Creeping gaseous flows through elastic tube and annulus micro-configurations

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2016-11-01

Gaseous flows in elastic micro-configurations is relevant to biological systems (e.g. alveolar ducts in the lungs) as well as to applications such as gas actuated soft micro-robots. We here examine the effect of low-Mach-number compressibility on creeping gaseous axial flows through linearly elastic tube and annulus micro-configurations. For steady flows, the leading-order effects of elasticity on the pressure distribution and mass-flux are obtained. For transient flow in a tube with small deformations, elastic effects are shown to be negligible in leading order due to compressibility. We then examine transient flows in annular configurations where the deformation is significant compared with the gap between the inner and outer cylinders defining the annulus. Both compressibility and elasticity are obtained as dominant terms interacting with viscosity. For a sudden flux impulse, the governing non-linear leading order diffusion equation is initially approximated by a porous-medium-equation of order 2.5 for the pressure square. However, as the fluid expand and the pressure decreases, the governing equation degenerates to a porous-medium-equation of order 2 for the pressure.

Linear Scaling of the Exciton Binding Energy versus the Band Gap of Two-Dimensional Materials

NASA Astrophysics Data System (ADS)

Choi, Jin-Ho; Cui, Ping; Lan, Haiping; Zhang, Zhenyu

2015-08-01

The exciton is one of the most crucial physical entities in the performance of optoelectronic and photonic devices, and widely varying exciton binding energies have been reported in different classes of materials. Using first-principles calculations within the G W -Bethe-Salpeter equation approach, here we investigate the excitonic properties of two recently discovered layered materials: phosphorene and graphene fluoride. We first confirm large exciton binding energies of, respectively, 0.85 and 2.03 eV in these systems. Next, by comparing these systems with several other representative two-dimensional materials, we discover a striking linear relationship between the exciton binding energy and the band gap and interpret the existence of the linear scaling law within a simple hydrogenic picture. The broad applicability of this novel scaling law is further demonstrated by using strained graphene fluoride. These findings are expected to stimulate related studies in higher and lower dimensions, potentially resulting in a deeper understanding of excitonic effects in materials of all dimensionalities.

Propagation of thickness-twist waves in a piezoelectric ceramic plate with unattached electrodes.

PubMed

Qian, Zheng-Hua; Kishimoto, Kikuo; Yang, Jiashi

2009-06-01

We analyze the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with air gaps between the plate surfaces and two electrodes. These waves are also called anti-plane or shear-horizontal waves with one displacement component only. An exact solution is obtained from the equations of the linear theory of piezoelectricity. Dispersion relations of the waves are obtained and plotted. Results show that the wave frequency or speed is sensitive to the air gap thickness. This effect can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.

Numerical reconstruction of unknown Robin inclusions inside a heat conductor by a non-iterative method

NASA Astrophysics Data System (ADS)

Nakamura, Gen; Wang, Haibing

2017-05-01

Consider the problem of reconstructing unknown Robin inclusions inside a heat conductor from boundary measurements. This problem arises from active thermography and is formulated as an inverse boundary value problem for the heat equation. In our previous works, we proposed a sampling-type method for reconstructing the boundary of the Robin inclusion and gave its rigorous mathematical justification. This method is non-iterative and based on the characterization of the solution to the so-called Neumann- to-Dirichlet map gap equation. In this paper, we give a further investigation of the reconstruction method from both the theoretical and numerical points of view. First, we clarify the solvability of the Neumann-to-Dirichlet map gap equation and establish a relation of its solution to the Green function associated with an initial-boundary value problem for the heat equation inside the Robin inclusion. This naturally provides a way of computing this Green function from the Neumann-to-Dirichlet map and explains what is the input for the linear sampling method. Assuming that the Neumann-to-Dirichlet map gap equation has a unique solution, we also show the convergence of our method for noisy measurements. Second, we give the numerical implementation of the reconstruction method for two-dimensional spatial domains. The measurements for our inverse problem are simulated by solving the forward problem via the boundary integral equation method. Numerical results are presented to illustrate the efficiency and stability of the proposed method. By using a finite sequence of transient input over a time interval, we propose a new sampling method over the time interval by single measurement which is most likely to be practical.

Switching effects and spin-valley Andreev resonant peak shifting in silicene superconductor

NASA Astrophysics Data System (ADS)

Soodchomshom, Bumned; Niyomsoot, Kittipong; Pattrawutthiwong, Eakkarat

2018-03-01

The magnetoresistance and spin-valley transport properties in a silicene-based NM/FB/SC junction are investigated, where NM, FB and SC are normal, ferromagnetic and s-wave superconducting silicene, respectively. In the FB region, perpendicular electric and staggered exchange fields are applied. The quasiparticles may be described by Dirac Bogoliubov-de Gennes equation due to Cooper pairs formed by spin-valley massive fermions. The spin-valley conductances are calculated based on the modified Blonder-Tinkham-Klapwijk formalism. We find the spin-valley dependent Andreev resonant peaks in the junction shifted by applying exchange field. Perfect conductance switch generated by interplay of intrinsic spin orbit interaction and superconducting gap has been predicted. Spin and valley polarizations are almost linearly dependent on biased voltage near zero bias and then turn into perfect switch at biased voltage approaching the superconducting gap. The perfect switching of large magnetoresistance has been also predicted at biased energy near the superconducting gap. These switching effects may be due to the presence of spin-valley Andreev resonant peak near the superconducting gap. Our work reveals potential of silicene as applications of electronic switching devices and linear control of spin and valley polarizations.

Air-Gapped Structures as Magnetic Elements for Use in Power Processing Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Ohri, A. K.

1977-01-01

Methodical approaches to the design of inductors for use in LC filters and dc-to-dc converters using air gapped magnetic structures are presented. Methods for the analysis and design of full wave rectifier LC filter circuits operating with the inductor current in both the continuous conduction and the discontinuous conduction modes are also described. In the continuous conduction mode, linear circuit analysis techniques are employed, while in the case of the discontinuous mode, the method of analysis requires computer solutions of the piecewise linear differential equations which describe the filter in the time domain. Procedures for designing filter inductors using air gapped cores are presented. The first procedure requires digital computation to yield a design which is optimized in the sense of minimum core volume and minimum number of turns. The second procedure does not yield an optimized design as defined above, but the design can be obtained by hand calculations or with a small calculator. The third procedure is based on the use of specially prepared magnetic core data and provides an easy way to quickly reach a workable design.

Bands dispersion and charge transfer in β-BeH2

NASA Astrophysics Data System (ADS)

Trivedi, D. K.; Galav, K. L.; Joshi, K. B.

2018-04-01

Predictive capabilities of ab-initio method are utilised to explore bands dispersion and charge transfer in β-BeH2. Investigations are carried out using the linear combination of atomic orbitals method at the level of density functional theory. The crystal structure and related parameters are settled by coupling total energy calculations with the Murnaghan equation of state. Electronic bands dispersion from PBE-GGA is reported. The PBE-GGA, and PBE0 hybrid functional, show that β-BeH2 is a direct gap semiconductor with 1.18 and 2.40 eV band gap. The band gap slowly decreases with pressure and beyond l00 GPa overlap of conduction and valence bands at the r point is observed. Charge transfer is studied by means of Mullikan population analysis.

Drive mechanisms to the inner and outer hair cell stereocilia

NASA Astrophysics Data System (ADS)

Maftoon, Nima; Motallebzadeh, Hamid; Guinan, John J.; Puria, Sunil

2018-05-01

It has been long believed that inner hair cell (IHC) stimulation can be gleaned from the classic ter-Kuile shear motion between the reticular lamina (RL) and tectorial membrane (TM). The present study explores this and other IHC stimulation mechanisms using a finite-element-model representation of an organ of Corti (OoC) cross section with fluid-structure interaction. A 3-D model of a cross section of the OoC including soft tissue and the fluid in the sub-tectorial space, tunnel of Corti and above the TM was formulated based on anatomical measurements from the gerbil apical turn. The outer hair cells (OHCs), Deiter's cells and their phalangeal processes are represented as Y-shaped building-block elements. Each of the IHC and OHC bundles is represented by a single sterocilium. Linearized Navier-Stokes equations coupled with linear-elastic equations discretized with tetrahedral elements are solved in the frequency domain. We evaluated the dynamic changes in the OoC motion including sub-tectorial gap dimensions for 0.1 to 10 kHz input frequencies. Calculations show the classic ter-Kuile motion but more importantly they show that the gap-height changes which produce oscillatory radial flow in the subtectorial space. Phase changes in the stereocilia across OHC rows and the IHC are also observed.

High-contrast imaging with an arbitrary aperture: active correction of aperture discontinuities

NASA Astrophysics Data System (ADS)

Pueyo, Laurent; Norman, Colin; Soummer, Rémi; Perrin, Marshall; N'Diaye, Mamadou; Choquet, Elodie

2013-09-01

We present a new method to achieve high-contrast images using segmented and/or on-axis telescopes. Our approach relies on using two sequential Deformable Mirrors to compensate for the large amplitude excursions in the telescope aperture due to secondary support structures and/or segment gaps. In this configuration the parameter landscape of Deformable Mirror Surfaces that yield high contrast Point Spread Functions is not linear, and non-linear methods are needed to find the true minimum in the optimization topology. We solve the highly non-linear Monge-Ampere equation that is the fundamental equation describing the physics of phase induced amplitude modulation. We determine the optimum configuration for our two sequential Deformable Mirror system and show that high-throughput and high contrast solutions can be achieved using realistic surface deformations that are accessible using existing technologies. We name this process Active Compensation of Aperture Discontinuities (ACAD). We show that for geometries similar to JWST, ACAD can attain at least 10-7 in contrast and an order of magnitude higher for future Extremely Large Telescopes, even when the pupil features a missing segment" . We show that the converging non-linear mappings resulting from our Deformable Mirror shapes actually damp near-field diffraction artifacts in the vicinity of the discontinuities. Thus ACAD actually lowers the chromatic ringing due to diffraction by segment gaps and strut's while not amplifying the diffraction at the aperture edges beyond the Fresnel regime and illustrate the broadband properties of ACAD in the case of the pupil configuration corresponding to the Astrophysics Focused Telescope Assets. Since details about these telescopes are not yet available to the broader astronomical community, our test case is based on a geometry mimicking the actual one, to the best of our knowledge.

Non linear dynamics of flame cusps: from experiments to modeling

NASA Astrophysics Data System (ADS)

Almarcha, Christophe; Radisson, Basile; Al-Sarraf, Elias; Quinard, Joel; Villermaux, Emmanuel; Denet, Bruno; Joulin, Guy

2016-11-01

The propagation of premixed flames in a medium initially at rest exhibits the appearance and competition of elementary local singularities called cusps. We investigate this problem both experimentally and numerically. An analytical solution of the two-dimensional Michelson Sivashinsky equation is obtained as a composition of pole solutions, which is compared with experimental flames fronts propagating between glass plates separated by a thin gap width. We demonstrate that the front dynamics can be reproduced numerically with a good accuracy, from the linear stages of destabilization to its late time evolution, using this model-equation. In particular, the model accounts for the experimentally observed steady distribution of distances between cusps, which is well-described by a one-parameter Gamma distribution, reflecting the aggregation type of interaction between the cusps. A modification of the Michelson Sivashinsky equation taking into account gravity allows to reproduce some other special features of these fronts. Aix-Marseille Univ., IRPHE, UMR 7342 CNRS, Centrale Marseille, Technopole de Château Gombert, 49 rue F. Joliot Curie, 13384 Marseille Cedex 13, France.

On the Rate of Relaxation for the Landau Kinetic Equation and Related Models

NASA Astrophysics Data System (ADS)

Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong

2017-08-01

We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.

Fluid-structure interaction in Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Kempf, Martin Horst Willi

1998-10-01

The linear stability of a viscous fluid between two concentric, rotating cylinders is considered. The inner cylinder is a rigid boundary and the outer cylinder has an elastic layer exposed to the fluid. The subject is motivated by flow between two adjoining rollers in a printing press. The governing equations of the fluid layer are the incompressible Navier-Stokes equations, and the governing equations of the elastic layer are Navier's equations. A narrow gap, neutral stability, and axisymmetric disturbances are assumed. The solution involves a novel technique for treating two layer stability problems, where an exact solution in the elastic layer is used to isolate the problem in the fluid layer. The results show that the presence of the elastic layer has only a slight effect on the critical Taylor numbers for the elastic parameters of modern printing presses. However, there are parameter values where the critical Taylor number is dramatically different than the classical Taylor-Couette problem.

Inside black holes with synchronized hair

NASA Astrophysics Data System (ADS)

Brihaye, Yves; Herdeiro, Carlos; Radu, Eugen

2016-09-01

Recently, various examples of asymptotically flat, rotating black holes (BHs) with synchronized hair have been explicitly constructed, including Kerr BHs with scalar or Proca hair, and Myers-Perry BHs with scalar hair and a mass gap, showing there is a general mechanism at work. All these solutions have been found numerically, integrating the fully non-linear field equations of motion from the event horizon outwards. Here, we address the spacetime geometry of these solutions inside the event horizon. Firstly, we provide arguments, within linear theory, that there is no regular inner horizon for these solutions. Then, we address this question fully non-linearly, using as a tractable model five dimensional, equal spinning, Myers-Perry hairy BHs. We find that, for non-extremal solutions: (1) the inside spacetime geometry in the vicinity of the event horizon is smooth and the equations of motion can be integrated inwards; (2) before an inner horizon is reached, the spacetime curvature grows (apparently) without bound. In all cases, our results suggest the absence of a smooth Cauchy horizon, beyond which the metric can be extended, for hairy BHs with synchronized hair.

The gap equation for spin-polarized fermions

NASA Astrophysics Data System (ADS)

Freiji, Abraham; Hainzl, Christian; Seiringer, Robert

2012-01-01

We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δμ/T) ⩽ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal. 17, 559-567 (2007), 10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys. 281, 349-367 (2008), 10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B 77, 184517-110 435 (2008)], 10.1103/PhysRevB.77.184517. For cosh (δμ/T) > 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.

Quasi-particle energies and optical excitations of hydrogenated and fluorinated germanene.

PubMed

Shu, Huabing; Li, Yunhai; Wang, Shudong; Wang, Jinlan

2015-02-14

Using density functional theory, the G0W0 method and Bethe-Salpeter equation calculations, we systematically explore the structural, electronic and optical properties of hydrogenated and fluorinated germanene. The hydrogenated/fluorinated germanene tends to form chair and zigzag-line configurations and its electronic and optical properties show close geometry dependence. The chair hydrogenated/fluorinated and zigzag-line fluorinated germanene are direct band-gap semiconductors, while the zigzag-line hydrogenated germanene owns an indirect band-gap. Moreover, the quasi-particle corrections are significant and strong excitonic effects with large exciton binding energies are observed. Moreover, the zigzag-line hydrogenated/fluorinated germanene shows highly anisotropic optical responses, which may be used as a good optical linear polarizer.

A de Sitter tachyon thick braneworld

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

Germán, Gabriel; Herrera-Aguilar, Alfredo; Malagón-Morejón, Dagoberto

2013-02-01

Among the multiple 5D thick braneworld models that have been proposed in the last years, in order to address several open problems in modern physics, there is a specific one involving a tachyonic bulk scalar field. Delving into this framework, a thick braneworld with a cosmological background induced on the brane is here investigated. The respective field equations — derived from the model with a warped 5D geometry — are highly non-linear equations, admitting a non-trivial solution for the warp factor and the tachyon scalar field as well, in a de Sitter 4D cosmological background. Moreover, the non-linear tachyonic scalarmore » field, that generates the brane in complicity with warped gravity, has the form of a kink-like configuration. Notwithstanding, the non-linear field equations restricting character does not allow one to easily find thick brane solutions with a decaying warp factor which leads to the localization of 4D gravity and other matter fields. We derive such a thick brane configuration altogether in this tachyon-gravity setup. When analyzing the spectrum of gravity fluctuations in the transverse traceless sector, the 4D gravity is shown to be localized due to the presence of a single zero mode bound state, separated by a continuum of massive Kaluza-Klein (KK) modes by a mass gap. It contrasts with previous results, where there is a KK massive bound excitation providing no clear physical interpretation. The mass gap is determined by the scale of the metric parameter H. Finally, the corrections to Newton's law in this model are computed and shown to decay exponentially. It is in full compliance to corrections reported in previous results (up to a constant factor) within similar braneworlds with induced 4D de Sitter metric, despite the fact that the warp factor and the massive modes have a different form.« less

Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps

NASA Astrophysics Data System (ADS)

Fang, En; Wu, Xiaojie; Yu, Yuesen; Xiu, Junrui

2017-03-01

In this paper, a numerical model is developed by combining thermodynamics with heat transfer theory. Taking inner and external multi-irreversibility into account, it is with a complementary equation for heat circulation in air gaps of a steady cooling system with commercial thermoelectric modules operating in refrigeration mode. With two modes concerned, the equation presents the heat flowing through air gaps which forms heat circulations between both sides of thermoelectric coolers (TECs). In numerical modelling, a TEC is separated as two temperature controlled constant heat flux reservoirs in a thermal resistance network. In order to obtain the parameter values, an experimental apparatus with a commercial thermoelectric cooler was built to characterize the performance of a TEC with heat source and sink assembly. At constant power dissipation, steady temperatures of heat source and both sides of the thermoelectric cooler were compared with those in a standard numerical model. The method displayed that the relationship between Φf and the ratio Φ_{c}'/Φ_{c} was linear as expected. Then, for verifying the accuracy of proposed numerical model, the data in another system were recorded. It is evident that the experimental results are in good agreement with simulation(proposed model) data at different heat transfer rates. The error is small and mainly results from the instabilities of thermal resistances with temperature change and heat flux, heat loss of the device vertical surfaces and measurements.

Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincaré symmetry

NASA Astrophysics Data System (ADS)

Barbosa-Cendejas, Nandinii; Herrera-Aguilar, Alfredo; Kanakoglou, Konstantinos; Nucamendi, Ulises; Quiros, Israel

2014-01-01

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with , in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to analytically compute the corrections to Newton's law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states—the massless 4D graviton free of tachyonic instabilities and a massive KK excitation—as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken-Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar-tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld configuration.

On Pokrovskii's anisotropic gap equations in superconductivity theory

NASA Astrophysics Data System (ADS)

Yang, Yisong

2003-11-01

An existence and uniqueness theorem for Pokrovskii's zero-temperature anisotropic gap equation is proved. Furthermore, it is shown that Pokrovskii's finite-temperature equation is inconsistent with the Bardeen-Cooper-Schrieffer (BCS) theory. A reformulation of the anisotropic gap equation is presented along the line of Pokrovskii and it is shown that the new equation is consistent with the BCS theory for the whole temperature range. As an application, the Markowitz-Kadanoff model for anisotropic superconductivity is considered and a rigorous proof of the half-integer-exponent isotope effect is obtained. Furthermore, a sharp estimate of the gap solution near the transition temperature is established.

Gas Dynamics of a Recessed Nozzle in Its Displacement in the Radial Direction

NASA Astrophysics Data System (ADS)

Volkov, K. N.; Denisikhin, S. V.; Emel'yanov, V. N.

2017-07-01

Numerical simulation of gasdynamic processes accompanying the operation of the recessed nozzle of a solid-propellant rocket motor in its linear displacement is carried out. Reynolds-averaged Navier-Stokes equations closed using the equations of a k-ɛ turbulence model are used for calculations. The calculations are done for different rates of flow of the gas in the main channel and in the over-nozzle gap, and also for different displacements of the nozzle from an axisymmetric position. The asymmetry of geometry gives rise to a complicated spatial flow pattern characterized by the presence of singular points of spreading and by substantially inhomogeneous velocity and pressure distributions. The vortex flow pattern resulting from the linear displacement of the nozzle from an axisymmetric position is compared with the data of experimental visualization. The change in the vortex pattern of the flow and in the position of the singular points as a function of the flow coefficient and the displacement of the nozzle from the symmetry axis is discussed.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-10-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ω_i while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-09-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev

2017-11-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

On the use of the Reciprocity Gap Functional in inverse scattering with near-field data: An application to mammography

NASA Astrophysics Data System (ADS)

Delbary, Fabrice; Aramini, Riccardo; Bozza, Giovanni; Brignone, Massimo; Piana, Michele

2008-11-01

Microwave tomography is a non-invasive approach to the early diagnosis of breast cancer. However the problem of visualizing tumors from diffracted microwaves is a difficult nonlinear ill-posed inverse scattering problem. We propose a qualitative approach to the solution of such a problem, whereby the shape and location of cancerous tissues can be detected by means of a combination of the Reciprocity Gap Functional method and the Linear Sampling method. We validate this approach to synthetic near-fields produced by a finite element method for boundary integral equations, where the breast is mimicked by the axial view of two nested cylinders, the external one representing the skin and the internal one representing the fat tissue.

The Shock and Vibration Bulletin. Part 2. Modal and Impedance Analysis, Human Response to Vibration and Shock, Isolation and Damping, Dynamic Analysis

DTIC Science & Technology

1979-09-01

a " high performance fast timing" engine thrust with a mismatch between right and left SRfls...examine the dynamic behavior of a blade having a root geometry compatible with low frictional forces at high rotational speeds , somewhat like a "Christmas...Tree" root, but with a gap introduced which will close up only at high speed . Approximate non-linear equations of motion are derived and solved

Follow-on to a report on the Applicability of the “Gallet equation” to the vegetation clearances of NERC Reliability Standard FAC-003-2

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

Kirkham, Harold

2012-08-31

In earlier work, a study done at the Pacific Northwest National Laboratory examined a NERC proposed standard specifying clearances between vegetation and power lines. The method proposed for calculating the clearances was based on the results of testing for high-voltage line designs. An equation developed to relate the results of testing with rod-plane gaps to proposed tower window sizes was incorporated into the calculations. The equation in question, sometimes called the “Gallet equation,” describes the insulation performance of the atmosphere for air gaps of a few meters. The equation was described in the PNNL study as a good and simple-to-usemore » way to solve a problem made difficult by the nonlinear interactions of the variables. For calculations based on this equation, a certain set of assumptions must be made. In particular, a value for a quantity called the “gap factor” is needed. This is the amount by which the gap to be modeled by the equation is stronger than the reference gap that was used in developing the Gallet equation. That reference gap is the gap between a rod and a plane. This follow-on report examines the effect on flashover probabilities of assuming an incorrect value for the gap factor. In particular, the flashover probability is found that would result from using a value of 1.3 when a gap factor of 1.0 should be applied. It is shown that with these assumptions the probability of a flashover changes from being extremely unlikely (about 1 in 1000 chance) to a virtual certainty (about 97% chance).« less

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

Konyashov, Vadim V.; Krasnov, Alexander M.

Results are provided of the experimental investigation of radioactive fission product (RFP) release, i.e., krypton, xenon, and iodine radionuclides from fuel elements with initial defects during long-term (3 to 5 yr) irradiation under low linear power (5 to 12 kW/m) and during special experiments in the VK-50 vessel-type boiling water reactor.The calculation model for the RFP release from the fuel-to-cladding gap of the defective fuel element into coolant was developed. It takes into account the convective transport in the fuel-to-cladding gap and RFP sorption on the internal cladding surface and is in good agreement with the available experimental data. Anmore » approximate analytical solution of the transport equation is given. The calculation dependencies of the RFP release coefficients on the main parameters such as defect size, fuel-to-cladding gap, temperature of the internal cladding surface, and radioactive decay constant were analyzed.It is shown that the change of the RFP release from the fuel elements with the initial defects during long-term irradiation is, mainly, caused by fuel swelling followed by reduction of the fuel-to-cladding gap and the fuel temperature. The calculation model for the RFP release from defective fuel elements applicable to light water reactors (LWRs) was developed. It takes into account the change of the defective fuel element parameters during long-term irradiation. The calculation error according to the program does not exceed 30% over all the linear power change range of the LWR fuel elements (from 5 to 26 kW/m)« less

Dramatic dwindling of the power spectrum of high order harmonics by shrinking of the gap size in bowtie nanostructures

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

Hosseinzadeh, F.; Batebi, S., E-mail: s-batebi@guilan.ac.ir; Soofi, M. Q.

2017-03-15

Our work is based on high harmonic generation in a gaseous medium (helium ion), by exploiting gold bowtie nanostructures as laser field amplifiers. As the result of emission of a laser pulse, the wave function of the atom varies with time; so, it is necessary to solve 1D time-dependent Schrödinger equation by means of split operator method. By illumination of a short duration, long wavelength three color laser pulse inside the gap, the enhanced field not only changes with time, but also varies in space. In this work we considered this space inhomogeneity in linear and nonlinear schemes. We showmore » that in nonlinear case, the plateau region is more extended. We also show that in larger gaps, cutoff occurs on higher frequencies. But limitation of electron motion in bowtie nanostructures leads to the choice of an optimum 16 nm gap size in our case. We predict that, by the superposition of supercontinuum harmonics, a 26 attosecond pulse can be generated.« less

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

Method and Apparatus for Separating Particles by Dielectrophoresis

NASA Technical Reports Server (NTRS)

Pant, Kapil (Inventor); Wang, Yi (Inventor); Bhatt, Ketan (Inventor); Prabhakarpandian, Balabhasker (Inventor)

2014-01-01

Particle separation apparatus separate particles and particle populations using dielectrophoretic (DEP) forces generated by one or more pairs of electrically coupled electrodes separated by a gap. Particles suspended in a fluid are separated by DEP forces generated by the at least one electrode pair at the gap as they travel over a separation zone comprising the electrode pair. Selected particles are deflected relative to the flow of incoming particles by DEP forces that are affected by controlling applied potential, gap width, and the angle linear gaps with respect to fluid flow. The gap between an electrode pair may be a single, linear gap of constant gap, a single linear gap having variable width, or a be in the form of two or more linear gaps having constant or variable gap width having different angles with respect to one another and to the flow.

CORRECTING FOR MEASUREMENT ERROR IN LATENT VARIABLES USED AS PREDICTORS*

PubMed Central

Schofield, Lynne Steuerle

2015-01-01

This paper represents a methodological-substantive synergy. A new model, the Mixed Effects Structural Equations (MESE) model which combines structural equations modeling and item response theory is introduced to attend to measurement error bias when using several latent variables as predictors in generalized linear models. The paper investigates racial and gender disparities in STEM retention in higher education. Using the MESE model with 1997 National Longitudinal Survey of Youth data, I find prior mathematics proficiency and personality have been previously underestimated in the STEM retention literature. Pre-college mathematics proficiency and personality explain large portions of the racial and gender gaps. The findings have implications for those who design interventions aimed at increasing the rates of STEM persistence among women and under-represented minorities. PMID:26977218

AC-driven bilayer graphene: quasienergy spectrum of electrons and generation of soliton-like electromagnetic pulse

NASA Astrophysics Data System (ADS)

Kukhar, Egor I.

2018-01-01

Quasienergy spectrum of electrons in biased bigraphene subjected to the linear polarized high-frequency electromagnetic radiation has been derived. Quasienergy bands of ac-driven bigraphene have been investigated. Dynamical appearing of the saddle points in band structure of biased bigraphene and energy gap modification have been predicted. Electromagnetic field equation has been written using obtained quasienergy spectrum. The solution corresponding to the soliton-like electromagnetic wave has been obtained. The conditions of soliton-like wave generation in ac-driven bigraphene have been discussed.

Nonlinear properties of gated graphene in a strong electromagnetic field

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

Avetisyan, A. A., E-mail: artakav@ysu.am; Djotyan, A. P., E-mail: adjotyan@ysu.am; Moulopoulos, K., E-mail: cos@ucy.ac.cy

We develop a microscopic theory of a strong electromagnetic field interaction with gated bilayer graphene. Quantum kinetic equations for density matrix are obtained using a tight binding approach within second quantized Hamiltonian in an intense laser field. We show that adiabatically changing the gate potentials with time may produce (at resonant photon energy) a full inversion of the electron population with high density between valence and conduction bands. In the linear regime, excitonic absorption of an electromagnetic radiation in a graphene monolayer with opened energy gap is also studied.

Transportation of high-current ion and electron beams in the accelerator drift gap in the presence of an additional electron background

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

Karas’, V. I., E-mail: karas@kipt.kharkov.ua; Kornilov, E. A.; Manuilenko, O. V.

2015-12-15

The dynamics of a high-current ion beam propagating in the drift gap of a linear induction accelerator with collective focusing is studied using 3D numerical simulations in the framework of the full system of the Vlasov–Maxwell equations (code KARAT). The ion beam is neutralized by a comoving electron beam in the current density and, partially, in space charge, since the velocities of electrons and ions differ substantially. The dynamics of the high-current ion beam is investigated for different versions of additional neutralization of its space charge. It is established that, for a given configuration of the magnetic field and inmore » the presence of a specially programmed injection of additional electrons from the boundary opposite to the ion injection boundary, the angular divergence of the ion beam almost vanishes, whereas the current of the ion beam at the exit from the accelerator drift gap changes insignificantly and the beam remains almost monoenergetic.« less

Transportation of high-current ion and electron beams in the accelerator drift gap in the presence of an additional electron background

NASA Astrophysics Data System (ADS)

Karas', V. I.; Kornilov, E. A.; Manuilenko, O. V.; Tarakanov, V. P.; Fedorovskaya, O. V.

2015-12-01

The dynamics of a high-current ion beam propagating in the drift gap of a linear induction accelerator with collective focusing is studied using 3D numerical simulations in the framework of the full system of the Vlasov-Maxwell equations (code KARAT). The ion beam is neutralized by a comoving electron beam in the current density and, partially, in space charge, since the velocities of electrons and ions differ substantially. The dynamics of the high-current ion beam is investigated for different versions of additional neutralization of its space charge. It is established that, for a given configuration of the magnetic field and in the presence of a specially programmed injection of additional electrons from the boundary opposite to the ion injection boundary, the angular divergence of the ion beam almost vanishes, whereas the current of the ion beam at the exit from the accelerator drift gap changes insignificantly and the beam remains almost monoenergetic.

A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-11-28

A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.

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.

Linear and Nonlinear Analysis of Magnetic Bearing Bandwidth Due to Eddy Current Limitations

NASA Technical Reports Server (NTRS)

Kenny, Andrew; Palazzolo, Alan

2000-01-01

Finite element analysis was used to study the bandwidth of alloy hyperco50a and silicon iron laminated rotors and stators in magnetic bearings. A three dimensional model was made of a heteropolar bearing in which all the flux circulated in the plane of the rotor and stator laminate. A three dimensional model of a plate similar to the region of a pole near the gap was also studied with a very fine mesh. Nonlinear time transient solutions for the net flux carried by the plate were compared to steady state time harmonic solutions. Both linear and quasi-nonlinear steady state time harmonic solutions were calculated and compared. The finite element solutions for power loss and flux bandwidth were compared to those determined from classical analytical solutions to Maxwell's equations.

Gap Flows through Idealized Topography. Part I: Forcing by Large-Scale Winds in the Nonrotating Limit.

NASA Astrophysics Data System (ADS)

Gabersek, Sasa.; Durran, Dale R.

2004-12-01

Gap winds produced by a uniform airstream flowing over an isolated flat-top ridge cut by a straight narrow gap are investigated by numerical simulation. On the scale of the entire barrier, the proportion of the oncoming flow that passes through the gap is relatively independent of the nondimensional mountain height , even over that range of for which there is the previously documented transition from a “flow over the ridge” regime to a “flow around” regime.The kinematics and dynamics of the gap flow itself were investigated by examining mass and momentum budgets for control volumes at the entrance, central, and exit regions of the gap. These analyses suggest three basic behaviors: the linear regime (small ) in which there is essentially no enhancement of the gap flow; the mountain wave regime ( 1.5) in which vertical mass and momentum fluxes play a crucial role in creating very strong winds near the exit of the gap; and the upstream-blocking regime ( 5) in which lateral convergence generates the strongest winds near the entrance of the gap.Trajectory analysis of the flow in the strongest events, the mountain wave events, confirms the importance of net subsidence in creating high wind speeds. Neglect of vertical motion in applications of Bernoulli's equation to gap flows is shown to lead to unreasonable wind speed predictions whenever the temperature at the gap exit exceeds that at the gap entrance. The distribution of the Bernoulli function on an isentropic surface shows a correspondence between regions of high Bernoulli function and high wind speeds in the gap-exit jet similar to that previously documented for shallow-water flow.

