has been considered. The generalized Bloch equations which describe the spin-wave current propagation in the dielectric have been derived. Finally, two sides of the spin transport "coin" have been revealed: the diffusive nature of the magnon motion and magnon relaxation processes, responsible for the spin pumping, and the spin-torque effect.

An adaptive trajectory tracking control of four rotor hover vehicle using extended normalized radial basis function network

NASA Astrophysics Data System (ADS)

ul Amin, Rooh; Aijun, Li; Khan, Muhammad Umer; Shamshirband, Shahaboddin; Kamsin, Amirrudin

2017-01-01

In this paper, an adaptive trajectory tracking controller based on extended normalized radial basis function network (ENRBFN) is proposed for 3-degree-of-freedom four rotor hover vehicle subjected to external disturbance i.e. wind turbulence. Mathematical model of four rotor hover system is developed using equations of motions and a new computational intelligence based technique ENRBFN is introduced to approximate the unmodeled dynamics of the hover vehicle. The adaptive controller based on the Lyapunov stability approach is designed to achieve tracking of the desired attitude angles of four rotor hover vehicle in the presence of wind turbulence. The adaptive weight update based on the Levenberg-Marquardt algorithm is used to avoid weight drift in case the system is exposed to external disturbances. The closed-loop system stability is also analyzed using Lyapunov stability theory. Simulations and experimental results are included to validate the effectiveness of the proposed control scheme.

Hamiltonian approaches to spatial and temporal discretization of fully compressible equations

NASA Astrophysics Data System (ADS)

Dubos, Thomas; Dubey, Sarvesh

2017-04-01

The fully compressible Euler (FCE) equations are the most accurate for representing atmospheric motion, compared to approximate systems like the hydrostatic, anelastic or pseudo-incompressible systems. The price to pay for this accuracy is the presence of additional degrees of freedom and high-frequency acoustic waves that must be treated implicitly. In this work we explore a Hamiltonian approach to the issue of stable spatial and temporal discretization of the FCE using a non-Eulerian vertical coordinate. For scalability, a horizontally-explicit, vertically-implicit (HEVI) time discretization is adopted. The Hamiltonian structure of the equations is used to obtain the spatial finite-difference discretization and also in order to identify those terms of the equations of motion that need to be treated implicitly. A novel treatment of the lower boundary condition in the presence of orography is introduced: rather than enforcing a no-normal-flow boundary condition, which couples the horizontal and vertical velocity components and interferes with the HEVI structure, the ground is treated as a flexible surface with arbitrarily large stiffness, resulting in a decoupling of the horizontal and vertical dynamics and yielding a simple implicit problem which can be solved efficiently. Standard test cases performed in a vertical slice configuration suggest that an effective horizontal acoustic Courant number close to 1 can be achieved.

The Dirac equation and the normalization of its solutions in a closed Friedmann- Robertson-Walker universe

NASA Astrophysics Data System (ADS)

Finster, Felix; Reintjes, Moritz

2009-05-01

We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We compute the probability integral and analyze a spacetime normalization integral. This analysis allows us to introduce the fermionic projector in a closed Friedmann-Robertson-Walker geometry and to specify its global normalization as well as its local form. First author supported in part by the Deutsche Forschungsgemeinschaft.

An Integrable Approximation for the Fermi Pasta Ulam Lattice

NASA Astrophysics Data System (ADS)

Rink, Bob

This contribution presents a review of results obtained from computations of approximate equations of motion for the Fermi-Pasta-Ulam lattice. These approximate equations are obtained as a finite-dimensional Birkhoff normal form. It turns out that in many cases, the Birkhoff normal form is suitable for application of the KAM theorem. In particular, this proves Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal Birkhoff normal form computations of Nishida, the KAM theorem and discrete symmetry considerations.

A model for hormonal control of the menstrual cycle: structural consistency but sensitivity with regard to data.

PubMed

Selgrade, J F; Harris, L A; Pasteur, R D

2009-10-21

This study presents a 13-dimensional system of delayed differential equations which predicts serum concentrations of five hormones important for regulation of the menstrual cycle. Parameters for the system are fit to two different data sets for normally cycling women. For these best fit parameter sets, model simulations agree well with the two different data sets but one model also has an abnormal stable periodic solution, which may represent polycystic ovarian syndrome. This abnormal cycle occurs for the model in which the normal cycle has estradiol levels at the high end of the normal range. Differences in model behavior are explained by studying hysteresis curves in bifurcation diagrams with respect to sensitive model parameters. For instance, one sensitive parameter is indicative of the estradiol concentration that promotes pituitary synthesis of a large amount of luteinizing hormone, which is required for ovulation. Also, it is observed that models with greater early follicular growth rates may have a greater risk of cycling abnormally.

Rotating non-Boussinesq Rayleigh-Benard convection

NASA Astrophysics Data System (ADS)

Moroz, Vadim Vladimir

This thesis makes quantitative predictions about the formation and stability of hexagonal and roll patterns in convecting system unbounded in horizontal direction. Starting from the Navier-Stokes, heat and continuity equations, the convection problem is then reduced to normal form equations using equivariant bifurcation theory. The relative stabilities of patterns lying on a hexagonal lattice in Fourier space are then determined using appropriate amplitude equations, with coefficients obtained via asymptotic expansion of the governing partial differential equations, with the conducting state being the base state, and the control parameter and the non-Boussinesq effects being small. The software package Mathematica was used to calculate amplitude coefficients of the appropriate coupled Ginzburg-Landau equations for the rigid-rigid and free-free case. A Galerkin code (initial version of which was written by W. Pesch et al.) is used to determine pattern stability further from onset and for strongly non-Boussinesq fluids. Specific predictions about the stability of hexagon and roll patterns for realistic experimental conditions are made. The dependence of the stability of the convective patterns on the Rayleigh number, planform wavenumber and the rotation rate is studied. Long- and shortwave instabilities, both steady and oscillatory, are identified. For small Prandtl numbers oscillatory sideband instabilities are found already very close to onset. A resonant mode interaction in hexagonal patterns arising in non-Boussinesq Rayleigh-Benard convection is studied using symmetry group methods. The lowest-order coupling terms for interacting patterns are identified. A bifurcation analysis of the resulting system of equations shows that the bifurcation is transcritical. Stability properties of resulting patterns are discussed. It is found that for some fluid properties the traditional hexagon convection solution does not exist. Analytical results are supported by numerical solutions of the convection equations using the Galerkin procedure and a Floquet analysis.

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

Stable long-time semiclassical description of zero-point energy in high-dimensional molecular systems.

PubMed

Garashchuk, Sophya; Rassolov, Vitaly A

2008-07-14

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.

Delay Differential Equation Models of Normal and Diseased Electrocardiograms

NASA Astrophysics Data System (ADS)

Lainscsek, Claudia; Sejnowski, Terrence J.

Time series analysis with nonlinear delay differential equations (DDEs) is a powerful tool since it reveals spectral as well as nonlinear properties of the underlying dynamical system. Here global DDE models are used to analyze electrocardiography recordings (ECGs) in order to capture distinguishing features for different heart conditions such as normal heart beat, congestive heart failure, and atrial fibrillation. To capture distinguishing features of the different data types the number of terms and delays in the model as well as the order of nonlinearity of the DDE model have to be selected. The DDE structure selection is done in a supervised way by selecting the DDE that best separates different data types. We analyzed 24 h of data from 15 young healthy subjects in normal sinus rhythm (NSR) of 15 congestive heart failure (CHF) patients as well as of 15 subjects suffering from atrial fibrillation (AF) selected from the Physionet database. For the analysis presented here we used 5 min non-overlapping data windows on the raw data without any artifact removal. For classification performance we used the Cohen Kappa coefficient computed directly from the confusion matrix. The overall classification performance of the three groups was around 72-99 % on the 5 min windows for the different approaches. For 2 h data windows the classification for all three groups was above 95%.

Multiple Ignition, Normal and Catalytic Combustion and Quenching of Fuel/Air Mixtures.

DTIC Science & Technology

1980-05-10

spray ignition results. Spray systems will be produced using a TSI vibrating orifice aerosol generator. From a small liquid reservoir under high pressure...Liebman used laser ignition of electromagnetically -15- levitated particles. An interesting contradiction presents itself in Figures 7 and 8. Because...the substrate surface has been developed and tested. When the experimental wall temperature is used as boundary condition for the gas- phase equations

Modeling Pulse Transmission in the Monterey Bay Using Parabolic Equation Methods

DTIC Science & Technology

1991-12-01

Collins 9-13 was chosen for this purpose due its energy conservation scheme , and its ability to efficiently incorporate higher order terms in its...pressure field generated by the PE model into normal modes. Additionally, this process provides increased physical understanding of mode coupling and...separation of variables (i.e. normal modes or fast field), as well as pure numerical schemes such as the parabolic equation methods, can be used. However, as

High-frequency Born synthetic seismograms based on coupled normal modes

USGS Publications Warehouse

Pollitz, Fred F.

2011-01-01

High-frequency and full waveform synthetic seismograms on a 3-D laterally heterogeneous earth model are simulated using the theory of coupled normal modes. The set of coupled integral equations that describe the 3-D response are simplified into a set of uncoupled integral equations by using the Born approximation to calculate scattered wavefields and the pure-path approximation to modulate the phase of incident and scattered wavefields. This depends upon a decomposition of the aspherical structure into smooth and rough components. The uncoupled integral equations are discretized and solved in the frequency domain, and time domain results are obtained by inverse Fourier transform. Examples show the utility of the normal mode approach to synthesize the seismic wavefields resulting from interaction with a combination of rough and smooth structural heterogeneities. This approach is applied to an ∼4 Hz shallow crustal wave propagation around the site of the San Andreas Fault Observatory at Depth (SAFOD).

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Arnold Diffusion of Charged Particles in ABC Magnetic Fields

NASA Astrophysics Data System (ADS)

Luque, Alejandro; Peralta-Salas, Daniel

2017-06-01

We prove the existence of diffusing solutions in the motion of a charged particle in the presence of ABC magnetic fields. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of these parameters, we obtain a normally hyperbolic invariant manifold and we apply the so-called geometric methods for a priori unstable systems developed by A. Delshams, R. de la Llave and T.M. Seara. We characterize explicitly sufficient conditions for the existence of a transition chain of invariant tori having heteroclinic connections, thus obtaining global instability (Arnold diffusion). We also check the obtained conditions in a computer-assisted proof. ABC magnetic fields are the simplest force-free-type solutions of the magnetohydrodynamics equations with periodic boundary conditions, and can be considered as an elementary model for the motion of plasma-charged particles in a tokamak.

Phase space analysis for anisotropic universe with nonlinear bulk viscosity

NASA Astrophysics Data System (ADS)

Sharif, M.; Mumtaz, Saadia

2018-06-01

In this paper, we discuss phase space analysis of locally rotationally symmetric Bianchi type I universe model by taking a noninteracting mixture of dust like and viscous radiation like fluid whose viscous pressure satisfies a nonlinear version of the Israel-Stewart transport equation. An autonomous system of equations is established by defining normalized dimensionless variables. In order to investigate stability of the system, we evaluate corresponding critical points for different values of the parameters. We also compute power-law scale factor whose behavior indicates different phases of the universe model. It is found that our analysis does not provide a complete immune from fine-tuning because the exponentially expanding solution occurs only for a particular range of parameters. We conclude that stable solutions exist in the presence of nonlinear model for bulk viscosity with different choices of the constant parameter m for anisotropic universe.

Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

NASA Astrophysics Data System (ADS)

Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A. N.; Selvaraj, S.

2018-05-01

We present explicit generalized analytical solutions for a network of linearly-coupled simple chaotic systems. Analytical solutions are obtained for the normalized state equations of a network of linearly-coupled systems driven by a common chaotic drive system. Two parameter bifurcation diagrams revealing the various hidden synchronization regions, such as complete, phase and phase-lag synchronization are identified using the analytical results. The synchronization dynamics and their stability are studied using phase portraits and the master stability function, respectively. Further, experimental results for linearly-coupled simple chaotic systems are presented to confirm the analytical results. The synchronization dynamics of a network of chaotic systems studied analytically is reported for the first time.

Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures.

PubMed

Yang, Dong-Ping; Robinson, P A

2017-04-01

A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.

Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures

NASA Astrophysics Data System (ADS)

Yang, Dong-Ping; Robinson, P. A.

2017-04-01

A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.

Inversion of very large matrices encountered in large scale problems of photogrammetry and photographic astrometry

NASA Technical Reports Server (NTRS)

Brown, D. C.

1971-01-01

The simultaneous adjustment of very large nets of overlapping plates covering the celestial sphere becomes computationally feasible by virtue of a twofold process that generates a system of normal equations having a bordered-banded coefficient matrix, and solves such a system in a highly efficient manner. Numerical results suggest that when a well constructed spherical net is subjected to a rigorous, simultaneous adjustment, the exercise of independently established control points is neither required for determinancy nor for production of accurate results.

An Efficient Implementation of the GMC Micromechanics Model for Multi-Phased Materials with Complex Microstructures

NASA Technical Reports Server (NTRS)

Pindera, Marek-Jerzy; Bednarcyk, Brett A.

1997-01-01

An efficient implementation of the generalized method of cells micromechanics model is presented that allows analysis of periodic unidirectional composites characterized by repeating unit cells containing thousands of subcells. The original formulation, given in terms of Hill's strain concentration matrices that relate average subcell strains to the macroscopic strains, is reformulated in terms of the interfacial subcell tractions as the basic unknowns. This is accomplished by expressing the displacement continuity equations in terms of the stresses and then imposing the traction continuity conditions directly. The result is a mixed formulation wherein the unknown interfacial subcell traction components are related to the macroscopic strain components. Because the stress field throughout the repeating unit cell is piece-wise uniform, the imposition of traction continuity conditions directly in the displacement continuity equations, expressed in terms of stresses, substantially reduces the number of unknown subcell traction (and stress) components, and thus the size of the system of equations that must be solved. Further reduction in the size of the system of continuity equations is obtained by separating the normal and shear traction equations in those instances where the individual subcells are, at most, orthotropic. The reformulated version facilitates detailed analysis of the impact of the fiber cross-section geometry and arrangement on the response of multi-phased unidirectional composites with and without evolving damage. Comparison of execution times obtained with the original and reformulated versions of the generalized method of cells demonstrates the new version's efficiency.

The way from microscopic many-particle theory to macroscopic hydrodynamics.

PubMed

Haussmann, Rudolf

2016-03-23

Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena. We specify the densities of the conserved quantities as the relevant hydrodynamic variables and apply the methods of non-equilibrium statistical mechanics with projection operator techniques. As a result we obtain time-evolution equations for the hydrodynamic variables with three kinds of terms on the right-hand sides: reversible, dissipative and fluctuating terms. In their original form these equations are completely exact and contain nonlocal terms in space and time which describe nonlocal memory effects. Applying a few approximations the nonlocal properties and the memory effects are removed. As a result we find the well known hydrodynamic equations of a normal fluid with Gaussian fluctuating forces. In the following we investigate if and how the time-inversion invariance is broken and how the second law of thermodynamics comes about. Furthermore, we show that the hydrodynamic equations with fluctuating forces are equivalent to stochastic Langevin equations and the related Fokker-Planck equation. Finally, we investigate the fluctuation theorem and find a modification by an additional term.

Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics, production version (SOUSSA-P 1.1). Volume 1: Theoretical manual. [Green function

NASA Technical Reports Server (NTRS)

Morino, L.

1980-01-01

Recent developments of the Green's function method and the computer program SOUSSA (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed and summarized. Applying the Green's function method to the fully unsteady (transient) potential equation yields an integro-differential-delay equation. With spatial discretization by the finite-element method, this equation is approximated by a set of differential-delay equations in time. Time solution by Laplace transform yields a matrix relating the velocity potential to the normal wash. Premultiplying and postmultiplying by the matrices relating generalized forces to the potential and the normal wash to the generalized coordinates one obtains the matrix of the generalized aerodynamic forces. The frequency and mode-shape dependence of this matrix makes the program SOUSSA useful for multiple frequency and repeated mode-shape evaluations.

Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions

NASA Astrophysics Data System (ADS)

Holmes, Philip J.

1981-06-01

We study the instabilities known to aeronautical engineers as flutter and divergence. Mathematically, these states correspond to bifurcations to limit cycles and multiple equilibrium points in a differential equation. Making use of the center manifold and normal form theorems, we concentrate on the situation in which flutter and divergence become coupled, and show that there are essentially two ways in which this is likely to occur. In the first case the system can be reduced to an essential model which takes the form of a single degree of freedom nonlinear oscillator. This system, which may be analyzed by conventional phase-plane techniques, captures all the qualitative features of the full system. We discuss the reduction and show how the nonlinear terms may be simplified and put into normal form. Invariant manifold theory and the normal form theorem play a major role in this work and this paper serves as an introduction to their application in mechanics. Repeating the approach in the second case, we show that the essential model is now three dimensional and that far more complex behavior is possible, including nonperiodic and ‘chaotic’ motions. Throughout, we take a two degree of freedom system as an example, but the general methods are applicable to multi- and even infinite degree of freedom problems.

Wind direction change criteria for wind turbine design

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

Cliff, W.C.

1979-01-01

A method is presented for estimating the root mean square (rms) value of the wind direction change, ..delta..theta(tau) = theta(tau + tau) - theta(tau), that occurs over the swept area of wind turbine rotor systems. An equation is also given for the rms value of the wind direction change that occurs at a single point in space, i.e., a direcion change that a wind vane would measure. Assuming a normal probability density function for the lateral wind velocity change and relating this to angular changes, equations are given for calculating the expected number of wind direction changes, larger than anmore » arbitrary value, that will occur in 1 hr as well as the expected number that will occur during the design life of a wind turbine. The equations presented are developed using a small angle approximation and are, therefore, considered appropriate for wind direction changes of less than 30/sup 0/. The equations presented are based upon neutral atmospheric boundary-layer conditions and do not include information regarding events such as tornados, hurricanes, etc.« less

Quantifying wall turbulence via a symmetry approach: A Lie group theory

NASA Astrophysics Data System (ADS)

She, Zhen-Su; Chen, Xi; Hussain, Fazle

2017-11-01

We present a symmetry-based approach which yields analytic expressions for the mean velocity and kinetic energy profiles from a Lie-group analysis. After verifying the dilation-group invariance of the Reynolds averaged Navier-Stokes equation in the presence of a wall, we select a stress and energy length function as similarity variables which are assumed to have a simple dilation-invariant form. Three kinds of (local) invariant forms of the length functions are postulated, a combination of which yields a multi-layer formula giving its distribution in the entire flow region normal to the wall. The mean velocity profile is then predicted using the mean momentum equation, which yields, in particular, analytic expressions for the (universal) wall function and separate wake functions for pipe and channel - which are validated by data from direct numerical simulations (DNS). Future applications to a variety of wall flows such as flows around flat plate or airfoil, in a Rayleigh-Benard cell or Taylor-Couette system, etc., are discussed, for which the dilation group invariance is valid in the wall-normal direction.

Validation of Normalizations, Scaling, and Photofading Corrections for FRAP Data Analysis

PubMed Central

Kang, Minchul; Andreani, Manuel; Kenworthy, Anne K.

2015-01-01

Fluorescence Recovery After Photobleaching (FRAP) has been a versatile tool to study transport and reaction kinetics in live cells. Since the fluorescence data generated by fluorescence microscopy are in a relative scale, a wide variety of scalings and normalizations are used in quantitative FRAP analysis. Scaling and normalization are often required to account for inherent properties of diffusing biomolecules of interest or photochemical properties of the fluorescent tag such as mobile fraction or photofading during image acquisition. In some cases, scaling and normalization are also used for computational simplicity. However, to our best knowledge, the validity of those various forms of scaling and normalization has not been studied in a rigorous manner. In this study, we investigate the validity of various scalings and normalizations that have appeared in the literature to calculate mobile fractions and correct for photofading and assess their consistency with FRAP equations. As a test case, we consider linear or affine scaling of normal or anomalous diffusion FRAP equations in combination with scaling for immobile fractions. We also consider exponential scaling of either FRAP equations or FRAP data to correct for photofading. Using a combination of theoretical and experimental approaches, we show that compatible scaling schemes should be applied in the correct sequential order; otherwise, erroneous results may be obtained. We propose a hierarchical workflow to carry out FRAP data analysis and discuss the broader implications of our findings for FRAP data analysis using a variety of kinetic models. PMID:26017223

The Dynamics of HPV Infection and Cervical Cancer Cells.

PubMed

Asih, Tri Sri Noor; Lenhart, Suzanne; Wise, Steven; Aryati, Lina; Adi-Kusumo, F; Hardianti, Mardiah S; Forde, Jonathan

2016-01-01

The development of cervical cells from normal cells infected by human papillomavirus into invasive cancer cells can be modeled using population dynamics of the cells and free virus. The cell populations are separated into four compartments: susceptible cells, infected cells, precancerous cells and cancer cells. The model system of differential equations also has a free virus compartment in the system, which infect normal cells. We analyze the local stability of the equilibrium points of the model and investigate the parameters, which play an important role in the progression toward invasive cancer. By simulation, we investigate the boundary between initial conditions of solutions, which tend to stable equilibrium point, representing controlled infection, and those which tend to unbounded growth of the cancer cell population. Parameters affected by drug treatment are varied, and their effect on the risk of cancer progression is explored.

Brain-computer interface signal processing at the Wadsworth Center: mu and sensorimotor beta rhythms.

PubMed

McFarland, Dennis J; Krusienski, Dean J; Wolpaw, Jonathan R

2006-01-01

The Wadsworth brain-computer interface (BCI), based on mu and beta sensorimotor rhythms, uses one- and two-dimensional cursor movement tasks and relies on user training. This is a real-time closed-loop system. Signal processing consists of channel selection, spatial filtering, and spectral analysis. Feature translation uses a regression approach and normalization. Adaptation occurs at several points in this process on the basis of different criteria and methods. It can use either feedforward (e.g., estimating the signal mean for normalization) or feedback control (e.g., estimating feature weights for the prediction equation). We view this process as the interaction between a dynamic user and a dynamic system that coadapt over time. Understanding the dynamics of this interaction and optimizing its performance represent a major challenge for BCI research.

Quantitative and qualitative characterization of zigzag spatiotemporal chaos in a system of amplitude equations for nematic electroconvection.

PubMed

Oprea, Iuliana; Triandaf, Ioana; Dangelmayr, Gerhard; Schwartz, Ira B

2007-06-01

It has been suggested by experimentalists that a weakly nonlinear analysis of the recently introduced equations of motion for the nematic electroconvection by M. Treiber and L. Kramer [Phys. Rev. E 58, 1973 (1998)] has the potential to reproduce the dynamics of the zigzag-type extended spatiotemporal chaos and localized solutions observed near onset in experiments [M. Dennin, D. S. Cannell, and G. Ahlers, Phys. Rev. E 57, 638 (1998); J. T. Gleeson (private communication)]. In this paper, we study a complex spatiotemporal pattern, identified as spatiotemporal chaos, that bifurcates at the onset from a spatially uniform solution of a system of globally coupled complex Ginzburg-Landau equations governing the weakly nonlinear evolution of four traveling wave envelopes. The Ginzburg-Landau system can be derived directly from the weak electrolyte model for electroconvection in nematic liquid crystals when the primary instability is a Hopf bifurcation to oblique traveling rolls. The chaotic nature of the pattern and the resemblance to the observed experimental spatiotemporal chaos in the electroconvection of nematic liquid crystals are confirmed through a combination of techniques including the Karhunen-Loeve decomposition, time-series analysis of the amplitudes of the dominant modes, statistical descriptions, and normal form theory, showing good agreement between theory and experiments.

On the origin of heavy-tail statistics in equations of the Nonlinear Schrödinger type

NASA Astrophysics Data System (ADS)

Onorato, Miguel; Proment, Davide; El, Gennady; Randoux, Stephane; Suret, Pierre

2016-09-01

We study the formation of extreme events in incoherent systems described by the Nonlinear Schrödinger type of equations. We consider an exact identity that relates the evolution of the normalized fourth-order moment of the probability density function of the wave envelope to the rate of change of the width of the Fourier spectrum of the wave field. We show that, given an initial condition characterized by some distribution of the wave envelope, an increase of the spectral bandwidth in the focusing/defocusing regime leads to an increase/decrease of the probability of formation of rogue waves. Extensive numerical simulations in 1D+1 and 2D+1 are also performed to confirm the results.

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

NASA Technical Reports Server (NTRS)

Van Dommelen, Leon L.; Cowley, Stephen J.

1990-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

NASA Technical Reports Server (NTRS)

Vandommelen, Leon L.; Cowley, Stephen J.

1989-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Anomalous hydrodynamics and normal fluids in rapidly rotating Bose-Einstein condensates.

PubMed

Bourne, A; Wilkin, N K; Gunn, J M F

2006-06-23

In rapidly rotating condensed Bose systems we show that there is a regime of anomalous hydrodynamics which coincides with the mean field quantum Hall regime. A consequence is the absence of a normal fluid in any conventional sense. However, even the superfluid hydrodynamics is not described by conventional Bernoulli and continuity equations. We show that there are constraints which connect spatial variations of density and phase and that the vortex positions are not the simplest description of the dynamics. We demonstrate, inter alia, a simple relation between vortices and surface waves. We show that the surface waves can emulate a "normal fluid," allowing dissipation by energy and angular momentum absorbtion from vortex motion in the trap. The time scale is sensitive to the initial configuration, which can lead to long-lived vortex patches--perhaps related to those observed at JILA.

Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

NASA Astrophysics Data System (ADS)

Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

2010-05-01

The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low-Low Satellite-to-Satellite Tracking

A Maximum Likelihood Approach for Multisample Nonlinear Structural Equation Models with Missing Continuous and Dichotomous Data

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2006-01-01

Structural equation models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and models with a linear structural equation.…

An iterative method for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1983-01-01

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

A geometrically nonlinear theory of elastic plates

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Atilgan, Ali R.; Danielson, D. A.

1992-01-01

A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.

High-Frequency Normal Mode Propagation in Aluminum Cylinders

USGS Publications Warehouse

Lee, Myung W.; Waite, William F.

2009-01-01

Acoustic measurements made using compressional-wave (P-wave) and shear-wave (S-wave) transducers in aluminum cylinders reveal waveform features with high amplitudes and with velocities that depend on the feature's dominant frequency. In a given waveform, high-frequency features generally arrive earlier than low-frequency features, typical for normal mode propagation. To analyze these waveforms, the elastic equation is solved in a cylindrical coordinate system for the high-frequency case in which the acoustic wavelength is small compared to the cylinder geometry, and the surrounding medium is air. Dispersive P- and S-wave normal mode propagations are predicted to exist, but owing to complex interference patterns inside a cylinder, the phase and group velocities are not smooth functions of frequency. To assess the normal mode group velocities and relative amplitudes, approximate dispersion relations are derived using Bessel functions. The utility of the normal mode theory and approximations from a theoretical and experimental standpoint are demonstrated by showing how the sequence of P- and S-wave normal mode arrivals can vary between samples of different size, and how fundamental normal modes can be mistaken for the faster, but significantly smaller amplitude, P- and S-body waves from which P- and S-wave speeds are calculated.

Period and amplitude of non-volcanic tremors and repeaters: a dimensional analysis

NASA Astrophysics Data System (ADS)

Nielsen, Stefan

2017-04-01

Since its relatively recent discovery, the origin of non-volcanic tremor has been source of great curiosity and debate. Two main interpretations have been proposed, one based on fluid migration, the other relating to slow slip events on a plate boundary (the latter hypothesis has recently gained considerable ground). Here I define the conditions of slip of one or more small asperities embedded within a larger creeping fault patch. The radiation-damping equation coupled with rate-and-state friction evolution equations results in a system of ordinary differential equations. For a finite size asperity, the system equates to a peculiar non-linear damped oscillator, converging to a limit cycle. Dimensional analysis shows that period and amplitude of the oscillations depend on dimensional parameter combinations formed from a limited set of parameters: asperity dimension Γ, rate and state friction parameters (a, b, L), shear stiffness of the medium G, mass density ρ, background creep rate ˙V and normal stress σ. Under realistic parameter ranges, the asperity may show (1) tremor-like short period oscillations, accelerating to radiate sufficient energy to be barely detectable and a periodicity of the order of one to ten Hertz, as observed for non-volcanic tremor activity at the base of large inter-plate faults; (2) isolated stick-slip events with intervals in the order of days to months, as observed in repeater events of modest magnitude within creeping fault sections.

Colour vision in AIDS patients without HIV retinopathy.

PubMed

Sommerhalder, J; Baglivo, E; Barbey, C; Hirschel, B; Roth, A; Pelizzone, M

1998-11-01

Patients suffering from AIDS develop ocular complications, the most frequent being HIV retinopathy. It is however not clear, if functional visual impairments can be observed as early indicators of ocular complications, before clinical diagnosis of HIV retinopathy is made at fundus examination. To address this issue, we measured colour vision in a group of 49 AIDS subjects with normal clinical fundi using the 'two equation method'. This method, combining red-green Rayleigh and the blue-green Moreland metameric matches, enables more complete and quantitative assessments of colour vision than those based on pigmentary tests. Data were collected on our computer controlled colorimeter and compared to those of normal subjects. While most AIDS subjects without HIV retinopathy demonstrated normal colour vision, a significant portion of them had wider matches than normal subjects (11% for the Rayleigh equation and 16% for the Moreland equation). Furthermore, matching ranges of the Moreland equation were significantly correlated with CD4 lymphocyte counts. Patients with low CD4 values tended to produce larger matching ranges than the patients with high CD4 values. A within subject study on 17 patients confirmed this trend and showed that the patients who increased/decreased their CD4 blood counts generally improved/impaired their colour discrimination in the Moreland match. No such correlation was found between the matching ranges of the Rayleigh equation and the CD4 counts. These results show that colour discrimination is slightly reduced in some AIDS subjects, although there are no detectable ocular complications. They also suggest two different types of colour vision impairments in AIDS patients without retinopathy: one reversible process affecting colour discrimination in the blue-green range; and another irreversible process affecting colour discrimination in the red-green range.

Spike solutions in Gierer#x2013;Meinhardt model with a time dependent anomaly exponent

NASA Astrophysics Data System (ADS)

Nec, Yana

2018-01-01

Experimental evidence of complex dispersion regimes in natural systems, where the growth of the mean square displacement in time cannot be characterised by a single power, has been accruing for the past two decades. In such processes the exponent γ(t) in ⟨r2⟩ ∼ tγ(t) at times might be approximated by a piecewise constant function, or it can be a continuous function. Variable order differential equations are an emerging mathematical tool with a strong potential to model these systems. However, variable order differential equations are not tractable by the classic differential equations theory. This contribution illustrates how a classic method can be adapted to gain insight into a system of this type. Herein a variable order Gierer-Meinhardt model is posed, a generic reaction- diffusion system of a chemical origin. With a fixed order this system possesses a solution in the form of a constellation of arbitrarily situated localised pulses, when the components' diffusivity ratio is asymptotically small. The pattern was shown to exist subject to multiple step-like transitions between normal diffusion and sub-diffusion, as well as between distinct sub-diffusive regimes. The analytical approximation obtained permits qualitative analysis of the impact thereof. Numerical solution for typical cross-over scenarios revealed such features as earlier equilibration and non-monotonic excursions before attainment of equilibrium. The method is general and allows for an approximate numerical solution with any reasonably behaved γ(t).

Revisiting low-fidelity two-fluid models for gas-solids transport

NASA Astrophysics Data System (ADS)

Adeleke, Najeem; Adewumi, Michael; Ityokumbul, Thaddeus

2016-08-01

Two-phase gas-solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas-solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The model equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of Roe-Pike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.

RAXBOD- INVISCID TRANSONIC FLOW OVER AXISYMMETRIC BODIES

NASA Technical Reports Server (NTRS)

Keller, J. D.

1994-01-01

The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output can be generated for the Calcomp plotting system. The RAXBOD program was developed in 1976.

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

NASA Technical Reports Server (NTRS)

Peters, C. (Principal Investigator)

1980-01-01

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

An efficient reliable method to estimate the vaporization enthalpy of pure substances according to the normal boiling temperature and critical properties

PubMed Central

Mehmandoust, Babak; Sanjari, Ehsan; Vatani, Mostafa

2013-01-01

The heat of vaporization of a pure substance at its normal boiling temperature is a very important property in many chemical processes. In this work, a new empirical method was developed to predict vaporization enthalpy of pure substances. This equation is a function of normal boiling temperature, critical temperature, and critical pressure. The presented model is simple to use and provides an improvement over the existing equations for 452 pure substances in wide boiling range. The results showed that the proposed correlation is more accurate than the literature methods for pure substances in a wide boiling range (20.3–722 K). PMID:25685493

An efficient reliable method to estimate the vaporization enthalpy of pure substances according to the normal boiling temperature and critical properties.

