A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

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

Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch; Pappu, Rohit V.

2014-07-21

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear inmore » the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom.« less

On the Monge-Ampere equivalent of the sine-Gordon equation

NASA Astrophysics Data System (ADS)

Ferapontov, E. V.; Nutku, Y.

1994-12-01

Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampere equation for the graph of the surface. We present the explicit form of the correspondence between these two integrable non-linear partial differential equations using their well-known properties in differential geometry. We find that the cotangent of the angle between asymptotic directions is directly related to the mean curvature of the surface. This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere equations.

Collision group and renormalization of the Boltzmann collision integral.

PubMed

Saveliev, V L; Nanbu, K

2002-05-01

On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

Collision group and renormalization of the Boltzmann collision integral

NASA Astrophysics Data System (ADS)

Saveliev, V. L.; Nanbu, K.

2002-05-01

On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

Integral representations of solutions of the wave equation based on relativistic wavelets

NASA Astrophysics Data System (ADS)

Perel, Maria; Gorodnitskiy, Evgeny

2012-09-01

A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed.

The framed Standard Model (II) — A first test against experiment

NASA Astrophysics Data System (ADS)

Chan, Hong-Mo; Tsou, Sheung Tsun

2015-10-01

Apart from the qualitative features described in Paper I (Ref. 1), the renormalization group equation derived for the rotation of the fermion mass matrices are amenable to quantitative study. The equation depends on a coupling and a fudge factor and, on integration, on 3 integration constants. Its application to data analysis, however, requires the input from experiment of the heaviest generation masses mt, mb, mτ, mν3 all of which are known, except for mν3. Together then with the theta-angle in the QCD action, there are in all 7 real unknown parameters. Determining these 7 parameters by fitting to the experimental values of the masses mc, mμ, me, the CKM elements |Vus|, |Vub|, and the neutrino oscillation angle sin2θ 13, one can then calculate and compare with experiment the following 12 other quantities ms, mu/md, |Vud|, |Vcs|, |Vtb|, |Vcd|, |Vcb|, |Vts|, |Vtd|, J, sin22θ 12, sin22θ 23, and the results all agree reasonably well with data, often to within the stringent experimental error now achieved. Counting the predictions not yet measured by experiment, this means that 17 independent parameters of the standard model are now replaced by 7 in the FSM.

A study of isotropic-nematic transition of quadrupolar Gay-Berne fluid using density-functional theory approach

NASA Astrophysics Data System (ADS)

Singh, Ram Chandra; Ram, Jokhan

2011-11-01

The effects of quadrupole moments on the isotropic-nematic (IN) phase transitions are studied using the density-functional theory (DFT) for a Gay-Berne (GB) fluid for a range of length-to-breadth parameters ? in the reduced temperature range ? . The pair-correlation functions of the isotropic phase, which enter into the DFT as input parameters are found by solving the Percus-Yevick integral equation theory. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to 6 are considered. The numerical accuracy of the results depends on the number of spherical harmonic coefficients considered for each orientation-dependent function. As the length-to-breadth ratio of quadrupolar GB molecules is increased, the IN transition is seen to move to lower density (and pressure) at a given temperature. It has been observed that the DFT is good to study the IN transitions in such fluids. The theoretical results have also been compared with the computer simulation results wherever they are available.

Effect of the meniscus contact angle during early regimes of spontaneous imbibition in nanochannels.

PubMed

Karna, Nabin Kumar; Oyarzua, Elton; Walther, Jens H; Zambrano, Harvey A

2016-11-30

Nanoscale capillarity has been extensively investigated; nevertheless, many fundamental questions remain open. In spontaneous imbibition, the classical Lucas-Washburn equation predicts a singularity as the fluid enters the channel consisting of an anomalous infinite velocity of the capillary meniscus. Bosanquet's equation overcomes this problem by taking into account fluid inertia predicting an initial imbibition regime with constant velocity. Nevertheless, the initial constant velocity as predicted by Bosanquet's equation is much greater than those observed experimentally. In the present study, large scale atomistic simulations are conducted to investigate capillary imbibition of water in slit silica nanochannels with heights between 4 and 18 nm. We find that the meniscus contact angle remains constant during the inertial regime and its value depends on the height of the channel. We also find that the meniscus velocity computed at the channel entrance is related to the particular value of the meniscus contact angle. Moreover, during the subsequent visco-inertial regime, as the influence of viscosity increases, the meniscus contact angle is found to be time dependent for all the channels under study. Furthermore, we propose an expression for the time evolution of the dynamic contact angle in nanochannels which, when incorporated into Bosanquet's equation, satisfactorily explains the initial capillary rise.

The F(N) method for the one-angle radiative transfer equation applied to plant canopies

NASA Technical Reports Server (NTRS)

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

1992-01-01

The paper presents a semianalytical solution method, called the F(N) method, for the one-angle radiative transfer equation in slab geometry. The F(N) method is based on two integral equations specifying the intensities exiting the boundaries of the vegetation canopy; the solution is obtained through an expansion in a set of basis functions with expansion coefficients to be determined. The advantage of this method is that it avoids spatial truncation error entirely because it requires discretization only in the angular variable.

Investigating Whistler Mode Wave Diffusion Coefficients at Mars

NASA Astrophysics Data System (ADS)

Shane, A. D.; Liemohn, M. W.; Xu, S.; Florie, C.

2017-12-01

Observations of electron pitch angle distributions have suggested collisions are not the only pitch angle scattering process occurring in the Martian ionosphere. This unknown scattering process is causing high energy electrons (>100 eV) to become isotropized. Whistler mode waves are one pitch angle scattering mechanism known to preferentially scatter high energy electrons in certain plasma regimes. The distribution of whistler mode wave diffusion coefficients are dependent on the background magnetic field strength and thermal electron density, as well as the frequency and wave normal angle of the wave. We have solved for the whistler mode wave diffusion coefficients using the quasi-linear diffusion equations and have integrated them into a superthermal electron transport (STET) model. Preliminary runs have produced results that qualitatively match the observed electron pitch angle distributions at Mars. We performed parametric sweeps over magnetic field, thermal electron density, wave frequency, and wave normal angle to understand the relationship between the plasma parameters and the diffusion coefficient distributions, but also to investigate what regimes whistler mode waves scatter only high energy electrons. Increasing the magnetic field strength and lowering the thermal electron density shifts the distribution of diffusion coefficients toward higher energies and lower pitch angles. We have created an algorithm to identify Mars Atmosphere Volatile and EvolutioN (MAVEN) observations of high energy isotropic pitch angle distributions in the Martian ionosphere. We are able to map these distributions at Mars, and compare the conditions under which these are observed at Mars with the results of our parametric sweeps. Lastly, we will also look at each term in the kinetic diffusion equation to determine if the energy and mixed diffusion coefficients are important enough to incorporate into STET as well.

Time-marching transonic flutter solutions including angle-of-attack effects

NASA Technical Reports Server (NTRS)

Edwards, J. W.; Bennett, R. M.; Whitlow, W., Jr.; Seidel, D. A.

1982-01-01

Transonic aeroelastic solutions based upon the transonic small perturbation potential equation were studied. Time-marching transient solutions of plunging and pitching airfoils were analyzed using a complex exponential modal identification technique, and seven alternative integration techniques for the structural equations were evaluated. The HYTRAN2 code was used to determine transonic flutter boundaries versus Mach number and angle-of-attack for NACA 64A010 and MBB A-3 airfoils. In the code, a monotone differencing method, which eliminates leading edge expansion shocks, is used to solve the potential equation. When the effect of static pitching moment upon the angle-of-attack is included, the MBB A-3 airfoil can have multiple flutter speeds at a given Mach number.

Wave-vector and polarization dependent impedance model for a hexagonal periodic metasurface exemplified through finite-difference time-domain simulations.

PubMed

Ding, Yi S; He, Yang

2017-08-21

An isotropic impedance sheet model is proposed for a loop-type hexagonal periodic metasurface. Both frequency and wave-vector dispersion are considered near the resonance frequency. Therefore both the angle and polarization dependences of the metasurface impedance can be properly and simultaneously described in our model. The constitutive relation of this model is transformed into auxiliary differential equations which are integrated into the finite-difference time-domain algorithm. Finally, a finite large metasurface sample under oblique illumination is used to test the model and the algorithm. Our model and algorithm can significantly increase the accuracy of the homogenization methods for modeling periodic metasurfaces.

Electromagnetic inverse scattering

NASA Technical Reports Server (NTRS)

Bojarski, N. N.

1972-01-01

A three-dimensional electromagnetic inverse scattering identity, based on the physical optics approximation, is developed for the monostatic scattered far field cross section of perfect conductors. Uniqueness of this inverse identity is proven. This identity requires complete scattering information for all frequencies and aspect angles. A nonsingular integral equation is developed for the arbitrary case of incomplete frequence and/or aspect angle scattering information. A general closed-form solution to this integral equation is developed, which yields the shape of the scatterer from such incomplete information. A specific practical radar solution is presented. The resolution of this solution is developed, yielding short-pulse target resolution radar system parameter equations. The special cases of two- and one-dimensional inverse scattering and the special case of a priori knowledge of scatterer symmetry are treated in some detail. The merits of this solution over the conventional radar imaging technique are discussed.

A New Method for 3D Radiative Transfer with Adaptive Grids

NASA Astrophysics Data System (ADS)

Folini, D.; Walder, R.; Psarros, M.; Desboeufs, A.

2003-01-01

We present a new method for 3D NLTE radiative transfer in moving media, including an adaptive grid, along with some test examples and first applications. The central features of our approach we briefly outline in the following. For the solution of the radiative transfer equation, we make use of a generalized mean intensity approach. In this approach, the transfer eqation is solved directly, instead of using the moments of the transfer equation, thus avoiding the associated closure problem. In a first step, a system of equations for the transfer of each directed intensity is set up, using short characteristics. Next, the entity of systems of equations for each directed intensity is re-formulated in the form of one system of equations for the angle-integrated mean intensity. This system then is solved by a modern, fast BiCGStab iterative solver. An additional advantage of this procedure is that convergence rates barely depend on the spatial discretization. For the solution of the rate equations we use Housholder transformations. Lines are treated by a 3D generalization of the well-known Sobolev-approximation. The two parts, solution of the transfer equation and solution of the rate equations, are iteratively coupled. We recently have implemented an adaptive grid, which allows for recursive refinement on a cell-by-cell basis. The spatial resolution, which is always a problematic issue in 3D simulations, we can thus locally reduce or augment, depending on the problem to be solved.

Further studies of propellant sloshing under low-gravity conditions

NASA Technical Reports Server (NTRS)

Dodge, F. T.

1971-01-01

A variational integral is formulated from Hamilton's Principle and is proved to be equivalent to the usual differential equations of low-gravity sloshing in ellipsoidal tanks. It is shown that for a zero-degree contact angle the contact line boundary condition corresponds to the stuck condition, a result that is due to the linearization of the equations and the ambiguity in the definition of the wave height at the wall. The variational integral is solved by a Rayleigh-Ritz technique. Results for slosh frequency when the free surface is not bent-over compare well with previous numerical solutions. When the free surface is bent over, however, the results for slosh frequency are considerably larger than those predicted by previous finite-difference, numerical approaches: the difference may be caused by the use of a zero degree contact angle in the present theory in contrast to the nonzero contact angle used in the numerical approaches.

Two-dimensional radiative transfer. I - Planar geometry. [in stellar atmospheres

NASA Technical Reports Server (NTRS)

Mihalas, D.; Auer, L. H.; Mihalas, B. R.

1978-01-01

Differential-equation methods for solving the transfer equation in two-dimensional planar geometries are developed. One method, which uses a Hermitian integration formula on ray segments through grid points, proves to be extremely well suited to velocity-dependent problems. An efficient elimination scheme is developed for which the computing time scales linearly with the number of angles and frequencies; problems with large velocity amplitudes can thus be treated accurately. A very accurate and efficient method for performing a formal solution is also presented. A discussion is given of several examples of periodic media and free-standing slabs, both in static cases and with velocity fields. For the free-standing slabs, two-dimensional transport effects are significant near boundaries, but no important effects were found in any of the periodic cases studied.

Physical processes in the strong magnetic fields of accreting neutron stars

NASA Technical Reports Server (NTRS)

Meszaros, P.

1984-01-01

Analytical formulae are fitted to observational data on physical processes occurring in strong magnetic fields surrounding accreting neutron stars. The propagation of normal modes in the presence of a quantizing magnetic field is discussed in terms of a wave equation in Fourier space, quantum electrodynamic effects, polarization and mode ellipticity. The results are applied to calculating the Thomson scattering, bremsstrahlung and Compton scattering cross-sections, which are a function of the frequency, angle and polarization of the magnetic field. Numerical procedures are explored for solving the radiative transfer equations. When applied to modeling X ray pulsars, a problem arises in the necessity to couple the magnetic angle and frequency dependence of the cross-sections with the hydrodynamic equations. The use of time-dependent averaging and approximation techniques is indicated.

A selective review of ground based passive microwave radiometric probing of the atmosphere

NASA Technical Reports Server (NTRS)

Welch, W. J.

1969-01-01

The absorption of the various atmospheric constituents with significant microwave spectra is reviewed. Based on the available data, an estimate is made of the uncertainty in the microwave absorption coefficients of the major constituents, water vapor and oxygen. Then there is an examination of the integral equations which describe the three basic types of observations: measurement of the spectrum of absorption of the sun's radiation by an atmospheric constituent, measurement of the emission spectrum of a constituent, and measurement at one frequency of the zenith angle dependence of the absorption or emission of the atmosphere.

Integrability of geodesics and action-angle variables in Sasaki-Einstein space T^{1,1}

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2016-09-01

We briefly describe the construction of Stäkel-Killing and Killing-Yano tensors on toric Sasaki-Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Killing-Yano tensors of the homogeneous Sasaki-Einstein space T^{1,1}. We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed.

Magnetic Rotational Spectroscopy with Nanorods to Probe Time-Dependent Rheology of Microdroplets (Postprint)

DTIC Science & Technology

2012-05-10

this angle depends linearly on time, α = 2πf t, where f is the frequency of the rotating magnetic field. We assume that the magnetization vector M is... vector B (Figure 1). In order to derive an equation governing the nanorod rotation, it is convenient to count its revolutions with respect to the fixed... vector directed perpendicularly to the plane of the nanorod rotation.27,28 Substituting the definition of angle φ(t) through the angles α(t) and θ(t

Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

NASA Astrophysics Data System (ADS)

Mingari Scarpello, Giovanni; Ritelli, Daniele

2018-06-01

The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second (precession, ψ ) and third (spin, φ) Euler angles in explicit and real form by means of multiple hypergeometric (Lauricella) functions. Secondly, releasing the weight assumption but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle ψ completing the treatment of the Euler-Poinsot case. Thirdly, by integrating the relevant differential equation, we reach the finite polar equation of a special motion trajectory named the herpolhode. Finally, we keep the symmetry of the first problem, but without weight, and take into account a viscous dissipation. The use of motion first integrals—adopted for the first two problems—is no longer practicable in this situation; therefore, the Euler equations, faced directly, are driving to particular occurrences of Bessel functions of order - 1/2.

Algebraic features of some generalizations of the Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Bibik, Yu. V.; Sarancha, D. A.

2010-10-01

For generalizations of the Lotka-Volterra system, an integration method is proposed based on the nontrivial algebraic structure of these generalizations. The method makes use of an auxiliary first-order differential equation derived from the phase curve equation with the help of this algebraic structure. Based on this equation, a Hamiltonian approach can be developed and canonical variables (moreover, action-angle variables) can be constructed.

A Generalized Hydrodynamic-Impact Theory for the Loads and Motions of Deeply Immersed Prismatic Bodies

NASA Technical Reports Server (NTRS)

Markey, Melvin F.

1959-01-01

A theory is derived for determining the loads and motions of a deeply immersed prismatic body. The method makes use of a two-dimensional water-mass variation and an aspect-ratio correction for three-dimensional flow. The equations of motion are generalized by using a mean value of the aspect-ratio correction and by assuming a variation of the two-dimensional water mass for the deeply immersed body. These equations lead to impact coefficients that depend on an approach parameter which, in turn, depends upon the initial trim and flight-path angles. Comparison of experiment with theory is shown at maximum load and maximum penetration for the flat-bottom (0 deg dead-rise angle) model with bean-loading coefficients from 36.5 to 133.7 over a wide range of initial conditions. A dead-rise angle correction is applied and maximum-load data are compared with theory for the case of a model with 300 dead-rise angle and beam-loading coefficients from 208 to 530.

SU-F-T-414: Mathematical Formulation of Gantry Starting Angle for Right Medial Tangential Arc in Left Intact Partial Breast Irradiation Using Volumetric Modulated Arc Therapy (VMAT)

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

Giri, U; Sarkar, B; Kaur, H

Purpose: To choose appropriate gantry starting angle for partial left breast irradiation using volumetric modulated arc therapy (VMAT). Methods: A random patient of left breast carcinoma was selected for this study. The slice which was selected for this mathematical formulation was having maximum breast thickness and maximum medial and lateral tangential distance. After this appropriate isocenter was chosen on that CT slice. The distances between various points were measured by the measuring tool in Monaco 5.00.04. Using the various trigonometric equations, a final equation was derived which shows the relationship between Gantry start angle, isocenter Location and tissue thickness. Results:more » The final equation for gantry start for right medial tangential arc is given asStarting angle = 270°+tan^(−1)(sin(θ)/(x-1/x-2 +cosθ))The above equation was tested for 10 cases and it was found to be appropriate for all the cases. Conclusion: Gantry starting angle for partial arc irradiation depends upon Breast thickness, Distance between Medial and lateral tangent and isocenter location.« less

Contact angle and local wetting at contact line.

PubMed

Li, Ri; Shan, Yanguang

2012-11-06

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

Effect of nose shape on three-dimensional stagnation region streamlines and heating rates

NASA Technical Reports Server (NTRS)

Hassan, Basil; Dejarnette, Fred R.; Zoby, E. V.

1991-01-01

A new method for calculating the three-dimensional inviscid surface streamlines and streamline metrics using Cartesian coordinates and time as the independent variable of integration has been developed. The technique calculates the streamline from a specified point on the body to a point near the stagnation point by using a prescribed pressure distribution in the Euler equations. The differential equations, which are singular at the stagnation point, are of the two point boundary value problem type. Laminar heating rates are calculated using the axisymmetric analog concept for three-dimensional boundary layers and approximate solutions to the axisymmetric boundary layer equations. Results for elliptic conic forebody geometries show that location of the point of maximum heating depends on the type of conic in the plane of symmetry and the angle of attack, and that this location is in general different from the stagnation point. The new method was found to give smooth predictions of heat transfer in the nose region where previous methods gave oscillatory results.

Measurements of angular flux on surface of Li/sub 2/O slab assemblies and their analysis by a direct integration transport code ''BERMUDA''

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

Maekawa, H.; Oyama, Y.

1983-09-01

Angle-dependent neutron leakage spectra above 0.5 MeV from Li/sub 2/O slab assemblies were measured accurately by the time-of-flight method. The measured angles were 0/sup 0/, 12.2/sup 0/, 24.9/sup 0/, 41.8/sup 0/ and 66.8/sup 0/. The sizes of Li/sub 2/O assemblies were 31.4 cm in equivalent radius and 5.06, 20.24 and 40.48 cm in thickness. The data were analyzed by a new transport code ''BERMUDA-2DN''. Time-independent transport equation is solved for two-dimensional, cylindrical, multi-regional geometry using the direct integration method in a multi-group model. The group transfer kernels are accurately obtained from the double-differential cross section data without using Legendre expansion.more » The results were compared absolutely. While there exist discrepancies partially, the calculational spectra agree well with the experimental ones as a whole. The BERMUDA code was demonstrated to be useful for the analyses of the fusion neutronics and shielding.« less

Beyond Cassie equation: Local structure of heterogeneous surfaces determines the contact angles of microdroplets

PubMed Central

Zhang, Bo; Wang, Jianjun; Liu, Zhiping; Zhang, Xianren

2014-01-01

The application of Cassie equation to microscopic droplets is recently under intense debate because the microdroplet dimension is often of the same order of magnitude as the characteristic size of substrate heterogeneities, and the mechanism to describe the contact angle of microdroplets is not clear. By representing real surfaces statistically as an ensemble of patterned surfaces with randomly or regularly distributed heterogeneities (patches), lattice Boltzmann simulations here show that the contact angle of microdroplets has a wide distribution, either continuous or discrete, depending on the patch size. The origin of multiple contact angles observed is ascribed to the contact line pinning effect induced by substrate heterogeneities. We demonstrate that the local feature of substrate structure near the contact line determines the range of contact angles that can be stabilized, while the certain contact angle observed is closely related to the contact line width. PMID:25059292

Growth Angle: A Microscopic View

NASA Technical Reports Server (NTRS)

Mazuruk, Konstantin; Croll, Arne; Volz, Martin P.

2017-01-01

A microscopic continuum mechanical model of the growth angle is proposed. It is based on the van der Waals type framework that is used for surface force phenomena. The obtained augmented Laplace type integro-differential equations are, in general, difficult to analyze. Here we focused primarily on the particular case of equal melt and crystal surface energies. We derived an approximate equation for the meniscus shape, and obtained an analytical relationship between the contact and the growth angle. Interestingly, the same result can be obtained using the macroscopic model of Herring. The case of a macroscopically sharp corner is also considered. For this case, the macroscopic angle is not defined and it can be any angle between the contact angles of both flat surfaces. The microscopic model yields the smooth shape for the meniscus that also is not unique, but depends on the initial position of the meniscus.

Formation Flying Control Implementation in Highly Elliptical Orbits

NASA Technical Reports Server (NTRS)

Capo-Lugo, Pedro A.; Bainum, Peter M.

2009-01-01

The Tschauner-Hempel equations are widely used to correct the separation distance drifts between a pair of satellites within a constellation in highly elliptical orbits [1]. This set of equations was discretized in the true anomaly angle [1] to be used in a digital steady-state hierarchical controller [2]. This controller [2] performed the drift correction between a pair of satellites within the constellation. The objective of a discretized system is to develop a simple algorithm to be implemented in the computer onboard the satellite. The main advantage of the discrete systems is that the computational time can be reduced by selecting a suitable sampling interval. For this digital system, the amount of data will depend on the sampling interval in the true anomaly angle [3]. The purpose of this paper is to implement the discrete Tschauner-Hempel equations and the steady-state hierarchical controller in the computer onboard the satellite. This set of equations is expressed in the true anomaly angle in which a relation will be formulated between the time and the true anomaly angle domains.

Plane elasto-plastic analysis of v-notched plate under bending by boundary integral equation method. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Rzasnicki, W.

1973-01-01

A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.

Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

NASA Astrophysics Data System (ADS)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

A Zonal Approach for the Solution of Coupled Euler and Potential Solutions of Flows with Complex Geometries.

DTIC Science & Technology

1987-06-01

obtained from: A simple numerical intergration scheme is employed to perform the integral in Equations (B2) and (86) along the dividing streamline. A 11 4...angle of attack was small, the dividing streamline remained almost horizontal in this case. Results of a higher angle of attack case, in which the mesh

Mechanics of the taper integrated screwed-in (TIS) abutments used in dental implants.

PubMed

Bozkaya, Dinçer; Müftü, Sinan

2005-01-01

The tapered implant-abutment interface is becoming more popular due to the mechanical reliability of retention it provides. Consequently, understanding the mechanical properties of the tapered interface with or without a screw at the bottom has been the subject of a considerable amount of studies involving experiments and finite element (FE) analysis. This paper focuses on the tapered implant-abutment interface with a screw integrated at the bottom of the abutment. The tightening and loosening torques are the main factors in determining the reliability and the stability of the attachment. Analytical formulas are developed to predict tightening and loosening torque values by combining the equations related to the tapered interface with screw mechanics equations. This enables the identification of the effects of the parameters such as friction, geometric properties of the screw, the taper angle, and the elastic properties of the materials on the mechanics of the system. In particular, a relation between the tightening torque and the screw pretension is identified. It was shown that the loosening torque is smaller than the tightening torque for typical values of the parameters. Most of the tightening load is carried by the tapered section of the abutment, and in certain combinations of the parameters the pretension in the screw may become zero. The calculations performed to determine the loosening torque as a percentage of tightening torque resulted in the range 85-137%, depending on the values of taper angle and the friction coefficient.

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

NASA Technical Reports Server (NTRS)

Stern, D. P.

1977-01-01

The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift.

Nonlinear power flow feedback control for improved stability and performance of airfoil sections

DOEpatents

Wilson, David G.; Robinett, III, Rush D.

2013-09-03

A computer-implemented method of determining the pitch stability of an airfoil system, comprising using a computer to numerically integrate a differential equation of motion that includes terms describing PID controller action. In one model, the differential equation characterizes the time-dependent response of the airfoil's pitch angle, .alpha.. The computer model calculates limit-cycles of the model, which represent the stability boundaries of the airfoil system. Once the stability boundary is known, feedback control can be implemented, by using, for example, a PID controller to control a feedback actuator. The method allows the PID controller gain constants, K.sub.I, K.sub.p, and K.sub.d, to be optimized. This permits operation closer to the stability boundaries, while preventing the physical apparatus from unintentionally crossing the stability boundaries. Operating closer to the stability boundaries permits greater power efficiencies to be extracted from the airfoil system.

Solution of the wave equation for open surfaces involving a line integral over the edge. [for supersonic propeller noise prediction

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

A simple mathematical model of a stationary source distribution for the supersonic-propeller noise-prediction formula of Farassat (1983) is developed to test the validity of the formula solutions. The conventional thickness source term is used in place of the Isom thickness formula; the relative importance of the line and surface integrals in the solutions is evaluated; and the numerical results are compared with those obtained with a conventional retarded-time solution in tables. Good agreement is obtained over elevation angles from 10 to 90 deg, and the line-integral contribution is found to be significant at all elevation angles and of the same order of magnitude as the surface-integral contribution at angles less than 30 deg. The amplitude-normalized directivity patterns for the four cases computed (x = 1.5 or 10; k = 5.0 or 50) are presented graphically.

Doppler Effect on Structure Period of Nonlinear Laser Lithography

NASA Astrophysics Data System (ADS)

Yavuz, Ozgun; Kara, Semih; Tokel, Onur; Pavlov, Ihor; Ilday, Fatih Omer

Recently, Nonlinear Laser Lithography (NLL) was developed for large-area, nanopatterning of surfaces. In NLL, nanopatterns emerge through coherent scattering of the laser from the surface, and its interference with the incident beam. The period of the structures is determined by the laser wavelength. It has been shown by Sipe that the period depends on the laser incidence angle (θ) as λ / (1 +/- sinθ). Here, we show that the period not only depends on this angle, but also on the polarisation angle. We update the Sipe equation as λ / (1 +/- sinθsinα) , where ' α' is the angle between scanning direction and polarisation. The physical reason behind this is found through a formal analogy to Doppler effect. In Doppler effect, the measured wavelength of a moving emitter is given as λ / (1 +/- c / vsinθ) , where ' θ'is the angle between observer and the direction of emitter, 'c' is the speed of observer, 'v' is speed of source. In NLL, velocity of source can be written as vsinθ , and the period equation can be shown to take its new form. We believe that this is the first application of Doppler effect in laser-processing of solid materials.

Microwave inversion of leaf area and inclination angle distributions from backscattered data

NASA Technical Reports Server (NTRS)

Lang, R. H.; Saleh, H. A.

1985-01-01

The backscattering coefficient from a slab of thin randomly oriented dielectric disks over a flat lossy ground is used to reconstruct the inclination angle and area distributions of the disks. The disks are employed to model a leafy agricultural crop, such as soybeans, in the L-band microwave region of the spectrum. The distorted Born approximation, along with a thin disk approximation, is used to obtain a relationship between the horizontal-like polarized backscattering coefficient and the joint probability density of disk inclination angle and disk radius. Assuming large skin depth reduces the relationship to a linear Fredholm integral equation of the first kind. Due to the ill-posed nature of this equation, a Phillips-Twomey regularization method with a second difference smoothing condition is used to find the inversion. Results are obtained in the presence of 1 and 10 percent noise for both leaf inclination angle and leaf radius densities.

Multiplicative Quaternion Extended Kalman Filtering for Nonspinning Guided Projectiles

DTIC Science & Technology

2013-07-01

tactical applications are inertial. The advantages of using quaternions rather than Euler angles to represent projectile attitude are discussed, and...projectiles generally don’t experience a wide range of heading angles , this has not a primary concern. The other major advantage of quaternions (or...DCMs) over Euler angles is their propagation equations are linear with respect to the quaternion and only depend on the IMU’s angular velocity. This

Accuracy and efficiency considerations for wide-angle wavefield extrapolators and scattering operators

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2005-10-01

Several observations are made concerning the numerical implementation of wide-angle one-way wave equations, using for illustration scalar waves obeying the Helmholtz equation in two space dimensions. This simple case permits clear identification of a sequence of physically motivated approximations of use when the mathematically exact pseudo-differential operator (PSDO) one-way method is applied. As intuition suggests, these approximations largely depend on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow-angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so-called `standard-ordering' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane-wave synthesis lying at the heart of the calculations. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one-way propagator for the laterally varying case, representing the intuitive extension of classical integral-transform solutions for a laterally homogeneous medium. This exponential propagator permits larger forward stepsizes. Numerical comparisons with Helmholtz (i.e. full) wave-equation finite-difference solutions are presented for various canonical problems. These include propagation along an interfacial gradient, the effects of a compact inclusion and the formation of extended transmitted and backscattered wave trains by model roughness. The ideas extend to the 3-D, generally anisotropic case and to multiple scattering by invariant embedding. It is concluded that the method is very competitive, striking a new balance between simplifying approximations and computational labour. Complicated wave-scattering effects are retained without the need for expensive global solutions, providing a robust and flexible modelling tool.

A Non-Linear Simulation for an Autonomous Unmanned Air Vehicle

DTIC Science & Technology

1993-09-01

4D cos T cos 4D cos T r These equations can now be integrated to find the time history of the Euler angles . 2. Quaternions Another choice for the...is associated with the Euler angles . Quaternions haxe been in 15 use for quite some time. having been discovered by Euler in a search for complex... quaternions has the following advantages over Euler angles in repre- senting spatial orientation of a rigid body: "* Four states required to express the

Numerical Simulation of Forced and Free-to-Roll Delta-Wing Motions

NASA Technical Reports Server (NTRS)

Chaderjian, Neal M.; Schiff, Lewis B.

1996-01-01

The three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) equations are used to numerically simulate nonsteady vortical flow about a 65-deg sweep delta wing at 30-deg angle of attack. Two large-amplitude, high-rate, forced-roll motions, and a damped free-to-roll motion are presented. The free-to-roll motion is computed by coupling the time-dependent RANS equations to the flight dynamic equation of motion. The computed results are in good agreement with the forces, moments, and roll-angle time histories. Vortex breakdown is present in each case. Significant time lags in the vortex breakdown motions relative to the body motions strongly influence the dynamic forces and moments.

Capillary Rise: Validity of the Dynamic Contact Angle Models.

PubMed

Wu, Pingkeng; Nikolov, Alex D; Wasan, Darsh T

2017-08-15

The classical Lucas-Washburn-Rideal (LWR) equation, using the equilibrium contact angle, predicts a faster capillary rise process than experiments in many cases. The major contributor to the faster prediction is believed to be the velocity dependent dynamic contact angle. In this work, we investigated the dynamic contact angle models for their ability to correct the dynamic contact angle effect in the capillary rise process. We conducted capillary rise experiments of various wetting liquids in borosilicate glass capillaries and compared the model predictions with our experimental data. The results show that the LWR equations modified by the molecular kinetic theory and hydrodynamic model provide good predictions on the capillary rise of all the testing liquids with fitting parameters, while the one modified by Joos' empirical equation works for specific liquids, such as silicone oils. The LWR equation modified by molecular self-layering model predicts well the capillary rise of carbon tetrachloride, octamethylcyclotetrasiloxane, and n-alkanes with the molecular diameter or measured solvation force data. The molecular self-layering model modified LWR equation also has good predictions on the capillary rise of silicone oils covering a wide range of bulk viscosities with the same key parameter W(0), which results from the molecular self-layering. The advantage of the molecular self-layering model over the other models reveals the importance of the layered molecularly thin wetting film ahead of the main meniscus in the energy dissipation associated with dynamic contact angle. The analysis of the capillary rise of silicone oils with a wide range of bulk viscosities provides new insights into the capillary dynamics of polymer melts.

Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Zhou, Ye

1996-01-01

Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

Scattering from arbitrarily shaped microstrip patch antennas

NASA Technical Reports Server (NTRS)

Shively, David G.; Deshpande, Manohar D.; Cockrell, Capers R.

1992-01-01

The scattering properties of arbitrarily shaped microstrip patch antennas are examined. The electric field integral equation for a current element on a grounded dielectric slab is developed for a rectangular geometry based on Galerkin's technique with subdomain rooftop basis functions. A shape function is introduced that allows a rectangular grid approximation to the arbitrarily shaped patch. The incident field on the patch is expressed as a function of incidence angle theta(i), phi(i). The resulting system of equations is then solved for the unknown current modes on the patch, and the electromagnetic scattering is calculated for a given angle. Comparisons are made with other calculated results as well as with measurements.

Deflection of light by black holes and massless wormholes in massive gravity

NASA Astrophysics Data System (ADS)

Jusufi, Kimet; Sarkar, Nayan; Rahaman, Farook; Banerjee, Ayan; Hansraj, Sudan

2018-04-01

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov, JHEP 0904:100, 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass M and an extra parameter S namely `scalar charge'. These black hole reduce to the standard Schwarzschild black hole solutions when the scalar charge is zero and the mass is positive. In addition, a parameter λ in the metric characterizes so-called `hair'. The geodesic equations are used to examine the behavior of the deflection angle in four relevant cases of the parameter λ . Then, by introducing a simple coordinate transformation r^λ =S+v^2 into the black hole metric, we were able to find a massless wormhole solution of Einstein-Rosen (ER) (Einstein and Rosen, Phys Rev 43:73, 1935) type with scalar charge S. The programme is then repeated in terms of the Gauss-Bonnet theorem in the weak field limit after a method is established to deal with the angle of deflection using different domains of integration depending on the parameter λ . In particular, we have found new analytical results corresponding to four special cases which generalize the well known deflection angles reported in the literature. Finally, we have established the time delay problem in the spacetime of black holes and wormholes, respectively.

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

PubMed Central

Kang, Chang-kwon; Shyy, Wei

2014-01-01

In the analysis of flexible flapping wings of insects, the aerodynamic outcome depends on the combined structural dynamics and unsteady fluid physics. Because the wing shape and hence the resulting effective angle of attack are a priori unknown, predicting aerodynamic performance is challenging. Here, we show that a coupled aerodynamics/structural dynamics model can be established for hovering, based on a linear beam equation with the Morison equation to account for both added mass and aerodynamic damping effects. Lift strongly depends on the instantaneous angle of attack, resulting from passive pitch associated with wing deformation. We show that both instantaneous wing deformation and lift can be predicted in a much simplified framework. Moreover, our analysis suggests that resulting wing kinematics can be explained by the interplay between acceleration-related and aerodynamic damping forces. Interestingly, while both forces combine to create a high angle of attack resulting in high lift around the midstroke, they offset each other for phase control at the end of the stroke. PMID:25297319

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

NASA Technical Reports Server (NTRS)

Campbell, Joel

2009-01-01

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

Orientation dependence of grain-boundary energy in metals in the view of a pseudoheterophase dislocation core model

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

Missol, W.

A new dislocation model for symmetric tilt grain boundaries was developed as a basis for deriving the quantitative dependence of grain-boundary energy upon misorientation angle in the form of an expression similar to that given by Read and Shockley (Phys. Rev. 78: 275(1950)). The range of applicability of this equation was extended to over 20 degrees. A comparison of theory and experiment was made for Bi, Ag, Cu, and Fe--Si 3 percent in the teen-degree range of misorientation angles and for Au, ..cap alpha..-Fe, Mo, and W in the high-angle range.

Quantitative FLASH MRI at 3T using a rational approximation of the Ernst equation.

PubMed

Helms, Gunther; Dathe, Henning; Dechent, Peter

2008-03-01

From the half-angle substitution of trigonometric terms in the Ernst equation, rational approximations of the flip angle dependence of the FLASH signal can be derived. Even the rational function of the lowest order was in good agreement with the experiment for flip angles up to 20 degrees . Three-dimensional maps of the signal amplitude and longitudinal relaxation rates in human brain were obtained from eight subjects by dual-angle measurements at 3T (nonselective 3D-FLASH, 7 degrees and 20 degrees flip angle, TR = 30 ms, isotropic resolution of 0.95 mm, each 7:09 min). The corresponding estimates of T1 and signal amplitude are simple algebraic expressions and deviated about 1% from the exact solution. They are ill-conditioned to estimate the local flip angle deviation but can be corrected post hoc by division of squared RF maps obtained by independent measurements. Local deviations from the nominal flip angles strongly affected the relaxation estimates and caused considerable blurring of the T1 histograms. (c) 2008 Wiley-Liss, Inc.

Free polar motion of a triaxial and elastic body in Hamiltonian formalism: Application to the Earth and Mars

NASA Astrophysics Data System (ADS)

Folgueira, M.; Souchay, J.

2005-03-01

The purpose of this paper is to show how to solve in Hamiltonian formalism the equations of the polar motion of any arbitrarily shaped elastic celestial body, i.e. the motion of its rotation axis (or angular momentum) with respect to its figure axis. With this aim, we deduce from canonical equations related to the rotational Hamiltonian of the body, the analytical solution for its free polar motion which depends both on the elasticity and on its moments of inertia. In particular, we study the influence of the phase angle δ, responsible for the dissipation, on the damping of the polar motion. In order to validate our analytical equations, we show that, to first order, they are in complete agreement with those obtained from the classical Liouville equations. Then we adapt our calculations to the real data obtained from the polar motion of the Earth (polhody). For that purpose, we characterize precisely the differences in radius J-χ and in angle l-θ between the polar coordinates (χ,θ) and (J,l) representing respectively the motion of the axis of rotation of the Earth and the motion of its angular momentum axis, with respect to an Earth-fixed reference frame, after showing the influence of the choice of the origin on these coordinates, and on the determination of the Chandler period as well. Then we show that the phase lag δ responsible for the damping for the selected time interval, between Feb. 1982 and Apr. 1990, might be of the order of δ ≈ 6 °, according to a numerical integration starting from our analytical equations. Moreover, we emphasize the presence in our calculations for both χ and θ, of an oscillation with a period TChandler/2, due to the triaxial shape of our planet, and generally not taken into account. In a last step, we apply our analytical formulation to the polar motion of Mars, thus showing the high dependence of its damping on the poorly known value of its Love number k. Moreover we emphasize the large oscillations of Mars' polar motion due to the triaxiality of this planet.

Wetting of soap bubbles on hydrophilic, hydrophobic, and superhydrophobic surfaces

NASA Astrophysics Data System (ADS)

Arscott, Steve

2013-06-01

Wetting of sessile bubbles on various wetting surfaces (solid and liquid) has been studied. A model is presented for the apparent contact angle of a sessile bubble based on a modified Young's equation--the experimental results agree with the model. Wetting a hydrophilic surface results in a bubble contact angle of 90° whereas using a superhydrophobic surface one observes 134°. For hydrophilic surfaces, the bubble angle diminishes with bubble radius whereas on a superhydrophobic surface, the bubble angle increases. The size of the plateau borders governs the bubble contact angle, depending on the wetting of the surface.

Structure of Poly(dialkylsiloxane) Melts:  Comparisons of Wide-Angle X-ray Scattering, Molecular Dynamics Simulations, and Integral Equation Theory

DOE PAGES

Habenschuss, Anton; Tsige, Mesfin; Curro, John G.; ...

2007-08-21

Here, wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between themore » MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Finally, experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.« less

Motion of the angular momentum vector in body coordinates for torque-free dual-spin spacecraft

NASA Technical Reports Server (NTRS)

Fedor, J. V.

1981-01-01

The motion of the angular momentum vector in body coordinates for torque free, asymmetric dual spin spacecraft without and, for a special case, with energy dissipation on the main spacecraft is investigated. Without energy dissipation, two integrals can be obtained from the Euler equations of motion. Using the classical method of elimination of variable, the motion about the equilibrium points (six for the general case) are derived with these integrals. For small nutation angle, theta, the trajectories about the theta = 0 deg and theta = 180 deg points readily show the requirements for stable motion about these points. Also the conditions needed to eliminate stable motion about the theta = 180 deg point as well as the other undesireable equilibrium points follow directly from these equations. For the special case where the angular momentum vector moves about the principal axis which contains the momentum wheel, the notion of 'free variable' azimuth angle is used. Physically this angle must vary from 0 to 2 pi in a circular periodic fashion. Expressions are thus obtained for the nutation angle in terms of the free variable and other spacecraft parameters. Results show that in general there are two separate trajectory expressions that govern the motion of the angular momentum vector in body coordinates.

Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method

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

Davidenko, V. D., E-mail: Davidenko-VD@nrcki.ru; Zinchenko, A. S., E-mail: zin-sn@mail.ru; Harchenko, I. K.

2016-12-15

Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.

PIV-based estimation of unsteady loads on a flat plate at high angle of attack using momentum equation approaches

NASA Astrophysics Data System (ADS)

Guissart, Amandine; Bernal, Luis; Dimitriadis, Gregorios; Terrapon, Vincent

2015-11-01

The direct measurement of loads with force balance can become challenging when the forces are small or when the body is moving. An alternative is the use of Particle Image Velocimetry (PIV) velocity fields to indirectly obtain the aerodynamic coefficients. This can be done by the use of control volume approaches which lead to the integration of velocities, and other fields deriving from them, on a contour surrounding the studied body and its supporting surface. This work exposes and discusses results obtained with two different methods: the direct use of the integral formulation of the Navier-Stokes equations and the so-called Noca's method. The latter is a reformulation of the integral Navier-Stokes equations in order to get rid of the pressure. Results obtained using the two methods are compared and the influence of different parameters is discussed. The methods are applied to PIV data obtained from water channel testing for the flow around a 16:1 plate. Two cases are considered: a static plate at high angle of attack and a large amplitude imposed pitching motion. Two-dimensional PIV velocity fields are used to compute the aerodynamic forces. Direct measurements of dynamic loads are also carried out in order to assess the quality of the indirectly calculated coefficients.

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

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

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

Tables for Supersonic Flow of Helium Around Right Circular Cones at Zero Angle of Attack

NASA Technical Reports Server (NTRS)

Sims, J. L.

1973-01-01

The results of the calculation of supersonic flow of helium about right circular cones at zero angle of attack are presented in tabular form. The calculations were performed using the Taylor-Maccoll theory. Numerical integrations were performed using a Runge-Kutta method for second-order differential equations. Results were obtained for cone angles from 2.5 to 30 degrees in regular increments of 2.5 degrees. In all calculations the desired free-stream Mach number was obtained to five or more significant figures.

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

Nonlinear mode interaction in equal-leg angle struts susceptible to cellular buckling.

PubMed

Bai, L; Wang, F; Wadee, M A; Yang, J

2017-11-01

A variational model that describes the interactive buckling of a thin-walled equal-leg angle strut under pure axial compression is presented. A formulation combining the Rayleigh-Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Solving the equations using numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weak-axis flexural buckling mode and the strong-axis flexural-torsional buckling mode for the first time-the resulting behaviour being highly unstable. Physical experiments conducted on 10 cold-formed steel specimens are presented and the results show good agreement with the variational model.

Contact angle of a nanodrop on a nanorough solid surface.

PubMed

Berim, Gersh O; Ruckenstein, Eli

2015-02-21

The contact angle of a cylindrical nanodrop on a nanorough solid surface is calculated, for both hydrophobic and hydrophilic surfaces, using the density functional theory. The emphasis of the paper is on the dependence of the contact angle on roughness. The roughness is modeled by rectangular pillars of infinite length located on the smooth surface of a substrate, with fluid-pillar interactions different in strength from the fluid-substrate ones. It is shown that for hydrophobic substrates the trend of the contact angle to increase with increasing roughness, which was noted in all previous studies, is not universally valid, but depends on the fluid-pillar interactions, pillar height, interpillar distance, as well as on the size of the drop. For hydrophilic substrate, an unusual kink-like dependence of the contact angle on the nanodrop size is found which is caused by the change in the location of the leading edges of the nanodrop on the surface. It is also shown that the Wenzel and Cassie-Baxter equations can not explain all the peculiarities of the contact angle of a nanodrop on a nanorough surface.

Exact Solutions of Schrödinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

NASA Astrophysics Data System (ADS)

Ndem Ikot, Akpan; Akpan, Ita O.; Abbey, T. M.; Hassanabadi, Hassan

2016-05-01

We propose improved ring shaped like potential of the form, V(r, θ) = V(r) + (ħ2/2Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2 and its exact solutions are presented via the Nikiforov-Uvarov method. The angle dependent part V(θ) = (ħ2 / 2 Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2, which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.

Orientation-dependent integral equation theory for a two-dimensional model of water

NASA Astrophysics Data System (ADS)

Urbič, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.

2003-03-01

We develop an integral equation theory that applies to strongly associating orientation-dependent liquids, such as water. In an earlier treatment, we developed a Wertheim integral equation theory (IET) that we tested against NPT Monte Carlo simulations of the two-dimensional Mercedes Benz model of water. The main approximation in the earlier calculation was an orientational averaging in the multidensity Ornstein-Zernike equation. Here we improve the theory by explicit introduction of an orientation dependence in the IET, based upon expanding the two-particle angular correlation function in orthogonal basis functions. We find that the new orientation-dependent IET (ODIET) yields a considerable improvement of the predicted structure of water, when compared to the Monte Carlo simulations. In particular, ODIET predicts more long-range order than the original IET, with hexagonal symmetry, as expected for the hydrogen bonded ice in this model. The new theoretical approximation still errs in some subtle properties; for example, it does not predict liquid water's density maximum with temperature or the negative thermal expansion coefficient.

Nonlinear waves in electron-positron-ion plasmas including charge separation

NASA Astrophysics Data System (ADS)

Mugemana, A.; Moolla, S.; Lazarus, I. J.

2017-02-01

Nonlinear low-frequency electrostatic waves in a magnetized, three-component plasma consisting of hot electrons, hot positrons and warm ions have been investigated. The electrons and positrons are assumed to have Boltzmann density distributions while the motion of the ions are governed by fluid equations. The system is closed with the Poisson equation. This set of equations is numerically solved for the electric field. The effects of the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle are investigated. It is shown that depending on the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle, the numerical solutions exhibit waveforms that are sinusoidal, sawtooth and spiky. The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E 0 was reduced. The results are compared with satellite observations.