Technological pedagogical content knowledge of junior high school mathematics teachers in teaching linear equation

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-04-01

Linear equation is one of the topics in mathematics that are considered difficult. Student difficulties of understanding linear equation can be caused by lack of understanding this concept and the way of teachers teach. TPACK is a way to understand the complex relationships between teaching and content taught through the use of specific teaching approaches and supported by the right technology tools. This study aims to identify TPACK of junior high school mathematics teachers in teaching linear equation. The method used in the study was descriptive. In the first phase, a survey using a questionnaire was carried out on 45 junior high school mathematics teachers in teaching linear equation. While in the second phase, the interview involved three teachers. The analysis of data used were quantitative and qualitative technique. The result PCK revealed teachers emphasized developing procedural and conceptual knowledge through reliance on traditional in teaching linear equation. The result of TPK revealed teachers’ lower capacity to deal with the general information and communications technologies goals across the curriculum in teaching linear equation. The result indicated that PowerPoint constitutes TCK modal technological capability in teaching linear equation. The result of TPACK seems to suggest a low standard in teachers’ technological skills across a variety of mathematics education goals in teaching linear equation. This means that the ability of teachers’ TPACK in teaching linear equation still needs to be improved.

Nodal gap detection through polar angle-resolved density of states measurements in uniaxial superconductors

NASA Astrophysics Data System (ADS)

Tsutsumi, Yasumasa; Nomoto, Takuya; Ikeda, Hiroaki; Machida, Kazushige

2016-12-01

We propose a spectroscopic method to identify the nodal gap structure in unconventional superconductors. This method is best suited for locating the horizontal line node and for pinpointing the isolated point nodes by measuring polar angle (θ ) resolved zero-energy density of states N (θ ) . This is measured by specific heat or thermal conductivity at low temperatures under a magnetic field. We examine a variety of uniaxially symmetric nodal structures, including point and/or line nodes with linear and quadratic dispersions, by solving the Eilenberger equation in vortex states. It is found that (a) the maxima of N (θ ) continuously shift from the antinodal to the nodal direction (θn) as a field increases accompanying the oscillation pattern reversal at low and high fields. Furthermore, (b) local minima emerge next to θn on both sides, except for the case of the linear point node. These features are robust and detectable experimentally. Experimental results of N (θ ) performed on several superconductors, UPd2Al3,URu2Si2,CuxBi2Se3 , and UPt3, are examined and commented on in light of the present theory.

Premixed-Gas Flame Propagation in Hele-Shaw Cells

NASA Technical Reports Server (NTRS)

Sharif, J.; Abid, M.; Ronney, P. D.

1999-01-01

It is well known that buoyancy and thermal expansion affect the propagation ra and shapes of premixed gas flames. The understanding of such effects is complicated by the large density ratio between the reactants and products, which induces a baroclinic production of vorticity due to misalignment of density and pressure gradients at the front, which in turn leads to a complicated multi-dimensional flame/flow interaction. The Hele-Shaw cell, i.e., the region between closely-spaced flat parallel plates, is probably the simplest system in which multi-dimensional convection is presents consequently, the behavior of fluids in this system has been studied extensively (Homsy, 1987). Probably the most important characteristic of Hele-Shaw flows is that when the Reynolds number based on gap width is sufficiently small, the Navier-Stokes equations averaged over the gap reduce to a linear relation, namely a Laplace equation for pressure (Darcy's law). In this work, flame propagation in Hele-Shaw cells is studied to obtain a better understanding of buoyancy and thermal expansion effects on premixed flames. This work is also relevant to the study of unburned hydrocarbon emissions produced by internal combustion engines since these emissions are largely a result of the partial burning or complete flame quenching in the narrow, annular gap called the "crevice volume" between the piston and cylinder walls (Heywood, 1988). A better understanding of how flames propagate in these volumes through experiments using Hele-Shaw cells could lead to identification of means to reduce these emissions.

On supporting students' understanding of solving linear equation by using flowchart

NASA Astrophysics Data System (ADS)

Toyib, Muhamad; Kusmayadi, Tri Atmojo; Riyadi

2017-05-01

The aim of this study was to support 7th graders to gradually understand the concepts and procedures of solving linear equation. Thirty-two 7th graders of a Junior High School in Surakarta, Indonesia were involved in this study. Design research was used as the research approach to achieve the aim. A set of learning activities in solving linear equation with one unknown were designed based on Realistic Mathematics Education (RME) approach. The activities were started by playing LEGO to find a linear equation then solve the equation by using flowchart. The results indicate that using the realistic problems, playing LEGO could stimulate students to construct linear equation. Furthermore, Flowchart used to encourage students' reasoning and understanding on the concepts and procedures of solving linear equation with one unknown.

Unpacking the Complexity of Linear Equations from a Cognitive Load Theory Perspective

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Phan, Huy P.

2016-01-01

The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…

Schwarz maps of algebraic linear ordinary differential equations

NASA Astrophysics Data System (ADS)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

Effect of ladder diagrams on optical absorption spectra in a quasiparticle self-consistent GW framework

NASA Astrophysics Data System (ADS)

Cunningham, Brian; Grüning, Myrta; Azarhoosh, Pooya; Pashov, Dimitar; van Schilfgaarde, Mark

2018-03-01

We present an approach to calculate the optical absorption spectra that combines the quasiparticle self-consistent GW method [Phys. Rev. B 76, 165106 (2007), 10.1103/PhysRevB.76.165106] for the electronic structure with the solution of the ladder approximation to the Bethe-Salpeter equation for the macroscopic dielectric function. The solution of the Bethe-Salpeter equation has been implemented within an all-electron framework, using a linear muffin-tin orbital basis set, with the contribution from the nonlocal self-energy to the transition dipole moments (in the optical limit) evaluated explicitly. This approach addresses those systems whose electronic structure is poorly described within the standard perturbative GW approaches with density-functional theory calculations as a starting point. The merits of this approach have been exemplified by calculating optical absorption spectra of a strongly correlated transition metal oxide, NiO, and a narrow gap semiconductor, Ge. In both cases, the calculated spectrum is in good agreement with the experiment. It is also shown that for systems whose electronic structure is well-described within the standard perturbative GW , such as Si, LiF, and h -BN , the performance of the present approach is in general comparable to the standard GW plus Bethe-Salpeter equation. It is argued that both vertex corrections to the electronic screening and the electron-phonon interaction are responsible for the observed systematic overestimation of the fundamental band gap and spectrum onset.

Thermal Analysis of a Carbon Fiber Rope Barrier for Use in the Reusable Solid Rocket Motor Nozzle Joint-2

NASA Technical Reports Server (NTRS)

Clayton, J. Louie

2002-01-01

This study provides development and verification of analysis methods used to assess performance of a carbon fiber rope (CFR) thermal barrier system that is currently being qualified for use in Reusable Solid Rocket Motor (RSRM) nozzle joint-2. Modeled geometry for flow calculations considers the joint to be vented with the porous CFR barriers placed in the 'open' assembly gap. Model development is based on a 1-D volume filling approach where flow resistances (assembly gap and CFRs) are defined by serially connected internal flow and the porous media 'Darcy' relationships. Combustion gas flow rates are computed using the volume filling code by assuming a lumped distribution total joint fill volume on a per linear circumferential inch basis. Gas compressibility, friction and heat transfer are included in the modeling. Gas-to-wall heat transfer is simulated by concurrent solution of the compressible flow equations and a large thermal 2-D finite element (FE) conduction grid. The derived numerical technique loosely couples the FE conduction matrix with the compressible gas flow equations. Free constants that appear in the governing equations are calibrated by parametric model comparison to hot fire subscale test results. The calibrated model is then used to make full-scale motor predictions using RSRM aft dome environments. Model results indicate that CFR thermal barrier systems will provide a thermally benign and controlled pressurization environment for the RSRM nozzle joint-2 primary seal activation.

Thermal Analysis of a Carbon Fiber Rope Barrier for Use in the Reusable Solid Rocket Motor Nozzle Joint-2

NASA Technical Reports Server (NTRS)

Clayton, J. Louie; Phelps, Lisa (Technical Monitor)

2001-01-01

This study provides for development and verification of analysis methods used to assess performance of a carbon fiber rope (CFR) thermal barrier system that is currently being qualified for use in Reusable Solid Rocket Motor (RSRM) nozzle joint-2. Modeled geometry for flow calculations considers the joint to be vented with the porous CFR barriers placed in the "open' assembly gap. Model development is based on a 1-D volume filling approach where flow resistances (assembly gap and CFRs) are defined by serially connected internal flow and the porous media "Darcy" relationships. Combustion gas flow rates are computed using the volume filling code by assuming a lumped distribution total joint fill volume on a per linear circumferential inch basis. Gas compressibility, friction and heat transfer are included in the modeling. Gas-to-wall heat transfer is simulated by concurrent solution of the compressible flow equations and a large thermal 2-D finite element (FE) conduction grid. The derived numerical technique loosely couples the FE conduction matrix with the compressible gas flow equations, Free constants that appear in the governing equations are calibrated by parametric model comparison to hot fire subscale test results. The calibrated model is then used to make full-scale motor predictions using RSRM aft dome environments. Model results indicate that CFR thermal barrier systems will provide a thermally benign and controlled pressurization environment for the RSRM nozzle joint-2 primary seal activation.

A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems

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

Hansen, Glen, E-mail: Glen.Hansen@inl.gov

2011-07-20

Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO{sub 2}) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. Themore » accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.« less

A Jacobian-Free Newton Krylov Method for Mortar-Discretized Thermomechanical Contact Problems

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

Glen Hansen

2011-07-01

Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear reactor fuel rod, which consists of cylindrical pellets of uranium dioxide (UO2) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. Themore » accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.« less

Numerical simulation of stability and stability control of high speed compressible rotating couette flow

NASA Technical Reports Server (NTRS)

Biringen, Sedat; Hatay, Ferhat F.

1993-01-01

The nonlinear temporal evolution of disturbances in compressible flow between infinitely long, concentric cylinders is investigated through direct numerical simulations of the full, three-dimensional Navier-Stokes and energy equations. Counter-rotating cylinders separated by wide gaps are considered with supersonic velocities of the inner cylinder. Initially, the primary disturbance grows exponentially in accordance with linear stability theory. As the disturbances evolve, higher harmonics and subharmonics are generated in a cascading order eventually reaching a saturation state. Subsequent highly nonlinear stages of the evolution are governed by the interaction of the disturbance modes, particularly the axial subharmonics. Nonlinear evolution of the disturbance field is characterized by the formation of high-shear layers extending from the inner cylinder towards the center of the gap in the form of jets similar to the ejection events in transitional and turbulent wall-bounded shear flows.

Analysis of a Segmented Annular Coplanar Capacitive Tilt Sensor with Increased Sensitivity.

PubMed

Guo, Jiahao; Hu, Pengcheng; Tan, Jiubin

2016-01-21

An investigation of a segmented annular coplanar capacitor is presented. We focus on its theoretical model, and a mathematical expression of the capacitance value is derived by solving a Laplace equation with Hankel transform. The finite element method is employed to verify the analytical result. Different control parameters are discussed, and each contribution to the capacitance value of the capacitor is obtained. On this basis, we analyze and optimize the structure parameters of a segmented coplanar capacitive tilt sensor, and three models with different positions of the electrode gap are fabricated and tested. The experimental result shows that the model (whose electrode-gap position is 10 mm from the electrode center) realizes a high sensitivity: 0.129 pF/° with a non-linearity of <0.4% FS (full scale of ± 40°). This finding offers plenty of opportunities for various measurement requirements in addition to achieving an optimized structure in practical design.

Numerical investigation of tip clearance effects on the performance of ducted propeller

NASA Astrophysics Data System (ADS)

Ding, Yongle; Song, Baowei; Wang, Peng

2015-09-01

Tip clearance loss is a limitation of the improvement of turbomachine performance. Previous studies show the Tip clearance loss is generated by the leakage flow through the tip clearance, and is roughly linearly proportional to the gap size. This study investigates the tip clearance effects on the performance of ducted propeller. The investigation was carried out by solving the Navier-Stokes equations with the commercial Computational Fluid Dynamic (CFD) code CFX14.5. These simulations were carried out to determine the underlying mechanisms of the tip clearance effects. The calculations were performed at three different chosen advance ratios. Simulation results showed that the tip loss slope was not linearly at high advance due to the reversed pressure at the leading edge. Three type of vortical structures were observed in the tip clearance at different clearance size.

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

NASA Astrophysics Data System (ADS)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

Local Linear Observed-Score Equating

ERIC Educational Resources Information Center

Wiberg, Marie; van der Linden, Wim J.

2011-01-01

Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980)…

Students’ difficulties in solving linear equation problems

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

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.

Modulated wave formation in myocardial cells under electromagnetic radiation

NASA Astrophysics Data System (ADS)

Takembo, Clovis N.; Mvogo, A.; Ekobena Fouda, H. P.; Kofané, T. C.

2018-06-01

We exclusively analyze the onset and condition of formation of modulated waves in a diffusive FitzHugh-Nagumo model for myocardial cell excitations. The cells are connected through gap junction coupling. An additive magnetic flux variable is used to describe the effect of electromagnetic induction, while electromagnetic radiation is imposed on the magnetic flux variable as a periodic forcing. We used the discrete multiple scale expansion and obtained, from the model equations, a single differential-difference amplitude nonlinear equation. We performed the linear stability analysis of this equation and found that instability features are importantly influenced by the induced electromagnetic gain. We present the unstable and stable regions of modulational instability (MI). The resulting analytic predictions are confirmed by numerical experiments of the generic equations. The results reveal that due to MI, an initial steady state that consisted of a plane wave with low amplitude evolves into a modulated localized wave patterns, soliton-like in shape, with features of synchronization. Furthermore, the formation of periodic pulse train with breathing motion presents a disappearing pattern in the presence of electromagnetic radiation. This could provide guidance and better understanding of sudden heart failure exposed to heavily electromagnetic radiation.

Locality and Word Order in Active Dependency Formation in Bangla.

PubMed

Chacón, Dustin A; Imtiaz, Mashrur; Dasgupta, Shirsho; Murshed, Sikder M; Dan, Mina; Phillips, Colin

2016-01-01

Research on filler-gap dependencies has revealed that there are constraints on possible gap sites, and that real-time sentence processing is sensitive to these constraints. This work has shown that comprehenders have preferences for potential gap sites, and immediately detect when these preferences are not met. However, neither the mechanisms that select preferred gap sites nor the mechanisms used to detect whether these preferences are met are well-understood. In this paper, we report on three experiments in Bangla, a language in which gaps may occur in either a pre-verbal embedded clause or a post-verbal embedded clause. This word order variation allows us to manipulate whether the first gap linearly available is contained in the same clause as the filler, which allows us to dissociate structural locality from linear locality. In Experiment 1, an untimed ambiguity resolution task, we found a global bias to resolve a filler-gap dependency with the first gap linearly available, regardless of structural hierarchy. In Experiments 2 and 3, which use the filled-gap paradigm, we found sensitivity to disruption only when the blocked gap site is both structurally and linearly local, i.e., the filler and the gap site are contained in the same clause. This suggests that comprehenders may not show sensitivity to the disruption of all preferred gap resolutions.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; Lee, Henry

2014-01-01

The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no indication in Ref. II that the gaps are explicitly modeled as in Ref. 6. Computations using overset grids are reported in Ref. 12 for a case by adding moving control surface to an existing blade but with no validation either with an experiment or another computation.

Deterministic multidimensional nonuniform gap sampling.

PubMed

Worley, Bradley; Powers, Robert

2015-12-01

Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities. Copyright © 2015 Elsevier Inc. All rights reserved.

Mathematical analysis of the multiband BCS gap equations in superconductivity

NASA Astrophysics Data System (ADS)

Yang, Yisong

2005-01-01

In this paper, we present a mathematical analysis for the phonon-dominated multiband isotropic and anisotropic BCS gap equations at any finite temperature T. We establish the existence of a critical temperature T so that, when TT, the only nonnegative gap solution is the zero solution, representing the normal phase. Furthermore, when T=T, we prove that the only gap solution is the zero solution and that the positive gap solution depend on the temperature T

On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra

NASA Astrophysics Data System (ADS)

Ndogmo, J. C.

2017-06-01

Although every iterative scalar linear ordinary differential equation is of maximal symmetry algebra, the situation is different and far more complex for systems of linear ordinary differential equations, and an iterative system of linear equations need not be of maximal symmetry algebra. We illustrate these facts by examples and derive families of vector differential operators whose iterations are all linear systems of equations of maximal symmetry algebra. Some consequences of these results are also discussed.

Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

Quasi-Newton methods for parameter estimation in functional differential equations

NASA Technical Reports Server (NTRS)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Locality and Word Order in Active Dependency Formation in Bangla

PubMed Central

Chacón, Dustin A.; Imtiaz, Mashrur; Dasgupta, Shirsho; Murshed, Sikder M.; Dan, Mina; Phillips, Colin

2016-01-01

Research on filler-gap dependencies has revealed that there are constraints on possible gap sites, and that real-time sentence processing is sensitive to these constraints. This work has shown that comprehenders have preferences for potential gap sites, and immediately detect when these preferences are not met. However, neither the mechanisms that select preferred gap sites nor the mechanisms used to detect whether these preferences are met are well-understood. In this paper, we report on three experiments in Bangla, a language in which gaps may occur in either a pre-verbal embedded clause or a post-verbal embedded clause. This word order variation allows us to manipulate whether the first gap linearly available is contained in the same clause as the filler, which allows us to dissociate structural locality from linear locality. In Experiment 1, an untimed ambiguity resolution task, we found a global bias to resolve a filler-gap dependency with the first gap linearly available, regardless of structural hierarchy. In Experiments 2 and 3, which use the filled-gap paradigm, we found sensitivity to disruption only when the blocked gap site is both structurally and linearly local, i.e., the filler and the gap site are contained in the same clause. This suggests that comprehenders may not show sensitivity to the disruption of all preferred gap resolutions. PMID:27610090

Null boundary controllability of a one-dimensional heat equation with an internal point mass and variable coefficients

NASA Astrophysics Data System (ADS)

Ben Amara, Jamel; Bouzidi, Hedi

2018-01-01

In this paper, we consider a linear hybrid system which is composed by two non-homogeneous rods connected by a point mass with Dirichlet boundary conditions on the left end and a boundary control acts on the right end. We prove that this system is null controllable with Dirichlet or Neumann boundary controls. Our approach is mainly based on a detailed spectral analysis together with the moment method. In particular, we show that the associated spectral gap in both cases (Dirichlet or Neumann boundary controls) is positive without further conditions on the coefficients other than the regularities.

Equating Scores from Adaptive to Linear Tests

ERIC Educational Resources Information Center

van der Linden, Wim J.

2006-01-01

Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test…

Spacecraft Constrained Maneuver Planning Using Positively Invariant Constraint Admissible Sets (Postprint)

DTIC Science & Technology

2013-08-14

Connectivity Graph; Graph Search; Bounded Disturbances; Linear Time-Varying (LTV); Clohessy - Wiltshire -Hill (CWH) 16. SECURITY CLASSIFICATION OF: 17...the linearization of the relative motion model given by the Hill- Clohessy - Wiltshire (CWH) equations is used [14]. A. Nonlinear equations of motion...equations can be used to describe the motion of the debris. B. Linearized HCW equations in discrete-time For δr << R, the linearized Hill- Clohessy

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

User's manual for interactive LINEAR: A FORTRAN program to derive linear aircraft models

NASA Technical Reports Server (NTRS)

Antoniewicz, Robert F.; Duke, Eugene L.; Patterson, Brian P.

1988-01-01

An interactive FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models is documented in this report. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.

Supporting second grade lower secondary school students’ understanding of linear equation system in two variables using ethnomathematics

NASA Astrophysics Data System (ADS)

Nursyahidah, F.; Saputro, B. A.; Rubowo, M. R.

2018-03-01

The aim of this research is to know the students’ understanding of linear equation system in two variables using Ethnomathematics and to acquire learning trajectory of linear equation system in two variables for the second grade of lower secondary school students. This research used methodology of design research that consists of three phases, there are preliminary design, teaching experiment, and retrospective analysis. Subject of this study is 28 second grade students of Sekolah Menengah Pertama (SMP) 37 Semarang. The result of this research shows that the students’ understanding in linear equation system in two variables can be stimulated by using Ethnomathematics in selling buying tradition in Peterongan traditional market in Central Java as a context. All of strategies and model that was applied by students and also their result discussion shows how construction and contribution of students can help them to understand concept of linear equation system in two variables. All the activities that were done by students produce learning trajectory to gain the goal of learning. Each steps of learning trajectory of students have an important role in understanding the concept from informal to the formal level. Learning trajectory using Ethnomathematics that is produced consist of watching video of selling buying activity in Peterongan traditional market to construct linear equation in two variables, determine the solution of linear equation in two variables, construct model of linear equation system in two variables from contextual problem, and solving a contextual problem related to linear equation system in two variables.

Energy loss in spark gap switches

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

Oreshkin, V. I., E-mail: oreshkin@ovpe.hcei.tsc.ru; Lavrinovich, I. V.; National Research Tomsk Polytechnic University, Lenin Avenue 30, 634050 Tomsk

2014-04-15

The paper reports on numerical study of the energy loss in spark gap switches. The operation of the switches is analyzed using the Braginsky model which allows calculation of the time dependence of the spark channel resistance. The Braginsky equation is solved simultaneously with generator circuit equations for different load types. Based on the numerical solutions, expressions which determine both the energy released in a spark gap switch and the switching time are derived.

One- and two-dimensional gap solitons and dynamics in the PT-symmetric lattice potential and spatially-periodic momentum modulation

NASA Astrophysics Data System (ADS)

Chen, Yong; Yan, Zhenya; Li, Xin

2018-02-01

The influence of spatially-periodic momentum modulation on beam dynamics in parity-time (PT) symmetric optical lattice is systematically investigated in the one- and two-dimensional nonlinear Schrödinger equations. In the linear regime, we demonstrate that the momentum modulation can alter the first and second PT thresholds of the classical lattice, periodically or regularly change the shapes of the band structure, rotate and split the diffraction patterns of beams leading to multiple refraction and emissions. In the Kerr-nonlinear regime for one-dimension (1D) case, a large family of fundamental solitons within the semi-infinite gap can be found to be stable, even beyond the second PT threshold; it is shown that the momentum modulation can shrink the existing range of fundamental solitons and not change their stability. For two-dimension (2D) case, most solitons with higher intensities are relatively unstable in their existing regions which are narrower than those in 1D case, but we also find stable fundamental solitons corroborated by linear stability analysis and direct beam propagation. More importantly, the momentum modulation can also utterly change the direction of the transverse power flow and control the energy exchange among gain or loss regions.

Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

NASA Technical Reports Server (NTRS)

Sloss, J. M.; Kranzler, S. K.

1972-01-01

The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

New Results on the Linear Equating Methods for the Non-Equivalent-Groups Design

ERIC Educational Resources Information Center

von Davier, Alina A.

2008-01-01

The two most common observed-score equating functions are the linear and equipercentile functions. These are often seen as different methods, but von Davier, Holland, and Thayer showed that any equipercentile equating function can be decomposed into linear and nonlinear parts. They emphasized the dominant role of the linear part of the nonlinear…

Linear stability analysis of the Vlasov-Poisson equations in high density plasmas in the presence of crossed fields and density gradients

NASA Technical Reports Server (NTRS)

Kaup, D. J.; Hansen, P. J.; Choudhury, S. Roy; Thomas, Gary E.

1986-01-01

The equations for the single-particle orbits in a nonneutral high density plasma in the presence of inhomogeneous crossed fields are obtained. Using these orbits, the linearized Vlasov equation is solved as an expansion in the orbital radii in the presence of inhomogeneities and density gradients. A model distribution function is introduced whose cold-fluid limit is exactly the same as that used in many previous studies of the cold-fluid equations. This model function is used to reduce the linearized Vlasov-Poisson equations to a second-order ordinary differential equation for the linearized electrostatic potential whose eigenvalue is the perturbation frequency.

Electronic band gaps of confined linear carbon chains ranging from polyyne to carbyne

NASA Astrophysics Data System (ADS)

Shi, Lei; Rohringer, Philip; Wanko, Marius; Rubio, Angel; Waßerroth, Sören; Reich, Stephanie; Cambré, Sofie; Wenseleers, Wim; Ayala, Paola; Pichler, Thomas

2017-12-01

Ultralong linear carbon chains of more than 6000 carbon atoms have recently been synthesized within double-walled carbon nanotubes (DWCNTs), and they show a promising route to one-atom-wide semiconductors with a direct band gap. Theoretical studies predicted that this band gap can be tuned by the length of the chains, the end groups, and their interactions with the environment. However, different density functionals lead to very different values of the band gap of infinitely long carbyne. In this work, we applied resonant Raman excitation spectroscopy with more than 50 laser wavelengths to determine the band gap of long carbon chains encapsulated inside DWCNTs. The experimentally determined band gaps ranging from 2.253 to 1.848 eV follow a linear relation with Raman frequency. This lower bound is the smallest band gap of linear carbon chains observed so far. The comparison with experimental data obtained for short chains in gas phase or in solution demonstrates the effect of the DWCNT encapsulation, leading to an essential downshift of the band gap. This is explained by the interaction between the carbon chain and the host tube, which greatly modifies the chain's bond-length alternation.

Association Between Local Bipolar Voltage and Conduction Gap Along the Left Atrial Linear Ablation Lesion in Patients With Atrial Fibrillation.

PubMed

Masuda, Masaharu; Fujita, Masashi; Iida, Osamu; Okamoto, Shin; Ishihara, Takayuki; Nanto, Kiyonori; Kanda, Takashi; Sunaga, Akihiro; Tsujimura, Takuya; Matsuda, Yasuhiro; Mano, Toshiaki

2017-08-01

A bipolar voltage reflects a thick musculature where formation of a transmural lesion may be hard to achieve. The purpose of this study was to explore the association between local bipolar voltage and conduction gap in patients with persistent atrial fibrillation (AF) who underwent atrial roof or septal linear ablation. This prospective observational study included 42 and 36 consecutive patients with persistent AF who underwent roof or septal linear ablations, respectively. After pulmonary vein isolation, left atrial linear ablations were performed, and conduction gap sites were identified and ablated after first-touch radiofrequency application. Conduction gap(s) after the first-touch roof and septal linear ablation were observed in 13 (32%) and 19 patients (53%), respectively. Roof and septal area voltages were higher in patients with conduction gap(s) than in those without (roof, 1.23 ± 0.77 vs 0.73 ± 0.42 mV, p = 0.010; septal, 0.96 ± 0.43 vs 0.54 ± 0.18 mV, p = 0.001). Trisected regional analyses revealed that the voltage was higher at the region with a conduction gap than at the region without. Complete conduction block across the roof and septal lines was not achieved in 3 (7%) and 6 patients (17%), respectively. Patients in whom a linear conduction block could not be achieved demonstrated higher ablation area voltage than those with a successful conduction block (roof, 1.91 ± 0.74 vs 0.81 ± 0.51 mV, p = 0.001; septal, 1.15 ± 0.56 vs 0.69 ± 0.31 mV, p = 0.006). In conclusion, a high regional bipolar voltage predicts failure to achieve conduction block after left atrial roof or septal linear ablation. In addition, the conduction gap was located at the preserved voltage area. Copyright © 2017 Elsevier Inc. All rights reserved.

Chemical Equation Balancing.

ERIC Educational Resources Information Center

Blakley, G. R.

1982-01-01

Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen

2012-01-01

In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

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

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2011-06-01

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

Influence of Initial Moisture Content on Heat and Moisture Transfer in Firefighters' Protective Clothing

PubMed Central

He, Song

2017-01-01

This paper presents a model for heat and moisture transfer through firefighters' protective clothing (FPC) during radiation exposure. The model, which accounts for air gaps in the FPC as well as heat transfer through human skin, investigates the effect of different initial moisture contents on the thermal insulation performance of FPC. Temperature, water vapor density, and the volume fraction of liquid water profiles were monitored during the simulation, and the heat quantity absorbed by water evaporation was calculated. Then the maximum durations of heat before the wearer acquires first- and second-degree burns were calculated based on the bioheat transfer equation and the Henriques equation. The results show that both the moisture weight in each layer and the total moisture weight increase linearly within a given environmental humidity level. The initial moisture content in FPC samples significantly influenced the maximum water vapor density. The first- and second-degree burn injury time increase 16 sec and 18 sec when the RH increases from 0% to 90%. The total quantity of heat accounted for by water evaporation was about 10% when the relative humidity (RH) is 80%. Finally, a linear relationship was identified between initial moisture content and the human skin burn injury time before suffering first- and second-degree burn injuries. PMID:28466066

Influence of Initial Moisture Content on Heat and Moisture Transfer in Firefighters' Protective Clothing.

PubMed

Huang, Dongmei; He, Song

2017-01-01

This paper presents a model for heat and moisture transfer through firefighters' protective clothing (FPC) during radiation exposure. The model, which accounts for air gaps in the FPC as well as heat transfer through human skin, investigates the effect of different initial moisture contents on the thermal insulation performance of FPC. Temperature, water vapor density, and the volume fraction of liquid water profiles were monitored during the simulation, and the heat quantity absorbed by water evaporation was calculated. Then the maximum durations of heat before the wearer acquires first- and second-degree burns were calculated based on the bioheat transfer equation and the Henriques equation. The results show that both the moisture weight in each layer and the total moisture weight increase linearly within a given environmental humidity level. The initial moisture content in FPC samples significantly influenced the maximum water vapor density. The first- and second-degree burn injury time increase 16 sec and 18 sec when the RH increases from 0% to 90%. The total quantity of heat accounted for by water evaporation was about 10% when the relative humidity (RH) is 80%. Finally, a linear relationship was identified between initial moisture content and the human skin burn injury time before suffering first- and second-degree burn injuries.

Fast wavelet based algorithms for linear evolution equations

NASA Technical Reports Server (NTRS)

Engquist, Bjorn; Osher, Stanley; Zhong, Sifen

1992-01-01

A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.

Note on Solutions to a Class of Nonlinear Singular Integro-Differential Equations,

DTIC Science & Technology

1986-08-01

KdV) ut + 2uu x +Uxx x a 0, (1) the sine-Gordon equation Uxt a sin u, (2) and the Kadomtsev - Petviashvili (KP) equation (Ut + 2uu x + UXXx)x -3a 2u yy...SOUIN OA LSFNN ! /" / M.. \\boiz A.S ::-:- and ,M.O.. .- :1/1 / NOTE ON SOLUTIONS TO A CLASS OF NON \\ / LINEAR SINGULAR INTEGRO-DIFFERENTIA[ EQUATIONS by...important nonlinear evolution equations which can be linearized. Many of these equations fall into the category of linearization via soliton theory and

Analysis of radiative and phase-change phenomena with application to space-based thermal energy storage

NASA Technical Reports Server (NTRS)

Lund, Kurt O.

1991-01-01

The simplified geometry for the analysis is an infinite, axis symmetric annulus with a specified solar flux at the outer radius. The inner radius is either adiabatic (modeling Flight Experiment conditions), or convective (modeling Solar Dynamic conditions). Liquid LiF either contacts the outer wall (modeling ground based testing), or faces a void gap at the outer wall (modeling possible space based conditions). The analysis is presented in three parts: Part 3 considers and adiabatic inner wall and linearized radiation equations; part 2 adds effects of convection at the inner wall; and part 1 includes the effect of the void gap, as well as previous effects, and develops the radiation model further. The main results are the differences in melting behavior which can occur between ground based 1 g experiments and the microgravity flight experiments. Under 1 gravity, melted PCM will always contact the outer wall having the heat flux source, thus providing conductance from this source to the phase change front. In space based tests where a void gap may likely form during solidification, the situation is reversed; radiation is now the only mode of heat transfer and the majority of melting takes place from the inner wall.

Electronic, ductile, phase transition and mechanical properties of Lu-monopnictides under high pressures.

PubMed

Gupta, Dinesh C; Bhat, Idris Hamid

2013-12-01

The structural, elastic and electronic properties of lutatium-pnictides (LuN, LuP, LuAs, LuSb, and LuBi) were analyzed by using full-potential linearized augmented plane wave within generalized gradient approximation in the stable rock-salt structure (B1 phase) with space group Fm-3m and high-pressure CsCl structure (B2 phase) with space group Pm-3m. Hubbard-U and spin-orbit coupling were included to predict correctly the semiconducting band gap of LuN. Under compression, these materials undergo first-order structural transitions from B1 to B2 phases at 241, 98, 56.82, 25.2 and 32.3 GPa, respectively. The computed elastic properties show that LuBi is ductile by nature. The electronic structure calculations show that LuN is semiconductor at ambient conditions with an indirect band gap of 1.55 eV while other Lu-pnictides are metallic. It was observed that LuN shows metallization at high pressures. The structural properties, viz, equilibrium lattice constant, bulk modulus and its pressure derivative, transition pressure, equation of state, volume collapse, band gap and elastic moduli, show good agreement with available data.