PubMed

Mehmandoust, Babak; Sanjari, Ehsan; Vatani, Mostafa

2014-03-01

The heat of vaporization of a pure substance at its normal boiling temperature is a very important property in many chemical processes. In this work, a new empirical method was developed to predict vaporization enthalpy of pure substances. This equation is a function of normal boiling temperature, critical temperature, and critical pressure. The presented model is simple to use and provides an improvement over the existing equations for 452 pure substances in wide boiling range. The results showed that the proposed correlation is more accurate than the literature methods for pure substances in a wide boiling range (20.3-722 K).

High-frequency Born synthetic seismograms based on coupled normal modes

USGS Publications Warehouse

Pollitz, F.

2011-01-01

High-frequency and full waveform synthetic seismograms on a 3-D laterally heterogeneous earth model are simulated using the theory of coupled normal modes. The set of coupled integral equations that describe the 3-D response are simplified into a set of uncoupled integral equations by using the Born approximation to calculate scattered wavefields and the pure-path approximation to modulate the phase of incident and scattered wavefields. This depends upon a decomposition of the aspherical structure into smooth and rough components. The uncoupled integral equations are discretized and solved in the frequency domain, and time domain results are obtained by inverse Fourier transform. Examples show the utility of the normal mode approach to synthesize the seismic wavefields resulting from interaction with a combination of rough and smooth structural heterogeneities. This approach is applied to an ~4 Hz shallow crustal wave propagation around the site of the San Andreas Fault Observatory at Depth (SAFOD). ?? The Author Geophysical Journal International ?? 2011 RAS.

A theory of fine structure image models with an application to detection and classification of dementia

PubMed Central

Penn, Richard; Werner, Michael; Thomas, Justin

2015-01-01

Background Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. Methods In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. Results We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Conclusions Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible. PMID:26029638

System identification of analytical models of damped structures

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

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).

Equation-derived body fat percentage indicates metabolic abnormalities among normal-weight adults in a rural Chinese population.

PubMed

Liu, Xin; Zhao, Yaling; Li, Qiang; Dang, Shaonong; Yan, Hong

2017-07-08

Obesity classification using body mass index (BMI) may miss subjects with elevated body fat percentage (BF%) and related metabolic risk factors. We aimed to evaluate whether BF% calculated by equations could provide more information about metabolic risks, in addition to BMI classification, in a cross-sectional rural Chinese population. A total of 2,990 men and women aged 18-80 years were included in this study. BF% was calculated using previously validated Chinese-specific equations. Metabolic syndrome was defined according to the updated National Cholesterol Education Program Panel III criteria for Asian Americans. In total, 33.6% men and 32.9% women were overweight/obese according to BMI classification. Among those within the normal BMI range, 25.4% men and 54.7% women were indicated as overweight or obese given their elevated BF% (men: BF% ≥ 20%; women: BF% ≥ 30%). In both men and women, compared with those with normal BMI and BF% (NBB), subjects with normal BMI but elevated BF% (NBOB) were more likely to carry abnormal serum lipid profile and to have higher risks of metabolic syndrome. The multivariable adjusted odds ratios (95% confidence intervals) for metabolic syndrome were 5.45 (2.37-9.53, P < 0.001) and 5.65 (3.36-9.52, P < 0.001) for men and women, respectively. Moreover, the women with NBOB also showed higher blood pressure and serum uric acid than women with NBB. Our study suggested that high BF% based on equations may indicate adverse metabolic profiles among rural Chinese adults with a normal BMI. © 2017 Wiley Periodicals, Inc.

Using partially labeled data for normal mixture identification with application to class definition

NASA Technical Reports Server (NTRS)

Shahshahani, Behzad M.; Landgrebe, David A.

1992-01-01

The problem of estimating the parameters of a normal mixture density when, in addition to the unlabeled samples, sets of partially labeled samples are available is addressed. The density of the multidimensional feature space is modeled with a normal mixture. It is assumed that the set of components of the mixture can be partitioned into several classes and that training samples are available from each class. Since for any training sample the class of origin is known but the exact component of origin within the corresponding class is unknown, the training samples as considered to be partially labeled. The EM iterative equations are derived for estimating the parameters of the normal mixture in the presence of partially labeled samples. These equations can be used to combine the supervised and nonsupervised learning processes.

Three-dimensional wideband electromagnetic modeling on massively parallel computers

NASA Astrophysics Data System (ADS)

Alumbaugh, David L.; Newman, Gregory A.; Prevost, Lydie; Shadid, John N.

1996-01-01

A method is presented for modeling the wideband, frequency domain electromagnetic (EM) response of a three-dimensional (3-D) earth to dipole sources operating at frequencies where EM diffusion dominates the response (less than 100 kHz) up into the range where propagation dominates (greater than 10 MHz). The scheme employs the modified form of the vector Helmholtz equation for the scattered electric fields to model variations in electrical conductivity, dielectric permitivity and magnetic permeability. The use of the modified form of the Helmholtz equation allows for perfectly matched layer ( PML) absorbing boundary conditions to be employed through the use of complex grid stretching. Applying the finite difference operator to the modified Helmholtz equation produces a linear system of equations for which the matrix is sparse and complex symmetrical. The solution is obtained using either the biconjugate gradient (BICG) or quasi-minimum residual (QMR) methods with preconditioning; in general we employ the QMR method with Jacobi scaling preconditioning due to stability. In order to simulate larger, more realistic models than has been previously possible, the scheme has been modified to run on massively parallel (MP) computer architectures. Execution on the 1840-processor Intel Paragon has indicated a maximum model size of 280 × 260 × 200 cells with a maximum flop rate of 14.7 Gflops. Three different geologic models are simulated to demonstrate the use of the code for frequencies ranging from 100 Hz to 30 MHz and for different source types and polarizations. The simulations show that the scheme is correctly able to model the air-earth interface and the jump in the electric and magnetic fields normal to discontinuities. For frequencies greater than 10 MHz, complex grid stretching must be employed to incorporate absorbing boundaries while below this normal (real) grid stretching can be employed.

Spin-charge coupled dynamics driven by a time-dependent magnetization

NASA Astrophysics Data System (ADS)

Tölle, Sebastian; Eckern, Ulrich; Gorini, Cosimo

2017-03-01

The spin-charge coupled dynamics in a thin, magnetized metallic system are investigated. The effective driving force acting on the charge carriers is generated by a dynamical magnetic texture, which can be induced, e.g., by a magnetic material in contact with a normal-metal system. We consider a general inversion-asymmetric substrate/normal-metal/magnet structure, which, by specifying the precise nature of each layer, can mimic various experimentally employed setups. Inversion symmetry breaking gives rise to an effective Rashba spin-orbit interaction. We derive general spin-charge kinetic equations which show that such spin-orbit interaction, together with anisotropic Elliott-Yafet spin relaxation, yields significant corrections to the magnetization-induced dynamics. In particular, we present a consistent treatment of the spin density and spin current contributions to the equations of motion, inter alia, identifying a term in the effective force which appears due to a spin current polarized parallel to the magnetization. This "inverse-spin-filter" contribution depends markedly on the parameter which describes the anisotropy in spin relaxation. To further highlight the physical meaning of the different contributions, the spin-pumping configuration of typical experimental setups is analyzed in detail. In the two-dimensional limit the buildup of dc voltage is dominated by the spin-galvanic (inverse Edelstein) effect. A measuring scheme that could isolate this contribution is discussed.

Lorenz system in the thermodynamic modelling of leukaemia malignancy.

PubMed

Alexeev, Igor

2017-05-01

The core idea of the proposed thermodynamic modelling of malignancy in leukaemia is entropy arising within normal haematopoiesis. Mathematically its description is supposed to be similar to the Lorenz system of ordinary differential equations for simplified processes of heat flow in fluids. The hypothetical model provides a description of remission and relapse in leukaemia as two hierarchical and qualitatively different states of normal haematopoiesis with their own phase spaces. Phase space transition is possible through pitchfork bifurcation, which is considered the common symmetrical scenario for relapse, induced remission and the spontaneous remission of leukaemia. Cytopenia is regarded as an adaptive reaction of haematopoiesis to an increase in entropy caused by leukaemia clones. The following predictions are formulated: a) the percentage of leukaemia cells in marrow as a criterion of remission or relapse is not necessarily constant but is a variable value; b) the probability of remission depends upon normal haematopoiesis reaching bifurcation; c) the duration of remission depends upon the eradication of leukaemia cells through induction or consolidation therapies; d) excessively high doses of chemotherapy in consolidation may induce relapse. Copyright © 2017 Elsevier Ltd. All rights reserved.

Dark solitons in laser radiation build-up dynamics.

PubMed

Woodward, R I; Kelleher, E J R

2016-03-01

We reveal the existence of slowly decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schrödinger equation. The evolution of noise perturbations to quasistationary dark solitons is examined, and the significance of background shape and soliton-soliton collisions on the eventual soliton decay is established. We demonstrate the role of a restoring force in extending soliton interactions in conservative systems to include the effects of dissipation, as encountered in laser cavities, and generalize our observations to other nonlinear systems.

Echocardiographic estimation of systemic systolic blood pressure in dogs with mild mitral regurgitation.

PubMed

Tou, Sandra P; Adin, Darcy B; Estrada, Amara H

2006-01-01

Systemic hypertension is likely underdiagnosed in veterinary medicine because systemic blood pressure is rarely measured. Systemic blood pressure can theoretically be estimated by echocardiography. According to the modified Bernoulli equation (PG = 4v(2)), mitral regurgitation (MR) velocity should approximate systolic left ventricular pressure (sLVP), and therefore systolic systemic blood pressure (sSBP) in the presence of a normal left atrial pressure (LAP) and the absence of aortic stenosis. The aim of this study was to evaluate the use of echocardiography to estimate sSBP by means of the Bernoulli equation. Systemic blood pressure can be estimated by echocardiography. Seventeen dogs with mild MR. No dogs had aortic or subaortic stenosis, and all had MR with a clear continuous-wave Doppler signal and a left atrial to aorta ratio of < or = 1.6. Five simultaneous, blinded continuous-wave measurements of maximum MR velocity (Vmax) and indirect sSBP measurements (by Park's Doppler) were obtained for each dog. Pressure gradient was calculated from Vmax by means of the Bernoulli equation, averaged, and added to an assumed LAP of 8 mm Hg to calculate sLVP. Calculated sLVP was significantly correlated with indirectly measured sSBP within a range of 121 to 218 mm Hg (P = .0002, r = .78). Mean +/- SD bias was 0.1 +/- 15.3 mm Hg with limits of agreement of -29.9 to 30.1 mm Hg. Despite the significant correlation, the wide limits of agreement between the methods hinder the clinical utility of echocardiographic estimation of blood pressure.

Anomalous Hydrodynamics and Normal Fluids in Rapidly Rotating Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Bourne, A.; Wilkin, N. K.; Gunn, J. M. F.

2006-06-01

In rapidly rotating condensed Bose systems we show that there is a regime of anomalous hydrodynamics which coincides with the mean field quantum Hall regime. A consequence is the absence of a normal fluid in any conventional sense. However, even the superfluid hydrodynamics is not described by conventional Bernoulli and continuity equations. We show that there are constraints which connect spatial variations of density and phase and that the vortex positions are not the simplest description of the dynamics. We demonstrate, inter alia, a simple relation between vortices and surface waves. We show that the surface waves can emulate a “normal fluid,” allowing dissipation by energy and angular momentum absorbtion from vortex motion in the trap. The time scale is sensitive to the initial configuration, which can lead to long-lived vortex patches—perhaps related to those observed at JILA.

S-Wave Normal Mode Propagation in Aluminum Cylinders

USGS Publications Warehouse

Lee, Myung W.; Waite, William F.

2010-01-01

Large amplitude waveform features have been identified in pulse-transmission shear-wave measurements through cylinders that are long relative to the acoustic wavelength. The arrival times and amplitudes of these features do not follow the predicted behavior of well-known bar waves, but instead they appear to propagate with group velocities that increase as the waveform feature's dominant frequency increases. To identify these anomalous features, the wave equation is solved in a cylindrical coordinate system using an infinitely long cylinder with a free surface boundary condition. The solution indicates that large amplitude normal-mode propagations exist. Using the high-frequency approximation of the Bessel function, an approximate dispersion relation is derived. The predicted amplitude and group velocities using the approximate dispersion relation qualitatively agree with measured values at high frequencies, but the exact dispersion relation should be used to analyze normal modes for full ranges of frequency of interest, particularly at lower frequencies.

Effect of Prestresses on the Dispersion of Quasi-Lamb Waves in the System Consisting of an Ideal Liquid Layer and a Compressible Elastic Layer

NASA Astrophysics Data System (ADS)

Bagno, A. M.

2017-03-01

The propagation of quasi-Lamb waves in a prestrained compressible elastic layer interacting with a layer of an ideal compressible fluid is studied. The three-dimensional equations of linearized elasticity and the assumption of finite strains for the elastic layer and the three-dimensional linearized Euler equations for the fluid are used. The dispersion curves for the quasi-Lamb modes are plotted over a wide frequency range. The effect of prestresses and the thickness of the elastic and liquid layers on the frequency spectrum of normal quasi-Lamb waves is analyzed. The localization properties of the lower quasi-Lamb modes in the elastic-fluid waveguides are studied. The numerical results are presented in the form of graphs and analyzed

SSME thrust chamber simulation using Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of the PHOENICS fluid dynamics code in predicting two-dimensional, compressible, and reacting flow in the combustion chamber and nozzle of the space shuttle main engine (SSME) was evaluated. A non-orthogonal body fitted coordinate system was used to represent the nozzle geometry. The Navier-Stokes equations were solved for the entire nozzle with a turbulence model. The wall boundary conditions were calculated based on the wall functions which account for pressure gradients. Results of the demonstration test case reveal all expected features of the transonic nozzle flows. Of particular interest are the locations of normal and barrel shocks, and regions of highest temperature gradients. Calculated performance (global) parameters such as thrust chamber flow rate, thrust, and specific impulse are also in good agreement with available data.

Failure Assessment of Stainless Steel and Titanium Brazed Joints

NASA Technical Reports Server (NTRS)

Flom, Yury A.

2012-01-01

Following successful application of Coulomb-Mohr and interaction equations for evaluation of safety margins in Albemet 162 brazed joints, two additional base metal/filler metal systems were investigated. Specimens consisting of stainless steel brazed with silver-base filler metal and titanium brazed with 1100 Al alloy were tested to failure under combined action of tensile, shear, bending and torsion loads. Finite Element Analysis (FEA), hand calculations and digital image comparison (DIC) techniques were used to estimate failure stresses and construct Failure Assessment Diagrams (FAD). This study confirms that interaction equation R(sub sigma) + R(sub tau) = 1, where R(sub sigma) and R(sub t u) are normal and shear stress ratios, can be used as conservative lower bound estimate of the failure criterion in stainless steel and titanium brazed joints.

Compressible Flow Toolbox

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.

Explicit solutions of normal form of driven oscillatory systems in entrainment bands

NASA Astrophysics Data System (ADS)

Tsarouhas, George E.; Ross, John

1988-11-01

As in a prior article (Ref. 1), we consider an oscillatory dissipative system driven by external sinusoidal perturbations of given amplitude Q and frequency ω. The kinetic equations are transformed to normal form and solved for small Q near a Hopf bifurcation to oscillations in the autonomous system. Whereas before we chose irrational ratios of the frequency of the autonomous system ωn to ω, with quasiperiodic response of the system to the perturbation, we now choose rational coprime ratios, with periodic response (entrainment). The dissipative system has either two variables or is adequately described by two variables near the bifurcation. We obtain explicit solutions and develop these in detail for ωn/ω=1; 1:2; 2:1; 1:3; 3:1. We choose a specific dissipative model (Brusselator) and test the theory by comparison with full numerical solutions. The analytic solutions of the theory give an excellent approximation for the autonomous system near the bifurcation. The theoretically predicted and calculated entrainment bands agree very well for small Q in the vicinity of the bifurcation (small μ); deviations increase with increasing Q and μ. The theory is applicable to one or two external periodic perturbations.

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

PubMed

Guo, Xiao; Wei, Peijun

2016-03-01

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.

Local equilibrium and the second law of thermodynamics for irreversible systems with thermodynamic inertia.

PubMed

Glavatskiy, K S

2015-10-28

Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative values of the entropy production, which is in contradiction with the second law of thermodynamics. In this paper, we address this question by suggesting a variational formulation of irreversible evolution of a system with non-zero thermodynamic inertia. We introduce the Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" systems. We show that the standard evolution equations, in particular, the Maxwell-Cattaneo-Vernotte equation, can be derived from the variational procedure without going beyond the assumption of local equilibrium. We also argue that the second law of thermodynamics in non-equilibrium should be understood as a consequence of the variational procedure and the property of local equilibrium. For systems with instantaneous response this leads to the standard requirement of the local instantaneous entropy production being always positive. However, if a system is characterized by delayed response, the formulation of the second law of thermodynamics should be altered. In particular, the quantity, which is always positive, is not the instantaneous entropy production, but the entropy production averaged over a proper time interval.

Generalized Langevin equation with tempered memory kernel

NASA Astrophysics Data System (ADS)

Liemert, André; Sandev, Trifce; Kantz, Holger

2017-01-01

We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes.

A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth

PubMed Central

Macklin, Paul

2011-01-01

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth. PMID:21331304

Newtonian self-gravitating system in a relativistic huge void universe model

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

Nishikawa, Ryusuke; Nakao, Ken-ichi; Yoo, Chul-Moon, E-mail: ryusuke@sci.osaka-cu.ac.jp, E-mail: knakao@sci.osaka-cu.ac.jp, E-mail: yoo@gravity.phys.nagoya-u.ac.jp

We consider a test of the Copernican Principle through observations of the large-scale structures, and for this purpose we study the self-gravitating system in a relativistic huge void universe model which does not invoke the Copernican Principle. If we focus on the the weakly self-gravitating and slowly evolving system whose spatial extent is much smaller than the scale of the cosmological horizon in the homogeneous and isotropic background universe model, the cosmological Newtonian approximation is available. Also in the huge void universe model, the same kind of approximation as the cosmological Newtonian approximation is available for the analysis of themore » perturbations contained in a region whose spatial size is much smaller than the scale of the huge void: the effects of the huge void are taken into account in a perturbative manner by using the Fermi-normal coordinates. By using this approximation, we derive the equations of motion for the weakly self-gravitating perturbations whose elements have relative velocities much smaller than the speed of light, and show the derived equations can be significantly different from those in the homogeneous and isotropic universe model, due to the anisotropic volume expansion in the huge void. We linearize the derived equations of motion and solve them. The solutions show that the behaviors of linear density perturbations are very different from those in the homogeneous and isotropic universe model.« less

Time dependent Schrödinger equation for black hole evaporation: No information loss

NASA Astrophysics Data System (ADS)

Corda, Christian

2015-02-01

In 1976 S. Hawking claimed that "Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state".1 In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking's claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect 't Hooft's assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.

Simulating Bone Loss in Microgravity Using Mathematical Formulations of Bone Remodeling

NASA Technical Reports Server (NTRS)

Pennline, James A.

2009-01-01

Most mathematical models of bone remodeling are used to simulate a specific bone disease, by disrupting the steady state or balance in the normal remodeling process, and to simulate a therapeutic strategy. In this work, the ability of a mathematical model of bone remodeling to simulate bone loss as a function of time under the conditions of microgravity is investigated. The model is formed by combining a previously developed set of biochemical, cellular dynamics, and mechanical stimulus equations in the literature with two newly proposed equations; one governing the rate of change of the area of cortical bone tissue in a cross section of a cylindrical section of bone and one governing the rate of change of calcium in the bone fluid. The mechanical stimulus comes from a simple model of stress due to a compressive force on a cylindrical section of bone which can be reduced to zero to mimic the effects of skeletal unloading in microgravity. The complete set of equations formed is a system of first order ordinary differential equations. The results of selected simulations are displayed and discussed. Limitations and deficiencies of the model are also discussed as well as suggestions for further research.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Kreider, K. L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Dynamic Stability of a Cylindrical Shell Stiffened with a Cylinder and Longitudinal Diaphragms at External Pressure

NASA Astrophysics Data System (ADS)

Bakulin, V. N.; Danilkin, E. V.; Nedbai, A. Ya.

2018-05-01

A study has been made of the dynamic stability of a cylindrical orthotropic shell stiffened with a hollow cylinder and inhomogeneous longitudinal diaphragms under the action of axial forces and pulsating external pressure. The influence of the cylinder and diaphragms on the stability of the shell was taken account of in the form of elastic foundations whose moduli of subgrade reaction are determined from the equations of a three-dimensional theory of elasticity and the Timoshenko model respectively. A solution to the equation of motion of the shell has been found in the form of a trigonometric circumferential-coordinate series. To construct the principal region of instability of the shell, a binomial approximation was used in the obtained Mathieu-Hill equations. As a result, the problem was reduced to a system of two algebraic equations for normal displacement of the shell at diaphragm installation sites. For uniformly spaced identical diaphragms, a solution has been obtained in explicit form. The dependences of the principal region of instability of the shell on the number and rigidity of the diaphragms have been determined at different radii of the cylinder channel.

The Kolmogorov-Obukhov Statistical Theory of Turbulence

NASA Astrophysics Data System (ADS)

Birnir, Björn

2013-08-01

In 1941 Kolmogorov and Obukhov postulated the existence of a statistical theory of turbulence, which allows the computation of statistical quantities that can be simulated and measured in a turbulent system. These are quantities such as the moments, the structure functions and the probability density functions (PDFs) of the turbulent velocity field. In this paper we will outline how to construct this statistical theory from the stochastic Navier-Stokes equation. The additive noise in the stochastic Navier-Stokes equation is generic noise given by the central limit theorem and the large deviation principle. The multiplicative noise consists of jumps multiplying the velocity, modeling jumps in the velocity gradient. We first estimate the structure functions of turbulence and establish the Kolmogorov-Obukhov 1962 scaling hypothesis with the She-Leveque intermittency corrections. Then we compute the invariant measure of turbulence, writing the stochastic Navier-Stokes equation as an infinite-dimensional Ito process, and solving the linear Kolmogorov-Hopf functional differential equation for the invariant measure. Finally we project the invariant measure onto the PDF. The PDFs turn out to be the normalized inverse Gaussian (NIG) distributions of Barndorff-Nilsen, and compare well with PDFs from simulations and experiments.

How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics.

PubMed

Nguyen, Triet S; Nanguneri, Ravindra; Parkhill, John

2015-04-07

It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old concept, but we show how they can be derived with a combination of time-dependent perturbation theory and the extended normal ordering of Mukherjee and Kutzelnigg for a general electronic state. The resulting non-equilibrium kinetic equations generalize the usual Redfield theory to many-electron systems, while ensuring that the orbital occupations remain between zero and one. In numerical applications of our equations, we show that relaxation rates of molecules are not constant because of the blocking effect. Other applications to model atomic chains are also presented which highlight the importance of treating both dephasing and relaxation. Finally, we show how the bath localizes the electron density matrix.

Thermoluminescence kinetics of pyrite (FeS2)

NASA Astrophysics Data System (ADS)

Silverman, A. N.; Levy, P. W.; Kierstead, J. A.

Thermoluminescence of pyrite (FeS2) was investigated to study the kinetics of single peak glow curves. The material used normally exhibits one large and four small peaks. However a glow curve can be obtained with only the large single peak that is suitable for testing thermoluminescence kinetics. Glow curves from aliquots of a single natural pyrite crystal studied in detail contain two low intensity thermoluminescence (TL) peaks at approximately 90 and 250 C, and two chemiluminescence (CL) peaks at approximately 350 and 430 C. The CL peaks are largely removable by initially heating the sample chamber under vacuum, pumping through liquid nitrogen traps, and recording glow curves immediately after helium is introduced, procedures which reduce system contaminants that react with pyrite. The shape, the variation of the temperature of the peak maximum (T(sub max)) with dose, and the retrapping to recombination cross section ratio (sigma) of the large 250 C peak are better described by the general one trap (GOT) kinetic equation, the basic equation from which the 1st and 2nd order kinetic equations are obtained as special cases, than by the 1st and 2nd order equations.

Hydrodynamics of Normal Atomic Gases with Spin-orbit Coupling

PubMed Central

Hou, Yan-Hua; Yu, Zhenhua

2015-01-01

Successful realization of spin-orbit coupling in atomic gases by the NIST scheme opens the prospect of studying the effects of spin-orbit coupling on many-body physics in an unprecedentedly controllable way. Here we derive the linearized hydrodynamic equations for the normal atomic gases of the spin-orbit coupling by the NIST scheme with zero detuning. We show that the hydrodynamics of the system crucially depends on the momentum susceptibilities which can be modified by the spin-orbit coupling. We reveal the effects of the spin-orbit coupling on the sound velocities and the dipole mode frequency of the gases by applying our formalism to the ideal Fermi gas. We also discuss the generalization of our results to other situations. PMID:26483090

Hydrodynamics of Normal Atomic Gases with Spin-orbit Coupling.

PubMed

Hou, Yan-Hua; Yu, Zhenhua

2015-10-20

Successful realization of spin-orbit coupling in atomic gases by the NIST scheme opens the prospect of studying the effects of spin-orbit coupling on many-body physics in an unprecedentedly controllable way. Here we derive the linearized hydrodynamic equations for the normal atomic gases of the spin-orbit coupling by the NIST scheme with zero detuning. We show that the hydrodynamics of the system crucially depends on the momentum susceptibilities which can be modified by the spin-orbit coupling. We reveal the effects of the spin-orbit coupling on the sound velocities and the dipole mode frequency of the gases by applying our formalism to the ideal Fermi gas. We also discuss the generalization of our results to other situations.

Non-algebraic integrability of the Chew-Low reversible dynamical system of the Cremona type and the relation with the 7th Hilbert problem (non-resonant case)

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

A smooth reversible dynamical system (SRDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions (the Chew-Low equations for p- wave πN- scattering) are considered. This SRDS is splitted into 1- and 2-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous 3-point functional equation. Non-algebraic integrability of SRDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a non-resonant fixed point. The proof is based on the classical Feldman-Baker theorem on linear forms of logarithms of algebraic numbers, which, in turn, relies upon solving the 7th Hilbert problem by A.I. Gel'fond and T. Schneider and new powerful methods of A. Baker in the theory of transcendental numbers. The general theorem, following from the Feldman-Baker theorem, on applicability of the Siegel theorem to the set of the eigenvalues λ ɛ Cn of a mapping at a non-resonant fixed point which belong to the algebraic number field A is formulated and proved. The main results are presented in Theorems 1-3, 5, 7, 8 and Remarks 3, 7.

Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM

NASA Astrophysics Data System (ADS)

Asemi, S. R.; Farajpour, A.; Asemi, H. R.; Mohammadi, M.

2014-09-01

In this paper, a nonlocal continuum plate model is developed for the transverse vibration of double-piezoelectric-nanoplate systems (DPNPSs) with initial stress under an external electric voltage. The Pasternak foundation model is employed to take into account the effect of shearing between the two piezoelectric nanoplates in combination with normal behavior of coupling elastic medium. Size effects are taken into consideration using nonlocal continuum mechanics. Hamilton's principle is used to derive the differential equations of motion. The governing equations are solved for various boundary conditions by using the differential quadrature method (DQM). In addition, exact solutions are presented for the natural frequencies and critical electric voltages of DPNPS under biaxial prestressed conditions in in-phase and out-of-phase vibrational modes. It is shown that the natural frequencies of the DPNPS are quite sensitive to both nonlocal parameter and initial stress. The effects of in-plane preload and small scale are very important in the resonance mode of smart nanostructures using piezoelectric nanoplates.

Comparisons of Backscattering from Cylindrical Shells Described by Thin Shell and Elasticity Theories.

DTIC Science & Technology

1991-03-04

term that describes inextensional motion. The first equation represents the normal stress at the midsurface of the shell, which is equal to the...that the normal velocity at the midsurface of the shell is proportional to the normal derivative of the total pressw e. The scattered pressure ps can

3j Symbols: To Normalize or Not to Normalize?

ERIC Educational Resources Information Center

van Veenendaal, Michel

2011-01-01

The systematic use of alternative normalization constants for 3j symbols can lead to a more natural expression of quantities, such as vector products and spherical tensor operators. The redefined coupling constants directly equate tensor products to the inner and outer products without any additional square roots. The approach is extended to…

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

DOE PAGES

Moral, Pierre Del; Jasra, Ajay; Law, Kody J. H.; ...

2017-08-24

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of themore » solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.« less

Fluctuation, dissipation, and a non-equilibrium ``equation of state'' via nonlinear microrheology of hydrodynamically interacting colloids

NASA Astrophysics Data System (ADS)

Chu, Henry; Zia, Roseanna

2014-11-01

In our recently developed non-equilibrium Stokes-Einstein relation for microrheology, we showed that, in the absence of hydrodynamic interactions, the stress in a suspension is given by a balance between fluctuation and dissipation. Here we generalize our theory to develop a simple analytical relation connecting diffusive fluctuation, viscous dissipation and suspension stress in systems of hydrodynamically interacting colloids. In active microrheology, a Brownian probe is driven through a complex medium. The strength of probe forcing compared to the entropic restoring force defines a Peclet number, Pe. In the absence of hydrodynamics, normal stress differences scale as Pe4 and Pe for weak and strong probe forcing, respectively. But as hydrodynamics become important, interparticle forces give way to lubrication interactions and the normal stresses scale as Pe2 and Peδln(Pe), where 0.773 <= δ <= 1 as hydrodynamics vary from strong to weak. The new phenomenological theory is shown to agree with standard micromechanical definitions of the stress. A connection is made between the stress and an effective temperature of the medium, prompting the interpretation of the particle stress as the energy density, and the expression for osmotic pressure as a ``non-equilibrium equation of state.''

Electrocardiogram classification using delay differential equations

NASA Astrophysics Data System (ADS)

Lainscsek, Claudia; Sejnowski, Terrence J.

2013-06-01

Time series analysis with nonlinear delay differential equations (DDEs) reveals nonlinear as well as spectral properties of the underlying dynamical system. Here, global DDE models were used to analyze 5 min data segments of electrocardiographic (ECG) recordings in order to capture distinguishing features for different heart conditions such as normal heart beat, congestive heart failure, and atrial fibrillation. The number of terms and delays in the model as well as the order of nonlinearity of the model have to be selected that are the most discriminative. The DDE model form that best separates the three classes of data was chosen by exhaustive search up to third order polynomials. Such an approach can provide deep insight into the nature of the data since linear terms of a DDE correspond to the main time-scales in the signal and the nonlinear terms in the DDE are related to nonlinear couplings between the harmonic signal parts. The DDEs were able to detect atrial fibrillation with an accuracy of 72%, congestive heart failure with an accuracy of 88%, and normal heart beat with an accuracy of 97% from 5 min of ECG, a much shorter time interval than required to achieve comparable performance with other methods.

GOCO05c: A New Combined Gravity Field Model Based on Full Normal Equations and Regionally Varying Weighting

NASA Astrophysics Data System (ADS)

Fecher, T.; Pail, R.; Gruber, T.

2017-05-01

GOCO05c is a gravity field model computed as a combined solution of a satellite-only model and a global data set of gravity anomalies. It is resolved up to degree and order 720. It is the first model applying regionally varying weighting. Since this causes strong correlations among all gravity field parameters, the resulting full normal equation system with a size of 2 TB had to be solved rigorously by applying high-performance computing. GOCO05c is the first combined gravity field model independent of EGM2008 that contains GOCE data of the whole mission period. The performance of GOCO05c is externally validated by GNSS-levelling comparisons, orbit tests, and computation of the mean dynamic topography, achieving at least the quality of existing high-resolution models. Results show that the additional GOCE information is highly beneficial in insufficiently observed areas, and that due to the weighting scheme of individual data the spectral and spatial consistency of the model is significantly improved. Due to usage of fill-in data in specific regions, the model cannot be used for physical interpretations in these regions.

Evaluation of bridge-scour data at selected sites in Ohio

USGS Publications Warehouse

Jackson, K.S.