Integral equation approach to time-dependent kinematic dynamos in finite domains

NASA Astrophysics Data System (ADS)

Xu, Mingtian; Stefani, Frank; Gerbeth, Gunter

2004-11-01

The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of the Biot-Savart law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to time-dependent kinematic dynamos, with stationary dynamo sources, in finite domains. The time dependence is restricted to the magnetic field, whereas the velocity or corresponding mean-field sources of dynamo action are supposed to be stationary. For the spherically symmetric α2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and toroidal field components. The integral equation formulation for spherical dynamos with general stationary velocity fields is also derived. Two numerical examples—the α2 dynamo model with radially varying α and the Bullard-Gellman model—illustrate the equivalence of the approach with the usual differential equation method. The main advantage of the method is exemplified by the treatment of an α2 dynamo in rectangular domains.

Exact time-dependent solutions for a self-regulating gene.

PubMed

Ramos, A F; Innocentini, G C P; Hornos, J E M

2011-06-01

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

Propagators for the Time-Dependent Kohn-Sham Equations: Multistep, Runge-Kutta, Exponential Runge-Kutta, and Commutator Free Magnus Methods.

PubMed

Gómez Pueyo, Adrián; Marques, Miguel A L; Rubio, Angel; Castro, Alberto

2018-05-09

We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge-Kutta, exponential Runge-Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

The reflection for dense plant canopies from the one-angle radiative transfer equation

NASA Technical Reports Server (NTRS)

Ganapol, B. D.; Lawless, James G. (Technical Monitor)

1994-01-01

An essential component of remote sensing of vegetation canopies from satellites is fundamental understanding. Since passive remote is driven by photons, the modeling of photon interactions with vegetation is a basic building block in that understanding. Several such photon transport models have been developed during the past two decades and continue to be developed. Different approaches have been followed including monte carlo, radiosity methods, geometric shadowing, and radiative transfer. In general, each approach has application for canopies with specific attributes. This presentation concerns the application of radiative transfer to dense vegetation canopies in which the soil does not participate. The approach taken here is novel in that a consistent theory for photon transport for non-rotationally invariant leaf scattering is developed in a canopy with a general leaf angle distribution (LAD). The theory is limited to the one-angle approximation (azimuthally averaged radiance) and is based on Chandrasekhar's analytical theory. While such a model is admittedly only approximate, it does fulfill a unique function in our search for understanding. In particular, the model is simple in its construct yet contains the essential features of canopy architecture that are mainly responsible for observed responses. Thus, this model will not only be a predictive tool but also an educational one. The mathematical setting is the radiative transfer equation in a dense (semiinfinite) canopy. The leaf scattering phase function is assumed to be Lambertian with different reflectance and transmittance. In addition, abaxial and adaxial differentiation is allowed which effectively destroys optical reciprocity. The analytical solution for the canopy BRDF is obtained by manipulation of the integral transport equation (a la Chandrasekhar) for a general LAD. With discretization of the. leaf angle, the resulting set of integral equations are solved iteratively including an acceleration procedure when the single scatter albedo is near one (in the NIR). Results will be compared to the LARS soybean canopy radiances as well as to broadleaf results from a recent Ames experiment.

Nonlinear flap-lag-axial equations of a rotating beam with arbitrary precone angle

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; White, W. F., Jr.; Kaza, K. R. V.

1978-01-01

In an attempt both to unify and extend the analytical basis of several aspects of the dynamic behavior of flexible rotating beams, the second-degree nonlinear equations of motion for the coupled flapwise bending, lagwise bending, and axial extension of an untwisted, torsionally rigid, nonuniform, rotating beam having an arbitrary angle of precone with the plane perpendicular to the axis of rotation are derived using Hamilton's principle. The derivation of the equations is based on the geometric nonlinear theory of elasticity and the resulting equations are consistent with the assumption that the strains are negligible compared to unity. No restrictions are imposed on the relative displacements or angular rotations of the cross sections of the beam other than those implied by the assumption of small strains. Illustrative numerical results, obtained by using an integrating matrix as the basis for the method of solution, are presented both for the purpose of validating the present method of solution and indicating the range of applicability of the equations of motion and the method of solution.

The kinked interface crack

NASA Astrophysics Data System (ADS)

Heitzer, Joerg

1992-05-01

Two methods for the numerical solution of the integral equation describing the kinked interface crack, one proposed by Erdogan et al. (1973) and the other by Theokaris and Iokimidis (1979), are examined. The method of Erdogan et al. is then used to solve the equation in order to determine the kinking angle of the interface crack. Results are presented for two material combinations, aluminum/epoxy and glass/ceramic, under uniaxial tension in the direction normal to the interface.

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover.

PubMed

Kang, Chang-kwon; Shyy, Wei

2014-12-06

In the analysis of flexible flapping wings of insects, the aerodynamic outcome depends on the combined structural dynamics and unsteady fluid physics. Because the wing shape and hence the resulting effective angle of attack are a priori unknown, predicting aerodynamic performance is challenging. Here, we show that a coupled aerodynamics/structural dynamics model can be established for hovering, based on a linear beam equation with the Morison equation to account for both added mass and aerodynamic damping effects. Lift strongly depends on the instantaneous angle of attack, resulting from passive pitch associated with wing deformation. We show that both instantaneous wing deformation and lift can be predicted in a much simplified framework. Moreover, our analysis suggests that resulting wing kinematics can be explained by the interplay between acceleration-related and aerodynamic damping forces. Interestingly, while both forces combine to create a high angle of attack resulting in high lift around the midstroke, they offset each other for phase control at the end of the stroke. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

A Finite-Difference Time-Domain Model of Artificial Ionospheric Modification

NASA Astrophysics Data System (ADS)

Cannon, Patrick; Honary, Farideh; Borisov, Nikolay

Experiments in the artificial modification of the ionosphere via a radio frequency pump wave have observed a wide range of non-linear phenomena near the reflection height of an O-mode wave. These effects exhibit a strong aspect-angle dependence thought to be associated with the process by which, for a narrow range of off-vertical launch angles, the O-mode pump wave can propagate beyond the standard reflection height at X=1 as a Z-mode wave and excite additional plasma activity. A numerical model based on Finite-Difference Time-Domain method has been developed to simulate the interaction of the pump wave with an ionospheric plasma and investigate different non-linear processes involved in modification experiments. The effects on wave propagation due to plasma inhomogeneity and anisotropy are introduced through coupling of the Lorentz equation of motion for electrons and ions to Maxwell’s wave equations in the FDTD formulation, leading to a model that is capable of exciting a variety of plasma waves including Langmuir and upper-hybrid waves. Additionally, discretized equations describing the time-dependent evolution of the plasma fluid temperature and density are included in the FDTD update scheme. This model is used to calculate the aspect angle dependence and angular size of the radio window for which Z-mode excitation occurs, and the results compared favourably with both theoretical predictions and experimental observations. The simulation results are found to reproduce the angular dependence on electron density and temperature enhancement observed experimentally. The model is used to investigate the effect of different initial plasma density conditions on the evolution of non-linear effects, and demonstrates that the inclusion of features such as small field-aligned density perturbations can have a significant influence on wave propagation and the magnitude of temperature and density enhancements.

Microscopic description of a drop on a solid surface.

PubMed

Ruckenstein, Eli; Berim, Gersh O

2010-06-14

Two approaches recently suggested for the treatment of macro- or nanodrops on smooth or rough, planar or curved, solid surfaces, based on fluid-fluid and fluid-solid interaction potentials are reviewed. The first one employs the minimization of the total potential energy of a drop by assuming that the drop has a well defined profile and a constant liquid density in its entire volume with the exception of the monolayer nearest to the surface where the density has a different value. As a result, a differential equation for the drop profile as well as the necessary boundary conditions are derived which involve the parameters of the interaction potentials and do not contain such macroscopic characteristics as the surface tensions. As a consequence, the macroscopic and microscopic contact angles which the drop profile makes with the surface can be calculated. The macroscopic angle is obtained via the extrapolation of the circular part of the drop profile valid at some distance from the surface up to the solid surface. The microscopic angle is formed at the intersection of the real profile (which is not circular near the surface) with the surface. The theory provides a relation between these two angles. The ranges of the microscopic parameters of the interaction potentials for which (i) the drop can have any height (volume), (ii) the drop can have a restricted height but unrestricted volume, and (iii) a drop cannot be formed on the surface were identified. The theory was also extended to the description of a drop on a rough surface. The second approach is based on a nonlocal density functional theory (DFT), which accounts for the inhomogeneity of the liquid density and temperature effects, features which are missing in the first approach. Although the computational difficulties restrict its application to drops of only several nanometers, the theory can be applied indirectly to macrodrops by calculating the surface tensions and using the Young equation to determine the contact angle. Employing the canonical ensemble version of the DFT, nanodrops on smooth and rough solid surfaces could be investigated and their characteristics, such as the drop profile, contact angle, as well as the fluid density distribution inside the drop can be determined as functions of the parameters of the interaction potentials and temperature. It was found that the contact angle of the drop has a simple (quasi)universal dependence on the energy parameter epsilon(fs) of the fluid-solid interaction potential and temperature. The main feature of this dependence is the existence of a fixed value theta(0) of the contact angle theta which separates the solid substrates (characterized by the energy parameter epsilon(fs) of the fluid-solid interaction potential) into two classes with respect to their temperature dependence. For theta>theta(0) the contact angle monotonously increases and for theta

Rayleigh Scattering in Planetary Atmospheres: Corrected Tables Through Accurate Computation of X and Y Functions

NASA Astrophysics Data System (ADS)

Natraj, Vijay; Li, King-Fai; Yung, Yuk L.

2009-02-01

Tables that have been used as a reference for nearly 50 years for the intensity and polarization of reflected and transmitted light in Rayleigh scattering atmospheres have been found to be inaccurate, even to four decimal places. We convert the integral equations describing the X and Y functions into a pair of coupled integro-differential equations that can be efficiently solved numerically. Special care has been taken in evaluating Cauchy principal value integrals and their derivatives that appear in the solution of the Rayleigh scattering problem. The new approach gives results accurate to eight decimal places for the entire range of tabulation (optical thicknesses 0.02-1.0, surface reflectances 0-0.8, solar and viewing zenith angles 0°-88.85°, and relative azimuth angles 0°-180°), including the most difficult case of direct transmission in the direction of the sun. Revised tables have been created and stored electronically for easy reference by the planetary science and astrophysics community.

Large-Amplitude, High-Rate Roll Oscillations of a 65 deg Delta Wing at High Incidence

NASA Technical Reports Server (NTRS)

Chaderjian, Neal M.; Schiff, Lewis B.

2000-01-01

The IAR/WL 65 deg delta wing experimental results provide both detail pressure measurements and a wide range of flow conditions covering from simple attached flow, through fully developed vortex and vortex burst flow, up to fully-stalled flow at very high incidence. Thus, the Computational Unsteady Aerodynamics researchers can use it at different level of validating the corresponding code. In this section a range of CFD results are provided for the 65 deg delta wing at selected flow conditions. The time-dependent, three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) equations are used to numerically simulate the unsteady vertical flow. Two sting angles and two large- amplitude, high-rate, forced-roll motions and a damped free-to-roll motion are presented. The free-to-roll motion is computed by coupling the time-dependent RANS equations to the flight dynamic equation of motion. The computed results are compared with experimental pressures, forces, moments and roll angle time history. In addition, surface and off-surface flow particle streaks are also presented.

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

NASA Astrophysics Data System (ADS)

Wang, C. R.; Papell, S. S.; Graham, R. W.

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30 degree inclination angle.

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

NASA Technical Reports Server (NTRS)

Wang, C. R.; Papell, S. S.; Graham, R. W.

1981-01-01

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30 degree inclination angle.

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

NASA Astrophysics Data System (ADS)

Wang, C. R.; Papell, S. S.; Graham, R. W.

1981-03-01

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center-line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30-deg inclination angle.

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

NASA Technical Reports Server (NTRS)

Wang, C. R.; Papell, S. S.; Graham, R. W.

1981-01-01

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center-line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30-deg inclination angle.

Modeling the stress dependence of Barkhausen phenomena for stress axis linear and noncollinear with applied magnetic field (abstract)

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

Sablik, M.J.; Augustyniak, B.; Chmielewski, M.

1996-04-01

The almost linear dependence of the maximum Barkhausen noise signal amplitude on stress has made it a tool for nondestructive evaluation of residual stress. Recently, a model has been developed to account for the stress dependence of the Barkhausen noise signal. The model uses the development of Alessandro {ital et} {ital al}. who use coupled Langevin equations to derive an expression for the Barkhausen noise power spectrum. The model joins this expression to the magnetomechanical hysteresis model of Sablik {ital et} {ital al}., obtaining both a hysteretic and stress-dependent result for the magnetic-field-dependent Barkhausen noise envelope and obtaining specifically themore » almost linear stress dependence of the Barkhausen noise maximum experimentally. In this paper, we extend the model to derive the angular dependence observed by Kwun of the Barkhausen noise amplitude when stress axis is taken at different angles relative to magnetic field. We also apply the model to the experimental observation that in XC10 French steel, there is an apparent almost linear correlation with stress of hysteresis loss and of the integral of the Barkhausen noise signal over applied field {ital H}. Further, the two quantities, Barkhausen noise integral and hysteresis loss, are linearly correlated with each other. The model shows how that behavior is to be expected for the measured steel because of its sharply rising hysteresis curve. {copyright} {ital 1996 American Institute of Physics.}« less

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

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

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

Properties of seismic absorption induced reflections

NASA Astrophysics Data System (ADS)

Zhao, Haixia; Gao, Jinghuai; Peng, Jigen

2018-05-01

Seismic reflections at an interface are often regarded as the variation of the acoustic impedance (product of seismic velocity and density) in a medium. In fact, they can also be generated due to the difference in absorption of the seismic energy. In this paper, we investigate the properties of such reflections. Based on the diffusive-viscous wave equation and elastic diffusive-viscous wave equation, we investigate the dependency of the reflection coefficients on frequency, and their variations with incident angles. Numerical results at a boundary due to absorption contrasts are compared with those resulted from acoustic impedance variation. It is found that, the reflection coefficients resulted from absorption depend significantly on the frequency especially at lower frequencies, but vary very slowly at small incident angles. At the higher frequencies, the reflection coefficients of diffusive-viscous wave and elastic diffusive-viscous wave are close to those of acoustic and elastic cases, respectively. On the other hand, the reflections caused by acoustic impedance variation are independent of frequency but vary distinctly with incident angles before the critical angle. We also investigate the difference between the seismograms generated in the two different media. The numerical results show that the amplitudes of these reflected waves are attenuated and their phases are shifted. However, the reflections obtained by acoustic impedance contrast, show no significant amplitude attenuation and phase shift.

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1975-01-01

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Bonded half planes containing an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Aksogan, O.

1973-01-01

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin transforms, the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given include the stress intensity factors, tHe strain energy release rates, and tHe probable cleavage angles giving the direction of crack propagation.

Modified Kelvin Equations for Capillary Condensation in Narrow and Wide Grooves

NASA Astrophysics Data System (ADS)

Malijevský, Alexandr; Parry, Andrew O.

2018-03-01

We consider the location and order of capillary condensation transitions occurring in deep grooves of width L and depth D . For walls that are completely wet by liquid (contact angle θ =0 ) the transition is continuous and its location is not sensitive to the depth of the groove. However, for walls that are partially wet by liquid, where the transition is first order, we show that the pressure at which it occurs is determined by a modified Kelvin equation characterized by an edge contact angle θE describing the shape of the meniscus formed at the top of the groove. The dependence of θE on the groove depth D relies, in turn, on whether corner menisci are formed at the bottom of the groove in the low density gaslike phase. While for macroscopically wide grooves these are always present when θ <45 ° we argue that their formation is inhibited in narrow grooves. This has a number of implications including that the local pinning of the meniscus and location of the condensation transition is different depending on whether the contact angle is greater or less than a universal value θ*≈31 °. Our arguments are supported by detailed microscopic density functional theory calculations that show that the modified Kelvin equation remains highly accurate even when L and D are of the order of tens of molecular diameters.

Application of integral equation theory to analyze stability of electric field in multimode microwave heating cavity

NASA Astrophysics Data System (ADS)

Tang, Zhengming; Hong, Tao; Chen, Fangyuan; Zhu, Huacheng; Huang, Kama

2017-10-01

Microwave heating uniformity is mainly dependent on and affected by electric field. However, little study has paid attention to its stability characteristics in multimode cavity. In this paper, this problem is studied by the theory of Freedholm integral equation. Firstly, Helmholtz equation and the electric dyadic Green's function are used to derive the electric field integral equation. Then, the stability of electric field is demonstrated as the characteristics of solutions to Freedholm integral equation. Finally, the stability characteristics are obtained and verified by finite element calculation. This study not only can provide a comprehensive interpretation of electric field in multimode cavity but also help us make better use of microwave energy.

Simulation study of MEMS piezoelectric vibration energy harvester based on c-axis tilted AlN thin film for performance improvement

NASA Astrophysics Data System (ADS)

Kong, Lingfeng; Zhang, Jinhui; Wang, Huiyuan; Ma, Shenglin; Li, Fang; Wang, Qing-Ming; Qin, Lifeng

2016-12-01

In this paper, a MEMS piezoelectric cantilevered vibration energy harvester based on c-axis tilted AlN thin film is investigated. Based on basic piezoelectric equations and static analysis of cantilever beam, the equations for generated energy (E) and open circuit voltage (Vo) were derived, and simulations were carried out to study the effects of geometry parameters and c-axis tilted angle. Results show that E and Vo of energy harvesters are greatly dependent on c-axis tilted angle and geometry parameters, while the coupling between c-axis tilted angle and geometry parameters is not strong. For a given structure size, E and Vo can be almost simultaneously improved by controlling c-axis tilted angle; compared with the case of normal c-axis angle, E with optimal c-axis tilted angle can be amplified by more than 3 times, and the Vo is amplified by about 2 times. E or Vo could be further improved by geometry parameters, while there is trade-off between them. These results can be used for the design and application of piezoelectric cantilevered vibration energy harvester.

Computational methods for vortex dominated compressible flows

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.

Numerical research of parameters of interaction of the gas flow with rotary valve of the gas pipeline

NASA Astrophysics Data System (ADS)

Boldyrev, A. V.; Karelin, D. L.; Muljukin, V. L.

2016-11-01

Conducted numerical research of static characteristics of the rotary gate valve at different angles of its deviation. for this purpose were set different values of pressure differential on the valve depending on which, was determined the mass flow and torque on valve axes. The mathematical model is provided by continuity equations, average on Reynolds, Navier-Stokes and energy, the equation of the perfect gas, the equations of two-layer k-e of model of turbulence. When calculating the current near walls are used Wolfstein's model and the hybrid wall functions of Reichardt for the speed and temperature. The task is solved in three-dimensional statement with use of conditions of symmetry. The structure of the current is analyzed: zones of acceleration and flow separation, whirlwinds, etc. Noted growth of hydraulic resistance of the valve with reduction of slope angle of the valve and with the increase in mass flow. Established increase of torque with reduction of the deviation angle of the valve and with increase in the mass expense.

Integral Equations in Computational Electromagnetics: Formulations, Properties and Isogeometric Analysis

NASA Astrophysics Data System (ADS)

Lovell, Amy Elizabeth

Computational electromagnetics (CEM) provides numerical methods to simulate electromagnetic waves interacting with its environment. Boundary integral equation (BIE) based methods, that solve the Maxwell's equations in the homogeneous or piecewise homogeneous medium, are both efficient and accurate, especially for scattering and radiation problems. Development and analysis electromagnetic BIEs has been a very active topic in CEM research. Indeed, there are still many open problems that need to be addressed or further studied. A short and important list includes (1) closed-form or quasi-analytical solutions to time-domain integral equations, (2) catastrophic cancellations at low frequencies, (3) ill-conditioning due to high mesh density, multi-scale discretization, and growing electrical size, and (4) lack of flexibility due to re-meshing when increasing number of forward numerical simulations are involved in the electromagnetic design process. This dissertation will address those several aspects of boundary integral equations in computational electromagnetics. The first contribution of the dissertation is to construct quasi-analytical solutions to time-dependent boundary integral equations using a direct approach. Direct inverse Fourier transform of the time-harmonic solutions is not stable due to the non-existence of the inverse Fourier transform of spherical Hankel functions. Using new addition theorems for the time-domain Green's function and dyadic Green's functions, time-domain integral equations governing transient scattering problems of spherical objects are solved directly and stably for the first time. Additional, the direct time-dependent solutions, together with the newly proposed time-domain dyadic Green's functions, can enrich the time-domain spherical multipole theory. The second contribution is to create a novel method of moments (MoM) framework to solve electromagnetic boundary integral equation on subdivision surfaces. The aim is to avoid the meshing and re-meshing stages to accelerate the design process when the geometry needs to be updated. Two schemes to construct basis functions on the subdivision surface have been explored. One is to use the div-conforming basis function, and the other one is to create a rigorous iso-geometric approach based on the subdivision basis function with better smoothness properties. This new framework provides us better accuracy, more stability and high flexibility. The third contribution is a new stable integral equation formulation to avoid catastrophic cancellations due to low-frequency breakdown or dense-mesh breakdown. Many of the conventional integral equations and their associated post-processing operations suffer from numerical catastrophic cancellations, which can lead to ill-conditioning of the linear systems or serious accuracy problems. Examples includes low-frequency breakdown and dense mesh breakdown. Another instability may come from nontrivial null spaces of involving integral operators that might be related with spurious resonance or topology breakdown. This dissertation presents several sets of new boundary integral equations and studies their analytical properties. The first proposed formulation leads to the scalar boundary integral equations where only scalar unknowns are involved. Besides the requirements of gaining more stability and better conditioning in the resulting linear systems, multi-physics simulation is another driving force for new formulations. Scalar and vector potentials (rather than electromagnetic field) based formulation have been studied for this purpose. Those new contributions focus on different stages of boundary integral equations in an almost independent manner, e.g. isogeometric analysis framework can be used to solve different boundary integral equations, and the time-dependent solutions to integral equations from different formulations can be achieved through the same methodology proposed.

A wide-angle high Mach number modal expansion for infrasound propagation.

PubMed

Assink, Jelle; Waxler, Roger; Velea, Doru

2017-03-01

The use of modal expansions to solve the problem of atmospheric infrasound propagation is revisited. A different form of the associated modal equation is introduced, valid for wide-angle propagation in atmospheres with high Mach number flow. The modal equation can be formulated as a quadratic eigenvalue problem for which there are simple and efficient numerical implementations. A perturbation expansion for the treatment of attenuation, valid for stratified media with background flow, is derived as well. Comparisons are carried out between the proposed algorithm and a modal algorithm assuming an effective sound speed, including a real data case study. The comparisons show that the effective sound speed approximation overestimates the effect of horizontal wind on sound propagation, leading to errors in traveltime, propagation path, trace velocity, and absorption. The error is found to be dependent on propagation angle and Mach number.

All Source Sensor Integration Using an Extended Kalman Filter

DTIC Science & Technology

2012-03-22

Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 All...Positioning System . . . . . . . . . . . . . . . . . . 1 ASPN All Source Positioning Navigation . . . . . . . . . . . . . . 2 DARPA Defense Advanced...equations are developed for sensor preprocessed mea- 1 surements, and these navigation equations are not dependent upon the integrating filter. That is

Three paths toward the quantum angle operator

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

Gazeau, Jean Pierre, E-mail: gazeau@apc.univ-paris7.fr; Szafraniec, Franciszek Hugon, E-mail: franciszek.szafraniec@uj.edu.pl

2016-12-15

We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin–Klauder approaches. One method pertains to Weyl–Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of “weight”more » functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line.« less

The wide-angle equation and its solution through the short-time iterative Lanczos method.

PubMed

Campos-Martínez, José; Coalson, Rob D

2003-03-20

Properties of the wide-angle equation (WAEQ), a nonparaxial scalar wave equation used to propagate light through media characterized by inhomogeneous refractive-index profiles, are studied. In particular, it is shown that the WAEQ is not equivalent to the more complicated but more fundamental Helmholtz equation (HEQ) when the index of refraction profile depends on the position along the propagation axis. This includes all nonstraight waveguides. To study the quality of the WAEQ approximation, we present a novel method for computing solutions to the WAEQ. This method, based on a short-time iterative Lanczos (SIL) algorithm, can be applied directly to the full three-dimensional case, i.e., systems consisting of the propagation axis coordinate and two transverse coordinates. Furthermore, the SIL method avoids series-expansion procedures (e.g., Padé approximants) and thus convergence problems associated with such procedures. Detailed comparisons of solutions to the HEQ, WAEQ, and the paraxial equation (PEQ) are presented for two cases in which numerically exact solutions to the HEQ can be obtained by independent analysis, namely, (i) propagation in a uniform dielectric medium and (ii) propagation along a straight waveguide that has been tilted at an angle to the propagation axis. The quality of WAEQ and PEQ, compared with exact HEQ results, is investigated. Cases are found for which the WAEQ actually performs worse than the PEQ.

Numerical method for angle-of-incidence correction factors for diffuse radiation incident photovoltaic modules

DOE PAGES

Marion, Bill

2017-03-27

Here, a numerical method is provided for solving the integral equation for the angle-of-incidence (AOI) correction factor for diffuse radiation incident photovoltaic (PV) modules. The types of diffuse radiation considered include sky, circumsolar, horizon, and ground-reflected. The method permits PV module AOI characteristics to be addressed when calculating AOI losses associated with diffuse radiation. Pseudo code is provided to aid users in the implementation, and results are shown for PV modules with tilt angles from 0° to 90°. Diffuse AOI losses are greatest for small PV module tilt angles. Including AOI losses associated with the diffuse irradiance will improve predictionsmore » of PV system performance.« less

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

NASA Technical Reports Server (NTRS)

Shertzer, J.; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

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

NASA Technical Reports Server (NTRS)

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

2007-01-01

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

Addendum to "Free energies from integral equation theories: enforcing path independence".

PubMed

Kast, Stefan M

2006-01-01

The variational formalism developed for the analysis of the path dependence of free energies from integral equation theories [S. M. Kast, Phys. Rev. E 67, 041203 (2003)] is extended in order to allow for the three-dimensional treatment of arbitrarily shaped solutes.

The response of the SSM/I to the marine environment. I - An analytic model for the atmospheric component of observed brightness temperatures

NASA Technical Reports Server (NTRS)

Petty, Grant W.; Katsaros, Kristina B.

1992-01-01

A detailed parameterization is developed for the contribution of the nonprecipitating atmosphere to the microwave brightness temperatures observed by the Special Sensor Microwave/Imager (SSM/I). The atmospheric variables considered include the viewing angle, the integrated water vapor amount and scale height, the effective tropospheric lapse rate and near-surface temperature, the total cloud liquid water, the effective cloud height, and the surface pressure. The dependence of the radiative variables on meteorological variables is determined for each of the SSM/I frequencies 19.35, 22.235, 37.0, and 85.5 GHz, based on the values computed from 16,893 maritime temperature and humidity profiles representing all latitude belts and all seasons. A comparison of the predicted brightness temperatures with brightness temperatures obtained by direct numerical integration of the radiative transfer equation for the radiosonde-profile dataset yielded rms differences well below 1 K for all four SSM/I frequencies.

Scattering of SH wave by a semi-cylindrical salient near vertical interface in the bi-material half space

NASA Astrophysics Data System (ADS)

Qi, Hui; Zhang, Xi-meng

2017-10-01

With the aid of the Green function method and image method, the problem of scattering of SH-wave by a semi-cylindrical salient near vertical interface in bi-material half-space is considered to obtain its steady state response. Firstly, by the means of the image method, Green function which is the essential solution of displacement field is constructed to satisfy the stress-free condition on the horizontal boundary in a right-angle space including a semi-cylindrical salient and bearing a harmonic out-of-plane line source force at any point on the vertical boundary. Secondly, the bi-material is separated into two parts along the vertical interface, then unknown anti-plane forces are applied on the vertical interface, and according to the continuity condition, the first kind of Fredholm integral equations is established to determine unknown anti-plane forces by "the conjunction method", then the integral equations are reduced to the linear algebraic equations by effective truncation. Finally, the dynamic stress concentration factor (DSCF) around the edge of semi-cylindrical salient is calculated, and the influences of incident wave number, incident angle, effect of interface and different combination of material parameters, etc. on DSCF are discussed.

Polarized Line Formation in Arbitrary Strength Magnetic Fields Angle-averaged and Angle-dependent Partial Frequency Redistribution

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

Sampoorna, M.; Nagendra, K. N.; Stenflo, J. O., E-mail: sampoorna@iiap.res.in, E-mail: knn@iiap.res.in, E-mail: stenflo@astro.phys.ethz.ch

Magnetic fields in the solar atmosphere leave their fingerprints in the polarized spectrum of the Sun via the Hanle and Zeeman effects. While the Hanle and Zeeman effects dominate, respectively, in the weak and strong field regimes, both these effects jointly operate in the intermediate field strength regime. Therefore, it is necessary to solve the polarized line transfer equation, including the combined influence of Hanle and Zeeman effects. Furthermore, it is required to take into account the effects of partial frequency redistribution (PRD) in scattering when dealing with strong chromospheric lines with broad damping wings. In this paper, we presentmore » a numerical method to solve the problem of polarized PRD line formation in magnetic fields of arbitrary strength and orientation. This numerical method is based on the concept of operator perturbation. For our studies, we consider a two-level atom model without hyperfine structure and lower-level polarization. We compare the PRD idealization of angle-averaged Hanle–Zeeman redistribution matrices with the full treatment of angle-dependent PRD, to indicate when the idealized treatment is inadequate and what kind of polarization effects are specific to angle-dependent PRD. Because the angle-dependent treatment is presently computationally prohibitive when applied to realistic model atmospheres, we present the computed emergent Stokes profiles for a range of magnetic fields, with the assumption of an isothermal one-dimensional medium.« less

Full particle orbit effects in regular and stochastic magnetic fields

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

Ogawa, Shun; Cambon, Benjamin P.; Leoncini, Xavier

Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, themore » particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.« less

Full particle orbit effects in regular and stochastic magnetic fields

DOE PAGES

Ogawa, Shun; Cambon, Benjamin P.; Leoncini, Xavier; ...

2016-07-18

Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, themore » particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.« less

Full particle orbit effects in regular and stochastic magnetic fields

NASA Astrophysics Data System (ADS)

Ogawa, Shun; Cambon, Benjamin; Leoncini, Xavier; Vittot, Michel; del Castillo-Negrete, Diego; Dif-Pradalier, Guilhem; Garbet, Xavier

2016-07-01

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.

Efficient algorithms for single-axis attitude estimation

NASA Technical Reports Server (NTRS)

Shuster, M. D.

1981-01-01

The computationally efficient algorithms determine attitude from the measurement of art lengths and dihedral angles. The dependence of these algorithms on the solution of trigonometric equations was reduced. Both single time and batch estimators are presented along with the covariance analysis of each algorithm.

Chordwise and compressibility corrections to slender-wing theory

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Sluder, Loma

1952-01-01

Corrections to slender-wing theory are obtained by assuming a spanwise distribution of loading and determining the chordwise variation which satisfies the appropriate integral equation. Such integral equations are set up in terms of the given vertical induced velocity on the center line or, depending on the type of wing plan form, its average value across the span at a given chord station. The chordwise distribution is then obtained by solving these integral equations. Results are shown for flat-plate rectangular, and triangular wings.

Sensitivity of a Wave Structure to Initial Conditions

NASA Technical Reports Server (NTRS)

Duval, Walter M. B.; Duval, Walter M. B. (Technical Monitor)

2000-01-01

Microgravity experiments aimed at quantifying effects of gentler via controlled sinusoidal forcing transmitted on the interface between two miscible liquids have shown the evolution of a quasi -stationary four-mode wave structure oriented vertically. The sensitivity of the wave structure to phase angle variation is investigated computationally. We show that a slight variation of the phase angle is sufficient to cause a bifurcation to a two-mode structure. The dependence of phase angle on wave structure is attributed to sensitivity on initial conditions due to the strong nonlinearity of the coupled field equations for the parametric space of interest.

Integrated navigation fusion strategy of INS/UWB for indoor carrier attitude angle and position synchronous tracking.

PubMed

Fan, Qigao; Wu, Yaheng; Hui, Jing; Wu, Lei; Yu, Zhenzhong; Zhou, Lijuan

2014-01-01

In some GPS failure conditions, positioning for mobile target is difficult. This paper proposed a new method based on INS/UWB for attitude angle and position synchronous tracking of indoor carrier. Firstly, error model of INS/UWB integrated system is built, including error equation of INS and UWB. And combined filtering model of INS/UWB is researched. Simulation results show that the two subsystems are complementary. Secondly, integrated navigation data fusion strategy of INS/UWB based on Kalman filtering theory is proposed. Simulation results show that FAKF method is better than the conventional Kalman filtering. Finally, an indoor experiment platform is established to verify the integrated navigation theory of INS/UWB, which is geared to the needs of coal mine working environment. Static and dynamic positioning results show that the INS/UWB integrated navigation system is stable and real-time, positioning precision meets the requirements of working condition and is better than any independent subsystem.

CallFUSE Version 3: A Data Reduction Pipeline for the Far Ultraviolet Spectroscopic Explorer

DTIC Science & Technology

2007-05-01

Earth orbit with an inclination of 25 to the equator and an approximately 100 minute orbital period. Data obtained with the instrument are reduced...throughout the mis- sion reveal that the gratings’ orbital motion depends on three parameters: beta angle (the angle between the target and the anti- Sun ...University, Bal- timore, MD; wvd@pha.jhu.edu. 3 Space Telescope Science Institute, ESS/SSG, Baltimore, MD. 4 Current address: Earth Orientation Department

Computer simulations and theoretical aspects of the depletion interaction in protein-oligomer mixtures.

PubMed

Boncina, M; Rescic, J; Kalyuzhnyi, Yu V; Vlachy, V

2007-07-21

The depletion interaction between proteins caused by addition of either uncharged or partially charged oligomers was studied using the canonical Monte Carlo simulation technique and the integral equation theory. A protein molecule was modeled in two different ways: either as (i) a hard sphere of diameter 30.0 A with net charge 0, or +5, or (ii) as a hard sphere with discrete charges (depending on the pH of solution) of diameter 45.4 A. The oligomers were pictured as tangentially jointed, uncharged, or partially charged, hard spheres. The ions of a simple electrolyte present in solution were represented by charged hard spheres distributed in the dielectric continuum. In this study we were particularly interested in changes of the protein-protein pair-distribution function, caused by addition of the oligomer component. In agreement with previous studies we found that addition of a nonadsorbing oligomer reduces the phase stability of solution, which is reflected in the shape of the protein-protein pair-distribution function. The value of this function in protein-protein contact increases with increasing oligomer concentration, and is larger for charged oligomers. The range of the depletion interaction and its strength also depend on the length (number of monomer units) of the oligomer chain. The integral equation theory, based on the Wertheim Ornstein-Zernike approach applied in this study, was found to be in fair agreement with Monte Carlo results only for very short oligomers. The computer simulations for a model mimicking the lysozyme molecule (ii) are in qualitative agreement with small-angle neutron experiments for lysozyme-dextran mixtures.

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

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

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

2014-03-14

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

Continuous properties of the data-to-solution map for a generalized μ-Camassa-Holm integrable equation

NASA Astrophysics Data System (ADS)

Yu, Shengqi

2018-05-01

This work studies a generalized μ-type integrable equation with both quadratic and cubic nonlinearities; the μ-Camassa-Holm and modified μ-Camassa-Holm equations are members of this family of equations. It has been shown that the Cauchy problem for this generalized μ-Camassa-Holm integrable equation is locally well-posed for initial data u0 ∈ Hs, s > 5/2. In this work, we further investigate the continuity properties to this equation. It is proved in this work that the data-to-solution map of the proposed equation is not uniformly continuous. It is also found that the solution map is Hölder continuous in the Hr-topology when 0 ≤ r < s with Hölder exponent α depending on both s and r.

Excitation of a Parallel Plate Waveguide by an Array of Rectangular Waveguides

NASA Technical Reports Server (NTRS)

Rengarajan, Sembiam

2011-01-01

This work addresses the problem of excitation of a parallel plate waveguide by an array of rectangular waveguides that arises in applications such as the continuous transverse stub (CTS) antenna and dual-polarized parabolic cylindrical reflector antennas excited by a scanning line source. In order to design the junction region between the parallel plate waveguide and the linear array of rectangular waveguides, waveguide sizes have to be chosen so that the input match is adequate for the range of scan angles for both polarizations. Electromagnetic wave scattered by the junction of a parallel plate waveguide by an array of rectangular waveguides is analyzed by formulating coupled integral equations for the aperture electric field at the junction. The integral equations are solved by the method of moments. In order to make the computational process efficient and accurate, the method of weighted averaging was used to evaluate rapidly oscillating integrals encountered in the moment matrix. In addition, the real axis spectral integral is evaluated in a deformed contour for speed and accuracy. The MoM results for a large finite array have been validated by comparing its reflection coefficients with corresponding results for an infinite array generated by the commercial finite element code, HFSS. Once the aperture electric field is determined by MoM, the input reflection coefficients at each waveguide port, and coupling for each polarization over the range of useful scan angles, are easily obtained. Results for the input impedance and coupling characteristics for both the vertical and horizontal polarizations are presented over a range of scan angles. It is shown that the scan range is limited to about 35 for both polarizations and therefore the optimum waveguide is a square of size equal to about 0.62 free space wavelength.

Reduze - Feynman integral reduction in C++

NASA Astrophysics Data System (ADS)

Studerus, C.

2010-07-01

Reduze is a computer program for reducing Feynman integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic prefactors in the system of equations. Reduze offers the possibility to run reductions in parallel. Program summaryProgram title:Reduze Catalogue identifier: AEGE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:: yes No. of lines in distributed program, including test data, etc.: 55 433 No. of bytes in distributed program, including test data, etc.: 554 866 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Unix/Linux Number of processors used: The number of processors is problem dependent. More than one possible but not arbitrary many. RAM: Depends on the complexity of the system. Classification: 4.4, 5 External routines: CLN ( http://www.ginac.de/CLN/), GiNaC ( http://www.ginac.de/) Nature of problem: Solving large systems of linear equations with Feynman integrals as unknowns and rational polynomials as prefactors. Solution method: Using a Gauss/Laporta algorithm to solve the system of equations. Restrictions: Limitations depend on the complexity of the system (number of equations, number of kinematic invariants). Running time: Depends on the complexity of the system.

Surface albedo from bidirectional reflectance

NASA Technical Reports Server (NTRS)

Ranson, K. J.; Irons, J. R.; Daughtry, C. S. T.

1991-01-01

The validity of integrating over discrete wavelength bands is examined to estimate total shortwave bidirectional reflectance of vegetated and bare soil surfaces. Methods for estimating albedo from multiple angle, discrete wavelength band radiometer measurements are studied. These methods include a numerical integration technique and the integration of an empirically derived equation for bidirectional reflectance. It is concluded that shortwave albedos estimated through both techniques agree favorably with the independent pyranometer measurements. Absolute rms errors are found to be 0.5 percent or less for both grass sod and bare soil surfaces.

Edge contact angle and modified Kelvin equation for condensation in open pores.

PubMed

Malijevský, Alexandr; Parry, Andrew O; Pospíšil, Martin

2017-08-01

We consider capillary condensation transitions occurring in open slits of width L and finite height H immersed in a reservoir of vapor. In this case the pressure at which condensation occurs is closer to saturation compared to that occurring in an infinite slit (H=∞) due to the presence of two menisci that are pinned near the open ends. Using macroscopic arguments, we derive a modified Kelvin equation for the pressure p_{cc}(L;H) at which condensation occurs and show that the two menisci are characterized by an edge contact angle θ_{e} that is always larger than the equilibrium contact angle θ, only equal to it in the limit of macroscopic H. For walls that are completely wet (θ=0) the edge contact angle depends only on the aspect ratio of the capillary and is well described by θ_{e}≈sqrt[πL/2H] for large H. Similar results apply for condensation in cylindrical pores of finite length. We test these predictions against numerical results obtained using a microscopic density-functional model where the presence of an edge contact angle characterizing the shape of the menisci is clearly visible from the density profiles. Below the wetting temperature T_{w} we find very good agreement for slit pores of widths of just a few tens of molecular diameters, while above T_{w} the modified Kelvin equation only becomes accurate for much larger systems.

A constitutive material model for nonlinear finite element structural analysis using an iterative matrix approach

NASA Technical Reports Server (NTRS)

Koenig, Herbert A.; Chan, Kwai S.; Cassenti, Brice N.; Weber, Richard

1988-01-01

A unified numerical method for the integration of stiff time dependent constitutive equations is presented. The solution process is directly applied to a constitutive model proposed by Bodner. The theory confronts time dependent inelastic behavior coupled with both isotropic hardening and directional hardening behaviors. Predicted stress-strain responses from this model are compared to experimental data from cyclic tests on uniaxial specimens. An algorithm is developed for the efficient integration of the Bodner flow equation. A comparison is made with the Euler integration method. An analysis of computational time is presented for the three algorithms.

Results from Core-collapse Simulations with Multi-dimensional, Multi-angle Neutrino Transport

NASA Astrophysics Data System (ADS)

Brandt, Timothy D.; Burrows, Adam; Ott, Christian D.; Livne, Eli

2011-02-01

We present new results from the only two-dimensional multi-group, multi-angle calculations of core-collapse supernova evolution. The first set of results from these calculations was published in 2008 by Ott et al. We have followed a nonrotating and a rapidly rotating 20 M sun model for ~400 ms after bounce. We show that the radiation fields vary much less with angle than the matter quantities in the region of net neutrino heating. This happens because most neutrinos are emitted from inner radiative regions and because the specific intensity is an integral over sources from many angles at depth. The latter effect can only be captured by multi-angle transport. We then compute the phase relationship between dipolar oscillations in the shock radius and in matter and radiation quantities throughout the post-shock region. We demonstrate a connection between variations in neutrino flux and the hydrodynamical shock oscillations, and use a variant of the Rayleigh test to estimate the detectability of these neutrino fluctuations in IceCube and Super-Kamiokande. Neglecting flavor oscillations, fluctuations in our nonrotating model would be detectable to ~10 kpc in IceCube, and a detailed power spectrum could be measured out to ~5 kpc. These distances are considerably lower in our rapidly rotating model or with significant flavor oscillations. Finally, we measure the impact of rapid rotation on detectable neutrino signals. Our rapidly rotating model has strong, species-dependent asymmetries in both its peak neutrino flux and its light curves. The peak flux and decline rate show pole-equator ratios of up to ~3 and ~2, respectively.

Computation of oscillating airfoil flows with one- and two-equation turbulence models

NASA Technical Reports Server (NTRS)

Ekaterinaris, J. A.; Menter, F. R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

Characterization and Application of a Grazing Angle Objective for Quantitative Infrared Reflection Microspectroscopy

NASA Technical Reports Server (NTRS)

Pepper, Stephen V.

1995-01-01

A grazing angle objective on an infrared microspectrometer is studied for quantitative spectroscopy by considering the angular dependence of the incident intensity within the objective's angular aperture. The assumption that there is no angular dependence is tested by comparing the experimental reflectance of Si and KBr surfaces with the reflectance calculated by integrating the Fresnel reflection coefficient over the angular aperture under this assumption. Good agreement was found, indicating that the specular reflectance of surfaces can straight-forwardly be quantitatively integrated over the angular aperture without considering non-uniform incident intensity. This quantitative approach is applied to the thickness determination of dipcoated Krytox on gold. The infrared optical constants of both materials are known, allowing the integration to be carried out. The thickness obtained is in fair agreement with the value determined by ellipsometry in the visible. Therefore, this paper illustrates a method for more quantitative use of a grazing angle objective for infrared reflectance microspectroscopy.

Vibrational analysis of vertical axis wind turbine blades

NASA Astrophysics Data System (ADS)

Kapucu, Onur

The goal of this research is to derive a vibration model for a vertical axis wind turbine blade. This model accommodates the affects of varying relative flow angle caused by rotating the blade in the flow field, uses a simple aerodynamic model that assumes constant wind speed and constant rotation rate, and neglects the disturbance of wind due to upstream blade or post. The blade is modeled as elastic Euler-Bernoulli beam under transverse bending and twist deflections. Kinetic and potential energy equations for a rotating blade under deflections are obtained, expressed in terms of assumed modal coordinates and then plugged into Lagrangian equations where the non-conservative forces are the lift and drag forces and moments. An aeroelastic model for lift and drag forces, approximated with third degree polynomials, on the blade are obtained assuming an airfoil under variable angle of attack and airflow magnitudes. A simplified quasi-static airfoil theory is used, in which the lift and drag coefficients are not dependent on the history of the changing angle of attack. Linear terms on the resulting equations of motion will be used to conduct a numerical analysis and simulation, where numeric specifications are modified from the Sandia-17m Darrieus wind turbine by Sandia Laboratories.

Numerical and experimental studies on pulsatile flow in aneurysms arising laterally from a curved parent vessel at various angles.

PubMed

Liou, Tong-Miin; Li, Yi-Chen; Juan, Wei-Cheng

2007-01-01

Both numerical and experimental studies have been performed to characterize the fluid flow inside the lateral aneurysms arising from the curved parent vessels at various angles gamma. The implicit solver was based on the time-dependent Navier-Stokes equations of incompressible laminar flow. Solutions were generated by a cell-center finite-volume method that used second order upwind and second order center flux difference splitting for the convection and diffusion term, respectively. The second order Crank-Nicolson method was used in the time integration term while the SIMPLEC algorithm was adopted to handle the pressure-velocity coupling. Complementarily, the particle tracking velocimetry (PTV) was used to measure the velocity fields. The conditions selected were to simulate an internal carotid artery with a diameter of 5 mm by similarity rules. The values of gamma explored were 0 degrees, 45 degrees, 90 degrees, and 135 degrees. Pulsatile flow with Wormersley number 3.9 and Reynolds numbers varying from 350 to 850 was considered. The computed results are firstly verified by the PTV measured ones. Discussion of the results is in terms of pulsatile main and secondary velocity vector fields, inflow rates into the aneurysm, and the distributions of wall shear stress and static pressure. It is found that among the angles examined gamma=45( composite function) is the riskiest angle from a fluid dynamics point of view and the aneurysmal dome is at risk.