FAST TRACK COMMUNICATION: On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

NASA Astrophysics Data System (ADS)

Man, Yiu-Kwong

2010-10-01

In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided.

A refinement of the combination equations for evaporation

USGS Publications Warehouse

Milly, P.C.D.

1991-01-01

Most combination equations for evaporation rely on a linear expansion of the saturation vapor-pressure curve around the air temperature. Because the temperature at the surface may differ from this temperature by several degrees, and because the saturation vapor-pressure curve is nonlinear, this approximation leads to a certain degree of error in those evaporation equations. It is possible, however, to introduce higher-order polynomial approximations for the saturation vapor-pressure curve and to derive a family of explicit equations for evaporation, having any desired degree of accuracy. Under the linear approximation, the new family of equations for evaporation reduces, in particular cases, to the combination equations of H. L. Penman (Natural evaporation from open water, bare soil and grass, Proc. R. Soc. London, Ser. A193, 120-145, 1948) and of subsequent workers. Comparison of the linear and quadratic approximations leads to a simple approximate expression for the error associated with the linear case. Equations based on the conventional linear approximation consistently underestimate evaporation, sometimes by a substantial amount. ?? 1991 Kluwer Academic Publishers.

Nonlinear Diophantine equation 11 x +13 y = z 2

NASA Astrophysics Data System (ADS)

Sugandha, A.; Tripena, A.; Prabowo, A.; Sukono, F.

2018-03-01

This research aims to obtaining the solutions (if any) from the Non Linear Diophantine equation of 11 x + 13 y = z 2. There are 3 possibilities to obtain the solutions (if any) from the Non Linear Diophantine equation, namely single, multiple, and no solution. This research is conducted in two stages: (1) by utilizing simulation to obtain the solutions (if any) from the Non Linear Diophantine equation of 11 x + 13 y = z 2 and (2) by utilizing congruency theory with its characteristics proven that the Non Linear Diophantine equation has no solution for non negative whole numbers (integers) of x, y, z.

Lie algebras and linear differential equations.

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Rahimi, A.

1972-01-01

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

Analysis of a Segmented Annular Coplanar Capacitive Tilt Sensor with Increased Sensitivity

PubMed Central

Guo, Jiahao; Hu, Pengcheng; Tan, Jiubin

2016-01-01

An investigation of a segmented annular coplanar capacitor is presented. We focus on its theoretical model, and a mathematical expression of the capacitance value is derived by solving a Laplace equation with Hankel transform. The finite element method is employed to verify the analytical result. Different control parameters are discussed, and each contribution to the capacitance value of the capacitor is obtained. On this basis, we analyze and optimize the structure parameters of a segmented coplanar capacitive tilt sensor, and three models with different positions of the electrode gap are fabricated and tested. The experimental result shows that the model (whose electrode-gap position is 10 mm from the electrode center) realizes a high sensitivity: 0.129 pF/° with a non-linearity of <0.4% FS (full scale of ±40°). This finding offers plenty of opportunities for various measurement requirements in addition to achieving an optimized structure in practical design. PMID:26805844

Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Bertola, M.; Tovbis, A.

2017-09-01

Finite-gap (algebro-geometric) solutions to the focusing Nonlinear Schrödinger Equation (fNLS) i ψ_t + ψ_{xx} + 2|ψ|^2ψ=0, are quasi-periodic solutions that represent nonlinear multi-phase waves. In general, a finite-gap solution for (0-1) is defined by a collection of Schwarz symmetrical spectral bands and of real constants (initial phases), associated with the corresponding bands. In this paper we prove an interesting new formula for the maximal amplitude of a finite-gap solution to the focusing Nonlinear Schrödinger equation with given spectral bands: the amplitude does not exceed the sum of the imaginary parts of all the endpoints in the upper half plane. In the case of the straight vertical bands, that amounts to the half of the sum of the length of all the bands. The maximal amplitude will be attained for certain choices of the initial phases. This result is an important part of a criterion for the potential presence of the rogue waves in finite-gap solutions with a given set of spectral endpoints, obtained in Bertola et al. (Proc R Soc A, 2016. doi: 10.1098/rspa.2016.0340). A similar result was also obtained for the defocusing Nonlinear Schrödinger equation.

Simple taper: Taper equations for the field forester

Treesearch

David R. Larsen

2017-01-01

"Simple taper" is set of linear equations that are based on stem taper rates; the intent is to provide taper equation functionality to field foresters. The equation parameters are two taper rates based on differences in diameter outside bark at two points on a tree. The simple taper equations are statistically equivalent to more complex equations. The linear...

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

ERIC Educational Resources Information Center

Wang, Tianyou

2009-01-01

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

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

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2016-01-01

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

The stochastic Beer-Lambert-Bouguer law for discontinuous vegetation canopies

NASA Astrophysics Data System (ADS)

Shabanov, N.; Gastellu-Etchegorry, J.-P.

2018-07-01

The 3D distribution of canopy foliage affects the radiation regime and retrievals of canopy biophysical parameters. The gap fraction is one primary indicator of a canopy structure. Historically the Beer-Lambert-Bouguer law and the linear mixture model have served as a basis for multiple technologies for retrievals of the gap (or vegetation) fraction and Leaf Area Index (LAI). The Beer-Lambert-Bouguer law is a form of the Radiative Transfer (RT) equation for homogeneous canopies, which was later adjusted for a correlation between fitoelements using concept of the clumping index. The Stochastic Radiative Transfer (SRT) approach has been developed specifically for heterogeneous canopies, however the approach lacks a proper model of the vegetation fraction. This study is focused on the implementation of the stochastic version of the Beer-Lambert-Bouguer law for heterogeneous canopies, featuring the following principles: 1) two mechanisms perform photon transport- transmission through the turbid medium of foliage crowns and direct streaming through canopy gaps, 2) the radiation field is influenced by a canopy structure (quantified by the statistical moments of a canopy structure) and a foliage density (quantified by the gap fraction as a function of LAI), 3) the notions of canopy transmittance and gap fraction are distinct. The derived stochastic Beer-Lambert-Bouguer law is consistent with the Geometrical Optical and Radiative Transfer (GORT) derivations. Analytical and numerical analysis of the stochastic Beer-Lambert-Bouguer law presented in this study provides the basis to reformulate widely used technologies for retrievals of the gap fraction and LAI from ground and satellite radiation measurements.

The spectral applications of Beer-Lambert law for some biological and dosimetric materials

NASA Astrophysics Data System (ADS)

Içelli, Orhan; Yalçin, Zeynel; Karakaya, Vatan; Ilgaz, Işıl P.

2014-08-01

The aim of this study is to conduct quantitative and qualitative analysis of biological and dosimetric materials which contain organic and inorganic materials and to make the determination by using the spectral theorem Beer-Lambert law. Beer-Lambert law is a system of linear equations for the spectral theory. It is possible to solve linear equations with a non-zero coefficient matrix determinant forming linear equations. Characteristic matrix of the linear equation with zero determinant is called point spectrum at the spectral theory.

The numerical solution of linear multi-term fractional differential equations: systems of equations

NASA Astrophysics Data System (ADS)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

An Analysis of the Oil-Whirl Instability

NASA Astrophysics Data System (ADS)

Schultz, William W.; Han, Heng-Chu; Boyd, John P.; Schumack, Mark

1997-11-01

We investigate the hydrodynamic stability of a rotating journal translating inside a stationary bearing. A long (two-dimensional) journal bearing separated by a Newtonian non-cavitating lubricant is studied for shaft stability. Spectral element methods, perturbation methods, and linear stability analyses are used. The influences of fluid inertia, eccentricity, ellipticity, shaft mass, and finite gap on hydrodynamic stability are explored. Lubrication theory using Reynolds equation ignoring fluid inertia leads to erroneous conclusions. Without fluid inertia, the shaft is always unstable. However, the journal is conditionally stable even in the limit Rearrow 0 if fluid inertia is included. Increasing eccentricity helps stabilize a whirling shaft. Non-circular shaft bearings, for example elliptical bearings, are observed to have better dynamic stability.

Viscous cavity damping of a microlever in a simple fluid.

PubMed

Siria, A; Drezet, A; Marchi, F; Comin, F; Huant, S; Chevrier, J

2009-06-26

We consider the problem of oscillation damping in air of a thermally actuated microlever as it gradually approaches an infinite wall in parallel geometry. As the gap is decreased from 20 microm down to 400 nm, we observe the increasing damping of the lever Brownian motion in the fluid laminar regime. This manifests itself as a linear decrease in the lever quality factor accompanied by a dramatic softening of its resonance, and eventually leads to the freezing of the CL oscillation. We are able to quantitatively explain this behavior by analytically solving the Navier-Stokes equation with perfect slip boundary conditions. Our findings may have implications for microfluidics and micro- and nanoelectromechanical applications.

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2010-01-01

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

A canonical form of the equation of motion of linear dynamical systems

NASA Astrophysics Data System (ADS)

Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias

2018-03-01

The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.

An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher-KPP equation

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.; Trifonov, A. Yu.

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher-KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.

Operator Factorization and the Solution of Second-Order Linear Ordinary Differential Equations

ERIC Educational Resources Information Center

Robin, W.

2007-01-01

The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential equations (ODE). Using the operator factorization approach, the general second-order linear ODE is solved, exactly, in quadratures and the resulting…

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

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

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

The condition of regular degeneration for singularly perturbed systems of linear differential-difference equations.

NASA Technical Reports Server (NTRS)

Cooke, K. L.; Meyer, K. R.

1966-01-01

Extension of problem of singular perturbation for linear scalar constant coefficient differential- difference equation with single retardation to several retardations, noting degenerate equation solution

A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Yufeng; Zhang, Xiangzhi

2016-09-01

We first introduced a linear stationary equation with a quadratic operator in ∂x and ∂y, then a linear evolution equation is given by N-order polynomials of eigenfunctions. As applications, by taking N=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When taking N=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case of N=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. When N=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

Solution of Volterra and Fredholm Classes of Equations via Triangular Orthogonal Function (A Combination of Right Hand Triangular Function and Left Hand Triangular Function) and Hybrid Orthogonal Function (A Combination of Sample Hold Function and Right Hand Triangular Function)

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Anirban; Ganguly, Anindita; Chatterjee, Saumya Deep

2018-04-01

In this paper the authors have dealt with seven kinds of non-linear Volterra and Fredholm classes of equations. The authors have formulated an algorithm for solving the aforementioned equation types via Hybrid Function (HF) and Triangular Function (TF) piecewise-linear orthogonal approach. In this approach the authors have reduced integral equation or integro-differential equation into equivalent system of simultaneous non-linear equation and have employed either Newton's method or Broyden's method to solve the simultaneous non-linear equations. The authors have calculated the L2-norm error and the max-norm error for both HF and TF method for each kind of equations. Through the illustrated examples, the authors have shown that the HF based algorithm produces stable result, on the contrary TF-computational method yields either stable, anomalous or unstable results.

Linearized-moment analysis of the temperature jump and temperature defect in the Knudsen layer of a rarefied gas.

PubMed

Gu, Xiao-Jun; Emerson, David R

2014-06-01

Understanding the thermal behavior of a rarefied gas remains a fundamental problem. In the present study, we investigate the predictive capabilities of the regularized 13 and 26 moment equations. In this paper, we consider low-speed problems with small gradients, and to simplify the analysis, a linearized set of moment equations is derived to explore a classic temperature problem. Analytical solutions obtained for the linearized 26 moment equations are compared with available kinetic models and can reliably capture all qualitative trends for the temperature-jump coefficient and the associated temperature defect in the thermal Knudsen layer. In contrast, the linearized 13 moment equations lack the necessary physics to capture these effects and consistently underpredict kinetic theory. The deviation from kinetic theory for the 13 moment equations increases significantly for specular reflection of gas molecules, whereas the 26 moment equations compare well with results from kinetic theory. To improve engineering analyses, expressions for the effective thermal conductivity and Prandtl number in the Knudsen layer are derived with the linearized 26 moment equations.

Encouraging Students to Think Strategically when Learning to Solve Linear Equations

ERIC Educational Resources Information Center

Robson, Daphne; Abell, Walt; Boustead, Therese

2012-01-01

Students who are preparing to study science and engineering need to understand equation solving but adult students returning to study can find this difficult. In this paper, the design of an online resource, Equations2go, for helping students learn to solve linear equations is investigated. Students learning to solve equations need to consider…

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

NASA Astrophysics Data System (ADS)

Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

2018-04-01

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

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

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

Time and frequency domain analysis of sampled data controllers via mixed operation equations

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1981-01-01

Specification of the mathematical equations required to define the dynamic response of a linear continuous plant, subject to sampled data control, is complicated by the fact that the digital components of the control system cannot be modeled via linear ordinary differential equations. This complication can be overcome by introducing two new mathematical operations; namely, the operation of zero order hold and digial delay. It is shown that by direct utilization of these operations, a set of linear mixed operation equations can be written and used to define the dynamic response characteristics of the controlled system. It also is shown how these linear mixed operation equations lead, in an automatable manner, directly to a set of finite difference equations which are in a format compatible with follow on time and frequency domain analysis methods.

Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

ERIC Educational Resources Information Center

Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

2009-01-01

This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

Supporting Students' Understanding of Linear Equations with One Variable Using Algebra Tiles

ERIC Educational Resources Information Center

Saraswati, Sari; Putri, Ratu Ilma Indra; Somakim

2016-01-01

This research aimed to describe how algebra tiles can support students' understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students…

LINEAR - DERIVATION AND DEFINITION OF A LINEAR AIRCRAFT MODEL

NASA Technical Reports Server (NTRS)

Duke, E. L.

1994-01-01

The Derivation and Definition of a Linear Model program, LINEAR, provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models. LINEAR was developed to provide a standard, documented, and verified tool to derive linear models for aircraft stability analysis and control law design. Linear system models define the aircraft system in the neighborhood of an analysis point and are determined by the linearization of the nonlinear equations defining vehicle dynamics and sensors. LINEAR numerically determines a linear system model using nonlinear equations of motion and a user supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. LINEAR is capable of extracting both linearized engine effects, such as net thrust, torque, and gyroscopic effects and including these effects in the linear system model. The point at which this linear model is defined is determined either by completely specifying the state and control variables, or by specifying an analysis point on a trajectory and directing the program to determine the control variables and the remaining state variables. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to provide easy selection of state, control, and observation variables to be used in a particular model. Thus, the order of the system model is completely under user control. Further, the program provides the flexibility of allowing alternate formulations of both the state and observation equations. Data describing the aircraft and the test case is input to the program through a terminal or formatted data files. All data can be modified interactively from case to case. The aerodynamic model can be defined in two ways: a set of nondimensional stability and control derivatives for the flight point of interest, or a full non-linear aerodynamic model as used in simulations. LINEAR is written in FORTRAN and has been implemented on a DEC VAX computer operating under VMS with a virtual memory requirement of approximately 296K of 8 bit bytes. Both an interactive and batch version are included. LINEAR was developed in 1988.

Optical soliton solutions of the cubic-quintic non-linear Schrödinger's equation including an anti-cubic term

NASA Astrophysics Data System (ADS)

Kaplan, Melike; Hosseini, Kamyar; Samadani, Farzan; Raza, Nauman

2018-07-01

A wide range of problems in different fields of the applied sciences especially non-linear optics is described by non-linear Schrödinger's equations (NLSEs). In the present paper, a specific type of NLSEs known as the cubic-quintic non-linear Schrödinger's equation including an anti-cubic term has been studied. The generalized Kudryashov method along with symbolic computation package has been exerted to carry out this objective. As a consequence, a series of optical soliton solutions have formally been retrieved. It is corroborated that the generalized form of Kudryashov method is a direct, effectual, and reliable technique to deal with various types of non-linear Schrödinger's equations.

A new nonlinear diffusion formalism in a magnetized plasma - Application to space physics and astrophysics

NASA Technical Reports Server (NTRS)

Karimbadi, H.; Krauss-Varban, D.

1992-01-01

A novel diffusion formalism that takes into account the finite width of resonances is presented. The resonance diagram technique is shown to reproduce the details of the particle orbits very accurately, and can be used to determine the acceleration/scattering in the presence of a given wave spectrum. Ways in which the nonlinear orbits can be incorporated into the diffusion equation are shown. The resulting diffusion equation is an extension of the Q-L theory to cases where the waves have large amplitudes and/or are coherent. This new equation does not have a gap at 90 deg in cases where the individual orbits can cross the gap. The conditions under which the resonance gap at 90-deg pitch angle exits are also examined.

Prediction of Undsteady Flows in Turbomachinery Using the Linearized Euler Equations on Deforming Grids

NASA Technical Reports Server (NTRS)

Clark, William S.; Hall, Kenneth C.

1994-01-01

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the non-linear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting far-field boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, far-field nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semi-analytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one or two orders-of-magnitude less computational time than traditional time marching techniques making the present method a viable design tool for aeroelastic analyses.

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

A Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics. Part 1. Analysis Development

DTIC Science & Technology

1980-06-01

sufficient. Dropping the time lag terms, the equations for Xu, Xx’, and X reduce to linear algebraic equations.Y Hence in the quasistatic case the...quasistatic variables now are not described by differential equations but rather by linear algebraic equations. The solution for x0 then is simply -365...matrices for two-bladed rotor 414 7. LINEAR SYSTEM ANALYSIS 425 7,1 State Variable Form 425 7.2 Constant Coefficient System 426 7.2. 1 Eigen-analysis 426

Constructive Development of the Solutions of Linear Equations in Introductory Ordinary Differential Equations

ERIC Educational Resources Information Center

Mallet, D. G.; McCue, S. W.

2009-01-01

The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to…

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

NASA Technical Reports Server (NTRS)

Molenaar, J.

1996-01-01

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Solving a mixture of many random linear equations by tensor decomposition and alternating minimization.

DOT National Transportation Integrated Search

2016-09-01

We consider the problem of solving mixed random linear equations with k components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample...

Unified Framework for Deriving Simultaneous Equation Algorithms for Water Distribution Networks

EPA Science Inventory

The known formulations for steady state hydraulics within looped water distribution networks are re-derived in terms of linear and non-linear transformations of the original set of partly linear and partly non-linear equations that express conservation of mass and energy. All of ...

Perturbations of linear delay differential equations at the verge of instability.

PubMed

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

How Darcy's equation is linked to the linear reservoir at catchment scale

NASA Astrophysics Data System (ADS)

Savenije, Hubert H. G.

2017-04-01

In groundwater hydrology two simple linear equations exist that describe the relation between groundwater flow and the gradient that drives it: Darcy's equation and the linear reservoir. Both equations are empirical at heart: Darcy's equation at the laboratory scale and the linear reservoir at the watershed scale. Although at first sight they show similarity, without having detailed knowledge of the structure of the underlying aquifers it is not trivial to upscale Darcy's equation to the watershed scale. In this paper, a relatively simple connection is provided between the two, based on the assumption that the groundwater system is organized by an efficient drainage network, a mostly invisible pattern that has evolved over geological time scales. This drainage network provides equally distributed resistance to flow along the streamlines that connect the active groundwater body to the stream, much like a leaf is organized to provide all stomata access to moisture at equal resistance.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

A three operator split-step method covering a larger set of non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Zia, Haider

2017-06-01

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

A Unified Equation of State on a Microscopic Basis : Implications for Neutron Stars Structure and Cooling

NASA Astrophysics Data System (ADS)

Burgio, G. F.

2018-03-01

We discuss the structure of Neutron Stars by modelling the homogeneous nuclear matter of the core by a suitable microscopic Equation of State, based on the Brueckner-Hartree-Fock many-body theory, and the crust, including the pasta phase, by the BCPM energy density functional which is based on the same Equation of State. This allows for a uni ed description of the Neutron Star matter over a wide density range. A comparison with other uni ed approaches is discussed. With the same Equation of State, which features strong direct Urca processes and using consistent nuclear pairing gaps as well as effective masses, we model neutron star cooling, in particular the current rapid cooldown of the neutron star Cas A. We nd that several scenarios are possible to explain the features of Cas A, but only large and extended proton 1 S 0 gaps and small neutron 3 PF 2 gaps can accommodate also the major part of the complete current cooling data.

An extended harmonic balance method based on incremental nonlinear control parameters

NASA Astrophysics Data System (ADS)

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

2017-02-01

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.

Piecewise linear emulator of the nonlinear Schrödinger equation and the resulting analytic solutions for Bose-Einstein condensates.

PubMed

Theodorakis, Stavros

2003-06-01

We emulate the cubic term Psi(3) in the nonlinear Schrödinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a delta function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Psi(3) one. In particular, it can be used for the nonlinear Schrödinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions.

Dissipative behavior of some fully non-linear KdV-type equations

NASA Astrophysics Data System (ADS)

Brenier, Yann; Levy, Doron

2000-03-01

The KdV equation can be considered as a special case of the general equation u t+f(u) x-δg(u xx) x=0, δ>0, where f is non-linear and g is linear, namely f( u)= u2/2 and g( v)= v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [P.G. Drazin, Solitons, London Math. Soc. Lect. Note Ser. 85, Cambridge University Press, Cambridge, 1983; P.D. Lax, C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, III, Commun. Pure Appl. Math. 36 (1983) 809-829; G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974] and the references therein). We show through numerical evidence that a completely different, dissipative behavior occurs when g is non-linear, namely when g is an even concave function such as g( v)=-∣ v∣ or g( v)=- v2. In particular, our numerical results hint that as δ→0 the solutions strongly converge to the unique entropy solution of the formal limit equation, in total contrast with the solutions of the KdV equation.

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

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

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

A General Linear Method for Equating with Small Samples

ERIC Educational Resources Information Center

Albano, Anthony D.

2015-01-01

Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

ESEA Title I Linking Project. Final Report.

ERIC Educational Resources Information Center

Holmes, Susan E.

The Rasch model for test score equating was compared with three other equating procedures as methods for implementing the norm referenced method (RMC Model A) of evaluating ESEA Title I projects. The Rasch model and its theoretical limitations were described. The three other equating methods used were: linear observed score equating, linear true…

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

Fluid displacement between two parallel plates: a non-empirical model displaying change of type from hyperbolic to elliptic equations

NASA Astrophysics Data System (ADS)

Shariati, M.; Talon, L.; Martin, J.; Rakotomalala, N.; Salin, D.; Yortsos, Y. C.

2004-11-01

We consider miscible displacement between parallel plates in the absence of diffusion, with a concentration-dependent viscosity. By selecting a piecewise viscosity function, this can also be considered as ‘three-fluid’ flow in the same geometry. Assuming symmetry across the gap and based on the lubrication (‘equilibrium’) approximation, a description in terms of two quasi-linear hyperbolic equations is obtained. We find that the system is hyperbolic and can be solved analytically, when the mobility profile is monotonic, or when the mobility of the middle phase is smaller than its neighbours. When the mobility of the middle phase is larger, a change of type is displayed, an elliptic region developing in the composition space. Numerical solutions of Riemann problems of the hyperbolic system spanning the elliptic region, with small diffusion added, show good agreement with the analytical outside, but an unstable behaviour inside the elliptic region. In these problems, the elliptic region arises precisely at the displacement front. Crossing the elliptic region requires the solution of essentially an eigenvalue problem of the full higher-dimensional model, obtained here using lattice BGK simulations. The hyperbolic-to-elliptic change-of-type reflects the failing of the lubrication approximation, underlying the quasi-linear hyperbolic formalism, to describe the problem uniformly. The obtained solution is analogous to non-classical shocks recently suggested in problems with change of type.

Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes

ERIC Educational Resources Information Center

Seaman, Brian; Osler, Thomas J.

2004-01-01

A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

The Equation, the Whole Equation, and Nothing but the Equation! One Approach to the Teaching of Linear Equations.

ERIC Educational Resources Information Center

Pirie, Susan E. B.; Martin, Lyndon

1997-01-01

Presents the results of a case study which looked at the mathematics classroom of one teacher trying to teach mathematics with meaning to pupils or lower ability at the secondary level. Contrasts methods of teaching linear equations to a variety of ability levels and uses the Pirie-Kieren model to account for the successful growth in understanding…

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

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

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

A Novel Blast-mitigation Concept for Light Tactical Vehicles

DTIC Science & Technology

2013-01-01

analysis which utilizes the mass and energy (but not linear momentum ) conservation equations is provided. It should be noted that the identical final...results could be obtained using an analogous analysis which combines the mass and the linear momentum conservation equations. For a calorically...governing mass, linear momentum and energy conservation and heat conduction equations are solved within ABAQUS/ Explicit with a second-order accurate

Dirac topological insulator in the dz2 manifold of a honeycomb oxide

NASA Astrophysics Data System (ADS)

Lado, J. L.; Pardo, V.

2016-09-01

We show by means of ab initio calculations and tight-binding modeling that an oxide system based on a honeycomb lattice can sustain topologically nontrivial states if a single orbital dominates the spectrum close to the Fermi level. In such a situation, the low-energy spectrum is described by two Dirac equations that become nontrivially gapped when spin-orbit coupling (SOC) is switched on. We provide one specific example but the recipe is general. We discuss a realization of this starting from a conventional spin-1/2 honeycomb antiferromagnet whose states close to the Fermi energy are dz2 orbitals. Switching off magnetism by atomic substitution and ensuring that the electronic structure becomes two-dimensional is sufficient for topologicality to arise in such a system. By deriving a tight-binding Wannier Hamiltonian, we find that the gap in such a model scales linearly with SOC, opposed to other oxide-based topological insulators, where smaller gaps tend to appear by construction of the lattice. We show that the quantum spin Hall state in this system survives in the presence of off-plane magnetism and the orbital magnetic field and we discuss its Landau level spectra, showing that our recipe provides a dz2 realization of the Kane-Mele model.

Nonlinear optical transmittance of semiconductors in the presence of high-intensity radiation fields

NASA Astrophysics Data System (ADS)

Dong, H. M.; Han, F. W.; Duan, Y. F.; Huang, F.; Liu, J. L.

2018-04-01

We developed a systematic theoretical study of nonlinear optical properties of semiconductors. The eight-band kṡp model and the energy-balance equation are employed to calculate the transmission and optical absorption coefficients in the presence of both the linear one-photon absorption and the nonlinear two-photon absorption (TPA) processes. A substantial reduction of the optical transmittance far below the band-gap can be observed under relatively high-intensity radiation fields due to the nonlinear TPA. The TPA-induced optical transmittance decreases with increasing intensity of the radiation fields. Our theoretical results are in line with those observed experimentally. The theoretical approach can be applied to understand the nonlinear optical properties of semiconductors under high-field conditions.

Relativistic and thermal effects on the magnon spectrum of a ferromagnetic monolayer.

PubMed

Rózsa, L; Udvardi, L; Szunyogh, L

2013-12-18

A spin model including magnetic anisotropy terms and Dzyaloshinsky-Moriya interactions is studied for the case of a ferromagnetic monolayer with C2v symmetry like Fe/W(110). Using the quasiclassical stochastic Landau-Lifshitz-Gilbert equations, the magnon spectrum of the system is derived using linear response theory. The Dzyaloshinsky-Moriya interaction leads to asymmetry in the spectrum, while the anisotropy terms induce a gap. It is shown that, in the presence of lattice defects, both the Dzyaloshinsky-Moriya interactions and the two-site anisotropy lead to a softening of the magnon energies. Two methods are developed to investigate the magnon spectrum at finite temperatures. The theoretical results are compared to atomistic spin dynamics simulations and good agreement is found between them.

Linear-time reconstruction of zero-recombinant Mendelian inheritance on pedigrees without mating loops.

PubMed

Liu, Lan; Jiang, Tao

2007-01-01

With the launch of the international HapMap project, the haplotype inference problem has attracted a great deal of attention in the computational biology community recently. In this paper, we study the question of how to efficiently infer haplotypes from genotypes of individuals related by a pedigree without mating loops, assuming that the hereditary process was free of mutations (i.e. the Mendelian law of inheritance) and recombinants. We model the haplotype inference problem as a system of linear equations as in [10] and present an (optimal) linear-time (i.e. O(mn) time) algorithm to generate a particular solution (A particular solution of any linear system is an assignment of numerical values to the variables in the system which satisfies the equations in the system.) to the haplotype inference problem, where m is the number of loci (or markers) in a genotype and n is the number of individuals in the pedigree. Moreover, the algorithm also provides a general solution (A general solution of any linear system is denoted by the span of a basis in the solution space to its associated homogeneous system, offset from the origin by a vector, namely by any particular solution. A general solution for ZRHC is very useful in practice because it allows the end user to efficiently enumerate all solutions for ZRHC and performs tasks such as random sampling.) in O(mn2) time, which is optimal because the size of a general solution could be as large as Theta(mn2). The key ingredients of our construction are (i) a fast consistency checking procedure for the system of linear equations introduced in [10] based on a careful investigation of the relationship between the equations (ii) a novel linear-time method for solving linear equations without invoking the Gaussian elimination method. Although such a fast method for solving equations is not known for general systems of linear equations, we take advantage of the underlying loop-free pedigree graph and some special properties of the linear equations.

Semigroup theory and numerical approximation for equations in linear viscoelasticity

NASA Technical Reports Server (NTRS)

Fabiano, R. H.; Ito, K.

1990-01-01

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

Internal null controllability of a linear Schrödinger-KdV system on a bounded interval

NASA Astrophysics Data System (ADS)

Araruna, Fágner D.; Cerpa, Eduardo; Mercado, Alberto; Santos, Maurício C.

2016-01-01

The control of a linear dispersive system coupling a Schrödinger and a linear Korteweg-de Vries equation is studied in this paper. The system can be viewed as three coupled real-valued equations by taking real and imaginary parts in the Schrödinger equation. The internal null controllability is proven by using either one complex-valued control on the Schrödinger equation or two real-valued controls, one on each equation. Notice that the single Schrödinger equation is not known to be controllable with a real-valued control. The standard duality method is used to reduce the controllability property to an observability inequality, which is obtained by means of a Carleman estimates approach.

Extension of the N-point Padé approximants solution of the Eliashberg equations to T ˜ T c

NASA Astrophysics Data System (ADS)

Leavens, C. R.; Ritchie, D. S.

1985-01-01

Vidberg and Serene introduced a very useful technique for calculating the low temperature (T « T c) gap function of a superconductor which bypasses the real-frequency singular integral equations of Eliashberg. Blashke and Blocksdorf recognized and resolved a difficulty with the technique thereby extending it to higher temperatures. We present a much simpler method of doing essentially the same thing and, for a strong-coupling superconductor at a temperature near T c, compare the gap functions calculated using these methods with the accurate one computed directly from the real-frequency equations.

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

NASA Astrophysics Data System (ADS)

Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru

2018-02-01

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

Nonlinear (time domain) and linearized (time and frequency domain) solutions to the compressible Euler equations in conservation law form

NASA Technical Reports Server (NTRS)

Sreenivas, Kidambi; Whitfield, David L.

1995-01-01

Two linearized solvers (time and frequency domain) based on a high resolution numerical scheme are presented. The basic approach is to linearize the flux vector by expressing it as a sum of a mean and a perturbation. This allows the governing equations to be maintained in conservation law form. A key difference between the time and frequency domain computations is that the frequency domain computations require only one grid block irrespective of the interblade phase angle for which the flow is being computed. As a result of this and due to the fact that the governing equations for this case are steady, frequency domain computations are substantially faster than the corresponding time domain computations. The linearized equations are used to compute flows in turbomachinery blade rows (cascades) arising due to blade vibrations. Numerical solutions are compared to linear theory (where available) and to numerical solutions of the nonlinear Euler equations.

Gyrotron Gun Study Report,

DTIC Science & Technology

1981-09-18

of bern current to space-charge limited Langmuir current - Cathode surface current density S 2 a Cylindrical diode geometry function (tabulated in...design factor . t -13- " r =J... .. ::!, qm ! . ... ... - . , m- d nc- Cd (3) lsically, this equation arises from the recognition that the gap...S. Beam Current as a Fraction of the Limiting Langmuir Current (o/IL) Equation 5 in Table I is basically intended to provide a measure of the C

Generalized Couette Poiseuille flow with boundary mass transfer

NASA Astrophysics Data System (ADS)

Marques, F.; Sanchez, J.; Weidman, P. D.