1997-01-01

Scour data collected during 1989-94 were evaluated to determine whether pier scour and contraction scour occurred at 22 bridge sites in Ohio. Pier-scour depths computed from selected pier-scour prediction equations were compared with measured pier-scour depths, and the accuracy of the prediction equations were evaluated. Observed pier-scour relations were compared to relations developed through laboratory research. Mean streambed elevations were evaluated to determine the depth of contraction scour. Channel stability was assessed by use of mean streambed elevations at the approach section. Ground-penetrating radar was used at all sites to investigate the presence of historical scour. Pier scour was observed in 45 of 47 scour measurements made during floods; 84 cases of pier scour were documented, 83 at solid-wall piers and 1 at a capped-pile type pier. Estimated recurrence intervals for 27 of the 35 measured streamflows, all on unregulated streams, were less than 2 years. Seventeen pier-scour prediction equations were evaluated. The Froehlich Design equation was found to most closely meet the 'best design equation' criteria for all 84 cases of the observed data. The Larras equation was found to be the best design equation for the observed data where approach-flow attack angles were 10 degrees or less. Observed pier-scour depths and flow depths ranged from 0.5 to 6.1 feet and 3.0 to 19.8 feet, respectively. All pier-scour depths were less than 2.4 times the corresponding pier width. Selected factors were normalized by dividing by effective pier width. LOWESS curves were developed using the 84 cases of observed pier scour. Normalized scour depth increased with normalized flow depth; however, the rate of increase appeared to lessen as normalized flow depth exceeded 2.5. Normalized scour depths increased rapidly as flow intensity approached the threshold value of 1 and then decreased as flow intensities exceeded this threshold. Normalized scour depth was found to increase with Froude number, and a steeper slope was evident for Froude numbers exceeding 0.2. Normalized scour depth was found to increase with median grain size up to about 10 millimeters for bed material near the pier, then decrease for median grain sizes greater than 10 millimeters. Normalized scour depth was also found to decrease as sediment gradation of bed material near the pier increased. The observed pier-scour relations determined from the field measurements tend to support conclusions by previous researchers of streambed scour, except for the previous finding that normalized scour depth decreases consistently with increasing median grain size. Possible factors that may have influenced the observed trends in the relation between normalized scour depth and median grain size in this study are cohesion and scour measurements made at nonequilibrium conditions. LOWESS curves were developed for 45 of 84 cases of observed pier scour where approach-flow attack angles were less than or equal to 10 degrees. These curves were visually compared to LOWESS curves developed from all observations of pier scour. For three relations, differences in the trends of the LOWESS curves were of sufficient magnitude to warrant discussion. Contraction scour was observed in 4 of the 47 scour measurements and ranged from 0.8 to2.3 feet in depth. Analysis of annual mean streambed approach-section elevations indicated that approach sections were generally stable at 18 of the 22 sites. Ground-penetrating radar, a geophysical method that enables subsurface exploration of the streambed when conditions are favorable, was used at all sites to determine whether historical scour had occurred. Results of the ground-penetrating radar surveys at 20 sites in 1990 indicated the presence of historical scour surfaces at 5 sites. At four of the five sites showing evidence of possible historical scour, differences between the estimated depth of historical scour and the maximum observed scour were w

Ballistic limit regression analysis for Space Station Freedom meteoroid and space debris protection system

NASA Technical Reports Server (NTRS)

Jolly, William H.

1992-01-01

Relationships defining the ballistic limit of Space Station Freedom's (SSF) dual wall protection systems have been determined. These functions were regressed from empirical data found in Marshall Space Flight Center's (MSFC) Hypervelocity Impact Testing Summary (HITS) for the velocity range between three and seven kilometers per second. A stepwise linear least squares regression was used to determine the coefficients of several expressions that define a ballistic limit surface. Using statistical significance indicators and graphical comparisons to other limit curves, a final set of expressions is recommended for potential use in Probability of No Critical Flaw (PNCF) calculations for Space Station. The three equations listed below represent the mean curves for normal, 45 degree, and 65 degree obliquity ballistic limits, respectively, for a dual wall protection system consisting of a thin 6061-T6 aluminum bumper spaced 4.0 inches from a .125 inches thick 2219-T87 rear wall with multiple layer thermal insulation installed between the two walls. Normal obliquity is d(sub c) = 1.0514 v(exp 0.2983 t(sub 1)(exp 0.5228). Forty-five degree obliquity is d(sub c) = 0.8591 v(exp 0.0428) t(sub 1)(exp 0.2063). Sixty-five degree obliquity is d(sub c) = 0.2824 v(exp 0.1986) t(sub 1)(exp -0.3874). Plots of these curves are provided. A sensitivity study on the effects of using these new equations in the probability of no critical flaw analysis indicated a negligible increase in the performance of the dual wall protection system for SSF over the current baseline. The magnitude of the increase was 0.17 percent over 25 years on the MB-7 configuration run with the Bumper II program code.

Ballistic limit regression analysis for Space Station Freedom meteoroid and space debris protection system

NASA Astrophysics Data System (ADS)

Jolly, William H.

1992-05-01

Relationships defining the ballistic limit of Space Station Freedom's (SSF) dual wall protection systems have been determined. These functions were regressed from empirical data found in Marshall Space Flight Center's (MSFC) Hypervelocity Impact Testing Summary (HITS) for the velocity range between three and seven kilometers per second. A stepwise linear least squares regression was used to determine the coefficients of several expressions that define a ballistic limit surface. Using statistical significance indicators and graphical comparisons to other limit curves, a final set of expressions is recommended for potential use in Probability of No Critical Flaw (PNCF) calculations for Space Station. The three equations listed below represent the mean curves for normal, 45 degree, and 65 degree obliquity ballistic limits, respectively, for a dual wall protection system consisting of a thin 6061-T6 aluminum bumper spaced 4.0 inches from a .125 inches thick 2219-T87 rear wall with multiple layer thermal insulation installed between the two walls. Normal obliquity is d(sub c) = 1.0514 v(exp 0.2983 t(sub 1)(exp 0.5228). Forty-five degree obliquity is d(sub c) = 0.8591 v(exp 0.0428) t(sub 1)(exp 0.2063). Sixty-five degree obliquity is d(sub c) = 0.2824 v(exp 0.1986) t(sub 1)(exp -0.3874). Plots of these curves are provided. A sensitivity study on the effects of using these new equations in the probability of no critical flaw analysis indicated a negligible increase in the performance of the dual wall protection system for SSF over the current baseline. The magnitude of the increase was 0.17 percent over 25 years on the MB-7 configuration run with the Bumper II program code.

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.

Computation of Laminar and Turbulent Flow in 90-Degree Square-Duct and Pipe Bends Using the Navier-Stokes Equations

DTIC Science & Technology

1982-04-01

R.M. and Warming, R.F.: An Implicit Finite - Difference Algorithm for Hyperbolic Systems in Conservation Law Form. Journal of Computational Physics...Quincy Street C-40) Arlington, VA 22217 D 82 05-.10 I0, S4CURITY CLASSIFICATION OF THIS ’E(Wha, Doae Entotwed) Slength scale. Six different flow cases...forces upstream have produced a non-zero velocity gradient normal to the plane of curvature. Fluid with above (/below) average nioiiiei.tuili migrates

The hydrogen atom in D = 3 - 2ɛ dimensions

NASA Astrophysics Data System (ADS)

Adkins, Gregory S.

2018-06-01

The nonrelativistic hydrogen atom in D = 3 - 2 ɛ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the D-dimensional Schrödinger-Coulomb equation are given in the form of a double power series. Energies and normalization integrals are obtained numerically and also perturbatively in terms of ɛ. The utility of the series expansion is demonstrated by the calculation of the divergent expectation value <(V‧)2 >.

Proceedings of the Scientific Conference on Obscuration and Aerosol Research Held in Aberdeen Maryland on 27-30 June 1989

DTIC Science & Technology

1990-08-01

corneal structure for both normal and swollen corneas. Other problems of future interest are the understanding of the structure of scarred and dystrophied ...METHOD AND RESULTS The system of equations is solved numerically on a Cray X-MP by a finite element method with 9-node Lagrange quadrilaterals ( Becker ...Appl. Math., 42, 430. Becker , E. B., G. F. Carey, and J. T. Oden, 1981. Finite Elements: An Introduction (Vol. 1), Prentice- Hall, Englewood Cliffs, New

Navy Quality of Life and Reenlistment.

DTIC Science & Technology

1981-11-01

Problema with Unique Solution,- 20 pp., Jun 1976, 234-253) AD AOSS 536 AD AO SYSpp 223 pp 213 Mengel . Marc. *StOdetlc Mechanics of Moleoloion thloule... Mengel . Marc. ’Fluctuations In Systeme with Multiple Steady lesecttons.’ 21 pp.. Jan 1978. AD AD%6 227 Stetes. Application to Landmaster Equations,’ 12 pp...Qirrot Mengel , bee ead QuenAw*, Gould D.. ’Ilop aleam of a 0Ias~ Facing oer movet and Busanss Learsa presented by Slverlsto Normal Oe as Offet CIrcle

Decreased GFR estimated by MDRD or Cockcroft-Gault equation predicts incident CVD: the strong heart study.

PubMed

Shara, Nawar M; Resnick, Helaine E; Lu, Li; Xu, Jiaqiong; Vupputuri, Suma; Howard, Barbara V; Umans, Jason G

2009-01-01

Kidney function, expressed as glomerular filtration rate (GFR), is commonly estimated from serum creatinine (Scr) and, when decreased, may serve as a nonclassical risk factor for incident cardiovascular disease (CVD). The ability of estimated GFR (eGFR) to predict CVD events during 5-10 years of follow-up is assessed using data from the Strong Heart Study (SHS), a large cohort with a high prevalence of diabetes. eGFRs were calculated with the abbreviated Modification of Diet in Renal Disease study (MDRD) and the Cockcroft-Gault (CG) equations. These estimates were compared in participants with normal and abnormal Scr. The association between eGFR and incident CVD was assessed. More subjects were labeled as having low eGFR (<60 ml/min per 1.73 m2) by the MDRD or CG equation, than by Scr alone. When Scr was in the normal range, both equations labeled similar numbers of participants as having low eGFRs, although concordance between the equations was poor. However, when Scr was elevated, the MDRD equation labeled more subjects as having low eGFR. Persons with low eGFR had increased risk of CVD. The MDRD and CG equations labeled more participants as having decreased GFR than did Scr alone. Decreased eGFR was predictive of CVD in this American Indian population with a high prevalence of obesity and type 2 diabetes mellitus.

Inhomogeneous quasistationary state of dense fluids of inelastic hard spheres

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak

2014-05-01

We study closed dense collections of freely cooling hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (ISs) where the density profile is spatially nonuniform but constant in time. The states are exact solutions of nonlinear partial differential equations that describe the coupled distributions of density and temperature valid when inelastic losses of energy per collision are small. The derivation is performed without modeling the equations' coefficients that are unknown in the dense limit (such as the equation of state) using only their scaling form specific for hard spheres. Thus the IS is the exact state of this dense many-body system. It captures a fundamental property of inelastic collections of particles: the possibility of preserving nonuniform temperature via the interplay of inelastic cooling and heat conduction that generalizes previous results. We perform numerical simulations to demonstrate that arbitrary initial state evolves to the IS in the limit of long times where the container has the geometry of the channel. The evolution is like a gas-liquid transition. The liquid condenses in a vanishing part of the total volume but takes most of the mass of the system. However, the gaseous phase, which mass grows only logarithmically with the system size, is relevant because its fast particles carry most of the energy of the system. Remarkably, the system self-organizes to dissipate no energy: The inelastic decay of energy is a power law [1+t/tc]-2, where tc diverges in the thermodynamic limit. This is reinforced by observing that for supercritical systems the IS coincide in most of the space with the steady states of granular systems heated at one of the walls. We discuss the relation of our results to the recently proposed finite-time singularity in other container's geometries.

Solution of the Burnett equations for hypersonic flows near the continuum limit

NASA Technical Reports Server (NTRS)

Imlay, Scott T.

1992-01-01

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

Study of the convective fluid flows with evaporation on the basis of the exact solution in a three-dimensional infinite channel

NASA Astrophysics Data System (ADS)

Bekezhanova, V. B.; Goncharova, O. N.

2017-09-01

The solution of special type of the Boussinesq approximation of the Navier - Stokes equations is used to simulate the two-layer evaporative fluid flows. This solution is the 3D generalization of the Ostroumov - Birikh solution of the equations of free convection. Modeling of the 3D fluid flows is performed in an infinite channel of the rectangular cross section without assumption of the axis-symmetrical character of the flows. Influence of gravity and evaporation on the dynamic and thermal phenomena in the system is studied. The fluid flow patterns are determined by various thermal, mechanical and structural effects. Numerical investigations are performed for the liquid - gas system like ethanol - nitrogen and HFE-7100 - nitrogen under conditions of normal and low gravity. The solution allows one to describe a formation of the thermocapillary rolls and multi-vortex structures in the system. Alteration of topology and character of the flows takes place with change of the intensity of the applied thermal load, thermophysical properties of working media and gravity action. Flows with translational, translational-rotational or partially reverse motion can be formed in the system.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Revisiting low-fidelity two-fluid models for gas–solids transport

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

Adeleke, Najeem, E-mail: najm@psu.edu; Adewumi, Michael, E-mail: m2a@psu.edu; Ityokumbul, Thaddeus

Two-phase gas–solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas–solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The modelmore » equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of Roe–Pike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.« less

A coordinate free description of magnetohydrostatic equilibria

NASA Technical Reports Server (NTRS)

Martens, P. C. H.

1986-01-01

The question what geometrical restrictions are imposed on static magnetic fields by the magnetohydrostatic (MHS) equation is addressed. The general mathematical problem is therefore to determine the solutions of the MHS equations in the corona subject to an arbitrary normal component of the magnetic field at the boundary and arbitrary connectivity. What constraints the MHS equations impose on the geometry of the solutions, expressed in metric tensors, will be determined.

Renormalized vibrations and normal energy transport in 1d FPU-like discrete nonlinear Schrödinger equations.

PubMed

Li, Simeng; Li, Nianbei

2018-03-28

For one-dimensional (1d) nonlinear atomic lattices, the models with on-site nonlinearities such as the Frenkel-Kontorova (FK) and ϕ 4 lattices have normal energy transport while the models with inter-site nonlinearities such as the Fermi-Pasta-Ulam-β (FPU-β) lattice exhibit anomalous energy transport. The 1d Discrete Nonlinear Schrödinger (DNLS) equations with on-site nonlinearities has been previously studied and normal energy transport has also been found. Here, we investigate the energy transport of 1d FPU-like DNLS equations with inter-site nonlinearities. Extended from the FPU-β lattice, the renormalized vibration theory is developed for the FPU-like DNLS models and the predicted renormalized vibrations are verified by direct numerical simulations same as the FPU-β lattice. However, the energy diffusion processes are explored and normal energy transport is observed for the 1d FPU-like DNLS models, which is different from their atomic lattice counterpart of FPU-β lattice. The reason might be that, unlike nonlinear atomic lattices where models with on-site nonlinearities have one less conserved quantities than the models with inter-site nonlinearities, the DNLS models with on-site or inter-site nonlinearities have the same number of conserved quantities as the result of gauge transformation.

Three-dimensional inverse problem of geometrical optics: a mathematical comparison between Fermat's principle and the eikonal equation.

PubMed

Borghero, Francesco; Demontis, Francesco

2016-09-01

In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c₁,g(x,y,z)=c₂), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions.

DRBEM solution of the acid-mediated tumour invasion model with time-dependent carrying capacities

NASA Astrophysics Data System (ADS)

Meral, Gülnihal

2017-07-01

It is known that the pH level of the extracellular tumour environment directly effects the progression of the tumour. In this study, the mathematical model for the acid-mediated tumour cell invasion consisting of a system of nonlinear reaction diffusion equations describing the interaction between the density of the tumour cells, normal cells and the concentration of ? protons produced by the tumour cells is solved numerically using the combined application of dual reciprocity boundary element method (DRBEM) and finite difference method. The space derivatives in the model are discretised by DRBEM using the fundamental solution of Laplace equation considering the time derivative and the nonlinearities as the nonhomogenity. The resulting systems of ordinary differential equations after the application of DRBEM are then discretised using forward difference. Because of the highly nonlinear character of the model, there arises difficulties in solving the model especially for two-dimensions and the boundary-only nature of DRBEM discretisation gives the advantage of having solutions with a lower computational cost. The proposed method is tested with different kinds of carrying capacities which also depend on time. The results of the numerical simulations are compared among each case and seen to confirm the expected behaviour of the model.

Three-Dimensional Magnetohydrodynamic Modeling of the Solar Wind Including Pickup Protons and Turbulence Transport

NASA Technical Reports Server (NTRS)

Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.

2012-01-01

To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfer from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons.We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 deg - .90 deg and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.

Aspheric surface testing by irradiance transport equation

NASA Astrophysics Data System (ADS)

Shomali, Ramin; Darudi, Ahmad; Nasiri, Sadollah; Asgharsharghi Bonab, Armir

2010-10-01

In this paper a method for aspheric surface testing is presented. The method is based on solving the Irradiance Transport Equation (ITE).The accuracy of ITE normally depends on the amount of the pick to valley of the phase distribution. This subject is investigated by a simulation procedure.

Geometrically Nonlinear Transient Analysis of Laminated Composite Plates.

DTIC Science & Technology

1982-03-01

theory (CPT), in which normals to the midsurface before deformation are assumed to remain straight and normal to the midsurface after deformation (i.e...the plate are negligible when compared to the inplane stresses, and normals to the plate midsurface before deformation remain straight but not...necessarily normal to the midsurface after deformation. $ Equations of motion The plate under consideration is composed of a finite number of orthotropic

Dimensional scaling for impact cratering and perforation

NASA Technical Reports Server (NTRS)

Watts, Alan; Atkinson, Dale; Rieco, Steve

1993-01-01

This report summarizes the development of two physics-based scaling laws for describing crater depths and diameters caused by normal incidence impacts into aluminum and TFE Teflon. The report then describes equations for perforations in aluminum and TFE Teflon for normal impacts. Lastly, this report also studies the effects of non-normal incidence on cratering and perforation.

Development of an Integrated Modeling Framework for Simulations of Coastal Processes in Deltaic Environments Using High-Performance Computing

DTIC Science & Technology

2008-01-01

exceeds the local water depth. The approximation eliminates the vertical dimension of the elliptic equation that is normally required for the fully non...used for vertical resolution. The shallow water equations (SWE) are a set of non-linear hyperbolic equations. As the equations are derived under...linear standing wave with a wavelength of 10 m in a square 10 m by 10 m basin. The still water depth is 0.5 m. In order to compare with the analytical

Similarity of Turbulent Energy Scale Budget Equation of a Round Turbulent Jet

NASA Astrophysics Data System (ADS)

Sadeghi, Hamed; Lavoie, Philippe; Pollard, Andrew

2014-11-01

A novel extension to the similarity-based form of the transport equation for the second-order velocity structure function of <(δq) 2 > along the jet centreline (see Danaila et al., 2004) has been obtained. This new self-similar equation has the desirable benefit of requiring less extensive measurements to calculate the inhomogeneous (decay and production) terms of the transport equation. According to this equation, the normalized third-order structure function can be uniquely determined when the normalized second-order structure function, the power-law exponent of and the decay rate constants of and are available. In addition, on the basis of the current similarity analysis, the similarity assumptions in combination with power-law decay of mean velocity (U ~(x -x0) - 1) are strong enough to imply power-law decay of fluctuations ( ~(x -x0) m). The similarity solutions are then tested against new experimental data, which were taken along the centreline of a round jet at ReD = 50 , 000 . For the present set of initial conditions, exhibits a power-law behaviour with m = - 1 . 83 . This work was supported by grants from NSERC (Canada).

Evaluation and interpretation of Thematic Mapper ratios in equations for estimating corn growth parameters

NASA Technical Reports Server (NTRS)

Dardner, B. R.; Blad, B. L.; Thompson, D. R.; Henderson, K. E.

1985-01-01

Reflectance and agronomic Thematic Mapper (TM) data were analyzed to determine possible data transformations for evaluating several plant parameters of corn. Three transformation forms were used: the ratio of two TM bands, logarithms of two-band ratios, and normalized differences of two bands. Normalized differences and logarithms of two-band ratios responsed similarly in the equations for estimating the plant growth parameters evaluated in this study. Two-term equations were required to obtain the maximum predictability of percent ground cover, canopy moisture content, and total wet phytomass. Standard error of estimate values were 15-26 percent lower for two-term estimates of these parameters than for one-term estimates. The terms log(TM4/TM2) and (TM4/TM5) produced the maximum predictability for leaf area and dry green leaf weight, respectively. The middle infrared bands TM5 and TM7 are essential for maximizing predictability for all measured plant parameters except leaf area index. The estimating models were evaluated over bare soil to discriminate between equations which are statistically similar. Qualitative interpretations of the resulting prediction equations are consistent with general agronomic and remote sensing theory.

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.

Stability and global Hopf bifurcation in a delayed food web consisting of a prey and two predators

NASA Astrophysics Data System (ADS)

Meng, Xin-You; Huo, Hai-Feng; Zhang, Xiao-Bing

2011-11-01

This paper is concerned with a predator-prey system with Holling II functional response and hunting delay and gestation. By regarding the sum of delays as the bifurcation parameter, the local stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. We obtained explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation. Using a global Hopf bifurcation result of Wu [Wu JH. Symmetric functional differential equations and neural networks with memory, Trans Amer Math Soc 1998;350:4799-4838] for functional differential equations, we may show the global existence of the periodic solutions. Finally, several numerical simulations illustrating the theoretical analysis are also given.

Numerical modelling of bifurcation and localisation in cohesive-frictional materials

NASA Astrophysics Data System (ADS)

de Borst, René

1991-12-01

Methods are reviewed for analysing highly localised failure and bifurcation modes in discretised mechanical systems as typically arise in numerical simulations of failure in soils, rocks, metals and concrete. By the example of a plane-strain biaxial test it is shown that strain softening and lack of normality in elasto-plastic constitutive equations and the ensuing loss of ellipticity of the governing field equations cause a pathological mesh dependence of numerical solutions for such problems, thus rendering the results effectively meaningless. The need for introduction of higher-order continuum models is emphasised to remedy this shortcoming of the conventional approach. For one such a continuum model, namely the unconstrained Cosserat continuum, it is demonstrated that meaningful and convergent solutions (in the sense that a finite width of the localisation zone is computed upon mesh refinement) can be obtained.

New Metallicty Calibration for Dwarfs for the RGU-Photometry

NASA Astrophysics Data System (ADS)

Karaali, Salih; Bilir, Selçuk

2002-10-01

We adopted the procedure of Carney to obtain a metallicity calibration for dwarfs for the RGU photometry. For this purpose we selected 76 dwarfs of different metallicities from Carney, and Strobel et al., and evaluated their δ(U-G) ultra-violet excess relative to Hyades by transforming their UBV magnitudes to RGU via metallicity dependent equations of Ak-Güngör. The δ0.6/ΔM normalized factors of Sandage transform Δ(U-G) excess at any G-R to δ=δ1.08, i.e.: the ultra-violet excess at G-R = 1.08 mag, corresponding to B-V = 0.60 mag in the UBV-system. Finally, the (δ, [Fe/H]) couples were fitted by the equation [Fe/H] = 0.11-2.22δ-7.95δ2. This calibration covers the metallicity interval (-2.20, +0.20) dex.

Numerical implementation of isolated horizon boundary conditions

NASA Astrophysics Data System (ADS)

Jaramillo, José Luis; Ansorg, Marcus; Limousin, François

2007-01-01

We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasiequilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the conformal thin sandwich equations. As main results, we first establish the consistency of including in the set of boundary conditions a constant surface gravity prescription, interpretable as a lapse boundary condition, and second we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the conformal transverse traceless equations with quasiequilibrium horizon conditions extend to the conformal thin sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon.

TOPEX/El Nino Watch - Satellite shows El Nino-related Sea Surface Height, Mar, 14, 1998

NASA Technical Reports Server (NTRS)

1998-01-01

This image of the Pacific Ocean was produced using sea surface height measurements taken by the U.S.-French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on Mar. 14, 1998 and sea surface height is an indicator of the heat content of the ocean. The image shows that the sea surface height along the central equatorial Pacific has returned to a near normal state. Oceanographers indicate this is a classic pattern, typical of a mature El Nino condition. Remnants of the El Nino warm water pool, shown in red and white, are situated to the north and south of the equator. These sea surface height measurements have provided scientists with a detailed view of how the 1997-98 El Nino's warm pool behaves because the TOPEX/Poseidon satellite measures the changing sea surface height with unprecedented precision. In this image, the white and red areas indicate unusual patterns of heat storage; in the white areas, the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The green areas indicate normal conditions, while purple (the western Pacific) means at least 18 centimeters (7 inches) below normal sea level. The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. Using satellite imagery, buoy and ship data, and a forecasting model of the ocean-atmosphere system, the National Oceanic and Atmospheric Administration, (NOAA), has continued to issue an advisory indicating the so-called El Nino weather conditions that have impacted much of the United States and the world are expected to remain through the spring.

TOPEX/El Nino Watch - Warm Water Pool is Thinning, Feb, 5, 1998

NASA Technical Reports Server (NTRS)

1998-01-01

This image of the Pacific Ocean was produced using sea surface height measurements taken by the U.S.-French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on Feb. 5, 1998 and sea surface height is an indicator of the heat content of the ocean. The area and volume of the El Nino warm water pool that is affecting global weather patterns remains extremely large, but the pool has thinned along the equator and near the coast of South America. This 'thinning' means that the warm water is not as deep as it was a few months ago. Oceanographers indicate this is a classic pattern, typical of a mature El Nino condition that they would expect to see during the ocean's gradual transition back to normal sea level. In this image, the white and red areas indicate unusual patterns of heat storage; in the white areas, the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The green areas indicate normal conditions, while purple (the western Pacific) means at least 18 centimeters (7 inches) below normal sea level. The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. Using satellite imagery, buoy and ship data, and a forecasting model of the ocean-atmosphere system, the National Oceanic and Atmospheric Administration, (NOAA), has continued to issue an advisory indicating the so-called El Nino weather conditions that have impacted much of the United States and the world are expected to remain through the spring.

For more information, please visit the TOPEX/Poseidon project web page at http://topex-www.jpl.nasa.gov

Multiple normalized solutions for a planar gauged nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Luo, Xiao

2018-06-01

We study the existence, multiplicity, quantitative property and asymptotic behavior of normalized solutions for a gauged nonlinear Schrödinger equation arising from the Chern-Simons theory Δ u + ω u +|x|^2u+ λ ( {{h^2}(| x | )}/{{{| x | ^2}}} + \\int \\limits _{| x | }^{ + ∞} {{h(s)}/s} {u^2}(s)ds) u = {| u | ^{p - 2}}u,\\quad x\\in R^2, where ω \\in R, λ >0, p>4 and h(s) = 1/2\\int \\limits _0^s {r{u^2}(r)dr} . Combining constraint minimization method and minimax principle, we prove that the problem possesses at least two normalized solutions: One is a ground state and the other is an excited state. Furthermore, the asymptotic behavior and quantitative property of the ground state are analyzed.

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

NASA Technical Reports Server (NTRS)

Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)

1994-01-01

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

Nonlinear equations of motion for Landau resonance interactions with a whistler mode wave

NASA Technical Reports Server (NTRS)

Inan, U. S.; Tkalcevic, S.

1982-01-01

A simple set of equations is presented for the description of the cyclotron averaged motion of Landau resonant particles in a whistler mode wave propagating at an angle to the static magnetic field. A comparison is conducted of the wave magnetic field and electric field effects for the parameters of the magnetosphere, and the parameter ranges for which the wave magnetic field effects would be negligible are determined. It is shown that the effect of the wave magnetic field can be neglected for low pitch angles, high normal wave angles, and/or high normalized wave frequencies.

Stochastic modelling of non-stationary financial assets

NASA Astrophysics Data System (ADS)

Estevens, Joana; Rocha, Paulo; Boto, João P.; Lind, Pedro G.

2017-11-01

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely, biology, medicine, and geology.

Contact problem on indentation of an elastic half-plane with an inhomogeneous coating by a flat punch in the presence of tangential stresses on a surface

NASA Astrophysics Data System (ADS)

Volkov, Sergei S.; Vasiliev, Andrey S.; Aizikovich, Sergei M.; Sadyrin, Evgeniy V.

2018-05-01

Indentation of an elastic half-space with functionally graded coating by a rigid flat punch is studied. The half-plane is additionally subjected to distributed tangential stresses. Tangential stresses are represented in a form of Fourier series. The problem is reduced to the solution of two dual integral equations over even and odd functions describing distribution of unknown normal contact stresses. The solutions of these dual integral equations are constructed by the bilateral asymptotic method. Approximated analytical expressions for contact normal stresses are provided.

Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species.

PubMed

Meng, Xin-You; Qin, Ni-Ni; Huo, Hai-Feng

2018-12-01

In this paper, a predator-prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results.

Effect of Coannular Flow on Linearized Euler Equation Predictions of Jet Noise

NASA Technical Reports Server (NTRS)

Hixon, R.; Shih, S.-H.; Mankbadi, Reda R.

1997-01-01

An improved version of a previously validated linearized Euler equation solver is used to compute the noise generated by coannular supersonic jets. Results for a single supersonic jet are compared to the results from both a normal velocity profile and an inverted velocity profile supersonic jet.

A Robust Bayesian Approach for Structural Equation Models with Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum; Xia, Ye-Mao

2008-01-01

In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear…

Who Will Win?: Predicting the Presidential Election Using Linear Regression

ERIC Educational Resources Information Center

Lamb, John H.

2007-01-01

This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…

Some Properties of Estimated Scale Invariant Covariance Structures.

ERIC Educational Resources Information Center

Dijkstra, T. K.

1990-01-01

An example of scale invariance is provided via the LISREL model that is subject only to classical normalizations and zero constraints on the parameters. Scale invariance implies that the estimated covariance matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. (TJH)

Titration Calculations with Computer Algebra Software

ERIC Educational Resources Information Center

Lachance, Russ; Biaglow, Andrew

2012-01-01

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

Turbulent Fluid Motion 5: Fourier Analysis, the Spectral Form of the Continuum Equations, and Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1996-01-01

Background material on Fourier analysis and on the spectral form of the continuum equations, both averaged and unaveraged, are given. The equations are applied to a number of cases of homogeneous turbulence with and without mean gradients. Spectral transfer of turbulent activity between scales of motion is studied in some detail. The effects of mean shear, heat transfer, normal strain, and buoyancy are included in the analyses.

On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Shi, Yanling; Xu, Junxiang; Xu, Xindong

2015-02-01

In this paper, one-dimensional generalized Boussinesq equation: utt - uxx + (u2 + uxx)xx = 0 with boundary conditions ux(0, t) = ux(π, t) = uxxx(0, t) = uxxx(π, t) = 0 is considered. It is proved that the equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with 2-dimensional Diophantine frequencies. The proof is based on an infinite dimensional Kolmogorov-Arnold-Moser theorem and Birkhoff normal form.

An energy-saving nonlinear position control strategy for electro-hydraulic servo systems.

PubMed

Baghestan, Keivan; Rezaei, Seyed Mehdi; Talebi, Heidar Ali; Zareinejad, Mohammad

2015-11-01

The electro-hydraulic servo system (EHSS) demonstrates numerous advantages in size and performance compared to other actuation methods. Oftentimes, its utilization in industrial and machinery settings is limited by its inferior efficiency. In this paper, a nonlinear backstepping control algorithm with an energy-saving approach is proposed for position control in the EHSS. To achieve improved efficiency, two control valves including a proportional directional valve (PDV) and a proportional relief valve (PRV) are used to achieve the control objectives. To design the control algorithm, the state space model equations of the system are transformed to their normal form and the control law through the PDV is designed using a backstepping approach for position tracking. Then, another nonlinear set of laws is derived to achieve energy-saving through the PRV input. This control design method, based on the normal form representation, imposes internal dynamics on the closed-loop system. The stability of the internal dynamics is analyzed in special cases of operation. Experimental results verify that both tracking and energy-saving objectives are satisfied for the closed-loop system. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Predictive equations for respiratory muscle strength according to international and Brazilian guidelines.