Energy-dependent angular shifts in the photoelectron momentum distribution for atoms in elliptically polarized laser pulses

NASA Astrophysics Data System (ADS)

Xie, Hui; Li, Min; Luo, Siqiang; Li, Yang; Zhou, Yueming; Cao, Wei; Lu, Peixiang

2017-12-01

We measure the photoelectron momentum distributions from atoms ionized by strong elliptically polarized laser fields at the wavelengths of 400 and 800 nm, respectively. The momentum distributions show distinct angular shifts, which sensitively depend on the electron energy. We find that the deflection angle with respect to the major axis of the laser ellipse decreases with the increase of the electron energy for large ellipticities. This energy-dependent angular shift is well reproduced by both numerical solutions of the time-dependent Schrödinger equation and the classical-trajectory Monte Carlo model. We show that the ionization time delays among the electrons with different energies are responsible for the energy-dependent angular shifts. On the other hand, for small ellipticities, we find the deflection angle increases with increasing the electron energy, which might be caused by electron rescattering in the elliptically polarized fields.

Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients.

PubMed

Kedziora, D J; Ankiewicz, A; Chowdury, A; Akhmediev, N

2015-10-01

We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.

Concentration-Induced Association in a Protein System Caused by a Highly Directional Patch Attraction.

PubMed

Li, Weimin; Persson, Björn A; Lund, Mikael; Bergenholtz, Johan; Zackrisson Oskolkova, Malin

2016-09-01

Self-association of the protein lactoferrin is studied in solution using small-angle X-ray scattering techniques. Effective static structure factors have been shown to exhibit either a monotonic or a nonmonotonic dependence on protein concentration in the small wavevector limit, depending on salt concentration. The behavior correlates with a nonmonotonic dependence of the second virial coefficient on salt concentration, such that a maximum appears in the structure factor at a low protein concentration when the second virial coefficient is negative and close to a minimum. The results are interpreted in terms of an integral equation theory with explicit dimers, formulated by Wertheim, which provides a consistent framework able to explain the behavior in terms of a monomer-dimer equilibrium that appears because of a highly directional patch attraction. Short attraction ranges preclude trimer formation, which explains why the protein system behaves as if it were subject to a concentration-dependent isotropic protein-protein attraction. Superimposing an isotropic interaction, comprising screened Coulomb repulsion and van der Waals attraction, on the patch attraction allows for a semiquantitative modeling of the complete transition pathway from monomers in the dilute limit to monomer-dimer systems at somewhat higher protein concentrations.

A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation

NASA Astrophysics Data System (ADS)

Kazantsev, I. G.; Olsen, U. L.; Poulsen, H. F.; Hansen, P. C.

2018-02-01

We investigate the idealized mathematical model of single scatter in PET for a detector system possessing excellent energy resolution. The model has the form of integral transforms estimating the distribution of photons undergoing a single Compton scattering with a certain angle. The total single scatter is interpreted as the volume integral over scatter points that constitute a rotation body with a football shape, while single scattering with a certain angle is evaluated as the surface integral over the boundary of the rotation body. The equations for total and sample single scatter calculations are derived using a single scatter simulation approximation. We show that the three-dimensional slice-by-slice filtered backprojection algorithm is applicable for scatter data inversion provided that the attenuation map is assumed to be constant. The results of the numerical experiments are presented.

A momentum-space formulation without partial wave decomposition for scattering of two spin-half particles

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

Fachruddin, Imam, E-mail: imam.fachruddin@sci.ui.ac.id; Salam, Agus

2016-03-11

A new momentum-space formulation for scattering of two spin-half particles, both either identical or unidentical, is formulated. As basis states the free linear-momentum states are not expanded into the angular-momentum states, the system’s spin states are described by the product of the spin states of the two particles, and the system’s isospin states by the total isospin states of the two particles. We evaluate the Lippmann-Schwinger equations for the T-matrix elements in these basis states. The azimuthal behavior of the potential and of the T-matrix elements leads to a set of coupled integral equations for the T-matrix elements in twomore » variables only, which are the magnitude of the relative momentum and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved. A set of six spin operators to express any interaction of two spin-half particles is introduced. We show the spin-averaged differential cross section as being calculated in terms of the solution of the set of the integral equations.« less

Angle-domain inverse scattering migration/inversion in isotropic media

NASA Astrophysics Data System (ADS)

Li, Wuqun; Mao, Weijian; Li, Xuelei; Ouyang, Wei; Liang, Quan

2018-07-01

The classical seismic asymptotic inversion can be transformed into a problem of inversion of generalized Radon transform (GRT). In such methods, the combined parameters are linearly attached to the scattered wave-field by Born approximation and recovered by applying an inverse GRT operator to the scattered wave-field data. Typical GRT-style true-amplitude inversion procedure contains an amplitude compensation process after the weighted migration via dividing an illumination associated matrix whose elements are integrals of scattering angles. It is intuitional to some extent that performs the generalized linear inversion and the inversion of GRT together by this process for direct inversion. However, it is imprecise to carry out such operation when the illumination at the image point is limited, which easily leads to the inaccuracy and instability of the matrix. This paper formulates the GRT true-amplitude inversion framework in an angle-domain version, which naturally degrades the external integral term related to the illumination in the conventional case. We solve the linearized integral equation for combined parameters of different fixed scattering angle values. With this step, we obtain high-quality angle-domain common-image gathers (CIGs) in the migration loop which provide correct amplitude-versus-angle (AVA) behavior and reasonable illumination range for subsurface image points. Then we deal with the over-determined problem to solve each parameter in the combination by a standard optimization operation. The angle-domain GRT inversion method keeps away from calculating the inaccurate and unstable illumination matrix. Compared with the conventional method, the angle-domain method can obtain more accurate amplitude information and wider amplitude-preserved range. Several model tests demonstrate the effectiveness and practicability.

Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Zhu, Ying; Herbert, John M.

2018-01-01

The "real time" formulation of time-dependent density functional theory (TDDFT) involves integration of the time-dependent Kohn-Sham (TDKS) equation in order to describe the time evolution of the electron density following a perturbation. This approach, which is complementary to the more traditional linear-response formulation of TDDFT, is more efficient for computation of broad-band spectra (including core-excited states) and for systems where the density of states is large. Integration of the TDKS equation is complicated by the time-dependent nature of the effective Hamiltonian, and we introduce several predictor/corrector algorithms to propagate the density matrix, one of which can be viewed as a self-consistent extension of the widely used modified-midpoint algorithm. The predictor/corrector algorithms facilitate larger time steps and are shown to be more efficient despite requiring more than one Fock build per time step, and furthermore can be used to detect a divergent simulation on-the-fly, which can then be halted or else the time step modified.

Optimized effective potential in real time: Problems and prospects in time-dependent density-functional theory

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

Mundt, Michael; Kuemmel, Stephan

2006-08-15

The integral equation for the time-dependent optimized effective potential (TDOEP) in time-dependent density-functional theory is transformed into a set of partial-differential equations. These equations only involve occupied Kohn-Sham orbitals and orbital shifts resulting from the difference between the exchange-correlation potential and the orbital-dependent potential. Due to the success of an analog scheme in the static case, a scheme that propagates orbitals and orbital shifts in real time is a natural candidate for an exact solution of the TDOEP equation. We investigate the numerical stability of such a scheme. An approximation beyond the Krieger-Li-Iafrate approximation for the time-dependent exchange-correlation potential ismore » analyzed.« less

Effect of the cosmological constant on the deflection angle by a rotating cosmic string

NASA Astrophysics Data System (ADS)

Jusufi, Kimet; Övgün, Ali

2018-03-01

We report the effect of the cosmological constant and the internal energy density of a cosmic string on the deflection angle of light in the spacetime of a rotating cosmic string with internal structure. We first revisit the deflection angle by a rotating cosmic string and then provide a generalization using the geodesic equations and the Gauss-Bonnet theorem. We show there is an agreement between the two methods when employing higher-order terms of the linear mass density of the cosmic string. By modifying the integration domain for the global conical topology, we resolve the inconsistency between these two methods previously reported in the literature. We show that the deflection angle is not affected by the rotation of the cosmic string; however, the cosmological constant Λ strongly affects the deflection angle, which generalizes the well-known result.

A Measuring System for Well Logging Attitude and a Method of Sensor Calibration

PubMed Central

Ren, Yong; Wang, Yangdong; Wang, Mijian; Wu, Sheng; Wei, Biao

2014-01-01

This paper proposes an approach for measuring the azimuth angle and tilt angle of underground drilling tools with a MEMS three-axis accelerometer and a three-axis fluxgate sensor. A mathematical model of well logging attitude angle is deduced based on combining space coordinate transformations and algebraic equations. In addition, a system implementation plan of the inclinometer is given in this paper, which features low cost, small volume and integration. Aiming at the sensor and assembly errors, this paper analyses the sources of errors, and establishes two mathematical models of errors and calculates related parameters to achieve sensor calibration. The results show that this scheme can obtain a stable and high precision azimuth angle and tilt angle of drilling tools, with the deviation of the former less than ±1.4° and the deviation of the latter less than ±0.1°. PMID:24859028

A measuring system for well logging attitude and a method of sensor calibration.

PubMed

Ren, Yong; Wang, Yangdong; Wang, Mijian; Wu, Sheng; Wei, Biao

2014-05-23

This paper proposes an approach for measuring the azimuth angle and tilt angle of underground drilling tools with a MEMS three-axis accelerometer and a three-axis fluxgate sensor. A mathematical model of well logging attitude angle is deduced based on combining space coordinate transformations and algebraic equations. In addition, a system implementation plan of the inclinometer is given in this paper, which features low cost, small volume and integration. Aiming at the sensor and assembly errors, this paper analyses the sources of errors, and establishes two mathematical models of errors and calculates related parameters to achieve sensor calibration. The results show that this scheme can obtain a stable and high precision azimuth angle and tilt angle of drilling tools, with the deviation of the former less than ±1.4° and the deviation of the latter less than ±0.1°.

A Langevin model for fluctuating contact angle behaviour parametrised using molecular dynamics.

PubMed

Smith, E R; Müller, E A; Craster, R V; Matar, O K

2016-12-06

Molecular dynamics simulations are employed to develop a theoretical model to predict the fluid-solid contact angle as a function of wall-sliding speed incorporating thermal fluctuations. A liquid bridge between counter-sliding walls is studied, with liquid-vapour interface-tracking, to explore the impact of wall-sliding speed on contact angle. The behaviour of the macroscopic contact angle varies linearly over a range of capillary numbers beyond which the liquid bridge pinches off, a behaviour supported by experimental results. Nonetheless, the liquid bridge provides an ideal test case to study molecular scale thermal fluctuations, which are shown to be well described by Gaussian distributions. A Langevin model for contact angle is parametrised to incorporate the mean, fluctuation and auto-correlations over a range of sliding speeds and temperatures. The resulting equations can be used as a proxy for the fully-detailed molecular dynamics simulation allowing them to be integrated within a continuum-scale solver.

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.

2007-01-01

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

A theory of post-stall transients in axial compression systems. I - Development of equations

NASA Technical Reports Server (NTRS)

Moore, F. K.; Greitzer, E. M.

1985-01-01

An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

A new stream function formulation for the Euler equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Hassan, H. A.

1983-01-01

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

PubMed

Korayem, M H; Nekoo, S R

2015-07-01

This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Theory for noise of propellers in angular inflow with parametric studies and experimental verification

NASA Technical Reports Server (NTRS)

Hanson, Donald B.; Parzych, David J.

1993-01-01

This report presents the derivation of a frequency domain theory and working equations for radiation of propeller harmonic noise in the presence of angular inflow. In applying the acoustic analogy, integration over the tangential coordinate of the source region is performed numerically, permitting the equations to be solved without approximation for any degree of angular inflow. Inflow angle is specified in terms of yaw, pitch, and roll angles of the aircraft. Since these can be arbitrarily large, the analysis applies with equal accuracy to propellers and helicopter rotors. For thickness and loading, the derivation is given in complete detail with working equations for near and far field. However, the quadrupole derivation has been carried only far enough to show feasibility of the numerical approach. Explicit formulas are presented for computation of source elements, evaluation of Green's functions, and location of observer points in various visual and retarded coordinate systems. The resulting computer program, called WOBBLE has been written in FORTRAN and follows the notation of this report very closely. The new theory is explored to establish the effects of varying inflow angle on axial and circumferential directivity. Also, parametric studies were performed to evaluate various phenomena outside the capabilities of earlier theories, such as an unsteady thickness effect. Validity of the theory was established by comparison with test data from conventional propellers and Prop Fans in flight and in wind tunnels under a variety of operating conditions and inflow angles.

Optimum Projection Angle for Attaining Maximum Distance in a Soccer Punt Kick

PubMed Central

Linthorne, Nicholas P.; Patel, Dipesh S.

2011-01-01

To produce the greatest horizontal distance in a punt kick the ball must be projected at an appropriate angle. Here, we investigated the optimum projection angle that maximises the distance attained in a punt kick by a soccer goalkeeper. Two male players performed many maximum-effort kicks using projection angles of between 10° and 90°. The kicks were recorded by a video camera at 100 Hz and a 2 D biomechanical analysis was conducted to obtain measures of the projection velocity, projection angle, projection height, ball spin rate, and foot velocity at impact. The player’s optimum projection angle was calculated by substituting mathematical equations for the relationships between the projection variables into the equations for the aerodynamic flight of a soccer ball. The calculated optimum projection angles were in agreement with the player’s preferred projection angles (40° and 44°). In projectile sports even a small dependence of projection velocity on projection angle is sufficient to produce a substantial shift in the optimum projection angle away from 45°. In the punt kicks studied here, the optimum projection angle was close to 45° because the projection velocity of the ball remained almost constant across all projection angles. This result is in contrast to throwing and jumping for maximum distance, where the projection velocity the athlete is able to achieve decreases substantially with increasing projection angle and so the optimum projection angle is well below 45°. Key points The optimum projection angle that maximizes the distance of a punt kick by a soccer goalkeeper is about 45°. The optimum projection angle is close to 45° because the projection velocity of the ball is almost the same at all projection angles. This result is in contrast to throwing and jumping for maximum distance, where the optimum projection angle is well below 45° because the projection velocity the athlete is able to achieve decreases substantially with increasing projection angle. PMID:24149315

System Identification for Integrated Aircraft Development and Flight Testing (l’Identification des systemes pour le developpement integre des aeronefs et les essais en vol)

DTIC Science & Technology

1999-03-01

aerodynamics to affect load motions. The effects include a load trail angle in proportion to the drag specific force, and modification of the load pendulum...equations algorithm for flight data filtering architeture . and data consistency checking; and SCIDNT 8, an output architecture. error identification...accelerations at the seven sensor locations, identified system is proportional to the number When system identification is performed, as of flexible modes

Investigation of viscous/inviscid interaction in transonic flow over airfoils with suction

NASA Technical Reports Server (NTRS)

Vemuru, C. S.; Tiwari, S. N.

1988-01-01

The viscous/inviscid interaction over transonic airfoils with and without suction is studied. The streamline angle at the edge of the boundary layer is used to couple the viscous and inviscid flows. The potential flow equations are solved for the inviscid flow field. In the shock region, the Euler equations are solved using the method of integral relations. For this, the potential flow solution is used as the initial and boundary conditions. An integral method is used to solve the laminar boundary-layer equations. Since both methods are integral methods, a continuous interaction is allowed between the outer inviscid flow region and the inner viscous flow region. To avoid the Goldstein singularity near the separation point the laminar boundary-layer equations are derived in an inverse form to obtain solution for the flows with small separations. The displacement thickness distribution is specified instead of the usual pressure distribution to solve the boundry-layer equations. The Euler equations are solved for the inviscid flow using the finite volume technique and the coupling is achieved by a surface transpiration model. A method is developed to apply a minimum amount of suction that is required to have an attached flow on the airfoil. The turbulent boundary layer equations are derived using the bi-logarithmic wall law for mass transfer. The results are found to be in good agreement with available experimental data and with the results of other computational methods.

A Computer Program for the Computation of Running Gear Temperatures Using Green's Function

NASA Technical Reports Server (NTRS)

Koshigoe, S.; Murdock, J. W.; Akin, L. S.; Townsend, D. P.

1996-01-01

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

The evolution of methods for noise prediction of high speed rotors and propellers in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1986-01-01

Linear wave equation models which have been used over the years at NASA Langley for describing noise emissions from high speed rotating blades are summarized. The noise sources are assumed to lie on a moving surface, and analysis of the situation has been based on the Ffowcs Williams-Hawkings (FW-H) equation. Although the equation accounts for two surface and one volume source, the NASA analyses have considered only the surface terms. Several variations on the FW-H model are delineated for various types of applications, noting the computational benefits of removing the frequency dependence of the calculations. Formulations are also provided for compact and noncompact sources, and features of Long's subsonic integral equation and Farassat's high speed integral equation are discussed. The selection of subsonic or high speed models is dependent on the Mach number of the blade surface where the source is located.

A new treatment of nonlocality in scattering process

NASA Astrophysics Data System (ADS)

Upadhyay, N. J.; Bhagwat, A.; Jain, B. K.

2018-01-01

Nonlocality in the scattering potential leads to an integro-differential equation. In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schrödinger equation is usually handled by approximating r,{r}{\\prime }-dependence of the nonlocal kernel. The present work proposes a novel method to solve the integro-differential equation. The method, using the mean value theorem of integral calculus, converts the nonhomogeneous term to a homogeneous term. The effective local potential in this equation turns out to be energy independent, but has relative angular momentum dependence. This method is accurate and valid for any form of nonlocality. As illustrative examples, the total and differential cross sections for neutron scattering off 12C, 56Fe and 100Mo nuclei are calculated with this method in the low energy region (up to 10 MeV) and are found to be in reasonable accord with the experiments.

Solving differential equations for Feynman integrals by expansions near singular points

NASA Astrophysics Data System (ADS)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Particle Acceleration and Radiative Losses at Relativistic Shocks

NASA Astrophysics Data System (ADS)

Dempsey, P.; Duffy, P.

A semi-analytic approach to the relativistic transport equation with isotropic diffusion and consistent radiative losses is presented. It is based on the eigenvalue method first introduced in Kirk & Schneider [5]and Heavens & Drury [3]. We demonstrate the pitch-angle dependence of the cut-off in relativistic shocks.

Comprehensive design of omnidirectional high-performance perovskite solar cells

PubMed Central

Zhang, Yutao; Xuan, Yimin

2016-01-01

The comprehensive design approach is established with coupled optical-electrical simulation for perovskite-based solar cell, which emerged as one of the most promising competitors to silicon solar cell for its low-cost fabrication and high PCE. The selection of structured surface, effect of geometry parameters, incident angle-dependence and polarization-sensitivity are considered in the simulation. The optical modeling is performed via the finite-difference time-domain method whilst the electrical properties are obtained by solving the coupled nonlinear equations of Poisson, continuity, and drift-diffusion equations. The optical and electrical performances of five different structured surfaces are compared to select a best structured surface for perovskite solar cell. The effects of the geometry parameters on the optical and electrical properties of the perovskite cell are analyzed. The results indicate that the light harvesting is obviously enhanced by the structured surface. The electrical performance can be remarkably improved due to the enhanced light harvesting of the designed best structured surface. The angle-dependence for s- and p-polarizations is investigated. The structured surface exhibits omnidirectional behavior and favorable polarization-insensitive feature within a wide incident angle range. Such a comprehensive design approach can highlight the potential of perovskite cell for power conversion in the full daylight. PMID:27405419

Comprehensive design of omnidirectional high-performance perovskite solar cells.

PubMed

Zhang, Yutao; Xuan, Yimin

2016-07-13

The comprehensive design approach is established with coupled optical-electrical simulation for perovskite-based solar cell, which emerged as one of the most promising competitors to silicon solar cell for its low-cost fabrication and high PCE. The selection of structured surface, effect of geometry parameters, incident angle-dependence and polarization-sensitivity are considered in the simulation. The optical modeling is performed via the finite-difference time-domain method whilst the electrical properties are obtained by solving the coupled nonlinear equations of Poisson, continuity, and drift-diffusion equations. The optical and electrical performances of five different structured surfaces are compared to select a best structured surface for perovskite solar cell. The effects of the geometry parameters on the optical and electrical properties of the perovskite cell are analyzed. The results indicate that the light harvesting is obviously enhanced by the structured surface. The electrical performance can be remarkably improved due to the enhanced light harvesting of the designed best structured surface. The angle-dependence for s- and p-polarizations is investigated. The structured surface exhibits omnidirectional behavior and favorable polarization-insensitive feature within a wide incident angle range. Such a comprehensive design approach can highlight the potential of perovskite cell for power conversion in the full daylight.

Partially deuterated potassium dihydrogen phosphate optimized for ultra-broadband optical parametric amplification

NASA Astrophysics Data System (ADS)

Fujioka, K.; Fujimoto, Y.; Tsubakimoto, K.; Kawanaka, J.; Shoji, I.; Miyanaga, N.

2015-03-01

The refractive index of a potassium dihydrogen phosphate (KDP) crystal strongly depends on the deuteration fraction of the crystal. The wavelength dependence of the phase-matching angle in the near-infrared optical parametric process shows convex and concave characteristics for pure KDP and pure deuterated KDP (DKDP), respectively, when pumped by the second harmonic of Nd- or Yb-doped solid state lasers. Using these characteristics, ultra-broadband phase matching can be realized by optimization of the deuteration fraction. The refractive index of DKDP that was grown with a different deuteration fraction (known as partially deuterated KDP or pDKDP) was measured over a wide wavelength range of 0.4-1.5 μm by the minimum deviation method. The wavelength dispersions of the measured refractive indices were fitted using a modified Sellmeier equation, and the deuteration fraction dependence was analyzed using the Lorentz-Lorenz equation. The wavelength-dependent phase-matching angle for an arbitrary deuteration fraction was then calculated for optical parametric amplification with pumping at a wavelength of 526.5 nm. The results revealed that a refractive index database with precision of more than 2 × 10-5 was necessary for exact evaluation of the phase-matching condition. An ultra-broad gain bandwidth of up to 490 nm will be feasible when using the 68% pDKDP crystal.

T1 mapping with the variable flip angle technique: A simple correction for insufficient spoiling of transverse magnetization.

PubMed

Baudrexel, Simon; Nöth, Ulrike; Schüre, Jan-Rüdiger; Deichmann, Ralf

2018-06-01

The variable flip angle method derives T 1 maps from radiofrequency-spoiled gradient-echo data sets, acquired with different flip angles α. Because the method assumes validity of the Ernst equation, insufficient spoiling of transverse magnetization yields errors in T 1 estimation, depending on the chosen radiofrequency-spoiling phase increment (Δϕ). This paper presents a versatile correction method that uses modified flip angles α' to restore the validity of the Ernst equation. Spoiled gradient-echo signals were simulated for three commonly used phase increments Δϕ (50°/117°/150°), different values of α, repetition time (TR), T 1 , and a T 2 of 85 ms. For each parameter combination, α' (for which the Ernst equation yielded the same signal) and a correction factor C Δϕ (α, TR, T 1 ) = α'/α were determined. C Δϕ was found to be independent of T 1 and fitted as polynomial C Δϕ (α, TR), allowing to calculate α' for any protocol using this Δϕ. The accuracy of the correction method for T 2 values deviating from 85 ms was also determined. The method was tested in vitro and in vivo for variable flip angle scans with different acquisition parameters. The technique considerably improved the accuracy of variable flip angle-based T 1 maps in vitro and in vivo. The proposed method allows for a simple correction of insufficient spoiling in gradient-echo data. The required polynomial parameters are supplied for three common Δϕ. Magn Reson Med 79:3082-3092, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

A geometric viewpoint on generalized hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Spohn, Herbert; Yoshimura, Takato

2018-01-01

Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective ("dressed") velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.

Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

NASA Technical Reports Server (NTRS)

Boretti, A. A.

1990-01-01

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

Large Angle Transient Dynamics (LATDYN) user's manual

NASA Technical Reports Server (NTRS)

Abrahamson, A. Louis; Chang, Che-Wei; Powell, Michael G.; Wu, Shih-Chin; Bingel, Bradford D.; Theophilos, Paula M.

1991-01-01

A computer code for modeling the large angle transient dynamics (LATDYN) of structures was developed to investigate techniques for analyzing flexible deformation and control/structure interaction problems associated with large angular motions of spacecraft. This type of analysis is beyond the routine capability of conventional analytical tools without simplifying assumptions. In some instances, the motion may be sufficiently slow and the spacecraft (or component) sufficiently rigid to simplify analyses of dynamics and controls by making pseudo-static and/or rigid body assumptions. The LATDYN introduces a new approach to the problem by combining finite element structural analysis, multi-body dynamics, and control system analysis in a single tool. It includes a type of finite element that can deform and rotate through large angles at the same time, and which can be connected to other finite elements either rigidly or through mechanical joints. The LATDYN also provides symbolic capabilities for modeling control systems which are interfaced directly with the finite element structural model. Thus, the nonlinear equations representing the structural model are integrated along with the equations representing sensors, processing, and controls as a coupled system.

Computation of Separated and Unsteady Flows with One- and Two-Equation Turbulence Models

NASA Technical Reports Server (NTRS)

Ekaterinaris, John A.; Menter, Florian R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. The two-equation turbulence models are discretized in space with an upwind-biased, second order accurate total variation diminishing scheme. One and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading edge and where natural transition was allowed to occur naturally are considered. The more recently developed field-equation turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are obtained. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading edge transitional flow region in order to capture the correct physical mechanism that leads to dynamic stall.

Finite-Length Diocotron Modes in a Non-neutral Plasma Column

NASA Astrophysics Data System (ADS)

Walsh, Daniel; Dubin, Daniel

2017-10-01

Diocotron modes are 2D distortions of a non-neutral plasma column that propagate azimuthally via E × B drifts. While the infinite-length theory of diocotron modes is well-understood for arbitrary azimuthal mode number l, the finite-length mode frequency is less developed (with some exceptions), and is naturally of relevance to experiments. In this poster, we present an approach to address finite length effects, such as temperature dependence of the mode frequency. We use a bounce-averaged solution to the Vlasov Equation, in which the Vlasov Equation is solved using action-angle variables of the unperturbed Hamiltonian. We write the distribution function as a Fourier series in the bounce-angle variable ψ, keeping only the bounce-averaged term. We demonstrate a numerical solution to this equation for a realistic plasma with a finite Debye Length, compare to the existing l = 1 theory, and discuss possible extensions of the existing theory to l ≠ 1 . Supported by NSF/DOE Partnership Grants PHY1414570 and DESC0002451.

Dynamic analysis of propulsion mechanism directly driven by wave energy for marine mobile buoy

NASA Astrophysics Data System (ADS)

Yu, Zhenjiang; Zheng, Zhongqiang; Yang, Xiaoguang; Chang, Zongyu

2016-07-01

Marine mobile buoy(MMB) have many potential applications in the maritime industry and ocean science. Great progress has been made, however the technology in this area is far from maturity in theory and faced with many difficulties in application. A dynamic model of the propulsion mechanism is very necessary for optimizing the parameters of the MMB, especially with consideration of hydrodynamic force. The principle of wave-driven propulsion mechanism is briefly introduced. To set a theory foundation for study on the MMB, a dynamic model of the propulsion mechanism of the MMB is obtained. The responses of the motion of the platform and the hydrofoil are obtained by using a numerical integration method to solve the ordinary differential equations. A simplified form of the motion equations is reached by omitting terms with high order small values. The relationship among the heave motion of the buoy, stiffness of the elastic components, and the forward speed can be obtained by using these simplified equations. The dynamic analysis show the following: The angle of displacement of foil is fairly small with the biggest value around 0.3 rad; The speed of mobile buoy and the angle of hydrofoil increased gradually with the increase of heave motion of buoy; The relationship among heaven motion, stiffness and attack angle is that heave motion leads to the angle change of foil whereas the item of speed or push function is determined by vertical velocity and angle, therefore, the heave motion and stiffness can affect the motion of buoy significantly if the size of hydrofoil is kept constant. The proposed model is provided to optimize the parameters of the MMB and a foundation is laid for improving the performance of the MMB.

a Study of the Concentration Dependence of Macromolecular Diffusion Using Photon Correlation Spectroscopy.

NASA Astrophysics Data System (ADS)

Marlowe, Robert Lloyd

The dynamic light scattering technique of photon correlation spectroscopy has been used to investigate the dependence of the mutual diffusion coefficient of a macromolecular system upon concentration. The first part of the research was devoted to the design and construction of a single-clipping autocorrelator based on newly-developed integrated circuits. The resulting 128 channel instrument can perform real time autocorrelation for sample time intervals >(, )10 (mu)s, and batch processed autocorrelation for intervals down to 3 (mu)s. An improved design for a newer, all-digital autocorrelator is given. Homodyne light scattering experiments were then undertaken on monodisperse solutions of polystyrene spheres. The single-mode TEM(,oo) beam of an argon-ion laser ((lamda) = 5145 (ANGSTROM)) was used as the light source; all solutions were studied at room temperature. The scattering angle was varied from 30(DEGREES) to 110(DEGREES). Excellent agreement with the manufacturer's specification for the particle size was obtained from the photon correlation studies. Finally, aqueous solutions of the globular protein ovalbumin, ranging in concentration from 18.9 to 244.3 mg/ml, were illuminated under the same conditions of temperature and wavelength as before; the homodyne scattered light was detected at a fixed scattering angle of 30(DEGREES). The single-clipped photocount autocorrelation function was analyzed using the homodyne exponential integral method of Meneely et al. The resulting diffusion coefficients showed a general linear dependence upon concentration, as predicted by the generalized Stokes-Einstein equation. However, a clear peak in the data was evident at c (TURNEQ) 100 mg/ml, which could not be explained on the basis of a non -interacting particle theory. A semi-quantitative approach based on the Debye-Huckel theory of electrostatic interactions is suggested as the probable cause for the peak's rise, and an excluded volume effect for its decline.

A fully relativistic twisted disc around a slowly rotating Kerr black hole: derivation of dynamical equations and the shape of stationary configurations

NASA Astrophysics Data System (ADS)

Zhuravlev, V. V.; Ivanov, P. B.

2011-08-01

In this paper we derive equations describing the dynamics and stationary configurations of a twisted fully relativistic thin accretion disc around a slowly rotating black hole. We assume that the inclination angle of the disc is small and that the standard relativistic generalization of the α model of accretion discs is valid when the disc is flat. We find that similar to the case of non-relativistic twisted discs the disc dynamics and stationary shapes can be determined by a pair of equations formulated for two complex variables describing the orientation of the disc rings and velocity perturbations induced by the twist. We analyse analytically and numerically the shapes of stationary twisted configurations of accretion discs having non-zero inclinations with respect to the black hole equatorial plane at large distances r from the black hole. It is shown that the stationary configurations depend on two parameters - the viscosity parameter α and the parameter ?, where δ* is the opening angle (δ*˜h/r, where h is the disc half-thickness and r is large) of a flat disc and a is the black hole rotational parameter. When a > 0 and ? the shapes depend drastically on the value of α. When α is small the disc inclination angle oscillates with radius with amplitude and radial frequency of the oscillations dramatically increasing towards the last stable orbit, Rms. When α has a moderately small value the oscillations do not take place but the disc does not align with the equatorial plane at small radii. The disc inclination angle either is increasing towards Rms or exhibits a non-monotonic dependence on the radial coordinate. Finally, when α is sufficiently large the disc aligns with the equatorial plane at small radii. When a < 0 the disc aligns with the equatorial plane for all values of α. The results reported here may have implications for determining the structure and variability of accretion discs close to Rms as well as for modelling of emission spectra coming from different sources, which are supposed to contain black holes.

New dynamic variables for rotating spacecraft

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1993-01-01

This paper introduces two new seven-parameter representations for spacecraft attitude dynamics modeling. The seven parameters are the three components of the total system angular momentum in the spacecraft body frame; the three components of the angular momentum in the inertial reference frame; and an angle variable. These obey a single constraint as do parameterizations that include a quaternion; in this case the constraint is the equality of the sum of the squares of the angular momentum components in the two frames. The two representations are nonsingular if the system angular momentum is non-zero and obeys certain orientation constraints. The new parameterizations of the attitude matrix, the equations of motion, and the relation of the solution of these equations to Euler angles for torque-free motion are developed and analyzed. The superiority of the new parameterizations for numerical integration is shown in a specific example.

A new aerodynamic integral equation based on an acoustic formula in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

Floquet-Magnus expansion for general N-coupled spins systems in magic-angle spinning nuclear magnetic resonance spectra

NASA Astrophysics Data System (ADS)

Mananga, Eugene Stephane; Charpentier, Thibault

2015-04-01

In this paper we present a theoretical perturbative approach for describing the NMR spectrum of strongly dipolar-coupled spin systems under fast magic-angle spinning. Our treatment is based on two approaches: the Floquet approach and the Floquet-Magnus expansion. The Floquet approach is well known in the NMR community as a perturbative approach to get analytical approximations. Numerical procedures are based on step-by-step numerical integration of the corresponding differential equations. The Floquet-Magnus expansion is a perturbative approach of the Floquet theory. Furthermore, we address the " γ -encoding" effect using the Floquet-Magnus expansion approach. We show that the average over " γ " angle can be performed for any Hamiltonian with γ symmetry.

Shear flow simulations of biaxial nematic liquid crystals

NASA Astrophysics Data System (ADS)

Sarman, Sten

1997-08-01

We have calculated the viscosities of a biaxial nematic liquid crystal phase of a variant of the Gay-Berne fluid [J. G. Gay and B. J. Berne, J. Chem. Phys. 74, 3316 (1981)] by performing molecular dynamics simulations. The equations of motion have been augmented by a director constraint torque that fixes the orientation of the directors. This makes it possible to fix them at different angles relative to the stream lines in shear flow simulations. In equilibrium simulations the constraints generate a new ensemble. One finds that the Green-Kubo relations for the viscosities become linear combinations of time correlation function integrals in this ensemble whereas they are complicated rational functions in the conventional canonical ensemble. We have evaluated these Green-Kubo relations for all the shear viscosities and all the twist viscosities. We have also calculated the alignment angles, which are functions of the viscosity coefficients. We find that there are three real alignment angles but a linear stability analysis shows that only one of them corresponds to a stable director orientation. The Green-Kubo results have been cross checked by nonequilibrium shear flow simulations. The results from the different methods agree very well. Finally, we have evaluated the Miesowicz viscosities [D. Baalss, Z. Naturforsch. Teil A 45, 7 (1990)]. They vary by more than 2 orders of magnitude. The viscosity is consequently highly orientation dependent.

Analysis of Underactuated Dynamic Locomotion Systems Using Perturbation Expansion: The Twistcar Toy Example

NASA Astrophysics Data System (ADS)

Chakon, Ofir; Or, Yizhar

2017-08-01

Underactuated robotic locomotion systems are commonly represented by nonholonomic constraints where in mixed systems, these constraints are also combined with momentum evolution equations. Such systems have been analyzed in the literature by exploiting symmetries and utilizing advanced geometric methods. These works typically assume that the shape variables are directly controlled, and obtain the system's solutions only via numerical integration. In this work, we demonstrate utilization of the perturbation expansion method for analyzing a model example of mixed locomotion system—the twistcar toy vehicle, which is a variant of the well-studied roller-racer model. The system is investigated by assuming small-amplitude oscillatory inputs of either steering angle (kinematic) or steering torque (mechanical), and explicit expansions for the system's solutions under both types of actuation are obtained. These expressions enable analyzing the dependence of the system's dynamic behavior on the vehicle's structural parameters and actuation type. In particular, we study the reversal in direction of motion under steering angle oscillations about the unfolded configuration, as well as influence of the choice of actuation type on convergence properties of the motion. Some of the findings are demonstrated qualitatively by reporting preliminary motion experiments with a modular robotic prototype of the vehicle.

Cones in Supersonic Flow

NASA Technical Reports Server (NTRS)

Hantzsche, W.; Wendt, H.

1947-01-01

In the case of cones in axially symmetric flow of supersonic velocity, adiabatic compression takes place between shock wave and surface of the cone. Interpolation curves betwen shock polars and the surface are therefore necessary for the complete understanding of this type of flow. They are given in the present report by graphical-numerical integration of the differential equation for all cone angles and airspeeds.

Painlevé equations, elliptic integrals and elementary functions

NASA Astrophysics Data System (ADS)

Żołądek, Henryk; Filipuk, Galina

2015-02-01

The six Painlevé equations can be written in the Hamiltonian form, with time dependent Hamilton functions. We present a rather new approach to this result, leading to rational Hamilton functions. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems with two degrees of freedom. We realize the Bäcklund transformations of the Painlevé equations as symplectic birational transformations in C4 and we interpret the cases with classical solutions as the cases of partial integrability of the extended Hamiltonian systems. We prove that the extended Hamiltonian systems do not have any additional algebraic first integral besides the known special cases of the third and fifth Painlevé equations. We also show that the original Painlevé equations admit the first integrals expressed in terms of the elementary functions only in the special cases mentioned above. In the proofs we use equations in variations with respect to a parameter and Liouville's theory of elementary functions.

Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Ortenzi, G.

2013-12-01

The structure and properties of families of critical points for classes of functions W(z,{\\overline{z}}) obeying the elliptic Euler-Poisson-Darboux equation E(1/2, 1/2) are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented. There are the extended dispersionless Toda/nonlinear Schrödinger hierarchies, the ‘inverse’ hierarchy and equations associated with the real-analytic Eisenstein series E(\\beta ,{\\overline{\\beta }};1/2) among them. The specific bi-Hamiltonian structure of these equations is also discussed.

The reduced basis method for the electric field integral equation

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

Fares, M., E-mail: fares@cerfacs.f; Hesthaven, J.S., E-mail: Jan_Hesthaven@Brown.ed; Maday, Y., E-mail: maday@ann.jussieu.f

We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field integral equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first step consists of a computationally intense assembling of the reduced basis, that needs to be effected only once. In the second step, we compute output functionals of the solution, such as the Radar Cross Section (RCS), independently of the dimension of the discretization space, formore » many different parameter values in a many-query context at very little cost. Parameters include the wavenumber, the angle of the incident plane wave and its polarization.« less

Phase-resolved fluid dynamic forces of a flapping foil energy harvester based on PIV measurements

NASA Astrophysics Data System (ADS)

Liburdy, James

2017-11-01

Two-dimensional particle image velocimetry measurements are performed in a wind tunnel to evaluate the spatial and temporal fluid dynamic forces acting on a flapping foil operating in the energy harvesting regime. Experiments are conducted at reduced frequencies (k = fc/U) of 0.05 - 0.2, pitching angle of, and heaving amplitude of A / c = 0.6. The phase-averaged pressure field is obtained by integrating the pressure Poisson equation. Fluid dynamic forces are then obtained through the integral momentum equation. Results are compared with a simple force model based on the concept of flow impulse. These results help to show the detailed force distributions, their transient nature and aide in understanding the impact of the fluid flow structures that contribute to the power production.

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.

Binary collision model for neon Auger spectra from neon ion bombardment of the aluminum surface

NASA Technical Reports Server (NTRS)

Pepper, S. V.

1986-01-01

A model is developed to account for the angle-resolved Auger spectra from neon ion bombardment of the aluminum surface recently obtained by Pepper and Aron. The neon is assumed to be excited in a single asymmetric neon-aluminum-collision and scattered back into the vacuum where it emits an Auger electron. The velocity of the Auger electron acquires a Doppler shift by virtue of the emission from a moving source. The dependence of the Auger peak shape and energy on the incident ion energy, angle of incidence and on the angle of Auger electron emission with respect to the surface is presented. Satisfactory agreement with the angle resolved experimental observations is obtained. The dependence of the angle-integrated Auger yield on the incident ion energy and angle of incidence is also obtained and shown to be in satisfactory agreement with available experimental evidence.

Experiments on Frequency Dependence of the Deflection of Light in Yang-Mills Gravity

NASA Astrophysics Data System (ADS)

Hao, Yun; Zhu, Yiyi; Hsu, Jong-Ping

2018-01-01

In Yang-Mills gravity based on flat space-time, the eikonal equation for a light ray is derived from the modified Maxwell's wave equations in the geometric-optics limit. One obtains a Hamilton-Jacobi type equation, GLµv∂µΨ∂vΨ = 0 with an effective Riemannian metric tensor GLµv. According to Yang-Mills gravity, light rays (and macroscopic objects) move as if they were in an effective curved space-time with a metric tensor. The deflection angle of a light ray by the sun is about 1.53″ for experiments with optical frequencies ≈ 1014Hz. It is roughly 12% smaller than the usual value 1.75″. However, the experimental data in the past 100 years for the deflection of light by the sun in optical frequencies have uncertainties of (10-20)% due to large systematic errors. If one does not take the geometric-optics limit, one has the equation, GLµv[∂µΨ∂vΨcosΨ+ (∂µ∂vΨ)sinΨ] = 0, which suggests that the deflection angle could be frequency-dependent, according to Yang-Mills gravity. Nowadays, one has very accurate data in the radio frequencies ≈ 109Hz with uncertainties less than 0.1%. Thus, one can test this suggestion by using frequencies ≈ 1012 Hz, which could have a small uncertainty 0.1% due to the absence of systematic errors in the very long baseline interferometry.

On an example of a system of differential equations that are integrated in Abelian functions

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Sevastianov, L. A.

2017-12-01

The short review of the theory of Abelian functions and its applications in mechanics and analytical theory of differential equations is given. We think that Abelian functions are the natural generalization of commonly used functions because if the general solution of the 2nd order differential equation depends algebraically on the constants of integration, then integrating this equation does not lead out of the realm of commonly used functions complemented by the Abelian functions (Painlevé theorem). We present a relatively simple example of a dynamical system that is integrated in Abelian integrals by “pairing” two copies of a hyperelliptic curve. Unfortunately, initially simple formulas unfold into very long ones. Apparently the theory of Abelian functions hasn’t been finished in the last century because without computer algebra systems it was impossible to complete the calculations to the end. All calculations presented in our report are performed in Sage.

Integrated polarization-dependent sensor for autonomous navigation

NASA Astrophysics Data System (ADS)

Liu, Ze; Zhang, Ran; Wang, Zhiwen; Guan, Le; Li, Bin; Chu, Jinkui

2015-01-01

Based on the navigation strategy of insects utilizing the polarized skylight, an integrated polarization-dependent sensor for autonomous navigation is presented. The navigation sensor has the features of compact structure, high precision, strong robustness, and a simple manufacture technique. The sensor is composed by integrating a complementary-metal-oxide-semiconductor sensor with a multiorientation nanowire grid polarizer. By nanoimprint lithography, the multiorientation nanowire polarizer is fabricated in one step and the alignment error is eliminated. The statistical theory is added to the interval-division algorithm to calculate the polarization angle of the incident light. The laboratory and outdoor tests for the navigation sensor are implemented and the errors of the measured angle are ±0.02 deg and ±1.3 deg, respectively. The results show that the proposed sensor has potential for application in autonomous navigation.

Angular position of the cleat according to torsional parameters of the cyclist's lower limb.

PubMed

Ramos-Ortega, Javier; Domínguez, Gabriel; Castillo, José Manuel; Fernández-Seguín, Lourdes; Munuera, Pedro V

2014-05-01

The aim of this work was to study the relationship of torsional and rotational parameters of the lower limb with a specific angular position of the cleat to establish whether these variables affect the adjustment of the cleat. Correlational study. Motion analysis laboratory. Thirty-seven male cyclists of high performance. The variables studied of the cyclist's lower limb were hip rotation (internal and external), tibial torsion angle, Q angle, and forefoot adductus angle. The cleat angle was measured through a photograph of the sole and with an Rx of this using the software AutoCAD 2008. The variables were photograph angle (photograph), the variable denominated cleat-tarsus minor angle, and a variable denominated cleat-second metatarsal angle (Rx). Analysis included the intraclass correlation coefficient for the reliability of the measurements, Student's t test performed on the dependent variables to compare side, and the multiple linear regression models were calculated using the software SPSS 15.0 for Windows. The Student's t test performed on the dependent variables to compare side showed no significant differences (P = 0.209 for the photograph angle, P = 0.735 for the cleat-tarsus minor angle, and P = 0.801 for the cleat-second metatarsal angle). Values of R and R2 for the photograph angle model were 0.303 and 0.092 (P = 0.08), the cleat/tarsus minor angle model were 0.683 and 0.466 (P < 0.001), and the cleat/second metatarsal angle model were 0.618 and 0.382, respectively (P < 0.001). The equation given by the model was cleat-tarsus minor angle = 75.094 - (0.521 × forefoot adductus angle) + (0.116 × outward rotation of the hips) + (0.220 × Q angle).

Numerical integration of KPZ equation with restrictions

NASA Astrophysics Data System (ADS)

Torres, M. F.; Buceta, R. C.

2018-03-01

In this paper, we introduce a novel integration method of Kardar–Parisi–Zhang (KPZ) equation. It is known that if during the discrete integration of the KPZ equation the nearest-neighbor height-difference exceeds a critical value, instabilities appear and the integration diverges. One way to avoid these instabilities is to replace the KPZ nonlinear-term by a function of the same term that depends on a single adjustable parameter which is able to control pillars or grooves growing on the interface. Here, we propose a different integration method which consists of directly limiting the value taken by the KPZ nonlinearity, thereby imposing a restriction rule that is applied in each integration time-step, as if it were the growth rule of a restricted discrete model, e.g. restricted-solid-on-solid (RSOS). Taking the discrete KPZ equation with restrictions to its dimensionless version, the integration depends on three parameters: the coupling constant g, the inverse of the time-step k, and the restriction constant ε which is chosen to eliminate divergences while keeping all the properties of the continuous KPZ equation. We study in detail the conditions in the parameters’ space that avoid divergences in the 1-dimensional integration and reproduce the scaling properties of the continuous KPZ with a particular parameter set. We apply the tested methodology to the d-dimensional case (d = 3, 4 ) with the purpose of obtaining the growth exponent β, by establishing the conditions of the coupling constant g under which we recover known values reached by other authors, particularly for the RSOS model. This method allows us to infer that d  =  4 is not the critical dimension of the KPZ universality class, where the strong-coupling phase disappears.

A vectorized code for calculating laminar and turbulent hypersonic flows about blunt axisymmetric bodies at zero and small angles of attack

NASA Technical Reports Server (NTRS)

Kumar, A.; Graves, R. A., Jr.

1980-01-01

A user's guide is provided for a computer code which calculates the laminar and turbulent hypersonic flows about blunt axisymmetric bodies, such as spherically blunted cones, hyperboloids, etc., at zero and small angles of attack. The code is written in STAR FORTRAN language for the CDC-STAR-100 computer. Time-dependent, viscous-shock-layer-type equations are used to describe the flow field. These equations are solved by an explicit, two-step, time asymptotic, finite-difference method. For the turbulent flow, a two-layer, eddy-viscosity model is used. The code provides complete flow-field properties including shock location, surface pressure distribution, surface heating rates, and skin-friction coefficients. This report contains descriptions of the input and output, the listing of the program, and a sample flow-field solution.