1998-11-01

A generalized similarity formulation extending the work of Terrill (1967) for Couette Poiseuille flow in the annulus between concentric cylinders of infinite extent is given. Boundary conditions compatible with the formulation allow a study of the effects of inner and outer cylinder transpiration, rotation, translation, stretching and twisting, in addition to that of an externally imposed constant axial pressure gradient. The problem is governed by [eta], the ratio of inner to outer radii, a Poiseuille number, and nine Reynolds numbers. Single-cylinder and planar problems can be recovered in the limits [eta][rightward arrow]0 and [eta][rightward arrow]1, respectively. Two coupled primary nonlinear equations govern the meridional motion generated by uniform mass flux through the porous walls and the azimuthal motion generated by torsional movement of the cylinders; subsidiary equations linearly slaved to the primary flow govern the effects of cylinder translation, cylinder rotation, and an external pressure gradient. Steady solutions of the primary equations for uniform source/sink flow of strength F through the inner cylinder are reported for 0[less-than-or-eq, slant][eta][less-than-or-eq, slant]1. Asymptotic results corroborating the numerical solutions are found in different limiting cases. For F<0 fluid emitted through the inner cylinder fills the gap and flows uniaxially down the annulus; an asymptotic analysis leads to a scaling that removes the effect of [eta] in the pressure parameter [beta], namely [beta]=[pi]2R*2, where R*=F(1[minus sign][eta])/(1+[eta]). The case of sink flow for F>0 is more complex in that unique solutions are found at low Reynolds numbers, a region of triple solutions exists at moderate Reynolds numbers, and a two-cell solution prevails at large Reynolds numbers. The subsidiary linear equations are solved at [eta]=0.5 to exhibit the effects of cylinder translation, rotation, and an axial pressure gradient on the source/sink flows.

Symbolic Solution of Linear Differential Equations

NASA Technical Reports Server (NTRS)

Feinberg, R. B.; Grooms, R. G.

1981-01-01

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations

DTIC Science & Technology

2008-02-01

Craig interpolants has enabled the development of powerful hardware and software model checking techniques. Efficient algorithms are known for computing...interpolants in rational and real linear arithmetic. We focus on subsets of integer linear arithmetic. Our main results are polynomial time algorithms ...congruences), and linear diophantine disequations. We show the utility of the proposed interpolation algorithms for discovering modular/divisibility predicates

Superconductivity in correlated BEDT-TTF molecular conductors: Critical temperatures and gap symmetries

NASA Astrophysics Data System (ADS)

Zantout, Karim; Altmeyer, Michaela; Backes, Steffen; Valentí, Roser

2018-01-01

Starting from an ab initio-derived two-site dimer Hubbard Hamiltonian on a triangular lattice, we calculate the superconducting gap functions and critical temperatures for representative κ -(BEDT-TTF ) 2X superconductors by solving the linearized Eliashberg equation using the two-particle self-consistent approach (TPSC) extended to multisite problems. Such an extension allows for the inclusion of molecule degrees of freedom in the description of these systems. We present both benchmarking results for the half-filled dimer model as well as detailed investigations for the 3/4-filled molecule model. Remarkably, we find in the latter model that the phase boundary between the two most competing gap symmetries discussed in the context of these materials—dx y and the recently proposed eight-node s +dx2-y2 gap symmetry—is located within the regime of realistic model parameters and is especially sensitive to the degree of in-plane anisotropy in the materials as well as to the value of the on-site Hubbard repulsion. We show that these results provide a more complete and accurate description of the superconducting properties of κ -(BEDT-TTF ) 2X than previous random phase approximation (RPA) calculations and, in particular, we discuss predicted critical temperatures in comparison to experiments. Finally, our findings suggest that it may be even easier to experimentally switch between the two pairing symmetries as previously anticipated by invoking pressure, chemical doping, or disorder effects.

Stress stiffening and approximate equations in flexible multibody dynamics

NASA Technical Reports Server (NTRS)

Padilla, Carlos E.; Vonflotow, Andreas H.

1993-01-01

A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.

A formulation of rotor-airframe coupling for design analysis of vibrations of helicopter airframes

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; Walton, W. C., Jr.

1982-01-01

A linear formulation of rotor airframe coupling intended for vibration analysis in airframe structural design is presented. The airframe is represented by a finite element analysis model; the rotor is represented by a general set of linear differential equations with periodic coefficients; and the connections between the rotor and airframe are specified through general linear equations of constraint. Coupling equations are applied to the rotor and airframe equations to produce one set of linear differential equations governing vibrations of the combined rotor airframe system. These equations are solved by the harmonic balance method for the system steady state vibrations. A feature of the solution process is the representation of the airframe in terms of forced responses calculated at the rotor harmonics of interest. A method based on matrix partitioning is worked out for quick recalculations of vibrations in design studies when only relatively few airframe members are varied. All relations are presented in forms suitable for direct computer implementation.

Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

NASA Astrophysics Data System (ADS)

Zhou, L.-Q.; Meleshko, S. V.

2017-07-01

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R.

1985-01-01

The existence of Chandrasekhar equations for linear time-invariant systems defined on Hilbert spaces is investigated. An important consequence is that the solution to the evolutional Riccati equation is strongly differentiable in time, and that a strong solution of the Riccati differential equation can be defined. A discussion of the linear-quadratic optimal-control problem for hereditary differential systems is also included.

Whitham modulation theory for the Kadomtsev- Petviashvili equation.

PubMed

Ablowitz, Mark J; Biondini, Gino; Wang, Qiao

2017-08-01

The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

Whitham modulation theory for the Kadomtsev- Petviashvili equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Wang, Qiao

2017-08-01

The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

The Fundamental Solution of the Linearized Navier Stokes Equations for Spinning Bodies in Three Spatial Dimensions Time Dependent Case

NASA Astrophysics Data System (ADS)

Thomann, Enrique A.; Guenther, Ronald B.

2006-02-01

Explicit formulae for the fundamental solution of the linearized time dependent Navier Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L p (R 3), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

NASA Technical Reports Server (NTRS)

Cheyney, H., III; Arking, A.

1976-01-01

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

Oscillation criteria for half-linear dynamic equations on time scales

NASA Astrophysics Data System (ADS)

Hassan, Taher S.

2008-09-01

This paper is concerned with oscillation of the second-order half-linear dynamic equation(r(t)(x[Delta])[gamma])[Delta]+p(t)x[gamma](t)=0, on a time scale where [gamma] is the quotient of odd positive integers, r(t) and p(t) are positive rd-continuous functions on . Our results solve a problem posed by [R.P. Agarwal, D. O'Regan, S.H. Saker, Philos-type oscillation criteria for second-order half linear dynamic equations, Rocky Mountain J. Math. 37 (2007) 1085-1104; S.H. Saker, Oscillation criteria of second order half-linear dynamic equations on time scales, J. Comput. Appl. Math. 177 (2005) 375-387] and our results in the special cases when and involve and improve some oscillation results for second-order differential and difference equations; and when , and , etc., our oscillation results are essentially newE Some examples illustrating the importance of our results are also included.

Mathematical Modeling of Chemical Stoichiometry

ERIC Educational Resources Information Center

Croteau, Joshua; Fox, William P.; Varazo, Kristofoland

2007-01-01

In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…

Generalized Multilevel Structural Equation Modeling

ERIC Educational Resources Information Center

Rabe-Hesketh, Sophia; Skrondal, Anders; Pickles, Andrew

2004-01-01

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent…

Nonresonant Faraday rotation in glassy semiconductors

NASA Astrophysics Data System (ADS)

van den Keybus, P.; Grevendonk, W.

1986-06-01

Nonresonant interband Faraday rotation in amorphous semiconductors, as a function of photon energy, may be described by an equation derived for direct transitions in crystalline semiconductors. In this paper it is shown how this equation may be obtained for the former case also, assuming a parabolic density of states function N(E) and a correlation between valence- and conduction-band states. The analysis of experiments on chalcogenide glasses reveals a Faraday-rotation energy gap EFRg that is significantly larger than the optical gap Eoptg. The effect is attributed to transitions between extended states, so that it is meaningful to compare EFRg with the mobility gap Eμg. For oxide glasses both gaps are comparable but for chalcogenide glasses EFRg is too large by a few tenths of 1 eV.

Bridging a gap between continuum-QCD and ab initio predictions of hadron observables

DOE PAGES

Binosi, Daniele; Chang, Lei; Papavassiliou, Joannis; ...

2015-03-01

Within contemporary hadron physics there are two common methods for determining the momentum- dependence of the interaction between quarks: the top-down approach, which works toward an ab initiocomputation of the interaction via direct analysis of the gauge-sector gap equations; and the bottom-up scheme, which aims to infer the interaction by fitting data within a well-defined truncation of those equations in the matter sector that are relevant to bound-state properties. We unite these two approaches by demonstrating that the renormalisation-group-invariant running-interaction predicted by contemporary analyses of QCD’s gauge sector coincides with that required in order to describe ground-state hadron observables usingmore » a nonperturbative truncation of QCD’s Dyson–Schwinger equations in the matter sector. This bridges a gap that had lain between nonperturbative continuum-QCD and the ab initio prediction of bound-state properties.« less

Construction of reduced order models for the non-linear Navier-Stokes equations using the proper orthogonal fecomposition (POD)/Galerkin method.

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

Fike, Jeffrey A.

2013-08-01

The construction of stable reduced order models using Galerkin projection for the Euler or Navier-Stokes equations requires a suitable choice for the inner product. The standard L2 inner product is expected to produce unstable ROMs. For the non-linear Navier-Stokes equations this means the use of an energy inner product. In this report, Galerkin projection for the non-linear Navier-Stokes equations using the L2 inner product is implemented as a first step toward constructing stable ROMs for this set of physics.

A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

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

Addona, Davide, E-mail: d.addona@campus.unimib.it

2015-08-15

We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

Program for the solution of multipoint boundary value problems of quasilinear differential equations

NASA Technical Reports Server (NTRS)

1973-01-01

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

[Ultrasonic measurements of fetal thalamus, caudate nucleus and lenticular nucleus in prenatal diagnosis].

PubMed

Yang, Ruiqi; Wang, Fei; Zhang, Jialing; Zhu, Chonglei; Fan, Limei

2015-05-19

To establish the reference values of thalamus, caudate nucleus and lenticular nucleus diameters through fetal thalamic transverse section. A total of 265 fetuses at our hospital were randomly selected from November 2012 to August 2014. And the transverse and length diameters of thalamus, caudate nucleus and lenticular nucleus were measured. SPSS 19.0 statistical software was used to calculate the regression curve of fetal diameter changes and gestational weeks of pregnancy. P < 0.05 was considered as having statistical significance. The linear regression equation of fetal thalamic length diameter and gestational week was: Y = 0.051X+0.201, R = 0.876, linear regression equation of thalamic transverse diameter and fetal gestational week was: Y = 0.031X+0.229, R = 0.817, linear regression equation of fetal head of caudate nucleus length diameter and gestational age was: Y = 0.033X+0.101, R = 0.722, linear regression equation of fetal head of caudate nucleus transverse diameter and gestational week was: R = 0.025 - 0.046, R = 0.711, linear regression equation of fetal lentiform nucleus length diameter and gestational week was: Y = 0.046+0.229, R = 0.765, linear regression equation of fetal lentiform nucleus diameter and gestational week was: Y = 0.025 - 0.05, R = 0.772. Ultrasonic measurement of diameter of fetal thalamus caudate nucleus, and lenticular nucleus through thalamic transverse section is simple and convenient. And measurements increase with fetal gestational weeks and there is linear regression relationship between them.

Free electron laser

DOEpatents

Villa, Francesco

1990-01-01

A high gain, single-pass free electron laser formed of a high brilliance electron injector source, a linear accelerator which imparts high energy to the electron beam, and an undulator capable of extremely high magnetic fields, yet with a very short period. The electron injector source is the first stage (gap) of the linear accelerator or a radial line transformer driven by fast circular switch. The linear accelerator is formed of a plurality of accelerating gaps arranged in series. These gaps are energized in sequence by releasing a single pulse of energy which propagates simultaneously along a plurality of transmission lines, each of which feeds the gaps. The transmission lines are graduated in length so that pulse power is present at each gap as the accelerated electrons pass therethrough. The transmission lines for each gap are open circuited at their ends. The undualtor has a structure similar to the accelerator, except that the transmission lines for each gap are substantially short circuited at their ends, thus converting the electric field into magnetic field. A small amount of resistance is retained in order to generate a small electric field for replenishing the electron bunch with the energy lost as it traverses through the undulator structure.

Corrected Implicit Monte Carlo

DOE PAGES

Cleveland, Mathew Allen; Wollaber, Allan Benton

2018-01-02

Here in this work we develop a set of nonlinear correction equations to enforce a consistent time-implicit emission temperature for the original semi-implicit IMC equations. We present two possible forms of correction equations: one results in a set of non-linear, zero-dimensional, non-negative, explicit correction equations, and the other results in a non-linear, non-negative, Boltzman transport correction equation. The zero-dimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequency-dependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle formore » frequency-independent simulations, at the cost of evaluating a reduced source non-linear Boltzman equation. Finally, we present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequency-dependent simulations.« less

Local energy decay for linear wave equations with variable coefficients

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

2005-06-01

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

Corrected implicit Monte Carlo

NASA Astrophysics Data System (ADS)

Cleveland, M. A.; Wollaber, A. B.

2018-04-01

In this work we develop a set of nonlinear correction equations to enforce a consistent time-implicit emission temperature for the original semi-implicit IMC equations. We present two possible forms of correction equations: one results in a set of non-linear, zero-dimensional, non-negative, explicit correction equations, and the other results in a non-linear, non-negative, Boltzman transport correction equation. The zero-dimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequency-dependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle for frequency-independent simulations, at the cost of evaluating a reduced source non-linear Boltzman equation. We present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequency-dependent simulations.

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

Cleveland, Mathew Allen; Wollaber, Allan Benton

Here in this work we develop a set of nonlinear correction equations to enforce a consistent time-implicit emission temperature for the original semi-implicit IMC equations. We present two possible forms of correction equations: one results in a set of non-linear, zero-dimensional, non-negative, explicit correction equations, and the other results in a non-linear, non-negative, Boltzman transport correction equation. The zero-dimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequency-dependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle formore » frequency-independent simulations, at the cost of evaluating a reduced source non-linear Boltzman equation. Finally, we present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequency-dependent simulations.« less

Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

NASA Astrophysics Data System (ADS)

See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

2018-04-01

This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

Lyapunov stability and its application to systems of ordinary differential equations

NASA Technical Reports Server (NTRS)

Kennedy, E. W.

1979-01-01

An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R. K.

1985-01-01

Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

Approximating a nonlinear advanced-delayed equation from acoustics

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2016-10-01

We approximate the solution of a particular non-linear mixed type functional differential equation from physiology, the mucosal wave model of the vocal oscillation during phonation. The mathematical equation models a superficial wave propagating through the tissues. The numerical scheme is adapted from the work presented in [1, 2, 3], using homotopy analysis method (HAM) to solve the non linear mixed type equation under study.

On a new class of completely integrable nonlinear wave equations. I. Infinitely many conservation laws

NASA Astrophysics Data System (ADS)

Nutku, Y.

1985-06-01

We point out a class of nonlinear wave equations which admit infinitely many conserved quantities. These equations are characterized by a pair of exact one-forms. The implication that they are closed gives rise to equations, the characteristics and Riemann invariants of which are readily obtained. The construction of the conservation laws requires the solution of a linear second-order equation which can be reduced to canonical form using the Riemann invariants. The hodograph transformation results in a similar linear equation. We discuss also the symplectic structure and Bäcklund transformations associated with these equations.

Algebraic methods for the solution of some linear matrix equations

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

Using MathCAD to Teach One-Dimensional Graphs

ERIC Educational Resources Information Center

Yushau, B.

2004-01-01

Topics such as linear and nonlinear equations and inequalities, compound inequalities, linear and nonlinear absolute value equations and inequalities, rational equations and inequality are commonly found in college algebra and precalculus textbooks. What is common about these topics is the fact that their solutions and graphs lie in the real line…

A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation

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

Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co

2015-05-15

In this work, a non-Markovian non-linear Schrödinger–Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.

Universal equation for estimating ideal body weight and body weight at any BMI1

PubMed Central

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-01-01

Background: Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. Objective: For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. Design: With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Results: Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5–0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Conclusions: Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. PMID:27030535

Universal equation for estimating ideal body weight and body weight at any BMI.

PubMed

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-05-01

Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5-0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. © 2016 American Society for Nutrition.

Linear analysis of auto-organization in Hebbian neural networks.

PubMed

Carlos Letelier, J; Mpodozis, J

1995-01-01

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple "order" (or degree of organization) in this low-dimensionality model system is discussed.

Perfect commuting-operator strategies for linear system games

NASA Astrophysics Data System (ADS)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

Partner symmetries and non-invariant solutions of four-dimensional heavenly equations

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2004-07-01

We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.

The method of Ritz applied to the equation of Hamilton. [for pendulum systems

NASA Technical Reports Server (NTRS)

Bailey, C. D.

1976-01-01

Without any reference to the theory of differential equations, the initial value problem of the nonlinear, nonconservative double pendulum system is solved by the application of the method of Ritz to the equation of Hamilton. Also shown is an example of the reduction of the traditional eigenvalue problem of linear, homogeneous, differential equations of motion to the solution of a set of nonhomogeneous algebraic equations. No theory of differential equations is used. Solution of the time-space path of the linear oscillator is demonstrated and compared to the exact solution.

Low-temperature transport in out-of-equilibrium XXZ chains

NASA Astrophysics Data System (ADS)

Bertini, Bruno; Piroli, Lorenzo

2018-03-01

We study the low-temperature transport properties of out-of-equilibrium XXZ spin-1/2 chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times t and distances x from the junction become functions of the ratio \\zeta=x/t . By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures, but described by non-trivial functions of ζ. We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width \

Cathode fall model and current-voltage characteristics of field emission driven direct current microplasmas

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

Venkattraman, Ayyaswamy

2013-11-15

The post-breakdown characteristics of field emission driven microplasma are studied theoretically and numerically. A cathode fall model assuming a linearly varying electric field is used to obtain equations governing the operation of steady state field emission driven microplasmas. The results obtained from the model by solving these equations are compared with particle-in-cell with Monte Carlo collisions simulation results for parameters including the plasma potential, cathode fall thickness, ion number density in the cathode fall, and current density vs voltage curves. The model shows good overall agreement with the simulations but results in slightly overpredicted values for the plasma potential andmore » the cathode fall thickness attributed to the assumed electric field profile. The current density vs voltage curves obtained show an arc region characterized by negative slope as well as an abnormal glow discharge characterized by a positive slope in gaps as small as 10 μm operating at atmospheric pressure. The model also retrieves the traditional macroscale current vs voltage theory in the absence of field emission.« less

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Well-posedness, linear perturbations, and mass conservation for the axisymmetric Einstein equations

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

Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, FaMAF, Universidad Nacional de Cordoba, Instituto de Fisica Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria

2010-02-15

For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides a nonlinear control of the variables along the whole evolution. In this gauge, Einstein equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. As a first step in analyzing this system of equations we study linear perturbations on a flat background. We prove that the linear equations reduce to a very simple system of equations which provide, thoughmore » the mass formula, useful insight into the structure of the full system. However, the singular behavior of the coefficients at the axis makes the study of this linear system difficult from the analytical point of view. In order to understand the behavior of the solutions, we study the numerical evolution of them. We provide strong numerical evidence that the system is well-posed and that its solutions have the expected behavior. Finally, this linear system allows us to formulate a model problem which is physically interesting in itself, since it is connected with the linear stability of black hole solutions in axial symmetry. This model can contribute significantly to solve the nonlinear problem and at the same time it appears to be tractable.« less

Painlevé IV Solutions from Hamiltonians with Equidistant Gapped Spectrum

NASA Astrophysics Data System (ADS)

Estrada-Delgado, M. I.; Fernández C, D. J.

2016-03-01

Supersymmetry transformations are applied to the harmonic oscillator for generating potentials Vk j whose spectra have a gap with respect to the initial one. The extremal states are found and, as the reduction theorem conditions are satisfied, ensuring that the system has third order ladder operators and it is connected with Painlevé IV (PIV) equation, then solutions to this equation can be generated. An alternative transformation is applied, by adding the levels needed to recover the spectrum of Vk j . The extremal states are found and, as the reduction theorem is met again, we get also solutions to the PIV equation which will be analysed.

SU-E-T-598: Parametric Equation for Quick and Reliable Estimate of Stray Neutron Doses in Proton Therapy and Application for Intracranial Tumor Treatments

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

Bonfrate, A; Farah, J; Sayah, R

2015-06-15

Purpose: Development of a parametric equation suitable for a daily use in routine clinic to provide estimates of stray neutron doses in proton therapy. Methods: Monte Carlo (MC) calculations using the UF-NCI 1-year-old phantom were exercised to determine the variation of stray neutron doses as a function of irradiation parameters while performing intracranial treatments. This was done by individually changing the proton beam energy, modulation width, collimator aperture and thickness, compensator thickness and the air gap size while their impact on neutron doses were put into a single equation. The variation of neutron doses with distance from the target volumemore » was also included in it. Then, a first step consisted in establishing the fitting coefficients by using 221 learning data which were neutron absorbed doses obtained with MC simulations while a second step consisted in validating the final equation. Results: The variation of stray neutron doses with irradiation parameters were fitted with linear, polynomial, etc. model while a power-law model was used to fit the variation of stray neutron doses with the distance from the target volume. The parametric equation fitted well MC simulations while establishing fitting coefficients as the discrepancies on the estimate of neutron absorbed doses were within 10%. The discrepancy can reach ∼25% for the bladder, the farthest organ from the target volume. Finally, the validation showed results in compliance with MC calculations since the discrepancies were also within 10% for head-and-neck and thoracic organs while they can reach ∼25%, again for pelvic organs. Conclusion: The parametric equation presents promising results and will be validated for other target sites as well as other facilities to go towards a universal method.« less

User's manual for LINEAR, a FORTRAN program to derive linear aircraft models

NASA Technical Reports Server (NTRS)

Duke, Eugene L.; Patterson, Brian P.; Antoniewicz, Robert F.

1987-01-01

This report documents a FORTRAN program that provides a powerful and flexible tool for the linearization of aircraft models. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.

Nonlinear Riccati equations as a unifying link between linear quantum mechanics and other fields of physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-04-01

Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.

Nonlocal kinetic energy functional from the jellium-with-gap model: Applications to orbital-free density functional theory

NASA Astrophysics Data System (ADS)

Constantin, Lucian A.; Fabiano, Eduardo; Della Sala, Fabio

2018-05-01

Orbital-free density functional theory (OF-DFT) promises to describe the electronic structure of very large quantum systems, being its computational cost linear with the system size. However, the OF-DFT accuracy strongly depends on the approximation made for the kinetic energy (KE) functional. To date, the most accurate KE functionals are nonlocal functionals based on the linear-response kernel of the homogeneous electron gas, i.e., the jellium model. Here, we use the linear-response kernel of the jellium-with-gap model to construct a simple nonlocal KE functional (named KGAP) which depends on the band-gap energy. In the limit of vanishing energy gap (i.e., in the case of metals), the KGAP is equivalent to the Smargiassi-Madden (SM) functional, which is accurate for metals. For a series of semiconductors (with different energy gaps), the KGAP performs much better than SM, and results are close to the state-of-the-art functionals with sophisticated density-dependent kernels.

Topologically trivial and nontrivial edge bands in graphene induced by irradiation

NASA Astrophysics Data System (ADS)

Yang, Mou; Cai, Zhi-Jun; Wang, Rui-Qiang; Bai, Yan-Kui

2016-08-01

We proposed a minimal model to describe the Floquet band structure of two-dimensional materials with light-induced resonant inter-band transition. We applied it to graphene to study the band features caused by the light irradiation. Linearly polarized light induces pseudo gaps (gaps are functions of wavevector), and circularly polarized light causes real gaps on the quasi-energy spectrum. If the polarization of light is linear and along the longitudinal direction of zigzag ribbons, flat edge bands appear in the pseudo gaps, and if it is in the lateral direction of armchair ribbons, curved edge bands can be found. For the circularly polarized cases, edge bands arise and intersect in the gaps of both types of ribbons. The edge bands induced by the circularly polarized light are helical and those by linearly polarized light are topologically trivial ones. The Chern number of the Floquet band, which reflects the number of pairs of helical edge bands in graphene ribbons, can be reduced into the winding number at resonance.

Wave propagation problem for a micropolar elastic waveguide

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-04-01

A propagation problem for coupled harmonic waves of translational displacements and microrotations along the axis of a long cylindrical waveguide is discussed at present study. Microrotations modeling is carried out within the linear micropolar elasticity frameworks. The mathematical model of the linear (or even nonlinear) micropolar elasticity is also expanded to a field theory model by variational least action integral and the least action principle. The governing coupled vector differential equations of the linear micropolar elasticity are given. The translational displacements and microrotations in the harmonic coupled wave are decomposed into potential and vortex parts. Calibrating equations providing simplification of the equations for the wave potentials are proposed. The coupled differential equations are then reduced to uncoupled ones and finally to the Helmholtz wave equations. The wave equations solutions for the translational and microrotational waves potentials are obtained for a high-frequency range.

Symmetry and singularity properties of second-order ordinary differential equations of Lie's type III

NASA Astrophysics Data System (ADS)

Andriopoulos, K.; Leach, P. G. L.

2007-04-01

We extend the work of Abraham-Shrauner [B. Abraham-Shrauner, Hidden symmetries and linearization of the modified Painleve-Ince equation, J. Math. Phys. 34 (1993) 4809-4816] on the linearization of the modified Painleve-Ince equation to a wider class of nonlinear second-order ordinary differential equations invariant under the symmetries of time translation and self-similarity. In the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations.

Vectorial control of nonlinear emission via chiral butterfly nanoantennas: generation of pure high order nonlinear vortex beams.

PubMed

Lesina, Antonino Cala'; Berini, Pierre; Ramunno, Lora

2017-02-06

We report on a chiral gap-nanostructure, which we term a "butterfly nanoantenna," that offers full vectorial control over nonlinear emission. The field enhancement in its gap occurs for only one circular polarization but for every incident linear polarization. As the polarization, phase and amplitude of the linear field in the gap are highly controlled, the linear field can drive nonlinear emitters within the gap, which behave as an idealized Huygens source. A general framework is thereby proposed wherein the butterfly nanoantennas can be arranged in a metasurface, and the nonlinear Huygens sources exploited to produce a highly structured far-field optical beam. Nonlinearity allows us to shape the light at shorter wavelengths, not accessible by linear plasmonics, and resulting in high purity beams. The chirality of the butterfly allows us to create orbital angular momentum states using a linearly polarized excitation. A third harmonic Laguerre-Gauss beam carrying an optical orbital angular momentum of 41 is demonstrated as an example, through large-scale simulations on a high-performance computing platform of the full plasmonic metasurface with an area large enough to contain up to 3600 nanoantennas.

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.…

Demand for prescription drugs under non-linear pricing in Medicare Part D.

PubMed

Jung, Kyoungrae; Feldman, Roger; McBean, A Marshall

2014-03-01

We estimate the price elasticity of prescription drug use in Medicare Part D, which features a non-linear price schedule due to a coverage gap. We analyze patterns of drug utilization prior to the coverage gap, where the "effective price" is higher than the actual copayment for drugs because consumers anticipate that more spending will make them more likely to reach the gap. We find that enrollees' total pre-gap drug spending is sensitive to their effective prices: the estimated price elasticity of drug spending ranges between [Formula: see text]0.14 and [Formula: see text]0.36. This finding suggests that filling in the coverage gap, as mandated by the health care reform legislation passed in 2010, will influence drug utilization prior to the gap. A simulation analysis indicates that closing the gap could increase Part D spending by a larger amount than projected, with additional pre-gap costs among those who do not hit the gap.

On the growth of solutions of a class of higher order linear differential equations with coefficients having the same order

NASA Astrophysics Data System (ADS)

Tu, Jin; Yi, Cai-Feng

2008-04-01

In this paper, the authors investigate the growth of solutions of a class of higher order linear differential equationsf(k)+Ak-1f(k-1)+...+A0f=0 when most coefficients in the above equations have the same order with each other, and obtain some results which improve previous results due to K.H. Kwon [K.H. Kwon, Nonexistence of finite order solutions of certain second order linear differential equations, Kodai Math. J. 19 (1996) 378-387] and ZE-X. Chen [Z.-X. Chen, The growth of solutions of the differential equation f''+e-zf'+Q(z)f=0, Sci. China Ser. A 31 (2001) 775-784 (in Chinese); ZE-X. Chen, On the hyper order of solutions of higher order differential equations, Chinese Ann. Math. Ser. B 24 (2003) 501-508 (in Chinese); Z.-X. Chen, On the growth of solutions of a class of higher order differential equations, Acta Math. Sci. Ser. B 24 (2004) 52-60 (in Chinese); Z.-X. Chen, C.-C. Yang, Quantitative estimations on the zeros and growth of entire solutions of linear differential equations, Complex Var. 42 (2000) 119-133].

Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Powers, Robert K.

1987-01-01

A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

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.

Quasi-linear theory via the cumulant expansion approach

NASA Technical Reports Server (NTRS)

Jones, F. C.; Birmingham, T. J.

1974-01-01

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.

Dual exponential polynomials and linear differential equations

NASA Astrophysics Data System (ADS)

Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

2018-01-01

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

GVE-Based Dynamics and Control for Formation Flying Spacecraft

NASA Technical Reports Server (NTRS)

Breger, Louis; How, Jonathan P.

2004-01-01

Formation flying is an enabling technology for many future space missions. This paper presents extensions to the equations of relative motion expressed in Keplerian orbital elements, including new initialization techniques for general formation configurations. A new linear time-varying form of the equations of relative motion is developed from Gauss Variational Equations and used in a model predictive controller. The linearizing assumptions for these equations are shown to be consistent with typical formation flying scenarios. Several linear, convex initialization techniques are presented, as well as a general, decentralized method for coordinating a tetrahedral formation using differential orbital elements. Control methods are validated using a commercial numerical propagator.

Schwarzschild and linear potentials in Mannheim's model of conformal gravity

NASA Astrophysics Data System (ADS)

Phillips, Peter R.

2018-05-01

We study the equations of conformal gravity, as given by Mannheim, in the weak field limit, so that a linear approximation is adequate. Specialising to static fields with spherical symmetry, we obtain a second-order equation for one of the metric functions. We obtain the Green function for this equation, and represent the metric function in the form of integrals over the source. Near a compact source such as the Sun the solution no longer has a form that is compatible with observations. We conclude that a solution of Mannheim type (a Schwarzschild term plus a linear potential of galactic scale) cannot exist for these field equations.

A decentralized process for finding equilibria given by linear equations.

PubMed Central

Reiter, S

1994-01-01

I present a decentralized process for finding the equilibria of an economy characterized by a finite number of linear equilibrium conditions. The process finds all equilibria or, if there are none, reports that, in a finite number of steps at most equal to the number of equations. The communication and computational complexity compare favorably with other decentralized processes. The process may also be interpreted as an algorithm for solving a distributed system of linear equations. Comparisons with the Linpack program for LU (lower and upper triangular decomposition of the matrix of the equation system, a version of Gaussian elimination) are presented. PMID:11607486

The Influence of Solvent on the Structural Properties of trans-(NHC)PtI2Py Complex: A Platinum-Based Anticancer Drug

NASA Astrophysics Data System (ADS)

Sadigh Vishkaee, Teherh; Fazaeli, Reza

2018-06-01

Quantum chemical calculations using MPW1PW91 method were applied to analyze the solvent effect on the structural, spectral, and thermochemical parameters for a platinum-based anticancer drug trans-(NHC)PtI2Py complex. The solvent effects were examined by the self-consistent reaction field theory (SCRF) based on Polarizable Continuum Model (PCM). The linear correlations between the solvation energies, HOMO-LUMO gaps, IR-active stretching vibration of Pt-N bonds and N-H of NHC ligand with dielectric constants of solvents were studied. The wave numbers of these IR-active stretching vibrations in different solvents were correlated with the Kirkwood-Bauer-Magat equation (KBM). The thermodynamic activation parameter such free energy of solvation, enthalpy of solvation were also calculated.