PubMed

Pessoa, Isabela M B S; Houri Neto, Miguel; Montemezzo, Dayane; Silva, Luisa A M; Andrade, Armèle Dornelas De; Parreira, Verônica F

2014-01-01

The maximum static respiratory pressures, namely the maximum inspiratory pressure (MIP) and maximum expiratory pressure (MEP), reflect the strength of the respiratory muscles. These measures are simple, non-invasive, and have established diagnostic and prognostic value. This study is the first to examine the maximum respiratory pressures within the Brazilian population according to the recommendations proposed by the American Thoracic Society and European Respiratory Society (ATS/ERS) and the Brazilian Thoracic Association (SBPT). To establish reference equations, mean values, and lower limits of normality for MIP and MEP for each age group and sex, as recommended by the ATS/ERS and SBPT. We recruited 134 Brazilians living in Belo Horizonte, MG, Brazil, aged 20-89 years, with a normal pulmonary function test and a body mass index within the normal range. We used a digital manometer that operationalized the variable maximum average pressure (MIP/MEP). At least five tests were performed for both MIP and MEP to take into account a possible learning effect. We evaluated 74 women and 60 men. The equations were as follows: MIP=63.27-0.55 (age)+17.96 (gender)+0.58 (weight), r(2) of 34% and MEP= - 61.41+2.29 (age) - 0.03(age(2))+33.72 (gender)+1.40 (waist), r(2) of 49%. In clinical practice, these equations could be used to calculate the predicted values of MIP and MEP for the Brazilian population.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

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

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Research on the porous flow of the mechanism of viscous-elastic fluids displacing residual oil droplets in micro pores

NASA Astrophysics Data System (ADS)

Dong, Guanyu

2018-03-01

In order to analyze the microscopic stress field acting on residual oil droplets in micro pores, calculate its deformation, and explore the hydrodynamic mechanism of viscous-elastic fluids displacing oil droplets, the viscous-elastic fluid flow equations in micro pores are established by choosing the Upper Convected Maxwell constitutive equation; the numerical solutions of the flow field are obtained by volume control and Alternate Direction Implicit methods. From the above, the velocity field and microscopic stress field; the forces acting on residual oil droplets; the deformations of residual oil droplets by various viscous-elastic displacing fluids and at various Wiesenberg numbers are calculated and analyzed. The result demonstrated that both the normal stress and horizontal force acting on the residual oil droplets by viscous-elastic fluids are much larger compared to that of inelastic fluid; the distribution of normal stress changes abruptly; under the condition of the same pressure gradient in the system under investigation, the ratio of the horizontal forces acting on the residual oil droplets by different displacing fluids is about 1:8:20, which means that under the above conditions, the driving force on a oil droplet is 20 times higher for a viscous-elastic fluid compared to that of a Newtonian Fluid. The conclusions are supportive of the mechanism that viscous-elastic driving fluids can increase the Displacement Efficiency. This should be of help in designing new chemicals and selecting Enhanced Oil Recovery systems.

A theory of stationarity and asymptotic approach in dissipative systems

NASA Astrophysics Data System (ADS)

Rubel, Michael Thomas

2007-05-01

The approximate dynamics of many physical phenomena, including turbulence, can be represented by dissipative systems of ordinary differential equations. One often turns to numerical integration to solve them. There is an incompatibility, however, between the answers it can produce (i.e., specific solution trajectories) and the questions one might wish to ask (e.g., what behavior would be typical in the laboratory?) To determine its outcome, numerical integration requires more detailed initial conditions than a laboratory could normally provide. In place of initial conditions, experiments stipulate how tests should be carried out: only under statistically stationary conditions, for example, or only during asymptotic approach to a final state. Stipulations such as these, rather than initial conditions, are what determine outcomes in the laboratory.This theoretical study examines whether the points of view can be reconciled: What is the relationship between one's statistical stipulations for how an experiment should be carried out--stationarity or asymptotic approach--and the expected results? How might those results be determined without invoking initial conditions explicitly?To answer these questions, stationarity and asymptotic approach conditions are analyzed in detail. Each condition is treated as a statistical constraint on the system--a restriction on the probability density of states that might be occupied when measurements take place. For stationarity, this reasoning leads to a singular, invariant probability density which is already familiar from dynamical systems theory. For asymptotic approach, it leads to a new, more regular probability density field. A conjecture regarding what appears to be a limit relationship between the two densities is presented.By making use of the new probability densities, one can derive output statistics directly, avoiding the need to create or manipulate initial data, and thereby avoiding the conceptual incompatibility mentioned above. This approach also provides a clean way to derive reduced-order models, complete with local and global error estimates, as well as a way to compare existing reduced-order models objectively.The new approach is explored in the context of five separate test problems: a trivial one-dimensional linear system, a damped unforced linear oscillator in two dimensions, the isothermal Rayleigh-Plesset equation, Lorenz's equations, and the Stokes limit of Burgers' equation in one space dimension. In each case, various output statistics are deduced without recourse to initial conditions. Further, reduced-order models are constructed for asymptotic approach of the damped unforced linear oscillator, the isothermal Rayleigh-Plesset system, and Lorenz's equations, and for stationarity of Lorenz's equations.

An assessment of gravity model improvements using TOPEX/Poseidon TDRSS observations

NASA Technical Reports Server (NTRS)

Putney, B. H.; Teles, J.; Eddy, W. F.; Klosko, S. M.

1992-01-01

The contribution of TOPEX/Poseidon (T/P) TDRSS data to geopotential model recovery is assessed. Simulated TDRSS one-way and Bilateration Ranging Transponder System (BRTS) observations have been generated and orbitally reduced to form normal equations for geopotential parameters. These normals have been combined with those of the latest prelaunch T/P gravity model solution using data from over 30 satellites. A study of the resulting solution error covariance shows that TDRSS can make important contributions to geopotential recovery, especially for improving T/P specific effects like those arising from orbital resonance. It is argued that future effort is desirable both to establish TDRSS orbit determination limits in a reference frame compatible with that used for the precise laser/DORIS orbits, and the reduction of these TDRSS data for geopotential recovery.

Sonographic study of the development of fetal corpus callosum in a Chinese population.

PubMed

Zhang, Hai-chun; Yang, Jie; Chen, Zhong-ping; Ma, Xiao-yan

2009-02-01

The observation of fetal corpus callosum (CC) is important for the prenatal sonographic assessment of fetal central nervous system development. The aim of this study was to investigate the development of normal Chinese fetal CC. CC measurements were performed using high-resolution transabdominal sonography on 622 Chinese fetuses between 16 and 39 weeks' gestation. The correlation between CC size and gestational age was investigated. The fetal CC length increased in a linear fashion during pregnancy. The length of the CC as a function of gestational age was expressed by the following regression equation: length (mm) = -9.567 + 1.495 x gestational age (weeks) (r = 0.932, p < 0.001). Knowledge of normal CC appearance may help identify developmental anomalies and enable accurate prenatal counseling. (c) 2008 Wiley Periodicals, Inc.

Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse

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

Kawakami, Hayato; Mitsuda, Eiji; Nambu, Yasusada

In considering the gravitational collapse of matter, it is an important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla et al. to the spherically symmetric gravitational collapse of a perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecturemore » that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.« less

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA Technical Reports Server (NTRS)

Segerman, Alan M.; Zedd, Michael F.

2003-01-01

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

[Clinical exercise testing and the Fick equation: strategic thinking for optimizing diagnosis].

PubMed

Perrault, H; Richard, R

2012-04-01

This article examines the expected exercise-induced changes in the components of the oxygen transport system as described by the Fick equation with a view to enable a critical analysis of a standard incremental exercise test to identify normal and abnormal patterns of responses and generate hypotheses as to potential physiological and/or pathophysiological causes. The text reviews basic physiological principals and provides useful reminders of standard equations that serve to integrate circulatory, respiratory and skeletal muscle functions. More specifically, the article provides a conceptual and quantitative framework linking the exercise-induced increase in whole body oxygen uptake to central circulatory and peripheral circulatory factors with the view to establish the normalcy of response. Thus, the article reviews the exercise response to cardiac output determinants and provides qualitative and quantitative perspective bases for making assumptions on the peripheral circulatory factors and oxygen use. Finally, the article demonstrates the usefulness of exercise testing as an effective integrative physiological approach to develop clinical reasoning or verify pathophysiological outcomes. Copyright © 2012 SPLF. Published by Elsevier Masson SAS. All rights reserved.

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

PubMed

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

2008-11-01

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

Quantitative cervical vertebral maturation assessment in adolescents with normal occlusion: a mixed longitudinal study.

PubMed

Chen, Li-Li; Xu, Tian-Min; Jiang, Jiu-Hui; Zhang, Xing-Zhong; Lin, Jiu-Xiang

2008-12-01

The purpose of this study was to establish a quantitative cervical vertebral maturation (CVM) system for adolescents with normal occlusion. Mixed longitudinal data were used. The subjects included 87 children and adolescents from 8 to 18 years old with normal occlusion (32 boys, 55 girls) selected from 901 candidates. Sequential lateral cephalograms and hand-wrist films were taken once a year for 6 years. The lateral cephalograms of all subjects were divided into 11 maturation groups according to the Fishman skeletal maturity indicators. The morphologic characteristics of the second, third, and fourth cervical vertebrae at 11 developmental stages were measured and analyzed. Three characteristic parameters (H4/W4, AH3/PH3, @2) were selected to determine the classification of CVM. With 3 morphologic variables, the quantitative CVM system including 4 maturational stages was established. An equation that can accurately estimate the maturation of the cervical vertebrae was established: CVM stage=-4.13+3.57xH4/W4+4.07xAH3/PH3+0.03x@2. The quantitative CVM method is an efficient, objective, and relatively simple approach to assess the level of skeletal maturation during adolescence.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery such as inlets, ramjets, and scramjets. The discussion is separated into four sections: (1) computational fluid dynamics model for the entire nonlinear system or high order nonlinear models; (2) high order linearized model derived from fundamental physics; (3) low order linear models obtained from other high order models; and (4) low order nonlinear models. Included are special considerations on any relevant control system designs. The methods discussed are for the quasi-one dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, moving normal shocks, hammershocks, subsonic combustion via heat addition, temperature dependent gases, detonation, and thermal choking.

A Coupled Aeroelastic Model for Launch Vehicle Stability Analysis

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2010-01-01

A technique for incorporating distributed aerodynamic normal forces and aeroelastic coupling effects into a stability analysis model of a launch vehicle is presented. The formulation augments the linear state-space launch vehicle plant dynamics that are compactly derived as a system of coupled linear differential equations representing small angular and translational perturbations of the rigid body, nozzle, and sloshing propellant coupled with normal vibration of a set of orthogonal modes. The interaction of generalized forces due to aeroelastic coupling and thrust can be expressed as a set of augmenting non-diagonal stiffness and damping matrices in modal coordinates with no penalty on system order. While the eigenvalues of the structural response in the presence of thrust and aeroelastic forcing can be predicted at a given flight condition independent of the remaining degrees of freedom, the coupled model provides confidence in closed-loop stability in the presence of rigid-body, slosh, and actuator dynamics. Simulation results are presented that characterize the coupled dynamic response of the Ares I launch vehicle and the impact of aeroelasticity on control system stability margins.

Local equilibrium and the second law of thermodynamics for irreversible systems with thermodynamic inertia

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

Glavatskiy, K. S.

Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative values of the entropy production, which is in contradiction with the second law of thermodynamics. In this paper, we address this question by suggesting a variational formulation of irreversible evolution of a system with non-zero thermodynamic inertia. We introduce the Lagrangian, which depends on the properties of the normal and the so-called “mirror-image” systems. We show that the standard evolution equations, in particular, the Maxwell-Cattaneo-Vernotte equation, can bemore » derived from the variational procedure without going beyond the assumption of local equilibrium. We also argue that the second law of thermodynamics in non-equilibrium should be understood as a consequence of the variational procedure and the property of local equilibrium. For systems with instantaneous response this leads to the standard requirement of the local instantaneous entropy production being always positive. However, if a system is characterized by delayed response, the formulation of the second law of thermodynamics should be altered. In particular, the quantity, which is always positive, is not the instantaneous entropy production, but the entropy production averaged over a proper time interval.« less

A reference equation for maximal aerobic power for treadmill and cycle ergometer exercise testing: Analysis from the FRIEND registry.

PubMed

de Souza E Silva, Christina G; Kaminsky, Leonard A; Arena, Ross; Christle, Jeffrey W; Araújo, Claudio Gil S; Lima, Ricardo M; Ashley, Euan A; Myers, Jonathan

2018-05-01

Background Maximal oxygen uptake (VO 2 max) is a powerful predictor of health outcomes. Valid and portable reference values are integral to interpreting measured VO 2 max; however, available reference standards lack validation and are specific to exercise mode. This study was undertaken to develop and validate a single equation for normal standards for VO 2 max for the treadmill or cycle ergometer in men and women. Methods Healthy individuals ( N = 10,881; 67.8% men, 20-85 years) who performed a maximal cardiopulmonary exercise test on either a treadmill or a cycle ergometer were studied. Of these, 7617 and 3264 individuals were randomly selected for development and validation of the equation, respectively. A Brazilian sample (1619 individuals) constituted a second validation cohort. The prediction equation was determined using multiple regression analysis, and comparisons were made with the widely-used Wasserman and European equations. Results Age, sex, weight, height and exercise mode were significant predictors of VO 2 max. The regression equation was: VO 2 max (ml kg -1  min -1 ) = 45.2 - 0.35*Age - 10.9*Sex (male = 1; female = 2) - 0.15*Weight (pounds) + 0.68*Height (inches) - 0.46*Exercise Mode (treadmill = 1; bike = 2) ( R = 0.79, R 2  = 0.62, standard error of the estimate = 6.6 ml kg -1  min -1 ). Percentage predicted VO 2 max for the US and Brazilian validation cohorts were 102.8% and 95.8%, respectively. The new equation performed better than traditional equations, particularly among women and individuals ≥60 years old. Conclusion A combined equation was developed for normal standards for VO 2 max for different exercise modes derived from a US national registry. The equation provided a lower average error between measured and predicted VO 2 max than traditional equations even when applied to an independent cohort. Additional studies are needed to determine its portability.

Instability, rupture and fluctuations in thin liquid films: Theory and computations

NASA Astrophysics Data System (ADS)

Gvalani, Rishabh; Duran-Olivencia, Miguel; Kalliadasis, Serafim; Pavliotis, Grigorios

2017-11-01

Thin liquid films are ubiquitous in natural phenomena and technological applications. They are commonly studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that still needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. Here we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. We scrutinise the behaviour of the stochastic thin film equation in the limit of perfectly correlated noise along the wall-normal direction. We also perform Monte Carlo simulations of the stochastic equation by adopting a numerical scheme based on a spectral collocation method. The numerical scheme allows us to explore the fluctuating dynamics of the thin film and the behaviour of the system's free energy close to rupture. Finally, we also study the effect of the noise intensity on the rupture time, which is in good agreement with previous works. Imperial College London (ICL) President's PhD Scholarship; European Research Council Advanced Grant No. 247031; EPSRC Grants EP/L025159, EP/L020564, EP/P031587, EP/L024926, and EP/L016230/1.

The Interaction of Turbulence with Parallel and Perpendicular Shocks: Theory and Observations at 1 au

NASA Astrophysics Data System (ADS)

Adhikari, L.; Zank, G. P.; Hunana, P.; Hu, Q.

2016-12-01

Shocks are thought to be responsible for the amplification of turbulence as well as for generating turbulence throughout the heliosphere. We study the interaction of turbulence with parallel and perpendicular shock waves using the six-coupled-equation turbulence transport model of Zank et al. We model a 1D stationary shock wave using a hyperbolic tangent function and the Rankine-Hugoniot conditions for both a reduced model with four coupled equations and the full model. Eight quasi-parallel and five quasi-perpendicular events in the WIND spacecraft data sets are identified, and we compute the fluctuating magnetic and kinetic energy, the energy in forward and backward propagating modes, the total turbulent energy, the normalized residual energy, and the normalized cross helicity upstream and downstream of the observed shocks. We compare the observed fitted values upstream and downstream of the shock with numerical solutions to our model equations. The comparison shows that our theoretical results are in reasonable agreement with observations for both quasi-parallel and perpendicular shocks. We find that (1) the total turbulent energy, the energy in forward and backward propagating modes, and the normalized residual energy increase across the shock, (2) the normalized cross helicity increases or decreases across the shock, and (3) the correlation length increases upstream and downstream of the shock, and slightly flattens or decreases across the shock.

THE INTERACTION OF TURBULENCE WITH PARALLEL AND PERPENDICULAR SHOCKS: THEORY AND OBSERVATIONS AT 1 au

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

Adhikari, L.; Zank, G. P.; Hunana, P.

Shocks are thought to be responsible for the amplification of turbulence as well as for generating turbulence throughout the heliosphere. We study the interaction of turbulence with parallel and perpendicular shock waves using the six-coupled-equation turbulence transport model of Zank et al. We model a 1D stationary shock wave using a hyperbolic tangent function and the Rankine–Hugoniot conditions for both a reduced model with four coupled equations and the full model. Eight quasi-parallel and five quasi-perpendicular events in the WIND spacecraft data sets are identified, and we compute the fluctuating magnetic and kinetic energy, the energy in forward and backwardmore » propagating modes, the total turbulent energy, the normalized residual energy, and the normalized cross helicity upstream and downstream of the observed shocks. We compare the observed fitted values upstream and downstream of the shock with numerical solutions to our model equations. The comparison shows that our theoretical results are in reasonable agreement with observations for both quasi-parallel and perpendicular shocks. We find that (1) the total turbulent energy, the energy in forward and backward propagating modes, and the normalized residual energy increase across the shock, (2) the normalized cross helicity increases or decreases across the shock, and (3) the correlation length increases upstream and downstream of the shock, and slightly flattens or decreases across the shock.« less

A General Theory of Unsteady Compressible Potential Aerodynamics

NASA Technical Reports Server (NTRS)

Morino, L.

1974-01-01

The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the potential is obtained for both supersonic and subsonic flow. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface, sigma, of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface sigma. For the important practical case of small harmonic oscillation around a rest position, the equation reduces to a two-dimensional Fredholm integral equation of second-type. It is shown that this equation reduces properly to the lifting surface theories as well as other classical mathematical formulas. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings.

Reference breast temperature: proposal of an equation.

PubMed

Souza, Gladis Aparecida Galindo Reisemberger de; Brioschi, Marcos Leal; Vargas, José Viriato Coelho; Morais, Keli Cristiane Correia; Dalmaso Neto, Carlos; Neves, Eduardo Borba

2015-01-01

To develop an equation to estimate the breast reference temperature according to the variation of room and core body temperatures. Four asymptomatic women were evaluated for three consecutive menstrual cycles. Using thermography, the temperature of breasts and eyes was measured as indirect reference of core body and room temperatures. To analyze the thermal behavior of the breasts during the cycle, the core body and room temperatures were normalized by means of a mathematical equation. We performed 180 observations and the core temperature had the highest correlation with the breast temperature, followed by room temperature. The proposed prediction model could explain 45.3% of the breast temperature variation, with variable room temperature variable; it can be accepted as a way to estimate the reference breast temperature at different room temperatures. The average breast temperature in healthy women had a direct relation with the core and room temperature and can be estimated mathematically. It is suggested that an equation could be used in clinical practice to estimate the normal breast reference temperature in young women, regardless of the day of the cycle, therefore assisting in evaluation of anatomical studies.

A finite-element analysis for steady and oscillatory supersonic flows around complex configurations

NASA Technical Reports Server (NTRS)

Morino, L.; Chen, L. T.

1974-01-01

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, sigma sub i, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element, and this yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements, sigma sub i. The results obtained using the above formulation are compared with existing analytical and experimental results.

Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model

DOE PAGES

Barnard, Richard C.; Frank, Martin; Krycki, Kai

2016-02-09

In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker–Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker–Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion (P N) and an Harten-Lax-van Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities. Finally, we present numerical results of the sensitivities for the normalized average dose depositionmore » depth with respect to the stopping power and the transport coefficients, demonstrating the increase in relative sensitivities as beam energy decreases. In conclusion, this in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present.« less

Numerical solutions of Navier-Stokes equations for compressible turbulent two/three dimensional flows in terminal shock region of an inlet/diffuser

NASA Technical Reports Server (NTRS)

Liu, N. S.; Shamroth, S. J.; Mcdonald, H.

1983-01-01

The multidimensional ensemble averaged compressible time dependent Navier Stokes equations in conjunction with mixing length turbulence model and shock capturing technique were used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations were carried out: (1) 2 D, steady, subsonic; (2) 2 D, steady, transonic with normal shock; (3) 2 D, steady, supersonic with terminal shock; (4) 2 D, transient process of shock development and (5) 3 D, steady, transonic with normal shock. The numerical results obtained for the 2 D and 3 D transonic shocked flows were compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data.

Dirac equation on a curved surface

NASA Astrophysics Data System (ADS)

Brandt, F. T.; Sánchez-Monroy, J. A.

2016-09-01

The dynamics of Dirac particles confined to a curved surface is examined employing the thin-layer method. We perform a perturbative expansion to first-order and split the Dirac field into normal and tangential components to the surface. In contrast to the known behavior of second order equations like Schrödinger, Maxwell and Klein-Gordon, we find that there is no geometric potential for the Dirac equation on a surface. This implies that the non-relativistic limit does not commute with the thin-layer method. Although this problem can be overcome when second-order terms are retained in the perturbative expansion, this would preclude the decoupling of the normal and tangential degrees of freedom. Therefore, we propose to introduce a first-order term which rescues the non-relativistic limit and also clarifies the effect of the intrinsic and extrinsic curvatures on the dynamics of the Dirac particles.

Scaling analysis for the direct reactor auxiliary cooling system for FHRs

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

Lv, Q.; Kim, I. H.; Sun, X.

2015-04-01

The Direct Reactor Auxiliary Cooling System (DRACS) is a passive residual heat removal system proposed for the Fluoride-salt-cooled High-temperature Reactor (FHR) that combines the coated particle fuel and graphite moderator with a liquid fluoride salt as the coolant. The DRACS features three natural circulation/convection loops that rely on buoyancy as the driving force and are coupled via two heat exchangers, namely, the DRACS heat exchanger and the natural draft heat exchanger. A fluidic diode is employed to minimize the parasitic flow into the DRACS primary loop and correspondingly the heat loss to the DRACS during reactor normal operation, and tomore » activate the DRACS in accidents when the reactor is shut down. While the DRACS concept has been proposed, there are no actual prototypic DRACS systems for FHRs built or tested in the literature. In this paper, a detailed scaling analysis for the DRACS is performed, which will provide guidance for the design of scaled-down DRACS test facilities. Based on the Boussinesq assumption and one-dimensional flow formulation, the governing equations are non-dimensionalized by introducing appropriate dimensionless parameters. The key dimensionless numbers that characterize the DRACS system are obtained from the non-dimensional governing equations. Based on the dimensionless numbers and non-dimensional governing equations, similarity laws are proposed. In addition, a scaling methodology has been developed, which consists of a core scaling and a loop scaling. The consistency between the core and loop scaling is examined via the reference volume ratio, which can be obtained from both the core and loop scaling processes. The scaling methodology and similarity laws have been applied to obtain a scientific design of a scaled-down high-temperature DRACS test facility.« less

Salt dependence of compression normal forces of quenched polyelectrolyte brushes

NASA Astrophysics Data System (ADS)

Hernandez-Zapata, Ernesto; Tamashiro, Mario N.; Pincus, Philip A.

2001-03-01

We obtained mean-field expressions for the compression normal forces between two identical opposing quenched polyelectrolyte brushes in the presence of monovalent salt. The brush elasticity is modeled using the entropy of ideal Gaussian chains, while the entropy of the microions and the electrostatic contribution to the grand potential is obtained by solving the non-linear Poisson-Boltzmann equation for the system in contact with a salt reservoir. For the polyelectrolyte brush we considered both a uniformly charged slab as well as an inhomogeneous charge profile obtained using a self-consistent field theory. Using the Derjaguin approximation, we related the planar-geometry results to the realistic two-crossed cylinders experimental set up. Theoretical predictions are compared to experimental measurements(Marc Balastre's abstract, APS March 2001 Meeting.) of the salt dependence of the compression normal forces between two quenched polyelectrolyte brushes formed by the adsorption of diblock copolymers poly(tert-butyl styrene)-sodium poly(styrene sulfonate) [PtBs/NaPSS] onto an octadecyltriethoxysilane (OTE) hydrophobically modified mica, as well as onto bare mica.

Proximity-induced superconductivity in all-silicon superconductor /normal-metal junctions

NASA Astrophysics Data System (ADS)

Chiodi, F.; Duvauchelle, J.-E.; Marcenat, C.; Débarre, D.; Lefloch, F.

2017-07-01

We have realized laser-doped all-silicon superconducting (S)/normal metal (N) bilayers of tunable thickness and dopant concentration. We observed a strong reduction of the bilayers' critical temperature when increasing the normal metal thickness, a signature of the highly transparent S/N interface associated to the epitaxial sharp laser doping profile. We extracted the interface resistance by fitting with the linearized Usadel equations, demonstrating a reduction of 1 order of magnitude from previous superconductor/doped Si interfaces. In this well-controlled crystalline system we exploited the low-resistance S/N interfaces to elaborate all-silicon lateral SNS junctions with long-range proximity effect. Their dc transport properties, such as the critical and retrapping currents, could be well understood in the diffusive regime. Furthermore, this work led to the estimation of important parameters in ultradoped superconducting Si, such as the Fermi velocity, the coherence length, or the electron-phonon coupling constant, fundamental to conceive all-silicon superconducting electronics.

Iterative absolute electroanalytical approach to characterization of bulk redox conducting systems.

PubMed

Lewera, Adam; Miecznikowski, Krzysztof; Chojak, Malgorzata; Makowski, Oktawian; Golimowski, Jerzy; Kulesza, Pawel J

2004-05-15

A novel electroanalytical approach is proposed here, and it is demonstrated with the direct and simultaneous determination of two unknowns: the concentration of redox sites and the apparent diffusion coefficient for charge propagation in a single crystal of dodecatungstophosphoric acid. This Keggin-type polyoxometalate serves as a model bulk redox conducting inorganic material for solid-state voltammetry. The system has been investigated using an ultramicrodisk working electrode in the absence of external liquid supporting electrolyte. The analytical method requires numerical solution of the combination of two equations in which the first one describes current (or charge) in a well-defined (either spherical or linear) diffusional regime and the second general equation describes chronoamperometric (or normal pulse voltammetric current) under mixed (linear-spherical) conditions. The iterative approach is based on successive approximations through calculation and minimizing the least-squares error function. The method is fairly universal, and in principle, it can be extended to the investigation of other bulk systems including sol-gel processed materials, redox melts, and solutions on condition that they are electroactive and well behaved, they contain redox centers at sufficiently high level, and a number of electrons for the redox reaction considered is known.

A low-order model of the equatorial ocean-atmosphere system

NASA Astrophysics Data System (ADS)

Legnani, Roberto

A low order model of the equatorial ocean-atmosphere coupled system is presented. The model atmosphere includes a hydrological cycle with cloud-radiation interaction. The model ocean is based on mixed layer dynamics with a parameterization of entrainment processes. The coupling takes place via transfer to momentum, sensible heat, latent heat and short wave and long wave radiation through the ocean surface. The dynamical formulation is that of the primitive equations of an equatorial beta-plane, with zonally periodic and meridionally infinite geometry. The system is expanded into the set of normal modes pertinent to the linear problem and severly truncated to a few modes; 54 degrees of freedom are retained. Some nonlinear terms of the equations are evaluated in physical space and then projected onto the functional space; other terms are evaluated directly in the functional space. Sensitivity tests to variations of the parameters are performed, and some results from 10-year initial value simulations are presented. The model is capable of supporting oscillations of different time scales, ranging from a few days to a few years; it prefers a particular zonally asymmetric state, but temporarily switches to a different (opposite) zonally asymmetric state in an event-like fashion.

a Low-Order Model of the Equatorial Ocean-Atmosphere System.

NASA Astrophysics Data System (ADS)

Legnani, Roberto

A low order model of the equatorial ocean-atmosphere coupled system is presented. The model atmosphere includes a hydrological cycle with cloud-radiation interaction. The model ocean is based on mixed layer dynamics with a parameterization of entrainment processes. The coupling takes place via transfer to momentum, sensible heat, latent heat and short -wave and long-wave radiation through the ocean surface. The dynamical formulation is that of the primitive equations of an equatorial beta-plane, with zonally periodic and meridionally infinite geometry. The system is expanded into the set of normal modes pertinent to the linear problem and severely truncated to a few modes; 54 degrees of freedom are retained. Some nonlinear terms of the equations are evaluated in physical space and then projected onto the functional space; other terms are evaluated directly in the functional space. Sensitivity tests to variations of the parameters are performed, and some results from 10-year initial value simulations are presented. The model is capable of supporting oscillations of different time scales, ranging from a few days to a few years; it prefers a particular zonally asymmetric state, but temporarily switches to a different (opposite) zonally asymmetric state in an event-like fashion.

Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems

NASA Astrophysics Data System (ADS)

Bäcker, A.

Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.

The IVS data input to ITRF2014

NASA Astrophysics Data System (ADS)

Nothnagel, Axel; Alef, Walter; Amagai, Jun; Andersen, Per Helge; Andreeva, Tatiana; Artz, Thomas; Bachmann, Sabine; Barache, Christophe; Baudry, Alain; Bauernfeind, Erhard; Baver, Karen; Beaudoin, Christopher; Behrend, Dirk; Bellanger, Antoine; Berdnikov, Anton; Bergman, Per; Bernhart, Simone; Bertarini, Alessandra; Bianco, Giuseppe; Bielmaier, Ewald; Boboltz, David; Böhm, Johannes; Böhm, Sigrid; Boer, Armin; Bolotin, Sergei; Bougeard, Mireille; Bourda, Geraldine; Buttaccio, Salvo; Cannizzaro, Letizia; Cappallo, Roger; Carlson, Brent; Carter, Merri Sue; Charlot, Patrick; Chen, Chenyu; Chen, Maozheng; Cho, Jungho; Clark, Thomas; Collioud, Arnaud; Colomer, Francisco; Colucci, Giuseppe; Combrinck, Ludwig; Conway, John; Corey, Brian; Curtis, Ronald; Dassing, Reiner; Davis, Maria; de-Vicente, Pablo; De Witt, Aletha; Diakov, Alexey; Dickey, John; Diegel, Irv; Doi, Koichiro; Drewes, Hermann; Dube, Maurice; Elgered, Gunnar; Engelhardt, Gerald; Evangelista, Mark; Fan, Qingyuan; Fedotov, Leonid; Fey, Alan; Figueroa, Ricardo; Fukuzaki, Yoshihiro; Gambis, Daniel; Garcia-Espada, Susana; Gaume, Ralph; Gaylard, Michael; Geiger, Nicole; Gipson, John; Gomez, Frank; Gomez-Gonzalez, Jesus; Gordon, David; Govind, Ramesh; Gubanov, Vadim; Gulyaev, Sergei; Haas, Ruediger; Hall, David; Halsig, Sebastian; Hammargren, Roger; Hase, Hayo; Heinkelmann, Robert; Helldner, Leif; Herrera, Cristian; Himwich, Ed; Hobiger, Thomas; Holst, Christoph; Hong, Xiaoyu; Honma, Mareki; Huang, Xinyong; Hugentobler, Urs; Ichikawa, Ryuichi; Iddink, Andreas; Ihde, Johannes; Ilijin, Gennadiy; Ipatov, Alexander; Ipatova, Irina; Ishihara, Misao; Ivanov, D. V.; Jacobs, Chris; Jike, Takaaki; Johansson, Karl-Ake; Johnson, Heidi; Johnston, Kenneth; Ju, Hyunhee; Karasawa, Masao; Kaufmann, Pierre; Kawabata, Ryoji; Kawaguchi, Noriyuki; Kawai, Eiji; Kaydanovsky, Michael; Kharinov, Mikhail; Kobayashi, Hideyuki; Kokado, Kensuke; Kondo, Tetsuro; Korkin, Edward; Koyama, Yasuhiro; Krasna, Hana; Kronschnabl, Gerhard; Kurdubov, Sergey; Kurihara, Shinobu; Kuroda, Jiro; Kwak, Younghee; La Porta, Laura; Labelle, Ruth; Lamb, Doug; Lambert, Sébastien; Langkaas, Line; Lanotte, Roberto; Lavrov, Alexey; Le Bail, Karine; Leek, Judith; Li, Bing; Li, Huihua; Li, Jinling; Liang, Shiguang; Lindqvist, Michael; Liu, Xiang; Loesler, Michael; Long, Jim; Lonsdale, Colin; Lovell, Jim; Lowe, Stephen; Lucena, Antonio; Luzum, Brian; Ma, Chopo; Ma, Jun; Maccaferri, Giuseppe; Machida, Morito; MacMillan, Dan; Madzak, Matthias; Malkin, Zinovy; Manabe, Seiji; Mantovani, Franco; Mardyshkin, Vyacheslav; Marshalov, Dmitry; Mathiassen, Geir; Matsuzaka, Shigeru; McCarthy, Dennis; Melnikov, Alexey; Michailov, Andrey; Miller, Natalia; Mitchell, Donald; Mora-Diaz, Julian Andres; Mueskens, Arno; Mukai, Yasuko; Nanni, Mauro; Natusch, Tim; Negusini, Monia; Neidhardt, Alexander; Nickola, Marisa; Nicolson, George; Niell, Arthur; Nikitin, Pavel; Nilsson, Tobias; Ning, Tong; Nishikawa, Takashi; Noll, Carey; Nozawa, Kentarou; Ogaja, Clement; Oh, Hongjong; Olofsson, Hans; Opseth, Per Erik; Orfei, Sandro; Pacione, Rosa; Pazamickas, Katherine; Petrachenko, William; Pettersson, Lars; Pino, Pedro; Plank, Lucia; Ploetz, Christian; Poirier, Michael; Poutanen, Markku; Qian, Zhihan; Quick, Jonathan; Rahimov, Ismail; Redmond, Jay; Reid, Brett; Reynolds, John; Richter, Bernd; Rioja, Maria; Romero-Wolf, Andres; Ruszczyk, Chester; Salnikov, Alexander; Sarti, Pierguido; Schatz, Raimund; Scherneck, Hans-Georg; Schiavone, Francesco; Schreiber, Ulrich; Schuh, Harald; Schwarz, Walter; Sciarretta, Cecilia; Searle, Anthony; Sekido, Mamoru; Seitz, Manuela; Shao, Minghui; Shibuya, Kazuo; Shu, Fengchun; Sieber, Moritz; Skjaeveland, Asmund; Skurikhina, Elena; Smolentsev, Sergey; Smythe, Dan; Sousa, Don; Sovers, Ojars; Stanford, Laura; Stanghellini, Carlo; Steppe, Alan; Strand, Rich; Sun, Jing; Surkis, Igor; Takashima, Kazuhiro; Takefuji, Kazuhiro; Takiguchi, Hiroshi; Tamura, Yoshiaki; Tanabe, Tadashi; Tanir, Emine; Tao, An; Tateyama, Claudio; Teke, Kamil; Thomas, Cynthia; Thorandt, Volkmar; Thornton, Bruce; Tierno Ros, Claudia; Titov, Oleg; Titus, Mike; Tomasi, Paolo; Tornatore, Vincenza; Trigilio, Corrado; Trofimov, Dmitriy; Tsutsumi, Masanori; Tuccari, Gino; Tzioumis, Tasso; Ujihara, Hideki; Ullrich, Dieter; Uunila, Minttu; Venturi, Tiziana; Vespe, Francesco; Vityazev, Veniamin; Volvach, Alexandr; Vytnov, Alexander; Wang, Guangli; Wang, Jinqing; Wang, Lingling; Wang, Na; Wang, Shiqiang; Wei, Wenren; Weston, Stuart; Whitney, Alan; Wojdziak, Reiner; Yatskiv, Yaroslav; Yang, Wenjun; Ye, Shuhua; Yi, Sangoh; Yusup, Aili; Zapata, Octavio; Zeitlhoefler, Reinhard; Zhang, Hua; Zhang, Ming; Zhang, Xiuzhong; Zhao, Rongbing; Zheng, Weimin; Zhou, Ruixian; Zubko, Nataliya

2015-01-01

Very Long Baseline Interferometry (VLBI) is a primary space-geodetic technique for determining precise coordinates on the Earth, for monitoring the variable Earth rotation and orientation with highest precision, and for deriving many other parameters of the Earth system. The International VLBI Service for Geodesy and Astrometry (IVS, http://ivscc.gsfc.nasa.gov/) is a service of the International Association of Geodesy (IAG) and the International Astronomical Union (IAU). The datasets published here are the results of individual Very Long Baseline Interferometry (VLBI) sessions in the form of normal equations in SINEX 2.0 format (http://www.iers.org/IERS/EN/Organization/AnalysisCoordinator/SinexFormat/sinex.html, the SINEX 2.0 description is attached as pdf) provided by IVS as the input for the next release of the International Terrestrial Reference System (ITRF): ITRF2014. This is a new version of the ITRF2008 release (Bockmann et al., 2009). For each session/ file, the normal equation systems contain elements for the coordinate components of all stations having participated in the respective session as well as for the Earth orientation parameters (x-pole, y-pole, UT1 and its time derivatives plus offset to the IAU2006 precession-nutation components dX, dY (https://www.iau.org/static/resolutions/IAU2006_Resol1.pdf). The terrestrial part is free of datum. The data sets are the result of a weighted combination of the input of several IVS Analysis Centers. The IVS contribution for ITRF2014 is described in Bachmann et al (2015), Schuh and Behrend (2012) provide a general overview on the VLBI method, details on the internal data handling can be found at Behrend (2013).