A compressible solution of the Navier-Stokes equations for turbulent flow about an airfoil

NASA Technical Reports Server (NTRS)

Shamroth, S. J.; Gibeling, H. J.

1979-01-01

A compressible time dependent solution of the Navier-Stokes equations including a transition turbulence model is obtained for the isolated airfoil flow field problem. The equations are solved by a consistently split linearized block implicit scheme. A nonorthogonal body-fitted coordinate system is used which has maximum resolution near the airfoil surface and in the region of the airfoil leading edge. The transition turbulence model is based upon the turbulence kinetic energy equation and predicts regions of laminar, transitional, and turbulent flow. Mean flow field and turbulence field results are presented for an NACA 0012 airfoil at zero and nonzero incidence angles of Reynolds number up to one million and low subsonic Mach numbers.

Analysis of an unswept propfan blade with a semiempirical dynamic stall model

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Kaza, K. R. V.

1989-01-01

The time history response of a propfan wind tunnel model with dynamic stall is studied analytically. The response obtained from the analysis is compared with available experimental data. The governing equations of motion are formulated in terms of blade normal modes which are calculated using the COSMIC-NASTRAN computer code. The response analysis considered the blade plunging and pitching motions. The lift, drag and moment coefficients for angles of attack below the static stall angle are obtained from a quasi-steady theory. For angles above static stall angles, a semiempirical dynamic stall model based on a correction to angle of attack is used to obtain lift, drag and moment coefficients. Using these coefficients, the aerodynamic forces are calculated at a selected number of strips, and integrated to obtain the total generalized forces. The combined momentum-blade element theory is used to calculate the induced velocity. The semiempirical stall model predicted a limit cycle oscillation near the setting angle at which large vibratory stresses were observed in an experiment. The predicted mode and frequency of oscillation also agreed with those measured in the experiment near the setting angle.

Toward Realistic Dynamics of Rotating Orbital Debris, and Implications for Lightcurve Interpretation

NASA Technical Reports Server (NTRS)

Ojakangas, Gregory W.; Cowardin, H.; Hill, N.

2011-01-01

Optical observations of rotating space debris near GEO contain important information on size, shape, composition, and rotational states, but these aspects are difficult to extract due to data limitations and the high number of degrees of freedom in the modeling process. For tri-axial rigid debris objects created by satellite fragmentations, the most likely initial rotation state has a large component of initial angular velocity directed along the intermediate axis of inertia, leading to large angular reorientations of the body on the timescale of the rotation period. This lends some support to the simplest possible interpretation of light curves -- that they represent sets of random orientations of the objects of study. However, effects of internal friction and solar radiation are likely to cause significant modification of rotation states within a time as short as a few orbital periods. In order to examine the rotational dynamics of debris objects under the influences of these effects, a set of seven first-order coupled equations of motion were assembled in state form: three are Euler equations describing the rates of change of the components of angular velocity in the body frame, and four describe the rates of change of the components of the unit quaternion. Quaternions are a four-dimensional extension of complex numbers that form a seamless, singularity-free representation of body orientation on S3. The Euler equations contain explicit terms describing torque from solar radiation in terms of spherical harmonics, and terms representing effects of a prescribed rate of internal friction. Numerical integrations of these equations of motion are being performed, and results will be presented. Initial tests show that internal friction without solar radiation torque leads to rotation about the maximum principal axis of inertia, as required, and solar radiation torque is expected to lead to spin-up of objects. Because the axis of maximum rotational inertia tends to be roughly coincident with the normal to the largest projected cross-sectional area, internal friction is expected to lead to reduced variation of light curve amplitudes at a given phase angle, but a large dependence of the same on phase angle. At a given phase angle, databases are generated which contain reflected intensities for comprehensive sets of equally-likely orientations, represented as unit quaternions. When projected onto three dimensions (S2) and color-coded by intensity, the set is depicted as points within a solid, semi-transparent unit sphere, within which all possible reflected intensities for an object at a given phase angle may be inspected simultaneously. Rotational sequences are represented by trajectories through the sphere. Databases are generated for each of a set of phase angles separately, forming a comprehensive dataset of reflected intensities spanning all object orientations and solar phase angles. Symmetries in the problem suggest that preferred rotation states are likely, defined relative to the object-sun direction in inertial space and relative to the maximum principal axis of inertia in the body coordinate system. Such rotation states may greatly simplify the problem of light curve interpretation by reducing the number of degrees of freedom in the problem.

Implementation of Laminate Theory Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

2000-01-01

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were implemented into a mechanics of materials based micromechanics method. In the current work, the computation of the effective inelastic strain in the micromechanics model was modified to fully incorporate the Poisson effect. The micromechanics equations were also combined with classical laminate theory to enable the analysis of symmetric multilayered laminates subject to in-plane loading. A quasi-incremental trapezoidal integration method was implemented to integrate the constitutive equations within the laminate theory. Verification studies were conducted using an AS4/PEEK composite using a variety of laminate configurations and strain rates. The predicted results compared well with experimentally obtained values.

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

NASA Astrophysics Data System (ADS)

Yuzbashyan, Emil A.

2018-05-01

We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

Opening of an interface flaw in a layered elastic half-plane under compressive loading

NASA Technical Reports Server (NTRS)

Kennedy, J. M.; Fichter, W. B.; Goree, J. G.

1984-01-01

A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.

Excitation of propagating magnetization waves by microstrip antennas

NASA Astrophysics Data System (ADS)

Dmitriev, V. F.; Kalinikos, B. A.

1988-11-01

We discuss the self-consistent theory of excitation of dipole-exchange magnetization waves by microstrip antennas in a metal-dielectric-ferrite-dielectric-metal stratified structure, magnetized under an arbitrary angle to the surface. Spin-wave Green's functions are derived, describing the response of the spin-system to a spatially inhomogeneous varying magnetic field. The radiative resistance of microstrip antenna is calculated. In this case the distribution of surface current density in the antenna is found on the basis of the analytic solution of a singular integral equation. The nature of the effect of metallic screens and redistributed surface current densities in the antenna on the frequency dependence of the resistive radiation is investigated. Approximate relations are obtained, convenient for practical calculations of radiative resistance of microstrip antennas both in a free and in a screened ferromagnetic film. The theoretical calculations are verified by data of experiments carried out on monocrystalline films of iron-yttrium garnet.

Coin state properties in quantum walks

PubMed Central

Andrade, R. F. S.

2013-01-01

Recent experimental advances have measured individual coin components in discrete time quantum walks, which have not received the due attention in most theoretical studies on the theme. Here is presented a detailed investigation of the properties of M, the difference between square modulus of coin states of discrete quantum walks on a linear chain. Local expectation values are obtained in terms of real and imaginary parts of the Fourier transformed wave function. A simple expression is found for the average difference between coin states in terms of an angle θ gauging the coin operator and its initial state. These results are corroborated by numerical integration of dynamical equations in real space. The local dependence is characterized both by large and short period modulations. The richness of revealed patterns suggests that the amount of information stored and retrieved from quantum walks is significantly enhanced if M is taken into account. PMID:23756358

Numerical Simulation of Liquid Jet Atomization Including Turbulence Effects

NASA Technical Reports Server (NTRS)

Trinh, Huu P.; Chen, C. P.; Balasubramanyam, M. S.

2005-01-01

This paper describes numerical implementation of a newly developed hybrid model, T-blob/T-TAB, into an existing computational fluid dynamics (CFD) program for primary and secondary breakup simulation of liquid jet atomization. This model extend two widely used models, the Kelvin-Helmholtz (KH) instability of Reitz (blob model) and the Taylor-Analogy-Breakup (TAB) secondary droplet breakup by O'Rourke and Amsden to include turbulence effects. In the primary breakup model, the level of the turbulence effect on the liquid breakup depends on the characteristic scales and the initial flow conditions. For the secondary breakup, an additional turbulence force acted on parent drops is modeled and integrated into the TAB governing equation. Several assessment studies are presented and the results indicate that the existing KH and TAB models tend to under-predict the product drop size and spray angle, while the current model provides superior results when compared with the measured data.

Scale-dependent behavior of scale equations.

PubMed

Kim, Pilwon

2009-09-01

We propose a new mathematical framework to formulate scale structures of general systems. Stack equations characterize a system in terms of accumulative scales. Their behavior at each scale level is determined independently without referring to other levels. Most standard geometries in mathematics can be reformulated in such stack equations. By involving interaction between scales, we generalize stack equations into scale equations. Scale equations are capable to accommodate various behaviors at different scale levels into one integrated solution. On contrary to standard geometries, such solutions often reveal eccentric scale-dependent figures, providing a clue to understand multiscale nature of the real world. Especially, it is suggested that the Gaussian noise stems from nonlinear scale interactions.

Low speed airfoil design and analysis

NASA Technical Reports Server (NTRS)

Eppler, R.; Somers, D. M.

1979-01-01

A low speed airfoil design and analysis program was developed which contains several unique features. In the design mode, the velocity distribution is not specified for one but many different angles of attack. Several iteration options are included which allow the trailing edge angle to be specified while other parameters are iterated. For airfoil analysis, a panel method is available which uses third-order panels having parabolic vorticity distributions. The flow condition is satisfied at the end points of the panels. Both sharp and blunt trailing edges can be analyzed. The integral boundary layer method with its laminar separation bubble analog, empirical transition criterion, and precise turbulent boundary layer equations compares very favorably with other methods, both integral and finite difference. Comparisons with experiment for several airfoils over a very wide Reynolds number range are discussed. Applications to high lift airfoil design are also demonstrated.

Spreading dynamics of 2D dipolar Langmuir monolayer phases.

PubMed

Heinig, P; Wurlitzer, S; Fischer, Th M

2004-07-01

We study the spreading of a liquid 2D dipolar droplet in a Langmuir monolayer. Interfacial tensions (line tensions) and microscopic contact angles depend on the scale on which they are probed and obey a scaling law. Assuming rapid equilibration of the microscopic contact angle and ideal slippage of the 2D solid/liquid and solid/gas boundary, the driving force of spreading is merely expressed by the shape-dependent long-range interaction integrals. We obtain good agreement between experiment and numerical simulations using this theory.

A numerical scheme to solve unstable boundary value problems

NASA Technical Reports Server (NTRS)

Kalnay Derivas, E.

1975-01-01

A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.

Alfven waves associated with long cylindrical satellites

NASA Technical Reports Server (NTRS)

Venkataraman, N. S.; Gustafson, W. A.

1973-01-01

The Alfven wave excited by a long cylindrical satellite moving with a constant velocity at an angle relative to a uniform magnetic field has been calculated. Assuming a plasma with infinite conductivity, the linearized momentum equation and Maxwell's equations are applied to a cylindrical satellite carrying a variable current. The induced magnetic field is determined, and it is shown that the Alfven disturbance zone is of limited extent, depending on the satellite shape. The wave drag coefficient is calculated and shown to be small compared to the induction drag coefficient at all altitudes considered.

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. physical basis

USGS Publications Warehouse

Iverson, Richard M.; George, David L.

2014-01-01

To simulate debris-flow behaviour from initiation to deposition, we derive a depth-averaged, two-phase model that combines concepts of critical-state soil mechanics, grain-flow mechanics and fluid mechanics. The model's balance equations describe coupled evolution of the solid volume fraction, m, basal pore-fluid pressure, flow thickness and two components of flow velocity. Basal friction is evaluated using a generalized Coulomb rule, and fluid motion is evaluated in a frame of reference that translates with the velocity of the granular phase, vs. Source terms in each of the depth-averaged balance equations account for the influence of the granular dilation rate, defined as the depth integral of ∇⋅vs. Calculation of the dilation rate involves the effects of an elastic compressibility and an inelastic dilatancy angle proportional to m−meq, where meq is the value of m in equilibrium with the ambient stress state and flow rate. Normalization of the model equations shows that predicted debris-flow behaviour depends principally on the initial value of m−meq and on the ratio of two fundamental timescales. One of these timescales governs downslope debris-flow motion, and the other governs pore-pressure relaxation that modifies Coulomb friction and regulates evolution of m. A companion paper presents a suite of model predictions and tests.

Iterative discrete ordinates solution of the equation for surface-reflected radiance

NASA Astrophysics Data System (ADS)

Radkevich, Alexander

2017-11-01

This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

Angle-dependent spin-wave resonance spectroscopy of (Ga,Mn)As films

NASA Astrophysics Data System (ADS)

Dreher, L.; Bihler, C.; Peiner, E.; Waag, A.; Schoch, W.; Limmer, W.; Goennenwein, S. T. B.; Brandt, M. S.

2013-06-01

A modeling approach for standing spin-wave resonances based on a finite-difference formulation of the Landau-Lifshitz-Gilbert equation is presented. In contrast to a previous study [C. Bihler , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.79.045205 79, 045205 (2009)], this formalism accounts for elliptical magnetization precession and magnetic properties arbitrarily varying across the layer thickness, including the magnetic anisotropy parameters, the exchange stiffness, the Gilbert damping, and the saturation magnetization. To demonstrate the usefulness of our modeling approach, we experimentally study a set of (Ga,Mn)As samples grown by low-temperature molecular-beam epitaxy by means of angle-dependent standing spin-wave resonance spectroscopy and electrochemical capacitance-voltage measurements. By applying our modeling approach, the angle dependence of the spin-wave resonance data can be reproduced in a simulation with one set of simulation parameters for all external field orientations. We find that the approximately linear gradient in the out-of-plane magnetic anisotropy is related to a linear gradient in the hole concentrations of the samples.

Temperature Dependence in Homogeneous and Heterogeneous Nucleation

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

McGraw R. L.; Winkler, P. M.; Wagner, P. E.

2017-08-01

Heterogeneous nucleation on stable (sub-2 nm) nuclei aids the formation of atmospheric cloud condensation nuclei (CCN) by circumventing or reducing vapor pressure barriers that would otherwise limit condensation and new particle growth. Aerosol and cloud formation depend largely on the interaction between a condensing liquid and the nucleating site. A new paper published this year reports the first direct experimental determination of contact angles as well as contact line curvature and other geometric properties of a spherical cap nucleus at nanometer scale using measurements from the Vienna Size Analyzing Nucleus Counter (SANC) (Winkler et al., 2016). For water nucleating heterogeneouslymore » on silver oxide nanoparticles we find contact angles around 15 degrees compared to around 90 degrees for the macroscopically measured equilibrium angle for water on bulk silver. The small microscopic contact angles can be attributed via the generalized Young equation to a negative line tension that becomes increasingly dominant with increasing curvature of the contact line. These results enable a consistent theoretical description of heterogeneous nucleation and provide firm insight to the wetting of nanosized objects.« less

Reflection and emission models for deserts derived from Nimbus-7 ERB scanner measurements

NASA Technical Reports Server (NTRS)

Staylor, W. F.; Suttles, J. T.

1986-01-01

Broadband shortwave and longwave radiance measurements obtained from the Nimbus-7 Earth Radiation Budget scanner were used to develop reflectance and emittance models for the Sahara-Arabian, Gibson, and Saudi Deserts. The models were established by fitting the satellite measurements to analytic functions. For the shortwave, the model function is based on an approximate solution to the radiative transfer equation. The bidirectional-reflectance function was obtained from a single-scattering approximation with a Rayleigh-like phase function. The directional-reflectance model followed from integration of the bidirectional model and is a function of the sum and product of cosine solar and viewing zenith angles, thus satisfying reciprocity between these angles. The emittance model was based on a simple power-law of cosine viewing zenith angle.

Connectivity as an alternative to boundary integral equations: Construction of bases

PubMed Central

Herrera, Ismael; Sabina, Federico J.

1978-01-01

In previous papers Herrera developed a theory of connectivity that is applicable to the problem of connecting solutions defined in different regions, which occurs when solving partial differential equations and many problems of mechanics. In this paper we explain how complete connectivity conditions can be used to replace boundary integral equations in many situations. We show that completeness is satisfied not only in steady-state problems such as potential, reduced wave equation and static and quasi-static elasticity, but also in time-dependent problems such as heat and wave equations and dynamical elasticity. A method to obtain bases of connectivity conditions, which are independent of the regions considered, is also presented. PMID:16592522

Non-autonomous Hénon--Heiles systems

NASA Astrophysics Data System (ADS)

Hone, Andrew N. W.

1998-07-01

Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as non-autonomous Hamiltonian equations, which are time-dependent generalizations of the well-known integrable Hénon-Heiles systems. The (time-dependent) Hamiltonians are given by logarithmic derivatives of the tau-functions (inherited from the original PDEs). The ODEs for the similarity solutions also have inherited Bäcklund transformations, which may be used to generate sequences of rational solutions as well as other special solutions related to the first Painlevé transcendent.

Infiltration of Liquid Droplets Into Porous Media: Effects of Dynamic Contact Angle and Contact Angle Hysteresis

NASA Astrophysics Data System (ADS)

Hilpert, M.

2008-12-01

Infiltration of liquid droplets into dry porous media occurs when rain drops fall onto soil, when accidentally spilling organic liquid (e.g., gasoline and chlorinated solvents) onto ground, or when aerosol pesticides are not intercepted by the vegetation and then released to soils. If harmful chemicals are released from the droplet into the atmosphere through evaporation, it is important to know the time of infiltration. We developed a theory for infiltration, which accounts for a general model for the dynamic contact angle between the droplet and the porous medium as well as contact angle hysteresis. Our theory assumes the droplet to have the shape of a spherical cap and the pressure within the droplet to be uniform. The theory shows that droplet infiltration involves three phases due to contact angle hysteresis: (1) an increasing drawing area (IDA) phase during which the interface between the droplet and the porous medium increases, (2) a constant drawing area (CDA) phase during which the contact line of the droplet remains pinned, and (3) a decreasing drawing area (DDA) phase. We find that infiltration always consists of a cascade process formed by the IDA, CDA, and DDA phases, where the entire process may begin or end in any of the three phases. The entire process is formulated with four nondimensional parameters: three contact angles (initial, advancing, and receding) and a porous permeability parameter that depends on porous medium geometry. The total time of infiltration and the time dependence of drawing area are critically affected by the occurrence of the IDA, CDA, and DDA phases as well as by the permeability. In general, the IDA and DDA phases are described by integro-differential equations. With ordinary differential equations (ODEs), we are able to approximate the IDA phase and to describe exactly infiltration processes that starts out with the CDA or DDA phase.

Time-local equation for exact time-dependent optimized effective potential in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel; Chu, Shih-I.

2017-04-01

Solving and analyzing the exact time-dependent optimized effective potential (TDOEP) integral equation has been a longstanding challenge due to its highly nonlinear and nonlocal nature. To meet the challenge, we derive an exact time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham orbitals and effective memory orbitals. For illustration, the dipole evolution dynamics of a one-dimension-model chain of hydrogen atoms is numerically evaluated and examined to demonstrate the utility of the proposed time-local formulation. Importantly, it is shown that the zero-force theorem, violated by the time-dependent Krieger-Li-Iafrate approximation, is fulfilled in the current TDOEP framework. This work was partially supported by DOE.

Integrable Time-Dependent Quantum Hamiltonians

NASA Astrophysics Data System (ADS)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Contact angle adjustment in equation-of-state-based pseudopotential model.

PubMed

Hu, Anjie; Li, Longjian; Uddin, Rizwan; Liu, Dong

2016-05-01

The single component pseudopotential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many studies, it has been claimed that this model can be stable for density ratios larger than 1000. However, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in the present work show that, by applying the original contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with our contact angle adjustment method, the stability of the model is highly improved when the density ratio is relatively large, and it is independent of the surface tension.

Contact angle adjustment in equation-of-state-based pseudopotential model

NASA Astrophysics Data System (ADS)

Hu, Anjie; Li, Longjian; Uddin, Rizwan; Liu, Dong

2016-05-01

The single component pseudopotential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many studies, it has been claimed that this model can be stable for density ratios larger than 1000. However, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in the present work show that, by applying the original contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with our contact angle adjustment method, the stability of the model is highly improved when the density ratio is relatively large, and it is independent of the surface tension.

Extension of the KLI approximation toward the exact optimized effective potential.

PubMed

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Extension of the KLI approximation toward the exact optimized effective potential

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Krieger, J. B.

2013-03-01

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

NASA Technical Reports Server (NTRS)

Radhakrishnan, K.

1984-01-01

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

Direct solution for thermal stresses in a nose cap under an arbitrary axisymmetric temperature distribution

NASA Technical Reports Server (NTRS)

Davis, Randall C.

1988-01-01

The design of a nose cap for a hypersonic vehicle is an iterative process requiring a rapid, easy to use and accurate stress analysis. The objective of this paper is to develop such a stress analysis technique from a direct solution of the thermal stress equations for a spherical shell. The nose cap structure is treated as a thin spherical shell with an axisymmetric temperature distribution. The governing differential equations are solved by expressing the stress solution to the thermoelastic equations in terms of a series of derivatives of the Legendre polynomials. The process of finding the coefficients for the series solution in terms of the temperature distribution is generalized by expressing the temperature along the shell and through the thickness as a polynomial in the spherical angle coordinate. Under this generalization the orthogonality property of the Legendre polynomials leads to a sequence of integrals involving powers of the spherical shell coordinate times the derivative of the Legendre polynomials. The coefficients of the temperature polynomial appear outside of these integrals. Thus, the integrals are evaluated only once and their values tabulated for use with any arbitrary polynomial temperature distribution.

Renormalization group equation analysis of a pseudoscalar portal dark matter model

NASA Astrophysics Data System (ADS)

Ghorbani, Karim

2017-10-01

We investigate the vacuum stability and perturbativity of a pseudoscalar portal dark matter (DM) model with a Dirac DM candidate, through the renormalization group equation analysis at one-loop order. The model has a particular feature which can evade the direct detection upper bounds measured by XENON100 and even that from planned experiment XENON1T. We first find the viable regions in the parameter space which will give rise to correct DM relic density and comply with the constraints from Higgs physics. We show that for a given mass of the pseudoscalar, the mixing angle plays no significant role in the running of the couplings. Then we study the running of the couplings for various pseudoscalar masses at mixing angle θ =6^\\circ , and find the scale of validity in terms of the dark coupling, {λ }d. Depending on our choice of the cutoff scale, the resulting viable parameter space will be determined.

Kinetics of gravity-driven slug flow in partially wettable capillaries of varying cross section

NASA Astrophysics Data System (ADS)

Nissan, Alon; Wang, Qiuling; Wallach, Rony

2016-11-01

A mathematical model for slug (finite liquid volume) motion in not-fully-wettable capillary tubes with sinusoidally varying cross-sectional areas was developed. The model, based on the Navier-Stokes equation, accounts for the full viscous terms due to nonuniform geometry, the inertial term, the slug's front and rear meniscus hysteresis effect, and dependence of contact angle on flow velocity (dynamic contact angle). The model includes a velocity-dependent film that is left behind the advancing slug, reducing its mass. The model was successfully verified experimentally by recording slug movement in uniform and sinusoidal capillary tubes with a gray-scale high-speed camera. Simulation showed that tube nonuniformity has a substantial effect on slug flow pattern: in a uniform tube it is monotonic and depends mainly on the slug's momentary mass/length; an undulating tube radius results in nonmonotonic flow characteristics. The static nonzero contact angle varies locally in nonuniform tubes owing to the additional effect of wall slope. Moreover, the nonuniform cross-sectional area induces slug acceleration, deceleration, blockage, and metastable-equilibrium locations. Increasing contact angle further amplifies the geometry effect on slug propagation. The developed model provides a modified means of emulating slug flow in differently wettable porous media for intermittent inlet water supply (e.g., raindrops on the soil surface).

Ground-Support Algorithms for Simulation, Processing, and Calibration of Barnes Static Earth Sensor Measurements: Applications to Tropical Rainfall Measuring Mission Observatory

NASA Technical Reports Server (NTRS)

Natanson, G. A.

1997-01-01

New algorithms are described covering the simulation, processing, and calibration of penetration angles of the Barnes static Earth sensor assembly (SESA) as implemented in the Goddard Space Flight Center Flight Dynamics Division ground support system for the Tropical Rainfall Measuring Mission (TRMM) Observatory. The new treatment involves a detailed analysis of the measurements by individual quadrants. It is shown that, to a good approximation, individual quadrant misalignments can be treated simply as penetration angle biases. Simple formulas suitable for real-time applications are introduced for computing quadrant-dependent effects. The simulator generates penetration angles by solving a quadratic equation with coefficients uniquely determined by the spacecraft's position and the quadrant's orientation in GeoCentric Inertial (GCI) coordinates. Measurement processing for attitude determination is based on linearized equations obtained by expanding the coefficients of the aforementioned quadratic equation as a Taylor series in both the Earth oblateness coefficient (alpha approx. 1/150) and the angle between the pointing axis and the geodetic nadir vector. A simple formula relating a measured value of the penetration angle to the deviation of the Earth-pointed axis from the geodetic nadir vector is derived. It is shown that even near the very edge of the quadrant's Field Of View (FOV), attitude errors resulting from quadratic effects are a few hundredths of a degree, which is small compared to the attitude determination accuracy requirement (0.18 degree, 3 sigma) of TRMM. Calibration of SESA measurements is complicated by a first-order filtering used in the TRMM onboard algorithm to compute penetration angles from raw voltages. A simple calibration scheme is introduced where these complications are avoided by treating penetration angles as the primary raw measurements, which are adjusted using biases and scale factors. In addition to three misalignment parameters, the calibration state vector contains only two average penetration angle biases (one per each pair of opposite quadrants) since, because of the very narrow sensor FOV (+/- 2.6 degrees), differences between biases of the penetration angles measured by opposite quadrants cannot be distinguished from roll and pitch sensor misalignments. After calibration, the estimated misalignments and average penetration angle biases are converted to the four penetration angle biases and to the yaw misalignment angle. The resultant biases and the estimated scale factors are finally used to update the coefficients necessary for onboard computations of penetration angles from measured voltages.

Evaluating Models of The Neutral, Barotropic Planetary Boundary Layer using Integral Measures: Part I. Overview

NASA Astrophysics Data System (ADS)

Hess, G. D.; Garratt, J. R.

Data for the cross-isobaric angle 0, the geostrophic drag coefficient Cg, and the functions A and B of Rossby number similarity theory, obtained from meteorological field experiments, are used to evaluate a range of models of the neutral, barotropic planetary boundary layer. The data give well-defined relationships for 0, Cg, and the integrated dissipation rate over the boundary layer, as a function of the surface Rossby number. Lettau's first-order closure mixing-length model gives an excellent fit to the data; other simple models give reasonable agreement. However more sophisticated models, e.g., higher-order closure, large-eddy simulation, direct numerical simulation and laboratory models, give poor fits to the data. The simplemodels have (at least) one free parameter in their turbulence closure that is matched toatmospheric observations; the more sophisticated models either base their closure onmore general flows or have no free closure parameters. It is suggested that all of theatmospheric experiments that we could locate violate the strict simplifying assumptionsof steady, homogeneous, neutral, barotropic flow required by the sophisticated models.The angle 0 is more sensitive to violations of the assumptions than is Cg.

Integral method for the calculation of three-dimensional, laminar and turbulent boundary layers

NASA Technical Reports Server (NTRS)

Stock, H. W.

1978-01-01

The method for turbulent flows is a further development of an existing method; profile families with two parameters and a lag entrainment method replace the simple entrainment method and power profiles with one parameter. The method for laminar flows is a new development. Moment of momentum equations were used for the solution of the problem, the profile families were derived from similar solutions of boundary layer equations. Laminar and turbulent flows at the wings were calculated. The influence of wing tapering on the boundary layer development was shown. The turbulent boundary layer for a revolution ellipsoid is calculated for 0 deg and 10 deg incidence angles.

Dual-shaped offset reflector antenna designs from solutions of the geometrical optics first-order partial differential equations

NASA Technical Reports Server (NTRS)

Galindo-Israel, V.; Imbriale, W.; Shogen, K.; Mittra, R.

1990-01-01

In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.

Equilibrium Contact Angle and Adsorption Layer Properties with Surfactants.

PubMed

Thiele, Uwe; Snoeijer, Jacco H; Trinschek, Sarah; John, Karin

2018-06-19

The three-phase contact line of a droplet on a smooth surface can be characterized by the Young equation. It relates the interfacial energies to the macroscopic contact angle θ e . On the mesoscale, wettability is modeled by a film-height-dependent wetting energy f( h). Macro- and mesoscale descriptions are consistent if γ cos θ e = γ + f( h a ), where γ and h a are the liquid-gas interface energy and the thickness of the equilibrium liquid adsorption layer, respectively. Here, we derive a similar consistency condition for the case of a liquid covered by an insoluble surfactant. At equilibrium, the surfactant is spatially inhomogeneously distributed, implying a nontrivial dependence of θ e on surfactant concentration. We derive macroscopic and mesoscopic descriptions of a contact line at equilibrium and show that they are consistent only if a particular dependence of the wetting energy on the surfactant concentration is imposed. This is illustrated by a simple example of dilute surfactants, for which we show excellent agreement between theory and time-dependent numerical simulations.

Waveguide Grating For Polarization Preprocessing Circuits

NASA Astrophysics Data System (ADS)

Voirin, Guy; Gradisnik, F.; Parriaux, Olivier M.; Gale, Michael T.; Kunz, Rino E.; Curtis, B. J.; Lehmann, Hans W.

1989-12-01

Periodically corrugated optical waveguides on glass with non-collinear coupling have been investigated both theoretically and experimentally. For a TE or TM polarized guided mode of a planar waveguide obliquely incident on a grating pad, there are four characteristic angles corresponding to the coupling with TE and TM reflected modes fulfilling the Bragg condition. The reflectivity is obtained by solving the coupled mode equations for the non-collinear case. The modelling shows that integrated passive functions such as polarization splitting and interference can be achieved. The polarization interference element uses the property that the coupling coefficients TM-TE and TE-TE are equal at defined incidence angles. Since the angle between the two reflected TE beams is only a few minutes of arc, the two beams can interfere. The waveguides are made by K+ ion exchange in BK7 glass for 3 hours at 380°C. The structure was designed for use at a wavelength of 633 nm and uses a 485 nm period grating which was fabricated by holographic exposure and plasma etching techniques in a 50 nm TiO2 layer e-beam evaporated onto the glass surface. The reflectivity of the grating structure was studied experimentally and compared with theory. The diffraction angles are within 30 " of arc of the predicted angles. The measured reflectivities reached 20 %. The feasibility of realizing an integrated optic preprocessing circuit for polarization interferometry has been demonstrated.

Optimizing lighting, thermal performance, and energy production of building facades by using automated blinds and PV cells

NASA Astrophysics Data System (ADS)

Alzoubi, Hussain Hendi

Energy consumption in buildings has recently become a major concern for environmental designers. Within this field, daylighting and solar energy design are attractive strategies for saving energy. This study seeks the integrity and the optimality of building envelopes' performance. It focuses on the transparent parts of building facades, specifically, the windows and their shading devices. It suggests a new automated method of utilizing solar energy while keeping optimal solutions for indoor daylighting. The method utilizes a statistical approach to produce mathematical equations based on physical experimentation. A full-scale mock-up representing an actual office was built. Heat gain and lighting levels were measured empirically and correlated with blind angles. Computational methods were used to estimate the power production from photovoltaic cells. Mathematical formulas were derived from the results of the experiments; these formulas were utilized to construct curves as well as mathematical equations for the purpose of optimization. The mathematical equations resulting from the optimization process were coded using Java programming language to enable future users to deal with generic locations of buildings with a broader context of various climatic conditions. For the purpose of optimization by automation under different climatic conditions, a blind control system was developed based on the findings of this study. This system calibrates the blind angles instantaneously based upon the sun position, the indoor daylight, and the power production from the photovoltaic cells. The functions of this system guarantee full control of the projected solar energy on buildings' facades for indoor lighting and heat gain. In winter, the system automatically blows heat into the space, whereas it expels heat from the space during the summer season. The study showed that the optimality of building facades' performance is achievable for integrated thermal, energy, and lighting models in buildings. There are blind angles that produce maximum energy from the photovoltaic cells while keeping indoor light within the acceptable limits that prevent undesired heat gain in summer.

Probability density function evolution of power systems subject to stochastic variation of renewable energy

NASA Astrophysics Data System (ADS)

Wei, J. Q.; Cong, Y. C.; Xiao, M. Q.

2018-05-01

As renewable energies are increasingly integrated into power systems, there is increasing interest in stochastic analysis of power systems.Better techniques should be developed to account for the uncertainty caused by penetration of renewables and consequently analyse its impacts on stochastic stability of power systems. In this paper, the Stochastic Differential Equations (SDEs) are used to represent the evolutionary behaviour of the power systems. The stationary Probability Density Function (PDF) solution to SDEs modelling power systems excited by Gaussian white noise is analysed. Subjected to such random excitation, the Joint Probability Density Function (JPDF) solution to the phase angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the numerical method is adopted. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. Both weak and strong intensities of the stochastic excitations are considered in a single machine infinite bus power system. The numerical analysis has the same result as the one given by the Monte Carlo simulation. Potential studies on stochastic behaviour of multi-machine power systems with random excitations are discussed at the end.

Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at interface of topological insulator-chiral medium

NASA Astrophysics Data System (ADS)

Shoukat, Sobia; Naqvi, Qaisar A.

2016-12-01

In this manuscript, scattering from a perfect electric conducting strip located at planar interface of topological insulator (TI)-chiral medium is investigated using the Kobayashi Potential method. Longitudinal components of electric and magnetic vector potential in terms of unknown weighting function are considered. Use of related set of boundary conditions yields two algebraic equations and four dual integral equations (DIEs). Integrand of two DIEs are expanded in terms of the characteristic functions with expansion coefficients which must satisfy, simultaneously, the discontinuous property of the Weber-Schafheitlin integrals, required edge and boundary conditions. The resulting expressions are then combined with algebraic equations to express the weighting function in terms of expansion coefficients, these expansion coefficients are then substituted in remaining DIEs. The projection is applied using the Jacobi polynomials. This treatment yields matrix equation for expansion coefficients which is solved numerically. These unknown expansion coefficients are used to find the scattered field. The far zone scattering width is investigated with respect to different parameters of the geometry, i.e, chirality of chiral medium, angle of incidence, size of the strip. Significant effects of different parameters including TI parameter on the scattering width are noted.

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

NASA Technical Reports Server (NTRS)

Hicks, Raymond M.; Cliff, Susan E.

1991-01-01

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

Theoretical study of interactions of BSA protein in a NaCl aqueous solution

NASA Astrophysics Data System (ADS)

Pellicane, Giuseppe; Cavero, Miguel

2013-03-01

Bovine Serum Albumine (BSA) aqueous solutions in the presence of NaCl are investigated for different protein concentrations and low to intermediate ionic strengths. Protein interactions are modeled via a charge-screened colloidal model, in which the range of the potential is determined by the Debye-Hückel constant. We use Monte Carlo computer simulations to calculate the structure factor, and assume an oblate ellipsoidal form factor for BSA. The theoretical scattered intensities are found in good agreement with the experimental small angle X-ray scattering intensities available in the literature. The performance of well-known integral equation closures to the Ornstein-Zernike equation, namely the mean spherical approximation, the Percus-Yevick, and the hypernetted chain equations, is also assessed with respect to computer simulation.

Effect of Channel Geometry and Properties of a Vapor-Gas Mixture on Volume Condensation in a Flow through a Nozzle

NASA Astrophysics Data System (ADS)

Sidorov, A. A.; Yastrebov, A. K.

2018-01-01

A method of direct numerical solution of the kinetic equation for the droplet size distribution function was used for the numerical investigation of volume condensation in a supersonic vapor-gas flow. Distributions of temperature for the gas phase and droplets, degree of supersaturation, pressure, fraction of droplets by weight, the number of droplets per unit mass, and of the nucleation rate along the channel were determined. The influence of nozzle geometry, mixture composition, and temperature dependence of the mixture properties on the investigated process was evaluated. It has been found that the nozzle divergence angle determines the vapor-gas mixture expansion rate: an increase in the divergence angle enhances the temperature decrease rate and the supersaturation degree raise rate. With an increase or decrease in the partial pressure of incondensable gas, the droplet temperature approaches the gas phase temperature or the saturation temperature at the partial gas pressure, respectively. A considerable effect of the temperature dependence of the liquid surface tension and properties on gas phase parameters and the integral characteristics of condensation aerosol was revealed. However, the difference in results obtained with or without considering the temperature dependence of evaporation heat is negligible. The predictions are compared with experimental data of other investigations for two mixtures: a mixture of heavy water vapor with nitrogen (incondensable gas) or n-nonane vapor with nitrogen. The predictions agree quite well qualitatively and quantitatively with the experiment. The comparison of the predictions with numerical results from other publications obtained using the method of moments demonstrates the usefulness of the direct numerical solution method and the method of moments in a wide range of input data.

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

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

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

2016-06-07

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

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

NASA Astrophysics Data System (ADS)

Jang, Seogjoo

2016-06-01

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

What convention is used for the illumination and view angles?

Atmospheric Science Data Center

2014-12-08

... Azimuth angles are measured clockwise from the direction of travel to local north. For both the Sun and cameras, azimuth describes the ... to the equator, because of its morning equator crossing time. Additionally, the difference in view and solar azimuth angle will be near ...

Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA

NASA Astrophysics Data System (ADS)

Meyer, Christoph

2018-01-01

The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA, which implements a recently developed algorithm to automatize the transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant transformations.

Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.

PubMed

Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht

2013-09-21

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.

Separation of variables in the special diagonal Hamilton-Jacobi equation: Application to the dynamical problem of a particle constrained on a moving surface

NASA Technical Reports Server (NTRS)

Blanchard, D. L.; Chan, F. K.

1973-01-01

For a time-dependent, n-dimensional, special diagonal Hamilton-Jacobi equation a necessary and sufficient condition for the separation of variables to yield a complete integral of the form was established by specifying the admissible forms in terms of arbitrary functions. A complete integral was then expressed in terms of these arbitrary functions and also the n irreducible constants. As an application of the results obtained for the two-dimensional Hamilton-Jacobi equation, analysis was made for a comparatively wide class of dynamical problems involving a particle moving in Euclidean three-dimensional space under the action of external forces but constrained on a moving surface. All the possible cases in which this equation had a complete integral of the form were obtained and these are tubulated for reference.

Design of supercritical cascades with high solidity

NASA Technical Reports Server (NTRS)

Sanz, J. M.

1982-01-01

The method of complex characteristics of Garabedian and Korn was successfully used to design shockless cascades with solidities of up to one. A code was developed using this method and a new hodograph transformation of the flow onto an ellipse. This code allows the design of cascades with solidities of up to two and larger turning angles. The equations of potential flow are solved in a complex hodograph like domain by setting a characteristic initial value problem and integrating along suitable paths. The topology that the new mapping introduces permits a simpler construction of these paths of integration.

A model of transverse fuel injection applied to the computation of supersonic combustor flow

NASA Technical Reports Server (NTRS)

Rogers, R. C.

1979-01-01

A two-dimensional, nonreacting flow model of the aerodynamic interaction of a transverse hydrogen jet within a supersonic mainstream has been developed. The model assumes profile shapes of mass flux, pressure, flow angle, and hydrogen concentration and produces downstream profiles of the other flow parameters under the constraints of the integrated conservation equations. These profiles are used as starting conditions for an existing finite difference parabolic computer code for the turbulent supersonic combustion of hydrogen. Integrated mixing and flow profile results obtained from the computer code compare favorably with existing data for the supersonic combustion of hydrogen.

Stress and Fracture Analyses Under Elastic-plastic and Creep Conditions: Some Basic Developments and Computational Approaches

NASA Technical Reports Server (NTRS)

Reed, K. W.; Stonesifer, R. B.; Atluri, S. N.

1983-01-01

A new hybrid-stress finite element algorith, suitable for analyses of large quasi-static deformations of inelastic solids, is presented. Principal variables in the formulation are the nominal stress-rate and spin. A such, a consistent reformulation of the constitutive equation is necessary, and is discussed. The finite element equations give rise to an initial value problem. Time integration has been accomplished by Euler and Runge-Kutta schemes and the superior accuracy of the higher order schemes is noted. In the course of integration of stress in time, it has been demonstrated that classical schemes such as Euler's and Runge-Kutta may lead to strong frame-dependence. As a remedy, modified integration schemes are proposed and the potential of the new schemes for suppressing frame dependence of numerically integrated stress is demonstrated. The topic of the development of valid creep fracture criteria is also addressed.

The Interplay of School Readiness and Teacher Readiness for Educational Technology Integration: A Structural Equation Model

ERIC Educational Resources Information Center

Petko, Dominik; Prasse, Doreen; Cantieni, Andrea

2018-01-01

Decades of research have shown that technological change in schools depends on multiple interrelated factors. Structural equation models explaining the interplay of factors often suffer from high complexity and low coherence. To reduce complexity, a more robust structural equation model was built with data from a survey of 349 Swiss primary school…

Modeling rainfall infiltration on hillslopes using Flux-concentration relation and time compression approximation

NASA Astrophysics Data System (ADS)

Wang, Jie; Chen, Li; Yu, Zhongbo

2018-02-01

Rainfall infiltration on hillslopes is an important issue in hydrology, which is related to many environmental problems, such as flood, soil erosion, and nutrient and contaminant transport. This study aimed to improve the quantification of infiltration on hillslopes under both steady and unsteady rainfalls. Starting from Darcy's law, an analytical integral infiltrability equation was derived for hillslope infiltration by use of the flux-concentration relation. Based on this equation, a simple scaling relation linking the infiltration times on hillslopes and horizontal planes was obtained which is applicable for both small and large times and can be used to simplify the solution procedure of hillslope infiltration. The infiltrability equation also improved the estimation of ponding time for infiltration under rainfall conditions. For infiltration after ponding, the time compression approximation (TCA) was applied together with the infiltrability equation. To improve the computational efficiency, the analytical integral infiltrability equation was approximated with a two-term power-like function by nonlinear regression. Procedures of applying this approach to both steady and unsteady rainfall conditions were proposed. To evaluate the performance of the new approach, it was compared with the Green-Ampt model for sloping surfaces by Chen and Young (2006) and Richards' equation. The proposed model outperformed the sloping Green-Ampt, and both ponding time and infiltration predictions agreed well with the solutions of Richards' equation for various soil textures, slope angles, initial water contents, and rainfall intensities for both steady and unsteady rainfalls.

Pinning of the Contact Line during Evaporation on Heterogeneous Surfaces: Slowdown or Temporary Immobilization? Insights from a Nanoscale Study.

PubMed

Zhang, Jianguo; Müller-Plathe, Florian; Leroy, Frédéric

2015-07-14

The question of the effect of surface heterogeneities on the evaporation of liquid droplets from solid surfaces is addressed through nonequilibrium molecular dynamics simulations. The mechanism behind contact line pinning which is still unclear is discussed in detail on the nanoscale. Model systems with the Lennard-Jones interaction potential were employed to study the evaporation of nanometer-sized cylindrical droplets from a flat surface. The heterogeneity of the surface was modeled through alternating stripes of equal width but two chemical types. The first type leads to a contact angle of 67°, and the other leads to a contact angle of 115°. The stripe width was varied between 2 and 20 liquid-particle diameters. On the surface with the narrowest stripes, evaporation occurred at constant contact angle as if the surface was homogeneous, with a value of the contact angle as predicted by the regular Cassie-Baxter equation. When the width was increased, the contact angle oscillated during evaporation between two boundaries whose values depend on the stripe width. The evaporation behavior was thus found to be a direct signature of the typical size of the surface heterogeneity domains. The contact angle both at equilibrium and during evaporation could be predicted from a local Cassie-Baxter equation in which the surface composition within a distance of seven fluid-particle diameters around the contact line was considered, confirming the local nature of the interactions that drive the wetting behavior of droplets. More importantly, we propose a nanoscale explanation of pinning during evaporation. Pinning should be interpreted as a drastic slowdown of the contact line dynamics rather than a complete immobilization of it during a transition between two contact angle boundaries.

DREAM3D simulations of inner-belt dynamics

NASA Astrophysics Data System (ADS)

Cunningham, G.

2015-12-01

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere due to pitch-angle scattering from Coulomb and VLF wave-particle interactions. In this paper, equilibrium solutions to a set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium structure. Each diffusion equation incorporated an L- and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This model is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering, and that there is no acceleration caused by the VLF wave-particle interactions. We have revisited this model using our DREAM3D 3D diffusion code, which allows the user to explicitly model the diffusion in pitch-angle and momentum rather than using a lifetime. We find that a) replacing the lifetimes with an explicit model of pitch-angle diffusion, thus allowing for coupling between radial and pitch-angle diffusion, affects the equilibrium structure, and b) over the long time scales needed to reach equilibrium, significant acceleration due to VLF wave particle interactions takes place due to the 'cross-terms' in pitch-angle and momentum and the sharp gradient in the equilibrium pitch-angle distributions. We also find that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to fully understand the equilibirum nature of the trapped electron radiation belts.

Liquid sprays and flow studies in the direct-injection diesel engine under motored conditions

NASA Technical Reports Server (NTRS)

Nguyen, Hung Lee; Carpenter, Mark H.; Ramos, Juan I.; Schock, Harold J.; Stegeman, James D.

1988-01-01

A two dimensional, implicit finite difference method of the control volume variety, a two equation model of turbulence, and a discrete droplet model were used to study the flow field, turbulence levels, fuel penetration, vaporization, and mixing in diesel engine environments. The model was also used to study the effects of engine speed, injection angle, spray cone angle, droplet distribution, and intake swirl angle on the flow field, spray penetration and vaporization, and turbulence in motored two-stroke diesel engines. It is shown that there are optimum conditions for injection, which depend on droplet distribution, swirl, spray cone angle, and injection angle. The optimum conditions result in good spray penetration and vaporization and in good fuel mixing. The calculation presented clearly indicates that internal combustion engine models can be used to assess, at least qualitatively, the effects of injection characteristics and engine operating conditions on the flow field and on the spray penetration and vaporization in diesel engines.

Direct Numerical Simulation of Wetting and Spreading Behavior on Heterogeneous and Roughened Substrates

NASA Technical Reports Server (NTRS)

Schwartz, Leonard W.

1999-01-01

A method of calculation is presented that allows the simulation of the time-dependent three-dimensional motion of thin liquid layers on solid substrates for systems with finite equilibrium contact angles. The contact angle is a prescribed function of position on the substrate. Similar mathematical models are constructed for substrates with a pattern of roughness. Evolution equations are given, using the lubrication approximation, that include viscous, capillary and disjoining forces. Motion to and from dry substrate regions is made possible by use of a thin energetically-stable wetting layer. We simulate motion on heterogeneous substrates with periodic arrays of high contact-angle patches. Two different problems are treated for heterogenous substrates. The first is spontaneous motion driven only by wetting forces. If the contact-angle difference is sufficiently high, the droplet can find several different stable positions, depending on the previous history of the motion. A second simulation treats a forced cyclical motion. Energy dissipation per cycle for a heterogeneous substrate is found to be larger than for a uniform substrate with the same total energy. The Landau-Levich solution for plate removal from a liquid bath is extended to account for a pattern of roughness on the plate.