Sound wave resonances in micro-electro-mechanical systems devices vibrating at high frequencies according to the kinetic theory of gases

NASA Astrophysics Data System (ADS)

Desvillettes, Laurent; Lorenzani, Silvia

2012-09-01

The mechanism leading to gas damping in micro-electro-mechanical systems (MEMS) devices vibrating at high frequencies is investigated by using the linearized Boltzmann equation based on simplified kinetic models and diffuse reflection boundary conditions. Above a certain frequency of oscillation, the sound waves propagating through the gas are trapped in the gaps between the moving elements and the fixed boundaries of the microdevice. In particular, we found a scaling law, valid for all Knudsen numbers Kn (defined as the ratio between the gas mean free path and a characteristic length of the gas flow), that predicts a resonant response of the system. This response enables a minimization of the damping force exerted by the gas on the oscillating wall of the microdevice.

Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

NASA Astrophysics Data System (ADS)

Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

2018-01-01

Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

Alfvén wave interactions in the solar wind

NASA Astrophysics Data System (ADS)

Webb, G. M.; McKenzie, J. F.; Hu, Q.; le Roux, J. A.; Zank, G. P.

2012-11-01

Alfvén wave mixing (interaction) equations used in locally incompressible turbulence transport equations in the solar wind are analyzed from the perspective of linear wave theory. The connection between the wave mixing equations and non-WKB Alfven wave driven wind theories are delineated. We discuss the physical wave energy equation and the canonical wave energy equation for non-WKB Alfven waves and the WKB limit. Variational principles and conservation laws for the linear wave mixing equations for the Heinemann and Olbert non-WKB wind model are obtained. The connection with wave mixing equations used in locally incompressible turbulence transport in the solar wind are discussed.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

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

Numerical solution of distributed order fractional differential equations

NASA Astrophysics Data System (ADS)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Thermal-Interaction Matrix For Resistive Test Structure

NASA Technical Reports Server (NTRS)

Buehler, Martin G.; Dhiman, Jaipal K.; Zamani, Nasser

1990-01-01

Linear mathematical model predicts increase in temperature in each segment of 15-segment resistive structure used to test electromigration. Assumption of linearity based on fact: equations that govern flow of heat are linear and coefficients in equations (heat conductivities and capacities) depend only weakly on temperature and considered constant over limited range of temperature.

A modified homotopy perturbation method and the axial secular frequencies of a non-linear ion trap.

PubMed

Doroudi, Alireza

2012-01-01

In this paper, a modified version of the homotopy perturbation method, which has been applied to non-linear oscillations by V. Marinca, is used for calculation of axial secular frequencies of a non-linear ion trap with hexapole and octopole superpositions. The axial equation of ion motion in a rapidly oscillating field of an ion trap can be transformed to a Duffing-like equation. With only octopole superposition the resulted non-linear equation is symmetric; however, in the presence of hexapole and octopole superpositions, it is asymmetric. This modified homotopy perturbation method is used for solving the resulting non-linear equations. As a result, the ion secular frequencies as a function of non-linear field parameters are obtained. The calculated secular frequencies are compared with the results of the homotopy perturbation method and the exact results. With only hexapole superposition, the results of this paper and the homotopy perturbation method are the same and with hexapole and octopole superpositions, the results of this paper are much more closer to the exact results compared with the results of the homotopy perturbation method.

CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

NASA Technical Reports Server (NTRS)

Jamison, J. W.

1994-01-01

CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

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

Granita, E-mail: granitafc@gmail.com; Bahar, A.

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Fluid equations with nonlinear wave-particle resonances^

NASA Astrophysics Data System (ADS)

Mattor, Nathan

1997-11-01

We have derived fluid equations that include linear and nonlinear wave-particle resonance effects. This greatly extends previous ``Landau-fluid'' closures, which include linear Landau damping. (G.W. Hammett and F.W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990).^, (Z. Chang and J. D. Callen, Phys. Fluids B 4,) 1167 (1992). The new fluid equations are derived with no approximation regarding nonlinear kinetic interaction, and so additionally include numerous nonlinear kinetic effects. The derivation starts with the electrostatic drift kinetic equation for simplicity, with a Maxwellian distribution function. Fluid closure is accomplished through a simple integration trick applied to the drift kinetic equation, using the property that the nth moment of Maxwellian distribution is related to the nth derivative. The result is a compact closure term appearing in the highest moment equation, a term which involves a plasma dispersion function of the electrostatic field and its derivatives. The new term reduces to the linear closures in appropriate limits, so both approaches retain linear Landau damping. But the nonlinearly closed equations have additional desirable properties. Unlike linear closures, the nonlinear closure retains the time-reversibility of the original kinetic equation. We have shown directly that the nonlinear closure retains at least two nonlinear resonance effects: wave-particle trapping and Compton scattering. Other nonlinear kinetic effects are currently under investigation. The new equations correct two previous discrepancies between kinetic and Landau-fluid predictions, including a propagator discrepancy (N. Mattor, Phys. Fluids B 4,) 3952 (1992). and a numerical discrepancy for the 3-mode shearless bounded slab ITG problem. (S. E. Parker et al.), Phys. Plasmas 1, 1461 (1994). ^* In collaboration with S. E. Parker, Department of Physics, University of Colorado, Boulder. ^ Work performed at LLNL under DoE contract No. W7405-ENG-48.

Preprocessing Inconsistent Linear System for a Meaningful Least Squares Solution

NASA Technical Reports Server (NTRS)

Sen, Syamal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations. Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

NASA Technical Reports Server (NTRS)

Sen, Symal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

PubMed

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

Simulation and theory of spontaneous TAE frequency sweeping

NASA Astrophysics Data System (ADS)

Wang, Ge; Berk, H. L.

2012-09-01

A simulation model, based on the linear tip model of Rosenbluth, Berk and Van Dam (RBV), is developed to study frequency sweeping of toroidal Alfvén eigenmodes (TAEs). The time response of the background wave in the RBV model is given by a Volterra integral equation. This model captures the properties of TAE waves both in the gap and in the continuum. The simulation shows that phase space structures form spontaneously at frequencies close to the linearly predicted frequency, due to resonant particle-wave interactions and background dissipation. The frequency sweeping signals are found to chirp towards the upper and lower continua. However, the chirping signals penetrate only the lower continuum, whereupon the frequency chirps and mode amplitude increases in synchronism to produce an explosive solution. An adiabatic theory describing the evolution of a chirping signal is developed which replicates the chirping dynamics of the simulation in the lower continuum. This theory predicts that a decaying chirping signal will terminate at the upper continuum though in the numerical simulation the hole disintegrates before the upper continuum is reached.

Shear Stress in Magnetorheological FInishing for Glasses

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

Miao, C.; Shafrir, S.N.; Lambropoulos, J.C.

2009-04-28

We report in situ, simultaneous measurements of both drag and normal forces in magnetorheological finishing (MRF) for what is believed to be the first time, using a spot taking machine (STM) as a test bed to take MRF spots on stationary parts. The measurements are carried out over the entire area where material is being removed, i.e., the projected area of the MRF removal function/spot on the part surface, using a dual force sensor. This approach experimentally addresses the mechanisms governing material removal in MRF for optical glasses in terms of the hydrodynamic pressure and shear stress, applied by themore » hydrodynamic flow of magnetorheological fluid at the gap between the part surface and the STM wheel. This work demonstrates that the volumetric removal rate shows a positive linear dependence on shear stress. Shear stress exhibits a positive linear dependence on a material figure of merit that depends upon Young’s modulus, fracture toughness, and hardness. A modified Preston’s equation is proposed that better estimates MRF material removal rate for optical glasses by incorporating mechanical properties, shear stress, and velocity.« less

Shear stress in magnetorheological finishing for glasses.

PubMed

Miao, Chunlin; Shafrir, Shai N; Lambropoulos, John C; Mici, Joni; Jacobs, Stephen D

2009-05-01

We report in situ, simultaneous measurements of both drag and normal forces in magnetorheological finishing (MRF) for what is believed to be the first time, using a spot taking machine (STM) as a test bed to take MRF spots on stationary parts. The measurements are carried out over the entire area where material is being removed, i.e., the projected area of the MRF removal function/spot on the part surface, using a dual force sensor. This approach experimentally addresses the mechanisms governing material removal in MRF for optical glasses in terms of the hydrodynamic pressure and shear stress, applied by the hydrodynamic flow of magnetorheological fluid at the gap between the part surface and the STM wheel. This work demonstrates that the volumetric removal rate shows a positive linear dependence on shear stress. Shear stress exhibits a positive linear dependence on a material figure of merit that depends upon Young's modulus, fracture toughness, and hardness. A modified Preston's equation is proposed that better estimates MRF material removal rate for optical glasses by incorporating mechanical properties, shear stress, and velocity.

Symmetry operators and decoupled equations for linear fields on black hole spacetimes

NASA Astrophysics Data System (ADS)

Araneda, Bernardo

2017-02-01

In the class of vacuum Petrov type D spacetimes with cosmological constant, which includes the Kerr-(A)dS black hole as a particular case, we find a set of four-dimensional operators that, when composed off shell with the Dirac, Maxwell and linearized gravity equations, give a system of equations for spin weighted scalars associated with the linear fields, that decouple on shell. Using these operator relations we give compact reconstruction formulae for solutions of the original spinor and tensor field equations in terms of solutions of the decoupled scalar equations. We also analyze the role of Killing spinors and Killing-Yano tensors in the spin weight zero equations and, in the case of spherical symmetry, we compare our four-dimensional formulation with the standard 2  +  2 decomposition and particularize to the Schwarzschild-(A)dS black hole. Our results uncover a pattern that generalizes a number of previous results on Teukolsky-like equations and Debye potentials for higher spin fields.

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.

Numerical Solution of Systems of Loaded Ordinary Differential Equations with Multipoint Conditions

NASA Astrophysics Data System (ADS)

Assanova, A. T.; Imanchiyev, A. E.; Kadirbayeva, Zh. M.

2018-04-01

A system of loaded ordinary differential equations with multipoint conditions is considered. The problem under study is reduced to an equivalent boundary value problem for a system of ordinary differential equations with parameters. A system of linear algebraic equations for the parameters is constructed using the matrices of the loaded terms and the multipoint condition. The conditions for the unique solvability and well-posedness of the original problem are established in terms of the matrix made up of the coefficients of the system of linear algebraic equations. The coefficients and the righthand side of the constructed system are determined by solving Cauchy problems for linear ordinary differential equations. The solutions of the system are found in terms of the values of the desired function at the initial points of subintervals. The parametrization method is numerically implemented using the fourth-order accurate Runge-Kutta method as applied to the Cauchy problems for ordinary differential equations. The performance of the constructed numerical algorithms is illustrated by examples.

Voltage and pace-capture mapping of linear ablation lesions overestimates chronic ablation gap size.

PubMed

O'Neill, Louisa; Harrison, James; Chubb, Henry; Whitaker, John; Mukherjee, Rahul K; Bloch, Lars Ølgaard; Andersen, Niels Peter; Dam, Høgni; Jensen, Henrik K; Niederer, Steven; Wright, Matthew; O'Neill, Mark; Williams, Steven E

2018-04-26

Conducting gaps in lesion sets are a major reason for failure of ablation procedures. Voltage mapping and pace-capture have been proposed for intra-procedural identification of gaps. We aimed to compare gap size measured acutely and chronically post-ablation to macroscopic gap size in a porcine model. Intercaval linear ablation was performed in eight Göttingen minipigs with a deliberate gap of ∼5 mm left in the ablation line. Gap size was measured by interpolating ablation contact force values between ablation tags and thresholding at a low force cut-off of 5 g. Bipolar voltage mapping and pace-capture mapping along the length of the line were performed immediately, and at 2 months, post-ablation. Animals were euthanized and gap sizes were measured macroscopically. Voltage thresholds to define scar were determined by receiver operating characteristic analysis as <0.56 mV (acutely) and <0.62 mV (chronically). Taking the macroscopic gap size as gold standard, error in gap measurements were determined for voltage, pace-capture, and ablation contact force maps. All modalities overestimated chronic gap size, by 1.4 ± 2.0 mm (ablation contact force map), 5.1 ± 3.4 mm (pace-capture), and 9.5 ± 3.8 mm (voltage mapping). Error on ablation contact force map gap measurements were significantly less than for voltage mapping (P = 0.003, Tukey's multiple comparisons test). Chronically, voltage mapping and pace-capture mapping overestimated macroscopic gap size by 11.9 ± 3.7 and 9.8 ± 3.5 mm, respectively. Bipolar voltage and pace-capture mapping overestimate the size of chronic gap formation in linear ablation lesions. The most accurate estimation of chronic gap size was achieved by analysis of catheter-myocardium contact force during ablation.

Measurements of the near-surface flow over a hill

NASA Astrophysics Data System (ADS)

Vosper, S. B.; Mobbs, S. D.; Gardiner, B. A.

2002-10-01

The near-surface flow over a hill with moderate slope and height comparable with the boundary-layer depth is investigated through field measurements of the mean flow (at 2 m), surface pressure, and turbulent momentum flux divergence between 8 and 15 m. The measurements were made along an east-west transect across the hill Tighvein (height 458 m, approximate width 8 km) on the Isle of Arran, south-west Scotland, during two separate periods, each of around three-weeks duration. Radiosonde ascents are used to determine the variation of a Froude number, FL = U/NL, where U is the wind speed at the middle-layer height, hm, N is the mean Brunt-Väisälä frequency below this height and L is a hill length-scale. Measurements show that for moderately stratified flows (for which FL 0.25) a minimum in the hill-induced surface-pressure perturbation occurs across the summit and this is accompanied by a maximum in the near-surface wind speed. In the more strongly stratified case (FL 0.25) the pressure field is more asymmetric and the lee-slope flow is generally stronger than on the windward slope. Such a flow pattern is qualitatively consistent with that predicted by stratified linear boundary-layer and gravity-wave theories. The near-surface momentum budget is analysed by evaluating the dominant terms in a Bernoulli equation suitable for turbulent flow. Measurements during periods of westerly flow are used to evaluate the dominant terms, and the equation is shown to hold to a reasonable approximation on the upwind slope of the hill and also on the downwind slope, away from the summit. Immediately downwind of the summit, however, the Bernoulli equation does not hold. Possible reasons for this, such as non-separated sheltering and flow separation, are discussed.

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

The primer vector in linear, relative-motion equations. [spacecraft trajectory optimization

NASA Technical Reports Server (NTRS)

1980-01-01

Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.

Erosion potential from Missoula floods in the Pasco Basin, Washington

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

Craig, R.G.; Hanson, J.P.

Localities within the Pasco Basin preserve evidence of Missoula floods. Deposits are 46% sand-sized, 36% gravel-sized, and 18% finer than sand-sized. Mean thickness is 39 meters. High water marks at Wallula Gap require a discharge of approximately 12.5 Mcms. At Sentinel Gap, the slope-area method shows that the high water marks require a discharge of 34.6 Mcms. Since this discharge greatly exceeds any estimated for Missoula floods, there must have been backwater ponding from Wallula Gap. Projecting the slope of the water surface at the upper end of Wallula Gap to the downstream cross section at Gable Mountain leads tomore » a discharge of 9.5 Mcms at Sentinel Gap. The HEC-6 steady state code and four sediment transport equations were applied. Assuming sand-sized particles, DuBoys function estimated 4 to 9 meters of scour. Yang's equation estimated 3 to 4 meters of scour. These are a minimum. A hydrograph synthesized for the boundaries of the Pasco Basin shows the maxima of the flood would occur after 90 h at Sentinel Gap, and at 114 h at Wallula Gap. The 200 areas will remain inundated for four days and six hours. With a quasi-dynamic sediment transport computation, HEC-6 scour estimates range from 0.61 meters to 0.915 meters. This is a minimum amount and erosion is highly variable suggesting reworking of sediment. The Meyer-Peter Meuller equations show less than 1 meter of net scour in the 200 areas. More extensive erosion was achieved during particular time steps of this analysis suggesting that sediment re-working would occur.« less

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.

A Textbook for a First Course in Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Zingg, D. W.; Pulliam, T. H.; Nixon, David (Technical Monitor)

1999-01-01

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

ERIC Educational Resources Information Center

Camporesi, Roberto

2011-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

An application of small-gap equations in sealing devices

NASA Technical Reports Server (NTRS)

Vionnet, Carlos A.; Heinrich, Juan C.

1993-01-01

The study of a thin, incompressible Newtonian fluid layer trapped between two almost parallel, sliding surfaces has been actively pursued in the last decades. This subject includes lubrication applications such as slider bearings or the sealing of non-pressurized fluids with rubber rotary shaft seals. In the present work we analyze numerically the flow of lubricant fluid through a micro-gap of sealing devices. The first stage of this study is carried out assuming that a 'small-gap' parameter delta attains an extreme value in the Navier-Stokes equations. The precise meaning of small-gap is achieved by the particular limit delta = 0 which, within the bounds of the hypotheses, predicts transport of lubricant through the sealed area by centrifugal instabilities. Numerical results obtained with the penalty function approximation in the finite element method are presented. In particular, the influence of inflow and outflow boundary conditions, and their impact in the simulated flow, are discussed.

An application of small-gap equations in sealing devices

NASA Astrophysics Data System (ADS)

Vionnet, Carlos A.; Heinrich, Juan C.

1993-11-01

The study of a thin, incompressible Newtonian fluid layer trapped between two almost parallel, sliding surfaces has been actively pursued in the last decades. This subject includes lubrication applications such as slider bearings or the sealing of non-pressurized fluids with rubber rotary shaft seals. In the present work we analyze numerically the flow of lubricant fluid through a micro-gap of sealing devices. The first stage of this study is carried out assuming that a 'small-gap' parameter delta attains an extreme value in the Navier-Stokes equations. The precise meaning of small-gap is achieved by the particular limit delta = 0 which, within the bounds of the hypotheses, predicts transport of lubricant through the sealed area by centrifugal instabilities. Numerical results obtained with the penalty function approximation in the finite element method are presented. In particular, the influence of inflow and outflow boundary conditions, and their impact in the simulated flow, are discussed.

Conical Lens for 5-Inch/54 Gun Launched Missile

DTIC Science & Technology

1981-06-01

Propagation, Interferenceand Diffraction of Light, 2nd ed. (revised), p. 121-124, Pergamon Press, 1964. 10. Anton , Howard, Elementary Linear Algebra , p. 1-21...equations is nonlinear in x, but is linear in the coefficients. Therefore, the techniques of linear algebra can be used on equation (F-13). The method...This thesis assumes the air to be homogenous, isotropic, linear , time indepen- dent (HILT) and free of shock waves in order to investigate the

Experimental quantum computing to solve systems of linear equations.

PubMed

Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

2013-06-07

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

NASA Astrophysics Data System (ADS)

Agresti, Juri; De Pietri, Roberto; Lusanna, Luca; Martucci, Luca

2004-05-01

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy {\\hat E}ADM, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) r_{\\bar a}(\\tau ,\\vec \\sigma ), \\pi_{\\bar a}(\\tau ,\\vec \\sigma ), \\bar a = 1,2. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in {\\hat E}ADM. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's r_{\\bar a}(\\tau ,\\vec \\sigma ), which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.

Modeling Individual Damped Linear Oscillator Processes with Differential Equations: Using Surrogate Data Analysis to Estimate the Smoothing Parameter

ERIC Educational Resources Information Center

Deboeck, Pascal R.; Boker, Steven M.; Bergeman, C. S.

2008-01-01

Among the many methods available for modeling intraindividual time series, differential equation modeling has several advantages that make it promising for applications to psychological data. One interesting differential equation model is that of the damped linear oscillator (DLO), which can be used to model variables that have a tendency to…

Mechanisms Inducing Jet Rotation in Shear-Formed Shaped-Charge Liners.

DTIC Science & Technology

1990-03-01

of deviatoric strain, and compressibility affects only the equation of state , not the deviatoric stress /strain relation. An anisotropic formulation is...strains, a more accurate scalar equation of state should simultaneously be employed to account for non-linear compressibility effects . A4 A.3 Elastic... obtainable knowing the previous and present cycles’ average stress . However, many non-linear equations

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

NASA Astrophysics Data System (ADS)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1977-01-01

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

New compacton soliton solutions and solitary patterns solutions of nonlinearly dispersive Boussinesq equations

NASA Astrophysics Data System (ADS)

Yan, Zhenya; Bluman, George

2002-11-01

The special exact solutions of nonlinearly dispersive Boussinesq equations (called B( m, n) equations), utt- uxx- a( un) xx+ b( um) xxxx=0, is investigated by using four direct ansatze. As a result, abundant new compactons: solitons with the absence of infinite wings, solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions of these two equations are obtained. The variant is extended to include linear dispersion to support compactons and solitary patterns in the linearly dispersive Boussinesq equations with m=1. Moreover, another new compacton solution of the special case, B(2,2) equation, is also found.

Nonlinear and linear wave equations for propagation in media with frequency power law losses

NASA Astrophysics Data System (ADS)

Szabo, Thomas L.

2003-10-01

The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

Flutter and Forced Response Analyses of Cascades using a Two-Dimensional Linearized Euler Solver

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Srivastava, R.; Mehmed, O.

1999-01-01

Flutter and forced response analyses for a cascade of blades in subsonic and transonic flow is presented. The structural model for each blade is a typical section with bending and torsion degrees of freedom. The unsteady aerodynamic forces due to bending and torsion motions. and due to a vortical gust disturbance are obtained by solving unsteady linearized Euler equations. The unsteady linearized equations are obtained by linearizing the unsteady nonlinear equations about the steady flow. The predicted unsteady aerodynamic forces include the effect of steady aerodynamic loading due to airfoil shape, thickness and angle of attack. The aeroelastic equations are solved in the frequency domain by coupling the un- steady aerodynamic forces to the aeroelastic solver MISER. The present unsteady aerodynamic solver showed good correlation with published results for both flutter and forced response predictions. Further improvements are required to use the unsteady aerodynamic solver in a design cycle.

Systems of fuzzy equations in structural mechanics

NASA Astrophysics Data System (ADS)

Skalna, Iwona; Rama Rao, M. V.; Pownuk, Andrzej

2008-08-01

Systems of linear and nonlinear equations with fuzzy parameters are relevant to many practical problems arising in structure mechanics, electrical engineering, finance, economics and physics. In this paper three methods for solving such equations are discussed: method for outer interval solution of systems of linear equations depending linearly on interval parameters, fuzzy finite element method proposed by Rama Rao and sensitivity analysis method. The performance and advantages of presented methods are described with illustrative examples. Extended version of the present paper can be downloaded from the web page of the UTEP [I. Skalna, M.V. Rama Rao, A. Pownuk, Systems of fuzzy equations in structural mechanics, The University of Texas at El Paso, Department of Mathematical Sciences Research Reports Series, , Texas Research Report No. 2007-01, 2007].

Statistical Extremes of Turbulence and a Cascade Generalisation of Euler's Gyroscope Equation

NASA Astrophysics Data System (ADS)

Tchiguirinskaia, Ioulia; Scherzer, Daniel

2016-04-01

Turbulence refers to a rather well defined hydrodynamical phenomenon uncovered by Reynolds. Nowadays, the word turbulence is used to designate the loss of order in many different geophysical fields and the related fundamental extreme variability of environmental data over a wide range of scales. Classical statistical techniques for estimating the extremes, being largely limited to statistical distributions, do not take into account the mechanisms generating such extreme variability. An alternative approaches to nonlinear variability are based on a fundamental property of the non-linear equations: scale invariance, which means that these equations are formally invariant under given scale transforms. Its specific framework is that of multifractals. In this framework extreme variability builds up scale by scale leading to non-classical statistics. Although multifractals are increasingly understood as a basic framework for handling such variability, there is still a gap between their potential and their actual use. In this presentation we discuss how to dealt with highly theoretical problems of mathematical physics together with a wide range of geophysical applications. We use Euler's gyroscope equation as a basic element in constructing a complex deterministic system that preserves not only the scale symmetry of the Navier-Stokes equations, but some more of their symmetries. Euler's equation has been not only the object of many theoretical investigations of the gyroscope device, but also generalised enough to become the basic equation of fluid mechanics. Therefore, there is no surprise that a cascade generalisation of this equation can be used to characterise the intermittency of turbulence, to better understand the links between the multifractal exponents and the structure of a simplified, but not simplistic, version of the Navier-Stokes equations. In a given way, this approach is similar to that of Lorenz, who studied how the flap of a butterfly wing could generate a cyclone with the help of a 3D ordinary differential system. Being well supported by the extensive numerical results, the cascade generalisation of Euler's gyroscope equation opens new horizons for predictability and predictions of processes having long-range dependences.

Satellite Formation Control Using Atmospheric Drag

DTIC Science & Technology

2007-03-01

of the formation. The linearized Clohessy - Wiltshire equations of motion are used to describe the motion of the two-satellite formation about an empty...control methods were applied to both the linear and nonlinear forms of the Clohessy - Wiltshire equations, and the performance of each control method was...r0δθ̈ = −2nδṙ + fθ (2.16) δz̈ = −n2δz + fz (2.17) These three equations are commonly known as Hill’s equations or the Clohessy - Wiltshire (CW

Propagation of Disturbances in AC Electricity Grids.

PubMed

Tamrakar, Samyak; Conrath, Michael; Kettemann, Stefan

2018-04-24

The energy transition towards high shares of renewable energy will affect the stability of electricity grids in many ways. Here, we aim to study its impact on propagation of disturbances by solving nonlinear swing equations describing coupled rotating masses of synchronous generators and motors on different grid topologies. We consider a tree, a square grid and as a real grid topology, the german transmission grid. We identify ranges of parameters with different transient dynamics: the disturbance decays exponentially in time, superimposed by oscillations with the fast decay rate of a single node, or with a smaller decay rate without oscillations. Most remarkably, as the grid inertia is lowered, nodes may become correlated, slowing down the propagation from ballistic to diffusive motion, decaying with a power law in time. Applying linear response theory we show that tree grids have a spectral gap leading to exponential relaxation as protected by topology and independent on grid size. Meshed grids are found to have a spectral gap which decreases with increasing grid size, leading to slow power law relaxation and collective diffusive propagation of disturbances. We conclude by discussing consequences if no measures are undertaken to preserve the grid inertia in the energy transition.

Analysis and computation of a least-squares method for consistent mesh tying

DOE PAGES

Day, David; Bochev, Pavel

2007-07-10

We report in the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a first-order patch test [T.A. Laursen, M.W. Heinstein, Consistent mesh-tying methods for topologically distinct discretized surfaces in non-linear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a least-squares method for mesh tying [P. Bochev, D.M. Day, A least-squares method for consistent mesh tying, Internat. J.more » Numer. Anal. Modeling 4 (2007) 342–352], applied to the partial differential equation -∇ 2φ+αφ=f. We prove optimal convergence rates for domains represented as overlapping subdomains and show that the least-squares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Finally, theoretical error estimates are illustrated by numerical experiments.« less

A Fresh Look at Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

ERIC Educational Resources Information Center

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

Higher symmetries and exact solutions of linear and nonlinear Schr{umlt o}dinger equation

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

Fushchych, W.I.; Nikitin, A.G.

1997-11-01

A new approach for the analysis of partial differential equations is developed which is characterized by a simultaneous use of higher and conditional symmetries. Higher symmetries of the Schr{umlt o}dinger equation with an arbitrary potential are investigated. Nonlinear determining equations for potentials are solved using reductions to Weierstrass, Painlev{acute e}, and Riccati forms. Algebraic properties of higher order symmetry operators are analyzed. Combinations of higher and conditional symmetries are used to generate families of exact solutions of linear and nonlinear Schr{umlt o}dinger equations. {copyright} {ital 1997 American Institute of Physics.}

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1989-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

Effects of electric and magnetic fields on the electronic properties of zigzag carbon and boron nitride nanotubes

NASA Astrophysics Data System (ADS)

Chegel, Raad; Behzad, Somayeh; Ahmadi, Eghbal

2012-04-01

We have investigated the electronic properties of zigzag CNTs and BNNTs under the external transverse electric field and axial magnetic field, using tight binding approximation. It was found that after switching on the electric and magnetic fields, the band modification such as distortion of the degeneracy, change in energy dispersion, subband spacing and band gap size reduction occurs. The band gap of zigzag BNNTs decreases linearly with increasing the electric field strength but the band gap variation for CNTs increases first and later decreases (Metallic) or first hold constant and then decreases (semiconductor). For type (II) CNTs, at a weak magnetic field, by increasing the electric field strength, the band gap remains constant first and then decreases and in a stronger magnetic field the band gap reduction becomes parabolic. For type (III) CNTs, in any magnetic field, the band gap increases slowly until reaches a maximum value and then decreases linearly. Unlike to CNTs, the magnetic field has less effects on the BNNTs band gap variation.

Comparison of kinetic model for biogas production from corn cob

NASA Astrophysics Data System (ADS)

Shitophyta, L. M.; Maryudi

2018-04-01

Energy demand increases every day, while the energy source especially fossil energy depletes increasingly. One of the solutions to overcome the energy depletion is to provide renewable energies such as biogas. Biogas can be generated by corn cob and food waste. In this study, biogas production was carried out by solid-state anaerobic digestion. The steps of biogas production were the preparation of feedstock, the solid-state anaerobic digestion, and the measurement of biogas volume. This study was conducted on TS content of 20%, 22%, and 24%. The aim of this research was to compare kinetic models of biogas production from corn cob and food waste as a co-digestion using the linear, exponential equation, and first-kinetic models. The result showed that the exponential equation had a better correlation than the linear equation on the ascending graph of biogas production. On the contrary, the linear equation had a better correlation than the exponential equation on the descending graph of biogas production. The correlation values on the first-kinetic model had the smallest value compared to the linear and exponential models.

Calculation of biochemical net reactions and pathways by using matrix operations.

PubMed Central

Alberty, R A

1996-01-01

Pathways for net biochemical reactions can be calculated by using a computer program that solves systems of linear equations. The coefficients in the linear equations are the stoichiometric numbers in the biochemical equations for the system. The solution of the system of linear equations is a vector of the stoichiometric numbers of the reactions in the pathway for the net reaction; this is referred to as the pathway vector. The pathway vector gives the number of times the various reactions have to occur to produce the desired net reaction. Net reactions may involve unknown numbers of ATP, ADP, and Pi molecules. The numbers of ATP, ADP, and Pi in a desired net reaction can be calculated in a two-step process. In the first step, the pathway is calculated by solving the system of linear equations for an abbreviated stoichiometric number matrix without ATP, ADP, Pi, NADred, and NADox. In the second step, the stoichiometric numbers in the desired net reaction, which includes ATP, ADP, Pi, NADred, and NADox, are obtained by multiplying the full stoichiometric number matrix by the calculated pathway vector. PMID:8804633

Krylov subspace methods - Theory, algorithms, and applications

NASA Technical Reports Server (NTRS)

Sad, Youcef

1990-01-01

Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

HESS Opinions: Linking Darcy's equation to the linear reservoir

NASA Astrophysics Data System (ADS)

Savenije, Hubert H. G.

2018-03-01

In groundwater hydrology, two simple linear equations exist describing the relation between groundwater flow and the gradient driving it: Darcy's equation and the linear reservoir. Both equations are empirical and straightforward, but work at different scales: Darcy's equation at the laboratory scale and the linear reservoir at the watershed scale. Although at first sight they appear similar, it is not trivial to upscale Darcy's equation to the watershed scale without detailed knowledge of the structure or shape of the underlying aquifers. This paper shows that these two equations, combined by the water balance, are indeed identical provided there is equal resistance in space for water entering the subsurface network. This implies that groundwater systems make use of an efficient drainage network, a mostly invisible pattern that has evolved over geological timescales. This drainage network provides equally distributed resistance for water to access the system, connecting the active groundwater body to the stream, much like a leaf is organized to provide all stomata access to moisture at equal resistance. As a result, the timescale of the linear reservoir appears to be inversely proportional to Darcy's conductance, the proportionality being the product of the porosity and the resistance to entering the drainage network. The main question remaining is which physical law lies behind pattern formation in groundwater systems, evolving in a way that resistance to drainage is constant in space. But that is a fundamental question that is equally relevant for understanding the hydraulic properties of leaf veins in plants or of blood veins in animals.