On the nature of liquid junction and membrane potentials.

PubMed

Perram, John W; Stiles, Peter J

2006-09-28

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

Optimal Harvesting in a Periodic Food Chain Model with Size Structures in Predators

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

Zhang, Feng-Qin, E-mail: zhafq@263.net; Liu, Rong; Chen, Yuming, E-mail: ychen@wlu.ca

In this paper, we investigate a periodic food chain model with harvesting, where the predators have size structures and are described by first-order partial differential equations. First, we establish the existence of a unique non-negative solution by using the Banach fixed point theorem. Then, we provide optimality conditions by means of normal cone and adjoint system. Finally, we derive the existence of an optimal strategy by means of Ekeland’s variational principle. Here the objective functional represents the net economic benefit yielded from harvesting.

Engineering Design Handbook. Maintainability Engineering Theory and Practice

DTIC Science & Technology

1976-01-01

5—46 5—8.4.1.1 Human Body Measurement ( Anthropometry ) . 5—46 5-8.4.1.2 Man’s Sensory Capability and Psychological Makeup 5-46 5—8.4.1.3...Availability of System With Maintenance Time Ratio 1:4 2-32 2—9 Average and Pointwise Availability 2—34 2—10 Hypothetical...density function ( pdf ) of the normal distribution (Ref. 22, Chapter 10, and Ref. 23, Chapter 1) has the equation where cr is the standard deviation of

Fractional Dynamics of Single File Diffusion in Dusty Plasma Ring

NASA Astrophysics Data System (ADS)

Muniandy, S. V.; Chew, W. X.; Asgari, H.; Wong, C. S.; Lim, S. C.

2011-11-01

Single file diffusion (SFD) refers to the constrained motion of particles in quasi-one-dimensional channel such that the particles are unable to pass each other. Possible SFD of charged dust confined in biharmonic annular potential well with screened Coulomb interaction is investigated. Transition from normal diffusion to anomalous sub-diffusion behaviors is observed. Deviation from SFD's mean square displacement scaling behavior of 1/2-exponent may occur in strongly interacting systems. A phenomenological model based on fractional Langevin equation is proposed to account for the anomalous SFD behavior in dusty plasma ring.

Vortex creep and the internal temperature of neutron stars. I - General theory

NASA Technical Reports Server (NTRS)

Alpar, M. A.; Pines, D.; Anderson, P. W.; Shaham, J.

1984-01-01

The theory of a neutron star superfluid coupled to normal matter via thermal creep against pinning forces is developed in some detail. General equations of motion for a pinned rotating superfluid and their form for vortex creep are given. Steady state creep and the way in which the system approaches the steady state are discussed. The developed formalism is applied to the postglitch relaxation of a pulsar, and detailed models are developed which permit explicit calculation of the postglitch response. The energy dissipation associated with creep and glitches is considered.

KAM for Beating Solutions of the Quintic NLS

NASA Astrophysics Data System (ADS)

Haus, E.; Procesi, M.

2017-09-01

We consider the nonlinear Schrödinger equation of degree five on the circle T= R / 2π}. We prove the existence of quasi-periodic solutions with four frequencies which bifurcate from "resonant" solutions [studied in Grébert and Thomann (Ann Inst Henri Poincaré Anal Non Linéaire 29(3):455-477, 2012)] of the system obtained by truncating the Hamiltonian after one step of Birkhoff normal form, exhibiting recurrent exchange of energy between some Fourier modes. The existence of these quasi-periodic solutions is a purely nonlinear effect.

TOPEX/El Nino Watch - El Nino Warm Water Pool Returns to Near Normal State, Mar, 14, 1998

NASA Technical Reports Server (NTRS)

1998-01-01

This image of the Pacific Ocean was produced using sea surface height measurements taken by the U.S.-French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on Mar. 14, 1998 and sea surface height is an indicator of the heat content of the ocean. The image shows that the sea surface height along the central equatorial Pacific has returned to a near normal state. Oceanographers indicate this is a classic pattern, typical of a mature El Nino condition. Remnants of the El Nino warm water pool, shown in red and white, are situated to the north and south of the equator. These sea surface height measurements have provided scientists with a detailed view of how the 1997-98 El Nino's warm pool behaves because the TOPEX/Poseidon satellite measures the changing sea surface height with unprecedented precision. In this image, the white and red areas indicate unusual patterns of heat storage; in the white areas, the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The green areas indicate normal conditions, while purple (the western Pacific) means at least 18 centimeters (7 inches) below normal sea level. The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. Using satellite imagery, buoy and ship data, and a forecasting model of the ocean-atmosphere system, the National Oceanic and Atmospheric Administration, (NOAA), has continued to issue an advisory indicating the so-called El Nino weather conditions that have impacted much of the United States and the world are expected to remain through the spring.

For more information, please visit the TOPEX/Poseidon project web page at http://topex-www.jpl.nasa.gov

Probing the internal composition of neutron stars with gravitational waves

NASA Astrophysics Data System (ADS)

Chatziioannou, Katerina; Yagi, Kent; Klein, Antoine; Cornish, Neil; Yunes, Nicolás

2015-11-01

Gravitational waves from neutron star binary inspirals contain information about the as yet unknown equation of state of supranuclear matter. In the absence of definitive experimental evidence that determines the correct equation of state, a number of diverse models that give the pressure inside a neutron star as function of its density have been constructed by nuclear physicists. These models differ not only in the approximations and techniques they employ to solve the many-body Schrödinger equation, but also in the internal neutron star composition they assume. We study whether gravitational wave observations of neutron star binaries in quasicircular inspirals up to contact will allow us to distinguish between equations of state of differing internal composition, thereby providing important information about the properties and behavior of extremely high density matter. We carry out a Bayesian model selection analysis, and find that second generation gravitational wave detectors can heavily constrain equations of state that contain only quark matter, but hybrid stars containing both normal and quark matter are typically harder to distinguish from normal matter stars. A gravitational wave detection with a signal-to-noise ratio of 20 and masses around 1.4 M⊙ would provide indications of the existence or absence of strange quark stars, while a signal-to-noise ratio 30 detection could either detect or rule out strange quark stars with a 20 to 1 confidence. The presence of kaon condensates or hyperons in neutron star inner cores cannot be easily confirmed. For example, for the equations of state studied in this paper, even a gravitational wave signal with a signal-to-noise ratio as high as 60 would not allow us to claim a detection of kaon condensates or hyperons with confidence greater than 5 to 1. On the other hand, if kaon condensates and hyperons do not form in neutron stars, a gravitational wave signal with similar signal-to-noise ratio would be able to constrain their existence with an 11 to 1 confidence for high-mass systems. We, finally, find that combining multiple lower signal-to-noise ratio detections (stacking) must be handled with caution since it could fail in cases where the prior information dominates over new information from the data.

THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC MODELING OF THE SOLAR WIND INCLUDING PICKUP PROTONS AND TURBULENCE TRANSPORT

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

Usmanov, Arcadi V.; Matthaeus, William H.; Goldstein, Melvyn L., E-mail: arcadi.usmanov@nasa.gov

2012-07-20

To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfermore » from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons. We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 Degree-Sign -90 Degree-Sign and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.« less

An analysis of penetration and ricochet phenomena in oblique hypervelocity impact

NASA Technical Reports Server (NTRS)

Schonberg, William P.; Taylor, Roy A.; Horn, Jennifer R.

1988-01-01

An experimental investigation of phenomena associated with the oblique hypervelocity impact of spherical projectiles on multisheet aluminum structures is described. A model that can be employed in the design of meteoroid and space debris protection systems for space structures is developed. The model consists of equations that relate crater and perforation damage of a multisheet structure to parameters such as projectile size, impact velocity, and trajectory obliquity. The equations are obtained through a regression analysis of oblique hypervelocity impact test data. This data shows that the response of a multisheet structure to oblique impact is significantly different from its response to normal hypervelocity impact. It was found that obliquely incident projectiles produce ricochet debris that can severely damage panels or instrumentation located on the exterior of a space structure. Obliquity effects of high-speed impact must, therefore, be considered in the design of any structure exposed to the meteoroid and space debris environment.

LCP method for a planar passive dynamic walker based on an event-driven scheme

NASA Astrophysics Data System (ADS)

Zheng, Xu-Dong; Wang, Qi

2018-06-01

The main purpose of this paper is to present a linear complementarity problem (LCP) method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated as a planar multi-rigid-body system. The dynamic equations of the passive dynamic walker are obtained by using Lagrange's equations of the second kind. The normal forces and frictional forces acting on the feet of the passive walker are described based on a modified Hertz contact model and Coulomb's law of dry friction. The state transition problem of stick-slip between feet and floor is formulated as an LCP, which is solved with an event-driven scheme. Finally, to validate the methodology, four gaits of the walker are simulated: the stance leg neither slips nor bounces; the stance leg slips without bouncing; the stance leg bounces without slipping; the walker stands after walking several steps.

LCP method for a planar passive dynamic walker based on an event-driven scheme

NASA Astrophysics Data System (ADS)

Zheng, Xu-Dong; Wang, Qi

2018-02-01

The main purpose of this paper is to present a linear complementarity problem (LCP) method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated as a planar multi-rigid-body system. The dynamic equations of the passive dynamic walker are obtained by using Lagrange's equations of the second kind. The normal forces and frictional forces acting on the feet of the passive walker are described based on a modified Hertz contact model and Coulomb's law of dry friction. The state transition problem of stick-slip between feet and floor is formulated as an LCP, which is solved with an event-driven scheme. Finally, to validate the methodology, four gaits of the walker are simulated: the stance leg neither slips nor bounces; the stance leg slips without bouncing; the stance leg bounces without slipping; the walker stands after walking several steps.

Numerical implementation of isolated horizon boundary conditions

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

Jaramillo, Jose Luis; Ansorg, Marcus; Limousin, Francois

2007-01-15

We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasiequilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the conformal thin sandwich equations. As main results, we first establish the consistency of including in the set of boundary conditions a constant surface gravity prescription, interpretable as a lapse boundary condition, and second we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the conformalmore » transverse traceless equations with quasiequilibrium horizon conditions extend to the conformal thin sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon.« less

Master equations and the theory of stochastic path integrals

NASA Astrophysics Data System (ADS)

Weber, Markus F.; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Spatiotemporal optical pulse transformation by a resonant diffraction grating

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

Golovastikov, N. V.; Bykov, D. A., E-mail: bykovd@gmail.com; Doskolovich, L. L., E-mail: leonid@smr.ru

The diffraction of a spatiotemporal optical pulse by a resonant diffraction grating is considered. The pulse diffraction is described in terms of the signal (the spatiotemporal incident pulse envelope) passage through a linear system. An analytic approximation in the form of a rational function of two variables corresponding to the angular and spatial frequencies has been obtained for the transfer function of the system. A hyperbolic partial differential equation describing the general form of the incident pulse envelope transformation upon diffraction by a resonant diffraction grating has been derived from the transfer function. A solution of this equation has beenmore » obtained for the case of normal incidence of a pulse with a central frequency lying near the guided-mode resonance of a diffraction structure. The presented results of numerical simulations of pulse diffraction by a resonant grating show profound changes in the pulse envelope shape that closely correspond to the proposed theoretical description. The results of the paper can be applied in creating new devices for optical pulse shape transformation, in optical information processing problems, and analog optical computations.« less

A simple derivation of the exact quasiparticle theory and its extension to arbitrary initial excited eigenstates.

PubMed

Ohno, Kaoru; Ono, Shota; Isobe, Tomoharu

2017-02-28

The quasiparticle (QP) energies, which are minus of the energies required by removing or produced by adding one electron from/to the system, corresponding to the photoemission or inverse photoemission (PE/IPE) spectra, are determined together with the QP wave functions, which are not orthonormal and even not linearly independent but somewhat similar to the normal spin orbitals in the theory of the configuration interaction, by self-consistently solving the QP equation coupled with the equation for the self-energy. The electron density, kinetic, and all interaction energies can be calculated using the QP wave functions. We prove in a simple way that the PE/IPE spectroscopy and therefore this QP theory can be applied to an arbitrary initial excited eigenstate. In this proof, we show that the energy-dependence of the self-energy is not an essential difficulty, and the QP picture holds exactly if there is no relaxation mechanism in the system. The validity of the present theory for some initial excited eigenstates is tested using the one-shot GW approximation for several atoms and molecules.

Macroscopic response in active nonlinear photonic crystals.

PubMed

Alagappan, Gandhi; John, Sajeev; Li, Er Ping

2013-09-15

We derive macroscopic equations of motion for the slowly varying electric field amplitude in three-dimensional active nonlinear optical nanostructures. We show that the microscopic Maxwell equations and polarization dynamics can be simplified to a macroscopic one-dimensional problem in the direction of group velocity. For a three-level active material, we derive the steady-state equations for normal mode frequency, threshold pumping, nonlinear Bloch mode amplitude, and lasing in photonic crystals. Our analytical results accurately recapture the results of exact numerical methods.

Extended symmetry analysis of generalized Burgers equations

NASA Astrophysics Data System (ADS)

Pocheketa, Oleksandr A.; Popovych, Roman O.

2017-10-01

Using enhanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form ut + uux + f(t, x)uxx = 0. This enhances all the previous results on symmetries of these equations and includes the description of admissible transformations, Lie symmetries, Lie and nonclassical reductions, hidden symmetries, conservation laws, potential admissible transformations, and potential symmetries. The study is based on the fact that the class is normalized, and its equivalence group is finite-dimensional.

Exact dark soliton solutions for a family of N coupled nonlinear Schrödinger equations in optical fiber media.

PubMed

Nakkeeran, K

2001-10-01

We consider a family of N coupled nonlinear Schrödinger equations which govern the simultaneous propagation of N fields in the normal dispersion regime of an optical fiber with various important physical effects. The linear eigenvalue problem associated with the integrable form of all the equations is constructed with the help of the Ablowitz-Kaup-Newell-Segur method. Using the Hirota bilinear method, exact dark soliton solutions are explicitly derived.

Transactions of the Army Conference on Applied Mathematics and Computing (4th) Held in Ithaca, New York on 27-31 May 1986

DTIC Science & Technology

1987-02-01

positive, nonincreaslng on 0 < t < *, and m decays rapidly at Infinity. Stronger power singularities at zero (a < 0) are also...considered. In this case the wavenumber appears to power four in the differential equation, the Orr-Sommerfeld equation, and to power five in the wall...normal mode, appears to power four in the differential equation. However it is this problem that is physically realistic in which fixed real frequency

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

NASA Astrophysics Data System (ADS)

Chang, Jing; Gao, Yixian; Li, Yong

2015-05-01

Consider the one dimensional nonlinear beam equation utt + uxxxx + mu + u3 = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form.

Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

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

Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina, E-mail: marina.lute@upt.ro

2015-12-15

We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.

electric dipole superconductor in bilayer exciton system

NASA Astrophysics Data System (ADS)

Sun, Qing-Feng; Jiang, Qing-Dong; Bao, Zhi-Qiang; Xie, X. C.

Recently, it was reported that the bilayer exciton systems could exhibit many new phenomena, including the large bilayer counterflow conductivity, the Coulomb drag, etc. These phenomena imply the formation of exciton condensate superfluid state. On the other hand, it is now well known that the superconductor is the condensate superfluid state of the Cooper pairs, which can be viewed as electric monopoles. In other words, the superconductor state is the electric monopole condensate superfluid state. Thus, one may wonder whether there exists electric dipole superfluid state. In this talk, we point out that the exciton in a bilayer system can be considered as a charge neutral electric dipole. And we derive the London-type and Ginzburg-Landau-type equations of electric dipole superconductivity. From these equations, we discover the Meissner-type effect (against spatial variation of magnetic fields), and the dipole current Josephson effect. The frequency in the AC Josephson effect of the dipole current is equal to that in the normal (monopole) superconductor. These results can provide direct evidence for the formation of exciton superfluid state in the bilayer systems and pave new ways to obtain the electric dipole current. We gratefully acknowledge the financial support by NBRP of China (2012CB921303 and 2015CB921102) and NSF-China under Grants Nos. 11274364 and 11574007.

Comparison of five equations for estimating resting energy expenditure in Chinese young, normal weight healthy adults

PubMed Central

2012-01-01

Background Most resting energy expenditure (REE) predictive equations for adults were derived from research conducted in western populations; whether they can also be used in Chinese young people is still unclear. Therefore, we conducted this study to determine the best REE predictive equation in Chinese normal weight young adults. Methods Forty-three (21 male, 22 female) healthy college students between the age of 18 and 25 years were recruited. REE was measured by the indirect calorimetry (IC) method. Harris-Benedict, World Health Organization (WHO), Owen, Mifflin and Liu’s equations were used to predictREE (REEe). REEe that was within 10% of measured REE (REEm) was defined as accurate. Student’s t test, Wilcoxon Signed Ranks Test, McNemar Test and the Bland-Altman method were used for data analysis. Results REEm was significantly lower (P < 0.05 or P < 0.01) than REEe from equations, except for Liu’s, Liu’s-s, Owen, Owen-s and Mifflin in men and Liu’s and Owen in women. REEe calculated by ideal body weight was significantly higher than REEe calculated by current body weight ( P < 0.01), the only exception being Harris-Benedict equation in men. Bland-Altman analysis showed that the Owen equation with current body weight generated the least bias. The biases of REEe from Owen with ideal body weight and Mifflin with both current and ideal weights were also lower. Conclusions Liu’s, Owen, and Mifflin equations are appropriate for the prediction of REE in young Chinese adults. However, the use of ideal body weight did not increase the accuracy of REEe. PMID:22937737

TOPEX/El Nino Watch - October 3, 1997

NASA Technical Reports Server (NTRS)

1997-01-01

This image of the Pacific Ocean was produced using sea surface height measurements taken by the U.S./French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on Oct. 3, 1997 as the warm water associated with El Nino (in white) spreads northward along the entire coast of North America from the equator all the way to Alaska. The warm water pool in tropical Pacific resulting from El Nino seems to have stabilized. The white and red areas indicate unusual patterns of heat storage; in the white areas, the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The surface area covered by the warm water mass is about one and one-half times the size of the continental United States. The added amount of oceanic warm water near the Americas, with a temperature between 21 and 30 C (70 to 85 F), carries the amount of heat equal to 100 times the amount of fossil fuel energy consumed by the entire U.S. population during one year. The green areas indicate normal conditions, while purple (the western Pacific) means at least 18 centimeters (7 inches) below normal sea level.

The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. Using these global data, limited regional measurements from buoys and ships, and a forecasting model of the ocean-atmosphere system, the National Centers for Environmental Prediction (NCEP) of the National Oceanic and Atmospheric Administration (NOAA) has issued an advisory indicating the presence of a strong El Nino condition throughout the coming winter.

For more information, please visit the TOPEX/Poseidon project web page at http://topex-www.jpl.nasa.gov/

A new formula for normal tissue complication probability (NTCP) as a function of equivalent uniform dose (EUD).

PubMed

Luxton, Gary; Keall, Paul J; King, Christopher R

2008-01-07

To facilitate the use of biological outcome modeling for treatment planning, an exponential function is introduced as a simpler equivalent to the Lyman formula for calculating normal tissue complication probability (NTCP). The single parameter of the exponential function is chosen to reproduce the Lyman calculation to within approximately 0.3%, and thus enable easy conversion of data contained in empirical fits of Lyman parameters for organs at risk (OARs). Organ parameters for the new formula are given in terms of Lyman model m and TD(50), and conversely m and TD(50) are expressed in terms of the parameters of the new equation. The role of the Lyman volume-effect parameter n is unchanged from its role in the Lyman model. For a non-homogeneously irradiated OAR, an equation relates d(ref), n, v(eff) and the Niemierko equivalent uniform dose (EUD), where d(ref) and v(eff) are the reference dose and effective fractional volume of the Kutcher-Burman reduction algorithm (i.e. the LKB model). It follows in the LKB model that uniform EUD irradiation of an OAR results in the same NTCP as the original non-homogeneous distribution. The NTCP equation is therefore represented as a function of EUD. The inverse equation expresses EUD as a function of NTCP and is used to generate a table of EUD versus normal tissue complication probability for the Emami-Burman parameter fits as well as for OAR parameter sets from more recent data.

On the Maxwell-Stefan approach to diffusion: a general resolution in the transient regime for one-dimensional systems.

PubMed

Leonardi, Erminia; Angeli, Celestino

2010-01-14

The diffusion process in a multicomponent system can be formulated in a general form by the generalized Maxwell-Stefan equations. This formulation is able to describe the diffusion process in different systems, such as, for instance, bulk diffusion (in the gas, liquid, and solid phase) and diffusion in microporous materials (membranes, zeolites, nanotubes, etc.). The Maxwell-Stefan equations can be solved analytically (only in special cases) or by numerical approaches. Different numerical strategies have been previously presented, but the number of diffusing species is normally restricted, with only few exceptions, to three in bulk diffusion and to two in microporous systems, unless simplifications of the Maxwell-Stefan equations are considered. In the literature, a large effort has been devoted to the derivation of the analytic expression of the elements of the Fick-like diffusion matrix and therefore to the symbolic inversion of a square matrix with dimensions n x n (n being the number of independent components). This step, which can be easily performed for n = 2 and remains reasonable for n = 3, becomes rapidly very complex in problems with a large number of components. This paper addresses the problem of the numerical resolution of the Maxwell-Stefan equations in the transient regime for a one-dimensional system with a generic number of components, avoiding the definition of the analytic expression of the elements of the Fick-like diffusion matrix. To this aim, two approaches have been implemented in a computational code; the first is the simple finite difference second-order accurate in time Crank-Nicolson scheme for which the full mathematical derivation and the relevant final equations are reported. The second is based on the more accurate backward differentiation formulas, BDF, or Gear's method (Shampine, L. F. ; Gear, C. W. SIAM Rev. 1979, 21, 1.), as implemented in the Livermore solver for ordinary differential equations, LSODE (Hindmarsh, A. C. Serial Fortran Solvers for ODE Initial Value Problems, Technical Report; https://computation.llnl.gov/casc/odepack/odepack_ home.html (2006).). Both methods have been applied to a series of specific problems, such as bulk diffusion of acetone and methanol through stagnant air, uptake of two components on a microporous material in a model system, and permeation across a microporous membrane in model systems, both with the aim to validate the method and to add new information to the comprehension of the peculiar behavior of these systems. The approach is validated by comparison with different published results and with analytic expressions for the steady-state concentration profiles or fluxes in particular systems. The possibility to treat a generic number of components (the limitation being essentially the computational power) is also tested, and results are reported on the permeation of a five component mixture through a membrane in a model system. It is worth noticing that the algorithm here reported can be applied also to the Fick formulation of the diffusion problem with concentration-dependent diffusion coefficients.

STEADY STATE FLAMMABLE GAS RELEASE RATE CALCULATION AND LOWER FLAMMABILITY LEVEL EVALUATION FOR HANFORD TANK WASTE

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

HU TA

2009-10-26

Assess the steady-state flammability level at normal and off-normal ventilation conditions. The hydrogen generation rate was calculated for 177 tanks using the rate equation model. Flammability calculations based on hydrogen, ammonia, and methane were performed for 177 tanks for various scenarios.

A Comparison of Normal and Elliptical Estimation Methods in Structural Equation Models.

ERIC Educational Resources Information Center

Schumacker, Randall E.; Cheevatanarak, Suchittra

Monte Carlo simulation compared chi-square statistics, parameter estimates, and root mean square error of approximation values using normal and elliptical estimation methods. Three research conditions were imposed on the simulated data: sample size, population contamination percent, and kurtosis. A Bentler-Weeks structural model established the…

Stability of a viscous fluid in a rectangular cavity in the presence of a magnetic field

NASA Technical Reports Server (NTRS)

Liang, C. Y.; Hung, Y. Y.

1976-01-01

The stability of an electrically conducting fluid subjected to two dimensional disturbance was investigated. A physical system consisting of two parallel infinite vertical plates which are thermally insulated was studied. An external magnetic field of constant strength was applied to normal plates. The fluid was heated from below so that a steady temperature gradient was maintained in the fluid. The governing equations were derived by perturbation technique, and solutions were obtained by a modified Galerkin method. It was found that the presence of the magnetic field increases the stability of the physical system and instability can occur in the form of neutral or oscillatory instability.

Relative Performance of Rescaling and Resampling Approaches to Model Chi Square and Parameter Standard Error Estimation in Structural Equation Modeling.

ERIC Educational Resources Information Center

Nevitt, Johnathan; Hancock, Gregory R.

Though common structural equation modeling (SEM) methods are predicated upon the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to use distribution-free estimation methods. Fortunately, promising alternatives are being integrated into…

Shock-wave structure based on the Navier-Stokes-Fourier equations.

PubMed

Uribe, F J; Velasco, R M

2018-04-01

We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature.

Shock-wave structure based on the Navier-Stokes-Fourier equations

NASA Astrophysics Data System (ADS)

Uribe, F. J.; Velasco, R. M.

2018-04-01

We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature.

Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Hayashi, Kentaro

2010-01-01

This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts…

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

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

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.« less

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

DOE PAGES

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

2017-09-28

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.« less

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

NASA Astrophysics Data System (ADS)

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

2018-01-01

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.

On the equilibrium contact angle of sessile liquid drops from molecular dynamics simulations.

PubMed

Ravipati, Srikanth; Aymard, Benjamin; Kalliadasis, Serafim; Galindo, Amparo

2018-04-28

We present a new methodology to estimate the contact angles of sessile drops from molecular simulations by using the Gaussian convolution method of Willard and Chandler [J. Phys. Chem. B 114, 1954-1958 (2010)] to calculate the coarse-grained density from atomic coordinates. The iso-density contour with average coarse-grained density value equal to half of the bulk liquid density is identified as the average liquid-vapor (LV) interface. Angles between the unit normal vectors to the average LV interface and unit normal vector to the solid surface, as a function of the distance normal to the solid surface, are calculated. The cosines of these angles are extrapolated to the three-phase contact line to estimate the sessile drop contact angle. The proposed methodology, which is relatively easy to implement, is systematically applied to three systems: (i) a Lennard-Jones (LJ) drop on a featureless LJ 9-3 surface; (ii) an SPC/E water drop on a featureless LJ 9-3 surface; and (iii) an SPC/E water drop on a graphite surface. The sessile drop contact angles estimated with our methodology for the first two systems are shown to be in good agreement with the angles predicted from Young's equation. The interfacial tensions required for this equation are computed by employing the test-area perturbation method for the corresponding planar interfaces. Our findings suggest that the widely adopted spherical-cap approximation should be used with caution, as it could take a long time for a sessile drop to relax to a spherical shape, of the order of 100 ns, especially for water molecules initiated in a lattice configuration on a solid surface. But even though a water drop can take a long time to reach the spherical shape, we find that the contact angle is well established much faster and the drop evolves toward the spherical shape following a constant-contact-angle relaxation dynamics. Making use of this observation, our methodology allows a good estimation of the sessile drop contact angle values even for moderate system sizes (with, e.g., 4000 molecules), without the need for long simulation times to reach the spherical shape.

On the equilibrium contact angle of sessile liquid drops from molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Ravipati, Srikanth; Aymard, Benjamin; Kalliadasis, Serafim; Galindo, Amparo

2018-04-01

We present a new methodology to estimate the contact angles of sessile drops from molecular simulations by using the Gaussian convolution method of Willard and Chandler [J. Phys. Chem. B 114, 1954-1958 (2010)] to calculate the coarse-grained density from atomic coordinates. The iso-density contour with average coarse-grained density value equal to half of the bulk liquid density is identified as the average liquid-vapor (LV) interface. Angles between the unit normal vectors to the average LV interface and unit normal vector to the solid surface, as a function of the distance normal to the solid surface, are calculated. The cosines of these angles are extrapolated to the three-phase contact line to estimate the sessile drop contact angle. The proposed methodology, which is relatively easy to implement, is systematically applied to three systems: (i) a Lennard-Jones (LJ) drop on a featureless LJ 9-3 surface; (ii) an SPC/E water drop on a featureless LJ 9-3 surface; and (iii) an SPC/E water drop on a graphite surface. The sessile drop contact angles estimated with our methodology for the first two systems are shown to be in good agreement with the angles predicted from Young's equation. The interfacial tensions required for this equation are computed by employing the test-area perturbation method for the corresponding planar interfaces. Our findings suggest that the widely adopted spherical-cap approximation should be used with caution, as it could take a long time for a sessile drop to relax to a spherical shape, of the order of 100 ns, especially for water molecules initiated in a lattice configuration on a solid surface. But even though a water drop can take a long time to reach the spherical shape, we find that the contact angle is well established much faster and the drop evolves toward the spherical shape following a constant-contact-angle relaxation dynamics. Making use of this observation, our methodology allows a good estimation of the sessile drop contact angle values even for moderate system sizes (with, e.g., 4000 molecules), without the need for long simulation times to reach the spherical shape.