Wetting of flat gradient surfaces.

PubMed

Bormashenko, Edward

2018-04-01

Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces is treated within the variational approach, under which the contact line is free to move along the substrate. Transversality conditions of the variational problem give rise to the generalized Young equation valid for gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet, placed on a gradient surface depends on the radius of the contact line and the values of derivatives of interfacial tensions. The linear approximation of the problem is considered. It is demonstrated that the contact angle hysteresis is inevitable on gradient surfaces. Electrowetting of gradient surfaces is discussed. Copyright © 2018 Elsevier Inc. All rights reserved.

Magic tilt angle for stabilizing two-dimensional solitons by dipole-dipole interactions

NASA Astrophysics Data System (ADS)

Chen, Xing-You; Chuang, You-Lin; Lin, Chun-Yan; Wu, Chien-Ming; Li, Yongyao; Malomed, Boris A.; Lee, Ray-Kuang

2017-10-01

In the framework of the Gross-Pitaevskii equation, we study the formation and stability of effectively two-dimensional solitons in dipolar Bose-Einstein condensates (BECs), with dipole moments polarized at an arbitrary angle θ relative to the direction normal to the system's plane. Using numerical methods and the variational approximation, we demonstrate that unstable Townes solitons, created by the contact attractive interaction, may be completely stabilized (with an anisotropic shape) by the dipole-dipole interaction (DDI), in the interval θcr<θ ≤π /2 . The stability boundary θcr weakly depends on the relative strength of the DDI, remaining close to the magic angle θm=arccos(1 /√{3 }) . The results suggest that DDIs provide a generic mechanism for the creation of stable BEC solitons in higher dimensions.

Calculations of atmospheric refraction for spacecraft remote-sensing applications

NASA Technical Reports Server (NTRS)

Chu, W. P.

1983-01-01

Analytical solutions to the refraction integrals appropriate for ray trajectories along slant paths through the atmosphere are derived in this paper. This type of geometry is commonly encountered in remote-sensing applications utilizing an occultation technique. The solutions are obtained by evaluating higher-order terms from expansion of the refraction integral and are dependent on the vertical temperature distributions. Refraction parameters such as total refraction angles, air masses, and path lengths can be accurately computed. It is also shown that the method can be used for computing refraction parameters in astronomical refraction geometry for large zenith angles.

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.; Gilat, Amos

2003-01-01

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

Modeling Particle Acceleration and Transport at a 2-D CME-Driven Shock

NASA Astrophysics Data System (ADS)

Hu, Junxiang; Li, Gang; Ao, Xianzhi; Zank, Gary P.; Verkhoglyadova, Olga

2017-11-01

We extend our earlier Particle Acceleration and Transport in the Heliosphere (PATH) model to study particle acceleration and transport at a coronal mass ejection (CME)-driven shock. We model the propagation of a CME-driven shock in the ecliptic plane using the ZEUS-3D code from 20 solar radii to 2 AU. As in the previous PATH model, the initiation of the CME-driven shock is simplified and modeled as a disturbance at the inner boundary. Different from the earlier PATH model, the disturbance is now longitudinally dependent. Particles are accelerated at the 2-D shock via the diffusive shock acceleration mechanism. The acceleration depends on both the parallel and perpendicular diffusion coefficients κ|| and κ⊥ and is therefore shock-obliquity dependent. Following the procedure used in Li, Shalchi, et al. (k href="#jgra53857-bib-0045"/>), we obtain the particle injection energy, the maximum energy, and the accelerated particle spectra at the shock front. Once accelerated, particles diffuse and convect in the shock complex. The diffusion and convection of these particles are treated using a refined 2-D shell model in an approach similar to Zank et al. (k href="#jgra53857-bib-0089"/>). When particles escape from the shock, they propagate along and across the interplanetary magnetic field. The propagation is modeled using a focused transport equation with the addition of perpendicular diffusion. We solve the transport equation using a backward stochastic differential equation method where adiabatic cooling, focusing, pitch angle scattering, and cross-field diffusion effects are all included. Time intensity profiles and instantaneous particle spectra as well as particle pitch angle distributions are shown for two example CME shocks.

Exponential integrators in time-dependent density-functional calculations

NASA Astrophysics Data System (ADS)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

Exact periodic solutions of the sixth-order generalized Boussinesq equation

NASA Astrophysics Data System (ADS)

Kamenov, O. Y.

2009-09-01

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): utt = uxx + 3(u2)xx + uxxxx + αuxxxxxx, α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

A global low order spectral model designed for climate sensitivity studies

NASA Technical Reports Server (NTRS)

Hanna, A. F.; Stevens, D. E.

1984-01-01

A two level, global, spectral model using pressure as a vertical coordinate is developed. The system of equations describing the model is nonlinear and quasi-geostrophic. A moisture budget is calculated in the lower layer only with moist convective adjustment between the two layers. The mechanical forcing of topography is introduced as a lower boundary vertical velocity. Solar forcing is specified assuming a daily mean zenith angle. On land and sea ice surfaces a steady state thermal energy equation is solved to calculate the surface temperature. Over the oceans the sea surface temperatures are prescribed from the climatological average of January. The model is integrated to simulate the January climate.

A Flight Dynamics Model for a Small Glider in Ambient Winds

NASA Technical Reports Server (NTRS)

Beeler, Scott C.; Moerder, Daniel D.; Cox, David E.

2003-01-01

In this paper we describe the equations of motion developed for a point-mass zero-thrust (gliding) aircraft model operating in an environment of spatially varying atmospheric winds. The wind effects are included as an integral part of the flight dynamics equations, and the model is controlled through the three aerodynamic control angles. Formulas for the aerodynamic coefficients for this model are constructed to include the effects of several different aspects contributing to the aerodynamic performance of the vehicle. Characteristic parameter values of the model are compared with those found in a different set of small glider simulations. We execute a set of example problems which solve the glider dynamics equations to find the aircraft trajectory given specified control inputs. The ambient wind conditions and glider characteristics are varied to compare the simulation results under these different circumstances.

A Flight Dynamics Model for a Small Glider in Ambient Winds

NASA Technical Reports Server (NTRS)

Beeler, Scott C.; Moerder, Daniel D.; Cox, David E.

2003-01-01

In this paper we describe the equations of motion developed for a point-mass zero-thrust (gliding) aircraft model operating in an environment of spatially varying atmospheric winds. The wind effects are included as an integral part of the flight dynamics equations, and the model is controlled through the three aerodynamic control angles. Formulas for the aerodynamic coefficients for this model are constructed to include the effects of several different aspects contributing to the aerodynamic performance of the vehicle. Characteristic parameter values of the model are compared with those found in a different set of small glider simulations. We execute a set of example problems which solve the glider dynamics equations to find aircraft trajectory given specified control inputs. The ambient wind conditions and glider characteristics are varied to compare the simulation results under these different circumstances.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Identification of aerodynamic models for maneuvering aircraft

NASA Technical Reports Server (NTRS)

Chin, Suei; Lan, C. Edward

1990-01-01

Due to the requirement of increased performance and maneuverability, the flight envelope of a modern fighter is frequently extended to the high angle-of-attack regime. Vehicles maneuvering in this regime are subjected to nonlinear aerodynamic loads. The nonlinearities are due mainly to three-dimensional separated flow and concentrated vortex flow that occur at large angles of attack. Accurate prediction of these nonlinear airloads is of great importance in the analysis of a vehicle's flight motion and in the design of its flight control system. A satisfactory evaluation of the performance envelope of the aircraft may require a large number of coupled computations, one for each change in initial conditions. To avoid the disadvantage of solving the coupled flow-field equations and aircraft's motion equations, an alternate approach is to use a mathematical modeling to describe the steady and unsteady aerodynamics for the aircraft equations of motion. Aerodynamic forces and moments acting on a rapidly maneuvering aircraft are, in general, nonlinear functions of motion variables, their time rate of change, and the history of maneuvering. A numerical method was developed to analyze the nonlinear and time-dependent aerodynamic response to establish the generalized indicial function in terms of motion variables and their time rates of change.

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

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

Ciraolo, Giulio, E-mail: g.ciraolo@math.unipa.it; Gargano, Francesco, E-mail: gargano@math.unipa.it; Sciacca, Vincenzo, E-mail: sciacca@math.unipa.it

2013-08-01

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.

Contact angle hysteresis on superhydrophobic stripes.

PubMed

Dubov, Alexander L; Mourran, Ahmed; Möller, Martin; Vinogradova, Olga I

2014-08-21

We study experimentally and discuss quantitatively the contact angle hysteresis on striped superhydrophobic surfaces as a function of a solid fraction, ϕS. It is shown that the receding regime is determined by a longitudinal sliding motion of the deformed contact line. Despite an anisotropy of the texture the receding contact angle remains isotropic, i.e., is practically the same in the longitudinal and transverse directions. The cosine of the receding angle grows nonlinearly with ϕS. To interpret this we develop a theoretical model, which shows that the value of the receding angle depends both on weak defects at smooth solid areas and on the strong defects due to the elastic energy of the deformed contact line, which scales as ϕS(2)lnϕS. The advancing contact angle was found to be anisotropic, except in a dilute regime, and its value is shown to be determined by the rolling motion of the drop. The cosine of the longitudinal advancing angle depends linearly on ϕS, but a satisfactory fit to the data can only be provided if we generalize the Cassie equation to account for weak defects. The cosine of the transverse advancing angle is much smaller and is maximized at ϕS ≃ 0.5. An explanation of its value can be obtained if we invoke an additional energy due to strong defects in this direction, which is shown to be caused by the adhesion of the drop on solid sectors and is proportional to ϕS(2). Finally, the contact angle hysteresis is found to be quite large and generally anisotropic, but it becomes isotropic when ϕS ≤ 0.2.

A photometric function of planetary surfaces for gourmets

NASA Astrophysics Data System (ADS)

Shkuratov, Yuriy; Korokhin, Viktor; Shevchenko, Vasilij; Mikhalchenko, Olga; Belskaya, Irina; Kaydash, Vadym; Videen, Gorden; Zubko, Evgenij; Velikodsky, Yuriy

2018-03-01

A new photometric model with small number of parameters is presented. The model is based on an assumption that there exist such surfaces for which spatial brightness variations caused by small topography undulations can be reproduced exactly by corresponding spatial variations of albedo. This indistinguishability results in a differential equation suggesting a new photometric function that generalizes, in particular, the Akimov disk-function. Our model provides excellent fits in a wide phase-angle range for integral observations of asteroids of different albedos. We also carried out fitting to integral observations of the Moon and Mercury, confirming difficulties in describing Mercury's phase function at large phase angles, which were also found for the Hapke model. Comparisons of global latitude and longitude trends with our model calculations have shown good coincidence for the Moon. To retrieve the lunar trends, we use the phase-ratio technique, applying it to our telescope observations. Mapping the model parameters using LROC WAC data were carried out for a region comprising the Reiner Gamma formation. This mapping allows us to calculate phase-ratio images of the region, showing at large phase angles systematically steeper phase curves of young craters and smaller steepness for the very Reiner Gamma formation.

An Alternative Method to the Classical Partial Fraction Decomposition

ERIC Educational Resources Information Center

Cherif, Chokri

2007-01-01

PreCalculus students can use the Completing the Square Method to solve quadratic equations without the need to memorize the quadratic formula since this method naturally leads them to that formula. Calculus students, when studying integration, use various standard methods to compute integrals depending on the type of function to be integrated.…

Simulations of Jetted Relativistic Blastwaves in Astrophysics

NASA Astrophysics Data System (ADS)

Salmonson, Jay; Fragile, P. Chris; Anninos, Peter; Jauregui, Jeff

2006-10-01

We present relativistic hydrodynamic simulations of jetted blastwaves using the Cosmos++ astrophysics code. We post-process these simulations by integrating the radiative transfer equation thru a observer's space-time slices of the data, assuming relativistic self-absorbed synchrotron emission, to derive detailed multi-frequency lightcurves for the jet as viewed at arbitrary inclination angle. In particular, we simulate the asymmetric outflow resulting from the giant flare of December 27, 2004 from SGR 1806-20 and obtain excellent agreement with the data. We find that the asymmetric radio nebula that was observed to expand over the months following the flare cannot be explained by a simple ballistic ejection of material during the flare, but requires angular dependence of the energy injection with respect to the jet axis. In addition, we present simulations of jetted blastwaves of the relativistic afterglows resulting from gamma-ray bursts. This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

Faraday Rotation: Effect of Magnetic Field Reversals

NASA Astrophysics Data System (ADS)

Melrose, D. B.

2010-12-01

The standard formula for the rotation measure (RM), which determines the position angle, ψ = RMλ2, due to Faraday rotation, includes contributions only from the portions of the ray path where the natural modes of the plasma are circularly polarized. In small regions of the ray path where the projection of the magnetic field on the ray path reverses sign (called QT regions) the modes are nearly linearly polarized. The neglect of QT regions in estimating RM is not well justified at frequencies below a transition frequency where mode coupling changes from strong to weak. By integrating the polarization transfer equation across a QT region in the latter limit, I estimate the additional contribution Δψ needed to correct this omission. In contrast with a result proposed by Broderick & Blandford, Δψ is small and probably unobservable. I identify a new source of circular polarization, due to mode coupling in an asymmetric QT region. I also identify a new circular-polarization-dependent correction to the dispersion measure at low frequencies.

3D calculation of Tucson-Melbourne 3NF effect in triton binding energy

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

Hadizadeh, M. R.; Tomio, L.; Bayegan, S.

2010-08-04

As an application of the new realistic three-dimensional (3D) formalism reported recently for three-nucleon (3N) bound states, an attempt is made to study the effect of three-nucleon forces (3NFs) in triton binding energy in a non partial wave (PW) approach. The spin-isospin dependent 3N Faddeev integral equations with the inclusion of 3NFs, which are formulated as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them, are solved with Bonn-B and Tucson-Melbourne NN and 3N forces in operator forms which can be incorporated in our 3D formalism. The comparison with numerical results in both,more » novel 3D and standard PW schemes, shows that non PW calculations avoid the very involved angular momentum algebra occurring for the permutations and transformations and it is more efficient and less cumbersome for considering the 3NF.« less

Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit

NASA Technical Reports Server (NTRS)

Balsa, Thomas F.; Gartside, James

1995-01-01

The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.

Water based on a molecular model behaves like a hard-sphere solvent for a nonpolar solute when the reference interaction site model and related theories are employed

NASA Astrophysics Data System (ADS)

Hayashi, Tomohiko; Oshima, Hiraku; Harano, Yuichi; Kinoshita, Masahiro

2016-09-01

For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko-Hirata (K-H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K-H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein.

Gravity dependence of the effect of optokinetic stimulation on the subjective visual vertical.

PubMed

Ward, Bryan K; Bockisch, Christopher J; Caramia, Nicoletta; Bertolini, Giovanni; Tarnutzer, Alexander Andrea

2017-05-01

Accurate and precise estimates of direction of gravity are essential for spatial orientation. According to Bayesian theory, multisensory vestibular, visual, and proprioceptive input is centrally integrated in a weighted fashion based on the reliability of the component sensory signals. For otolithic input, a decreasing signal-to-noise ratio was demonstrated with increasing roll angle. We hypothesized that the weights of vestibular (otolithic) and extravestibular (visual/proprioceptive) sensors are roll-angle dependent and predicted an increased weight of extravestibular cues with increasing roll angle, potentially following the Bayesian hypothesis. To probe this concept, the subjective visual vertical (SVV) was assessed in different roll positions (≤ ± 120°, steps = 30°, n = 10) with/without presenting an optokinetic stimulus (velocity = ± 60°/s). The optokinetic stimulus biased the SVV toward the direction of stimulus rotation for roll angles ≥ ± 30° ( P < 0.005). Offsets grew from 3.9 ± 1.8° (upright) to 22.1 ± 11.8° (±120° roll tilt, P < 0.001). Trial-to-trial variability increased with roll angle, demonstrating a nonsignificant increase when providing optokinetic stimulation. Variability and optokinetic bias were correlated ( R 2 = 0.71, slope = 0.71, 95% confidence interval = 0.57-0.86). An optimal-observer model combining an optokinetic bias with vestibular input reproduced measured errors closely. These findings support the hypothesis of a weighted multisensory integration when estimating direction of gravity with optokinetic stimulation. Visual input was weighted more when vestibular input became less reliable, i.e., at larger roll-tilt angles. However, according to Bayesian theory, the variability of combined cues is always lower than the variability of each source cue. If the observed increase in variability, although nonsignificant, is true, either it must depend on an additional source of variability, added after SVV computation, or it would conflict with the Bayesian hypothesis. NEW & NOTEWORTHY Applying a rotating optokinetic stimulus while recording the subjective visual vertical in different whole body roll angles, we noted the optokinetic-induced bias to correlate with the roll angle. These findings allow the hypothesis that the established optimal weighting of single-sensory cues depending on their reliability to estimate direction of gravity could be extended to a bias caused by visual self-motion stimuli. Copyright © 2017 the American Physiological Society.

Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar-integral data

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

Zhang, B.; Zeng, G. L.

2006-09-15

A rotating slat collimator can be used to acquire planar-integral data. It achieves higher geometric efficiency than a parallel-hole collimator by accepting more photons, but the planar-integral data contain less tomographic information that may result in larger noise amplification in the reconstruction. Lodge evaluated the rotating slat system and the parallel-hole system based on noise behavior for an FBP reconstruction. Here, we evaluate the noise propagation properties of the two collimation systems for iterative reconstruction. We extend Huesman's noise propagation analysis of the line-integral system to the planar-integral case, and show that approximately 2.0(D/dp) SPECT angles, 2.5(D/dp) self-spinning angles atmore » each detector position, and a 0.5dp detector sampling interval are required in order for the planar-integral data to be efficiently utilized. Here, D is the diameter of the object and dp is the linear dimension of the voxels that subdivide the object. The noise propagation behaviors of the two systems are then compared based on a least-square reconstruction using the ratio of the SNR in the image reconstructed using a planar-integral system to that reconstructed using a line-integral system. The ratio is found to be proportional to {radical}(F/D), where F is a geometric efficiency factor. This result has been verified by computer simulations. It confirms that for an iterative reconstruction, the noise tradeoff of the two systems is not only dependent on the increase of the geometric efficiency afforded by the planar projection method, but also dependent on the size of the object. The planar-integral system works better for small objects, while the line-integral system performs better for large ones. This result is consistent with Lodge's results based on the FBP method.« less

Angle-resolved effective potentials for disk-shaped molecules

NASA Astrophysics Data System (ADS)

Heinemann, Thomas; Palczynski, Karol; Dzubiella, Joachim; Klapp, Sabine H. L.

2014-12-01

We present an approach for calculating coarse-grained angle-resolved effective pair potentials for uniaxial molecules. For integrating out the intramolecular degrees of freedom we apply umbrella sampling and steered dynamics techniques in atomistically-resolved molecular dynamics (MD) computer simulations. Throughout this study we focus on disk-like molecules such as coronene. To develop the methods we focus on integrating out the van der Waals and intramolecular interactions, while electrostatic charge contributions are neglected. The resulting coarse-grained pair potential reveals a strong temperature and angle dependence. In the next step we fit the numerical data with various Gay-Berne-like potentials to be used in more efficient simulations on larger scales. The quality of the resulting coarse-grained results is evaluated by comparing their pair and many-body structure as well as some thermodynamic quantities self-consistently to the outcome of atomistic MD simulations of many-particle systems. We find that angle-resolved potentials are essential not only to accurately describe crystal structures but also for fluid systems where simple isotropic potentials start to fail already for low to moderate packing fractions. Further, in describing these states it is crucial to take into account the pronounced temperature dependence arising in selected pair configurations due to bending fluctuations.

Tricritical points in a Vicsek model of self-propelled particles with bounded confidence

NASA Astrophysics Data System (ADS)

Romensky, Maksym; Lobaskin, Vladimir; Ihle, Thomas

2014-12-01

We study the orientational ordering in systems of self-propelled particles with selective interactions. To introduce the selectivity we augment the standard Vicsek model with a bounded-confidence collision rule: a given particle only aligns to neighbors who have directions quite similar to its own. Neighbors whose directions deviate more than a fixed restriction angle α are ignored. The collective dynamics of this system is studied by agent-based simulations and kinetic mean-field theory. We demonstrate that the reduction of the restriction angle leads to a critical noise amplitude decreasing monotonically with that angle, turning into a power law with exponent 3/2 for small angles. Moreover, for small system sizes we show that upon decreasing the restriction angle, the kind of the transition to polar collective motion changes from continuous to discontinuous. Thus, an apparent tricritical point with different scaling laws is identified and calculated analytically. We investigate the shifting and vanishing of this point due to the formation of density bands as the system size is increased. Agent-based simulations in small systems with large particle velocities show excellent agreement with the kinetic theory predictions. We also find that at very small interaction angles, the polar ordered phase becomes unstable with respect to the apolar phase. We derive analytical expressions for the dependence of the threshold noise on the restriction angle. We show that the mean-field kinetic theory also permits stationary nematic states below a restriction angle of 0.681 π . We calculate the critical noise, at which the disordered state bifurcates to a nematic state, and find that it is always smaller than the threshold noise for the transition from disorder to polar order. The disordered-nematic transition features two tricritical points: At low and high restriction angle, the transition is discontinuous but continuous at intermediate α . We generalize our results to systems that show fragmentation into more than two groups and obtain scaling laws for the transition lines and the corresponding tricritical points. A numerical method to evaluate the nonlinear Fredholm integral equation for the stationary distribution function is also presented. This method is shown to give excellent agreement with agent-based simulations, even in strongly ordered systems at noise values close to zero.

PIV-based estimation of unsteady loads on a flat plate at high angle of attack using momentum equation approaches

NASA Astrophysics Data System (ADS)

Guissart, A.; Bernal, L. P.; Dimitriadis, G.; Terrapon, V. E.

2017-05-01

This work presents, compares and discusses results obtained with two indirect methods for the calculation of aerodynamic forces and pitching moment from 2D Particle Image Velocimetry (PIV) measurements. Both methodologies are based on the formulations of the momentum balance: the integral Navier-Stokes equations and the "flux equation" proposed by Noca et al. (J Fluids Struct 13(5):551-578, 1999), which has been extended to the computation of moments. The indirect methods are applied to spatio-temporal data for different separated flows around a plate with a 16:1 chord-to-thickness ratio. Experimental data are obtained in a water channel for both a plate undergoing a large amplitude imposed pitching motion and a static plate at high angle of attack. In addition to PIV data, direct measurements of aerodynamic loads are carried out to assess the quality of the indirect calculations. It is found that indirect methods are able to compute the mean and the temporal evolution of the loads for two-dimensional flows with a reasonable accuracy. Nonetheless, both methodologies are noise sensitive, and the parameters impacting the computation should thus be chosen carefully. It is also shown that results can be improved through the use of dynamic mode decomposition (DMD) as a pre-processing step.

A transonic interactive boundary-layer theory for laminar and turbulent flow over swept wings

NASA Technical Reports Server (NTRS)

Woodson, Shawn H.; Dejarnette, Fred R.

1988-01-01

A 3-D laminar and turbulent boundary-layer method is developed for compressible flow over swept wings. The governing equations and curvature terms are derived in detail for a nonorthogonal, curvilinear coordinate system. Reynolds shear-stress terms are modeled by the Cebeci-Smith eddy-viscosity formulation. The governing equations are descretized using the second-order accurate, predictor-corrector finite-difference technique of Matsuno, which has the advantage that the crossflow difference formulas are formed independent of the sign of the crossflow velocity component. The method is coupled with a full potential wing/body inviscid code (FLO-30) and the inviscid-viscous interaction is performed by updating the original wing surface with the viscous displacement surface calculated by the boundary-layer code. The number of these global iterations ranged from five to twelve depending on Mach number, sweep angle, and angle of attack. Several test cases are computed by this method and the results are compared with another inviscid-viscous interaction method (TAWFIVE) and with experimental data.

The correlation between calcaneal valgus angle and asymmetrical thoracic-lumbar rotation angles in patients with adolescent scoliosis.

PubMed

Park, Jaeyong; Lee, Sang Gil; Bae, Jongjin; Lee, Jung Chul

2015-12-01

[Purpose] This study aimed to provide a predictable evaluation method for the progression of scoliosis in adolescents based on quick and reliable measurements using the naked eye, such as the calcaneal valgus angle of the foot, which can be performed at public facilities such as schools. [Subjects and Methods] Idiopathic scoliosis patients with a Cobb's angle of 10° or more (96 females, 22 males) were included in this study. To identify relationships between factors, Pearson's product-moment correlation coefficient was computed. The degree of scoliosis was set as a dependent variable to predict thoracic and lumbar scoliosis using ankle angle and physique factors. Height, weight, and left and right calcaneal valgus angles were set as independent variables; thereafter, multiple regression analysis was performed. This study extracted variables at a significance level (α) of 0.05 by applying a stepwise method, and calculated a regression equation. [Results] Negative correlation (R=-0.266) was shown between lumbar lordosis and asymmetrical lumbar rotation angles. A correlation (R=0.281) was also demonstrated between left calcaneal valgus angles and asymmetrical thoracic rotation angles. [Conclusion] Prediction of scoliosis progress was revealed to be possible through ocular inspection of the calcaneus and Adams forward bending test and the use of a scoliometer.

Dependence of reflection and transmission of soliton on angle of incidence at an interface between chalcogenide fibre and gallium nanoparticle film by phase plane trajectories

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

Naruka, Preeti, E-mail: preety-naruka@Yyahoo.co.in; Bissa, Shivangi; Nagar, A. K.

In the present paper, we study propagation of a soliton at an interface formed between special type of chalcogenide fibre and gallium in three different phases with the help of equivalent particle theory. Critical angle of incidence and critical power required for transmission and reflection of soliton beam have investigated. Here it is found that if the incident angle of the beam or initial velocity of the equivalent particle is insufficient to overcome the maximum increase in potential energy then the particle (light beam) is reflected by the interface and if this incident angle is greater than a critical anglemore » then light beam will be transmitted by the interface. From an equation these critical angles for α-gallium, one of a metastable phase and liquid gallium are calculated and concluded that at large incident angles, the soliton is transmitted through the boundary, whereas at small incidence angles the soliton get reflected on keeping the power of incident beam constant. These results are explained by phase plane trajectories of the effective potential which are experimentally as well as theoretically proved.« less

Numerical calculations of velocity and pressure distribution around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.; Kobiske, M.

1974-01-01

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

An exact solution for the solidification of a liquid slab of binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.; Collins, F. G.; Aumalia, A. E.

1986-01-01

The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations.

Fundamental Review ’Chemometrics’.

DTIC Science & Technology

1982-02-01

using the inverted Abel integral equation to evaluate spectroscopic sources. They found that the selection of one of three methods tested depends...nonlinear simultaneous equations are then solved for the concentration of each component in a mixture. When more spectrometric data can be obtained (e.g...Liu (R12) uses six simultaneous equations to resolve overlapping 1-.ic-S-;-inping voltammograms. The use of the Kalman filter (R3) is very effective

Enhancing the stabilization of aircraft pitch motion control via intelligent and classical method

NASA Astrophysics Data System (ADS)

Lukman, H.; Munawwarah, S.; Azizan, A.; Yakub, F.; Zaki, S. A.; Rasid, Z. A.

2017-12-01

The pitching movement of an aircraft is very important to ensure passengers are intrinsically safe and the aircraft achieve its maximum stability. The equations governing the motion of an aircraft are a complex set of six nonlinear coupled differential equations. Under certain assumptions, it can be decoupled and linearized into longitudinal and lateral equations. Pitch control is a longitudinal problem and thus, only the longitudinal dynamics equations are involved in this system. It is a third order nonlinear system, which is linearized about the operating point. The system is also inherently unstable due to the presence of a free integrator. Because of this, a feedback controller is added in order to solve this problem and enhance the system performance. This study uses two approaches in designing controller: a conventional controller and an intelligent controller. The pitch control scheme consists of proportional, integral and derivatives (PID) for conventional controller and fuzzy logic control (FLC) for intelligent controller. Throughout the paper, the performance of the presented controllers are investigated and compared based on the common criteria of step response. Simulation results have been obtained and analysed by using Matlab and Simulink software. The study shows that FLC controller has higher ability to control and stabilize the aircraft's pitch angle as compared to PID controller.

Methodology for calculating power consumption of planetary mixers

NASA Astrophysics Data System (ADS)

Antsiferov, S. I.; Voronov, V. P.; Evtushenko, E. I.; Yakovlev, E. A.

2018-03-01

The paper presents the methodology and equations for calculating the power consumption necessary to overcome the resistance of a dry mixture caused by the movement of cylindrical rods in the body of a planetary mixer, as well as the calculation of the power consumed by idling mixers of this type. The equations take into account the size and physico-mechanical properties of mixing material, the size and shape of the mixer's working elements and the kinematics of its movement. The dependence of the power consumption on the angle of rotation in the plane perpendicular to the axis of rotation of the working member is presented.

Numerical Simulation of the Flow over a Segment-Conical Body on the Basis of Reynolds Equations

NASA Astrophysics Data System (ADS)

Egorov, I. V.; Novikov, A. V.; Palchekovskaya, N. V.

2018-01-01

Numerical simulation was used to study the 3D supersonic flow over a segment-conical body similar in shape to the ExoMars space vehicle. The nonmonotone behavior of the normal force acting on the body placed in a supersonic gas flow was analyzed depending on the angle of attack. The simulation was based on the numerical solution of the unsteady Reynolds-averaged Navier-Stokes equations with a two-parameter differential turbulence model. The solution of the problem was obtained using the in-house solver HSFlow with an efficient parallel algorithm intended for multiprocessor super computers.

An Improved Theoretical Aerodynamic Derivatives Computer Program for Sounding Rockets

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Optical inverse-square displacement sensor

DOEpatents

Howe, R.D.; Kychakoff, G.

1989-09-12

This invention comprises an optical displacement sensor that uses the inverse-square attenuation of light reflected from a diffused surface to calculate the distance from the sensor to the reflecting surface. Light emerging from an optical fiber or the like is directed onto the surface whose distance is to be measured. The intensity I of reflected light is angle dependent, but within a sufficiently small solid angle it falls off as the inverse square of the distance from the surface. At least a pair of optical detectors are mounted to detect the reflected light within the small solid angle, their ends being at different distances R and R + [Delta]R from the surface. The distance R can then be found in terms of the ratio of the intensity measurements and the separation length as given in an equation. 10 figs.

Pitch Angle Scattering of Upgoing Electron Beams in Jupiter's Polar Regions by Whistler Mode Waves

NASA Astrophysics Data System (ADS)

Elliott, S. S.; Gurnett, D. A.; Kurth, W. S.; Clark, G.; Mauk, B. H.; Bolton, S. J.; Connerney, J. E. P.; Levin, S. M.

2018-02-01

The Juno spacecraft's Jupiter Energetic-particle Detector Instrument has observed field-aligned, unidirectional (upgoing) electron beams throughout most of Jupiter's entire polar cap region. The Waves instrument detected intense broadband whistler mode emissions occurring in the same region. In this paper, we investigate the pitch angle scattering of the upgoing electron beams due to interactions with the whistler mode waves. Profiles of intensity versus pitch angle for electron beams ranging from 2.53 to 7.22 Jovian radii show inconsistencies with the expected adiabatic invariant motion of the electrons. It is believed that the observed whistler mode waves perturb the electron motion and scatter them away from the magnetic field line. The diffusion equation has been solved by using diffusion coefficients which depend on the magnetic intensity of the whistler mode waves.

An implicit fast Fourier transform method for integration of the time dependent Schrodinger equation

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

Riley, M.E.; Ritchie, A.B.

1997-12-31

One finds that the conventional exponentiated split operator procedure is subject to difficulties when solving the time-dependent Schrodinger equation for Coulombic systems. By rearranging the kinetic and potential energy terms in the temporal propagator of the finite difference equations, one can find a propagation algorithm for three dimensions that looks much like the Crank-Nicholson and alternating direction implicit methods for one- and two-space-dimensional partial differential equations. The authors report investigations of this novel implicit split operator procedure. The results look promising for a purely numerical approach to certain electron quantum mechanical problems. A charge exchange calculation is presented as anmore » example of the power of the method.« less

Optical properties and refractive indices of Gd3Al2Ga3O12:Ce3+ crystals

NASA Astrophysics Data System (ADS)

Kozlova, N. S.; Busanov, O. A.; Zabelina, E. V.; Kozlova, A. P.; Kasimova, V. M.

2016-05-01

Crystals of cerium-doped gadolinium-gallium-aluminum garnet have been grown by the Czochralski method. The transmission and reflection spectra of these crystals in the wavelength range of 250-800 nm have been obtained by optical spectroscopy. Refractive indices are calculated based on the measured Brewster angles, the experimental results are approximated using the Cauchy equation, and a dispersion dependence is obtained.

Extremely correlated Fermi liquid theory of the t-J model in 2 dimensions: low energy properties

NASA Astrophysics Data System (ADS)

Shastry, B. Sriram; Mai, Peizhi

2018-01-01

Low energy properties of the metallic state of the two-dimensional t-J model are presented for second neighbor hopping with hole-doping (t\\prime ≤slant 0) and electron-doping (t\\prime > 0), with various superexchange energy J. We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory. These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density n≳ 0.8, implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T, followed by an interesting kink at higher T. The Hall number exhibits strong renormalization due to correlations. Flipping the sign of t\\prime changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.

Experiment of constraining symmetry energy at supra-saturation density with π-/π+ at HIRFL-CSR

NASA Astrophysics Data System (ADS)

Zhang, Ming; Xiao, Zhi-Gang; Zhu, Sheng-Jiang

2010-08-01

The possibility of the experiment for constraining the symmetry energy Esym(ρ) at supra-densities via π-/π+ probe on the external target experiment of phase I (ETE(I)) with part coverage at forward angle at HIRFL-CSR is studied for the first time by using the isospin and momentum dependent hadronic transport model IBUU04. Based on the transport simulation with Au+Au collisions at 400 MeV/u, it is found that the differential π-/π+ ratios are more sensitive to Esym(ρ) at forward angles in laboratory reference, compared with the total yield ratio widely proposed. The insufficient coverage at lower transverse momentum maintains the sensitivity of the dependence of π-/π+ ratio on the Esym(ρ) at high density, indicating that the ETF (I) under construction in Lanzhou provides the possibility of performing the experiment for probing the asymmetric nuclear equation of state.

Master equations and the theory of stochastic path integrals

NASA Astrophysics Data System (ADS)

Weber, Markus F.; Frey, Erwin

2017-04-01

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

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

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

Distribution theory for Schrödinger’s integral equation

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

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

2015-12-15

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

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

NASA Technical Reports Server (NTRS)

Morrison, Joseph H.

1992-01-01

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Effect of dynamic disorder on charge transport along a pentacene chain

NASA Astrophysics Data System (ADS)

Böhlin, J.; Linares, M.; Stafström, S.

2011-02-01

The lattice equation of motion and a numerical solution of the time-dependent Schrödinger equation provide us with a microscopic picture of charge transport in highly ordered molecular crystals. We have chosen the pentacene single crystal as a model system, and we study charge transport as a function of phonon-mode time-dependent fluctuations in the intermolecular electron transfer integral. For comparison, we include similar fluctuations also in the intramolecular potentials. The variance in these energy quantities is closely related to the temperature of the system. The pentacene system is shown to be very sensitive to fluctuation in the intermolecular transfer integral, revealing a transition from adiabatic to nonadiabatic polaron transport for increasing temperatures. The extension of the polaron at temperatures above 200 K is limited by the electron localization length rather than the interplay between the electron transfer integral and the electron-phonon coupling strength.

The Aerodynamics of Axisymmetric Blunt Bodies Flying at Angle of Attack

NASA Technical Reports Server (NTRS)

Schoenenberger, Mark; Kutty, Prasad; Queen, Eric; Karlgaard, Chris

2014-01-01

The Mars Science Laboratory entry capsule is used as an example to demonstrate how a blunt body of revolution must be treated as asymmetric in some respects when flying at a non-zero trim angle of attack. A brief description of the axisymmetric moment equations are provided before solving a system of equations describing the lateral-directional moment equations for a blunt body trimming at an angle of attack. Simplifying assumptions are made which allow the solution to the equations to be rearranged to relate the roll and yaw stability with sideslip angle to the frequency of oscillation of the vehicle body rates. The equations show that for a blunt body the roll and yaw rates are in phase and proportional to each other. The ratio of the rates is determined by the static stability coefficients and mass properties about those axes. A trajectory simulation is used to validate the static yaw stability parameter identification equation and a simple method of identifying the oscillation frequency from the body rates. The approach is shown to successfully extract the modeled yaw stability coefficient along a simulated Mars entry in agreement with data earlier analysis of MSL flight data.

Investigation of Laser Parameters in Silicon Pulsed Laser Conduction Welding

NASA Astrophysics Data System (ADS)

Shayganmanesh, Mahdi; Khoshnoud, Afsaneh

2016-03-01

In this paper, laser welding of silicon in conduction mode is investigated numerically. In this study, the effects of laser beam characteristics on the welding have been studied. In order to model the welding process, heat conduction equation is solved numerically and laser beam energy is considered as a boundary condition. Time depended heat conduction equation is used in our calculations to model pulsed laser welding. Thermo-physical and optical properties of the material are considered to be temperature dependent in our calculations. Effects of spatial and temporal laser beam parameters such as laser beam spot size, laser beam quality, laser beam polarization, laser incident angle, laser pulse energy, laser pulse width, pulse repetition frequency and welding speed on the welding characteristics are assessed. The results show that how the temperature dependent thermo-physical and optical parameters of the material are important in laser welding modeling. Also the results show how the parameters of the laser beam influence the welding characteristics.

A new operational approach for solving fractional variational problems depending on indefinite integrals

NASA Astrophysics Data System (ADS)

Ezz-Eldien, S. S.; Doha, E. H.; Bhrawy, A. H.; El-Kalaawy, A. A.; Machado, J. A. T.

2018-04-01

In this paper, we propose a new accurate and robust numerical technique to approximate the solutions of fractional variational problems (FVPs) depending on indefinite integrals with a type of fixed Riemann-Liouville fractional integral. The proposed technique is based on the shifted Chebyshev polynomials as basis functions for the fractional integral operational matrix (FIOM). Together with the Lagrange multiplier method, these problems are then reduced to a system of algebraic equations, which greatly simplifies the solution process. Numerical examples are carried out to confirm the accuracy, efficiency and applicability of the proposed algorithm

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

PubMed

Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C

2017-08-01

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

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

NASA Technical Reports Server (NTRS)

Farassat, F.

1983-01-01

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

Electrostatic Interactions Between Glycosaminoglycan Molecules

NASA Astrophysics Data System (ADS)

Song, Fan; Moyne, Christian; Bai, Yi-Long

2005-02-01

The electrostatic interactions between nearest-neighbouring chondroitin sulfate glycosaminoglycan (CS-GAG) molecular chains are obtained on the bottle brush conformation of proteoglycan aggrecan based on an asymptotic solution of the Poisson-Boltzmann equation the CS-GAGs satisfy under the physiological conditions of articular cartilage. The present results show that the interactions are associated intimately with the minimum separation distance and mutual angle between the molecular chains themselves. Further analysis indicates that the electrostatic interactions are not only expressed to be purely exponential in separation distance and decrease with the increasing mutual angle but also dependent sensitively on the saline concentration in the electrolyte solution within the tissue, which is in agreement with the existed relevant conclusions.

Controllable magnetic thermal rectification in a SMM dimmer with the Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

Xu, Ai-Hua; Liu, Juan; Luo, Bo

2016-10-01

Using the quantum master equation, we studied the thermally driven magnonic spin current in a single-molecule magnet (SMM) dimer with the Dzyaloshinskii-Moriya interaction (DMI). Due to the asymmetric DMI, one can observe the thermal rectifying effect in the case of the spatial symmetry coupling with the thermal reservoirs. The properties of the thermal rectification can be controlled by tuning the angle and intensity of the magnetic field. Specially, when the DM vector and magnetic field point at the specific angles, the thermal rectifying effect disappears. And this phenomenon does not depend on the intensities of DMI and magnetic field, the temperature bias and the magnetic anisotropies of the SMM.

An Approximate Solution to the Equation of Motion for Large-Angle Oscillations of the Simple Pendulum with Initial Velocity

ERIC Educational Resources Information Center

Johannessen, Kim

2010-01-01

An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…

Tunable valley polarization by a gate voltage when an electron tunnels through multiple line defects in graphene.

PubMed

Liu, Zhe; Jiang, Liwei; Zheng, Yisong

2015-02-04

By means of an appropriate wave function connection condition, we study the electronic structure of a line defect superlattice of graphene with the Dirac equation method. We obtain the analytical dispersion relation, which can simulate well the tight-binding numerical result about the band structure of the superlattice. Then, we generalize this theoretical method to study the electronic transmission through a potential barrier where multiple line defects are periodically patterned. We find that there exists a critical incident angle which restricts the electronic transmission through multiple line defects within a specific incident angle range. The critical angle depends sensitively on the potential barrier height, which can be modulated by a gate voltage. As a result, non-trivial transmissions of K and K' valley electrons are restricted, respectively, in two distinct ranges of the incident angle. Our theoretical result demonstrates that a gate voltage can act as a feasible measure to tune the valley polarization when electrons tunnel through multiple line defects.

Dependency of the apparent contact angle on nonisothermal conditions

NASA Astrophysics Data System (ADS)

Krahl, Rolf; Gerstmann, Jens; Behruzi, Philipp; Bänsch, Eberhard; Dreyer, Michael E.

2008-04-01

The dynamic behavior of liquids in partly filled containers is influenced to a large extend by the angle between the gas-liquid phase boundary and the solid container wall at the contact line. This contact angle in turn is influenced by nonisothermal conditions. In the case of a cold liquid meniscus spreading over a hot solid wall, the contact angle apparently becomes significantly larger. In this paper we want to establish a quantitative equation for this enlargement, both from experimental and numerical data. Our findings can be used to build a subgrid model for computations, where the resolution is not sufficient to resolve the boundary layers. This might be the case for large containers which are exposed to low accelerations and where the contact angle boundary condition determines the position of the free surface. These types of computation are performed, for example, to solve propellant management problems in launcher and satellite tanks. In this application, the knowledge of the position of the free surface is very important for the withdrawal of liquid and the calculation of heat and mass transfer.

Reduced Fokker-Planck models for fast particle distribution across a transition layer of disparate plasma temperatures

NASA Astrophysics Data System (ADS)

Tang, Xian-Zhu; Berk, H. L.; Guo, Zehua; McDevitt, C. J.

2014-03-01

Across a transition layer of disparate plasma temperatures, the high energy tail of the plasma distribution can have appreciable deviations from the local Maxwellian distribution due to the Knudson layer effect. The Fokker-Planck equation for the tail particle population can be simplified in a series of practically useful limiting cases. The first is the approximation of background Maxwellian distribution for linearizing the collision operator. The second is the supra-thermal particle speed ordering of vTi ≪ v ≪ vTe for the tail ions and vTi ≪ vTe ≪ v for the tail electrons. Keeping both the collisional drag and energy scattering is essential for the collision operator to produce a Maxwellian tail distribution. The Fokker-Planck model for following the tail ion distribution for a given background plasma profile is explicitly worked out for systems of one spatial dimension, in both slab and spherical geometry. A third simplification is an expansion of the tail particle distribution using the spherical harmonics, which are eigenfunctions of the pitch angle scattering operator. This produces a set of coupled Fokker-Planck equations that contain energy-dependent spatial diffusion terms in two coordinates (position and energy), which originate from pitch angle scattering in the original Fokker-Planck equation. It is shown that the well-known diffusive Fokker-Planck model is a poor approximation of the two-mode truncation model, which itself has fundamental deficiency compared with the three-mode truncation model. The cause is the lack of even-symmetry representation in pitch dependence in the two-mode truncation model.

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.

Frequency Dependence of Low-Voltage Electrowetting Investigated by Impedance Spectroscopy.

PubMed

Li, Ying-Jia; Cahill, Brian P

2017-11-14

An electrowetting-on-dielectric (EWOD) electrode was developed that facilitates the use of low alternating voltages (≤5 V AC ). This allows online investigation of the frequency dependence of electrowetting by means of impedance spectroscopy. The EWOD electrode is based on a dielectric bilayer consisting of an anodic tantalum pentoxide (Ta 2 O 5 ) thin film (d = 59.35 nm) with a high relative permittivity (ε d = 26.3) and a self-assembled hydrophobic silane monolayer. The frequency dependence of electrowetting was studied using an aqueous μL-sized sessile droplet on the planar EWOD electrode in oil. Experiments using electrochemical impedance spectroscopy and optical imaging indicate the frequency dependence of all three variables in the Young-Lippmann equation: the voltage drop across the dielectric layers, capacitance per unit area, and contact angle under voltage. The electrowetting behavior induced by AC voltages is shown to be well described by the Young-Lippmann equation for AC applications below a frequency threshold. Moreover, the dielectric layers act as a capacitor and the stored electrostatic potential energy is revealed to only partially contribute to the electrowetting.

Correlation of nonorthogonality of best hybrid bond orbitals with bond strength of orthogonal orbitals

PubMed Central

Pauling, Linus

1976-01-01

An expression is derived for the bond length of two spd orbitals with maximum values in two directions forming a given bond angle by consideration of the nonorthogonality integral of two best orbitals in these directions. This equation is equivalent to the expression derived by formulating the pair of orthogonal orbitals. Similar expressions are derived for spdf orbitals. Applications are made to icosahedral and cuboctahedral bonds and to the packing of nucleons in atomic nuclei. PMID:16578736

Correlation of nonorthogonality of best hybrid bond orbitals with bond strength of orthogonal orbitals.

PubMed

Pauling, L

1976-02-01

An expression is derived for the bond length of two spd orbitals with maximum values in two directions forming a given bond angle by consideration of the nonorthogonality integral of two best orbitals in these directions. This equation is equivalent to the expression derived by formulating the pair of orthogonal orbitals. Similar expressions are derived for spdf orbitals. Applications are made to icosahedral and cuboctahedral bonds and to the packing of nucleons in atomic nuclei.

Application of chaos theory to the particle dynamics of asymmetry-induced transport

NASA Astrophysics Data System (ADS)

Eggleston, D. L.