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. II - Equivalent linearization

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

The classical method of equivalent linearization is extended to a particular class of nonlinear difference equations. It is shown that the method can be used to obtain an approximation of the periodic solutions of these equations. In particular, the parameters of the limit cycle and the limit points can be determined. Three examples illustrating the method are presented.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1989-01-01

transform provides a linearization.’ Well known systems include the Kadomtsev - Petviashvili , Davey-Stewartson and Self-Dual Yang-Mills equations . The d...which employs inverse scattering theory in order to linearize the given nonlinear equation . I.S.T. has led to new developments in both fields: inverse...scattering and nonlinear wave equations . Listed below are some of the problems studied and a short description of results. - Multidimensional

Non-Linear Acoustic Concealed Weapons Detector

DTIC Science & Technology

2006-05-01

signature analysis 8 the interactions of the beams with concealed objects. The Khokhlov- Zabolotskaya-Kuznetsov ( KZK ) equation is the most widely used...Hamilton developed a finite difference method based on the KZK equation to model pulsed acoustic emissions from axial symmetric sources. Using a...College of William & Mary, we have developed a simulation code using the KZK equation to model non-linear acoustic beams and visualize beam patterns

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

PubMed

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

LETTER TO THE EDITOR: Bicomplexes and conservation laws in non-Abelian Toda models

NASA Astrophysics Data System (ADS)

Gueuvoghlanian, E. P.

2001-08-01

A bicomplex structure is associated with the Leznov-Saveliev equation of integrable models. The linear problem associated with the zero-curvature condition is derived in terms of the bicomplex linear equation. The explicit example of a non-Abelian conformal affine Toda model is discussed in detail and its conservation laws are derived from the zero-curvature representation of its equation of motion.

Permanent-magnet linear alternators. I - Fundamental equations. II - Design guidelines

NASA Astrophysics Data System (ADS)

Boldea, I.; Nasar, S. A.

1987-01-01

The general equations of permanent-magnet heteropolar three-phase and single-phase linear alternators, powered by free-piston Stirling engines, are presented, with application to space power stations and domestic applications including solar power plants. The equations are applied to no-load and short-circuit conditions, illustrating the end-effect caused by the speed-reversal process. In the second part, basic design guidelines for a three-phase tubular linear alternator are given, and the procedure is demonstrated with the numerical example of the design of a 25-kVA, 14.4-m/s, 120/220-V, 60-Hz alternator.

Second-order discrete Kalman filtering equations for control-structure interaction simulations

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith; Alvin, Kenneth F.

1991-01-01

A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.

An efficient parallel algorithm for the solution of a tridiagonal linear system of equations

NASA Technical Reports Server (NTRS)

Stone, H. S.

1971-01-01

Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

Variational formulation for dissipative continua and an incremental J-integral

NASA Astrophysics Data System (ADS)

Rahaman, Md. Masiur; Dhas, Bensingh; Roy, D.; Reddy, J. N.

2018-01-01

Our aim is to rationally formulate a proper variational principle for dissipative (viscoplastic) solids in the presence of inertia forces. As a first step, a consistent linearization of the governing nonlinear partial differential equations (PDEs) is carried out. An additional set of complementary (adjoint) equations is then formed to recover an underlying variational structure for the augmented system of linearized balance laws. This makes it possible to introduce an incremental Lagrangian such that the linearized PDEs, including the complementary equations, become the Euler-Lagrange equations. Continuous groups of symmetries of the linearized PDEs are computed and an analysis is undertaken to identify the variational groups of symmetries of the linearized dissipative system. Application of Noether's theorem leads to the conservation laws (conserved currents) of motion corresponding to the variational symmetries. As a specific outcome, we exploit translational symmetries of the functional in the material space and recover, via Noether's theorem, an incremental J-integral for viscoplastic solids in the presence of inertia forces. Numerical demonstrations are provided through a two-dimensional plane strain numerical simulation of a compact tension specimen of annealed mild steel under dynamic loading.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals.

PubMed

Theocharis, G; Boechler, N; Kevrekidis, P G; Job, S; Porter, Mason A; Daraio, C

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals

NASA Astrophysics Data System (ADS)

Theocharis, G.; Boechler, N.; Kevrekidis, P. G.; Job, S.; Porter, Mason A.; Daraio, C.

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

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

Schmidt, T.; Zimoch, D.

The operation of an APPLE II based undulator beamline with all its polarization states (linear horizontal and vertical, circular and elliptical, and continous variation of the linear vector) requires an effective description allowing an automated calculation of gap and shift parameter as function of energy and operation mode. The extension of the linear polarization range from 0 to 180 deg. requires 4 shiftable magnet arrrays, permitting use of the APU (adjustable phase undulator) concept. Studies for a pure fixed gap APPLE II for the SLS revealed surprising symmetries between circular and linear polarization modes allowing for simplified operation. A semi-analyticalmore » model covering all types of APPLE II and its implementation will be presented.« less

About APPLE II Operation

NASA Astrophysics Data System (ADS)

Schmidt, T.; Zimoch, D.

2007-01-01

The operation of an APPLE II based undulator beamline with all its polarization states (linear horizontal and vertical, circular and elliptical, and continous variation of the linear vector) requires an effective description allowing an automated calculation of gap and shift parameter as function of energy and operation mode. The extension of the linear polarization range from 0 to 180° requires 4 shiftable magnet arrrays, permitting use of the APU (adjustable phase undulator) concept. Studies for a pure fixed gap APPLE II for the SLS revealed surprising symmetries between circular and linear polarization modes allowing for simplified operation. A semi-analytical model covering all types of APPLE II and its implementation will be presented.

Chemically functionalized ZnS quantum dots as new optical nanosensor of herbicides

NASA Astrophysics Data System (ADS)

Masteri-Farahani, M.; Mahdavi, S.; Khanmohammadi, H.

2018-03-01

Surface chemical functionalization of ZnS quantum dots (ZnS-QDs) with cysteamine hydrochloride resulted in the preparation of an optical nanosensor for detection of herbicides. Characterization of the functionalized ZnS-QDs was performed with physicochemical methods such as x-ray diffraction (XRD), transmission electron microscopy (TEM), Fourier transform infrared (FT-IR) spectroscopy, energy dispersive x-ray (EDX) analysis, ultraviolet-visible (UV–vis) and photoluminescence (PL) spectroscopies. The optical band gap of the functionalized ZnS-QDs was determined by using Tauc plot as 4.1 eV. Addition of various herbicides resulted in the linearly fluorescence quenching of the functionalized ZnS-QDs according to the Stern-Volmer equation. The functionalized ZnS-QDs can be used as simple, rapid, and inexpensive nanosensor for practical detection and measurement of various herbicides.

Diverging conductance at the contact between random and pure quantum XX spin chains

NASA Astrophysics Data System (ADS)

Chatelain, Christophe

2017-11-01

A model consisting of two quantum XX spin chains, one homogeneous and the second with random couplings drawn from a binary distribution, is considered. The two chains are coupled to two different non-local thermal baths and their dynamics is governed by a Lindblad equation. In the steady state, a current J is induced between the two chains by coupling them together by their edges and imposing different chemical potentials μ to the two baths. While a regime of linear characteristics J versus Δμ is observed in the absence of randomness, a gap opens as the disorder strength is increased. In the infinite-randomness limit, this behavior is related to the density of states of the localized states contributing to the current. The conductance is shown to diverge in this limit.

Dependence of Tc on the q -ω structure of the spin-fluctuation spectrum

NASA Astrophysics Data System (ADS)

Dahm, Thomas; Scalapino, D. J.

2018-05-01

A phenomenological spin-fluctuation analysis [Dahm et al., Nat. Phys. 5, 217 (2009), 10.1038/nphys1180], based upon inelastic neutron scattering (INS) and angular resolved photoemission spectroscopy (ARPES) data for YBCO6.6(Tc=61 K) , is used to calculate the functional derivative of the d -wave eigenvalue λd of the linearized gap equation with respect to the imaginary part of the spin susceptibility χ''(q ,ω ) at 70 K. For temperatures near Tc, the variation of Tc with respect to χ''(q ,ω ) is proportional to this functional derivative. We find that above an energy ˜4 Tc the functional derivative becomes positive so that adding spin-fluctuation spectral weight at higher frequencies leads to an increase in Tc. The strongest pairing occurs for large momentum transfers, and small momentum spin-fluctuations suppress the pairing.

Nonlinear conductivity of a holographic superconductor under constant electric field

NASA Astrophysics Data System (ADS)

Zeng, Hua Bi; Tian, Yu; Fan, Zheyong; Chen, Chiang-Mei

2017-02-01

The dynamics of a two-dimensional superconductor under a constant electric field E is studied by using the gauge-gravity correspondence. The pair breaking current induced by E first increases to a peak value and then decreases to a constant value at late times, where the superconducting gap goes to zero, corresponding to a normal conducting phase. The peak value of the current is found to increase linearly with respect to the electric field. Moreover, the nonlinear conductivity, defined as an average of the conductivity in the superconducting phase, scales as ˜E-2 /3 when the system is close to the critical temperature Tc, which agrees with predictions from solving the time-dependent Ginzburg-Landau equation. Away from Tc, the E-2 /3 scaling of the conductivity still holds when E is large.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

A linearized Euler analysis of unsteady flows in turbomachinery

NASA Technical Reports Server (NTRS)

Hall, Kenneth C.; Crawley, Edward F.

1987-01-01

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Dilations and the Equation of a Line

ERIC Educational Resources Information Center

Yopp, David A.

2016-01-01

Students engage in proportional reasoning when they use covariance and multiple comparisons. Without rich connections to proportional reasoning, students may develop inadequate understandings of linear relationships and the equations that model them. Teachers can improve students' understanding of linear relationships by focusing on realistic…

On Polynomial Solutions of Linear Differential Equations with Polynomial Coefficients

ERIC Educational Resources Information Center

Si, Do Tan

1977-01-01

Demonstrates a method for solving linear differential equations with polynomial coefficients based on the fact that the operators z and D + d/dz are known to be Hermitian conjugates with respect to the Bargman and Louck-Galbraith scalar products. (MLH)

Development and validation of a general purpose linearization program for rigid aircraft models

NASA Technical Reports Server (NTRS)

Duke, E. L.; Antoniewicz, R. F.

1985-01-01

A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.

Waves and instabilities in plasmas

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

Chen, L.

1987-01-01

The contents of this book are: Plasma as a Dielectric Medium; Nyquist Technique; Absolute and Convective Instabilities; Landau Damping and Phase Mixing; Particle Trapping and Breakdown of Linear Theory; Solution of Viasov Equation via Guilding-Center Transformation; Kinetic Theory of Magnetohydrodynamic Waves; Geometric Optics; Wave-Kinetic Equation; Cutoff and Resonance; Resonant Absorption; Mode Conversion; Gyrokinetic Equation; Drift Waves; Quasi-Linear Theory; Ponderomotive Force; Parametric Instabilities; Problem Sets for Homework, Midterm and Final Examinations.

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

Rodigas, Timothy J.; Hinz, Philip M.; Malhotra, Renu, E-mail: rodigas@as.arizona.edu

Planets can affect debris disk structure by creating gaps, sharp edges, warps, and other potentially observable signatures. However, there is currently no simple way for observers to deduce a disk-shepherding planet's properties from the observed features of the disk. Here we present a single equation that relates a shepherding planet's maximum mass to the debris ring's observed width in scattered light, along with a procedure to estimate the planet's eccentricity and minimum semimajor axis. We accomplish this by performing dynamical N-body simulations of model systems containing a star, a single planet, and an exterior disk of parent bodies and dustmore » grains to determine the resulting debris disk properties over a wide range of input parameters. We find that the relationship between planet mass and debris disk width is linear, with increasing planet mass producing broader debris rings. We apply our methods to five imaged debris rings to constrain the putative planet masses and orbits in each system. Observers can use our empirically derived equation as a guide for future direct imaging searches for planets in debris disk systems. In the fortuitous case of an imaged planet orbiting interior to an imaged disk, the planet's maximum mass can be estimated independent of atmospheric models.« less

Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer

NASA Astrophysics Data System (ADS)

Pikichyan, H. V.

2017-07-01

In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.

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

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

NASA Technical Reports Server (NTRS)

Bland, S. R.

1982-01-01

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

MagIC: Fluid dynamics in a spherical shell simulator

NASA Astrophysics Data System (ADS)

Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.

2017-09-01

MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.

Renormalizable Quantum Field Theories in the Large -n Limit

NASA Astrophysics Data System (ADS)

Guruswamy, Sathya

1995-01-01

In this thesis, we study two examples of renormalizable quantum field theories in the large-N limit. Chapter one is a general introduction describing physical motivations for studying such theories. In chapter two, we describe the large-N method in field theory and discuss the pioneering work of 't Hooft in large-N two-dimensional Quantum Chromodynamics (QCD). In chapter three we study a spherically symmetric approximation to four-dimensional QCD ('spherical QCD'). We recast spherical QCD into a bilocal (constrained) theory of hadrons which in the large-N limit is equivalent to large-N spherical QCD for all energy scales. The linear approximation to this theory gives an eigenvalue equation which is the analogue of the well-known 't Hooft's integral equation in two dimensions. This eigenvalue equation is a scale invariant one and therefore leads to divergences in the theory. We give a non-perturbative renormalization prescription to cure this and obtain a beta function which shows that large-N spherical QCD is asymptotically free. In chapter four, we review the essentials of conformal field theories in two and higher dimensions, particularly in the context of critical phenomena. In chapter five, we study the O(N) non-linear sigma model on three-dimensional curved spaces in the large-N limit and show that there is a non-trivial ultraviolet stable critical point at which it becomes conformally invariant. We study this model at this critical point on examples of spaces of constant curvature and compute the mass gap in the theory, the free energy density (which turns out to be a universal function of the information contained in the geometry of the manifold) and the two-point correlation functions. The results we get give an indication that this model is an example of a three-dimensional analogue of a rational conformal field theory. A conclusion with a brief summary and remarks follows at the end.

A computationally efficient scheme for the non-linear diffusion equation

NASA Astrophysics Data System (ADS)

Termonia, P.; Van de Vyver, H.

2009-04-01

This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank-Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation.

On the solubility of certain classes of non-linear integral equations in p-adic string theory

NASA Astrophysics Data System (ADS)

Khachatryan, Kh. A.

2018-04-01

We study classes of non-linear integral equations that have immediate application to p-adic mathematical physics and to cosmology. We prove existence and uniqueness theorems for non-trivial solutions in the space of bounded functions.

Generating Linear Equations Based on Quantitative Reasoning

ERIC Educational Resources Information Center

Lee, Mi Yeon

2017-01-01

The Common Core's Standards for Mathematical Practice encourage teachers to develop their students' ability to reason abstractly and quantitatively by helping students make sense of quantities and their relationships within problem situations. The seventh-grade content standards include objectives pertaining to developing linear equations in…

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

PubMed

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

Theoretical investigation of dielectric corona pre-ionization TEA nitrogen laser based on transmission line method

NASA Astrophysics Data System (ADS)

Bahrampour, Alireza; Fallah, Robabeh; Ganjovi, Alireza A.; Bahrampour, Abolfazl

2007-07-01

This paper models the dielectric corona pre-ionization, capacitor transfer type of flat-plane transmission line traveling wave transverse excited atmospheric pressure nitrogen laser by a non-linear lumped RLC electric circuit. The flat-plane transmission line and the pre-ionizer dielectric are modeled by a lumped linear RLC and time-dependent non-linear RC circuit, respectively. The main discharge region is considered as a time-dependent non-linear RLC circuit where its resistance value is also depends on the radiated pre-ionization ultra violet (UV) intensity. The UV radiation is radiated by the resistance due to the surface plasma on the pre-ionizer dielectric. The theoretical predictions are in a very good agreement with the experimental observations. The electric circuit equations (including the ionization rate equations), the equations of laser levels population densities and propagation equation of laser intensities, are solved numerically. As a result, the effects of pre-ionizer dielectric parameters on the electrical behavior and output laser intensity are obtained.

Linear Quantum Systems: Non-Classical States and Robust Stability

DTIC Science & Technology

2016-06-29

quantum linear systems subject to non-classical quantum fields. The major outcomes of this project are (i) derivation of quantum filtering equations for...derivation of quantum filtering equations for systems non-classical input states including single photon states, (ii) determination of how linear...history going back some 50 years, to the birth of modern control theory with Kalman’s foundational work on filtering and LQG optimal control

Instability of isolated planar shock waves

DTIC Science & Technology

2007-06-07

Note that multi-mode perturbations can be treated by the inclusion of additional terms in Eq. (4), but owing to the linear independence of the... Volterra equation Figure 4 shows five examples of the evolution of the amplitude of a linear sinusoidal perturbation on a shock front obtained by...showing the evolution of the amplitude of a linear sinusoidal perturbation on a shock front obtained by numerically solving the Volterra equation in

On the Duffin-Kemmer-Petiau equation with linear potential in the presence of a minimal length

NASA Astrophysics Data System (ADS)

Chargui, Yassine

2018-04-01

We point out an erroneous handling in the literature regarding solutions of the (1 + 1)-dimensional Duffin-Kemmer-Petiau equation with linear potentials in the context of quantum mechanics with minimal length. Furthermore, using Brau's approach, we present a perturbative treatment of the effect of the minimal length on bound-state solutions when a Lorentz-scalar linear potential is applied.

Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

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

Barnich, Glenn; Troessaert, Cedric

2009-04-15

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity, and massless higher spin gauge fields.

Recursive linearization of multibody dynamics equations of motion

NASA Technical Reports Server (NTRS)

Lin, Tsung-Chieh; Yae, K. Harold

1989-01-01

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

A systematic approach to sketch Bethe-Salpeter equation

NASA Astrophysics Data System (ADS)

Qin, Si-xue

2016-03-01

To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS) equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark-anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD's gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs) and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM) vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symmetry breaking (DCSB). The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.

Nonlocal equation for the superconducting gap parameter

NASA Astrophysics Data System (ADS)

Simonucci, S.; Strinati, G. Calvanese

2017-08-01

The properties are considered in detail of a nonlocal (integral) equation for the superconducting gap parameter, which is obtained by a coarse-graining procedure applied to the Bogoliubov-de Gennes (BdG) equations over the whole coupling-versus-temperature phase diagram associated with the superfluid phase. It is found that the limiting size of the coarse-graining procedure, which is dictated by the range of the kernel of this integral equation, corresponds to the size of the Cooper pairs over the whole coupling-versus-temperature phase diagram up to the critical temperature, even when Cooper pairs turn into composite bosons on the BEC side of the BCS-BEC crossover. A practical method is further implemented to solve numerically this integral equation in an efficient way, which is based on a novel algorithm for calculating the Fourier transforms. Application of this method to the case of an isolated vortex, throughout the BCS-BEC crossover and for all temperatures in the superfluid phase, helps clarifying the nature of the length scales associated with a single vortex and the kinds of details that are in practice disposed off by the coarse-graining procedure on the BdG equations.

A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

PubMed

Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

2010-02-01

Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Optical systolic solutions of linear algebraic equations

NASA Technical Reports Server (NTRS)

Neuman, C. P.; Casasent, D.

1984-01-01

The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

Estimating drain flow from measured water table depth in layered soils under free and controlled drainage

NASA Astrophysics Data System (ADS)

Saadat, Samaneh; Bowling, Laura; Frankenberger, Jane; Kladivko, Eileen

2018-01-01

Long records of continuous drain flow are important for quantifying annual and seasonal changes in the subsurface drainage flow from drained agricultural land. Missing data due to equipment malfunction and other challenges have limited conclusions that can be made about annual flow and thus nutrient loads from field studies, including assessments of the effect of controlled drainage. Water table depth data may be available during gaps in flow data, providing a basis for filling missing drain flow data; therefore, the overall goal of this study was to examine the potential to estimate drain flow using water table observations. The objectives were to evaluate how the shape of the relationship between drain flow and water table height above drain varies depending on the soil hydraulic conductivity profile, to quantify how well the Hooghoudt equation represented the water table-drain flow relationship in five years of measured data at the Davis Purdue Agricultural Center (DPAC), and to determine the impact of controlled drainage on drain flow using the filled dataset. The shape of the drain flow-water table height relationship was found to depend on the selected hydraulic conductivity profile. Estimated drain flow using the Hooghoudt equation with measured water table height for both free draining and controlled periods compared well to observed flow with Nash-Sutcliffe Efficiency values above 0.7 and 0.8 for calibration and validation periods, respectively. Using this method, together with linear regression for the remaining gaps, a long-term drain flow record for a controlled drainage experiment at the DPAC was used to evaluate the impacts of controlled drainage on drain flow. In the controlled drainage sites, annual flow was 14-49% lower than free drainage.

Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound

NASA Astrophysics Data System (ADS)

Perelomova, Anna

2006-08-01

The equation of energy balance is subdivided into two dynamics equations, one describing evolution of the dominative sound, and the second one responsible for acoustic heating. The first one is the famous KZK equation, and the second one is a novel equation governing acoustic heating. The novel dynamic equation considers both periodic and non-periodic sound. Quasi-plane geometry of flow is supposed. Subdividing is provided on the base of specific links of every mode. Media with arbitrary thermic T(p,ρ) and caloric e(p,ρ) equations of state are considered. Individual roles of thermal conductivity and viscosity in the heating induced by aperiodic sound in the ideal gases and media different from ideal gases are discussed.

On homogeneous second order linear general quantum difference equations.

PubMed

Faried, Nashat; Shehata, Enas M; El Zafarani, Rasha M

2017-01-01

In this paper, we prove the existence and uniqueness of solutions of the β -Cauchy problem of second order β -difference equations [Formula: see text] [Formula: see text], in a neighborhood of the unique fixed point [Formula: see text] of the strictly increasing continuous function β , defined on an interval [Formula: see text]. These equations are based on the general quantum difference operator [Formula: see text], which is defined by [Formula: see text], [Formula: see text]. We also construct a fundamental set of solutions for the second order linear homogeneous β -difference equations when the coefficients are constants and study the different cases of the roots of their characteristic equations. Finally, we drive the Euler-Cauchy β -difference equation.

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

NASA Astrophysics Data System (ADS)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

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.

A high performance linear equation solver on the VPP500 parallel supercomputer

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

Nakanishi, Makoto; Ina, Hiroshi; Miura, Kenichi

1994-12-31

This paper describes the implementation of two high performance linear equation solvers developed for the Fujitsu VPP500, a distributed memory parallel supercomputer system. The solvers take advantage of the key architectural features of VPP500--(1) scalability for an arbitrary number of processors up to 222 processors, (2) flexible data transfer among processors provided by a crossbar interconnection network, (3) vector processing capability on each processor, and (4) overlapped computation and transfer. The general linear equation solver based on the blocked LU decomposition method achieves 120.0 GFLOPS performance with 100 processors in the LIN-PACK Highly Parallel Computing benchmark.

Toward the prevention of childhood undernutrition: diet diversity strategies using locally produced food can overcome gaps in nutrient supply.

PubMed

Parlesak, Alexandr; Geelhoed, Diederike; Robertson, Aileen

2014-06-01

Chronic undernutrition is prevalent in Mozambique, where children suffer from stunting, vitamin A deficiency, anemia, and other nutrition-related disorders. Complete diet formulation products (CDFPs) are increasingly promoted to prevent chronic undernutrition. Using linear programming, to investigate whether diet diversification using local foods should be prioritized in order to reduce the prevalence of chronic undernutrition. Market prices of local foods were collected in Tete City, Mozambique. Linear programming was applied to calculate the cheapest possible fully nutritious food baskets (FNFB) by stepwise addition of micronutrient-dense localfoods. Only the top quintile of Mozambican households, using average expenditure data, could afford the FNFB that was designed using linear programming from a spectrum of local standard foods. The addition of beef heart or liver, dried fish and fresh moringa leaves, before applying linear programming decreased the price by a factor of up to 2.6. As a result, the top three quintiles could afford the FNFB optimized using both diversification strategy and linear programming. CDFPs, when added to the baskets, were unable to overcome the micronutrient gaps without greatly exceeding recommended energy intakes, due to their high ratio of energy to micronutrient density. Dietary diversification strategies using local, low-cost, nutrient-dense foods can meet all micronutrient recommendations and overcome all micronutrient gaps. The success of linear programming to identify a low-cost FNFB depends entirely on the investigators' ability to select appropriate micronutrient-dense foods. CDFPs added to food baskets are unable to overcome micronutrient gaps without greatly exceeding recommended energy intake.

Dark gap solitons in exciton-polariton condensates in a periodic potential.

PubMed

Cheng, Szu-Cheng; Chen, Ting-Wei

2018-03-01

We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.

Dark gap solitons in exciton-polariton condensates in a periodic potential

NASA Astrophysics Data System (ADS)

Cheng, Szu-Cheng; Chen, Ting-Wei

2018-03-01

We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.

A Common Mechanism for Resistance to Oxime Reactivation of Acetylcholinesterase Inhibited by Organophosphorus Compounds

DTIC Science & Technology

2013-01-01

application of the Hammett equation with the constants rph in the chemistry of organophosphorus compounds, Russ. Chem. Rev. 38 (1969) 795–811. [13...of oximes and OP compounds and the ability of oximes to reactivate OP- inhibited AChE. Multiple linear regression equations were analyzed using...phosphonate pairs, 21 oxime/ phosphoramidate pairs and 12 oxime/phosphate pairs. The best linear regression equation resulting from multiple regression anal

When is quasi-linear theory exact. [particle acceleration

NASA Technical Reports Server (NTRS)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

Bridging the Gap Between Stationary Homogeneous Isotropic Turbulence and Quantum Mechanics

NASA Astrophysics Data System (ADS)

Sohrab, Siavash

A statistical theory of stationary isotropic turbulence is presented with eddies possessing Gaussian velocity distribution, Maxwell-Boltzmann speed distribution in harmony with perceptions of Heisenberg, and Planck energy distribution in harmony with perceptions of Chandrasekhar and in agreement with experimental observations of Van Atta and Chen. Defining the action S = - mΦ in terms of velocity potential of atomic motion, scale-invariant Schrödinger equation is derivedfrom invariant Bernoulli equation. Thus, the gap between the problems of turbulence and quantum mechanics is closed through connections between Cauchy-Euler-Bernoulli equations of hydrodynamics, Hamilton-Jacobi equation of classical mechanics, and finally Schrödinger equation of quantum mechanics. Transitions of particle (molecular cluster cji) from a small rapidly-oscillating eddy ej (high-energy level-j) to a large slowly-oscillating eddy ei (low energy-level-i) leads to emission of a sub-particle (molecule mji) that carries away the excess energy ɛji = h (νj -νi) in harmony with Bohr theory of atomic spectra. ∖ ∖ NASA Grant No. NAG3-1863.

Method of Conjugate Radii for Solving Linear and Nonlinear Systems

NASA Technical Reports Server (NTRS)

Nachtsheim, Philip R.

1999-01-01

This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

Abel's Theorem Simplifies Reduction of Order

ERIC Educational Resources Information Center

Green, William R.

2011-01-01

We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.

Nonlinear magnetoacoustic wave propagation with chemical reactions

NASA Astrophysics Data System (ADS)

Margulies, Timothy Scott

2002-11-01

The magnetoacoustic problem with an application to sound wave propagation through electrically conducting fluids such as the ocean in the Earth's magnetic field, liquid metals, or plasmas has been addressed taking into account several simultaneous chemical reactions. Using continuum balance equations for the total mass, linear momentum, energy; as well as Maxwell's electrodynamic equations, a nonlinear beam equation has been developed to generalize the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a fluid with linear viscosity but nonlinear and diffraction effects. Thermodynamic parameters are used and not tailored to only an adiabatic fluid case. The chemical kinetic equations build on a relaxing media approach presented, for example, by K. Naugolnukh and L. Ostrovsky [Nonlinear Wave Processes in Acoustics (Cambridge Univ. Press, Cambridge, 1998)] for a linearized single reaction and thermodynamic pressure equation of state. Approximations for large and small relaxation times and for magnetohydrodynamic parameters [Korsunskii, Sov. Phys. Acoust. 36 (1990)] are examined. Additionally, Cattaneo's equation for heat conduction and its generalization for a memory process rather than a Fourier's law are taken into account. It was introduced for the heat flux depends on the temperature gradient at an earlier time to generate heat pulses of finite speed.

Turbulence model sensitivity and scour gap effect of unsteady flow around pipe: a CFD study.

PubMed

Ali, Abbod; Sharma, R K; Ganesan, P; Akib, Shatirah

2014-01-01

A numerical investigation of incompressible and transient flow around circular pipe has been carried out at different five gap phases. Flow equations such as Navier-Stokes and continuity equations have been solved using finite volume method. Unsteady horizontal velocity and kinetic energy square root profiles are plotted using different turbulence models and their sensitivity is checked against published experimental results. Flow parameters such as horizontal velocity under pipe, pressure coefficient, wall shear stress, drag coefficient, and lift coefficient are studied and presented graphically to investigate the flow behavior around an immovable pipe and scoured bed.

Optimal Control for Stochastic Delay Evolution Equations

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

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

A critical review and database of biomass and volume allometric equation for trees and shrubs of Bangladesh

NASA Astrophysics Data System (ADS)

Mahmood, H.; Siddique, M. R. H.; Akhter, M.

2016-08-01

Estimations of biomass, volume and carbon stock are important in the decision making process for the sustainable management of a forest. These estimations can be conducted by using available allometric equations of biomass and volume. Present study aims to: i. develop a compilation with verified allometric equations of biomass, volume, and carbon for trees and shrubs of Bangladesh, ii. find out the gaps and scope for further development of allometric equations for different trees and shrubs of Bangladesh. Key stakeholders (government departments, research organizations, academic institutions, and potential individual researchers) were identified considering their involvement in use and development of allometric equations. A list of documents containing allometric equations was prepared from secondary sources. The documents were collected, examined, and sorted to avoid repetition, yielding 50 documents. These equations were tested through a quality control scheme involving operational verification, conceptual verification, applicability, and statistical credibility. A total of 517 allometric equations for 80 species of trees, shrubs, palm, and bamboo were recorded. In addition, 222 allometric equations for 39 species were validated through the quality control scheme. Among the verified equations, 20%, 12% and 62% of equations were for green-biomass, oven-dried biomass, and volume respectively and 4 tree species contributed 37% of the total verified equations. Five gaps have been pinpointed for the existing allometric equations of Bangladesh: a. little work on allometric equation of common tree and shrub species, b. most of the works were concentrated on certain species, c. very little proportion of allometric equations for biomass estimation, d. no allometric equation for belowground biomass and carbon estimation, and d. lower proportion of valid allometric equations. It is recommended that site and species specific allometric equations should be developed and consistency in field sampling, sample processing, data recording and selection of allometric equations should be maintained to ensure accuracy in estimation of biomass, volume, and carbon stock in different forest types of Bangladesh.

A multiple linear regression analysis of hot corrosion attack on a series of nickel base turbine alloys

NASA Technical Reports Server (NTRS)

Barrett, C. A.

1985-01-01

Multiple linear regression analysis was used to determine an equation for estimating hot corrosion attack for a series of Ni base cast turbine alloys. The U transform (i.e., 1/sin (% A/100) to the 1/2) was shown to give the best estimate of the dependent variable, y. A complete second degree equation is described for the centered" weight chemistries for the elements Cr, Al, Ti, Mo, W, Cb, Ta, and Co. In addition linear terms for the minor elements C, B, and Zr were added for a basic 47 term equation. The best reduced equation was determined by the stepwise selection method with essentially 13 terms. The Cr term was found to be the most important accounting for 60 percent of the explained variability hot corrosion attack.

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.

Teaching Linear Equations: Case Studies from Finland, Flanders and Hungary

ERIC Educational Resources Information Center

Andrews, Paul; Sayers, Judy

2012-01-01

In this paper we compare how three teachers, one from each of Finland, Flanders and Hungary, introduce linear equations to grade 8 students. Five successive lessons were videotaped and analysed qualitatively to determine how teachers, each of whom was defined against local criteria as effective, addressed various literature-derived…

Discovering Linear Equations in Explicit Tables

ERIC Educational Resources Information Center

Burton, Lauren

2017-01-01

When teaching algebra concepts to middle school students, the author often hears questions that echo her own past confusion as a young student learning to write linear equations using data tables that show only input and output values. Students, expected to synthesize the relationship between these values in symbolic representation, grow…

Observed Score Linear Equating with Covariates

ERIC Educational Resources Information Center

Branberg, Kenny; Wiberg, Marie

2011-01-01

This paper examined observed score linear equating in two different data collection designs, the equivalent groups design and the nonequivalent groups design, when information from covariates (i.e., background variables correlated with the test scores) was included. The main purpose of the study was to examine the effect (i.e., bias, variance, and…

From Arithmetic Sequences to Linear Equations

ERIC Educational Resources Information Center

Matsuura, Ryota; Harless, Patrick

2012-01-01

The first part of the article focuses on deriving the essential properties of arithmetic sequences by appealing to students' sense making and reasoning. The second part describes how to guide students to translate their knowledge of arithmetic sequences into an understanding of linear equations. Ryota Matsuura originally wrote these lessons for…

On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

2018-04-01

We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

NASA Astrophysics Data System (ADS)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

Numerical Analysis of a Class of THM Coupled Model for Porous Materials

NASA Astrophysics Data System (ADS)

Liu, Tangwei; Zhou, Jingying; Lu, Hongzhi

2018-01-01

We consider the coupled models of the Thermo-hydro-mechanical (THM) problem for porous materials which arises in many engineering applications. Firstly, mathematical models of the THM coupled problem for porous materials were discussed. Secondly, for different cases, some numerical difference schemes of coupled model were constructed, respectively. Finally, aassuming that the original water vapour effect is neglectable and that the volume fraction of liquid phase and the solid phase are constants, the nonlinear equations can be reduced to linear equations. The discrete equations corresponding to the linear equations were solved by the Arnodli method.