Determination of stress intensity factors for interface cracks under mixed-mode loading

NASA Technical Reports Server (NTRS)

Naik, Rajiv A.; Crews, John H., Jr.

1992-01-01

A simple technique was developed using conventional finite element analysis to determine stress intensity factors, K1 and K2, for interface cracks under mixed-mode loading. This technique involves the calculation of crack tip stresses using non-singular finite elements. These stresses are then combined and used in a linear regression procedure to calculate K1 and K2. The technique was demonstrated by calculating three different bimaterial combinations. For the normal loading case, the K's were within 2.6 percent of an exact solution. The normalized K's under shear loading were shown to be related to the normalized K's under normal loading. Based on these relations, a simple equation was derived for calculating K1 and K2 for mixed-mode loading from knowledge of the K's under normal loading. The equation was verified by computing the K's for a mixed-mode case with equal and normal shear loading. The correlation between exact and finite element solutions is within 3.7 percent. This study provides a simple procedure to compute K2/K1 ratio which has been used to characterize the stress state at the crack tip for various combinations of materials and loadings. Tests conducted over a range of K2/K1 ratios could be used to fully characterize interface fracture toughness.

Solution of the surface Euler equations for accurate three-dimensional boundary-layer analysis of aerodynamic configurations

NASA Technical Reports Server (NTRS)

Iyer, V.; Harris, J. E.

1987-01-01

The three-dimensional boundary-layer equations in the limit as the normal coordinate tends to infinity are called the surface Euler equations. The present paper describes an accurate method for generating edge conditions for three-dimensional boundary-layer codes using these equations. The inviscid pressure distribution is first interpolated to the boundary-layer grid. The surface Euler equations are then solved with this pressure field and a prescribed set of initial and boundary conditions to yield the velocities along the two surface coordinate directions. Results for typical wing and fuselage geometries are presented. The smoothness and accuracy of the edge conditions obtained are found to be superior to the conventional interpolation procedures.

Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential

NASA Technical Reports Server (NTRS)

Campbell, Joel

2009-01-01

The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.

Optimization of selected molecular orbitals in group basis sets.

PubMed

Ferenczy, György G; Adams, William H

2009-04-07

We derive a local basis equation which may be used to determine the orbitals of a group of electrons in a system when the orbitals of that group are represented by a group basis set, i.e., not the basis set one would normally use but a subset suited to a specific electronic group. The group orbitals determined by the local basis equation minimize the energy of a system when a group basis set is used and the orbitals of other groups are frozen. In contrast, under the constraint of a group basis set, the group orbitals satisfying the Huzinaga equation do not minimize the energy. In a test of the local basis equation on HCl, the group basis set included only 12 of the 21 functions in a basis set one might ordinarily use, but the calculated active orbital energies were within 0.001 hartree of the values obtained by solving the Hartree-Fock-Roothaan (HFR) equation using all 21 basis functions. The total energy found was just 0.003 hartree higher than the HFR value. The errors with the group basis set approximation to the Huzinaga equation were larger by over two orders of magnitude. Similar results were obtained for PCl(3) with the group basis approximation. Retaining more basis functions allows an even higher accuracy as shown by the perfect reproduction of the HFR energy of HCl with 16 out of 21 basis functions in the valence basis set. When the core basis set was also truncated then no additional error was introduced in the calculations performed for HCl with various basis sets. The same calculations with fixed core orbitals taken from isolated heavy atoms added a small error of about 10(-4) hartree. This offers a practical way to calculate wave functions with predetermined fixed core and reduced base valence orbitals at reduced computational costs. The local basis equation can also be used to combine the above approximations with the assignment of local basis sets to groups of localized valence molecular orbitals and to derive a priori localized orbitals. An appropriately chosen localization and basis set assignment allowed a reproduction of the energy of n-hexane with an error of 10(-5) hartree, while the energy difference between its two conformers was reproduced with a similar accuracy for several combinations of localizations and basis set assignments. These calculations include localized orbitals extending to 4-5 heavy atoms and thus they require to solve reduced dimension secular equations. The dimensions are not expected to increase with increasing system size and thus the local basis equation may find use in linear scaling electronic structure calculations.

A minimization principle for the description of modes associated with finite-time instabilities

PubMed Central

Babaee, H.

2016-01-01

We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have finite lifetime, they can play a crucial role either by altering the system dynamics through the activation of other instabilities or by creating sudden nonlinear energy transfers that lead to extreme responses. However, their essentially transient character makes their description a particularly challenging task. We develop a minimization framework that focuses on the optimal approximation of the system dynamics in the neighbourhood of the system state. This minimization formulation results in differential equations that evolve a time-dependent basis so that it optimally approximates the most unstable directions. We demonstrate the capability of the method for two families of problems: (i) linear systems, including the advection–diffusion operator in a strongly non-normal regime as well as the Orr–Sommerfeld/Squire operator, and (ii) nonlinear problems, including a low-dimensional system with transient instabilities and the vertical jet in cross-flow. We demonstrate that the time-dependent subspace captures the strongly transient non-normal energy growth (in the short-time regime), while for longer times the modes capture the expected asymptotic behaviour. PMID:27118900

Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach.

PubMed

Mahasa, Khaphetsi Joseph; Eladdadi, Amina; de Pillis, Lisette; Ouifki, Rachid

2017-01-01

In the present paper, we address by means of mathematical modeling the following main question: How can oncolytic virus infection of some normal cells in the vicinity of tumor cells enhance oncolytic virotherapy? We formulate a mathematical model describing the interactions between the oncolytic virus, the tumor cells, the normal cells, and the antitumoral and antiviral immune responses. The model consists of a system of delay differential equations with one (discrete) delay. We derive the model's basic reproductive number within tumor and normal cell populations and use their ratio as a metric for virus tumor-specificity. Numerical simulations are performed for different values of the basic reproduction numbers and their ratios to investigate potential trade-offs between tumor reduction and normal cells losses. A fundamental feature unravelled by the model simulations is its great sensitivity to parameters that account for most variation in the early or late stages of oncolytic virotherapy. From a clinical point of view, our findings indicate that designing an oncolytic virus that is not 100% tumor-specific can increase virus particles, which in turn, can further infect tumor cells. Moreover, our findings indicate that when infected tissues can be regenerated, oncolytic viral infection of normal cells could improve cancer treatment.

On oscillating flows in randomly heterogeneous porous media.

PubMed

Trefry, M G; McLaughlin, D; Metcalfe, G; Lester, D; Ord, A; Regenauer-Lieb, K; Hobbs, B E

2010-01-13

The emergence of structure in reactive geofluid systems is of current interest. In geofluid systems, the fluids are supported by a porous medium whose physical and chemical properties may vary in space and time, sometimes sharply, and which may also evolve in reaction with the local fluids. Geofluids may also experience pressure and temperature conditions within the porous medium that drive their momentum relations beyond the normal Darcy regime. Furthermore, natural geofluid systems may experience forcings that are periodic in nature, or at least episodic. The combination of transient forcing, near-critical fluid dynamics and heterogeneous porous media yields a rich array of emergent geofluid phenomena that are only now beginning to be understood. One of the barriers to forward analysis in these geofluid systems is the problem of data scarcity. It is most often the case that fluid properties are reasonably well known, but that data on porous medium properties are measured with much less precision and spatial density. It is common to seek to perform an estimation of the porous medium properties by an inverse approach, that is, by expressing porous medium properties in terms of observed fluid characteristics. In this paper, we move toward such an inversion for the case of a generalized geofluid momentum equation in the context of time-periodic boundary conditions. We show that the generalized momentum equation results in frequency-domain responses that are governed by a second-order equation which is amenable to numerical solution. A stochastic perturbation approach demonstrates that frequency-domain responses of the fluids migrating in heterogeneous domains have spatial spectral densities that can be expressed in terms of the spectral densities of porous media properties. This journal is © 2010 The Royal Society

Features of self-organized plasma physics in tokamaks

NASA Astrophysics Data System (ADS)

Razumova, K. A.

2018-01-01

The history of investigations the role of self-organization processes in tokamak plasma confinement is presented. It was experimentally shown that the normalized pressure profile is the same for different tokamaks. Instead of the conventional Fick equation, where the thermal flux is proportional to a pressure gradient, processes in the plasma are well described by the Dyabilanin’s energy balance equation, in which the heat flux is proportional to the difference of normalized gradients for self-consistent and real pressure profiles. The transport coefficient depends on the values of heat flux, which compensates distortion of the pressure profile with external impacts. Radiative cooling of the plasma edge decreases the heat flux and improves the confinement.

Some aspects of the stability of the plane deformation mode of filaments of finite stiffness beyond the elasticity limits

NASA Astrophysics Data System (ADS)

Shimanovskii, A. V.

A method for calculating the plane bending of elastic-plastic filaments of finite stiffness is proposed on the basis of plastic flow theory. The problem considered is shown to reduce to relations similar to Kirchhoff equations for elastic work. Expressions are obtained for determining the normalized stiffness characteristics for the cross section of a filament with plastic regions containing beam theory equations as a particular case. A study is made of the effect of the plastic region size on the position of the elastic deformation-unloading interface and on the normalized stiffness of the filament cross section. Calculation results are presented in graphic form.

CICATRIZATION OF WOUNDS

PubMed Central

Du Noüy, P. Lecomte

1916-01-01

The cicatrization of sterile wounds may be studied in the same way as an ordinary physicochemical phenomenon. It is possible, therefore, to express the law of cicatrization by a mathematical equation as soon as an accurate measure of the wound can be obtained. By means of the equation, a curve is obtained which represents the theoretical evolution of the cicatrization of a wound. This curve, being an expression of what should happen on a normal wound, healing aseptically, on a normal man, is a daily point of comparison to what appears actually on the observed wound, and allows one to study accurately the fluctuations of cicatrization on a given individual, and the action of different dressings and antiseptic substances PMID:19868053

Low bias negative differential conductance and reversal of current in coupled quantum dots in different topological configurations

NASA Astrophysics Data System (ADS)

Devi, Sushila; Brogi, B. B.; Ahluwalia, P. K.; Chand, S.

2018-06-01

Electronic transport through asymmetric parallel coupled quantum dot system hybridized between normal leads has been investigated theoretically in the Coulomb blockade regime by using Non-Equilibrium Green Function formalism. A new decoupling scheme proposed by Rabani and his co-workers has been adopted to close the chain of higher order Green's functions appearing in the equations of motion. For resonant tunneling case; the calculations of current and differential conductance have been presented during transition of coupled quantum dot system from series to symmetric parallel configuration. It has been found that during this transition, increase in current and differential conductance of the system occurs. Furthermore, clear signatures of negative differential conductance and negative current appear in series case, both of which disappear when topology of system is tuned to asymmetric parallel configuration.

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

User Guide for Compressible Flow Toolbox Version 2.1 for Use With MATLAB(Registered Trademark); Version 7

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.

Time dependent Schrödinger equation for black hole evaporation: No information loss

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

Corda, Christian, E-mail: cordac.galilei@gmail.com

2015-02-15

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state”. This was the starting point of the popular “black hole (BH) information paradox”. In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model,more » a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking’s claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect ’t Hooft’s assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.« less

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

NASA Technical Reports Server (NTRS)

Walker, H. F.

1976-01-01

Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate were considered. These equations suggest certain successive approximations iterative procedures for obtaining maximum likelihood estimates. The procedures, which are generalized steepest ascent (deflected gradient) procedures, contain those of Hosmer as a special case.

Maximum Likelihood Methods in Treating Outliers and Symmetrically Heavy-Tailed Distributions for Nonlinear Structural Equation Models with Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum; Xia, Ye-Mao

2006-01-01

By means of more than a dozen user friendly packages, structural equation models (SEMs) are widely used in behavioral, education, social, and psychological research. As the underlying theory and methods in these packages are vulnerable to outliers and distributions with longer-than-normal tails, a fundamental problem in the field is the…

The Locus Equation as an Index of Coarticulation in Syllables Produced by Speakers with Profound Hearing Loss

ERIC Educational Resources Information Center

McCaffrey Morrison, Helen

2008-01-01

Locus equations (LEs) were derived from consonant-vowel-consonant (CVC) syllables produced by four speakers with profound hearing loss. Group data indicated that LE functions obtained for the separate CVC productions initiated by /b/, /d/, and /g/ were less well-separated in acoustic space than those obtained from speakers with normal hearing. A…

Reliable and More Powerful Methods for Power Analysis in Structural Equation Modeling

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Zhang, Zhiyong; Zhao, Yanyun

2017-01-01

The normal-distribution-based likelihood ratio statistic T[subscript ml] = nF[subscript ml] is widely used for power analysis in structural Equation modeling (SEM). In such an analysis, power and sample size are computed by assuming that T[subscript ml] follows a central chi-square distribution under H[subscript 0] and a noncentral chi-square…

Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion

PubMed Central

Grimshaw, Roger; Stepanyants, Yury; Alias, Azwani

2016-01-01

It is well known that the Ostrovsky equation with normal dispersion does not support steady solitary waves. An initial Korteweg–de Vries solitary wave decays adiabatically through the radiation of long waves and is eventually replaced by an envelope solitary wave whose carrier wave and envelope move with different velocities (phase and group velocities correspondingly). Here, we examine the same initial condition for the Ostrovsky equation with anomalous dispersion, when the wave frequency increases with wavenumber in the limit of very short waves. The essential difference is that now there exists a steady solitary wave solution (Ostrovsky soliton), which in the small-amplitude limit can be described asymptotically through the solitary wave solution of a nonlinear Schrödinger equation, based at that wavenumber where the phase and group velocities coincide. Long-time numerical simulations show that the emergence of this steady envelope solitary wave is a very robust feature. The initial Korteweg–de Vries solitary wave transforms rapidly to this envelope solitary wave in a seemingly non-adiabatic manner. The amplitude of the Ostrovsky soliton strongly correlates with the initial Korteweg–de Vries solitary wave. PMID:26997887

Reference breast temperature: proposal of an equation

PubMed Central

de Souza, Gladis Aparecida Galindo Reisemberger; Brioschi, Marcos Leal; Vargas, José Viriato Coelho; Morais, Keli Cristiane Correia; Dalmaso, Carlos; Neves, Eduardo Borba

2015-01-01

ABSTRACT Objective To develop an equation to estimate the breast reference temperature according to the variation of room and core body temperatures. Methods Four asymptomatic women were evaluated for three consecutive menstrual cycles. Using thermography, the temperature of breasts and eyes was measured as indirect reference of core body and room temperatures. To analyze the thermal behavior of the breasts during the cycle, the core body and room temperatures were normalized by means of a mathematical equation. Results We performed 180 observations and the core temperature had the highest correlation with the breast temperature, followed by room temperature. The proposed prediction model could explain 45.3% of the breast temperature variation, with variable room temperature variable; it can be accepted as a way to estimate the reference breast temperature at different room temperatures. Conclusion The average breast temperature in healthy women had a direct relation with the core and room temperature and can be estimated mathematically. It is suggested that an equation could be used in clinical practice to estimate the normal breast reference temperature in young women, regardless of the day of the cycle, therefore assisting in evaluation of anatomical studies. PMID:26761549

Structural Equation Analysis of the Wechsler Adult Intelligence Scale-Revised in a Normal Elderly Sample.

ERIC Educational Resources Information Center

Burton, D. Bradley; And Others

1994-01-01

A maximum-likelihood confirmatory factor analysis was performed by applying LISREL VII to the Wechsler Adult Intelligence Scale-Revised results of a normal elderly sample of 225 adults. Results indicate that a three-factor model fits best across all sample combinations. A mild gender effect is discussed. (SLD)

Normal versus Noncentral Chi-Square Asymptotics of Misspecified Models

ERIC Educational Resources Information Center

Chun, So Yeon; Shapiro, Alexander

2009-01-01

The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…

A normalized model for the half-bridge series resonant converter

NASA Technical Reports Server (NTRS)

King, R.; Stuart, T. A.

1981-01-01

Closed-form steady-state equations are derived for the half-bridge series resonant converter with a rectified (dc) load. Normalized curves for various currents and voltages are then plotted as a function of the circuit parameters. Experimental results based on a 10-kHz converter are presented for comparison with the calculations.

Normal stress effects on Knudsen flow

NASA Astrophysics Data System (ADS)

Eu, Byung Chan

2018-01-01

Normal stress effects are investigated on tube flow of a single-component non-Newtonian fluid under a constant pressure gradient in a constant temperature field. The generalized hydrodynamic equations are employed, which are consistent with the laws of thermodynamics. In the cylindrical tube flow configuration, the solutions of generalized hydrodynamic equations are exactly solvable and the flow velocity is obtained in a simple one-dimensional integral quadrature. Unlike the case of flow in the absence of normal stresses, the flow develops an anomaly in that the flow in the boundary layer becomes stagnant and the thickness of such a stagnant velocity boundary layer depends on the pressure gradient, the aspect ratio of the radius to the length of the tube, and the pressure (or density and temperature) at the entrance of the tube. The volume flow rate formula through the tube is derived for the flow. It generalizes the Knudsen flow rate formula to the case of a non-Newtonian stress tensor in the presence of normal stress differences. It also reduces to the Navier-Stokes theory formula in the low shear rate limit near equilibrium.

Design, manufacture and performance evaluation of HTS electromagnets for the hybrid magnetic levitation system

NASA Astrophysics Data System (ADS)

Chu, S. Y.; Hwang, Y. J.; Choi, S.; Na, J. B.; Kim, Y. J.; Chang, K. S.; Bae, D. K.; Lee, C. Y.; Ko, T. K.

2011-11-01

A high speed electromagnetic suspension (EMS) maglev has emerged as the solution to speed limit problem that conventional high-speed railroad has. In the EMS maglev, small levitation gap needs uniform guide-way which leads to increase the construction cost. The large levitation gap can reduce the construction cost. However it is hard for normal conducting electromagnet to produce larger magneto-motive force (MMF) for generating levitation force as increased levitation gap. This is because normal conductors have limited rating current to their specific volume. Therefore, the superconducting electromagnet can be one of the solutions for producing both large levitation gap and sufficient MMF. The superconducting electromagnets have incomparably high allowable current density than what normal conductors have. In this paper, the prototype of high temperature superconducting (HTS) electromagnets were designed and manufactured applicable to hybrid electromagnetic suspension system (H-EMS). The H-EMS consists of control coils for levitation control and superconducting coils for producing MMF for levitation. The required MMF for generating given levitation force was calculated by both equations of ideal U-core magnet and magnetic field analysis using the finite element method (FEM). The HTS electromagnets were designed as double pancakes with Bi-2223/Ag tapes. Experiments to confirm its operating performance were performed in liquid nitrogen (LN2).

Cotton-type and joint invariants for linear elliptic systems.

PubMed

Aslam, A; Mahomed, F M

2013-01-01

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

Cotton-Type and Joint Invariants for Linear Elliptic Systems

PubMed Central

Aslam, A.; Mahomed, F. M.

2013-01-01

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

The nonlinear wave equation for higher harmonics in free-electron lasers

NASA Technical Reports Server (NTRS)

Colson, W. B.

1981-01-01

The nonlinear wave equation and self-consistent pendulum equation are generalized to describe free-electron laser operation in higher harmonics; this can significantly extend their tunable range to shorter wavelengths. The dynamics of the laser field's amplitude and phase are explored for a wide range of parameters using families of normalized gain curves applicable to both the fundamental and harmonics. The electron phase-space displays the fundamental physics driving the wave, and this picture is used to distinguish between the effects of high gain and Coulomb forces.

Numerical computation of linear instability of detonations

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry; Kasimov, Aslan

2017-11-01

We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

On the solution of integral equations with a generalized Cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Preconditioning the Helmholtz Equation for Rigid Ducts

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1998-01-01

An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.

Equidistant map projections of a triaxial ellipsoid with the use of reduced coordinates

NASA Astrophysics Data System (ADS)

Pędzich, Paweł

2017-12-01

The paper presents a new method of constructing equidistant map projections of a triaxial ellipsoid as a function of reduced coordinates. Equations for x and y coordinates are expressed with the use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows to use common known and widely described in literature methods of solving such integrals and functions. The main advantage of this method is the fact that the calculations of x and y coordinates are practically based on a single algorithm that is required to solve the elliptic integral of the second kind. Equations are provided for three types of map projections: cylindrical, azimuthal and pseudocylindrical. These types of projections are often used in planetary cartography for presentation of entire and polar regions of extraterrestrial objects. The paper also contains equations for the calculation of the length of a meridian and a parallel of a triaxial ellipsoid in reduced coordinates. Moreover, graticules of three coordinates systems (planetographic, planetocentric and reduced) in developed map projections are presented. The basic properties of developed map projections are also described. The obtained map projections may be applied in planetary cartography in order to create maps of extraterrestrial objects.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Day, Brad A.; Meade, Andrew J., Jr.

1993-01-01

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Mode localization in a class of multidegree-of-freedom nonlinear systems with cyclic symmetry

NASA Astrophysics Data System (ADS)

Vakakis, Alexander F.; Cetinkaya, Cetin

1993-02-01

The free oscillations of n-degree-of-freedom (DOF) nonlinear systems with cyclic symmetry and weak coupling between substructures are examined. An asymptotic methodology is used to detect localized nonsimilar normal modes, i.e., free periodic motions spatially confined to only a limited number of substructures of the cyclic system. It is shown that nonlinear mode localization occurs in the perfectly symmetric, weakly coupled structure, in contrast to linear mode localization, which exists only in the presence of substructure 'mistuning'. In addition to the localized modes, nonlocalized modes are also found in the weakly coupled system. The stability of the identified modes is investigated by means of an approximate two-timing averaging mothodology, and the general theory is applied to the case of a cyclic system with three-DOF. The theoretical results are then verified by direct numerical integrations of the equations of motion.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations - Part 1: Nonhydrostatic inertia-gravity modes

NASA Astrophysics Data System (ADS)

Konor, Celal S.; Randall, David A.

2018-05-01

We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia-gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelastic equations that are discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of both horizontal grid spacing and vertical wavenumber are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by running linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined.Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone-resolving scales (with low horizontal wavenumbers). We conclude that, aided by nonhydrostatic effects, the Z and C grids become overall more accurate for cloud-resolving resolutions (with high horizontal wavenumbers) than for the cyclone-resolving scales.A companion paper, Part 2, discusses the impacts of the discretization on the Rossby modes on a midlatitude β plane.

Trace elements in lenses of normal Wistar Kyoto rats

NASA Astrophysics Data System (ADS)

Kinoshita, Akio; Gong, Huaqing; Amemiya, Tsugio; Takaya, Kenichi; Tozu, Miyako; Ohashi, Yoshiharu

2003-01-01

Chemical analysis of the element and organic substance at the site of pathological changes due to aging is one of the approaches of cataract research. Time of flight secondary ion mass spectrometry (TOF-SIMS) microscopy is expected to analyze elements and organic substances in the lens. The purpose of the present study is to compare elements and organic substances in the lenses of normal 4-month-old rats with those of normal 15-month-old rats by means of a TOF-SIMS microscope. The present study showed that the concentration of Ca and Fe was significantly higher, and that of Na and Mg was significantly lower in 15-month-old rats than that in 4-month-old rats. No changes were found in the concentration of K. The present study also showed that the equator contained more Ca, Na and Mg than the nucleus; in contrast, the Cu concentration was higher in the nucleus than in the equator. In 15-month-old rats, Mg and Vit. A in the equator and Zn in the nucleus were significantly lower than those in 4-month-old rats. TOF-SIMS microscopy could detect elemental changes in the rat lens with age, and is expected to be useful approach of cataract studies.

Transport of water and ions in partially water-saturated porous media. Part 1. Constitutive equations

NASA Astrophysics Data System (ADS)

Revil, A.

2017-05-01

I developed a model of cross-coupled flow in partially saturated porous media based on electrokinetic coupling including the effect of ion filtration (normal and reverse osmosis) and the multi-component nature of the pore water (wetting) phase. The model also handles diffusion and membrane polarization but is valid only for saturations above the irreducible water saturation. I start with the local Nernst-Planck and Stokes equations and I use a volume-averaging procedure to obtain the generalized Ohm, Fick, and Darcy equations with cross-coupling terms at the scale of a representative elementary volume of the porous rock. These coupling terms obey Onsager's reciprocity, which is a required condition, at the macroscale, to keep the total dissipation function of the system positive. Rather than writing the electrokinetic terms in terms of zeta potential (the double layer electrical potential on the slipping plane located in the pore water), I developed the model in terms of an effective charge density dragged by the flow of the pore water. This effective charge density is found to be strongly controlled by the permeability and the water saturation. I also developed an electrical conductivity equation including the effect of saturation on both bulk and surface conductivities, the surface conductivity being associated with electromigration in the electrical diffuse layer coating the grains. This surface conductivity depends on the CEC of the porous material.

TOPEX/El Nino Watch - Satellite Shows Pacific Running Hot and Cold, September 12, 1998

NASA Technical Reports Server (NTRS)

1998-01-01

This image of the Pacific Ocean was produced using sea-surface height measurements taken by the U.S.-French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on September 12, 1998; these sea surface heights are an indicator of the changing amount of heat stored in the ocean. The tropical Pacific Ocean continues to exhibit the complicated characteristics of both a lingering El Nino, and a possibly waning La Nina situation. This image shows that the rapid cooling of the central tropical Pacific has slowed and this area of low sea level (shown in purple) has decreased slightly since last month. It is still uncertain, scientists say, that this cold pool will evolve into a long-lasting La Nina situation. Remnants of the El Nino warm water pool, shown here in red and white, are still lingering to the north and south of the equator. The coexistence of these two contrasting conditions indicates that the ocean and the climate system remain in transition. These strong patterns have remained in the climate system for many months and will continue to influence weather conditions around the world in the coming fall and winter. The satellite's sea-surface height measurements have provided scientists with a detailed view of the 1997-98 El Nino because the TOPEX/Poseidon satellite measures the changing sea-surface height with unprecedented precision. The purple areas are about 18 centimeters (7 inches) below normal, creating a deficit in the heat supply to the surface waters. The white areas show the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The green areas indicate normal conditions. The purple areas are 14 to 18 centimeters (6 to 7 inches) below normal and the blue areas are 5 to 13 centimeters (2 to 5 inches) below normal. The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. A La Nina situation is essentially the opposite of an El Nino condition, but during La Nina the trade winds are stronger than normal and the cold water that normally exists along the coast of South America extends to the central equatorial Pacific. A La Nina situation also changes global weather patterns, and is associated with less moisture in the air resulting in less rain along the west coasts of North and South America.

For more information, please visit the TOPEX/Poseidon project web page at http://topex-www.jpl.nasa.gov

Shelf-life of a 2.5% sodium hypochlorite solution as determined by Arrhenius equation.

PubMed

Nicoletti, Maria Aparecida; Siqueira, Evandro Luiz; Bombana, Antonio Carlos; Oliveira, Gabriella Guimarães de

2009-01-01

Accelerated stability tests are indicated to assess, within a short time, the degree of chemical degradation that may affect an active substance, either alone or in a formula, under normal storage conditions. This method is based on increased stress conditions to accelerate the rate of chemical degradation. Based on the equation of the straight line obtained as a function of the reaction order (at 50 and 70 degrees C) and using Arrhenius equation, the speed of the reaction was calculated for the temperature of 20 degrees C (normal storage conditions). This model of accelerated stability test makes it possible to predict the chemical stability of any active substance at any given moment, as long as the method to quantify the chemical substance is available. As an example of the applicability of Arrhenius equation in accelerated stability tests, a 2.5% sodium hypochlorite solution was analyzed due to its chemical instability. Iodometric titration was used to quantify free residual chlorine in the solutions. Based on data obtained keeping this solution at 50 and 70 degrees C, using Arrhenius equation and considering 2.0% of free residual chlorine as the minimum acceptable threshold, the shelf-life was equal to 166 days at 20 degrees C. This model, however, makes it possible to calculate shelf-life at any other given temperature.

Hypothesis: the regulation of the partial pressure of oxygen by the serotonergic nervous system in hypoxia.

PubMed

Devereux, Diana; Ikomi-Kumm, Julie

2013-03-01

The regulation of the partial pressure of oxygen by the serotonergic nervous system in hypoxia is a hypothesis, which proposes an inherent operative system in homo sapiens that allows central nervous system and endocrine-mediated vascular system adaption to variables in partial pressure of oxygen, pH and body composition, while maintaining sufficient oxygen saturation for the immune system and ensuring protection of major organs in hypoxic and suboptimal conditions. While acknowledging the importance of the Henderson-Hasselbalch equation in the regulation of acid base balance, the hypothesis seeks to define the specific neuroendocrine/vascular mechanisms at work in regulating acid base balance in hypoxia and infection. The SIA (serotonin-immune-adrenergic) system is proposed as a working model, which allows central nervous system and endocrine-mediated macro- and micro vascular 'fine tuning'. The neurotransmitter serotonin serves as a 'hypoxic sensor' in concert with other operators to orchestrate homeostatic balance in normal and pathological states. The SIA system finely regulates oxygen, fuel and metabolic buffering systems at local sites to ensure optimum conditions for the immune response. The SIA system is fragile and its operation may be affected by infection, stress, diet, environmental toxins and lack of exercise. The hypothesis provides new insight in the area of neuro-gastroenterology, and emphasizes the importance of diet and nutrition as a complement in the treatment of infection, as well as the normalization of intestinal flora following antibiotic therapy. Copyright © 2012 Elsevier Ltd. All rights reserved.

The Use of a Code-generating System for the Derivation of the Equations for Wind Turbine Dynamics

NASA Astrophysics Data System (ADS)

Ganander, Hans

2003-10-01

For many reasons the size of wind turbines on the rapidly growing wind energy market is increasing. Relations between aeroelastic properties of these new large turbines change. Modifications of turbine designs and control concepts are also influenced by growing size. All these trends require development of computer codes for design and certification. Moreover, there is a strong desire for design optimization procedures, which require fast codes. General codes, e.g. finite element codes, normally allow such modifications and improvements of existing wind turbine models. This is done relatively easy. However, the calculation times of such codes are unfavourably long, certainly for optimization use. The use of an automatic code generating system is an alternative for relevance of the two key issues, the code and the design optimization. This technique can be used for rapid generation of codes of particular wind turbine simulation models. These ideas have been followed in the development of new versions of the wind turbine simulation code VIDYN. The equations of the simulation model were derived according to the Lagrange equation and using Mathematica®, which was directed to output the results in Fortran code format. In this way the simulation code is automatically adapted to an actual turbine model, in terms of subroutines containing the equations of motion, definitions of parameters and degrees of freedom. Since the start in 1997, these methods, constituting a systematic way of working, have been used to develop specific efficient calculation codes. The experience with this technique has been very encouraging, inspiring the continued development of new versions of the simulation code as the need has arisen, and the interest for design optimization is growing.

Numerical simulation of the processes in the normal incidence tube for high acoustic pressure levels

NASA Astrophysics Data System (ADS)

Fedotov, E. S.; Khramtsov, I. V.; Kustov, O. Yu.

2016-10-01

Numerical simulation of the acoustic processes in an impedance tube at high levels of acoustic pressure is a way to solve a problem of noise suppressing by liners. These studies used liner specimen that is one cylindrical Helmholtz resonator. The evaluation of the real and imaginary parts of the liner acoustic impedance and sound absorption coefficient was performed for sound pressure levels of 130, 140 and 150 dB. The numerical simulation used experimental data having been obtained on the impedance tube with normal incidence waves. At the first stage of the numerical simulation it was used the linearized Navier-Stokes equations, which describe well the imaginary part of the liner impedance whatever the sound pressure level. These equations were solved by finite element method in COMSOL Multiphysics program in axisymmetric formulation. At the second stage, the complete Navier-Stokes equations were solved by direct numerical simulation in ANSYS CFX in axisymmetric formulation. As the result, the acceptable agreement between numerical simulation and experiment was obtained.

Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers.

PubMed

Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S

2016-05-01

Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.

Erratum: ``The Luminosity Function of IRAS Point Source Catalog Redshift Survey Galaxies'' (ApJ, 587, L89 [2003])

NASA Astrophysics Data System (ADS)

Takeuchi, Tsutomu T.; Yoshikawa, Kohji; Ishii, Takako T.