2018-03-01

The techniques of chaos theory are employed in an effort to better understand the complex single-particle dynamics of asymmetry-induced transport in non-neutral plasmas. The dynamical equations are re-conceptualized as describing time-independent trajectories in a four-dimensional space consisting of the radius r, rotating frame angle ψ, axial position z, and axial velocity v. Results include the identification of an integral of the motion, fixed-point analysis of the dynamical equations, the construction and interpretation of Poincaré sections to visualize the dynamics, and, for the case of chaotic motion, numerical calculation of the largest Lyapunov exponent. Chaotic cases are shown to be associated with the overlap of resonance islands formed by the applied asymmetry.

Simulation on Natural Convection of a Nanofluid along an Isothermal Inclined Plate

NASA Astrophysics Data System (ADS)

Mitra, Asish

2017-08-01

A numerical algorithm is presented for studying laminar natural convection flow of a nanofluid along an isothermal inclined plate. By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a set of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Dimensionless velocity, temperature profiles and nanoparticle concentration for various angles of inclination are illustrated graphically. The effects of Prandtl number, Brownian motion parameter and thermophoresis parameter on Nusselt number are also discussed. The results of the present simulation are then compared with previous one available in literature with good agreement.

New fundamental parameters for attitude representation

NASA Astrophysics Data System (ADS)

Patera, Russell P.

2017-08-01

A new attitude parameter set is developed to clarify the geometry of combining finite rotations in a rotational sequence and in combining infinitesimal angular increments generated by angular rate. The resulting parameter set of six Pivot Parameters represents a rotation as a great circle arc on a unit sphere that can be located at any clocking location in the rotation plane. Two rotations are combined by linking their arcs at either of the two intersection points of the respective rotation planes. In a similar fashion, linking rotational increments produced by angular rate is used to derive the associated kinematical equations, which are linear and have no singularities. Included in this paper is the derivation of twelve Pivot Parameter elements that represent all twelve Euler Angle sequences, which enables efficient conversions between Pivot Parameters and any Euler Angle sequence. Applications of this new parameter set include the derivation of quaternions and the quaternion composition rule, as well as, the derivation of the analytical solution to time dependent coning motion. The relationships between Pivot Parameters and traditional parameter sets are included in this work. Pivot Parameters are well suited for a variety of aerospace applications due to their effective composition rule, singularity free kinematic equations, efficient conversion to and from Euler Angle sequences and clarity of their geometrical foundation.

Equations on knot polynomials and 3d/5d duality

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

Mironov, A.; Morozov, A.; ITEP, Moscow

2012-09-24

We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. Themore » shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.« less

Non-invertible transformations of differential-difference equations

NASA Astrophysics Data System (ADS)

Garifullin, R. N.; Yamilov, R. I.; Levi, D.

2016-09-01

We discuss aspects of the theory of non-invertible transformations of differential-difference equations and, in particular, the notion of Miura type transformation. We introduce the concept of non-Miura type linearizable transformation and we present techniques that allow one to construct simple linearizable transformations and might help one to solve classification problems. This theory is illustrated by the example of a new integrable differential-difference equation depending on five lattice points, interesting from the viewpoint of the non-invertible transformation, which relate it to an Itoh-Narita-Bogoyavlensky equation.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

NASA Astrophysics Data System (ADS)

Colmenares, Pedro J.

2018-05-01

This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

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

Heinemann, Thomas, E-mail: thomas.heinemann@tu-berlin.de; Klapp, Sabine H. L., E-mail: klapp@physik.tu-berlin.de; Palczynski, Karol, E-mail: karol.palczynski@helmholtz-berlin.de

We present an approach for calculating coarse-grained angle-resolved effective pair potentials for uniaxial molecules. For integrating out the intramolecular degrees of freedom we apply umbrella sampling and steered dynamics techniques in atomistically-resolved molecular dynamics (MD) computer simulations. Throughout this study we focus on disk-like molecules such as coronene. To develop the methods we focus on integrating out the van der Waals and intramolecular interactions, while electrostatic charge contributions are neglected. The resulting coarse-grained pair potential reveals a strong temperature and angle dependence. In the next step we fit the numerical data with various Gay-Berne-like potentials to be used in moremore » efficient simulations on larger scales. The quality of the resulting coarse-grained results is evaluated by comparing their pair and many-body structure as well as some thermodynamic quantities self-consistently to the outcome of atomistic MD simulations of many-particle systems. We find that angle-resolved potentials are essential not only to accurately describe crystal structures but also for fluid systems where simple isotropic potentials start to fail already for low to moderate packing fractions. Further, in describing these states it is crucial to take into account the pronounced temperature dependence arising in selected pair configurations due to bending fluctuations.« less

Robust Integration Schemes for Generalized Viscoplasticity with Internal-State Variables

NASA Technical Reports Server (NTRS)

Saleeb, Atef F.; Li, W.; Wilt, Thomas E.

1997-01-01

The scope of the work in this presentation focuses on the development of algorithms for the integration of rate dependent constitutive equations. In view of their robustness; i.e., their superior stability and convergence properties for isotropic and anisotropic coupled viscoplastic-damage models, implicit integration schemes have been selected. This is the simplest in its class and is one of the most widely used implicit integrators at present.

Next Generation 3D Mixed Mode Fracture Propagation Theory Including HCF-LCF Interaction (Preprint)

DTIC Science & Technology

2010-01-01

vectors. Depending on processing symmetries, the six principal fracture resistance values may not all be unique. If they are all equal, and l m=1...detail, see [26]. Table 1. Inco 718 Crack Kink angle Data Measured Kink Angles Spec No RI RII RIII KI+ KII+ KIII+ Mean Beq Primary Secondary In Phase 1...R. Ingraffea, “Interactive Finite-Element Analyses of Fracture Processes : An Integrated Approach”, Theoretical and Applied Fracture Mechanics, Vol

Recent Developments and Open Problems in the Mathematical Theory of Viscoelasticity.

DTIC Science & Technology

1984-11-01

integral terms . At each step of the iteration, we have to solve a linear parabolic equation with time-dependent coefficients. In Sobolevskii’s... parabolic Volterra integro- differential equation, SIAN J. Math. Anal. 13 (1982), ’ ~81-105. :-- 12. Heard, M. L., A class of hyperbolic Volterra ...then puts an n + 1 on the highest derivatives (the "principal terms " in the equation) and an n on lower order derivatives. Two things must then be

A validated computational model for the design of surface textures in full-film lubricated sliding

NASA Astrophysics Data System (ADS)

Schuh, Jonathon; Lee, Yong Hoon; Allison, James; Ewoldt, Randy

2016-11-01

Our recent experimental work showed that asymmetry is needed for surface textures to decrease friction in full-film lubricated sliding (thrust bearings) with Newtonian fluids; textures reduce the shear load and produce a separating normal force. The sign of the separating normal force is not predicted by previous 1-D theories. Here we model the flow with the Reynolds equation in cylindrical coordinates, numerically implemented with a pseudo-spectral method. The model predictions match experiments, rationalize the sign of the normal force, and allow for design of surface texture geometry. To minimize sliding friction with angled cylindrical textures, an optimal angle of asymmetry β exists. The optimal angle depends on the film thickness but not the sliding velocity within the applicable range of the model. The model has also been used to optimize generalized surface texture topography while satisfying manufacturability constraints.

Conical Euler simulation and active suppression of delta wing rocking motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon.

The line integral approach to radarclinometry

USGS Publications Warehouse

Wildey, R.L.

1987-01-01

Radarclinometry, the invention of which has been previously reported, is a technique for deriving a topographic map from a single radar image by using the dependence upon terrain-surface orientation of the integrated signal of an individual image pixel. The radiometric calibration required for precise operation and testing does not yet exist, but the imminence of important applications justifies parallel, rather than serial, development of radarclinometry and radiometrically calibrated radar. The present investigation reports three developmental advances: (1) The solid angle of integration of back-scattered specific intensity constituting a pixel signal is more accurately accounted for in its dependence on surface orientation than in previous work. (2) The local curvature hypothesis, which removes the requirement of a ground-truth profile as a boundary condition and enables the formulation of the theory in terms of a line integral, has been expanded to include the three possibilities of Local Cylindricity, Local Biaxial Ellipsoidal Hyperbolicity, and Least-Squares Local Sphericity. (3) The theory is integrated in the cross-ground-range direction, which is ill-conditioned compared to the ground-range direction, whereas the original formulation was based on enforced isotropy in the two-dimensional power spectrum of the topography. It was found necessary to prohibit the hypothesis of Local Biaxial Ellipsoidal Hyperbolicity in the cross-range stepping, for reasons not completely clear. Variation in the proportioning between curvature assumptions had produced topographic maps that are in good mutual agreement but not realistic in appearance. They are severely banded parallel to the ground-range direction, most especially at small radar zenith angles. Numerical experimentation with the falsification of topography through incorrect decalibration as performed on a Gaussian hill suggests that the banding and its exaggeration at high radar incidence angles could easily be due to our lack of radiometric calibration. ?? 1987 D. Reidel Publishing Company.

Comparison between collective coordinate models for domain wall motion in PMA nanostrips in the presence of the Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

Vandermeulen, J.; Nasseri, S. A.; Van de Wiele, B.; Durin, G.; Van Waeyenberge, B.; Dupré, L.

2018-03-01

Lagrangian-based collective coordinate models for magnetic domain wall (DW) motion rely on an ansatz for the DW profile and a Lagrangian approach to describe the DW motion in terms of a set of time-dependent collective coordinates: the DW position, the DW magnetization angle, the DW width and the DW tilting angle. Another approach was recently used to derive similar equations of motion by averaging the Landau-Lifshitz-Gilbert equation without any ansatz, and identifying the relevant collective coordinates afterwards. In this paper, we use an updated version of the semi-analytical equations to compare the Lagrangian-based collective coordinate models with micromagnetic simulations for field- and STT-driven (spin-transfer torque-driven) DW motion in Pt/CoFe/MgO and Pt/Co/AlOx nanostrips. Through this comparison, we assess the accuracy of the different models, and provide insight into the deviations of the models from simulations. It is found that the lack of terms related to DW asymmetry in the Lagrangian-based collective coordinate models significantly contributes to the discrepancy between the predictions of the most accurate Lagrangian-based model and the micromagnetic simulations in the field-driven case. This is in contrast to the STT-driven case where the DW remains symmetric.

Integrability and solitons for the higher-order nonlinear Schrödinger equation with space-dependent coefficients in an optical fiber

NASA Astrophysics Data System (ADS)

Su, Jing-Jing; Gao, Yi-Tian

2018-03-01

Under investigation in this paper is a higher-order nonlinear Schrödinger equation with space-dependent coefficients, related to an optical fiber. Based on the self-similarity transformation and Hirota method, related to the integrability, the N-th-order bright and dark soliton solutions are derived under certain constraints. It is revealed that the velocities and trajectories of the solitons are both affected by the coefficient of the sixth-order dispersion term while the amplitudes of the solitons are determined by the gain function. Amplitudes increase when the gain function is positive and decrease when the gain function is negative. Furthermore, we find that the intensities of dark solitons are presented as a superposition of the solitons and stationary waves.

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

Dustin Popp; Zander Mausolff; Sedat Goluoglu

We are proposing to use the code, TDKENO, to model TREAT. TDKENO solves the time dependent, three dimensional Boltzmann transport equation with explicit representation of delayed neutrons. Instead of directly integrating this equation, the neutron flux is factored into two components – a rapidly varying amplitude equation and a slowly varying shape equation and each is solved separately on different time scales. The shape equation is solved using the 3D Monte Carlo transport code KENO, from Oak Ridge National Laboratory’s SCALE code package. Using the Monte Carlo method to solve the shape equation is still computationally intensive, but the operationmore » is only performed when needed. The amplitude equation is solved deterministically and frequently, so the solution gives an accurate time-dependent solution without having to repeatedly We have modified TDKENO to incorporate KENO-VI so that we may accurately represent the geometries within TREAT. This paper explains the motivation behind using generalized geometry, and provides the results of our modifications. TDKENO uses the Improved Quasi-Static method to accomplish this. In this method, the neutron flux is factored into two components. One component is a purely time-dependent and rapidly varying amplitude function, which is solved deterministically and very frequently (small time steps). The other is a slowly varying flux shape function that weakly depends on time and is only solved when needed (significantly larger time steps).« less

Reflective properties of randomly rough surfaces under large incidence angles.

PubMed

Qiu, J; Zhang, W J; Liu, L H; Hsu, P-f; Liu, L J

2014-06-01

The reflective properties of randomly rough surfaces at large incidence angles have been reported due to their potential applications in some of the radiative heat transfer research areas. The main purpose of this work is to investigate the formation mechanism of the specular reflection peak of rough surfaces at large incidence angles. The bidirectional reflectance distribution function (BRDF) of rough aluminum surfaces with different roughnesses at different incident angles is measured by a three-axis automated scatterometer. This study used a validated and accurate computational model, the rigorous coupled-wave analysis (RCWA) method, to compare and analyze the measurement BRDF results. It is found that the RCWA results show the same trend of specular peak as the measurement. This paper mainly focuses on the relative roughness at the range of 0.16<σ/λ<5.35. As the relative roughness decreases, the specular peak enhancement dramatically increases and the scattering region significantly reduces, especially under large incidence angles. The RCWA and the Rayleigh criterion results have been compared, showing that the relative error of the total integrated scatter increases as the roughness of the surface increases at large incidence angles. In addition, the zero-order diffractive power calculated by RCWA and the reflectance calculated by Fresnel equations are compared. The comparison shows that the relative error declines sharply when the incident angle is large and the roughness is small.

Integrated Electro-optical Laser-Beam Scanners

NASA Technical Reports Server (NTRS)

Boord, Warren T.

1990-01-01

Scanners using solid-state devices compact, consume little power, and have no moving parts. Integrated electro-optical laser scanner, in conjunction with external lens, points outgoing beam of light in any number of different directions, depending on number of upper electrodes. Offers beam-deflection angles larger than those of acousto-optic scanners. Proposed for such diverse applications as nonimpact laser printing, color imaging, ranging, barcode reading, and robotic vision.

A Direct and Non-Singular UKF Approach Using Euler Angle Kinematics for Integrated Navigation Systems

PubMed Central

Ran, Changyan; Cheng, Xianghong

2016-01-01

This paper presents a direct and non-singular approach based on an unscented Kalman filter (UKF) for the integration of strapdown inertial navigation systems (SINSs) with the aid of velocity. The state vector includes velocity and Euler angles, and the system model contains Euler angle kinematics equations. The measured velocity in the body frame is used as the filter measurement. The quaternion nonlinear equality constraint is eliminated, and the cross-noise problem is overcome. The filter model is simple and easy to apply without linearization. Data fusion is performed by an UKF, which directly estimates and outputs the navigation information. There is no need to process navigation computation and error correction separately because the navigation computation is completed synchronously during the filter time updating. In addition, the singularities are avoided with the help of the dual-Euler method. The performance of the proposed approach is verified by road test data from a land vehicle equipped with an odometer aided SINS, and a singularity turntable test is conducted using three-axis turntable test data. The results show that the proposed approach can achieve higher navigation accuracy than the commonly-used indirect approach, and the singularities can be efficiently removed as the result of dual-Euler method. PMID:27598169

Quadrature imposition of compatibility conditions in Chebyshev methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Streett, C. L.

1990-01-01

Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Illumination angle and layer thickness influence on the photo current generation in organic solar cells: A combined simulative and experimental study

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

Mescher, Jan, E-mail: jan.mescher@kit.edu; Mertens, Adrian; Egel, Amos

2015-07-15

In most future organic photovoltaic applications, such as fixed roof installations, facade or clothing integration, the solar cells will face the sun under varying angles. By a combined simulative and experimental study, we investigate the mutual interdependencies of the angle of light incidence, the absorber layer thickness and the photon harvesting efficiency within a typical organic photovoltaic device. For thin absorber layers, we find a steady decrease of the effective photocurrent towards increasing angles. For 90-140 nm thick absorber layers, however, we observe an effective photocurrent enhancement, exhibiting a maximum yield at angles of incidence of about 50°. Both effectsmore » mainly originate from the angle-dependent spatial broadening of the optical interference pattern inside the solar cell and a shift of the absorption maximum away from the metal electrode.« less

Illumination angle and layer thickness influence on the photo current generation in organic solar cells: A combined simulative and experimental study

NASA Astrophysics Data System (ADS)

Mescher, Jan; Mertens, Adrian; Egel, Amos; Kettlitz, Siegfried W.; Lemmer, Uli; Colsmann, Alexander

2015-07-01

In most future organic photovoltaic applications, such as fixed roof installations, facade or clothing integration, the solar cells will face the sun under varying angles. By a combined simulative and experimental study, we investigate the mutual interdependencies of the angle of light incidence, the absorber layer thickness and the photon harvesting efficiency within a typical organic photovoltaic device. For thin absorber layers, we find a steady decrease of the effective photocurrent towards increasing angles. For 90-140 nm thick absorber layers, however, we observe an effective photocurrent enhancement, exhibiting a maximum yield at angles of incidence of about 50°. Both effects mainly originate from the angle-dependent spatial broadening of the optical interference pattern inside the solar cell and a shift of the absorption maximum away from the metal electrode.

Solvent dynamics and electron transfer reactions

NASA Astrophysics Data System (ADS)

Rasaiah, Jayendran C.; Zhu, Jianjun

1994-02-01

Recent experimental and theoretical studies of the influence of solvent dynamics on electron transfer (ET) reactions are discussed. It is seen that the survival probabilities of the reactants and products can be obtained as the solution to an integral equation using experimental or simulation data on the solvation dynamics. The theory developed for ET between thermally equilibrated reactants in solution, in which the ligand vibrations were treated classically, is extended to include quantum effects on the inner-shell ligand vibration and electron transfer from a nonequilibrium initial state prepared, for example, by laser excitation. This leads to a slight modification of the integral equation which is easily solved on a personal computer to provide results that can be directly compared with experiment. Analytic approximations to the solutions of the integral equation, ranging from a single exponential to multiexponential time dependence of the survival probabilities are discussed. The rate constant for the single exponential decay of the reactants interpolates between the thermal equilibrium rate constant kie (that is independent of solvent dynamics) and a diffusion controlled rate constant kid (determined by solvent dynamics) and also between the wide (A=0) and narrow (A=1) window limits dominated by inner-sphere ligand vibration and outer-sphere solvent reorganization respectively. The explicit dependence of the integral equation solutions on solvation dynamics S(t), the free energy of reaction ΔG0, the total reorganization energy λ and its partitioning between ligand vibration λq and solvent polarization fluctuations λ0, and the nature of the initial state should be useful in the analysis and design of ET experiments in different solvents.

Wedge-Shaped GaN Nanowalls: A Potential Candidate for Two-Dimensional Electronics and Spintronics

NASA Astrophysics Data System (ADS)

Deb, Swarup; Dhar, Subhabrata

Schrödingerand Poisson equations are solved self-consistently in order to obtain the potential and charge density distribution in n-type GaN nanowalls tapered along c-axis by different angles. The study shows two-dimensional (2D) quantum confinement of electrons in the central vertical plane of the wall for the entire range of tapering. Calculation of room temperature electron mobility in the 2D channel shows a steady decrease with the increase of the inclination angle of the side facets with respect to the base. However, it is interesting to note that the mobility remains to be much larger than that of bulk GaN even for the inclination angle of 65∘. The properties of high mobility and the vertical orientation of the 2DEG plane in this system can be exploited in fabricating highly conducting transparent interconnects and field effect transistors, which can lead to large scale integration of 2D devices in future.

High-frequency Born synthetic seismograms based on coupled normal modes

USGS Publications Warehouse

Pollitz, Fred F.

2011-01-01

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

Correcting the initialization of models with fractional derivatives via history-dependent conditions

NASA Astrophysics Data System (ADS)

Du, Maolin; Wang, Zaihua

2016-04-01

Fractional differential equations are more and more used in modeling memory (history-dependent, non-local, or hereditary) phenomena. Conventional initial values of fractional differential equations are defined at a point, while recent works define initial conditions over histories. We prove that the conventional initialization of fractional differential equations with a Riemann-Liouville derivative is wrong with a simple counter-example. The initial values were assumed to be arbitrarily given for a typical fractional differential equation, but we find one of these values can only be zero. We show that fractional differential equations are of infinite dimensions, and the initial conditions, initial histories, are defined as functions over intervals. We obtain the equivalent integral equation for Caputo case. With a simple fractional model of materials, we illustrate that the recovery behavior is correct with the initial creep history, but is wrong with initial values at the starting point of the recovery. We demonstrate the application of initial history by solving a forced fractional Lorenz system numerically.

Unsteady aerodynamic forces and torques on falling parallelograms in coupled tumbling-helical motions

NASA Astrophysics Data System (ADS)

Varshney, Kapil; Chang, Song; Wang, Z. Jane

2013-05-01

Falling parallelograms exhibit coupled motion of autogyration and tumbling, similar to the motion of falling tulip seeds, unlike maple seeds which autogyrate but do not tumble, or rectangular cards which tumble but do not gyrate. This coupled tumbling and autogyrating motion are robust, when card parameters, such as aspect ratio, internal angle, and mass density, are varied. We measure the three-dimensional (3D) falling kinematics of the parallelograms and quantify their descending speed, azimuthal rotation, tumbling rotation, and cone angle in each falling. The cone angle is insensitive to the variation of the card parameters, and the card tumbling axis does not overlap with but is close to the diagonal axis. In addition to this connection to the dynamics of falling seeds, these trajectories provide an ideal set of data to analyze 3D aerodynamic force and torque at an intermediate range of Reynolds numbers, and the results will be useful for constructing 3D aerodynamic force and torque models. Tracking these free falling trajectories gives us a nonintrusive method for deducing instantaneous aerodynamic forces. We determine the 3D aerodynamic forces and torques based on Newton-Euler equations. The dynamical analysis reveals that, although the angle of attack changes dramatically during tumbling, the aerodynamic forces have a weak dependence on the angle of attack. The aerodynamic lift is dominated by the coupling of translational and rotational velocities. The aerodynamic torque has an unexpectedly large component perpendicular to the card. The analysis of the Euler equation suggests that this large torque is related to the deviation of the tumbling axis from the principle axis of the card.

Unsteady aerodynamic forces and torques on falling parallelograms in coupled tumbling-helical motions.

PubMed

Varshney, Kapil; Chang, Song; Wang, Z Jane

2013-05-01

Falling parallelograms exhibit coupled motion of autogyration and tumbling, similar to the motion of falling tulip seeds, unlike maple seeds which autogyrate but do not tumble, or rectangular cards which tumble but do not gyrate. This coupled tumbling and autogyrating motion are robust, when card parameters, such as aspect ratio, internal angle, and mass density, are varied. We measure the three-dimensional (3D) falling kinematics of the parallelograms and quantify their descending speed, azimuthal rotation, tumbling rotation, and cone angle in each falling. The cone angle is insensitive to the variation of the card parameters, and the card tumbling axis does not overlap with but is close to the diagonal axis. In addition to this connection to the dynamics of falling seeds, these trajectories provide an ideal set of data to analyze 3D aerodynamic force and torque at an intermediate range of Reynolds numbers, and the results will be useful for constructing 3D aerodynamic force and torque models. Tracking these free falling trajectories gives us a nonintrusive method for deducing instantaneous aerodynamic forces. We determine the 3D aerodynamic forces and torques based on Newton-Euler equations. The dynamical analysis reveals that, although the angle of attack changes dramatically during tumbling, the aerodynamic forces have a weak dependence on the angle of attack. The aerodynamic lift is dominated by the coupling of translational and rotational velocities. The aerodynamic torque has an unexpectedly large component perpendicular to the card. The analysis of the Euler equation suggests that this large torque is related to the deviation of the tumbling axis from the principle axis of the card.

DREAM3D simulations of inner-belt dynamics

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

Cunningham, Gregory Scott

2015-05-26

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere, where the loss to the atmosphere is enabled by pitch-angle scattering from Coulomb and wave-particle interactions. In the 1973 paper, equilibrium solutions to a decoupled set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium two-belt structure. Each 1D radial diffusion equation incorporated an L-and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This decoupling of themore » problem is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering. However, for some values of μ and L the lifetime associated with pitch-angle scattering is comparable to the timescale associated with radial diffusion, suggesting that the true equilibrium solutions might reflect `coupled modes' involving pitch-angle scattering and radial diffusion and thus requiring a 3D diffusion model. In the work we show here, we have computed the equilibrium solutions using our 3D diffusion model, DREAM3D, that allows for such coupling. We find that the 3D equilibrium solutions are quite similar to the solutions shown in the 1973 paper when we use the same physical models for radial diffusion and pitch-angle scattering from hiss. However, we show that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to understand the two-belt structure.« less

Nonalgebraic integrability of one reversible dynamical system of the Cremona type

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

1998-05-01

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

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux

NASA Astrophysics Data System (ADS)

Balasuriya, Sanjeeva

2016-12-01

State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses destroy the smooth invariant manifolds, necessitating new definitions for stable and unstable pseudo-manifolds. Their time-evolution is characterised by solving a Volterra integral equation of the second kind with discontinuous inhomogeniety. A criteria for heteroclinic trajectory persistence in this impulsive context is developed, as is a quantification of an instantaneous flux across broken heteroclinic manifolds. Several examples, including a kicked Duffing oscillator and an underwater explosion in the vicinity of an eddy, are used to illustrate the theory.

Theory for rates, equilibrium constants, and Brønsted slopes in F1-ATPase single molecule imaging experiments

PubMed Central

Volkán-Kacsó, Sándor; Marcus, Rudolph A.

2015-01-01

A theoretical model of elastically coupled reactions is proposed for single molecule imaging and rotor manipulation experiments on F1-ATPase. Stalling experiments are considered in which rates of individual ligand binding, ligand release, and chemical reaction steps have an exponential dependence on rotor angle. These data are treated in terms of the effect of thermodynamic driving forces on reaction rates, and lead to equations relating rate constants and free energies to the stalling angle. These relations, in turn, are modeled using a formalism originally developed to treat electron and other transfer reactions. During stalling the free energy profile of the enzymatic steps is altered by a work term due to elastic structural twisting. Using biochemical and single molecule data, the dependence of the rate constant and equilibrium constant on the stall angle, as well as the Børnsted slope are predicted and compared with experiment. Reasonable agreement is found with stalling experiments for ATP and GTP binding. The model can be applied to other torque-generating steps of reversible ligand binding, such as ADP and Pi release, when sufficient data become available. PMID:26483483

An investigation of the sound field above the audience in large lecture halls with a scale model.

PubMed

Kahn, D W; Tichy, J

1986-09-01

Measurements of steady-state sound pressure levels above the audience in large lecture halls show that the classical equation for predicting the sound pressure level is not accurate. The direct field above the seats was measured on a 1:10 scale model and was found to be dependent on the incidence angle and direction of sound propagation across the audience. The reverberant field above the seats in the model was calculated by subtracting the direct field from the measured total field and was found to be dependent on the magnitude and particularly on the placement of absorption. The decrease of sound pressure level versus distance in the total field depends on the angle (controlled by absorption placement) at which the strong reflections are incident upon the audience area. Sound pressure level decreases at a fairly constant rate with distance from the sound source in both the direct and reverberant field, and the decrease rate depends strongly on the absorption placement. The lowest rate of decay occurs when the side walls are absorptive, and both the ceiling and rear wall are reflective. These consequences are discussed with respect to prediction of speech intelligibility.

Pseudo-time algorithms for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, E.

1986-01-01

A pseudo-time method is introduced to integrate the compressible Navier-Stokes equations to a steady state. This method is a generalization of a method used by Crocco and also by Allen and Cheng. We show that for a simple heat equation that this is just a renormalization of the time. For a convection-diffusion equation the renormalization is dependent only on the viscous terms. We implement the method for the Navier-Stokes equations using a Runge-Kutta type algorithm. This permits the time step to be chosen based on the inviscid model only. We also discuss the use of residual smoothing when viscous terms are present.

Effect of surface roughness on contact line dynamics of a thin droplet

NASA Astrophysics Data System (ADS)

Bhattacharjee, Debanik; Soltannia, Babak; Nazaripoor, Hadi; Sadrzadeh, Mohtada

2017-11-01

Any surface possesses inherent roughness. Droplet spreading on a surface is an example of a contact line problem. The tri-phase contact line is prone to stress singularity which can be relieved by using precursor film assumption and disjoining pressure. In this study, an axisymmetric, incompressible, Newtonian droplet spreading on a surface was investigated. An evolution equation which tracks the droplet height over time was obtained considering the lubrication approximation. The nonlinear PDE of evolution equation was solved using finite difference scheme. A simplified Gaussian model was used as a starting point to assess the role of roughness in the dynamics of contact line. The preliminary results revealed that, for both impermeable and permeable surfaces, the apparent contact angle increased in the presence of defects whereas the equilibrium stage remained unaffected. The apparent contact angle, however, was more strongly dependent on the nature and density of defects for impermeable surfaces due to the longer droplet lifetime. Furthermore, random self-affine and non-Gaussian models are employed. The mathematical model results are finally compared with theoretical models like the Cassie-Baxter, Wenzel, and Penetration modes. NSERC.

Precipitation regions on the Earth of high energy electrons, injected by a point source moving along a circular Earth orbit

NASA Astrophysics Data System (ADS)

Kolesnikov, E. K.; Klyushnikov, G. N.

2018-05-01

In the paper we continue the study of precipitation regions of high-energy charged particles, carried out by the authors since 2002. In contrast to previous papers, where a stationary source of electrons was considered, it is assumed that the source moves along a low circular near-earth orbit with a constant velocity. The orbit position is set by the inclination angle of the orbital plane to the equatorial plane and the longitude of the ascending node. The total number of injected electrons is determined by the source strength and the number of complete revolutions that the source makes along the circumference. Construction of precipitation regions is produced using the computational algorithm based on solving of the system of ordinary differential equations. The features of the precipitation regions structure for the dipole approximation of the geomagnetic field and the symmetrical arrangement of the orbit relative to the equator are noted. The dependencies of the precipitation regions on different orbital parametres such as the incline angle, the ascending node position and kinetic energy of injected particles have been considered.

Field line twist and field-aligned currents in an axially symmetric equilibrium magnetosphere. [of Uranus

NASA Technical Reports Server (NTRS)

Voigt, Gerd-Hannes

1986-01-01

Field-aligned Birkeland currents and the angle of the magnetic line twist were calculated for an axially symmetric pole-on magnetosphere (assumed to be in MHD equilibrium). The angle of the field line twist was shown to have a strong radial dependence on the axisymmetric magnetotail as well as on the ionospheric conductivity and the amount of thermal plasma contained in closed magnetotail flux tubes. The field line twist results from the planetary rotation, which leads to the development of a toroidal magnetic B-sub-phi component and to differentially rotating magnetic field lines. It was shown that the time development of the toroidal magnetic B-sub-phi component and the rotation frequency are related through an induction equation.

Analysis of mixed-mode crack propagation using the boundary integral method

NASA Technical Reports Server (NTRS)

Mendelson, A.; Ghosn, L. J.

1986-01-01

Crack propagation in a rotating inner raceway of a high speed roller bearing is analyzed using the boundary integral equation method. The method consists of an edge crack in a plate under tension, upon which varying Hertzian stress fields are superimposed. A computer program for the boundary integral equation method was written using quadratic elements to determine the stress and displacement fields for discrete roller positions. Mode I and Mode II stress intensity factors and crack extension forces G sub 00 (energy release rate due to tensile opening mode) and G sub r0 (energy release rate due to shear displacement mode) were computed. These calculations permit determination of that crack growth angle for which the change in the crack extension forces is maximum. The crack driving force was found to be the alternating mixed-mode loading that occurs with each passage of the most heavily loaded roller. The crack is predicted to propagate in a step-like fashion alternating between radial and inclined segments, and this pattern was observed experimentally. The maximum changes DeltaG sub 00 and DeltaG sub r0 of the crack extension forces are found to be good measures of the crack propagation rate and direction.

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

NASA Technical Reports Server (NTRS)

Bond, Victor R.; Fraietta, Michael F.

1991-01-01

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Discretization analysis of bifurcation based nonlinear amplifiers

NASA Astrophysics Data System (ADS)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2017-09-01

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

[Predicting the probability of development and progression of primary open angle glaucoma by regression modeling].

PubMed

Likhvantseva, V G; Sokolov, V A; Levanova, O N; Kovelenova, I V

2018-01-01

Prediction of the clinical course of primary open-angle glaucoma (POAG) is one of the main directions in solving the problem of vision loss prevention and stabilization of the pathological process. Simple statistical methods of correlation analysis show the extent of each risk factor's impact, but do not indicate the total impact of these factors in personalized combinations. The relationships between the risk factors is subject to correlation and regression analysis. The regression equation represents the dependence of the mathematical expectation of the resulting sign on the combination of factor signs. To develop a technique for predicting the probability of development and progression of primary open-angle glaucoma based on a personalized combination of risk factors by linear multivariate regression analysis. The study included 66 patients (23 female and 43 male; 132 eyes) with newly diagnosed primary open-angle glaucoma. The control group consisted of 14 patients (8 male and 6 female). Standard ophthalmic examination was supplemented with biochemical study of lacrimal fluid. Concentration of matrix metalloproteinase MMP-2 and MMP-9 in tear fluid in both eyes was determined using 'sandwich' enzyme-linked immunosorbent assay (ELISA) method. The study resulted in the development of regression equations and step-by-step multivariate logistic models that can help calculate the risk of development and progression of POAG. Those models are based on expert evaluation of clinical and instrumental indicators of hydrodynamic disturbances (coefficient of outflow ease - C, volume of intraocular fluid secretion - F, fluctuation of intraocular pressure), as well as personalized morphometric parameters of the retina (central retinal thickness in the macular area) and concentration of MMP-2 and MMP-9 in the tear film. The newly developed regression equations are highly informative and can be a reliable tool for studying of the influence vector and assessment of pathogenic potential of the independent risk factors in specific personalized combinations.

On the performance of the moment approximation for the numerical computation of fiber stress in turbulent channel flow

NASA Astrophysics Data System (ADS)

Gillissen, J. J. J.; Boersma, B. J.; Mortensen, P. H.; Andersson, H. I.

2007-03-01

Fiber-induced drag reduction can be studied in great detail by means of direct numerical simulation [J. S. Paschkewitz et al., J. Fluid Mech. 518, 281 (2004)]. To account for the effect of the fibers, the Navier-Stokes equations are supplemented by the fiber stress tensor, which depends on the distribution function of fiber orientation angles. We have computed this function in turbulent channel flow, by solving the Fokker-Planck equation numerically. The results are used to validate an approximate method for calculating fiber stress, in which the second moment of the orientation distribution is solved. Since the moment evolution equations contain higher-order moments, a closure relation is required to obtain as many equations as unknowns. We investigate the performance of the eigenvalue-based optimal fitted closure scheme [J. S. Cintra and C. L. Tucker, J. Rheol. 39, 1095 (1995)]. The closure-predicted stress and flow statistics in two-way coupled simulations are within 10% of the "exact" Fokker-Planck solution.

Stability of a dual-spin satellite with two dampers

NASA Technical Reports Server (NTRS)

Alfriend, K. T.; Hubert, C. H.

1974-01-01

The rotational stability of a dual-spin satellite consisting of a main body and a symmetric rotor, both spinning about a common axis, is investigated. The main body is equipped with a spring-mass damper, while a partially filled viscous ring damper is mounted on the rapidly spinning rotor. The effect of fluid motion on the rotational stability of the satellite is calculated, considering the fluid as a single particle moving in a tube with viscous damping. Time constants are obtained by solving approximate equations of motion for the nutation-synchronous and the spin-synchronous modes, and the results are found to agree well with the numerical integrations of the exact equations. A limit cycle may exist for some configurations; the nutation angle tends to increase in such cases.

Photon emission from quark-gluon plasma out of equilibrium

NASA Astrophysics Data System (ADS)

Hauksson, Sigtryggur; Jeon, Sangyong; Gale, Charles

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Finster, Felix; Reintjes, Moritz

2009-05-01

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

Quasiclassical description of a superconductor with a spin density wave

NASA Astrophysics Data System (ADS)

Moor, A.; Volkov, A. F.; Efetov, K. B.

2011-04-01

We derive equations for the quasiclassical Green’s functions ǧ within a simple model of a two-band superconductor with a spin density wave (SDW). The elements of the matrix ǧ are the retarded, advanced, and Keldysh functions, each of which is an 8×8 matrix in the Gor’kov-Nambu, the spin, and the band space. In equilibrium, these equations are a generalization of the Eilenberger equation. On the basis of the derived equations, we analyze the Knight shift, the proximity, and the dc Josephson effects in the superconductors under consideration. The Knight shift is shown to depend on the orientation of the external magnetic field with respect to the direction of the vector of the magnetization of the SDW. The proximity effect is analyzed for an interface between a superconductor with the SDW and a normal metal. The function describing both superconducting and magnetic correlations is shown to penetrate the normal metal or a metal with the SDW due to the proximity effect. The dc Josephson current in an SSDW/N/SSDW junction is also calculated as a function of the phase difference φ. It is shown that in our model, the Josephson current does not depend on the mutual orientation of the magnetic moments in the superconductors SSDW and is proportional to sinφ. The dissipationless spin current jsp depends on the angle α between the magnetization vectors in the same way (jsp~sinα) and is not zero above the superconducting transition temperature.

Nonlinearity in the effect of an inhomogeneous Hall angle

NASA Astrophysics Data System (ADS)

Koon, Daniel W.

2007-03-01

The differential equation for the electric potential in a conducting material with an inhomogeneous Hall angle is extended to the large-field limit. This equation is solved for a square specimen, using a successive over-relaxation [SOR] technique for matrices of up to 101x101 size, and the Hall weighting function -- the effect of local pointlike perturbations on the measured Hall angle -- is calculated as both the unperturbed Hall angle, θH, and the perturbation, δθH, exceed the linear, small angle limit. Preliminary results show that the Hall angle varies by no more than 5% if both | θH |<1 and | δθH |<1. Thus, previously calculated results for the Hall weighting function can be used for most materials in all but the most extreme magnetic fields.

Unsteady blade pressures on a propfan at takeoff: Euler analysis and flight data

NASA Technical Reports Server (NTRS)

Nallasamy, M.

1991-01-01

The unsteady blade pressures due to the operation of the propfan at an angle to the direction of the mean flow are obtained by solving the unsteady three dimensional Euler equations. The configuration considered is the eight bladed SR7L propfan at takeoff conditions and the inflow angles considered are 6.3 deg, 8.3 deg, 11.3 deg. The predicted blade pressure waveforms are compared with inflight measurements. At the inboard radial station (r/R = 0.68) the phase of the predicted waveforms show reasonable agreement with the measurements while the amplitudes are over predicted in the leading edge region of the blade. At the outboard radial station (r/R = 0.95), the predicted amplitudes of the waveforms on the pressure surface are in good agreement with flight data for all inflow angles. The measured (installed propfan) waveforms show a relative phase lag compared to the computed (propfan alone) waveforms. The phase lag depends on the axial location of the transducer and the surface of the blade. On the suction surface, in addition to the relative phase lag, the measurements show distortion (widening and steepening) of the waveforms. The extent of distortion increases with increase in inflow angle. This distortion seems to be due to viscous separation effects which depend on the azimuthal location of the blade and the axial location of the transducer.

Method for Measuring the Volume-Scattering Function of Water

NASA Technical Reports Server (NTRS)

Agrawal, Yogesh C.

2009-01-01

The volume scattering function (VSF) of seawater affects visibility, remote sensing properties, in-water light propagation, lidar performance, and the like. Currently, it s possible to measure only small forward angles of VSF, or to use cumbersome, large, and non-autonomous systems. This innovation is a method of measuring the full range of VSF using a portable instrument. A single rapid-sensing photosensor is used to scan a green laser beam, which delivers the desired measurement. By using a single sensor, inter-calibration is avoided. A compact design is achieved by using drift-free detector electronics, fiber optics, and a new type of photomultiplier. This provides a high angular resolution of 1 or better, as well as the ability to focus in on a VSF region of particular interest. Currently, the total scattering of light is measured as a difference from the other two parts of the light budget equation. This innovation will allow the direct calculation of the total scattering of light by taking an integral of the VSF over all angles. This directly provides one of the three components of the light budget equation, allowing greater versatility in its calculation.

Deployment of a multi-link flexible structure

NASA Astrophysics Data System (ADS)

Na, Kyung-Su; Kim, Ji-Hwan

2006-06-01

Deployment of a multi-link beam structure undergoing locking is analyzed in the Timoshenko beam theory. In the modeling of the system, dynamic forces are assumed to be torques and restoring forces due to the torsion spring at each joint. Hamilton's principle is used to determine the equations of motion and the finite element method is adopted to analyze the system. Newmark time integration and Newton-Raphson iteration methods are used to solve for the non-linear equations of motion at each time step. The locking at the joints of the multi-link flexible structure is analyzed by the momentum balance method. Numerical results are compared with the previous experimental data. The angles and angular velocities of each joint, tip displacement, and velocity of each link are investigated to study the motions of the links at each time step. To analyze the effect of thickness on the motion of the link, the angle and the tip displacement of each link are compared according to the various slenderness ratios. Additionally, in order to investigate the effect of shear, the tip displacements of a Timoshenko beam are compared with those of an Euler-Bernoulli beam.

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Coupled dynamics in gluon mass generation and the impact of the three-gluon vertex

NASA Astrophysics Data System (ADS)

Binosi, Daniele; Papavassiliou, Joannis

2018-03-01

We present a detailed study of the subtle interplay transpiring at the level of two integral equations that are instrumental for the dynamical generation of a gluon mass in pure Yang-Mills theories. The main novelty is the joint treatment of the Schwinger-Dyson equation governing the infrared behavior of the gluon propagator and of the integral equation that controls the formation of massless bound-state excitations, whose inclusion is instrumental for obtaining massive solutions from the former equation. The self-consistency of the entire approach imposes the requirement of using a single value for the gauge coupling entering in the two key equations; its fulfilment depends crucially on the details of the three-gluon vertex, which contributes to both of them, but with different weight. In particular, the characteristic suppression of this vertex at intermediate and low energies enables the convergence of the iteration procedure to a single gauge coupling, whose value is reasonably close to that extracted from related lattice simulations.

Numerical computation of viscous flow about unconventional airfoil shapes

NASA Technical Reports Server (NTRS)

Ahmed, S.; Tannehill, J. C.

1990-01-01

A new two-dimensional computer code was developed to analyze the viscous flow around unconventional airfoils at various Mach numbers and angles of attack. The Navier-Stokes equations are solved using an implicit, upwind, finite-volume scheme. Both laminar and turbulent flows can be computed. A new nonequilibrium turbulence closure model was developed for computing turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present code was evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the present code in conjunction with the new nonequilibrium turbulence model gives excellent results.

Thermally induced vibrations of smart solar panel in a low-orbit satellite

NASA Astrophysics Data System (ADS)

Azadi, E.; Fazelzadeh, S. Ahmad; Azadi, M.

2017-03-01

In this paper, a smart flexible satellite moving in a circular orbit with two flexible panels are studied. The panels have been modeled as clamped-free-free-free rectangular plates with attached piezoelectric actuators. It is assumed that the satellite has a pitch angle rotation maneuver. Rapid temperature changes at day-night transitions in orbit generate time dependent bending moments. Satellite maneuver and temperature varying induce vibrations in the appendages. So, to simulate the system, heat radiation effects on the appendages have been considered. The nonlinear equations of motion and the heat transfer equations are coupled and solved simultaneously. So, the governing equations of motion are nonlinear and very complicated ones. Finally, the whole system is simulated and the effects of the heat radiation, radius of the orbit, piezoelectric voltages, and piezoelectric locations on the response of the system are studied.

Contact Angle and Adhesion Dynamics and Hysteresis on Molecularly Smooth Chemically Homogeneous Surfaces.

PubMed

Chen, Szu-Ying; Kaufman, Yair; Schrader, Alex M; Seo, Dongjin; Lee, Dong Woog; Page, Steven H; Koenig, Peter H; Isaacs, Sandra; Gizaw, Yonas; Israelachvili, Jacob N

2017-09-26

Measuring truly equilibrium adhesion energies or contact angles to obtain the thermodynamic values is experimentally difficult because it requires loading/unloading or advancing/receding boundaries to be measured at rates that can be slower than 1 nm/s. We have measured advancing-receding contact angles and loading-unloading adhesion energies for various systems and geometries involving molecularly smooth and chemically homogeneous surfaces moving at different but steady velocities in both directions, ±V, focusing on the thermodynamic limit of ±V → 0. We have used the Bell Theory (1978) to derive expressions for the dynamic (velocity-dependent) adhesion energies and contact angles suitable for both (i) dynamic adhesion measurements using the classic Johnson-Kendall-Roberts (JKR, 1971) theory of "contact mechanics" and (ii) dynamic contact angle hysteresis measurements of both rolling droplets and syringe-controlled (sessile) droplets on various surfaces. We present our results for systems that exhibited both steady and varying velocities from V ≈ 10 mm/s to 1 nm/s, where in all cases but one, the advancing (V > 0) and receding (V < 0) adhesion energies and/or contact angles converged toward the same theoretical (thermodynamic) values as V → 0. Our equations for the dynamic contact angles are similar to the classic equations of Blake & Haynes (1969) and fitted the experimental adhesion data equally well over the range of velocities studied, although with somewhat different fitting parameters for the characteristic molecular length/dimension or area and characteristic bond formation/rupture lifetime or velocity. Our theoretical and experimental methods and results unify previous kinetic theories of adhesion and contact angle hysteresis and offer new experimental methods for testing kinetic models in the thermodynamic, quasi-static, limit. Our analyses are limited to kinetic effects only, and we conclude that hydrodynamic, i.e., viscous, and inertial effects do not play a role at the interfacial velocities of our experiments, i.e., V < (1-10) mm/s (for water and hexadecane, but for viscous polymers it may be different), consistent with previously reported studies.

A complete analytical solution of the Fokker-Planck and balance equations for nucleation and growth of crystals

NASA Astrophysics Data System (ADS)

Makoveeva, Eugenya V.; Alexandrov, Dmitri V.

2018-01-01

This article is concerned with a new analytical description of nucleation and growth of crystals in a metastable mushy layer (supercooled liquid or supersaturated solution) at the intermediate stage of phase transition. The model under consideration consisting of the non-stationary integro-differential system of governing equations for the distribution function and metastability level is analytically solved by means of the saddle-point technique for the Laplace-type integral in the case of arbitrary nucleation kinetics and time-dependent heat or mass sources in the balance equation. We demonstrate that the time-dependent distribution function approaches the stationary profile in course of time. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

Mathematical modeling of two phase stratified flow in a microchannel with curved interface

NASA Astrophysics Data System (ADS)

Dandekar, Rajat; Picardo, Jason R.; Pushpavanam, S.