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

Algebraic methods are used to construct the exact solution P of the linear matrix equation PA + BP = - C, where A, B, and C are matrices with real entries. The emphasis of this equation is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The paper is divided into six sections which include the proof of the basic lemma, the Liapunov equation, and the computer implementation for the rational, integer and modular algorithms. Two numerical examples are given and the entire calculation process is depicted.

Gyro-Landau fluid models for toroidal geometry

NASA Astrophysics Data System (ADS)

Waltz, R. E.; Dominguez, R. R.; Hammett, G. W.

1992-10-01

Gyro-Landau fluid model equations provide first-order time advancement for a limited number of moments of the gyrokinetic equation, while approximately preserving the effects of the gyroradius averaging and Landau damping. This paper extends the work of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for electrostatic motion parallel to the magnetic field and E×B motion to include the gyroaveraging linearly and the curvature drift motion. The equations are tested by comparing the ion-temperature-gradient mode linear growth rates for the model equations with those of the exact gyrokinetic theory over a full range of parameters.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

The application of MINIQUASI to thermal program boundary and initial value problems

NASA Technical Reports Server (NTRS)

1974-01-01

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

Comparison of linear and non-linear method in estimating the sorption isotherm parameters for safranin onto activated carbon.

PubMed

Kumar, K Vasanth; Sivanesan, S

2005-08-31

Comparison analysis of linear least square method and non-linear method for estimating the isotherm parameters was made using the experimental equilibrium data of safranin onto activated carbon at two different solution temperatures 305 and 313 K. Equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherm equations. All the three isotherm equations showed a better fit to the experimental equilibrium data. The results showed that non-linear method could be a better way to obtain the isotherm parameters. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity.

Glottal flow through a two-mass model: comparison of Navier-Stokes solutions with simplified models.

PubMed

de Vries, M P; Schutte, H K; Veldman, A E P; Verkerke, G J

2002-04-01

A new numerical model of the vocal folds is presented based on the well-known two-mass models of the vocal folds. The two-mass model is coupled to a model of glottal airflow based on the incompressible Navier-Stokes equations. Glottal waves are produced using different initial glottal gaps and different subglottal pressures. Fundamental frequency, glottal peak flow, and closed phase of the glottal waves have been compared with values known from the literature. The phonation threshold pressure was determined for different initial glottal gaps. The phonation threshold pressure obtained using the flow model with Navier-Stokes equations corresponds better to values determined in normal phonation than the phonation threshold pressure obtained using the flow model based on the Bernoulli equation. Using the Navier-Stokes equations, an increase of the subglottal pressure causes the fundamental frequency and the glottal peak flow to increase, whereas the fundamental frequency in the Bernoulli-based model does not change with increasing pressure.

Electromagnetic momentum and the energy–momentum tensor in a linear medium with magnetic and dielectric properties

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

Crenshaw, Michael E., E-mail: michael.e.crenshaw4.civ@mail.mil

2014-04-15

In a continuum setting, the energy–momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy–momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derivemore » electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material four-divergence of the traceless, symmetric total energy–momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the Abraham–Minkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy–momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.« less

New Galerkin operational matrices for solving Lane-Emden type equations

NASA Astrophysics Data System (ADS)

Abd-Elhameed, W. M.; Doha, E. H.; Saad, A. S.; Bassuony, M. A.

2016-04-01

Lane-Emden type equations model many phenomena in mathematical physics and astrophysics, such as thermal explosions. This paper is concerned with introducing third and fourth kind Chebyshev-Galerkin operational matrices in order to solve such problems. The principal idea behind the suggested algorithms is based on converting the linear or nonlinear Lane-Emden problem, through the application of suitable spectral methods, into a system of linear or nonlinear equations in the expansion coefficients, which can be efficiently solved. The main advantage of the proposed algorithm in the linear case is that the resulting linear systems are specially structured, and this of course reduces the computational effort required to solve such systems. As an application, we consider the solar model polytrope with n=3 to show that the suggested solutions in this paper are in good agreement with the numerical results.

Examining longitudinal train dynamics in ore car tipplers

NASA Astrophysics Data System (ADS)

Cole, Colin; Spiryagin, Maksym; Bosomworth, Chris

2017-04-01

Train simulation has been adapted in this paper to model the behaviour of indexing operations in ore car tippler operations. An important consideration in simulations at these low speeds (less than 4 km/h) is the increased rolling resistance transitioning from stationary conditions to motion. Most formulations of rolling resistance equations do not include this range although there are empirical values in some railway standards. The indexer control utilised here has a target trapezoidal velocity profile. The indexer to train connection was modelled as a stiff linear spring, a damper and a gap element. A sensitivity analysis was completed considering variations in wagon connections including wedge static friction, preload, coupling slack and tippler slack. Track topography including downhill grades of 0.1% and 0.2% and a valley profile were also investigated. Results showed high sensitivity to draft gear parameters of static friction and preload, but minimal benefit from downhill grades and changes in coupling slack.

A conformal approach for the analysis of the non-linear stability of radiation cosmologies

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

Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk; Department of Mathematics, University of Leicester, University Road, LE1 8RH; Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk

2013-01-15

The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.

Systems of Inhomogeneous Linear Equations

NASA Astrophysics Data System (ADS)

Scherer, Philipp O. J.

Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

A Zonal Approach for Prediction of Jet Noise

NASA Technical Reports Server (NTRS)

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

1995-01-01

A zonal approach for direct computation of sound generation and propagation from a supersonic jet is investigated. The present work splits the computational domain into a nonlinear, acoustic-source regime and a linear acoustic wave propagation regime. In the nonlinear regime, the unsteady flow is governed by the large-scale equations, which are the filtered compressible Navier-Stokes equations. In the linear acoustic regime, the sound wave propagation is described by the linearized Euler equations. Computational results are presented for a supersonic jet at M = 2. 1. It is demonstrated that no spurious modes are generated in the matching region and the computational expense is reduced substantially as opposed to fully large-scale simulation.

Simple linear and multivariate regression models.

PubMed

Rodríguez del Águila, M M; Benítez-Parejo, N

2011-01-01

In biomedical research it is common to find problems in which we wish to relate a response variable to one or more variables capable of describing the behaviour of the former variable by means of mathematical models. Regression techniques are used to this effect, in which an equation is determined relating the two variables. While such equations can have different forms, linear equations are the most widely used form and are easy to interpret. The present article describes simple and multiple linear regression models, how they are calculated, and how their applicability assumptions are checked. Illustrative examples are provided, based on the use of the freely accessible R program. Copyright © 2011 SEICAP. Published by Elsevier Espana. All rights reserved.

Simple Derivation of the Lindblad Equation

ERIC Educational Resources Information Center

Pearle, Philip

2012-01-01

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

Northeastern forest survey revised cubic-foot volume equations

Treesearch

Charles T. Scott

1981-01-01

Cubic-foot volume equations are presented for the 17 species groups used in the forest survey of the 14 northeastern states. The previous cubic- foot volume equations were simple linear in form; the revised cubic-foot volume equations are nonlinear.

Isotherm investigation for the sorption of fluoride onto Bio-F: comparison of linear and non-linear regression method

NASA Astrophysics Data System (ADS)

Yadav, Manish; Singh, Nitin Kumar

2017-12-01

A comparison of the linear and non-linear regression method in selecting the optimum isotherm among three most commonly used adsorption isotherms (Langmuir, Freundlich, and Redlich-Peterson) was made to the experimental data of fluoride (F) sorption onto Bio-F at a solution temperature of 30 ± 1 °C. The coefficient of correlation (r2) was used to select the best theoretical isotherm among the investigated ones. A total of four Langmuir linear equations were discussed and out of which linear form of most popular Langmuir-1 and Langmuir-2 showed the higher coefficient of determination (0.976 and 0.989) as compared to other Langmuir linear equations. Freundlich and Redlich-Peterson isotherms showed a better fit to the experimental data in linear least-square method, while in non-linear method Redlich-Peterson isotherm equations showed the best fit to the tested data set. The present study showed that the non-linear method could be a better way to obtain the isotherm parameters and represent the most suitable isotherm. Redlich-Peterson isotherm was found to be the best representative (r2 = 0.999) for this sorption system. It is also observed that the values of β are not close to unity, which means the isotherms are approaching the Freundlich but not the Langmuir isotherm.

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Shape in Picture: Mathematical Description of Shape in Grey-Level Images

DTIC Science & Technology

1992-09-11

representation is scale-space, derived frrr- the linear isotropic diffusion equation; recently other types of equations have been considered. Multiscale...recognition of dimensions in the general case of an arbitrary denominator is similar to that just explained. 3 Linear Inequalities in the Two-Dimensional...solid region containing all pixels of the space, whose coordinates satisfy a linear inequality. A Um C scspt fr Digital Geometry 41 s a a v--’ -0 7 O

Small-Caliber Projectile Target Impact Angle Determined From Close Proximity Radiographs

DTIC Science & Technology

2006-10-01

discrete motion data that can be numerically modeled using linear aerodynamic theory or 6-degrees-of- freedom equations of motion. The values of Fφ...Prediction Excel® Spreadsheet shown in figure 9. The Gamma at Impact Spreadsheet uses the linear aerodynamics model , equations 5 and 6, to calculate αT...trajectory angle error via consideration of the RMS fit errors of the actual firings. However, the linear aerodynamics model does not include this effect

Aircraft Airframe Cost Estimation Using a Random Coefficients Model

DTIC Science & Technology

1979-12-01

approach will also be used here. 2 Model Formulation Several different types of equations could be used for the basic form of the CER, such as linear ...5) Marcotte developed several CER’s for fighter aircraft airframes using the log- linear model . A plot of the residuals from the CER for recurring...of the natural logarithm. Ordinary Least Squares The ordinary least squares procedure starts with the equation for the general linear model . The

Determination of strong ion gap in healthy dogs.

PubMed

Fettig, Pamela K; Bailey, Dennis B; Gannon, Kristi M

2012-08-01

To determine and compare reference intervals of the strong ion gap (SIG) in a group of healthy dogs determined with 2 different equations. Prospective observational study. Tertiary referral and teaching hospital. Fifty-four healthy dogs. None. Serum biochemistry and blood gas analyses were performed for each dog. From these values, SIG was calculated using 2 different equations: SIG(1) = SID(a) {[Na (+)] + [K(+)] - [Cl(-)]+ [2 × Ca(2+)] + [2 × Mg(2+)] - [L-lactate]}- SID(e) {TCO(2) + A(-)} and SIG(2) = [albumin] × 4.9-anion gap. Reference intervals were established for each SIG equation using the mean ± 1.96 × standard deviation (SD). For SIG(1), the median was 7.13 mEq/L (range, 1.05-11.30 mEq/L) and the derived reference interval was 1.85-10.61 mEq/L. Median SIG(2) was -0.22 mEq/L (range, -5.34-6.61 mEq/L) and the mean SIG(2) was -0.09 mEq/L (95% confidence interval for the mean, -0.82-0.65 mEq/L). The derived reference interval was -5.36-5.18 mEq/L. The results of the SIG calculations were significantly different (P < 0.0001) between the 2 equations used. The 2 equations used to calculate SIG yielded significantly different results and cannot be used interchangeably. The authors believe SIG(2) to be a more accurate reflection of acid-base status in healthy dogs, and recommend that this calculation be used for future studies. © Veterinary Emergency and Critical Care Society 2012.

Linear network representation of multistate models of transport.

PubMed Central

Sandblom, J; Ring, A; Eisenman, G

1982-01-01

By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models. PMID:7093425

Runge-Kutta Methods for Linear Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Zingg, David W.; Chisholm, Todd T.

1997-01-01

Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

A Brief Historical Introduction to Matrices and Their Applications

ERIC Educational Resources Information Center

Debnath, L.

2014-01-01

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

Modelling and Inverse-Modelling: Experiences with O.D.E. Linear Systems in Engineering Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor

2009-01-01

In engineering careers courses, differential equations are widely used to solve problems concerned with modelling. In particular, ordinary differential equations (O.D.E.) linear systems appear regularly in Chemical Engineering, Food Technology Engineering and Environmental Engineering courses, due to the usefulness in modelling chemical kinetics,…

The Multifaceted Variable Approach: Selection of Method in Solving Simple Linear Equations

ERIC Educational Resources Information Center

Tahir, Salma; Cavanagh, Michael

2010-01-01

This paper presents a comparison of the solution strategies used by two groups of Year 8 students as they solved linear equations. The experimental group studied algebra following a multifaceted variable approach, while the comparison group used a traditional approach. Students in the experimental group employed different solution strategies,…

Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations

ERIC Educational Resources Information Center

Rasmussen, Chris; Keynes, Michael

2003-01-01

The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant coefficients. The significance of this paper is two-fold. First, it represents an innovative alternative…

Solving rational matrix equations in the state space with applications to computer-aided control-system design

NASA Technical Reports Server (NTRS)

Packard, A. K.; Sastry, S. S.

1986-01-01

A method of solving a class of linear matrix equations over various rings is proposed, using results from linear geometric control theory. An algorithm, successfully implemented, is presented, along with non-trivial numerical examples. Applications of the method to the algebraic control system design methodology are discussed.

Three Interpretations of the Matrix Equation Ax = b

ERIC Educational Resources Information Center

Larson, Christine; Zandieh, Michelle

2013-01-01

Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

Secondary Pre-Service Teachers' Algebraic Reasoning about Linear Equation Solving

ERIC Educational Resources Information Center

Alvey, Christina; Hudson, Rick A.; Newton, Jill; Males, Lorraine M.

2016-01-01

This study analyzes the responses of 12 secondary pre-service teachers on two tasks focused on reasoning when solving linear equations. By documenting the choices PSTs made while engaging in these tasks, we gain insight into how new teachers work mathematically, reason algebraically, communicate their thinking, and make pedagogical decisions. We…

Synthesizing Strategies Creatively: Solving Linear Equations

ERIC Educational Resources Information Center

Ponce, Gregorio A.; Tuba, Imre

2015-01-01

New strategies can ignite teachers' imagination to create new lessons or adapt lessons created by others. In this article, the authors present the experience of an algebra teacher and his students solving linear and literal equations and explain how the use of ideas found in past NCTM journals helped bring this lesson to life. The…

HIFU procedures at moderate intensities--effect of large blood vessels.

PubMed

Hariharan, P; Myers, M R; Banerjee, R K

2007-06-21

A three-dimensional computational model is presented for studying the efficacy of high-intensity focused ultrasound (HIFU) procedures targeted near large blood vessels. The analysis applies to procedures performed at intensities below the threshold for cavitation, boiling and highly nonlinear propagation, but high enough to increase tissue temperature a few degrees per second. The model is based upon the linearized KZK equation and the bioheat equation in tissue. In the blood vessel the momentum and energy equations are satisfied. The model is first validated in a tissue phantom, to verify the absence of bubble formation and nonlinear effects. Temperature rise and lesion-volume calculations are then shown for different beam locations and orientations relative to a large vessel. Both single and multiple ablations are considered. Results show that when the vessel is located within about a beam width (few mm) of the ultrasound beam, significant reduction in lesion volume is observed due to blood flow. However, for gaps larger than a beam width, blood flow has no major effect on the lesion formation. Under the clinically representative conditions considered, the lesion volume is reduced about 40% (relative to the no-flow case) when the beam is parallel to the blood vessel, compared to about 20% for a perpendicular orientation. Procedures involving multiple ablation sites are affected less by blood flow than single ablations. The model also suggests that optimally focused transducers can generate lesions that are significantly larger (>2 times) than the ones produced by highly focused beams.

HIFU procedures at moderate intensities—effect of large blood vessels

NASA Astrophysics Data System (ADS)

Hariharan, P.; Myers, M. R.; Banerjee, R. K.

2007-07-01

A three-dimensional computational model is presented for studying the efficacy of high-intensity focused ultrasound (HIFU) procedures targeted near large blood vessels. The analysis applies to procedures performed at intensities below the threshold for cavitation, boiling and highly nonlinear propagation, but high enough to increase tissue temperature a few degrees per second. The model is based upon the linearized KZK equation and the bioheat equation in tissue. In the blood vessel the momentum and energy equations are satisfied. The model is first validated in a tissue phantom, to verify the absence of bubble formation and nonlinear effects. Temperature rise and lesion-volume calculations are then shown for different beam locations and orientations relative to a large vessel. Both single and multiple ablations are considered. Results show that when the vessel is located within about a beam width (few mm) of the ultrasound beam, significant reduction in lesion volume is observed due to blood flow. However, for gaps larger than a beam width, blood flow has no major effect on the lesion formation. Under the clinically representative conditions considered, the lesion volume is reduced about 40% (relative to the no-flow case) when the beam is parallel to the blood vessel, compared to about 20% for a perpendicular orientation. Procedures involving multiple ablation sites are affected less by blood flow than single ablations. The model also suggests that optimally focused transducers can generate lesions that are significantly larger (>2 times) than the ones produced by highly focused beams.

A new Newton-like method for solving nonlinear equations.

PubMed

Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

2016-01-01

This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

An approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives

NASA Technical Reports Server (NTRS)

Korivi, V. M.; Taylor, A. C., III; Newman, P. A.; Hou, G. J.-W.; Jones, H. E.

1992-01-01

An incremental strategy is presented for iteratively solving very large systems of linear equations, which are associated with aerodynamic sensitivity derivatives for advanced CFD codes. It is shown that the left-hand side matrix operator and the well-known factorization algorithm used to solve the nonlinear flow equations can also be used to efficiently solve the linear sensitivity equations. Two airfoil problems are considered as an example: subsonic low Reynolds number laminar flow and transonic high Reynolds number turbulent flow.

Computer programs for the solution of systems of linear algebraic equations

NASA Technical Reports Server (NTRS)

Sequi, W. T.

1973-01-01

FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

Time domain convergence properties of Lyapunov stable penalty methods

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Sunkel, John

1991-01-01

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

Local projection stabilization for linearized Brinkman-Forchheimer-Darcy equation

NASA Astrophysics Data System (ADS)

Skrzypacz, Piotr

2017-09-01

The Local Projection Stabilization (LPS) is presented for the linearized Brinkman-Forchheimer-Darcy equation with high Reynolds numbers. The considered equation can be used to model porous medium flows in chemical reactors of packed bed type. The detailed finite element analysis is presented for the case of nonconstant porosity. The enriched variant of LPS is based on the equal order interpolation for the velocity and pressure. The optimal error bounds for the velocity and pressure errors are justified numerically.

Conservation properties of numerical integration methods for systems of ordinary differential equations

NASA Technical Reports Server (NTRS)

Rosenbaum, J. S.

1976-01-01

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

From Feynman rules to conserved quantum numbers, I

NASA Astrophysics Data System (ADS)

Nogueira, P.

2017-05-01

In the context of Quantum Field Theory (QFT) there is often the need to find sets of graph-like diagrams (the so-called Feynman diagrams) for a given physical model. If negative, the answer to the related problem 'Are there any diagrams with this set of external fields?' may settle certain physical questions at once. Here the latter problem is formulated in terms of a system of linear diophantine equations derived from the Lagrangian density, from which necessary conditions for the existence of the required diagrams may be obtained. Those conditions are equalities that look like either linear diophantine equations or linear modular (i.e. congruence) equations, and may be found by means of fairly simple algorithms that involve integer computations. The diophantine equations so obtained represent (particle) number conservation rules, and are related to the conserved (additive) quantum numbers that may be assigned to the fields of the model.

The linear Boltzmann equation in slab geometry - Development and verification of a reliable and efficient solution

NASA Technical Reports Server (NTRS)

Stamnes, K.; Lie-Svendsen, O.; Rees, M. H.

1991-01-01

The linear Boltzmann equation can be cast in a form mathematically identical to the radiation-transport equation. A multigroup procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative-transfer problem, and existing software is used to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well-suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of the formalism to include external forces and spherical geometry are also feasible.

SC-GRAPPA: Self-constraint noniterative GRAPPA reconstruction with closed-form solution.

PubMed

Ding, Yu; Xue, Hui; Ahmad, Rizwan; Ting, Samuel T; Simonetti, Orlando P

2012-12-01

Parallel MRI (pMRI) reconstruction techniques are commonly used to reduce scan time by undersampling the k-space data. GRAPPA, a k-space based pMRI technique, is widely used clinically because of its robustness. In GRAPPA, the missing k-space data are estimated by solving a set of linear equations; however, this set of equations does not take advantage of the correlations within the missing k-space data. All k-space data in a neighborhood acquired from a phased-array coil are correlated. The correlation can be estimated easily as a self-constraint condition, and formulated as an extra set of linear equations to improve the performance of GRAPPA. The authors propose a modified k-space based pMRI technique called self-constraint GRAPPA (SC-GRAPPA) which combines the linear equations of GRAPPA with these extra equations to solve for the missing k-space data. Since SC-GRAPPA utilizes a least-squares solution of the linear equations, it has a closed-form solution that does not require an iterative solver. The SC-GRAPPA equation was derived by incorporating GRAPPA as a prior estimate. SC-GRAPPA was tested in a uniform phantom and two normal volunteers. MR real-time cardiac cine images with acceleration rate 5 and 6 were reconstructed using GRAPPA and SC-GRAPPA. SC-GRAPPA showed a significantly lower artifact level, and a greater than 10% overall signal-to-noise ratio (SNR) gain over GRAPPA, with more significant SNR gain observed in low-SNR regions of the images. SC-GRAPPA offers improved pMRI reconstruction, and is expected to benefit clinical imaging applications in the future.

ML 3.0 smoothed aggregation user's guide.

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

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-05-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Az = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the AZTEC 2.1 and AZTECOO iterative package [15]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

ML 3.1 smoothed aggregation user's guide.

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

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-10-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the Aztec 2.1 and AztecOO iterative package [16]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and nonsymmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

Use of the Bethe equation for inner-shell ionization by electron impact

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

Powell, Cedric J.; Llovet, Xavier; Salvat, Francesc

2016-05-14

We analyzed calculated cross sections for K-, L-, and M-shell ionization by electron impact to determine the energy ranges over which these cross sections are consistent with the Bethe equation for inner-shell ionization. Our analysis was performed with K-shell ionization cross sections for 26 elements, with L-shell ionization cross sections for seven elements, L{sub 3}-subshell ionization cross sections for Xe, and M-shell ionization cross sections for three elements. The validity (or otherwise) of the Bethe equation could be checked with Fano plots based on a linearized form of the Bethe equation. Our Fano plots, which display theoretical cross sections andmore » available measured cross sections, reveal two linear regions as predicted by de Heer and Inokuti [in Electron Impact Ionization, edited by T. D. Märk and G. H. Dunn, (Springer-Verlag, Vienna, 1985), Chap. 7, pp. 232–276]. For each region, we made linear fits and determined values of the two element-specific Bethe parameters. We found systematic variations of these parameters with atomic number for both the low- and the high-energy linear regions of the Fano plots. We also determined the energy ranges over which the Bethe equation can be used.« less

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

NASA Astrophysics Data System (ADS)

Spannenberg, Jescica; Atangana, Abdon; Vermeulen, P. D.

2017-09-01

Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Nonlinearization and waves in bounded media: old wine in a new bottle

NASA Astrophysics Data System (ADS)

Mortell, Michael P.; Seymour, Brian R.

2017-02-01

We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.

Tori and chaos in a simple C1-system

NASA Astrophysics Data System (ADS)

Roessler, O. E.; Kahiert, C.; Ughleke, B.

A piecewise-linear autonomous 3-variable ordinary differential equation is presented which permits analytical modeling of chaotic attractors. A once-differentiable system of equations is defined which consists of two linear half-systems which meet along a threshold plane. The trajectories described by each equation is thereby continuous along the divide, forming a one-parameter family of invariant tori. The addition of a damping term produces a system of equations for various chaotic attractors. Extension of the system by means of a 4-variable generalization yields hypertori and hyperchaos. It is noted that the hierarchy established is amenable to analysis by the use of Poincare half-maps. Applications of the systems of ordinary differential equations to modeling turbulent flows are discussed.

Toxicity prediction of ionic liquids based on Daphnia magna by using density functional theory

NASA Astrophysics Data System (ADS)

Nu’aim, M. N.; Bustam, M. A.

2018-04-01

By using a model called density functional theory, the toxicity of ionic liquids can be predicted and forecast. It is a theory that allowing the researcher to have a substantial tool for computation of the quantum state of atoms, molecules and solids, and molecular dynamics which also known as computer simulation method. It can be done by using structural feature based quantum chemical reactivity descriptor. The identification of ionic liquids and its Log[EC50] data are from literature data that available in Ismail Hossain thesis entitled “Synthesis, Characterization and Quantitative Structure Toxicity Relationship of Imidazolium, Pyridinium and Ammonium Based Ionic Liquids”. Each cation and anion of the ionic liquids were optimized and calculated. The geometry optimization and calculation from the software, produce the value of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). From the value of HOMO and LUMO, the value for other toxicity descriptors were obtained according to their formulas. The toxicity descriptor that involves are electrophilicity index, HOMO, LUMO, energy gap, chemical potential, hardness and electronegativity. The interrelation between the descriptors are being determined by using a multiple linear regression (MLR). From this MLR, all descriptors being analyzed and the descriptors that are significant were chosen. In order to develop the finest model equation for toxicity prediction of ionic liquids, the selected descriptors that are significant were used. The validation of model equation was performed with the Log[EC50] data from the literature and the final model equation was developed. A bigger range of ionic liquids which nearly 108 of ionic liquids can be predicted from this model equation.

Turbulence Model Sensitivity and Scour Gap Effect of Unsteady Flow around Pipe: A CFD Study

PubMed Central

Ali, Abbod; Sharma, R. K.; Ganesan, P.

2014-01-01

A numerical investigation of incompressible and transient flow around circular pipe has been carried out at different five gap phases. Flow equations such as Navier-Stokes and continuity equations have been solved using finite volume method. Unsteady horizontal velocity and kinetic energy square root profiles are plotted using different turbulence models and their sensitivity is checked against published experimental results. Flow parameters such as horizontal velocity under pipe, pressure coefficient, wall shear stress, drag coefficient, and lift coefficient are studied and presented graphically to investigate the flow behavior around an immovable pipe and scoured bed. PMID:25136666

Electron-acoustic Instability Simulated By Modified Zakharov Equations

NASA Astrophysics Data System (ADS)

Jásenský, V.; Fiala, V.; Vána, O.; Trávnícek, P.; Hellinger, P.

We present non-linear equations describing processes in plasma when electron - acoustic waves are excited. These waves are present for instance in the vicinity of Earth's bow shock and in the polar ionosphere. Frequently they are excited by an elec- tron beam in a plasma with two electron populations, a cold and hot one. We derive modified Zakharov equations from kinetic theory for such a case together with numer- ical method for solving of this type of equations. Bispectral analysis is used to show which non-linear wave processes are of importance in course of the instability. Finally, we compare these results with similar simulations using Vlasov approach.

Conservation laws and conserved quantities for (1+1)D linearized Boussinesq equations

NASA Astrophysics Data System (ADS)

Carvalho, Cindy; Harley, Charis

2017-05-01

Conservation laws and physical conserved quantities for the (1+1)D linearized Boussinesq equations at a constant water depth are presented. These equations describe incompressible, inviscid, irrotational fluid flow in the form of a non steady solitary wave. A systematic multiplier approach is used to obtain the conservation laws of the system of third order partial differential equations (PDEs) in dimensional form. Physical conserved quantities are derived by integrating the conservation laws in the direction of wave propagation and imposing decaying boundary conditions in the horizontal direction. One of these is a newly discovered conserved quantity which relates to an energy flux density.

Linear transformation and oscillation criteria for Hamiltonian systems

NASA Astrophysics Data System (ADS)

Zheng, Zhaowen

2007-08-01

Using a linear transformation similar to the Kummer transformation, some new oscillation criteria for linear Hamiltonian systems are established. These results generalize and improve the oscillation criteria due to I.S. Kumari and S. Umanaheswaram [I. Sowjaya Kumari, S. Umanaheswaram, Oscillation criteria for linear matrix Hamiltonian systems, J. Differential Equations 165 (2000) 174-198], Q. Yang et al. [Q. Yang, R. Mathsen, S. Zhu, Oscillation theorems for self-adjoint matrix Hamiltonian systems, J. Differential Equations 190 (2003) 306-329], and S. Chen and Z. Zheng [Shaozhu Chen, Zhaowen Zheng, Oscillation criteria of Yan type for linear Hamiltonian systems, Comput. Math. Appl. 46 (2003) 855-862]. These criteria also unify many of known criteria in literature and simplify the proofs.

Bukhvostov-Lipatov model and quantum-classical duality

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

General equations for optimal selection of diagnostic image acquisition parameters in clinical X-ray imaging.

PubMed

Zheng, Xiaoming

2017-12-01

The purpose of this work was to examine the effects of relationship functions between diagnostic image quality and radiation dose on the governing equations for image acquisition parameter variations in X-ray imaging. Various equations were derived for the optimal selection of peak kilovoltage (kVp) and exposure parameter (milliAmpere second, mAs) in computed tomography (CT), computed radiography (CR), and direct digital radiography. Logistic, logarithmic, and linear functions were employed to establish the relationship between radiation dose and diagnostic image quality. The radiation dose to the patient, as a function of image acquisition parameters (kVp, mAs) and patient size (d), was used in radiation dose and image quality optimization. Both logistic and logarithmic functions resulted in the same governing equation for optimal selection of image acquisition parameters using a dose efficiency index. For image quality as a linear function of radiation dose, the same governing equation was derived from the linear relationship. The general equations should be used in guiding clinical X-ray imaging through optimal selection of image acquisition parameters. The radiation dose to the patient could be reduced from current levels in medical X-ray imaging.

Bright and dark gap solitons in a negative index Fabry-Pérot etalon.

PubMed

D'Aguanno, Giuseppe; Mattiucci, Nadia; Scalora, Michael; Bloemer, Mark J

2004-11-19

We predict the existence of bright and dark gap solitons in a single slab of negative index material. The formation of gap solitons is made possible by the exceptional interplay between the linear dispersive properties of the negative index etalon and the effect of a cubic nonlinearity.

Equilibrium, kinetics and process design of acid yellow 132 adsorption onto red pine sawdust.

PubMed

Can, Mustafa

2015-01-01

Linear and non-linear regression procedures have been applied to the Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich, and Redlich-Peterson isotherms for adsorption of acid yellow 132 (AY132) dye onto red pine (Pinus resinosa) sawdust. The effects of parameters such as particle size, stirring rate, contact time, dye concentration, adsorption dose, pH, and temperature were investigated, and interaction was characterized by Fourier transform infrared spectroscopy and field emission scanning electron microscope. The non-linear method of the Langmuir isotherm equation was found to be the best fitting model to the equilibrium data. The maximum monolayer adsorption capacity was found as 79.5 mg/g. The calculated thermodynamic results suggested that AY132 adsorption onto red pine sawdust was an exothermic, physisorption, and spontaneous process. Kinetics was analyzed by four different kinetic equations using non-linear regression analysis. The pseudo-second-order equation provides the best fit with experimental data.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Linearly exact parallel closures for slab geometry

NASA Astrophysics Data System (ADS)

Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun

2013-08-01

Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Improved pedagogy for linear differential equations by reconsidering how we measure the size of solutions

NASA Astrophysics Data System (ADS)

Tisdell, Christopher C.