2004-05-01

We have mentioned that we normalized the parameters for the luminosity function by the Hubble constant H0=100 km s-1 Mpc-1 however, for the characteristic luminosity L* we erroneously normalized it by H0=70 km s-1 Mpc-1. As a result, we have proposed wrong numerical factors for L*. In addition, there is a typographic error in the exponent of equation (6) of the published manuscript. Correct values are as follows: L*=(4.34+/-0.86)×108 h-2 [Lsolar] for equation (4), and L*=(2.50+/-0.44)×109 h-2 [Lsolar] and L*=(9.55+/-0.20)×108 h-2 [Lsolar] for equations (5) and (6), respectively. All the other parameters are correct. The errors have occurred only in the final conversion, and they do not affect our discussions and conclusions at all. We thank P. Ranalli for pointing out the errors.

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Modelling Spread of Oncolytic Viruses in Heterogeneous Cell Populations

NASA Astrophysics Data System (ADS)

Ellis, Michael; Dobrovolny, Hana

2014-03-01

One of the most promising areas in current cancer research and treatment is the use of viruses to attack cancer cells. A number of oncolytic viruses have been identified to date that possess the ability to destroy or neutralize cancer cells while inflicting minimal damage upon healthy cells. Formulation of predictive models that correctly describe the evolution of infected tumor systems is critical to the successful application of oncolytic virus therapy. A number of different models have been proposed for analysis of the oncolytic virus-infected tumor system, with approaches ranging from traditional coupled differential equations such as the Lotka-Volterra predator-prey models, to contemporary modeling frameworks based on neural networks and cellular automata. Existing models are focused on tumor cells and the effects of virus infection, and offer the potential for improvement by including effects upon normal cells. We have recently extended the traditional framework to a 2-cell model addressing the full cellular system including tumor cells, normal cells, and the impacts of viral infection upon both populations. Analysis of the new framework reveals complex interaction between the populations and potential inability to simultaneously eliminate the virus and tumor populations.

Whitham modulation theory for the two-dimensional Benjamin-Ono equation.

PubMed

Ablowitz, Mark; Biondini, Gino; Wang, Qiao

2017-09-01

Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.

User's Guide of TOUGH2-EGS. A Coupled Geomechanical and Reactive Geochemical Simulator for Fluid and Heat Flow in Enhanced Geothermal Systems Version 1.0

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

Fakcharoenphol, Perapon; Xiong, Yi; Hu, Litang

TOUGH2-EGS is a numerical simulation program coupling geomechanics and chemical reactions for fluid and heat flows in porous media and fractured reservoirs of enhanced geothermal systems. The simulator includes the fully-coupled geomechanical (THM) module, the fully-coupled geochemical (THC) module, and the sequentially coupled reactive geochemistry (THMC) module. The fully-coupled flow-geomechanics model is developed from the linear elastic theory for the thermo-poro-elastic system and is formulated with the mean normal stress as well as pore pressure and temperature. The chemical reaction is sequentially coupled after solution of flow equations, which provides the flow velocity and phase saturation for the solute transportmore » calculation at each time step. In addition, reservoir rock properties, such as porosity and permeability, are subjected to change due to rock deformation and chemical reactions. The relationships between rock properties and geomechanical and chemical effects from poro-elasticity theories and empirical correlations are incorporated into the simulator. This report provides the user with detailed information on both mathematical models and instructions for using TOUGH2-EGS for THM, THC or THMC simulations. The mathematical models include the fluid and heat flow equations, geomechanical equation, reactive geochemistry equations, and discretization methods. Although TOUGH2-EGS has the capability for simulating fluid and heat flows coupled with both geomechanical and chemical effects, it is up to the users to select the specific coupling process, such as THM, THC, or THMC in a simulation. There are several example problems illustrating the applications of this program. These example problems are described in details and their input data are presented. The results demonstrate that this program can be used for field-scale geothermal reservoir simulation with fluid and heat flow, geomechanical effect, and chemical reaction in porous and fractured media.« less

Computational and theoretical analysis of free surface flow in a thin liquid film under zero and normal gravity

NASA Technical Reports Server (NTRS)

Faghri, Amir; Swanson, Theodore D.

1988-01-01

The results of a numerical computation and theoretical analysis are presented for the flow of a thin liquid film in the presence and absence of a gravitational body force. Five different flow systems were used. Also presented are the governing equations and boundary conditions for the situation of a thin liquid emanating from a pressure vessel; traveling along a horizontal plate with a constant initial height and uniform initial velocity; and traveling radially along a horizontal disk with a constant initial height and uniform initial velocity.

Variational theorems for superimposed motions in elasticity, with application to beams

NASA Technical Reports Server (NTRS)

Doekmeci, M. C.

1976-01-01

Variational theorems are presented for a theory of small motions superimposed on large static deformations and governing equations for prestressed beams on the basis of 3-D theory of elastodynamics. First, the principle of virtual work is modified through Friedrichs's transformation so as to describe the initial stress problem of elastodynamics. Next, the modified principle together with a chosen displacement field is used to derive a set of 1-D macroscopic governing equations of prestressed beams. The resulting equations describe all the types of superimposed motions in elastic beams, and they include all the effects of transverse shear and normal strains, and the rotatory inertia. The instability of the governing equations is discussed briefly.

What can we learn from the Wells, NV earthquake sequence about seismic hazard in the intermountain west?

USGS Publications Warehouse

Petersen, M.D.; Pankow, K.L.; Biasi, G.P.; Meremonte, M.

2008-01-01

The February 21, 2008 Wells, NV earthquake (M 6) was felt throughout eastern Nevada, southern Idaho, and western Utah. The town of Wells sustained significant damage to unreinforced masonry buildings. The earthquake occurred in a region of low seismic hazard with little seismicity, low geodetic strain rates, and few mapped faults. The peak horizontal ground acceleration predicted by the USGS National Seismic Hazard Maps is about 0.2 g at 2% probability of exceedance in 50 years, with the contributions coming mostly from the Ruby Mountain fault and background seismicity (M5-7.0). The hazard model predicts that the probability of occurrence of an M>6 event within 50 km of Wells is about 15% in 100 years. Although the earthquake was inside the USArray Transportable Array network, the nearest on-scale recordings of ground motions from the mainshock were too distant to estimate accelerations in town. The University of Nevada Reno, the University of Utah, and the U.S. Geological Survey deployed portable instruments to capture the ground motions from aftershocks of this rare normal-faulting event. Shaking from a M 4.7 aftershock recorded on portable instruments at distances less than 10 km exceeded 0.3 g, and sustained accelerations above 0.1 g lasted for about 5 seconds. For a magnitude 5 earthquake at 10 km distance the NGA equations predict median peak ground accelerations about 0.1 g. Ground motions from normal faulting earthquakes are poorly represented in the ground motion prediction equations. We compare portable and Transportable Array ground-motion recordings with prediction equations. Advanced National Seismic System stations in Utah recorded ground motions 250 km from the mainshock of about 2% g. The maximum ground motion recorded in Salt Lake City was in the center of the basin. We analyze the spatial variability of ground motions (rock vs. soil) and the influence of the Salt Lake Basin in modifying the ground motions. We then compare this data with the September 28, 2004 Parkfield aftershocks to contrast the differences between strike-slip and normal ground motions.

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

NASA Technical Reports Server (NTRS)

Spangler, Steven R.

1990-01-01

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

Theory of strong turbulence by renormalization

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1981-01-01

The hydrodynamical equations of turbulent motions are inhomogeneous and nonlinear in their inertia and force terms and will generate a hierarchy. A kinetic method was developed to transform the hydrodynamic equations into a master equation governing the velocity distribution, as a function of the time, the position and the velocity as an independent variable. The master equation presents the advantage of being homogeneous and having fewer nonlinear terms and is therefore simpler for the investigation of closure. After the closure by means of a cascade scaling procedure, the kinetic equation is derived and possesses a memory which represents the nonMarkovian character of turbulence. The kinetic equation is transformed back to the hydrodynamical form to yield an energy balance in the cascade form. Normal and anomalous transports are analyzed. The theory is described for incompressible, compressible and plasma turbulence. Applications of the method to problems relating to sound generation and the propagation of light in a nonfrozen turbulence are considered.

Experimental evidence of intermittent chaos in a glow discharge plasma without external forcing and its numerical modelling

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

Ghosh, S., E-mail: sabuj.ghosh@saha.ac.in; Kumar Shaw, Pankaj; Sekar Iyengar, A. N.

Intermittent chaos was observed in a glow discharge plasma as the system evolved from regular type of relaxation oscillations (of larger amplitude) to an irregular type of oscillations (of smaller amplitude) as the discharge voltage was increased. Floating potential fluctuations were analyzed by different statistical and spectral methods. Features like a gradual change in the normal variance of the interpeak time intervals, a dip in the skewness, and a hump in the kurtosis with variation in the control parameter have been seen, which are strongly indicative of intermittent behavior in the system. Detailed analysis also suggests that the intrinsic noisemore » level in the experiment increases with the increasing discharge voltage. An attempt has been made to model the experimental observations by a second order nonlinear ordinary differential equation derived from the fluid equations for an unmagnetized plasma. Though the experiment had no external forcing, it was conjectured that the intrinsic noise in the experiment could be playing a vital role in the dynamics of the system. Hence, a constant bias and noise as forcing terms were included in the model. Results from the theoretical model are in close qualitative agreement with the experimental results.« less

[The implementation of computer model in research of dynamics of proliferation of cells of thyroid gland follicle].

PubMed

Abduvaliev, A A; Gil'dieva, M S; Khidirov, B N; Saĭdalieva, M; Khasanov, A A; Musaeva, Sh N; Saatov, T S

2012-04-01

The article deals with the results of computational experiments in research of dynamics of proliferation of cells of thyroid gland follicle in normal condition and in the case of malignant neoplasm. The model studies demonstrated that the chronic increase of parameter of proliferation of cells of thyroid gland follicle results in abnormal behavior of numbers of cell cenosis of thyroid gland follicle. The stationary state interrupts, the auto-oscillations occur with transition to irregular oscillations with unpredictable cell proliferation and further to the "black hole" effect. It is demonstrated that the present medical biologic experimental data and theory propositions concerning the structural functional organization of thyroid gland on cell level permit to develop mathematical models for quantitative analysis of numbers of cell cenosis of thyroid gland follicle in normal conditions. The technique of modeling of regulative mechanisms of living systems and equations of cell cenosis regulations was used

Cancer Theory from Systems Biology Point of View

NASA Astrophysics Data System (ADS)

Wang, Gaowei; Tang, Ying; Yuan, Ruoshi; Ao, Ping

In our previous work, we have proposed a novel cancer theory, endogenous network theory, to understand mechanism underlying cancer genesis and development. Recently, we apply this theory to hepatocellular carcinoma (HCC). A core endogenous network of hepatocyte was established by integrating the current understanding of hepatocyte at molecular level. Quantitative description of the endogenous network consisted of a set of stochastic differential equations which could generate many local attractors with obvious or non-obvious biological functions. By comparing with clinical observation and experimental data, the results showed that two robust attractors from the model reproduced the main known features of normal hepatocyte and cancerous hepatocyte respectively at both modular and molecular level. In light of our theory, the genesis and progression of cancer is viewed as transition from normal attractor to HCC attractor. A set of new insights on understanding cancer genesis and progression, and on strategies for cancer prevention, cure, and care were provided.

Determination of Resting Energy Expenditure After Severe Burn

DTIC Science & Technology

2013-02-01

increase in metab- olism after burn. However, the Society of Critical Care Medicine along with the American Society for Parenteral and Enteral... Nutrition recommended in their 2009 Guidelines that predictive equations to estimate nutritional requirements be used with cau- tion.3 Equations normally...Department of Nutritional Medicine at San Antonio Military Medical Center, the United States Army Institute of Surgical Research, Fort Sam Houston

Normalization and extension of single-collector efficiency correlation equation

NASA Astrophysics Data System (ADS)

Messina, Francesca; Marchisio, Daniele; Sethi, Rajandrea

2015-04-01

The colloidal transport and deposition are important phenomena involved in many engineering problems. In the environmental engineering field the use of micro- and nano-scale zerovalent iron (M-NZVI) is one of the most promising technologies for groundwater remediation. Colloid deposition is normally studied from a micro scale point of view and the results are then implemented in macro scale models that are used to design field-scale applications. The single collector efficiency concept predicts particles deposition onto a single grain of a complex porous medium in terms of probability that an approaching particle would be retained on the solid grain. In literature, many different approaches and equations exist to predict it, but most of them fail under specific conditions (e.g. very small or very big particle size and very low fluid velocity) because they predict efficiency values exceeding unity. By analysing particle fluxes and deposition mechanisms and performing a mass balance on the entire domain, the traditional definition of efficiency was reformulated and a novel total flux normalized correlation equation is proposed for predicting single-collector efficiency under a broad range of parameters. It has been formulated starting from a combination of Eulerian and Lagrangian numerical simulations, performed under Smoluchowski-Levich conditions, in a geometry which consists of a sphere enveloped by a control volume. In order to guarantee the independence of each term, the correlation equation is derived through a rigorous hierarchical parameter estimation process, accounting for single and mutual interacting transport mechanisms. The correlation equation provides efficiency values lower than one over a wide range of parameters and is valid both for point and finite-size particles. A reduced form is also proposed by elimination of the less relevant terms. References 1. Yao, K. M.; Habibian, M. M.; Omelia, C. R., Water and Waste Water Filtration - Concepts and Applications. Environ Sci Technol 1971, 5, (11), 1105-&. 2. Tufenkji, N., and M. Elimelech, Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environmental Science & Technology 2004 38(2):529-536. 3. Boccardo, G.; Marchisio, D. L.; Sethi, R., Microscale simulation of particle deposition in porous media. J Colloid Interface Sci 2014, 417, 227-37

The roles of time and displacement in velocity-dependent volumetric strain of fault zones

USGS Publications Warehouse

Beeler, N.M.; Tullis, T.E.

1997-01-01

The relationship between measured friction??A and volumetric strain during frictional sliding was determined using a rate and state variable dependent friction constitutive equation, a common work balance relating friction and volume change, and two types of experimental faults: initially bare surfaces of Westerly granite and rock surfaces separated by a 1 mm layer of < 90 ??m Westerly granite gouge. The constitutive equation is the sum of a constant term representing the nominal resistance to sliding and two smaller terms: a rate dependent term representing the shear viscosity of the fault surface (direct effect), and a term which represents variations in the area of contact (evolution effect). The work balance relationship requires that ??A differs from the frictional resistance that leads to shear heating by the derivative of fault normal displacement with respect shear displacement, d??n ld??s. An implication of this relationship is that the rate dependence of d??n ld??s contributes to the rate dependence of ??A. Experiments show changes in sliding velocity lead to changes in both fault strength and volume. Analysis of data with the rate and state equations combined with the work balance relationship preclude the conventional interpretation of the direct effect in the rate and state variable constitutive equations. Consideration of a model bare surface fault consisting of an undeformable indentor sliding on a deformable surface reveals a serious flaw in the work balance relationship if volume change is time-dependent. For the model, at zero slip rate indentation creep under the normal load leads to time-dependent strengthening of the fault surface but, according to the work balance relationship, no work is done because compaction or dilatancy can only be induced by shearing. Additional tests on initially bare surfaces and gouges show that fault normal strain in experiments is time-dependent, consistent with the model. This time-dependent fault normal strain, which is not accounted for in the work balance relationship, explains the inconsistency between the constitutive equations and the work balance. For initially bare surface faults, all rate dependence of volume change is due to time dependence. Similar results are found for gouge. We conclude that ??A reflects the frictional resistance that results in shear heating, and no correction needs to be made for the volume changes. The result that time-dependent volume changes do not contribute to ??A is a general result and extends beyond these experiments, the simple indentor model and particular constitutive equations used to illustrate the principle.

Spatial and temporal compact equations for water waves

NASA Astrophysics Data System (ADS)

Dyachenko, Alexander; Kachulin, Dmitriy; Zakharov, Vladimir

2016-04-01

A one-dimensional potential flow of an ideal incompressible fluid with a free surface in a gravity field is the Hamiltonian system with the Hamiltonian: H = 1/2intdxint-∞^η |nablaφ|^2dz + g/2ont η^2dxŗφ(x,z,t) - is the potential of the fluid, g - gravity acceleration, η(x,t) - surface profile Hamiltonian can be expanded as infinite series of steepness: {Ham4} H &=& H2 + H3 + H4 + dotsŗH2 &=& 1/2int (gη2 + ψ hat kψ) dx, ŗH3 &=& -1/2int \\{(hat kψ)2 -(ψ_x)^2}η dx,ŗH4 &=&1/2int {ψxx η2 hat kψ + ψ hat k(η hat k(η hat kψ))} dx. where hat k corresponds to the multiplication by |k| in Fourier space, ψ(x,t)= φ(x,η(x,t),t). This truncated Hamiltonian is enough for gravity waves of moderate amplitudes and can not be reduced. We have derived self-consistent compact equations, both spatial and temporal, for unidirectional water waves. Equations are written for normal complex variable c(x,t), not for ψ(x,t) and η(x,t). Hamiltonian for temporal compact equation can be written in x-space as following: {SPACE_C} H = intc^*hat V c dx + 1/2int [ i/4(c2 partial/partial x {c^*}2 - {c^*}2 partial/partial x c2)- |c|2 hat K(|c|^2) ]dx Here operator hat V in K-space is so that Vk = ω_k/k. If along with this to introduce Gardner-Zakharov-Faddeev bracket (for the analytic in the upper half-plane function) {GZF} partial^+x Leftrightarrow ikθk Hamiltonian for spatial compact equation is the following: {H24} &&H=1/gint1/ω|cω|2 dω +ŗ&+&1/2g^3int|c|^2(ddot c^*c + ddot c c^*)dt + i/g^2int |c|^2hatω(dot c c* - cdot c^*)dt. equation of motion is: {t-space} &&partial /partial xc +i/g partial^2/partial t^2c =ŗ&=& 1/2g^3partial^3/partial t3 [ partial^2/partial t^2(|c|^2c) +2 |c|^2ddot c +ddot c^*c2 ]+ŗ&+&i/g3 partial^3/partial t3 [ partial /partial t( chatω |c|^2) + dot c hatω |c|2 + c hatω(dot c c* - cdot c^*) ]. It solves the spatial Cauchy problem for surface gravity wave on the deep water. Main features of the equations are: Equations are written for complex normal variable c(x,t) which is analytic function in the upper half-planeHamiltonians both for temporal and spatial equations are very simple It can be easily implemented for numerical simulation The equations can be generalized for "almost" 2-D waves like KdV is generalized to KP. This work was supported by was Grant "Wave turbulence: theory, numerical simulation, experiment" #14-22-00174 of Russian Science Foundation.

Solvability and Regularity for an Elliptic System Prescribing the Curl, Divergence, and Partial Trace of a Vector Field on Sobolev-Class Domains

NASA Astrophysics Data System (ADS)

Cheng, C. H. Arthur; Shkoller, Steve

2017-09-01

We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field u are prescribed in an open, bounded, Sobolev-class domain {Ω \\subseteq R^n}, and either the normal component {{u} \\cdot {N}} or the tangential components of the vector field {{u} × {N}} are prescribed on the boundary {partial Ω}. For {k > n/2}, we prove that u is in the Sobolev space {H^k+1(Ω)} if {Ω} is an {H^k+1}-domain, and the divergence, curl, and either the normal or tangential trace of u has sufficient regularity. The proof is based on a regularity theory for vector elliptic equations set on Sobolev-class domains and with Sobolev-class coefficients, and with a rather general set of Dirichlet and Neumann boundary conditions. The resulting regularity theory for the vector u is fundamental in the analysis of free-boundary and moving interface problems in fluid dynamics.

WEST-3 wind turbine simulator development

NASA Technical Reports Server (NTRS)

Hoffman, J. A.; Sridhar, S.

1985-01-01

The software developed for WEST-3, a new, all digital, and fully programmable wind turbine simulator is given. The process of wind turbine simulation on WEST-3 is described in detail. The major steps are, the processing of the mathematical models, the preparation of the constant data, and the use of system software generated executable code for running on WEST-3. The mechanics of reformulation, normalization, and scaling of the mathematical models is discussed in detail, in particulr, the significance of reformulation which leads to accurate simulations. Descriptions for the preprocessor computer programs which are used to prepare the constant data needed in the simulation are given. These programs, in addition to scaling and normalizing all the constants, relieve the user from having to generate a large number of constants used in the simulation. Also given are brief descriptions of the components of the WEST-3 system software: Translator, Assembler, Linker, and Loader. Also included are: details of the aeroelastic rotor analysis, which is the center of a wind turbine simulation model, analysis of the gimbal subsystem; and listings of the variables, constants, and equations used in the simulation.

Normals to a Parabola

ERIC Educational Resources Information Center

Srinivasan, V. K.

2013-01-01

Given a parabola in the standard form y[superscript 2] = 4ax, corresponding to three points on the parabola, such that the normals at these three points P, Q, R concur at a point M = (h, k), the equation of the circumscribing circle through the three points P, Q, and R provides a tremendous opportunity to illustrate "The Art of Algebraic…

Cadmium Sorption Characteristics of Soil Amendments and its Relationship with the Cadmium Uptake by Hyperaccumulator and Normal Plants in Amended Soils

PubMed Central

Sun, Yan; Wu, Qi-Tang; Lee, Charles C.C.; Li, Baoqin; Long, Xinxian

2013-01-01

In order to select appropriate amendments for cropping hyperaccumulator or normal plants on contaminated soils and establish the relationship between Cd sorption characteristics of soil amendments and their capacity to reduce Cd uptake by plants, batch sorption experiments with 11 different clay minerals and organic materials and a pot experiment with the same amendments were carried out. The pot experiment was conducted with Sedum alfredii and maize (Zea mays) in a co-cropping system. The results showed that the highest sorption amount was by montmorillonite at 40.82 mg/g, while mica was the lowest at only 1.83 mg/g. There was a significant negative correlation between the n value of Freundlich equation and Cd uptake by plants, and between the logarithm of the stability constant K of the Langmuir equation and plant uptake. Humic acids (HAs) and mushroom manure increased Cd uptake by S. alfredii, but not maize, thus they are suitable as soil amendments for the co-cropping S. alfredii and maize. The stability constant K in these cases was 0.14–0.16 L/mg and n values were 1.51–2.19. The alkaline zeolite and mica had the best fixation abilities and significantly decreased Cd uptake by the both plants, with K ≥ 1.49 L/mg and n ≥ 3.59. PMID:24912231

Quantifying the relative contributions of different solute carriers to aggregate substrate transport

PubMed Central

Taslimifar, Mehdi; Oparija, Lalita; Verrey, Francois; Kurtcuoglu, Vartan; Olgac, Ufuk; Makrides, Victoria

2017-01-01

Determining the contributions of different transporter species to overall cellular transport is fundamental for understanding the physiological regulation of solutes. We calculated the relative activities of Solute Carrier (SLC) transporters using the Michaelis-Menten equation and global fitting to estimate the normalized maximum transport rate for each transporter (Vmax). Data input were the normalized measured uptake of the essential neutral amino acid (AA) L-leucine (Leu) from concentration-dependence assays performed using Xenopus laevis oocytes. Our methodology was verified by calculating Leu and L-phenylalanine (Phe) data in the presence of competitive substrates and/or inhibitors. Among 9 potentially expressed endogenous X. laevis oocyte Leu transporter species, activities of only the uniporters SLC43A2/LAT4 (and/or SLC43A1/LAT3) and the sodium symporter SLC6A19/B0AT1 were required to account for total uptake. Furthermore, Leu and Phe uptake by heterologously expressed human SLC6A14/ATB0,+ and SLC43A2/LAT4 was accurately calculated. This versatile systems biology approach is useful for analyses where the kinetics of each active protein species can be represented by the Hill equation. Furthermore, its applicable even in the absence of protein expression data. It could potentially be applied, for example, to quantify drug transporter activities in target cells to improve specificity. PMID:28091567

A Novel Approach for Adaptive Signal Processing

NASA Technical Reports Server (NTRS)

Chen, Ya-Chin; Juang, Jer-Nan

1998-01-01

Adaptive linear predictors have been used extensively in practice in a wide variety of forms. In the main, their theoretical development is based upon the assumption of stationarity of the signals involved, particularly with respect to the second order statistics. On this basis, the well-known normal equations can be formulated. If high- order statistical stationarity is assumed, then the equivalent normal equations involve high-order signal moments. In either case, the cross moments (second or higher) are needed. This renders the adaptive prediction procedure non-blind. A novel procedure for blind adaptive prediction has been proposed and considerable implementation has been made in our contributions in the past year. The approach is based upon a suitable interpretation of blind equalization methods that satisfy the constant modulus property and offers significant deviations from the standard prediction methods. These blind adaptive algorithms are derived by formulating Lagrange equivalents from mechanisms of constrained optimization. In this report, other new update algorithms are derived from the fundamental concepts of advanced system identification to carry out the proposed blind adaptive prediction. The results of the work can be extended to a number of control-related problems, such as disturbance identification. The basic principles are outlined in this report and differences from other existing methods are discussed. The applications implemented are speech processing, such as coding and synthesis. Simulations are included to verify the novel modelling method.

Microwave Limb Sounder/El Nino Watch - 1997 Research Data Reveal Clues about El Nino's Influence

NASA Technical Reports Server (NTRS)

1998-01-01

This image displays wind measurements taken by the satellite-borne NASA Scatterometer (NSCAT) during the last 10 days of May 1997, showing the relationship between the ocean and the atmosphere at the onset of the 1997-98 El Nino condition. The data have helped scientists confirm that the event began as an unusual weakening of the trade winds that preceded an increase in sea surface temperatures. The arrows represent wind speed and direction while the colors indicate sea surface temperature. The sea surface temperatures were measured by the Advanced Very High Resolution Radiometer, a joint mission of NASA and the National Oceanographic and Atmospheric Administration (NOAA). The trade winds normally blow from east to west, but the small arrows in the center of the image show the winds have changed direction and are blowing in the opposite direction. The areas shown in red are above normal sea surface temperatures -- along the equator, off the west coast of the U.S., and along the west coast of Mexico. This image also shows an unusual low pressure system with cyclonic (counterclockwise) circulation near the western North American coast. NSCAT also observed that winds associated with this circulation pattern branched off from the equator, bypassed Hawaii, and brought heat and moisture from the tropical ocean towards San Francisco, in what is often called the 'pineapple express.'

Comparison Between Navier-Stokes and Thin-Layer Computations for Separated Supersonic Flow

NASA Technical Reports Server (NTRS)

Degani, David; Steger, Joseph L.

1983-01-01

In the numerical simulation of high Reynolds-number flow, one can frequently supply only enough grid points to resolve the viscous terms in a thin layer. As a consequence, a body-or stream-aligned coordinate system is frequently used and viscous terms in this direction are discarded. It is argued that these terms cannot be resolved and computational efficiency is gained by their neglect. Dropping the streamwise viscous terms in this manner has been termed the thin-layer approximation. The thin-layer concept is an old one, and similar viscous terms are dropped, for example, in parabolized Navier-Stokes schemes. However, such schemes also make additional assumptions so that the equations can be marched in space, and such a restriction is not usually imposed on a thin-layer model. The thin-layer approximation can be justified in much the same way as the boundary-layer approximation; it requires, therefore, a body-or stream-aligned coordinate and a high Reynolds number. Unlike the boundary-layer approximation, the same equations are used throughout, so there is no matching problem. Furthermore, the normal momentum equation is not simplified and the convection terms are not one-sided differenced for marching. Consequently, the thin-layer equations are numerically well behaved at separation and require no special treatment there. Nevertheless, the thin-layer approximation receives criticism. It has been suggested that the approximation is invalid at separation and, more recently, that it is inadequate for unsteady transonic flow. Although previous comparisons between the thin-layer and Navier-Stokes equations have been made, these comparisons have not been adequately documented.

Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium

USGS Publications Warehouse

Iverson, R.M.

1993-01-01

Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass conservation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameter B, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of Iverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data. ?? 1993 International Association for Mathematical Geology.

Serum proteins by capillary zone electrophoresis: approaches to the definition of reference values.

PubMed

Petrini, C; Alessio, M G; Scapellato, L; Brambilla, S; Franzini, C

1999-10-01

The Paragon CZE 2000 (Beckman Analytical, Milan, Italy) is an automatic dedicated capillary zone electrophoresis (CZE) system, producing a five-zone serum protein pattern with quantitative estimation of the zones. With the view of substituting this instrument for two previously used serum protein electrophoresis techniques, we planned to produce reference values for the "new" systems leading to compatible interpretation of the results. High resolution cellulose acetate electrophoresis with visual inspection and descriptive reporting (HR-CAE) and five-zone cellulose acetate electrophoresis with densitometry (CAE-D) were the previously used techniques. Serum samples (n = 167) giving "normal pattern" with HR-CAE were assayed with the CZE system, and the results were statistically assessed to yield 0.95 reference intervals. One thousand normal and pathological serum samples were then assayed with the CAE-D and the CZE techniques, and the regression equations of the CAE-D values over the CZE values for the five zones were used to transform the CAE-D reference limits into the CZE reference limits. The two sets of reference values thereby produced were in good agreement with each other and also with reference values previously reported for the CZE system. Thus, reference values for the CZE techniques permit interpretation of results coherent with the previously used techniques and reporting modes.

Computational tools for fitting the Hill equation to dose-response curves.

PubMed

Gadagkar, Sudhindra R; Call, Gerald B

2015-01-01

Many biological response curves commonly assume a sigmoidal shape that can be approximated well by means of the 4-parameter nonlinear logistic equation, also called the Hill equation. However, estimation of the Hill equation parameters requires access to commercial software or the ability to write computer code. Here we present two user-friendly and freely available computer programs to fit the Hill equation - a Solver-based Microsoft Excel template and a stand-alone GUI-based "point and click" program, called HEPB. Both computer programs use the iterative method to estimate two of the Hill equation parameters (EC50 and the Hill slope), while constraining the values of the other two parameters (the minimum and maximum asymptotes of the response variable) to fit the Hill equation to the data. In addition, HEPB draws the prediction band at a user-defined confidence level, and determines the EC50 value for each of the limits of this band to give boundary values that help objectively delineate sensitive, normal and resistant responses to the drug being tested. Both programs were tested by analyzing twelve datasets that varied widely in data values, sample size and slope, and were found to yield estimates of the Hill equation parameters that were essentially identical to those provided by commercial software such as GraphPad Prism and nls, the statistical package in the programming language R. The Excel template provides a means to estimate the parameters of the Hill equation and plot the regression line in a familiar Microsoft Office environment. HEPB, in addition to providing the above results, also computes the prediction band for the data at a user-defined level of confidence, and determines objective cut-off values to distinguish among response types (sensitive, normal and resistant). Both programs are found to yield estimated values that are essentially the same as those from standard software such as GraphPad Prism and the R-based nls. Furthermore, HEPB also has the option to simulate 500 response values based on the range of values of the dose variable in the original data and the fit of the Hill equation to that data. Copyright © 2014. Published by Elsevier Inc.

Analytical and molecular dynamics studies on the impact loading of single-layered graphene sheet by fullerene

NASA Astrophysics Data System (ADS)

Hosseini-Hashemi, Shahrokh; Sepahi-Boroujeni, Amin; Sepahi-Boroujeni, Saeid

2018-04-01

Normal impact performance of a system including a fullerene molecule and a single-layered graphene sheet is studied in the present paper. Firstly, through a mathematical approach, a new contact law is derived to describe the overall non-bonding interaction forces of the "hollow indenter-target" system. Preliminary verifications show that the derived contact law gives a reliable picture of force field of the system which is in good agreements with the results of molecular dynamics (MD) simulations. Afterwards, equation of the transversal motion of graphene sheet is utilized on the basis of both the nonlocal theory of elasticity and the assumptions of classical plate theory. Then, to derive dynamic behavior of the system, a set including the proposed contact law and the equations of motion of both graphene sheet and fullerene molecule is solved numerically. In order to evaluate outcomes of this method, the problem is modeled by MD simulation. Despite intrinsic differences between analytical and MD methods as well as various errors arise due to transient nature of the problem, acceptable agreements are established between analytical and MD outcomes. As a result, the proposed analytical method can be reliably used to address similar impact problems. Furthermore, it is found that a single-layered graphene sheet is capable of trapping fullerenes approaching with low velocities. Otherwise, in case of rebound, the sheet effectively absorbs predominant portion of fullerene energy.

The limitation and applicability of Musher-Sturman equation to two dimensional lower hybrid wave collapse

NASA Technical Reports Server (NTRS)

Tam, Sunny W. Y.; Chang, Tom

1995-01-01

The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non-linear two-timescale coupling process. In this Letter, we demonstrate that the leading non-linear term in the standard Musher-Sturman equation vanishes identically in strict two-dimensions (normal to the magnetic field). Instead, the new two-dimensional equation is characterized by a much weaker non-linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time-evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher-Sturman equation in quasi-two-dimensions. Only within all these limits can Musher-Sturman equation adequately describe the collapse of lower hybrid waves.