2017-11-01

Stratified or layered two-phase flows are encountered in several applications of microchannels, such as solvent extraction. Assuming steady, unidirectional creeping flow, it is possible to solve the Stokes equations by the method of eigenfunctions, provided the interface is flat and meets the wall with a 90 degree contact angle. However, in reality the contact angle depends on the pair of liquids and the material of the channel, and differs significantly from 90 degrees in many practical cases. For unidirectional flow, this implies that the interface is a circular arc (of constant curvature). We solve this problem within the framework of eigenfunctions, using the procedure developed by Shankar. We consider two distinct cases: (a) the interface meets the wall with the equilibrium contact angle; (b) the interface is pinned by surface treatment of the walls, so that the flow rates determine the apparent contact angle. We show that the contact angle appreciably affects the velocity profile and the volume fractions of the liquids, while limiting the range of flow rates that can be sustained without the interface touching the top/bottom walls. Non-intuitively, we find that the pressure drop is reduced when the more viscous liquid wets the wall.

Transonic flow of steam with non-equilibrium and homogenous condensation

NASA Astrophysics Data System (ADS)

Virk, Akashdeep Singh; Rusak, Zvi

2017-11-01

A small-disturbance model for studying the physical behavior of a steady transonic flow of steam with non-equilibrium and homogeneous condensation around a thin airfoil is derived. The steam thermodynamic behavior is described by van der Waals equation of state. The water condensation rate is calculated according to classical nucleation and droplet growth models. The current study is based on an asymptotic analysis of the fluid flow and condensation equations and boundary conditions in terms of the small thickness of the airfoil, small angle of attack, closeness of upstream flow Mach number to unity and small amount of condensate. The asymptotic analysis gives the similarity parameters that govern the problem. The flow field may be described by a non-homogeneous transonic small-disturbance equation coupled with a set of four ordinary differential equations for the calculation of the condensate mass fraction. An iterative numerical scheme which combines Murman & Cole's (1971) method with Simpson's integration rule is applied to solve the coupled system of equations. The model is used to study the effects of energy release from condensation on the aerodynamic performance of airfoils operating at high pressures and temperatures and near the vapor-liquid saturation conditions.

Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft

NASA Technical Reports Server (NTRS)

Ardema, Mark D.; Windhorst, Robert; Phillips, James

1998-01-01

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Optimization of Supersonic Transport Trajectories

NASA Technical Reports Server (NTRS)

Ardema, Mark D.; Windhorst, Robert; Phillips, James

1998-01-01

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Anomalous diffusion and scaling in coupled stochastic processes

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

Bel, Golan; Nemenman, Ilya

2009-01-01

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

Neutron radiation characteristics of plutonium dioxide fuel

NASA Technical Reports Server (NTRS)

Taherzadeh, M.

1972-01-01

The major sources of neutrons from plutonium dioxide nuclear fuel are considered in detail. These sources include spontaneous fission of several of the Pu isotopes, (alpha, n) reactions with low Z impurities in the fuel, and (alpha, n) reactions with O-18. For spontaneous fission neutrons a value of (1.95 + or - 0.07) X 1,000 n/s/g PuO2 is obtained. The neutron yield from (alpha, n) reactions with oxygen is calculated by integrating the reaction rate equation over all alpha-particle energies and all center-of-mass angles. The results indicate a neutron emission rate of (1.14 + or - 0.26) X 10,000 n/s/g PuO2. The neutron yield from (alpha, n) reactions with low Z impurities in the fuel is presented in tabular form for one part part per million of each impurity. The total neutron yield due to the combined effects of all the impurities depends upon the fractional weight concentration of each impurity. The total neutron flux emitted from a particular fuel geometry is estimated by adding the neutron yield due to the induced fission to the other neutron sources.

Numerical simulation of low gravity draining. [computerized simulation of liquid sloshing in cylindrical tanks, and boundary value problems

NASA Technical Reports Server (NTRS)

Bizzell, G. D.; Crane, G. E.

1976-01-01

A boundary value problem was solved numerically for a liquid that is assumed to be inviscid and incompressible, having a motion that is irrotational and axisymmetric, and having a constant (5 degrees) solid-liquid contact angle. The avoidance of excessive mesh distortion, encountered with strictly Lagrangian or Eulerian kinematics, was achieved by introducing an auxiliary kinematic velocity field along the free surface in order to vary the trajectories used in integrating the ordinary differential equations simulating the moving boundary. The computation of the velocity potential was based upon a nonuniform triangular mesh which was automatically revised to varying depths to accommodate the motion of the free surface. These methods permitted calculation of draining induced axisymmetric slosh through the many (or fractional) finite amplitude oscillations that can occur depending upon the balance of draining, gravitational, and surface tension forces. Velocity fields, evolution of the free surface with time, and liquid residual volumes were computed for three and one half decades of Weber number and for two Bond numbers, tank fill levels, and drain radii. Comparisons with experimental data are very satisfactory.

Development of programs for computing characteristics of ultraviolet radiation

NASA Technical Reports Server (NTRS)

Dave, J. V.

1972-01-01

Efficient programs were developed for computing all four characteristics of the radiation scattered by a plane-parallel, turbid, terrestrial atmospheric model. They were developed (FORTRAN 4) and tested on the IBM /360 computers with 2314 direct access storage facility. The storage requirement varies between 200K and 750K bytes depending upon the task. The scattering phase matrix (or function) is expanded in a Fourier series whose number of terms depend upon the zenith angles of the incident and scattered radiations, as well as on the nature of aerosols. A Gauss-Seidel procedure is used for obtaining the numerical solution of the transfer equation.

Effects of thermal fluctuations and fluid compressibility on hydrodynamic synchronization of microrotors at finite oscillatory Reynolds number: a multiparticle collision dynamics simulation study.

PubMed

Theers, Mario; Winkler, Roland G

2014-08-28

We investigate the emergent dynamical behavior of hydrodynamically coupled microrotors by means of multiparticle collision dynamics (MPC) simulations. The two rotors are confined in a plane and move along circles driven by active forces. Comparing simulations to theoretical results based on linearized hydrodynamics, we demonstrate that time-dependent hydrodynamic interactions lead to synchronization of the rotational motion. Thermal noise implies large fluctuations of the phase-angle difference between the rotors, but synchronization prevails and the ensemble-averaged time dependence of the phase-angle difference agrees well with analytical predictions. Moreover, we demonstrate that compressibility effects lead to longer synchronization times. In addition, the relevance of the inertia terms of the Navier-Stokes equation are discussed, specifically the linear unsteady acceleration term characterized by the oscillatory Reynolds number ReT. We illustrate the continuous breakdown of synchronization with the Reynolds number ReT, in analogy to the continuous breakdown of the scallop theorem with decreasing Reynolds number.

Free Body Dynamics of a Spinning Cylinder with Planar Restraint-(a.k.a. Barrel of Fun). Part 2

NASA Technical Reports Server (NTRS)

Moraru, Laurentiu; Dimofte, Florin; Hendricks, Robert C.

2011-01-01

The dynamic motion of a cylinder is analyzed based on rotation about its center of mass and is restrained by a plane normal to the axis passing through its center of mass at an angle. The first part of this work presented an analysis of the stability of the motion. In the current report, the governing equations are numerically integrated in time and the steady state is obtained as a limit of the transient numerical solution. The calculated data are compared with observed behaviors.

SAR Polarimetry

NASA Technical Reports Server (NTRS)

vanZyl, Jakob J.

2012-01-01

Radar Scattering includes: Surface Characteristics, Geometric Properties, Dielectric Properties, Rough Surface Scattering, Geometrical Optics and Small Perturbation Method Solutions, Integral Equation Method, Magellan Image of Pancake Domes on Venus, Dickinson Impact Crater on Venus (Magellan), Lakes on Titan (Cassini Radar, Longitudinal Dunes on Titan (Cassini Radar), Rough Surface Scattering: Effect of Dielectric Constant, Vegetation Scattering, Effect of Soil Moisture. Polarimetric Radar includes: Principles of Polarimetry: Field Descriptions, Wave Polarizations: Geometrical Representations, Definition of Ellipse Orientation Angles, Scatter as Polarization Transformer, Scattering Matrix, Coordinate Systems, Scattering Matrix, Covariance Matrix, Pauli Basis and Coherency Matrix, Polarization Synthesis, Polarimeter Implementation.

Involution and Difference Schemes for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.

In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Meade, Andrew James, Jr.

1989-01-01

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Stochastic analysis of pitch angle scattering of charged particles by transverse magnetic waves

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

Lemons, Don S.; Liu Kaijun; Winske, Dan

2009-11-15

This paper describes a theory of the velocity space scattering of charged particles in a static magnetic field composed of a uniform background field and a sum of transverse, circularly polarized, magnetic waves. When that sum has many terms the autocorrelation time required for particle orbits to become effectively randomized is small compared with the time required for the particle velocity distribution to change significantly. In this regime the deterministic equations of motion can be transformed into stochastic differential equations of motion. The resulting stochastic velocity space scattering is described, in part, by a pitch angle diffusion rate that ismore » a function of initial pitch angle and properties of the wave spectrum. Numerical solutions of the deterministic equations of motion agree with the theory at all pitch angles, for wave energy densities up to and above the energy density of the uniform field, and for different wave spectral shapes.« less

Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator

NASA Astrophysics Data System (ADS)

Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.

2017-10-01

In position dependent mass (PDM) problems, the quantum dynamics of the associated systems have been understood well in the literature for particular orderings. However, no efforts seem to have been made to solve such PDM problems for general orderings to obtain a global picture. In this connection, we here consider the general ordered quantum Hamiltonian of an interesting position dependent mass problem, namely, the Mathews-Lakshmanan oscillator, and try to solve the quantum problem for all possible orderings including Hermitian and non-Hermitian ones. The other interesting point in our study is that for all possible orderings, although the Schrödinger equation of this Mathews-Lakshmanan oscillator is uniquely reduced to the associated Legendre differential equation, their eigenfunctions cannot be represented in terms of the associated Legendre polynomials with integral degree and order. Rather the eigenfunctions are represented in terms of associated Legendre polynomials with non-integral degree and order. We here explore such polynomials and represent the discrete and continuum states of the system. We also exploit the connection between associated Legendre polynomials with non-integral degree with other orthogonal polynomials such as Jacobi and Gegenbauer polynomials.

Angular distribution of scission neutrons studied with time-dependent Schrödinger equation

NASA Astrophysics Data System (ADS)

Wada, Takahiro; Asano, Tomomasa; Carjan, Nicolae

2018-03-01

We investigate the angular distribution of scission neutrons taking account of the effects of fission fragments. The time evolution of the wave function of the scission neutron is obtained by integrating the time-dependent Schrodinger equation numerically. The effects of the fission fragments are taken into account by means of the optical potentials. The angular distribution is strongly modified by the presence of the fragments. In the case of asymmetric fission, it is found that the heavy fragment has stronger effects. Dependence on the initial distribution and on the properties of fission fragments is discussed. We also discuss on the treatment of the boundary to avoid artificial reflections

A Full-Maxwell Approach for Large-Angle Polar Wander of Viscoelastic Bodies

NASA Astrophysics Data System (ADS)

Hu, H.; van der Wal, W.; Vermeersen, L. L. A.

2017-12-01

For large-angle long-term true polar wander (TPW) there are currently two types of nonlinear methods which give approximated solutions: those assuming that the rotational axis coincides with the axis of maximum moment of inertia (MoI), which simplifies the Liouville equation, and those based on the quasi-fluid approximation, which approximates the Love number. Recent studies show that both can have a significant bias for certain models. Therefore, we still lack an (semi)analytical method which can give exact solutions for large-angle TPW for a model based on Maxwell rheology. This paper provides a method which analytically solves the MoI equation and adopts an extended iterative procedure introduced in Hu et al. (2017) to obtain a time-dependent solution. The new method can be used to simulate the effect of a remnant bulge or models in different hydrostatic states. We show the effect of the viscosity of the lithosphere on long-term, large-angle TPW. We also simulate models without hydrostatic equilibrium and show that the choice of the initial stress-free shape for the elastic (or highly viscous) lithosphere of a given model is as important as its thickness for obtaining a correct TPW behavior. The initial shape of the lithosphere can be an alternative explanation to mantle convection for the difference between the observed and model predicted flattening. Finally, it is concluded that based on the quasi-fluid approximation, TPW speed on Earth and Mars is underestimated, while the speed of the rotational axis approaching the end position on Venus is overestimated.

Scale relativity theory and integrative systems biology: 1. Founding principles and scale laws.

PubMed

Auffray, Charles; Nottale, Laurent

2008-05-01

In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. Then we introduce the fundamental principles and the successive steps that have been followed in the construction of the scale relativity theory, and discuss how scale laws of increasing complexity can be used to model and understand the behaviour of complex biological systems. In scale relativity theory, the geometry of space is considered to be continuous but non-differentiable, therefore fractal (i.e., explicitly scale-dependent). One writes the equations of motion in such a space as geodesics equations, under the constraint of the principle of relativity of all scales in nature. To this purpose, covariant derivatives are constructed that implement the various effects of the non-differentiable and fractal geometry. In this first review paper, the scale laws that describe the new dependence on resolutions of physical quantities are obtained as solutions of differential equations acting in the scale space. This leads to several possible levels of description for these laws, from the simplest scale invariant laws to generalized laws with variable fractal dimensions. Initial applications of these laws to the study of species evolution, embryogenesis and cell confinement are discussed.

Procedure for noise prediction and optimization of advanced technology propellers

NASA Technical Reports Server (NTRS)

Jou, W. H.; Bernstein, S.

1979-01-01

The sound field due to a propeller operating at supersonic tip speed in a uniform flow was investigated. Using the fact that the wave front in a uniform stream is a convected sphere, the fundamental solution to the convected wave equation was easily obtained. The Fourier coefficients of the pressure signature were obtained by a far field approximation, and are expressed as an integral over the blade platform. It is shown that cones of silence exist fore and aft the propeller plane. The semiapex angles are shown. These angles are independent of the individual Mach components such as the flight Mach number and the rotation Mach number. The result is confirmed by the computation of the ray path of the emitted Mach waves. The Doppler amplification factor strengthens the signal behind the propeller while it weakens that upstream.

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

NASA Astrophysics Data System (ADS)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

TOPICAL REVIEW: Electrowetting: from basics to applications

NASA Astrophysics Data System (ADS)

Mugele, Frieder; Baret, Jean-Christophe

2005-07-01

Electrowetting has become one of the most widely used tools for manipulating tiny amounts of liquids on surfaces. Applications range from 'lab-on-a-chip' devices to adjustable lenses and new kinds of electronic displays. In the present article, we review the recent progress in this rapidly growing field including both fundamental and applied aspects. We compare the various approaches used to derive the basic electrowetting equation, which has been shown to be very reliable as long as the applied voltage is not too high. We discuss in detail the origin of the electrostatic forces that induce both contact angle reduction and the motion of entire droplets. We examine the limitations of the electrowetting equation and present a variety of recent extensions to the theory that account for distortions of the liquid surface due to local electric fields, for the finite penetration depth of electric fields into the liquid, as well as for finite conductivity effects in the presence of AC voltage. The most prominent failure of the electrowetting equation, namely the saturation of the contact angle at high voltage, is discussed in a separate section. Recent work in this direction indicates that a variety of distinct physical effects—rather than a unique one—are responsible for the saturation phenomenon, depending on experimental details. In the presence of suitable electrode patterns or topographic structures on the substrate surface, variations of the contact angle can give rise not only to continuous changes of the droplet shape, but also to discontinuous morphological transitions between distinct liquid morphologies. The dynamics of electrowetting are discussed briefly. Finally, we give an overview of recent work aimed at commercial applications, in particular in the fields of adjustable lenses, display technology, fibre optics, and biotechnology-related microfluidic devices.

An experimental and computational investigation of the flow field about a transonic airfoil in supercritical flow with turbulent boundary-layer separation

NASA Technical Reports Server (NTRS)

Rubesin, M. W.; Okuno, A. F.; Levy, L. L., Jr.; Mcdevitt, J. B.; Seegmiller, H. L.

1976-01-01

A combined experimental and computational research program is described for testing and guiding turbulence modeling within regions of separation induced by shock waves incident in turbulent boundary layers. Specifically, studies are made of the separated flow the rear portion of an 18%-thick circular-arc airfoil at zero angle of attack in high Reynolds number supercritical flow. The measurements include distributions of surface static pressure and local skin friction. The instruments employed include highfrequency response pressure cells and a large array of surface hot-wire skin-friction gages. Computations at the experimental flow conditions are made using time-dependent solutions of ensemble-averaged Navier-Stokes equations, plus additional equations for the turbulence modeling.

Radarclinometry of the Earth and Venus from space-shuttle and Venera-15 imagery

USGS Publications Warehouse

Wildey, R.L.

1990-01-01

The project to develop a line-integral approach to 2-dimensional radarclinometry and to bring it to the status of producing topographic maps from real radar images has been concluded. The final developments of the theory itself have involved a trial-and-error resolution of the curvature decision process at each integration step over range as follows: (1) Locally Indeterminate Azimuth-Azimuth Curvature is invoked if the range-directed path of integration is within 1 ??? in angle of the tangent to a local characteristic curve of the partial differential equation of radarclinometry (equivalent to a lapse in the necessity for an auxiliary curvature assumption); (2) Local Cylindricity is invoked if the local image isophote has a radius-of-curvature greater than 50 pixels; (3) Least-Squared Local Sphericity is invoked if the characteristic curve trends at greater than 70 ??? to the range direction (the auxiliary curvature assumption is becoming a sufficiently strong influence as to warrant the overconstraint), and (4) the default hypothesis, which is invoked most often, is the localization through the Euler/Lagrange equation from the calculus of variations of the global principle of minimization of the surface area of the terrain. The development of the set of line integrals into a 2-dimensional topographic surface is not practically achieved by branching the line integral at the range threshold, because the radarclinometry equations are too frequently coupled but weakly to the slope component in the direction of radar-azimuth, and under circumstances for which the powerfully influential auxiliary curvature assumption is too unrealistic. In other words, a line integration in radar-azimuth is far more frequently directed orthogonally to the local characteristic curve than is one carried out over range. Such orthogonality results in stepping the strike under the exclusive control of the curvature assumption. Instead, a quasi-surface-integration step is taken by modeling the dependence on initial strike of the gravitational potential energy of the vertical slab of terrain under the range-profile. The adopted starting strike for the range integral is the one which minimizes the gravitational potential energy. This radarclinometric method, in combination with my recently published method for determining an effective radar back-scattering function from one-dimensional slope statistics and image pixel-signal statistics, was applied to three images. First, to separate theoretical difficulties from experimental impediments, an artificial radar image was generated from a topographic map of the Lake Champlain West quadrangle in the Adirondack Mountains. Except for the regional trend in elevation, to which radarclinometry is insensitive by design, the agreement between the original and derived topography appears good. The morphologies agree and the range of relief is the same to within 4%. As an example of data of the highest quality available from space-borne radar at the present time, a SIR-B image of very rugged terrain in the coastal mountains of Oregon was similarly processed. The result, after filtering to redistribute photoclinometric errors about the two-dimensional spatial spectrum, agrees with ground truth almost as well. As an example of the worst possible data, in terms of signal-to-noise ratio and radar incidence angle (no detraction from the praise due the first high resolution space-borne radar-imaging of Venus intended), a Venera-15 image segment in Sedna Planitia just north-east of Sapho was processed, using Venera altimetry and Pioneer roughness data for slope statistics, in spite of the resolution mis-match. Considerably more trial-and-error filtering was required. The result appears plausible, but an error check is, of course, impossible. ?? 1990 Kluwer Academic Publishers.

Investigating the wetting behavior of a surface with periodic reentrant structures using integrated microresonators

NASA Astrophysics Data System (ADS)

Klingel, S.; Oesterschulze, E.

2017-08-01

The apparent contact angle is frequently used as an indicator of the wetting state of a surface in contact with a liquid. However, the apparent contact angle is subject to hysteresis that depends furthermore strongly on both the material properties and the roughness and structure of the sample surface. In this work, we show that integrated microresonators can be exploited to determine the wetting state by measuring both the frequency shift caused by the hydrodynamic mass of the liquid and the change in the quality factor as a result of damping. For this, we integrated electrically driven hybrid bridge resonators (HBRs) into a periodically structured surface intended for wetting experiments. We could clearly differentiate between the Wenzel state and the Cassie-Baxter state because the resonant frequency and quality factor of the HBR changed by over 35% and 40%, respectively. This offers the capability to unambiguously distinguish between the different wetting states.

Optical superimposed vortex beams generated by integrated holographic plates with blazed grating

NASA Astrophysics Data System (ADS)

Zhang, Xue-Dong; Su, Ya-Hui; Ni, Jin-Cheng; Wang, Zhong-Yu; Wang, Yu-Long; Wang, Chao-Wei; Ren, Fei-Fei; Zhang, Zhen; Fan, Hua; Zhang, Wei-Jie; Li, Guo-Qiang; Hu, Yan-Lei; Li, Jia-Wen; Wu, Dong; Chu, Jia-Ru

2017-08-01

In this paper, we demonstrate that the superposition of two vortex beams with controlled topological charges can be realized by integrating two holographic plates with blazed grating. First, the holographic plate with blazed grating was designed and fabricated by laser direct writing for generating well-separated vortex beam. Then, the relationship between the periods of blazed grating and the discrete angles of vortex beams was systemically investigated. Finally, through setting the discrete angle and different revolving direction of the holographic plates, the composite fork-shaped field was realized by the superposition of two vortex beams in a particular position. The topological charges of composite fork-shaped field (l = 1, 0, 3, and 4) depend on the topological charges of compositional vortex beams, which are well agreed with the theoretical simulation. The method opens up a wide range of opportunities and possibilities for applying in optical communication, optical manipulations, and photonic integrated circuits.

A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

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

Ohsuga, Ken; Takahashi, Hiroyuki R.

2016-02-20

We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitlymore » solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.« less

Optimized resolved rate control of seven-degree-of-freedom Laboratory Telerobotic Manipulator (LTM) with application to three-dimensional graphics simulation

NASA Technical Reports Server (NTRS)

Barker, L. Keith; Mckinney, William S., Jr.

1989-01-01

The Laboratory Telerobotic Manipulator (LTM) is a seven-degree-of-freedom robot arm. Two of the arms were delivered to Langley Research Center for ground-based research to assess the use of redundant degree-of-freedom robot arms in space operations. Resolved-rate control equations for the LTM are derived. The equations are based on a scheme developed at the Oak Ridge National Laboratory for computing optimized joint angle rates in real time. The optimized joint angle rates actually represent a trade-off, as the hand moves, between small rates (least-squares solution) and those rates which work toward satisfying a specified performance criterion of joint angles. In singularities where the optimization scheme cannot be applied, alternate control equations are devised. The equations developed were evaluated using a real-time computer simulation to control a 3-D graphics model of the LTM.

The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy

NASA Astrophysics Data System (ADS)

Li, Chunxia; Li, Shi-Hao

2018-06-01

This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable hierarchy with the help of orthogonal polynomial theory and Toda-type equations. Starting from the symmetric reduction in Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the τ -function of the CKP hierarchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.

Soliton solutions, stability analysis and conservation laws for the brusselator reaction diffusion model with time- and constant-dependent coefficients

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Isa Aliyu, Aliyu; Hashemi, M. S.

2018-05-01

This paper studies the brusselator reaction diffusion model (BRDM) with time- and constant-dependent coefficients. The soliton solutions for BRDM with time-dependent coefficients are obtained via first integral (FIM), ansatz, and sine-Gordon expansion (SGEM) methods. Moreover, it is well known that stability analysis (SA), symmetry analysis and conservation laws (CLs) give several information for modelling a system of differential equations (SDE). This is because they can be used for investigating the internal properties, existence, uniqueness and integrability of different SDE. For this reason, we investigate the SA via linear stability technique, symmetry analysis and CLs for BRDM with constant-dependent coefficients in order to extract more physics and information on the governing equation. The constraint conditions for the existence of the solutions are also examined. The new solutions obtained in this paper can be useful for describing the concentrations of diffusion problems of the BRDM. It is shown that the examined dependent coefficients are some of the factors that are affecting the diffusion rate. So, the present paper provides much motivational information in comparison to the existing results in the literature.

The derivation of vector magnetic fields from Stokes profiles - Integral versus least squares fitting techniques

NASA Technical Reports Server (NTRS)

Ronan, R. S.; Mickey, D. L.; Orrall, F. Q.

1987-01-01

The results of two methods for deriving photospheric vector magnetic fields from the Zeeman effect, as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA), are compared. The first method does not take magnetooptical effects into account, but determines the vector magnetic field from the integral properties of the Stokes profiles. The second method is an iterative least-squares fitting technique which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. For sunspot fields above about 1500 gauss, the two methods are found to agree in derived azimuthal and inclination angles to within about + or - 20 deg.

Numerical study of delta wing leading edge blowing

NASA Technical Reports Server (NTRS)

Yeh, David; Tavella, Domingo; Roberts, Leonard

1988-01-01

Spanwise and tangential leading edge blowing as a means of controlling the position and strength of the leading edge vortices are studied by numerical solution of the three-dimensional Navier-Stokes equations. The leading edge jet is simulated by defining a permeable boundary, corresponding to the jet slot, where suitable boundary conditions are implemented. Numerical results are shown to compare favorably with experimental measurements. It is found that the use of spanwise leading edge blowing at moderate angle of attack magnifies the size and strength of the leading edge vortices, and moves the vortex cores outboard and upward. The increase in lift primarily comes from the greater nonlinear vortex lift. However, spanwise blowing causes earlier vortex breakdown, thus decreasing the stall angle. The effects of tangential blowing at low to moderate angles of attack tend to reduce the pressure peaks associated with leading edge vortices and to increase the suction peak around the leading edge, so that the integrated value of the surface pressure remains about the same. Tangential leading edge blowing in post-stall conditions is shown to re-establish vortical flow and delay vortex bursting, thus increasing C sub L sub max and stall angle.

A unified model for transfer alignment at random misalignment angles based on second-order EKF

NASA Astrophysics Data System (ADS)

Cui, Xiao; Mei, Chunbo; Qin, Yongyuan; Yan, Gongmin; Liu, Zhenbo

2017-04-01

In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles.

A time-domain Kirchhoff formula for the convective acoustic wave equation

NASA Astrophysics Data System (ADS)

Ghorbaniasl, Ghader; Siozos-Rousoulis, Leonidas; Lacor, Chris

2016-03-01

Kirchhoff's integral method allows propagated sound to be predicted, based on the pressure and its derivatives in time and space obtained on a data surface located in the linear flow region. Kirchhoff's formula for noise prediction from high-speed rotors and propellers suffers from the limitation of the observer located in uniform flow, thus requiring an extension to arbitrarily moving media. This paper presents a Kirchhoff formulation for moving surfaces in a uniform moving medium of arbitrary configuration. First, the convective wave equation is derived in a moving frame, based on the generalized functions theory. The Kirchhoff formula is then obtained for moving surfaces in the time domain. The formula has a similar form to the Kirchhoff formulation for moving surfaces of Farassat and Myers, with the presence of additional terms owing to the moving medium effect. The equation explicitly accounts for the influence of mean flow and angle of attack on the radiated noise. The formula is verified by analytical cases of a monopole source located in a moving medium.

Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

NASA Astrophysics Data System (ADS)

Kitzmann, D.; Bolte, J.; Patzer, A. B. C.

2016-11-01

The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case owing to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.

A numerical method for computing unsteady 2-D boundary layer flows

NASA Technical Reports Server (NTRS)

Krainer, Andreas

1988-01-01

A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.

Time dependent shear stress and temperature distribution over an insulated flat plate moving at hypersonic speed.

NASA Technical Reports Server (NTRS)

Rodkiewicz, C. M.; Gupta, R. N.

1971-01-01

The laminar two-dimensional flow over a stepwise accelerated flat plate moving with hypersonic speed at zero angle of attack is analysed. The governing equations in the self-similar form are linearized and solved numerically for small times. The solutions obtained are the deviations of the velocity and the temperature profiles from those of steady state. The presented results may be used to find the first order boundary layer induced pressure on the plate.

Fiber-dependent deautonomization of integrable 2D mappings and discrete Painlevé equations

NASA Astrophysics Data System (ADS)

Carstea, Adrian Stefan; Dzhamay, Anton; Takenawa, Tomoyuki

2017-10-01

It is well known that two-dimensional mappings preserving a rational elliptic fibration, like the Quispel-Roberts-Thompson mappings, can be deautonomized to discrete Painlevé equations. However, the dependence of this procedure on the choice of a particular elliptic fiber has not been sufficiently investigated. In this paper we establish a way of performing the deautonomization for a pair of an autonomous mapping and a fiber. Starting from a single autonomous mapping but varying the type of a chosen fiber, we obtain different types of discrete Painlevé equations using this deautonomization procedure. We also introduce a technique for reconstructing a mapping from the knowledge of its induced action on the Picard group and some additional geometric data. This technique allows us to obtain factorized expressions of discrete Painlevé equations, including the elliptic case. Further, by imposing certain restrictions on such non-autonomous mappings we obtain new and simple elliptic difference Painlevé equations, including examples whose symmetry groups do not appear explicitly in Sakai’s classification.

Theory of ice-skating

NASA Astrophysics Data System (ADS)

Le Berre, Martine; Pomeau, Yves

2015-10-01

Almost frictionless skating on ice relies on a thin layer of melted water insulating mechanically the blade of the skate from ice. Using the basic equations of fluid mechanics and Stefan law, we derive a set of two coupled equations for the thickness of the film and the length of contact, a length scale which cannot be taken as its value at rest. The analytical study of these equations allows to define a small a-dimensional parameter depending on the longitudinal coordinate which can be neglected everywhere except close to the contact points at the front and the end of the blade, where a boundary layer solution is given. This solution provides without any calculation the order of magnitude of the film thickness, and its dependence with respect to external parameters like the velocity and mass of the skater and the radius of profile and bite angle of the blade, in good agreement with the numerical study. Moreover this solution also shows that a lubricating water layer of macroscopic thickness always exists for standard values of ice skating data, contrary to what happens in the case of cavitation of droplets due to thermal heating (Leidenfrost effect).

A fresh look at the catenary

NASA Astrophysics Data System (ADS)

Behroozi, F.

2014-09-01

A hanging chain takes the familiar form known as the catenary which is one of the most ubiquitous curves students encounter in their daily life. Yet most introductory physics and mathematics texts ignore the subject entirely. In more advanced texts the catenary equation is usually derived as an application of the calculus of variations. Although the variational approach is mathematically elegant, it is suitable for more advanced students. Here we derive the catenary equation in special and rectangular coordinates by considering the equilibrium conditions for an element of the hanging chain and without resorting to the calculus of variations. One advantage of this approach is its simplicity which makes it accessible to undergraduate students; another is the concurrent derivation of a companion equation which gives the tension along the chain. These solutions provide an excellent opportunity for undergraduates to explore the underlying physics. One interesting result is that the shape of a hanging chain does not depend on its linear mass density or on the strength of the gravitational field. Therefore, within a scale factor, all catenaries are copies of the same universal curve. We give the functional dependence of the scale factor on the length and terminal angle of the hanging chain.

Persisting roughness when deposition stops.

PubMed

Schwartz, Moshe; Edwards, S F

2004-12-01

Useful theories for growth of surfaces under random deposition of material have been developed by several authors. The simplest theory is that introduced by Edwards and Wilkinson (EW), which is linear and soluble. Its nonlinear generalization by Kardar, Parisi, and Zhang (KPZ) resulted in many subsequent studies. Yet both EW and KPZ theories contain an unphysical feature. When deposition of material is stopped, both theories predict that as time tends to infinity, the surface becomes flat. In fact, of course, the final surface is not flat, but simply has no gradients larger than the gradient related to the angle of repose. We modify the EW and KPZ theories to accommodate this feature and study the consequences for the simpler system which is a modification of the EW equation. In spite of the fact that the equation describing the evolution of the surface is not linear, we find that the steady state in the presence of noise is not very different in the long-wavelength limit from that of the linear EW equation. The situation is quite different from that of EW when deposition stops. Initially there is still some rearrangement of the surface, but that stops as everywhere on the surface the gradient is less than that related to the angle of repose. The most interesting feature observed after deposition stops is the emergence of history-dependent steady-state distributions.

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

An investigation of the information propagation and entropy transport aspects of Stirling machine numerical simulation

NASA Technical Reports Server (NTRS)

Goldberg, Louis F.

1992-01-01

Aspects of the information propagation modeling behavior of integral machine computer simulation programs are investigated in terms of a transmission line. In particular, the effects of pressure-linking and temporal integration algorithms on the amplitude ratio and phase angle predictions are compared against experimental and closed-form analytic data. It is concluded that the discretized, first order conservation balances may not be adequate for modeling information propagation effects at characteristic numbers less than about 24. An entropy transport equation suitable for generalized use in Stirling machine simulation is developed. The equation is evaluated by including it in a simulation of an incompressible oscillating flow apparatus designed to demonstrate the effect of flow oscillations on the enhancement of thermal diffusion. Numerical false diffusion is found to be a major factor inhibiting validation of the simulation predictions with experimental and closed-form analytic data. A generalized false diffusion correction algorithm is developed which allows the numerical results to match their analytic counterparts. Under these conditions, the simulation yields entropy predictions which satisfy Clausius' inequality.

Supercritical flow past a symmetrical bicircular arc airfoil

NASA Technical Reports Server (NTRS)

Holt, Maurice; Yew, Khoy Chuah

1989-01-01

A numerical scheme is developed for computing steady supercritical flow about symmetrical airfoils, applying it to an ellipse for zero angle of attack. An algorithmic description of this new scheme is presented. Application to a symmetrical bicircular arc airfoil is also proposed. The flow field before the shock is region 1. For transonic flow, singularity can be avoided by integrating the resulting ordinary differential equations away from the body. Region 2 contains the shock which will be located by shock fitting techniques. The shock divides region 2 into supersonic and subsonic regions and there is no singularity problem in this case. The Method of Lines is used in this region and it is advantageous to integrate the resulting ordinary differential equation along the body for shock fitting. Coaxial coordinates have to be used for the bicircular arc airfoil so that boundary values on the airfoil body can be taken with one direction of the coaxial coordinates fixed. To avoid taking boundary values at + or - infinity in the coaxial co-ordinary system, approximate analytical representation of the flow field near the tips of the airfoil is proposed.

Propagation of Finite Amplitude Sound in Multiple Waveguide Modes.

NASA Astrophysics Data System (ADS)

van Doren, Thomas Walter

1993-01-01

This dissertation describes a theoretical and experimental investigation of the propagation of finite amplitude sound in multiple waveguide modes. Quasilinear analytical solutions of the full second order nonlinear wave equation, the Westervelt equation, and the KZK parabolic wave equation are obtained for the fundamental and second harmonic sound fields in a rectangular rigid-wall waveguide. It is shown that the Westervelt equation is an acceptable approximation of the full nonlinear wave equation for describing guided sound waves of finite amplitude. A system of first order equations based on both a modal and harmonic expansion of the Westervelt equation is developed for waveguides with locally reactive wall impedances. Fully nonlinear numerical solutions of the system of coupled equations are presented for waveguides formed by two parallel planes which are either both rigid, or one rigid and one pressure release. These numerical solutions are compared to finite -difference solutions of the KZK equation, and it is shown that solutions of the KZK equation are valid only at frequencies which are high compared to the cutoff frequencies of the most important modes of propagation (i.e., for which sound propagates at small grazing angles). Numerical solutions of both the Westervelt and KZK equations are compared to experiments performed in an air-filled, rigid-wall, rectangular waveguide. Solutions of the Westervelt equation are in good agreement with experiment for low source frequencies, at which sound propagates at large grazing angles, whereas solutions of the KZK equation are not valid for these cases. At higher frequencies, at which sound propagates at small grazing angles, agreement between numerical solutions of the Westervelt and KZK equations and experiment is only fair, because of problems in specifying the experimental source condition with sufficient accuracy.

Visual slant misperception and the Black-Hole landing situation

NASA Technical Reports Server (NTRS)

Perrone, J. A.

1983-01-01

A theory which explains the tendency for dangerously low approaches during night landing situations is presented. The two dimensional information at the pilot's eye contains sufficient information for the visual system to extract the angle of slant of the runway relative to the approach path. The analysis is depends upon perspective information which is available at a certain distance out from the aimpoint, to either side of the runway edgelights. Under black hole landing conditions, however, this information is not available, and it is proposed that the visual system use instead the only available information, the perspective gradient of the runway edgelights. An equation is developed which predicts the perceived approach angle when this incorrect parameter is used. The predictions are in close agreement with existing experimental data.

Wetting of a partially immersed compliant rod

NASA Astrophysics Data System (ADS)

Hui, Chung-Yuen; Jagota, Anand

2016-11-01

The force on a solid rod partially immersed in a liquid is commonly used to determine the liquid-vapor surface tension by equating the measured force required to remove the rod from the liquid to the vertical component of the liquid-vapor surface tension. Here, we study how this process is affected when the rod is compliant. For equilibrium, we enforce force and configurational energy balance, including contributions from elastic energy. We show that, in general, the contact angle does not equal that given by Young's equation. If surface stresses are tensile, the strain in the immersed part of the rod is found to be compressive and to depend only on the solid-liquid surface stress. The strain in the dry part of the rod can be either tensile or compressive, depending on a combination of parameters that we identify. We also provide results for compliant plates partially immersed in a liquid under plane strain and plane stress. Our results can be used to extract solid surface stresses from such experiments.

Influence of friction forces on the motion of VTOL aircraft during landing operations on ships at sea

NASA Technical Reports Server (NTRS)

Howard, J. C.; Chin, D. O.

1981-01-01

Equations describing the friction forces generated during landing operations on ships at sea were formulated. These forces depend on the platform reaction and the coefficient of friction. The platform reaction depends on the relative sink rate and the shock absorbing capability of the landing gear. The friction coefficient varies with the surface condition of the landing platform and the angle of yaw of the aircraft relative to the landing platform. Landings by VTOL aircraft, equipped with conventional oleopneumatic landing gears are discussed. Simplifications are introduced to reduce the complexity of the mathematical description of the tire and shock strut characteristics. Approximating the actual complicated force deflection characteristic of the tire by linear relationship is adequate. The internal friction forces in the shock strut are included in the landing gear model. A set of relatively simple equations was obtained by including only those tire and shock strut characteristics that contribute significantly to the generation of landing gear forces.

Spectral evolution of weakly nonlinear random waves: kinetic description vs direct numerical simulations

NASA Astrophysics Data System (ADS)

Annenkov, Sergei; Shrira, Victor

2016-04-01

We study numerically the long-term evolution of water wave spectra without wind forcing, using three different models, aiming at understanding the role of different sets of assumptions. The first model is the classical Hasselmann kinetic equation (KE). We employ the WRT code kindly provided by G. van Vledder. Two other models are new. As the second model, we use the generalised kinetic equation (gKE), derived without the assumption of quasi-stationarity. Thus, unlike the KE, the gKE is valid in the cases when a wave spectrum is changing rapidly (e.g. at the initial stage of evolution of a narrow spectrum). However, the gKE employs the same statistical closure as the KE. The third model is based on the Zakharov integrodifferential equation for water waves and does not depend on any statistical assumptions. Since the Zakharov equation plays the role of the primitive equation of the theory of wave turbulence, we refer to this model as direct numerical simulation of spectral evolution (DNS-ZE). For initial conditions, we choose two narrow-banded spectra with the same frequency distribution (a JONSWAP spectrum with high peakedness γ = 6) and different degrees of directionality. These spectra are from the set of observations collected in a directional wave tank by Onorato et al (2009). Spectrum A is very narrow in angle (corresponding to N = 840 in the cosN directional model). Spectrum B is initially wider in angle (corresponds to N = 24). Short-term evolution of both spectra (O(102) wave periods) has been studied numerically by Xiao et al (2013) using two other approaches (broad-band modified nonlinear Schrödinger equation and direct numerical simulation based on the high-order spectral method). We use these results to verify the initial stage of our DNS-ZE simulations. However, the advantage of the DNS-ZE method is that it allows to study long-term spectral evolution (up to O(104) periods), which was previously possible only with the KE. In the short-term evolution, we find a good agreement between our DNS-ZE results and simulations by Xiao et al (2013), both for the evolution of frequency spectra and for the directional spreading. In the long term, all three approaches demonstrate very close evolution of integral characteristics of spectra, approaching for large time the theoretical asymptotes of the self-similar stage of evolution. However, the detailed comparison of the spectral evolution shows certain notable differences. Both kinetic equations give virtually identical evolution of spectrum B, but in the case of initially nearly one-dimensional spectrum A the KE overestimates the amplitude of the spectral peak. Meanwhile, the DNS-ZE results show considerably wider spectra with less pronounced peak. There is a striking difference for the rate of spectral broadening, which is much larger for the gKE and especially for the KE, than for the DNS-ZE. We show that the rates of change of the spectra obtained with the DNS-ZE are proportional to the fourth power of nonlinearity, corresponding to the dynamical timescale of evolution, rather than the statistical timescale of both kinetic equations.

Development of a size reduction equation for woody biomass: The influence of branch wood properties on Rittinger's constant

DOE PAGES

Naimi, Ladan J.; Sokhansanj, Shahabaddine; Bi, Xiaotao; ...

2015-11-25

Size reduction is an essential but energy-intensive process for preparing biomass for conversion processes. Three well-known scaling equations (Bond, Kick, and Rittinger) are used to estimate energy input for grinding minerals and food particles. Previous studies have shown that the Rittinger equation has the best fit to predict energy input for grinding cellulosic biomass. In the Rittinger equation, Rittinger's constant (k R) is independent of the size of ground particles, yet we noted large variations in k R among similar particle size ranges. In this research, the dependence of k R on the physical structure and chemical composition of amore » number of woody materials was explored. Branches from two softwood species (Douglas fir and pine) and two hardwood species (aspen and poplar) were ground in a laboratory knife mill. The recorded data included power input, mass flow rate, and particle size before and after grinding. Nine material properties were determined: particle density, solid density (pycnometer and x-ray diffraction methods), microfibril angle, fiber coarseness, fiber length, and composition (lignin and cellulose glucan contents). The correlation matrix among the nine properties revealed high degrees of interdependence between properties. The k R value had the largest positive correlation (+0.60) with particle porosity across the species tested. As a result, particle density was strongly correlated with lignin content (0.85), microfibril angle (0.71), fiber length (0.87), and fiber coarseness (0.78). An empirical model relating k R to particle density was developed.« less

Development of a size reduction equation for woody biomass: The influence of branch wood properties on Rittinger's constant

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

Naimi, Ladan J.; Sokhansanj, Shahabaddine; Bi, Xiaotao

Size reduction is an essential but energy-intensive process for preparing biomass for conversion processes. Three well-known scaling equations (Bond, Kick, and Rittinger) are used to estimate energy input for grinding minerals and food particles. Previous studies have shown that the Rittinger equation has the best fit to predict energy input for grinding cellulosic biomass. In the Rittinger equation, Rittinger's constant (k R) is independent of the size of ground particles, yet we noted large variations in k R among similar particle size ranges. In this research, the dependence of k R on the physical structure and chemical composition of amore » number of woody materials was explored. Branches from two softwood species (Douglas fir and pine) and two hardwood species (aspen and poplar) were ground in a laboratory knife mill. The recorded data included power input, mass flow rate, and particle size before and after grinding. Nine material properties were determined: particle density, solid density (pycnometer and x-ray diffraction methods), microfibril angle, fiber coarseness, fiber length, and composition (lignin and cellulose glucan contents). The correlation matrix among the nine properties revealed high degrees of interdependence between properties. The k R value had the largest positive correlation (+0.60) with particle porosity across the species tested. As a result, particle density was strongly correlated with lignin content (0.85), microfibril angle (0.71), fiber length (0.87), and fiber coarseness (0.78). An empirical model relating k R to particle density was developed.« less

A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger-Poisson equations with discontinuous potentials

NASA Astrophysics Data System (ADS)

Lu, Tiao; Cai, Wei

2008-10-01

In this paper, we propose a high order Fourier spectral-discontinuous Galerkin method for time-dependent Schrödinger-Poisson equations in 3-D spaces. The Fourier spectral Galerkin method is used for the two periodic transverse directions and a high order discontinuous Galerkin method for the longitudinal propagation direction. Such a combination results in a diagonal form for the differential operators along the transverse directions and a flexible method to handle the discontinuous potentials present in quantum heterojunction and supperlattice structures. As the derivative matrices are required for various time integration schemes such as the exponential time differencing and Crank Nicholson methods, explicit derivative matrices of the discontinuous Galerkin method of various orders are derived. Numerical results, using the proposed method with various time integration schemes, are provided to validate the method.

RF sheaths for arbitrary B field angles

NASA Astrophysics Data System (ADS)

D'Ippolito, Daniel; Myra, James

2014-10-01

RF sheaths occur in tokamaks when ICRF waves encounter conducting boundaries and accelerate electrons out of the plasma. Sheath effects reduce the efficiency of ICRF heating, cause RF-specific impurity influxes from the edge plasma, and increase the plasma-facing component damage. The rf sheath potential is sensitive to the angle between the B field and the wall, the ion mobility and the ion magnetization. Here, we obtain a numerical solution of the non-neutral rf sheath and magnetic pre-sheath equations (for arbitrary values of these parameters) and attempt to infer the parametric dependences of the Child-Langmuir law. This extends previous work on the magnetized, immobile ion regime. An important question is how the rf sheath voltage distributes itself between sheath and pre-sheath for various B field angles. This will show how generally previous estimates of the rf sheath voltage and capacitance were reasonable, and to improve the RF sheath BC. Work supported by US DOE grants DE-FC02-05ER54823 and DE-FG02-97ER54392.

A Thermo-Optic Propagation Modeling Capability.

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

Schrader, Karl; Akau, Ron

2014-10-01

A new theoretical basis is derived for tracing optical rays within a finite-element (FE) volume. The ray-trajectory equations are cast into the local element coordinate frame and the full finite-element interpolation is used to determine instantaneous index gradient for the ray-path integral equation. The FE methodology (FEM) is also used to interpolate local surface deformations and the surface normal vector for computing the refraction angle when launching rays into the volume, and again when rays exit the medium. The method is implemented in the Matlab(TM) environment and compared to closed- form gradient index models. A software architecture is also developedmore » for implementing the algorithms in the Zemax(TM) commercial ray-trace application. A controlled thermal environment was constructed in the laboratory, and measured data was collected to validate the structural, thermal, and optical modeling methods.« less

Fluid dynamical description of relativistic nuclear collisions

NASA Technical Reports Server (NTRS)

Nix, J. R.; Strottman, D.