2017-11-01

For over 50 years, the learning of teaching of a priori bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to a priori bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving second-order, linear problems with constant co-efficients, we believe it is not pedagogically optimal. Moreover, the Euclidean method becomes pedagogically unwieldy in the proofs involving higher-order cases. The purpose of this work is to propose a simpler pedagogical approach to establish a priori bounds on solutions by considering a different way of measuring the size of a solution to linear problems, which we refer to as the Uber size. The Uber form enables a simplification of pedagogy from the literature and the ideas are accessible to learners who have an understanding of the Fundamental Theorem of Calculus and the exponential function, both usually seen in a first course in calculus. We believe that this work will be of mathematical and pedagogical interest to those who are learning and teaching in the area of differential equations or in any of the numerous disciplines where linear differential equations are used.

Non-linear power spectra in the synchronous gauge

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

Hwang, Jai-chan; Noh, Hyerim; Jeong, Donghui

2015-05-01

We study the non-linear corrections to the matter and velocity power spectra in the synchronous gauge (SG). For the leading correction to the non-linear power spectra, we consider the perturbations up to third order in a zero-pressure fluid in a flat cosmological background. Although the equations in the SG happen to coincide with those in the comoving gauge (CG) to linear order, they differ from second order. In particular, the second order hydrodynamic equations in the SG are apparently in the Lagrangian form, whereas those in the CG are in the Eulerian form. The non-linear power spectra naively presented inmore » the original SG show rather pathological behavior quite different from the result of the Newtonian theory even on sub-horizon scales. We show that the pathology in the nonlinear power spectra is due to the absence of the convective terms in, thus the Lagrangian nature of, the SG. We show that there are many different ways of introducing the corrective convective terms in the SG equations. However, the convective terms (Eulerian modification) can be introduced only through gauge transformations to other gauges which should be the same as the CG to the second order. In our previous works we have shown that the density and velocity perturbation equations in the CG exactly coincide with the Newtonian equations to the second order, and the pure general relativistic correction terms starting to appear from the third order are substantially suppressed compared with the relativistic/Newtonian terms in the power spectra. As a result, we conclude that the SG per se is an inappropriate coordinate choice in handling the non-linear matter and velocity power spectra of the large-scale structure where observations meet with theories.« less

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

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

The Schrödinger–Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger–Langevin equation yields the complex quantum Hamilton–Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide.more » The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.« less

Standard Errors of Equating Differences: Prior Developments, Extensions, and Simulations

ERIC Educational Resources Information Center

Moses, Tim; Zhang, Wenmin

2011-01-01

The purpose of this article was to extend the use of standard errors for equated score differences (SEEDs) to traditional equating functions. The SEEDs are described in terms of their original proposal for kernel equating functions and extended so that SEEDs for traditional linear and traditional equipercentile equating functions can be computed.…

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

NASA Technical Reports Server (NTRS)

Mitchell, L. D.; David, J. W.

1983-01-01

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

An approximation of herd effect due to vaccinating children against seasonal influenza - a potential solution to the incorporation of indirect effects into static models.

PubMed

Van Vlaenderen, Ilse; Van Bellinghen, Laure-Anne; Meier, Genevieve; Nautrup, Barbara Poulsen

2013-01-22

Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination. Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals. The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation. This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses.

Color superconductivity from the chiral quark-meson model

NASA Astrophysics Data System (ADS)

Sedrakian, Armen; Tripolt, Ralf-Arno; Wambach, Jochen

2018-05-01

We study the two-flavor color superconductivity of low-temperature quark matter in the vicinity of chiral phase transition in the quark-meson model where the interactions between quarks are generated by pion and sigma exchanges. Starting from the Nambu-Gorkov propagator in real-time formulation we obtain finite temperature (real axis) Eliashberg-type equations for the quark self-energies (gap functions) in terms of the in-medium spectral function of mesons. Exact numerical solutions of the coupled nonlinear integral equations for the real and imaginary parts of the gap function are obtained in the zero temperature limit using a model input spectral function. We find that these components of the gap display a complicated structure with the real part being strongly suppressed above 2Δ0, where Δ0 is its on-shell value. We find Δ0 ≃ 40MeV close to the chiral phase transition.

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

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

Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp; Yamada, Michio; Chian, Abraham C.-L.

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originatemore » from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.« less

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation.

PubMed

Saiki, Yoshitaka; Yamada, Michio; Chian, Abraham C-L; Miranda, Rodrigo A; Rempel, Erico L

2015-10-01

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.

Frequency analysis via the method of moment functionals

NASA Technical Reports Server (NTRS)

Pearson, A. E.; Pan, J. Q.

1990-01-01

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Regularization of Grad’s 13 -Moment-Equations in Kinetic Gas Theory

DTIC Science & Technology

2011-01-01

variant of the moment method has been proposed by Eu (1980) and is used, e.g., in Myong (2001). Recently, a maximum- entropy 10-moment system has been used...small amplitude linear waves, the R13 system is linearly stable in time for all modes and wave lengths. The instability of the Burnett system indicates...Boltzmann equation. Related to the problem of global hyperbolicity is the questions of the existence of an entropy law for the R13 system . In the linear

A Maple package for computing Gröbner bases for linear recurrence relations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Robertz, Daniel

2006-04-01

A Maple package for computing Gröbner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for example, for automatic generation of difference schemes for linear partial differential equations and for reduction of multiloop Feynman integrals. These two possible applications are illustrated by simple examples of the Laplace equation and a one-loop scalar integral of propagator type.

N-soliton interactions: Effects of linear and nonlinear gain and loss

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Gerdjikov, V. S.; Todorov, M. D.

2017-10-01

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the nonlinear Schrödinger equation perturbed simultaneously by linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain in the case of a combination of linear, cubic, and/or quintic terms. We show that the soliton interactions dynamics for this reduced PCTC model compares favorably to full numerical results of the original perturbed nonlinear Schrödinger equation.

Computing anticipatory systems with incursion and hyperincursion

NASA Astrophysics Data System (ADS)

Dubois, Daniel M.

1998-07-01

An anticipatory system is a system which contains a model of itself and/or of its environment in view of computing its present state as a function of the prediction of the model. With the concepts of incursion and hyperincursion, anticipatory discrete systems can be modelled, simulated and controlled. By definition an incursion, an inclusive or implicit recursion, can be written as: x(t+1)=F[…,x(t-1),x(t),x(t+1),…] where the value of a variable x(t+1) at time t+1 is a function of this variable at past, present and future times. This is an extension of recursion. Hyperincursion is an incursion with multiple solutions. For example, chaos in the Pearl-Verhulst map model: x(t+1)=a.x(t).[1-x(t)] is controlled by the following anticipatory incursive model: x(t+1)=a.x(t).[1-x(t+1)] which corresponds to the differential anticipatory equation: dx(t)/dt=a.x(t).[1-x(t+1)]-x(t). The main part of this paper deals with the discretisation of differential equation systems of linear and non-linear oscillators. The non-linear oscillator is based on the Lotka-Volterra equations model. The discretisation is made by incursion. The incursive discrete equation system gives the same stability condition than the original differential equations without numerical instabilities. The linearisation of the incursive discrete non-linear Lotka-Volterra equation system gives rise to the classical harmonic oscillator. The incursive discretisation of the linear oscillator is similar to define backward and forward discrete derivatives. A generalized complex derivative is then considered and applied to the harmonic oscillator. Non-locality seems to be a property of anticipatory systems. With some mathematical assumption, the Schrödinger quantum equation is derived for a particle in a uniform potential. Finally an hyperincursive system is given in the case of a neural stack memory.

Evaluation of Piecewise Polynomial Equations for Two Types of Thermocouples

PubMed Central

Chen, Andrew; Chen, Chiachung

2013-01-01

Thermocouples are the most frequently used sensors for temperature measurement because of their wide applicability, long-term stability and high reliability. However, one of the major utilization problems is the linearization of the transfer relation between temperature and output voltage of thermocouples. The linear calibration equation and its modules could be improved by using regression analysis to help solve this problem. In this study, two types of thermocouple and five temperature ranges were selected to evaluate the fitting agreement of different-order polynomial equations. Two quantitative criteria, the average of the absolute error values |e|ave and the standard deviation of calibration equation estd, were used to evaluate the accuracy and precision of these calibrations equations. The optimal order of polynomial equations differed with the temperature range. The accuracy and precision of the calibration equation could be improved significantly with an adequate higher degree polynomial equation. The technique could be applied with hardware modules to serve as an intelligent sensor for temperature measurement. PMID:24351627

Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.

PubMed

Holm, Darryl D.

2002-06-01

We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.

The Integration of Teacher's Pedagogical Content Knowledge Components in Teaching Linear Equation

ERIC Educational Resources Information Center

Yusof, Yusminah Mohd.; Effandi, Zakaria

2015-01-01

This qualitative research aimed to explore the integration of the components of pedagogical content knowledge (PCK) in teaching Linear Equation with one unknown. For the purpose of the study, a single local case study with multiple participants was used. The selection of the participants was made based on various criteria: having more than 5 years…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.

PubMed

Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients

PubMed Central

Boyko, Vyacheslav M.; Popovych, Roman O.; Shapoval, Nataliya M.

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach. PMID:23564972

Improved Pedagogy for Linear Differential Equations by Reconsidering How We Measure the Size of Solutions

ERIC Educational Resources Information Center

Tisdell, Christopher C.

2017-01-01

For over 50 years, the learning of teaching of "a priori" bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to "a priori" bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving…

Insights into the School Mathematics Tradition from Solving Linear Equations

ERIC Educational Resources Information Center

Buchbinder, Orly; Chazan, Daniel; Fleming, Elizabeth

2015-01-01

In this article, we explore how the solving of linear equations is represented in English­-language algebra text books from the early nineteenth century when schooling was becoming institutionalized, and then survey contemporary teachers. In the text books, we identify the increasing presence of a prescribed order of steps (a canonical method) for…

Instructional Supports for Representational Fluency in Solving Linear Equations with Computer Algebra Systems and Paper-and-Pencil

ERIC Educational Resources Information Center

Fonger, Nicole L.; Davis, Jon D.; Rohwer, Mary Lou

2018-01-01

This research addresses the issue of how to support students' representational fluency--the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is…

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…

40 CFR 92.121 - Oxides of nitrogen analyzer calibration and check.

Code of Federal Regulations, 2010 CFR

2010-07-01

... of full-scale concentration. It is permitted to use additional concentrations. (v) Perform a linear least-square regression on the data generated. Use an equation of the form y=mx where x is the actual chart deflection and y is the concentration. (vi) Use the equation z=y/m to find the linear chart...

Flipping an Algebra Classroom: Analyzing, Modeling, and Solving Systems of Linear Equations

ERIC Educational Resources Information Center

Kirvan, Rebecca; Rakes, Christopher R.; Zamora, Regie

2015-01-01

The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…

Investigating High-School Students' Reasoning Strategies when They Solve Linear Equations

ERIC Educational Resources Information Center

Huntley, Mary Ann; Marcus, Robin; Kahan, Jeremy; Miller, Jane Lincoln

2007-01-01

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third-year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from one problem that involved solving a set of three linear equations of…

Solution of the Schrodinger Equation for a Diatomic Oscillator Using Linear Algebra: An Undergraduate Computational Experiment

ERIC Educational Resources Information Center

Gasyna, Zbigniew L.

2008-01-01

Computational experiment is proposed in which a linear algebra method is applied to the solution of the Schrodinger equation for a diatomic oscillator. Calculations of the vibration-rotation spectrum for the HCl molecule are presented and the results show excellent agreement with experimental data. (Contains 1 table and 1 figure.)

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R.

2003-01-01

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

Regularity gradient estimates for weak solutions of singular quasi-linear parabolic equations

NASA Astrophysics Data System (ADS)

Phan, Tuoc

2017-12-01

This paper studies the Sobolev regularity for weak solutions of a class of singular quasi-linear parabolic problems of the form ut -div [ A (x , t , u , ∇u) ] =div [ F ] with homogeneous Dirichlet boundary conditions over bounded spatial domains. Our main focus is on the case that the vector coefficients A are discontinuous and singular in (x , t)-variables, and dependent on the solution u. Global and interior weighted W 1 , p (ΩT , ω)-regularity estimates are established for weak solutions of these equations, where ω is a weight function in some Muckenhoupt class of weights. The results obtained are even new for linear equations, and for ω = 1, because of the singularity of the coefficients in (x , t)-variables.

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-04-15

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilizemore » the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-01-28

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modi ed Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in ow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then a modelbased feedback controller is designed for the reduced order model using linear quadratic regulators (LQR). Finally, a linear quadratic gaussian (LQG) controller, which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHWmore » equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.« less

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard

1950-01-01

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.

Data correlation and analysis of arc tunnel and wind tunnel tests of RSI joints and gaps. Volume 1: Technical report

NASA Technical Reports Server (NTRS)

Christensen, H. E.; Kipp, H. W.

1974-01-01

Heat transfer data measured in gaps typical of those under consideration for joints in space shuttle reusable surface insulation protection systems have been assimilated, analyzed and correlated. The data were obtained in four NASA facilities. Several types of gaps were investigated with emphasis on simple butt joints. Gap widths ranged from 0.07 to 0.7 cm and depths ranged from 1 to 6 cm. Laminar, transitional and turbulent boundary layer flows over the gap opening were investigated. Three-dimensional heating variations were observed within gaps in the absence of external flow pressure gradients. Heat transfer correlation equations were obtained for several of the tests. Thermal protection system performance with and without gaps was compared for a representative shuttle entry trajectory.

Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

DOE PAGES

Till, Andrew T.; Warsa, James S.; Morel, Jim E.

2018-06-15

The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a group-dependent state size but may be formulated without inner iterations in the presence ofmore » scattering, while ARF has a group-independent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.« less

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

NASA Astrophysics Data System (ADS)

Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

2018-05-01

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

Nodal-line pairing with 1D-3D coupled Fermi surfaces: A model motivated by Cr-based superconductors

NASA Astrophysics Data System (ADS)

Wachtel, Gideon; Kim, Yong Baek

2016-09-01

Motivated by the recent discovery of a new family of chromium-based superconductors, we consider a two-band model, where a band of electrons dispersing only in one direction interacts with a band of electrons dispersing in all three directions. Strong 2 kf density fluctuations in the one-dimensional band induces attractive interactions between the three-dimensional electrons, which, in turn, makes the system superconducting. Solving the associated Eliashberg equations, we obtain a gap function which is peaked at the "poles" of the three-dimensional Fermi sphere, and decreases towards the "equator." When strong enough local repulsion is included, the gap actually changes sign around the equator and nodal rings are formed. These nodal rings manifest themselves in several experimentally observable quantities, some of which resemble unconventional observations in the newly discovered superconductors which motivated this work.

The novel application of artificial neural network on bioelectrical impedance analysis to assess the body composition in elderly

PubMed Central

2013-01-01

Background This study aims to improve accuracy of Bioelectrical Impedance Analysis (BIA) prediction equations for estimating fat free mass (FFM) of the elderly by using non-linear Back Propagation Artificial Neural Network (BP-ANN) model and to compare the predictive accuracy with the linear regression model by using energy dual X-ray absorptiometry (DXA) as reference method. Methods A total of 88 Taiwanese elderly adults were recruited in this study as subjects. Linear regression equations and BP-ANN prediction equation were developed using impedances and other anthropometrics for predicting the reference FFM measured by DXA (FFMDXA) in 36 male and 26 female Taiwanese elderly adults. The FFM estimated by BIA prediction equations using traditional linear regression model (FFMLR) and BP-ANN model (FFMANN) were compared to the FFMDXA. The measuring results of an additional 26 elderly adults were used to validate than accuracy of the predictive models. Results The results showed the significant predictors were impedance, gender, age, height and weight in developed FFMLR linear model (LR) for predicting FFM (coefficient of determination, r2 = 0.940; standard error of estimate (SEE) = 2.729 kg; root mean square error (RMSE) = 2.571kg, P < 0.001). The above predictors were set as the variables of the input layer by using five neurons in the BP-ANN model (r2 = 0.987 with a SD = 1.192 kg and relatively lower RMSE = 1.183 kg), which had greater (improved) accuracy for estimating FFM when compared with linear model. The results showed a better agreement existed between FFMANN and FFMDXA than that between FFMLR and FFMDXA. Conclusion When compared the performance of developed prediction equations for estimating reference FFMDXA, the linear model has lower r2 with a larger SD in predictive results than that of BP-ANN model, which indicated ANN model is more suitable for estimating FFM. PMID:23388042

Minimizing Secular J2 Perturbation Effects on Satellite Formations

DTIC Science & Technology

2008-03-01

linear set of differential equations describing the relative motion was established by Hill as well as Clohessy and Wiltshire , with a slightly... Wiltshire (CW) equations, and Hill- Clohessy - Wiltshire (HCW) equations. In the simplest form these differential equations can be expressed as: 2 2 2 3 2...different orientation. Because these equations are much alike, the differential equations established are referred to as Hill’s equations, Clohessy

Positioner with long travel in two dimensions

DOEpatents

Trumper, David L.; Williams, Mark E.

1997-12-23

A precision positioning system is provided which provides long travel in two of the linear dimensions, while using non-contact bearings for both a first subassembly which provides long travel in one of the linear dimension and a second subassembly which provides long travel in the second linear dimension. The first or upper subassembly is preferably a magnetic subassembly which, in addition to providing long travel, also compensates or positions in three rotary dimensions and in the third linear dimension. The second subassembly is preferably either an air bearing or magnetic subassembly and is normally used only to provide long travel. Angled surfaces may be provided for magnetic bearings and capacitive or other gap sensing probes may be mounted to the stage and ground flush with the bearing actuators to provide more precise gap measurements.

Comparison of linear and non-linear models for the adsorption of fluoride onto geo-material: limonite.

PubMed

Sahin, Rubina; Tapadia, Kavita

2015-01-01

The three widely used isotherms Langmuir, Freundlich and Temkin were examined in an experiment using fluoride (F⁻) ion adsorption on a geo-material (limonite) at four different temperatures by linear and non-linear models. Comparison of linear and non-linear regression models were given in selecting the optimum isotherm for the experimental results. The coefficient of determination, r², was used to select the best theoretical isotherm. The four Langmuir linear equations (1, 2, 3, and 4) are discussed. Langmuir isotherm parameters obtained from the four Langmuir linear equations using the linear model differed but they were the same when using the nonlinear model. Langmuir-2 isotherm is one of the linear forms, and it had the highest coefficient of determination (r² = 0.99) compared to the other Langmuir linear equations (1, 3 and 4) in linear form, whereas, for non-linear, Langmuir-4 fitted best among all the isotherms because it had the highest coefficient of determination (r² = 0.99). The results showed that the non-linear model may be a better way to obtain the parameters. In the present work, the thermodynamic parameters show that the absorption of fluoride onto limonite is both spontaneous (ΔG < 0) and endothermic (ΔH > 0). Scanning electron microscope and X-ray diffraction images also confirm the adsorption of F⁻ ion onto limonite. The isotherm and kinetic study reveals that limonite can be used as an adsorbent for fluoride removal. In future we can develop new technology for fluoride removal in large scale by using limonite which is cost-effective, eco-friendly and is easily available in the study area.

Wave theory in rotating systems: Schrödinger equations bridge the gaps between the equatorial β-plane and the spherical earth

NASA Astrophysics Data System (ADS)

Paldor, N.

2017-12-01

The concise and elegant wave theory developed on the equatorial β-plane by Matsuno (1966, M66 hereafter) is based on the formulation of a Schrödinger equation associated with the governing Linear Rotating Shallow Water Equations (LRSWE). The theory yields explicit expressions for the dispersion relations and meridional amplitude structures of all zonally propagating waves - Rossby, Inertia-Gravity, Kelvin and Yanai. In contrast, the spherical wave theory of Longuet-Higgins (1968) is a collection of asymptotic expansions in many sub-ranges e.g. large, small (and even negative) Lamb Number; high and low frequency; low-latitudes, etc. that rests upon extensive numerical solutions of several Ordinary Differential Equations. The difference between the two theories is highlighted by their lengths. The essential elements of the former planar study are completely revealed in just 3-4 pages including the derivation of explicit formulae for the phase speeds and amplitude meridional structures. In comtrast, the latter spherical theory contains 97 pages and the results of the numerical calculations are summarized in 30 pages of tables filled with numerical values and about 31 figures, each of which containing many separate curves! In my talk I will re-visit the wave problem on a sphere by developing several Schrödinger equations that approximate the governing eigenvalue equation associated with zonally propagating waves. Each of the Schrödinger equations approximates the original second order Ordinary Differential Equation in a different range of the 3 parameters: Lamb-Number, frequency and zonal wavenumber. As in M66, each of the Schrödinger equations yields explicit expressions for the dispersion relations and meridional amplitude structure of Rossby and Inertia-Gravity waves. In addition, the analysis shows that Yanai wave exists on a sphere even tough the zonal velocity is regular everywhere there (in contrast to the β-plane where the zonal velocity is singular everywhere) and that Kelvin waves do not exist as a separate mode (but the eastward propagating n=0 Inertia-Gravity is nearly non-dispersive). References Longuet-Higgins, M. S. Phil. Trans. Roy. Soc. London; 262, 511-607; 1968 Matsuno, T.; J. Met. Soc. Japan. 44(1), 25-43; 1966

Linear stability analysis of collective neutrino oscillations without spurious modes

NASA Astrophysics Data System (ADS)

Morinaga, Taiki; Yamada, Shoichi

2018-01-01

Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.

Toroidal-Core Microinductors Biased by Permanent Magnets

NASA Technical Reports Server (NTRS)

Lieneweg, Udo; Blaes, Brent

2003-01-01

The designs of microscopic toroidal-core inductors in integrated circuits of DC-to-DC voltage converters would be modified, according to a proposal, by filling the gaps in the cores with permanent magnets that would apply bias fluxes (see figure). The magnitudes and polarities of the bias fluxes would be tailored to counteract the DC fluxes generated by the DC components of the currents in the inductor windings, such that it would be possible to either reduce the sizes of the cores or increase the AC components of the currents in the cores without incurring adverse effects. Reducing the sizes of the cores could save significant amounts of space on integrated circuits because relative to other integrated-circuit components, microinductors occupy large areas - of the order of a square millimeter each. An important consideration in the design of such an inductor is preventing magnetic saturation of the core at current levels up to the maximum anticipated operating current. The requirement to prevent saturation, as well as other requirements and constraints upon the design of the core are expressed by several equations based on the traditional magnetic-circuit approximation. The equations involve the core and gap dimensions and the magnetic-property parameters of the core and magnet materials. The equations show that, other things remaining equal, as the maximum current is increased, one must increase the size of the core to prevent the flux density from rising to the saturation level. By using a permanent bias flux to oppose the flux generated by the DC component of the current, one would reduce the net DC component of flux in the core, making it possible to reduce the core size needed to prevent the total flux density (sum of DC and AC components) from rising to the saturation level. Alternatively, one could take advantage of the reduction of the net DC component of flux by increasing the allowable AC component of flux and the corresponding AC component of current. In either case, permanent-magnet material and the slant (if any) and thickness of the gap must be chosen according to the equations to obtain the required bias flux. In modifying the design of the inductor, one must ensure that the inductance is not altered. The simplest way to preserve the original value of inductance would be to leave the gap dimensions unchanged and fill the gap with a permanent- magnet material that, fortuitously, would produce just the required bias flux. A more generally applicable alternative would be to partly fill either the original gap or a slightly enlarged gap with a suitable permanent-magnet material (thereby leaving a small residual gap) so that the reluctance of the resulting magnetic circuit would yield the desired inductance.

Nonlinear Waves.

DTIC Science & Technology

1988-02-01

in Multi- dimensions II, P.M. Santini and A.S. Fokas, preprint INS#67, 1986. The Recursion Operator of the Kadomtsev - Petviashvili Equation and the...solitons, multidimensional inverse problems, Painleve equations , direct linearizations of certain nonlinear wave equations , DBAR problems, Riemann...the Navy is (a) the recent discovery that many of the equations describing ship hydrodynamics in channels of finite depth obey nonlinear equations

Nonlinear equations of dynamics for spinning paraboloidal antennas

NASA Technical Reports Server (NTRS)

Utku, S.; Shoemaker, W. L.; Salama, M.

1983-01-01

The nonlinear strain-displacement and velocity-displacement relations of spinning imperfect rotational paraboloidal thin shell antennas are derived for nonaxisymmetrical deformations. Using these relations with the admissible trial functions in the principle functional of dynamics, the nonlinear equations of stress inducing motion are expressed in the form of a set of quasi-linear ordinary differential equations of the undetermined functions by means of the Rayleigh-Ritz procedure. These equations include all nonlinear terms up to and including the third degree. Explicit expressions are given for the coefficient matrices appearing in these equations. Both translational and rotational off-sets of the axis of revolution (and also the apex point of the paraboloid) with respect to the spin axis are considered. Although the material of the antenna is assumed linearly elastic, it can be anisotropic.

An accelerated lambda iteration method for multilevel radiative transfer. I - Non-overlapping lines with background continuum

NASA Technical Reports Server (NTRS)

Rybicki, G. B.; Hummer, D. G.

1991-01-01

A method is presented for solving multilevel transfer problems when nonoverlapping lines and background continuum are present and active continuum transfer is absent. An approximate lambda operator is employed to derive linear, 'preconditioned', statistical-equilibrium equations. A method is described for finding the diagonal elements of the 'true' numerical lambda operator, and therefore for obtaining the coefficients of the equations. Iterations of the preconditioned equations, in conjunction with the transfer equation's formal solution, are used to solve linear equations. Some multilevel problems are considered, including an eleven-level neutral helium atom. Diagonal and tridiagonal approximate lambda operators are utilized in the problems to examine the convergence properties of the method, and it is found to be effective for the line transfer problems.

Parental Characteristics and the Achievement Gap in Mathematics: Hierarchical Linear Modeling Analysis of Longitudinal Study of American Youth (LSAY)

ERIC Educational Resources Information Center

Shoraka, Mohammad; Arnold, Robert; Kim, Eun Sook; Salinitri, Geri; Kromrey, Jeffrey

2015-01-01

One of the most salient problems in education is the achievement gap. The researchers investigated the effects of parental education and parental occupations in science, technology, engineering, mathematics, or medical professions (STEMM) on the achievement gap in mathematics. Because students were nested within schools, two-level Hierarchical…

Structural and electronic properties of GaAs and GaP semiconductors

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

Rani, Anita; Kumar, Ranjan

2015-05-15

The Structural and Electronic properties of Zinc Blende phase of GaAs and GaP compounds are studied using self consistent SIESTA-code, pseudopotentials and Density Functional Theory (DFT) in Local Density Approximation (LDA). The Lattice Constant, Equillibrium Volume, Cohesive Energy per pair, Compressibility and Band Gap are calculated. The band gaps calcultated with DFT using LDA is smaller than the experimental values. The P-V data fitted to third order Birch Murnaghan equation of state provide the Bulk Modulus and its pressure derivatives. Our Structural and Electronic properties estimations are in agreement with available experimental and theoretical data.

Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons ``piloted'' (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations

NASA Astrophysics Data System (ADS)

Vigier, Jean-Pierre

1991-02-01

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, (1) Nelson, (2) de Broglie, (3) Guerra et al. (4) ), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm (5) real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

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

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials.

PubMed

Scalora, Michael; Syrchin, Maxim S; Akozbek, Neset; Poliakov, Evgeni Y; D'Aguanno, Giuseppe; Mattiucci, Nadia; Bloemer, Mark J; Zheltikov, Aleksei M

2005-07-01

A new generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability is derived and used to characterize wave propagation in a negative index material. The equation has new features that are distinct from ordinary materials (mu=1): the linear and nonlinear coefficients can be tailored through the linear properties of the medium to attain any combination of signs unachievable in ordinary matter, with significant potential to realize a wide class of solitary waves.

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

PubMed

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

2013-05-13

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

On exponential stability of linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Tien Dung, Nguyen

2015-02-01

The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].

FINITE ELEMENT MODEL FOR TIDAL AND RESIDUAL CIRCULATION.

USGS Publications Warehouse

Walters, Roy A.

1986-01-01

Harmonic decomposition is applied to the shallow water equations, thereby creating a system of equations for the amplitude of the various tidal constituents and for the residual motions. The resulting equations are elliptic in nature, are well posed and in practice are shown to be numerically well-behaved. There are a number of strategies for choosing elements: the two extremes are to use a few high-order elements with continuous derivatives, or to use a large number of simpler linear elements. In this paper simple linear elements are used and prove effective.

Coarse-grained description of cosmic structure from Szekeres models

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

Sussman, Roberto A.; Gaspar, I. Delgado; Hidalgo, Juan Carlos, E-mail: sussman@nucleares.unam.mx, E-mail: ismael.delgadog@uaem.edu.mx, E-mail: hidalgo@fis.unam.mx

2016-03-01

We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3-dimensional networks of cold dark matter structures (over-densities and/or density voids) undergoing ''pancake'' collapse. By reducing Einstein's field equations to a set of evolution equations, which themselves reduce in the linear limit to evolution equations for linear perturbations, we determine the dynamics of such structures, with the spatial comoving location of each structure uniquely specified by standard early Universe initial conditions. By means of a representative example we examine in detail the density contrast, the Hubble flow and peculiar velocities ofmore » structures that evolved, from linear initial data at the last scattering surface, to fully non-linear 10–20 Mpc scale configurations today. To motivate further research, we provide a qualitative discussion on the connection of Szekeres models with linear perturbations and the pancake collapse of the Zeldovich approximation. This type of structure modelling provides a coarse grained—but fully relativistic non-linear and non-perturbative —description of evolving large scale cosmic structures before their virialisation, and as such it has an enormous potential for applications in cosmological research.« less

An Evaluation of Kernel Equating: Parallel Equating with Classical Methods in the SAT Subject Tests[TM] Program. Research Report. ETS RR-09-06

ERIC Educational Resources Information Center

Grant, Mary C.; Zhang, Lilly; Damiano, Michele

2009-01-01

This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating…

[Response of forest bird communities to forest gap in winter in southwestern China].

PubMed

Zhao, Dong-Dong; Wu, Ying-Huan; Lu, Zhou; Jiang, Guang-Wei; Zhou, Fang

2013-06-01

Although forest gap ecology is an important field of study, research remains limited. By plot setting and point counted observation, the response of birds to forest gaps in winter as well as bird distribution patterns in forest gaps and intact canopies were studied in a north tropical monsoon forest of southwestern China from November 2011 to February 2012 in the Fangcheng Golden Camellia National Nature Reserve, Guangxi. The regression equation of bird species diversity to habitat factor was Y1=0.611+0.002 X13+0.043 X2+0.002 X5-0.003 X8+0.006 X10+0.008 X1 and the regression equation of bird species dominance index to habitat factor was Y3=0.533+0.001 X13+0.019 X2+0.002 X3-0.017 X4+0.002 X1. There were 45 bird species (2 orders and 13 families) recorded in the forest gap, accounting for 84.9% of all birds (n=45), with an average of 9.6 species (range: 2-22). Thirty-nine bird species (5 orders and 14 families) were recorded in non-gap areas, accounting for 73.6% of all birds (n=39), with an average of 5.3 species (range: 1-12). These results suggested that gap size, arbor average height (10 m from gap margin), arbor quantity (10 m from gap margin), shrub quantity (10 m from gap margin), herbal average coverage (1 m from gap margin) and bare land ratio were the key forest gap factors that influenced bird diversities. On the whole, bird diversity in the forest gap was greater than in the intact canopy. Spatial distributions in the forest gaps were also observed in the bird community. Most birds foraged in the "middle" and "canopy" layers in the vertical stratification. In addition, "nearly from" and "close from" contained more birds in relation to horizontal stratification. Feeding niche differentiation was suggested as the main reason for these distribution patterns.

Predicting Diameter at Breast Height from Stump Diameters for Northeastern Tree Species

Treesearch

Eric H. Wharton; Eric H. Wharton

1984-01-01

Presents equations to predict diameter at breast height from stump diameter measurements for 17 northeastern tree species. Simple linear regression was used to develop the equations. Application of the equations is discussed.

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Alternate solution to generalized Bernoulli equations via an integrating factor: an exact differential equation approach

NASA Astrophysics Data System (ADS)

Tisdell, C. C.

2017-08-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem through a substitution. The purpose of this note is to present an alternative approach using 'exact methods', illustrating that a substitution and linearization of the problem is unnecessary. The ideas may be seen as forming a complimentary and arguably simpler approach to Azevedo and Valentino that have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics. We illustrate how to apply the ideas through an analysis of the Gompertz equation, which is of interest in biomathematical models of tumour growth.