Constrained multibody system dynamics: An automated approach

NASA Technical Reports Server (NTRS)

Kamman, J. W.; Huston, R. L.

1982-01-01

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

One Dimension Analytical Model of Normal Ballistic Impact on Ceramic/Metal Gradient Armor

NASA Astrophysics Data System (ADS)

Liu, Lisheng; Zhang, Qingjie; Zhai, Pengcheng; Cao, Dongfeng

2008-02-01

An analytical model of normal ballistic impact on the ceramic/metal gradient armor, which is based on modified Alekseevskii-Tate equations, has been developed. The process of gradient armour impacted by the long rod can be divided into four stages in this model. First stage is projectile's mass erosion or flowing phase, mushrooming phase and rigid phase; second one is the formation of comminuted ceramic conoid; third one is the penetration of gradient layer and last one is the penetration of metal back-up plate. The equations of third stage have been advanced by assuming the behavior of gradient layer as rigid-plastic and considering the effect of strain rate on the dynamic yield strength.

Effect on Gaseous Film Cooling of Coolant Injection Through Angled Slots and Normal Holes

NASA Technical Reports Server (NTRS)

Papell, S. Stephen

1960-01-01

A study was made to determine the effect of coolant injection angularity on gaseous film-cooling effectiveness. In the correlation of experimental data an effective injection angle was defined by a vector summation of the coolant and mainstream gas flows. The cosine of this angle was used as a parameter to empirically develop a corrective term to qualify a correlating equation presented in Technical Note D-130 that was limited to tangential injection of the coolant. Data were also obtained for coolant injection through rows of holes normal to the test plate. The slot correlating equation was adapted to fit these data by the definition of an effective slot height. An additional corrective term was then determined to correlate these data.

Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal

NASA Astrophysics Data System (ADS)

Zhou, Y.-B.; Li, X.-F.

2018-07-01

The electroelastic problem related to two collinear cracks of equal length and normal to the boundaries of a one-dimensional hexagonal piezoelectric quasicrystal layer is analysed. By using the finite Fourier transform, a mixed boundary value problem is solved when antiplane mechanical loading and inplane electric loading are applied. The problem is reduce to triple series equations, which are then transformed to a singular integral equation. For uniform remote loading, an exact solution is obtained in closed form, and explicit expressions for the electroelastic field are determined. The intensity factors of the electroelastic field and the energy release rate at the inner and outer crack tips are given and presented graphically.

Unsteady MHD blood flow through porous medium in a parallel plate channel

NASA Astrophysics Data System (ADS)

Latha, R.; Rushi Kumar, B.

2017-11-01

In this study, we have analyzed heat and mass transfer effects on unsteady blood flow through parallel plate channel in a saturated porous medium in the presence of a transverse magnetic field with thermal radiation. The governing higher order nonlinear PDE’S are converted to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using boundary conditions by choosing the axial flow transport and the fields of concentration and temperature apart from the normal velocity as a function of y and t. The effects of different pertinent parameters appeared in this model viz thermal radiation, Prandtl number, Heat source parameter, Hartmann number, Permeability parameter, Decay parameter on axial flow transport and the normal velocity are analyzed in detail.

VLBI-SLR Combination Solution Using GEODYN

NASA Technical Reports Server (NTRS)

MacMillan, Dan; Pavlis, Despina; Lemoine, Frank; Chinn, Douglas; Rowlands, David

2010-01-01

We would like to generate a multi-technique solution combining all of the geodetic techniques (VLBI, SLR, GPS, and DORIS) using the same software and using the same a priori models. Here we use GEODYN software and consider only the VLBI-SLR combination. Here we report initial results of our work on the combination. We first performed solutions with GEODYN using only VLBI data and found that VLBI EOP solution results produced with GEODYN agree with results using CALC/SOLVE at the 1-sigma level. We then combined the VLBI normal equations in GEODYN with weekly SLR normal equations for the period 2007-2008. Agreement of estimated Earth orientation parameters with IERS C04 were not significantly different for the VLBI-only, SLR-only, and VLBI+SLR solutions

One Dimension Analytical Model of Normal Ballistic Impact on Ceramic/Metal Gradient Armor

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

Liu Lisheng; Zhang Qingjie; Zhai Pengcheng

2008-02-15

An analytical model of normal ballistic impact on the ceramic/metal gradient armor, which is based on modified Alekseevskii-Tate equations, has been developed. The process of gradient armour impacted by the long rod can be divided into four stages in this model. First stage is projectile's mass erosion or flowing phase, mushrooming phase and rigid phase; second one is the formation of comminuted ceramic conoid; third one is the penetration of gradient layer and last one is the penetration of metal back-up plate. The equations of third stage have been advanced by assuming the behavior of gradient layer as rigid-plastic andmore » considering the effect of strain rate on the dynamic yield strength.« less

Do over 200 million healthy altitude residents really suffer from chronic Acid-base disorders?

PubMed

Zubieta-Calleja, Gustavo; Zubieta-Castillo, Gustavo; Zubieta-Calleja, Luis; Ardaya-Zubieta, Gustavo; Paulev, Poul-Erik

2011-01-01

As the oxygen tension of inspired air falls with increasing altitude in normal subjects, hyperventilation ensues. This acute respiratory alkalosis, induces increased renal excretion of bicarbonate, returning the pH back to normal, giving rise to compensated respiratory alkalosis or chronic hypocapnia. It seems a contradiction that so many normal people at high altitude should permanently live as chronic acid-base patients. Blood gas analyses of 1,865 subjects at 3,510 m, reported a P(a)CO(2) (arterial carbon dioxide tension ± SEM) = 29.4 ± 0.16 mmHg and pH = 7.40 ± 0.005. Base excess, calculated with the Van Slyke sea level equation, is -5 mM (milliMolar or mmol/l) as an average, suggesting chronic hypocapnia. THID, a new term replacing "Base Excess" is determined by titration to a pH of 7.40 at a P(a)CO(2) of 5.33 kPa (40 mmHg) at sea level, oxygen saturated and at 37°C blood temperature. Since our new modified Van Slyke equations operate with normal values for P(a)CO(2) at the actual altitude, a calculation of THID will always result in normal values-that is, zero.

Modeling of bioheat equation for skin and a preliminary study on a noninvasive diagnostic method for skin burn wounds.

PubMed

Lee, Shong-Leih; Lu, Yung-Hsiang

2014-08-01

Heat transfer in a unit three-dimensional skin tissue with an embedded vascular system of actual histology structure is computed in the present work. The tissue temperature and the blood temperatures in artery and vein vessels are solved with a multi-grid system. The mean temperature of the tissue over the cross-section of the unit skin area is evaluated. The resulting one-dimensional function is regarded as the temperature of healthy tissue (or injured skin but the blood perfusion is still normally working) for large area of skin in view of the symmetric and periodic structure of the paired artery-vein vessels in nature. A three-dimensional bioheat equation then is formulated by the superposition of the skin burn wound effect and the healthy skin temperature with and without thermal radiation exposure. When this bioheat equation is employed to simulate ADT process on burn wounds, the decaying factor of the skin surface temperature is found to be a sharply decreasing function of time in the self-cooling stage after a thermal radiation heating. Nevertheless, the boundary of non-healing (needing surgery) and healing regions in a large burn wound can be estimated by tracking the peak of the gradient of decaying factor within 30 s after the thermal radiation is turned off. Experimental studies on the full ADT procedure are needed to justify the assumptions in the present computation. Copyright © 2013 Elsevier Ltd and ISBI. All rights reserved.

On the accuracy of estimation of basic pharmacokinetic parameters by the traditional noncompartmental equations and the prediction of the steady-state volume of distribution in obese patients based upon data derived from normal subjects.

PubMed

Berezhkovskiy, Leonid M

2011-06-01

The steady-state and terminal volumes of distribution, as well as the mean residence time of drug in the body (V(ss), V(β), and MRT) are the common pharmacokinetic parameters calculated using the drug plasma concentration-time profile C(p) (t) following intravenous (i.v. bolus or constant rate infusion) drug administration. These calculations are valid for the linear pharmacokinetic system with central elimination (i.e., elimination rate being proportional to drug concentration in plasma). Formally, the assumption of central elimination is not normally met because the rate of drug elimination is proportional to the unbound drug concentration at elimination site, although equilibration between systemic circulation and the site of clearance for majority of small molecule drugs is fast. Thus, the assumption of central elimination is practically quite adequate. It appears reasonable to estimate the extent of possible errors in determination of these pharmacokinetic parameters due to the absence of central elimination. The comparison of V(ss), V(β), and MRT calculated by exact equations and the commonly used ones was made considering a simplified physiologically based pharmacokinetic model. It was found that if the drug plasma concentration profile is detected accurately, determination of drug distribution volumes and MRT using the traditional noncompartmental calculations of these parameters from C(p) (t) yields the values very close to that obtained from exact equations. Though in practice, the accurate measurement of C(p) (t), especially its terminal phase, may not always be possible. This is particularly applicable for obtaining the distribution volumes of lipophilic compounds in obese subjects, when the possibility of late terminal phase at low drug concentration is quite likely, specifically for compounds with high clearance. An accurate determination of V(ss) is much needed in clinical practice because it is critical for the proper selection of drug treatment regimen. For that reason, we developed a convenient method for calculation of V(ss) in obese (or underweight) subjects. It is based on using the V(ss) values obtained from pharmacokinetic studies in normal subjects and the physicochemical properties of drug molecule. A simple criterion that determines either the increase or decrease of V(ss) (per unit body weight) due to obesity is obtained. The accurate determination of adipose tissue-plasma partition coefficient is crucial for the practical application of suggested method. Copyright © 2011 Wiley-Liss, Inc.

Quantification of cardiorespiratory fitness in healthy nonobese and obese men and women.

PubMed

Lorenzo, Santiago; Babb, Tony G

2012-04-01

The quantification and interpretation of cardiorespiratory fitness (CRF) in obesity is important for adequately assessing cardiovascular conditioning, underlying comorbidities, and properly evaluating disease risk. We retrospectively compared peak oxygen uptake (VO(2)peak) (ie, CRF) in absolute terms, and relative terms (% predicted) using three currently suggested prediction equations (Equations R, W, and G). There were 19 nonobese and 66 obese participants. Subjects underwent hydrostatic weighing and incremental cycling to exhaustion. Subject characteristics were analyzed by independent t test, and % predicted VO(2)peak by a two-way analysis of variance (group and equation) with repeated measures on one factor (equation). VO(2)peak (L/min) was not different between nonobese and obese adults (2.35 ± 0.80 [SD] vs 2.39 ± 0.68 L/min). VO(2)peak was higher (P < .02) relative to body mass and lean body mass in the nonobese (34 ± 8 mL/min/kg vs 22 ± 5 mL/min/kg, 42 ± 9 mL/min/lean body mass vs 37 ± 6 mL/min/lean body mass). Cardiorespiratory fitness assessed as % predicted was not different in the nonobese and obese (91% ± 17% predicted vs 95% ± 15% predicted) using Equation R, while using Equation W and G, CRF was lower (P < .05) but within normal limits in the obese (94 ± 15 vs 87 ± 11; 101% ± 17% predicted vs 90% ± 12% predicted, respectively), depending somewhat on sex. Traditional methods of reporting VO(2)peak do not allow adequate assessment and quantification of CRF in obese adults. Predicted VO(2)peak does allow a normalized evaluation of CRF in the obese, although care must be taken in selecting the most appropriate prediction equation, especially in women. In general, otherwise healthy obese are not grossly deconditioned as is commonly believed, although CRF may be slightly higher in nonobese subjects depending on the uniqueness of the prediction equation.

Rogue waves and large deviations in deep sea.

PubMed

Dematteis, Giovanni; Grafke, Tobias; Vanden-Eijnden, Eric

2018-01-30

The appearance of rogue waves in deep sea is investigated by using the modified nonlinear Schrödinger (MNLS) equation in one spatial dimension with random initial conditions that are assumed to be normally distributed, with a spectrum approximating realistic conditions of a unidirectional sea state. It is shown that one can use the incomplete information contained in this spectrum as prior and supplement this information with the MNLS dynamics to reliably estimate the probability distribution of the sea surface elevation far in the tail at later times. Our results indicate that rogue waves occur when the system hits unlikely pockets of wave configurations that trigger large disturbances of the surface height. The rogue wave precursors in these pockets are wave patterns of regular height, but with a very specific shape that is identified explicitly, thereby allowing for early detection. The method proposed here combines Monte Carlo sampling with tools from large deviations theory that reduce the calculation of the most likely rogue wave precursors to an optimization problem that can be solved efficiently. This approach is transferable to other problems in which the system's governing equations contain random initial conditions and/or parameters.

Phase space methods for Majorana fermions

NASA Astrophysics Data System (ADS)

Rushin Joseph, Ria; Rosales-Zárate, Laura E. C.; Drummond, Peter D.

2018-06-01

Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The resulting phase-space of covariance matrices belongs to the symmetry class D, one of the non-standard symmetry classes. This was originally proposed to study mesoscopic normal-metal-superconducting hybrid structures, which is the type of structure that has led to recent experimental observations of Majorana fermions. Under a unitary transformation, it is possible to express these Gaussian operators using real anti-symmetric matrices and Majorana operators, which are much simpler mathematical objects. We derive differential identities involving Majorana fermion operators and an antisymmetric matrix which are relevant to the derivation of the corresponding Fokker–Planck equations on symmetric space. These enable stochastic simulations either in real or imaginary time. This formalism has direct relevance to the study of fermionic systems in which there are Majorana type excitations, and is an alternative to using expansions involving conventional Fermi operators. The approach is illustrated by showing how a linear coupled Hamiltonian as used to study topological excitations can be transformed to Fokker–Planck and stochastic equation form, including dissipation through particle losses.

Minimal norm constrained interpolation. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Irvine, L. D.

1985-01-01

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Soft tissue deformation estimation by spatio-temporal Kalman filter finite element method.

PubMed

Yarahmadian, Mehran; Zhong, Yongmin; Gu, Chengfan; Shin, Jaehyun

2018-01-01

Soft tissue modeling plays an important role in the development of surgical training simulators as well as in robot-assisted minimally invasive surgeries. It has been known that while the traditional Finite Element Method (FEM) promises the accurate modeling of soft tissue deformation, it still suffers from a slow computational process. This paper presents a Kalman filter finite element method to model soft tissue deformation in real time without sacrificing the traditional FEM accuracy. The proposed method employs the FEM equilibrium equation and formulates it as a filtering process to estimate soft tissue behavior using real-time measurement data. The model is temporally discretized using the Newmark method and further formulated as the system state equation. Simulation results demonstrate that the computational time of KF-FEM is approximately 10 times shorter than the traditional FEM and it is still as accurate as the traditional FEM. The normalized root-mean-square error of the proposed KF-FEM in reference to the traditional FEM is computed as 0.0116. It is concluded that the proposed method significantly improves the computational performance of the traditional FEM without sacrificing FEM accuracy. The proposed method also filters noises involved in system state and measurement data.

Asymptotic inference in system identification for the atom maser.

PubMed

Catana, Catalin; van Horssen, Merlijn; Guta, Madalin

2012-11-28

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

Finite-difference simulation and visualization of elastodynamics in time-evolving generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Kaul, Upender K. (Inventor)

2009-01-01

Modeling and simulation of free and forced structural vibrations is essential to an overall structural health monitoring capability. In the various embodiments, a first principles finite-difference approach is adopted in modeling a structural subsystem such as a mechanical gear by solving elastodynamic equations in generalized curvilinear coordinates. Such a capability to generate a dynamic structural response is widely applicable in a variety of structural health monitoring systems. This capability (1) will lead to an understanding of the dynamic behavior of a structural system and hence its improved design, (2) will generate a sufficiently large space of normal and damage solutions that can be used by machine learning algorithms to detect anomalous system behavior and achieve a system design optimization and (3) will lead to an optimal sensor placement strategy, based on the identification of local stress maxima all over the domain.

A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes

NASA Astrophysics Data System (ADS)

Wang, Shuai; Hang, Xudeng; Yuan, Guangwei

2017-12-01

In this paper, a new cell-centered finite volume scheme is proposed for three-dimensional diffusion equations on polyhedral meshes, which is called as pyramid scheme (P-scheme). The scheme is designed for polyhedral cells with nonplanar cell-faces. The normal flux on a nonplanar cell-face is discretized on a planar face, which is determined by a simple optimization procedure. The resulted discrete form of the normal flux involves only cell-centered and cell-vertex unknowns, and is free from face-centered unknowns. In the case of hexahedral meshes with skewed nonplanar cell-faces, a quite simple expression is obtained for the discrete normal flux. Compared with the second order accurate O-scheme [31], the P-scheme is more robust and the discretization cost is reduced remarkably. Numerical results are presented to show the performance of the P-scheme on various kinds of distorted meshes. In particular, the P-scheme is shown to be second order accurate.

Biomechanical basis of choosing the rational mass and its distribution throughout the lower limb prosthesis segments.

PubMed

Farber, B S; Moreinis, I Sh

1995-11-01

A solution for finding a rational distribution of mass in lower limb prostheses has been considered based on the formal premise favoring the identification of the movements of a prosthetic and an intact leg. For the purpose of simplicity, and analysis has been carried out for only the swing phase, the data about the properties of moving segments being determined without integrating differential equations of motion. At the formation of equations of motion, an assumption that body segments are absolutely rigid and have constant moments of inertia and locations of the center of mass was taken into consideration. Based on independent proportions formed of combinations of the coefficients of equations of motion, a system of three equations has been formulated and solved in relation to the mass values sought: a static radius and a radius of inertia of the prosthesis complex link "shin + foot + footwear." From the six unknowns included in the equations, three values are chosen as mean values determined empirically. The solution of obtained equations results in the following conclusions: the parameters of the mass distribution in a "shin + foot + footwear" complex link depend on the amputation level and the patient's mass. These data, reported in appropriate tables, may be used in prosthetics practice. Recommendations have also been presented with regard to a prosthesic mass relative to the age of the person with amputation and a method of a balancing of prostheses aimed at the achievement of a rational distribution of masses. The analysis of obtained equations has also allowed us to make recommendations about the artificial foot mass. It has been concluded that a reasonable desire to reduce the mass of the prosthetic segments is not an end in itself, but is only the means of a rational distribution by means of balancing. It has been proved that rational prosthetic fitting results in decreased energy costs and overloads are decreased and a normalized gait.

The exit-time problem for a Markov jump process

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

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies.

PubMed

Olives, Juan

2010-03-03

The thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the temperature, the chemical potentials and the surface strain tensor (true thermodynamic variables, for a viscoelastic solid or a viscous fluid). A new definition of the surface stress is given and the corresponding surface thermodynamics equations are presented. The mechanical equilibrium equation at the surface is then obtained. It involves the surface stress and is similar to the Cauchy equation for the volume. Its normal component is a generalization of the Laplace equation. At a (body-fluid-fluid) triple contact line, two equations are obtained, which represent: (i) the equilibrium of the forces (surface stresses) for a triple line fixed on the body; (ii) the equilibrium relative to the motion of the line with respect to the body. This last equation leads to a strong modification of Young's classical capillary equation.

On the integration of a class of nonlinear systems of ordinary differential equations

NASA Astrophysics Data System (ADS)

Talyshev, Aleksandr A.

2017-11-01

For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

Regularity estimates up to the boundary for elliptic systems of difference equations

NASA Technical Reports Server (NTRS)

Strikwerda, J. C.; Wade, B. A.; Bube, K. P.

1986-01-01

Regularity estimates up to the boundary for solutions of elliptic systems of finite difference equations were proved. The regularity estimates, obtained for boundary fitted coordinate systems on domains with smooth boundary, involve discrete Sobolev norms and are proved using pseudo-difference operators to treat systems with variable coefficients. The elliptic systems of difference equations and the boundary conditions which are considered are very general in form. The regularity of a regular elliptic system of difference equations was proved equivalent to the nonexistence of eigensolutions. The regularity estimates obtained are analogous to those in the theory of elliptic systems of partial differential equations, and to the results of Gustafsson, Kreiss, and Sundstrom (1972) and others for hyperbolic difference equations.

Generalized Freud's equation and level densities with polynomial potential

NASA Astrophysics Data System (ADS)

Boobna, Akshat; Ghosh, Saugata

2013-08-01

We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.

Modelling of charged satellite motion in Earth's gravitational and magnetic fields

NASA Astrophysics Data System (ADS)

Abd El-Bar, S. E.; Abd El-Salam, F. A.

2018-05-01

In this work Lagrange's planetary equations for a charged satellite subjected to the Earth's gravitational and magnetic force fields are solved. The Earth's gravity, and magnetic and electric force components are obtained and expressed in terms of orbital elements. The variational equations of orbit with the considered model in Keplerian elements are derived. The solution of the problem in a fully analytical way is obtained. The temporal rate of changes of the orbital elements of the spacecraft are integrated via Lagrange's planetary equations and integrals of the normalized Keplerian motion obtained by Ahmed (Astron. J. 107(5):1900, 1994).

Investigations Regarding Anesthesia during Hypovolemic Conditions.

DTIC Science & Technology

1982-09-25

i / b ,- 18 For each level of hemoglobin, the equation was "normalized" to a pH of 7.400 for a BE of zero and a PCO of 40.0 torr, Orr et al. (171...the shifted BE values. Curve nomogram. Using the equations resulting from the above curve- fitting procedure, we calculated the relationship between pH...model for a given BE (i.e., pH = m i log PCO 2 + bi). Solve the following set of equations for pHind and log dX - 0 d(PHind) where X = (pHl - pHind) 2

Stability switches and multistability coexistence in a delay-coupled neural oscillators system.

PubMed

Song, Zigen; Xu, Jian

2012-11-21

In this paper, we present a neural network system composed of two delay-coupled neural oscillators, where each of these can be regarded as the dynamical system describing the average activity of neural population. Analyzing the corresponding characteristic equation, the local stability of rest state is studied. The system exhibits the switch phenomenon between the rest state and periodic activity. Furthermore, the Hopf bifurcation is analyzed and the bifurcation curve is given in the parameters plane. The stability of the bifurcating periodic solutions and direction of the Hopf bifurcation are exhibited. Regarding time delay and coupled weight as the bifurcation parameters, the Fold-Hopf bifurcation is investigated in detail in terms of the central manifold reduction and normal form method. The neural system demonstrates the coexistence of the rest states and periodic activities in the different parameter regions. Employing the normal form of the original system, the coexistence regions are illustrated approximately near the Fold-Hopf singularity point. Finally, numerical simulations are performed to display more complex dynamics. The results illustrate that system may exhibit the rich coexistence of the different neuro-computational properties, such as the rest states, periodic activities, and quasi-periodic behavior. In particular, some periodic activities can evolve into the bursting-type behaviors with the varying time delay. It implies that the coexistence of the quasi-periodic activity and bursting-type behavior can be obtained if the suitable value of system parameter is chosen. Copyright © 2012 Elsevier Ltd. All rights reserved.

A class of exact solutions for biomacromolecule diffusion-reaction in live cells.

PubMed

Sadegh Zadeh, Kouroush; Montas, Hubert J

2010-06-07

A class of novel explicit analytic solutions for a system of n+1 coupled partial differential equations governing biomolecular mass transfer and reaction in living organisms are proposed, evaluated, and analyzed. The solution process uses Laplace and Hankel transforms and results in a recursive convolution of an exponentially scaled Gaussian with modified Bessel functions. The solution is developed for wide range of biomolecular binding kinetics from pure diffusion to multiple binding reactions. The proposed approach provides solutions for both Dirac and Gaussian laser beam (or fluorescence-labeled biomacromolecule) profiles during the course of a Fluorescence Recovery After Photobleaching (FRAP) experiment. We demonstrate that previous models are simplified forms of our theory for special cases. Model analysis indicates that at the early stages of the transport process, biomolecular dynamics is governed by pure diffusion. At large times, the dominant mass transfer process is effective diffusion. Analysis of the sensitivity equations, derived analytically and verified by finite difference differentiation, indicates that experimental biologists should use full space-time profile (instead of the averaged time series) obtained at the early stages of the fluorescence microscopy experiments to extract meaningful physiological information from the protocol. Such a small time frame requires improved bioinstrumentation relative to that in use today. Our mathematical analysis highlights several limitations of the FRAP protocol and provides strategies to improve it. The proposed model can be used to study biomolecular dynamics in molecular biology, targeted drug delivery in normal and cancerous tissues, motor-driven axonal transport in normal and abnormal nervous systems, kinetics of diffusion-controlled reactions between enzyme and substrate, and to validate numerical simulators of biological mass transport processes in vivo. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Integrated design and manufacturing for the high speed civil transport (a combined aerodynamics/propulsion optimization study)

NASA Technical Reports Server (NTRS)

Baecher, Juergen; Bandte, Oliver; DeLaurentis, Dan; Lewis, Kemper; Sicilia, Jose; Soboleski, Craig

1995-01-01

This report documents the efforts of a Georgia Tech High Speed Civil Transport (HSCT) aerospace student design team in completing a design methodology demonstration under NASA's Advanced Design Program (ADP). Aerodynamic and propulsion analyses are integrated into the synthesis code FLOPS in order to improve its prediction accuracy. Executing the integrated product and process development (IPPD) methodology proposed at the Aerospace Systems Design Laboratory (ASDL), an improved sizing process is described followed by a combined aero-propulsion optimization, where the objective function, average yield per revenue passenger mile ($/RPM), is constrained by flight stability, noise, approach speed, and field length restrictions. Primary goals include successful demonstration of the application of the response surface methodolgy (RSM) to parameter design, introduction to higher fidelity disciplinary analysis than normally feasible at the conceptual and early preliminary level, and investigations of relationships between aerodynamic and propulsion design parameters and their effect on the objective function, $/RPM. A unique approach to aircraft synthesis is developed in which statistical methods, specifically design of experiments and the RSM, are used to more efficiently search the design space for optimum configurations. In particular, two uses of these techniques are demonstrated. First, response model equations are formed which represent complex analysis in the form of a regression polynomial. Next, a second regression equation is constructed, not for modeling purposes, but instead for the purpose of optimization at the system level. Such an optimization problem with the given tools normally would be difficult due to the need for hard connections between the various complex codes involved. The statistical methodology presents an alternative and is demonstrated via an example of aerodynamic modeling and planform optimization for a HSCT.

Nonlinear water waves generated by impulsive motion of submerged obstacle

NASA Astrophysics Data System (ADS)

Makarenko, N.; Kostikov, V.

2012-04-01

The fully nonlinear problem on generation of unsteady water waves by impulsively moving obstacle is studied analytically. The method involves the reduction of basic Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at the free surface. Exact model equations are derived in explicit form when the isolated obstacle is presented by totally submerged circular- or elliptic cylinder. Small-time asymptotic solution is constructed for the cylinder which starts moving with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle, as well as the generation of diverging waves by horizontal- and combined motion of the obstacle under free surface. This work was supported by RFBR (grant No 10-01-00447) and by Research Program of the Russian Government (grant No 11.G34.31.0035).

New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.

PubMed

Ingo, Carson; Magin, Richard L; Parrish, Todd B

2014-11-01

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

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.

Supersonic Flow of Chemically Reacting Gas-Particle Mixtures. Volume 2: RAMP - A Computer Code for Analysis of Chemically Reacting Gas-Particle Flows

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Anderson, P. G.; Sulyma, P. R.; Pearson, M. L.

1976-01-01

A computer program written in conjunction with the numerical solution of the flow of chemically reacting gas-particle mixtures was documented. The solution to the set of governing equations was obtained by utilizing the method of characteristics. The equations cast in characteristic form were shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The characteristic directions for the gas-particle system are found to be the conventional gas Mach lines, the gas streamlines and the particle streamlines. The basic mesh construction for the flow solution is along streamlines and normals to the streamlines for axisymmetric or two-dimensional flow. The analysis gives detailed information of the supersonic flow and provides for a continuous solution of the nozzle and exhaust plume flow fields. Boundary conditions for the flow solution are either the nozzle wall or the exhaust plume boundary.

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Waag, Robert C

2010-05-01

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.

Spectral method for the static electric potential of a charge density in a composite medium

NASA Astrophysics Data System (ADS)

Bergman, David J.; Farhi, Asaf

2018-04-01

A spectral representation for the static electric potential field in a two-constituent composite medium is presented. A theory is developed for calculating the quasistatic eigenstates of Maxwell's equations for such a composite. The local physical potential field produced in the system by a given source charge density is expanded in this set of orthogonal eigenstates for any position r. The source charges can be located anywhere, i.e., inside any of the constituents. This is shown to work even if the eigenfunctions are normalized in an infinite volume. If the microstructure consists of a cluster of separate inclusions in a uniform host medium, then the quasistatic eigenstates of all the separate isolated inclusions can be used to calculate the eigenstates of the total structure as well as the local potential field. Once the eigenstates are known for a given host and a given microstructure, then calculation of the local field only involves calculating three-dimensional integrals of known functions and solving sets of linear algebraic equations.

Scilab software package for the study of dynamical systems

NASA Astrophysics Data System (ADS)

Bordeianu, C. C.; Beşliu, C.; Jipa, Al.; Felea, D.; Grossu, I. V.

2008-05-01

This work presents a new software package for the study of chaotic flows and maps. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well known examples are implemented, with the capability of the users inserting their own ODE. Program summaryProgram title: Chaos Catalogue identifier: AEAP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 885 No. of bytes in distributed program, including test data, etc.: 5925 Distribution format: tar.gz Programming language: Scilab 3.1.1 Computer: PC-compatible running Scilab on MS Windows or Linux Operating system: Windows XP, Linux RAM: below 100 Megabytes Classification: 6.2 Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE). Solution method: Numerical solving of ordinary differential equations. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincaré sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies. Restrictions: The package routines are normally able to handle ODE systems of high orders (up to order twelve and possibly higher), depending on the nature of the problem. Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE and Lyapunov exponents calculation.

Solving the Rational Polynomial Coefficients Based on L Curve

NASA Astrophysics Data System (ADS)

Zhou, G.; Li, X.; Yue, T.; Huang, W.; He, C.; Huang, Y.

2018-05-01

The rational polynomial coefficients (RPC) model is a generalized sensor model, which can achieve high approximation accuracy. And it is widely used in the field of photogrammetry and remote sensing. Least square method is usually used to determine the optimal parameter solution of the rational function model. However the distribution of control points is not uniform or the model is over-parameterized, which leads to the singularity of the coefficient matrix of the normal equation. So the normal equation becomes ill conditioned equation. The obtained solutions are extremely unstable and even wrong. The Tikhonov regularization can effectively improve and solve the ill conditioned equation. In this paper, we calculate pathological equations by regularization method, and determine the regularization parameters by L curve. The results of the experiments on aerial format photos show that the accuracy of the first-order RPC with the equal denominators has the highest accuracy. The high order RPC model is not necessary in the processing of dealing with frame images, as the RPC model and the projective model are almost the same. The result shows that the first-order RPC model is basically consistent with the strict sensor model of photogrammetry. Orthorectification results both the firstorder RPC model and Camera Model (ERDAS9.2 platform) are similar to each other, and the maximum residuals of X and Y are 0.8174 feet and 0.9272 feet respectively. This result shows that RPC model can be used in the aerial photographic compensation replacement sensor model.

Prediction equations for maximal respiratory pressures of Brazilian adolescents.

PubMed

Mendes, Raquel E F; Campos, Tania F; Macêdo, Thalita M F; Borja, Raíssa O; Parreira, Verônica F; Mendonça, Karla M P P

2013-01-01

The literature emphasizes the need for studies to provide reference values and equations able to predict respiratory muscle strength of Brazilian subjects at different ages and from different regions of Brazil. To develop prediction equations for maximal respiratory pressures (MRP) of Brazilian adolescents. In total, 182 healthy adolescents (98 boys and 84 girls) aged between 12 and 18 years, enrolled in public and private schools in the city of Natal-RN, were evaluated using an MVD300 digital manometer (Globalmed®) according to a standardized protocol. Statistical analysis was performed using SPSS Statistics 17.0 software, with a significance level of 5%. Data normality was verified using the Kolmogorov-Smirnov test, and descriptive analysis results were expressed as the mean and standard deviation. To verify the correlation between the MRP and the independent variables (age, weight, height and sex), the Pearson correlation test was used. To obtain the prediction equations, stepwise multiple linear regression was used. The variables height, weight and sex were correlated to MRP. However, weight and sex explained part of the variability of MRP, and the regression analysis in this study indicated that these variables contributed significantly in predicting maximal inspiratory pressure, and only sex contributed significantly to maximal expiratory pressure. This study provides reference values and two models of prediction equations for maximal inspiratory and expiratory pressures and sets the necessary normal lower limits for the assessment of the respiratory muscle strength of Brazilian adolescents.