1982-01-01

On the basis of both a conventional relativistic nuclear fluid dynamic model and a two fluid generalization that takes into account the interpenetration of the target and projectile upon contact, collisions between heavy nuclei moving at relativistic speeds are calculated. This is done by solving the relevant equations of motion numerically in three spatial dimensions by use of particle in cell finite difference computing techniques. The effect of incorporating a density isomer, or quasistable state, in the nuclear equation of state at three times normal nuclear density, and the effect of doubling the nuclear compressibility coefficient are studied. For the reaction 20Ne + 238U at a laboratory bombarding energy per nucleon of 393 MeV, the calculated distributions in energy and angle of outgoing charged particles are compared with recent experimental data both integrated over all impact parameters and for nearly central collisions.

Comparative atmosphere structure experiment

NASA Technical Reports Server (NTRS)

Sommer, S.

1974-01-01

Atmospheric structure of outer planets as determined by pressure, temperature, and accelerometers is reviewed and results obtained from the PAET earth entry are given. In order to describe atmospheric structure, entry is divided into two regimes, high and low speed. Acceleration is then measured: from these measurements density is determined as a function of time. The equations of motion are integrated to determine velocity, flight path angle, and altitude as a function of time. Density is then determined as a function of altitude from the previous determinations of density and altitude as a function of time. Hydrostatic equilibrium was assumed to determine pressure as a function of altitude. Finally the equation of space applied to determine temperature as a function of altitude, if the mean molecular weight is known. The mean molecular weight is obtained independently from either the low speed experiment or from the composition experiments.

Λ scattering equations

NASA Astrophysics Data System (ADS)

Gomez, Humberto

2016-06-01

The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

High-frequency Born synthetic seismograms based on coupled normal modes

USGS Publications Warehouse

Pollitz, F.

2011-01-01

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

Stability of the iterative solutions of integral equations as one phase freezing criterion.

PubMed

Fantoni, R; Pastore, G

2003-10-01

A recently proposed connection between the threshold for the stability of the iterative solution of integral equations for the pair correlation functions of a classical fluid and the structural instability of the corresponding real fluid is carefully analyzed. Direct calculation of the Lyapunov exponent of the standard iterative solution of hypernetted chain and Percus-Yevick integral equations for the one-dimensional (1D) hard rods fluid shows the same behavior observed in 3D systems. Since no phase transition is allowed in such 1D system, our analysis shows that the proposed one phase criterion, at least in this case, fails. We argue that the observed proximity between the numerical and the structural instability in 3D originates from the enhanced structure present in the fluid but, in view of the arbitrary dependence on the iteration scheme, it seems uneasy to relate the numerical stability analysis to a robust one-phase criterion for predicting a thermodynamic phase transition.

Observation of quantum interferences via light-induced conical intersections in diatomic molecules

DOE PAGES

Natan, Adi; Ware, Matthew R.; Prabhudesai, Vaibhav S.; ...

2016-04-07

We observe energy-dependent angle-resolved diffraction patterns in protons from strong-field dissociation of the molecular hydrogen ion H + 2. The interference is a characteristic of dissociation around a laser-induced conical intersection (LICI), which is a point of contact between two surfaces in the dressed 2-dimensional Born-Oppenheimer potential energy landscape of a diatomic molecule in a strong laser field. The interference magnitude and angular period depend strongly on the energy difference between the initial state and the LICI, consistent with coherent diffraction around a cone-shaped potential barrier whose width and thickness depend on the relative energy of the initial state andmore » the cone apex. As a result, these findings are supported by numerical solutions of the time-dependent Schrodinger equation for similar experimental conditions.« less

Observation of quantum interferences via light-induced conical intersections in diatomic molecules

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

Natan, Adi; Ware, Matthew R.; Prabhudesai, Vaibhav S.

We observe energy-dependent angle-resolved diffraction patterns in protons from strong-field dissociation of the molecular hydrogen ion H + 2. The interference is a characteristic of dissociation around a laser-induced conical intersection (LICI), which is a point of contact between two surfaces in the dressed 2-dimensional Born-Oppenheimer potential energy landscape of a diatomic molecule in a strong laser field. The interference magnitude and angular period depend strongly on the energy difference between the initial state and the LICI, consistent with coherent diffraction around a cone-shaped potential barrier whose width and thickness depend on the relative energy of the initial state andmore » the cone apex. As a result, these findings are supported by numerical solutions of the time-dependent Schrodinger equation for similar experimental conditions.« less

Comprehensive evaluation of broad-beam transmission of patient supports from three fluoroscopy-guided interventional systems.

PubMed

DeLorenzo, Matthew C; Yang, Kai; Li, Xinhua; Liu, Bob

2018-04-01

The purpose of the study was to measure, evaluate, and model the broad-beam x-ray transmission of the patient supports from representative modern fluoroscopy-guided interventional systems, for patient skin dose calculation. Broad-beam transmission was evaluated by varying incident angle, kVp, added copper (Cu) filter, and x-ray field size for three fluoroscopy systems: General Electric (GE) Innova 4100 with Omega V table and pad, Siemens Axiom Artis with Siemens tabletop "narrow" (CARD) table and pad, and Siemens Zeego with Trumpf TruSystem 7500 table and pad. Field size was measured on the table using a lead ruler for all setups in this study. Exposure rates were measured in service mode using a calibrated Radcal 10 × 6-60 ion chamber above the patient support at the assumed skin location. Broad-beam transmission factors were calculated by the ratio of air kerma rates measured with and without a patient support in the beam path. First, angle dependency was investigated on the GE system, with the chamber at isocenter, for angles of 0°, 15°, 30°, and 40°, for a variety of kVp, added Cu filters, and for two field sizes (small and large). Second, the broad-beam transmission factor at normal incidence was evaluated for all three fluoroscopes by varying kVp, added Cu filter, and field size (small, medium, and large). An analytical equation was created to fit the data as to maximize R 2 and minimize maximum percentage difference across all measurements for each system. For all patient supports, broad-beam transmission factor increased with field size, kVp, and added Cu filtration and decreased with incident angle. Oblique incidence measurements show that the transmission decreased by about 1%, 3%, and 6% for incident angles of 15°, 30°, and 40°, respectively. The broad-beam transmission factors at 0° for the table and table plus pad ranged from 0.73 to 0.96 and from 0.59 to 0.89, respectively. The GE and Siemens transmission factors were comparable, while the Trumpf transmission factors were the lowest. The data were successfully fitted to a function of angle, field size, kVp, and added Cu filtration using nine parameters, with an average R 2 value of 0.977 and maximum percentage difference of 4.08%. This study evaluated the broad-beam transmission for three representative fluoroscopy systems and their dependency on angle, kVp, added Cu filter, and field size. The comprehensive data provided for patient support transmission will facilitate accurate calculation of peak skin dose (PSD) and may potentially be integrated into real-time and retrospective dose monitoring with access to Radiation Dose Structured Reports (RDSR) and radiation event data. © 2018 American Association of Physicists in Medicine.

Thermal convection of liquid metal in a long inclined cylinder

NASA Astrophysics Data System (ADS)

Teimurazov, Andrei; Frick, Peter

2017-11-01

The turbulent convection of low-Prandtl-number fluids (Pr=0.0083 ) in a long cylindrical cell, heated at one end face and cooled at the other, inclined to the vertical at angle β , 0 ≤β ≤π /2 with step π /20 , is studied numerically by solving the Oberbeck-Boussinesq equations with the large-eddy-simulation approach for small-scale turbulence. The cylinder length is L =5 D , where D is the diameter. The Rayleigh number, determined by the cylinder diameter, is of the order of 5 ×106 . We show that the structure of the flow strongly depends on the inclination angle. A stable large-scale circulation (LSC) slightly disturbed by small-scale turbulence exists in the horizontal cylinder. The deviation from a horizontal position provides strong amplification of both LSC and small-scale turbulence. The energy of turbulent pulsations increases monotonically with decreasing inclination angle β , matching the energy of the LSC at β ≈π /5 . The intensity of the LSC has a wide, almost flat, maximum for an inclined cylinder and slumps approaching the vertical position, in which the LSC vanishes. The dependence of the Nusselt number on the inclination angle has a maximum at β ≈7 π /20 and generally follows the dependence of the intensity of LSC on the inclination. This indicates that the total heat transport is highly determined by LSC. We examine the applicability of idealized thermal boundary conditions (BCs) for modeling a real experiment with liquid sodium flows. Therefore, the simulations are done with two types of temperature BCs: fixed face temperature and fixed heat flux. The intensity of the LSC is slightly higher in the latter case and leads to a corresponding increase of the Nusselt number and enhancement of temperature pulsations.

Secular resonances between bodies on close orbits II: prograde and retrograde orbits for irregular satellites

NASA Astrophysics Data System (ADS)

Li, Daohai; Christou, Apostolos A.

2017-09-01

In extending the analysis of the four secular resonances between close orbits in Li and Christou (Celest Mech Dyn Astron 125:133-160, 2016) (Paper I), we generalise the semianalytical model so that it applies to both prograde and retrograde orbits with a one-to-one map between the resonances in the two regimes. We propose the general form of the critical angle to be a linear combination of apsidal and nodal differences between the two orbits b_1 Δ π + b_2 Δ Ω, forming a collection of secular resonances in which the ones studied in Paper I are among the strongest. Test of the model in the orbital vicinity of massive satellites with physical and orbital parameters similar to those of the irregular satellites Himalia at Jupiter and Phoebe at Saturn shows that {>}20 and {>}40% of phase space is affected by these resonances, respectively. The survivability of the resonances is confirmed using numerical integration of the full Newtonian equations of motion. We observe that the lowest order resonances with b_1+|b_2|≤ 3 persist, while even higher-order resonances, up to b_1+|b_2|≥ 7, survive. Depending on the mass, between 10 and 60% of the integrated test particles are captured in these secular resonances, in agreement with the phase space analysis in the semianalytical model.

SIMULATION OF ENERGETIC PARTICLE TRANSPORT AND ACCELERATION AT SHOCK WAVES IN A FOCUSED TRANSPORT MODEL: IMPLICATIONS FOR MIXED SOLAR PARTICLE EVENTS

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

Kartavykh, Y. Y.; Dröge, W.; Gedalin, M.

2016-03-20

We use numerical solutions of the focused transport equation obtained by an implicit stochastic differential equation scheme to study the evolution of the pitch-angle dependent distribution function of protons in the vicinity of shock waves. For a planar stationary parallel shock, the effects of anisotropic distribution functions, pitch-angle dependent spatial diffusion, and first-order Fermi acceleration at the shock are examined, including the timescales on which the energy spectrum approaches the predictions of diffusive shock acceleration theory. We then consider the case that a flare-accelerated population of ions is released close to the Sun simultaneously with a traveling interplanetary shock formore » which we assume a simplified geometry. We investigate the consequences of adiabatic focusing in the diverging magnetic field on the particle transport at the shock, and of the competing effects of acceleration at the shock and adiabatic energy losses in the expanding solar wind. We analyze the resulting intensities, anisotropies, and energy spectra as a function of time and find that our simulations can naturally reproduce the morphologies of so-called mixed particle events in which sometimes the prompt and sometimes the shock component is more prominent, by assuming parameter values which are typically observed for scattering mean free paths of ions in the inner heliosphere and energy spectra of the flare particles which are injected simultaneously with the release of the shock.« less

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

NASA Astrophysics Data System (ADS)

Mishchenko, M. I.

2010-12-01

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

Generalized Case ``Van Kampen theory for electromagnetic oscillations in a magnetized plasma

NASA Astrophysics Data System (ADS)

Bairaktaris, F.; Hizanidis, K.; Ram, A. K.

2017-10-01

The Case-Van Kampen theory is set up to describe electrostatic oscillations in an unmagnetized plasma. Our generalization to electromagnetic oscillations in magnetized plasma is formulated in the relativistic position-momentum phase space of the particles. The relativistic Vlasov equation includes the ambient, homogeneous, magnetic field, and space-time dependent electromagnetic fields that satisfy Maxwell's equations. The standard linearization technique leads to an equation for the perturbed distribution function in terms of the electromagnetic fields. The eigenvalues and eigenfunctions are obtained from three integrals `` each integral being over two different components of the momentum vector. Results connecting phase velocity, frequency, and wave vector will be presented. Supported in part by the Hellenic National Programme on Controlled Thermonuclear Fusion associated with the EUROfusion Consortium, and by DoE Grant DE-FG02-91ER-54109.

Implementation of parallel moment equations in NIMROD

NASA Astrophysics Data System (ADS)

Lee, Hankyu Q.; Held, Eric D.; Ji, Jeong-Young

2017-10-01

As collisionality is low (the Knudsen number is large) in many plasma applications, kinetic effects become important, particularly in parallel dynamics for magnetized plasmas. Fluid models can capture some kinetic effects when integral parallel closures are adopted. The adiabatic and linear approximations are used in solving general moment equations to obtain the integral closures. In this work, we present an effort to incorporate non-adiabatic (time-dependent) and nonlinear effects into parallel closures. Instead of analytically solving the approximate moment system, we implement exact parallel moment equations in the NIMROD fluid code. The moment code is expected to provide a natural convergence scheme by increasing the number of moments. Work in collaboration with the PSI Center and supported by the U.S. DOE under Grant Nos. DE-SC0014033, DE-SC0016256, and DE-FG02-04ER54746.

Shuttle program: Ground tracking data program document shuttle OFT launch/landing

NASA Technical Reports Server (NTRS)

Lear, W. M.

1977-01-01

The equations for processing ground tracking data during a space shuttle ascent or entry, or any nonfree flight phase of a shuttle mission are given. The resulting computer program processes data from up to three stations simultaneously: C-band station number 1; C-band station number 2; and an S-band station. The C-band data consists of range, azimuth, and elevation angle measurements. The S-band data consists of range, two angles, and integrated Doppler data in the form of cycle counts. A nineteen element state vector is used in Kalman filter to process the measurements. The acceleration components of the shuttle are taken to be independent exponentially-correlated random variables. Nine elements of the state vector are the measurement bias errors associated with range and two angles for each tracking station. The biases are all modeled as exponentially-correlated random variables with a typical time constant of 108 seconds. All time constants are taken to be the same for all nine state variables. This simplifies the logic in propagating the state error covariance matrix ahead in time.

Effects of RF profile on precision of quantitative T2 mapping using dual-echo steady-state acquisition.

PubMed

Wu, Pei-Hsin; Cheng, Cheng-Chieh; Wu, Ming-Long; Chao, Tzu-Cheng; Chung, Hsiao-Wen; Huang, Teng-Yi

2014-01-01

The dual echo steady-state (DESS) sequence has been shown successful in achieving fast T2 mapping with good precision. Under-estimation of T2, however, becomes increasingly prominent as the flip angle decreases. In 3D DESS imaging, therefore, the derived T2 values would become a function of the slice location in the presence of non-ideal slice profile of the excitation RF pulse. Furthermore, the pattern of slice-dependent variation in T2 estimates is dependent on the RF pulse waveform. Multi-slice 2D DESS imaging provides better inter-slice consistency, but the signal intensity is subject to integrated effects of within-slice distribution of the actual flip angle. Consequently, T2 measured using 2D DESS is prone to inaccuracy even at the designated flip angle of 90°. In this study, both phantom and human experiments demonstrate the above phenomena in good agreement with model prediction. © 2013.

Regional Soiling Stations for PV: Soling Loss Analysis

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

TamizhMani, G.; King, B.; Venkatesan, A.

The soiling loss factor (SLF) of photovoltaic (PV) modules/system is an interplay between the dust frequency and intensity of the site, rain frequency and intensity of the site, tilt angle and height of the module installation, and wind speed and humidity of the site. The integrated area of the downward peaks of the SLF time series plots for a year provides the annual soiling loss for the system at each tilt angle. Sandia National Laboratories, in collaboration with Arizona State University, installed five regional soiling stations around the country and collected soiling loss data over a year. Four of thesemore » soiling stations are located at the U.S. Department of Energy Regional Test Centers (Florida, Albuquerque, Colorado and Vermont), while the fifth station is located at the Arizona State University Photovoltaic Reliability Lab (Arizona). This paper presents an analysis on the SLF for each test site at ten different tilt angles. Based on the analysis of a yearlong data obtained in 2015, it appears to indicate that the Arizona site experienced the highest annual soiling loss with a significant dependence on the tilt angle while the other four sites experienced a negligibly small annual soiling loss with practically no dependence on the tilt angle.« less

Radio frequency sheaths in an oblique magnetic field

DOE PAGES

Myra, James R.; D'Ippolito, Daniel A.

2015-06-01

The physics of radio-frequency (rf) sheaths near a conducting surface is studied for plasmas immersed in a magnetic field that makes an oblique angle θ with the surface. A set of one-dimensional equations is developed that describe the dynamics of the time-dependent magnetic presheath and non-neutral Debye sheath. The model employs Maxwell-Boltzmann electrons, and the magnetization and mobility of the ions is determined by the magnetic field strength, and wave frequency, respectively. The angle, θ assumed to be large enough to insure an electron-poor sheath, is otherwise arbitrary. Concentrating on the ion-cyclotron range of frequencies, the equations are solved numericallymore » to obtain the rectified (dc) voltage, the rf voltage across the sheath and the rf current flowing through the sheath. As an application of this model, the sheath voltage-current relation is used to obtain the rf sheath impedance, which in turn gives an rf sheath boundary condition for the electric field at the sheath-plasma interface that can be used in rf wave codes. In general the impedance has both resistive and capacitive contributions, and generalizes previous sheath boundary condition models. The resistive part contributes to parasitic power dissipation at the wall.« less

Cosmic ray propagation in interplanetary space

NASA Technical Reports Server (NTRS)

Voelk, H. J.

1975-01-01

The validity of the test-particle picture, the approximation of static fields, and the spatial-diffusion approximation are discussed in a general way before specific technical assumptions are introduced. It is argued that the spatial-diffusion equation for the intensity per unit energy has a much wider range of applicability than the kinetic (Fokker-Planck) equation it is derived from. This gives strong weight to the phenomenological propagation theory. The general success (and possible failure at small energies) of the phenomenological theory for the modulation of galactic cosmic rays and solar events is described. Apparent effects such as the 'free boundary' are given disproportionate weight since they establish the connection with the detailed plasma physics of the solar wind. Greatest attention is paid to the pitch-angle diffusion theory. A general theory is presented which removes the well-known secularities of the quasi-linear approximation. The possible breakdown of any pitch-angle diffusion theory at very small energies is perhaps connected with the observed 'turn up' of the spectrum at low energies. A first attempt to derive the spatial dependence of the diffusion coefficient in the solar cavity, using such a divergence free scattering theory, is described and compared with recent observations out to 5 AU.

Spreading of blood drops over dry porous substrate: complete wetting case.

PubMed

Chao, Tzu Chieh; Arjmandi-Tash, Omid; Das, Diganta B; Starov, Victor M

2015-05-15

The process of dried blood spot sampling involves simultaneous spreading and penetration of blood into a porous filter paper with subsequent evaporation and drying. Spreading of small drops of blood, which is a non-Newtonian liquid, over a dry porous layer is investigated from both theoretical and experimental points of view. A system of two differential equations is derived, which describes the time evolution of radii of both the drop base and the wetted region inside the porous medium. The system of equations does not include any fitting parameters. The predicted time evolutions of both radii are compared with experimental data published earlier. For a given power law dependency of viscosity of blood with different hematocrit level, radii of both drop base and wetted region, and contact angle fell on three universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and the wetted region inside the porous layer and dynamic contact angle on dimensionless time. The predicted theoretical relationships are three universal curves accounting satisfactorily for the experimental data. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Scattering of elastic waves by a spheroidal inclusion

NASA Astrophysics Data System (ADS)

Johnson, Lane R.

2018-03-01

An analytical solution is presented for scattering of elastic waves by prolate and oblate spheroidal inclusions. The problem is solved in the frequency domain where separation of variables leads to a solution involving spheroidal wave functions of the angular and radial kind. Unlike the spherical problem, the boundary equations remain coupled with respect to one of the separation indices. Expanding the angular spheroidal wave functions in terms of associated Legendre functions and using their orthogonality properties leads to a set of linear equations that can be solved to simultaneously obtain solutions for all coupled modes of both scattered and interior fields. To illustrate some of the properties of the spheroidal solution, total scattering cross-sections for P, SV and SH plane waves incident at an oblique angle on a prolate spheroid, an oblate spheroid and a sphere are compared. The waveforms of the scattered field exterior to the inclusion are calculated for these same incident waves. The waveforms scattered by a spheroid are strongly dependent upon the angle of incidence, are different for incident SV and SH waves and are asymmetrical about the centre of the spheroid with the asymmetry different for prolate and oblate spheroids.

Verification of continuum drift kinetic equation solvers in NIMROD

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

Held, E. D.; Ji, J.-Y.; Kruger, S. E.

Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speedmore » coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.« less

Some exact velocity profiles for granular flow in converging hoppers

NASA Astrophysics Data System (ADS)

Cox, Grant M.; Hill, James M.

2005-01-01

Gravity flow of granular materials through hoppers occurs in many industrial processes. For an ideal cohesionless granular material, which satisfies the Coulomb-Mohr yield condition, the number of known analytical solutions is limited. However, for the special case of the angle of internal friction δ equal to ninety degrees, there exist exact parametric solutions for the governing coupled ordinary differential equations for both two-dimensional wedges and three-dimensional cones, both of which involve two arbitrary constants of integration. These solutions are the only known analytical solutions of this generality. Here, we utilize the double-shearing theory of granular materials to determine the velocity field corresponding to these exact parametric solutions for the two problems of gravity flow through converging wedge and conical hoppers. An independent numerical solution for other angles of internal friction is shown to coincide with the analytical solution.

An equilibrium method for prediction of transverse shear stresses in a thick laminated plate

NASA Technical Reports Server (NTRS)

Chaudhuri, R. Z.

1986-01-01

First two equations of equilibrium are utilized to compute the transverse shear stress variation through thickness of a thick laminated plate after in-plane stresses have been computed using an assumed quadratic displacement triangular element based on transverse inextensibility and layerwise constant shear angle theory (LCST). Centroid of the triangle is the point of exceptional accuracy for transverse shear stresses. Numerical results indicate close agreement with elasticity theory. An interesting comparison between the present theory and that based on assumed stress hybrid finite element approach suggests that the latter does not satisfy the condition of free normal traction at the edge. Comparison with numerical results obtained by using constant shear angle theory suggests that LCST is close to the elasticity solution while the CST is closer to classical (CLT) solution. It is also demonstrated that the reduced integration gives faster convergence when the present theory is applied to a thin plate.

A multidimensional finite element method for CFD

NASA Technical Reports Server (NTRS)

Pepper, Darrell W.; Humphrey, Joseph W.

1991-01-01

A finite element method is used to solve the equations of motion for 2- and 3-D fluid flow. The time-dependent equations are solved explicitly using quadrilateral (2-D) and hexahedral (3-D) elements, mass lumping, and reduced integration. A Petrov-Galerkin technique is applied to the advection terms. The method requires a minimum of computational storage, executes quickly, and is scalable for execution on computer systems ranging from PCs to supercomputers.

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

Liao, Haitao, E-mail: liaoht@cae.ac.cn

The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results inmore » an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.« less

Efficient sensitivity analysis method for chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Liao, Haitao

2016-05-01

The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.

Lattice Boltzmann simulation of immiscible displacement in the cavity with different channel configurations

NASA Astrophysics Data System (ADS)

Lou, Qin; Zang, Chenqiang; Yang, Mo; Xu, Hongtao

In this work, the immiscible displacement in a cavity with different channel configurations is studied using an improved pseudo-potential lattice Boltzmann equation (LBE) model. This model overcomes the drawback of the dependence of the fluid properties on the grid size, which exists in the original pseudo-potential LBE model. The approach is first validated by the Laplace law. Then, it is employed to study the immiscible displacement process. The influences of different factors, such as the surface wettability, the distance between the gas cavity and liquid cavity and the surface roughness of the channel are investigated. Numerical results show that the displacement efficiency increases and the displacement time decreases with the increase of the surface contact angle. On the other hand, the displacement efficiency increases with increasing distance between the gas cavity and the liquid cavity at first and finally reaches a constant value. As for the surface roughness, two structures (a semicircular cavity and a semicircular bulge) are studied. The comprehensive results show that although the displacement processes for both the structures depend on the surface wettability, they present quite different behaviors. Specially, for the roughness structure constituted by the semicircular cavity, the displacement efficiency decreases and displacement time increases evidently with the size of the semicircular cavity for the small contact angle. The trend slows down as the increase of the contact angle. Once the contact angle exceeds a certain value, the size of the semicircular cavity almost has no influence on the displacement process. While for the roughness structure of a semicircular bulge, the displacement efficiency increases with the size of bulge first and then it decreases for the small contact angle. The displacement efficiency increases first and finally reaches a constant for the large contact angle. The results also show that the displacement time has an extreme value in these cases for the small contact angles.

Exponential propagators for the Schrödinger equation with a time-dependent potential.

PubMed

Bader, Philipp; Blanes, Sergio; Kopylov, Nikita

2018-06-28

We consider the numerical integration of the Schrödinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential propagators that have shown to be highly efficient for general time-dependent Hamiltonians. We propose new CF propagators that are tailored for Hamiltonians of the said structure, showing a considerably improved performance. We obtain new fourth- and sixth-order CF propagators as well as a novel sixth-order propagator that incorporates a double commutator that only depends on coordinates, so this term can be considered as cost-free. The algorithms require the computation of the action of exponentials on a vector similar to the well-known exponential midpoint propagator, and this is carried out using the Lanczos method. We illustrate the performance of the new methods on several numerical examples.

Single and Double Photoionization of Mg

NASA Astrophysics Data System (ADS)

Abdel-Naby, Shahin; Pindzola, M. S.; Colgan, J.

2014-05-01

Single and double photoionization cross sections for Mg are calculated using a time-dependent close-coupling method. The correlation between the two 3 s subshell electrons of Mg is obtained by relaxation of the close-coupled equations in imaginary time. An implicit method is used to propagate the close-coupled equations in real time to obtain single and double ionization cross sections for Mg. Energy and angle triple differential cross sections for double photoionization at equal energy sharing of E1 =E2 = 16 . 4 eV are compared with Elettra experiments and previous theoretical calculations. This work was supported in part by grants from NSF and US DoE. Computational work was carried out at NERSC in Oakland, California, NICS in Knoxville, Tennessee, and OLCF in Oak Ridge, Tennessee.

Analytic Development of a Reference Profile for the First Entry in a Skip Atmospheric Entry

NASA Technical Reports Server (NTRS)

Garcia-Llama, Eduardo

2010-01-01

This note shows that a feasible reference drag profile for the first entry portion of a skip entry can be generated as a polynomial expression of the velocity. The coefficients of that polynomial are found through the resolution of a system composed of m + 1 equations, where m is the degree of the drag polynomial. It has been shown that a minimum of five equations (m = 4) are required to establish the range and the initial and final conditions on velocity and flight path angle. It has been shown that at least one constraint on the trajectory can be imposed through the addition of one extra equation in the system, which must be accompanied by the increase in the degree of the drag polynomial. In order to simplify the resolution of the system of equations, the drag was considered as being a probability density function of the velocity, with the velocity as a distribution function of the drag. Combining this notion with the introduction of empirically derived constants, it has been shown that the system of equations required to generate the drag profile can be successfully reduced to a system of linear algebraic equations. For completeness, the resulting drag profiles have been flown using the feedback linearization method of differential geometric control as a guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. Satisfactory results were achieved when the gains in the error dynamics were changed at a certain point along the trajectory that is dependent on the velocity and the curvature of the drag as a function of the velocity. Future work should study the capacity to update the drag profile in flight when dispersions are introduced. Also, future studies should attempt to link the first entry, as presented and controlled in this note, with a more standard control concept for the second entry, such as the Apollo entry guidance, to try to assess the overall skip entry performance. A guidance law that includes an integral feedback term, as is the case in the actual Space Shuttle entry guidance and as is proposed in Ref 29, could be tried in future studies to assess whether its use results in an improvement of the tracking performance, and to evaluate the design needs when determining the control gains.

A Comparative Study of Some Dynamic Stall Models

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Kaza, K. R. V.

1987-01-01

Three semi-empirical aerodynamic stall models are compared with respect to their lift and moment hysteresis loop prediction, limit cycle behavior, easy implementation, and feasibility in developing the parameters required for stall flutter prediction of advanced turbines. For the comparison of aeroelastic response prediction including stall, a typical section model and a plate structural model are considered. The response analysis includes both plunging and pitching motions of the blades. In model A, a correction to the angle of attack is applied when the angle of attack exceeds the static stall angle. In model B, a synthesis procedure is used for angles of attack above static stall angles and the time history effects are accounted through the Wagner function. In both models the life and moment coefficients for angle of attack below stall are obtained from tabular data for a given Mach number and angle of attack. In model C, referred to an the ONERA model, the life and moment coefficients are given in the form of two differential equations, one for angles below stall, and the other for angles above stall. The parameters of those equations are nonlinear functions of the angle of attack.

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

NASA Technical Reports Server (NTRS)

Evvard, John C

1950-01-01

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

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Stress intensity factors in bonded half planes containing inclined cracks and subjected to antiplane shear loading

NASA Technical Reports Server (NTRS)

Bassani, J. L.; Erdogan, F.

1979-01-01

The antiplane shear problem for two bonded dissimilar half planes containing a semi-infinite crack or two arbitrarily located collinear cracks is considered. For the semi-infinite crack the problem is solved for a concentrated wedge load and the stress intensity factor and the angular distribution of stresses are calculated. For finite cracks the problem is reduced to a pair of integral equations. Numerical results are obtained for cracks fully imbedded in a homogeneous medium, one crack tip touching the interface, and a crack crossing the interface for various crack angles.

An abbreviated Reynolds stress turbulence model for airfoil flows

NASA Technical Reports Server (NTRS)

Gaffney, R. L., Jr.; Hassan, H. A.; Salas, M. D.

1990-01-01

An abbreviated Reynolds stress turbulence model is presented for solving turbulent flow over airfoils. The model consists of two partial differential equations, one for the Reynolds shear stress and the other for the turbulent kinetic energy. The normal stresses and the dissipation rate of turbulent kinetic energy are computed from algebraic relationships having the correct asymptotic near wall behavior. This allows the model to be integrated all the way to the wall without the use of wall functions. Results for a flat plate at zero angle of attack, a NACA 0012 airfoil and a RAE 2822 airfoil are presented.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1974-01-01

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Contact and crack problems for an elastic wedge. [stress concentration in elastic half spaces

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.

1974-01-01

The contact and the crack problems for an elastic wedge of arbitrary angle are considered. The problem is reduced to a singular integral equation which, in the general case, may have a generalized Cauchy kernel. The singularities under the stamp as well as at the wedge apex were studied, and the relevant stress intensity factors are defined. The problem was solved for various wedge geometries and loading conditions. The results may be applicable to certain foundation problems and to crack problems in symmetrically loaded wedges in which cracks initiate from the apex.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1976-01-01

The paper deals with the plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Stress intensity factors in bonded half planes containing inclined cracks and subjected to antiplane shear loading

NASA Technical Reports Server (NTRS)

Bassani, J. L.; Erdogan, F.

1978-01-01

The antiplane shear problem for two bonded dissimilar half planes containing a semi-infinite crack or two arbitrarily located collinear cracks was considered. For the semi-infinite crack the problem was solved for a concentrated wedge load and the stress intensity factor and the angular distribution of stresses were calculated. For finite cracks the problem was reduced to a pair of integral equations. Numerical results were obtained for cracks fully imbedded in a homogeneous medium, one crack tip touching the interface, and a crack crossing the interface for various crack angles.

MOSES - Inflatable Causeway

DTIC Science & Technology

2007-08-01

Diameter ........................................................... 13 Figure 14: Braid Angle...must be resisted, and Beta which is the bias angle of the braid . This equation is specific to a fabric that is braided and not woven. Figure 14...shows what the bias angle in a braided fabric. Figure 14: Braid Angle Because braided fabrics are stronger than woven for air beams, braided

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

Obtaining the Bidirectional Transfer Distribution Function ofIsotropically Scattering Materials Using an Integrating Sphere

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

Jonsson, Jacob C.; Branden, Henrik

2006-10-19

This paper demonstrates a method to determine thebidirectional transfer distribution function (BTDF) using an integratingsphere. Information about the sample's angle dependent scattering isobtained by making transmittance measurements with the sample atdifferent distances from the integrating sphere. Knowledge about theilluminated area of the sample and the geometry of the sphere port incombination with the measured data combines to an system of equationsthat includes the angle dependent transmittance. The resulting system ofequations is an ill-posed problem which rarely gives a physical solution.A solvable system is obtained by using Tikhonov regularization on theill-posed problem. The solution to this system can then be usedmore » to obtainthe BTDF. Four bulk-scattering samples were characterised using both twogoniophotometers and the described method to verify the validity of thenew method. The agreement shown is great for the more diffuse samples.The solution to the low-scattering samples contains unphysicaloscillations, butstill gives the correct shape of the solution. Theorigin of the oscillations and why they are more prominent inlow-scattering samples are discussed.« less

Development and Application of Compatible Discretizations of Maxwell's Equations

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

White, D; Koning, J; Rieben, R

We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we havemore » designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve.« less

Review of the fundamental theories behind small angle X-ray scattering, molecular dynamics simulations, and relevant integrated application.

PubMed

Boldon, Lauren; Laliberte, Fallon; Liu, Li

2015-01-01

In this paper, the fundamental concepts and equations necessary for performing small angle X-ray scattering (SAXS) experiments, molecular dynamics (MD) simulations, and MD-SAXS analyses were reviewed. Furthermore, several key biological and non-biological applications for SAXS, MD, and MD-SAXS are presented in this review; however, this article does not cover all possible applications. SAXS is an experimental technique used for the analysis of a wide variety of biological and non-biological structures. SAXS utilizes spherical averaging to produce one- or two-dimensional intensity profiles, from which structural data may be extracted. MD simulation is a computer simulation technique that is used to model complex biological and non-biological systems at the atomic level. MD simulations apply classical Newtonian mechanics' equations of motion to perform force calculations and to predict the theoretical physical properties of the system. This review presents several applications that highlight the ability of both SAXS and MD to study protein folding and function in addition to non-biological applications, such as the study of mechanical, electrical, and structural properties of non-biological nanoparticles. Lastly, the potential benefits of combining SAXS and MD simulations for the study of both biological and non-biological systems are demonstrated through the presentation of several examples that combine the two techniques.

Path integral analysis of Jarzynski's equality: Analytical results

NASA Astrophysics Data System (ADS)

Minh, David D. L.; Adib, Artur B.

2009-02-01

We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski’s equality.

Developing interface localized liquid dielectrophoresis for optical applications

NASA Astrophysics Data System (ADS)

McHale, Glen; Brown, Carl V.; Newton, Michael I.; Wells, Gary G.; Sampara, Naresh

2012-11-01

Electrowetting charges the solid-liquid interface to change the contact area of a droplet of a conducting liquid. It is a powerful technique used to create variable focus liquid lenses, electronic paper and other devices, but it depends upon ions within the liquid. Liquid dielectrophoresis (L-DEP) is a bulk force acting on the dipoles throughout a dielectric liquid and is not normally considered to be a localized effect acting at the interface between the liquid and a solid or other fluid. In this work, we show theoretically how non-uniform electric fields generated by interdigitated electrodes can effectively convert L-DEP into an interface localized form. We show that for droplets of sufficient thickness, the change in the cosine of the contact angle is proportional to the square of the applied voltage and so obeys a similar equation to that for electrowetting - this we call dielectrowetting. However, a major difference to electrowetting is that the strength of the effect is controlled by the electrode spacing and the liquid permittivity rather than the properties of an insulator in a sandwich structure. Experimentally, we show that that this dielectrowetting equation accurately describes the contact angle of a droplet of oil viewed across parallel interdigitated electrodes. Importantly, the induced spreading can be complete, such that contact angle saturation does not occur. We then show that for thin films, L-DEP can shape the liquid-air interface creating a spatially periodic wrinkle and that such a wrinkle can be used to create a voltage programmable phase diffraction grating.

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeiste, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

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

NASA Technical Reports Server (NTRS)

Inan, U. S.; Tkalcevic, S.

1982-01-01

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

Rotation Matrix from the Mean Dynamical Equator and Equinox at J2000.0 to the ICRS

DTIC Science & Technology

2004-01-01

the ICRS is offset from its equinox by ∆o. The angle 0 is the obliquity of the ecliptic on the ICRS, that is the angle between the ICRS equator and... obliquity is caused solely by a change in the position of the pole of the mean ecliptic . Thus, the sole effect of using the rotating definition of the mean...the mean ecliptic as determined by Chapront et al. from LLR observations (23◦26′21.′′41100 ± 0.′′00005). The angle γy is the separation between the

Implications of a frame dependent gravitational effective action for perturbations on the Robertson-Walker metric

NASA Astrophysics Data System (ADS)

Adler, Stephen L.

In earlier work we showed that a frame dependent effective action motivated by the postulates of three-space general coordinate invariance and Weyl scaling invariance exactly mimics a cosmological constant in Robertson-Walker (RW) spacetimes. Here we study the implications of this effective action for small fluctuations around a spatially flat RW background geometry. The equations for the conserving extension of the modified stress-energy tensor can be integrated in closed form, and involve only the metric perturbation h00. Hence the equations for tensor and vector perturbations are unmodified, but there are Hubble scale additions to the scalar perturbation equations, which nonetheless admit no propagating wave solutions. Consequently, there are no modifications to standard gravitational wave propagation theory, but there may be observable implications for cosmology. We give a self-contained discussion, including an analysis of the restricted class of gauge transformations that act when a frame dependent effective action is present.

Numerical method to optimize the polar-azimuthal orientation of infrared superconducting-nanowire single-photon detectors.

PubMed

Csete, Mária; Sipos, Áron; Najafi, Faraz; Hu, Xiaolong; Berggren, Karl K

2011-11-01

A finite-element method for calculating the illumination-dependence of absorption in three-dimensional nanostructures is presented based on the radio frequency module of the Comsol Multiphysics software package (Comsol AB). This method is capable of numerically determining the optical response and near-field distribution of subwavelength periodic structures as a function of illumination orientations specified by polar angle, φ, and azimuthal angle, γ. The method was applied to determine the illumination-angle-dependent absorptance in cavity-based superconducting-nanowire single-photon detector (SNSPD) designs. Niobium-nitride stripes based on dimensions of conventional SNSPDs and integrated with ~ quarter-wavelength hydrogen-silsesquioxane-filled nano-optical cavity and covered by a thin gold film acting as a reflector were illuminated from below by p-polarized light in this study. The numerical results were compared to results from complementary transfer-matrix-method calculations on composite layers made of analogous film-stacks. This comparison helped to uncover the optical phenomena contributing to the appearance of extrema in the optical response. This paper presents an approach to optimizing the absorptance of different sensing and detecting devices via simultaneous numerical optimization of the polar and azimuthal illumination angles. © 2011 Optical Society of America

Fluid-structure interaction of a rolling restrained body of revolution at high angles of attack

NASA Astrophysics Data System (ADS)

Degani, D.; Ishay, M.; Gottlieb, O.

2017-03-01

The current work investigates numerically rolling instabilities of a free-to-roll slender rigid-body of revolution placed in a wind tunnel at a high angle of attack. The resistance to the roll moment is represented by a linear torsion spring and equivalent linear damping representing friction in the bearings of a simulated wind tunnel model. The body is subjected to a three-dimensional, compressible, laminar flow. The full Navier-Stokes equations are solved using the second-order implicit finite difference Beam-Warming scheme, adapted to a curvilinear coordinate system, whereas the coupled structural second order equation of motion for roll is solved by a fourth-order Runge-Kutta method. The body consists of a 3.5-diameter tangent ogive forebody with a 7.0-diameter long cylindrical afterbody extending aft of the nose-body junction to x/D = 10.5. We describe in detail the investigation of three angles of attack 20°, 40°, and 65°, at a Reynolds number of 30 000 (based on body diameter) and a Mach number of 0.2. Three distinct configurations are investigated as follows: a fixed body, a free-to-roll body with a weak torsion spring, and a free-to-roll body with a strong torsion spring. For each angle of attack the free-to-roll configuration portrays a distinct and different behavior pattern, including bi-stable limit-cycle oscillations. The bifurcation structure incorporates both large and small amplitude periodic roll oscillations where the latter lose their periodicity with increasing stiffness of the restraining spring culminating with distinct quasiperiodic oscillations. We note that removal of an applied upstream disturbance for a restrained body does not change the magnitude or complexity of the oscillations or of the flow patterns along the body. Depending on structure characteristics and flow conditions even a small rolling moment coefficient at the relatively low angle of attack of 20° may lead to large amplitude resonant roll oscillations.

Properties of multivariable root loci. M.S. Thesis

NASA Technical Reports Server (NTRS)

Yagle, A. E.

1981-01-01

Various properties of multivariable root loci are analyzed from a frequency domain point of view by using the technique of Newton polygons, and some generalizations of the SISO root locus rules to the multivariable case are pointed out. The behavior of the angles of arrival and departure is related to the Smith-MacMillan form of G(s) and explicit equations for these angles are obtained. After specializing to first order and a restricted class of higher order poles and zeros, some simple equations for these angles that are direct generalizations of the SISO equations are found. The unusual behavior of root loci on the real axis at branch points is studied. The SISO root locus rules for break-in and break-out points are shown to generalize directly to the multivariable case. Some methods for computing both types of points are presented.

Refractive index of dark-adapted bacteriorhodopsin and tris(hydroxymethyl)aminomethane buffer between 390 and 880 nm.

PubMed

Heiner, Zsuzsanna; Osvay, Károly

2009-08-10

The refractivity of wild-type bacteriorhodopsin (bR(WT)) suspended in tris(hydroxymethyl)aminomethane (TRIS) buffer has been measured in the spectral range of 390-840 nm by the method of angle of minimal deviation with the use of a hollow glass prism. The refractive indices of pure bR(WT) as well as of TRIS buffer have been determined from the concentration dependent refraction values. Sellmeier-type dispersion equations have been fitted for both the TRIS buffer and pure bR(WT).

Dark matter at DeepCore and IceCube

NASA Astrophysics Data System (ADS)

Barger, V.; Gao, Y.; Marfatia, D.

2011-03-01

With the augmentation of IceCube by DeepCore, the prospect for detecting dark matter annihilation in the Sun is much improved. To complement this experimental development, we provide a thorough template analysis of the particle physics issues that are necessary to precisely interpret the data. Our study is about nitty-gritty and is intended as a framework for detailed work on a variety of dark matter candidates. To accurately predict the source neutrino spectrum, we account for spin-correlations of the final state particles and the helicity-dependence of their decays, and absorption effects at production. We fully treat the propagation of neutrinos through the Sun, including neutrino oscillations, energy losses and tau regeneration. We simulate the survival probability of muons produced in the Earth by using the Muon Monte Carlo program, reproduce the published IceCube effective area, and update the parameters in the differential equation that approximates muon energy losses. To evaluate the zenith-angle dependent atmospheric background event rate, we track the Sun and determine the time it spends at each zenith-angle. Throughout, we employ neutralino dark matter as our example.

An investigation of dynamic-analysis methods for variable-geometry structures

NASA Technical Reports Server (NTRS)

Austin, F.

1980-01-01

Selected space structure configurations were reviewed in order to define dynamic analysis problems associated with variable geometry. The dynamics of a beam being constructed from a flexible base and the relocation of the completed beam by rotating the remote manipulator system about the shoulder joint were selected. Equations of motion were formulated in physical coordinates for both of these problems, and FORTRAN programs were developed to generate solutions by numerically integrating the equations. These solutions served as a standard of comparison to gauge the accuracy of approximate solution techniques that were developed and studied. Good control was achieved in both problems. Unstable control system coupling with the system flexibility did not occur. An approximate method was developed for each problem to enable the analyst to investigate variable geometry effects during a short time span using standard fixed geometry programs such as NASTRAN. The average angle and average length techniques are discussed.

Conical Euler solution for a highly-swept delta wing undergoing wing-rock motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

Modifications to an unsteady conical Euler code for the free-to-roll analysis of highly-swept delta wings are described. The modifications involve the addition of the rolling rigid-body equation of motion for its simultaneous time-integration with the governing flow equations. The flow solver utilized in the Euler code includes a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization on an unstructured mesh made up of triangles. Steady and unsteady results are presented for a 75 deg swept delta wing at a freestream Mach number of 1.2 and an angle of attack of 30 deg. The unsteady results consist of forced harmonic and free-to-roll calculations. The free-to-roll case exhibits a wing rock response produced by unsteady aerodynamics consistent with the aerodynamics of the forced harmonic results. Similarities are shown with a wing-rock time history from a low-speed wind tunnel test.

Electron collisions with ethylene

NASA Astrophysics Data System (ADS)

Panajotovic, R.; Kitajima, M.; Tanaka, H.; Jelisavcic, M.; Lower, J.; Campbell, L.; Brunger, M. J.; Buckman, S. J.

2003-04-01

We have measured absolute elastic scattering and vibrational excitation cross sections for electron impact on ethylene. The experimental data have been obtained on two different crossed-beam electron spectrometers and they cover the energy range from 1 to 100 eV and scattering angles between 10° and 130°. Both differential (in angle) and energy-dependent cross sections have been measured. The differential cross sections have also been analysed using a molecular phase shift analysis technique in order to derive the integral elastic and elastic momentum transfer cross sections. Comparison is made with earlier data, where available, and also with a number of recent theoretical calculations.

Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

NASA Astrophysics Data System (ADS)

Berkeley, George; Igonin, Sergei

2016-07-01

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita-Itoh-Bogoyavlensky, Toda, and Adler-Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new.

Obliquity of the Ecliptic

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

The angle between the planes of the ecliptic and the equator. On the celestial sphere, the angle at which the ecliptic intersects the celestial equator. The current (year 2000) value of the obliquity of ecliptic, which is denoted by the symbol ɛ, is 23° 26' 21''. Its value varies by ±9'' over a period of 18.6 years as a consequence of a phenomenon called nutation. Over a much longer period (abou...

Differential equations in airplane mechanics

NASA Technical Reports Server (NTRS)

Carleman, M T

1922-01-01

In the following report, we will first draw some conclusions of purely theoretical interest, from the general equations of motion. At the end, we will consider the motion of an airplane, with the engine dead and with the assumption that the angle of attack remains constant. Thus we arrive at a simple result, which can be rendered practically utilizable for determining the trajectory of an airplane descending at a constant steering angle.