Hamiltonian thermodynamics of three-dimensional dilatonic black holes

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

Dias, Goncalo A. S.; Lemos, Jose P. S.

2008-08-15

The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free {omega} parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcationmore » 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates (M,P{sub M}), M being the mass parameter and P{sub M} its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

The analytical solution of the problem of a shock focusing in a gas for one-dimensional case

NASA Astrophysics Data System (ADS)

Shestakovskaya, E. S.; Magazov, F. G.

2018-03-01

The analytical solution of the problem of an imploding shock wave in the vessel with an impermeable wall is constructed for the cases of planar, cylindrical and spherical symmetry. The negative velocity is set at the vessel boundary. The velocity of cold ideal gas is zero. At the initial time the shock spreads from this point into the center of symmetry. The boundary moves under the particular law which conforms to the movement of the shock. In Euler variables it moves but in Lagrangian variables its trajectory is a vertical line. Equations that determine the structure of the gas flow between the shock front and the boundary as a function of time and the Lagrangian coordinate as well as the dependence of the entropy on the shock wave velocity are obtained. Self-similar coefficients and corresponding critical values of self-similar coordinates were found for a wide range of adiabatic index. The problem is solved for Lagrangian coordinates.

Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates

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

Mezzacappa, Anthony; Endeve, Eirik; Hauck, Cory D.

We extend the positivity-preserving method of Zhang & Shu [49] to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibrium transport problems in general relativity and also in science and engineering applications with specific geometries. The method achieves high-order accuracy using Discontinuous Galerkin (DG) discretization of phase space and strong stabilitypreserving, Runge-Kutta (SSP-RK) time integration. Special care in taken to ensure that the method preserves strict bounds for the phase space distribution function f; i.e., f ϵ [0, 1]. The combination of suitable CFL conditions and themore » use of the high-order limiter proposed in [49] is su cient to ensure positivity of the distribution function. However, to ensure that the distribution function satisfies the upper bound, the discretization must, in addition, preserve the divergencefree property of the phase space ow. Proofs that highlight the necessary conditions are presented for general curvilinear coordinates, and the details of these conditions are worked out for some commonly used coordinate systems (i.e., spherical polar spatial coordinates in spherical symmetry and cylindrical spatial coordinates in axial symmetry, both with spherical momentum coordinates). Results from numerical experiments - including one example in spherical symmetry adopting the Schwarzschild metric - demonstrate that the method achieves high-order accuracy and that the distribution function satisfies the maximum principle.« less

Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

Effect of the refractive index on the hawking temperature: an application of the Hamilton-Jacobi method

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

Sakalli, I., E-mail: izzet.sakalli@emu.edu.tr; Mirekhtiary, S. F., E-mail: fatemeh.mirekhtiary@emu.edu.tr

2013-10-15

Hawking radiation of a non-asymptotically flat 4-dimensional spherically symmetric and static dilatonic black hole (BH) via the Hamilton-Jacobi (HJ) method is studied. In addition to the naive coordinates, we use four more different coordinate systems that are well-behaved at the horizon. Except for the isotropic coordinates, direct computation by the HJ method leads to the standard Hawking temperature for all coordinate systems. The isotropic coordinates allow extracting the index of refraction from the Fermat metric. It is explicitly shown that the index of refraction determines the value of the tunneling rate and its natural consequence, the Hawking temperature. The isotropicmore » coordinates in the conventional HJ method produce a wrong result for the temperature of the linear dilaton. Here, we explain how this discrepancy can be resolved by regularizing the integral possessing a pole at the horizon.« less

Spherical-shell boundaries for two-dimensional compressible convection in a star

NASA Astrophysics Data System (ADS)

Pratt, J.; Baraffe, I.; Goffrey, T.; Geroux, C.; Viallet, M.; Folini, D.; Constantino, T.; Popov, M.; Walder, R.

2016-10-01

Context. Studies of stellar convection typically use a spherical-shell geometry. The radial extent of the shell and the boundary conditions applied are based on the model of the star investigated. We study the impact of different two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from an established one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star, like our sun at 106 years of age. Aims: We analyze how the radial extent of the spherical shell changes the convective dynamics that result in the deep interior of the young sun model, far from the surface. In the near-surface layers, simple small-scale convection develops from the profiles of temperature and density. A central radiative zone below the convection zone provides a lower boundary on the convection zone. The inclusion of either of these physically distinct layers in the spherical shell can potentially affect the characteristics of deep convection. Methods: We perform hydrodynamic implicit large eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over tens or even hundreds of convective turnover times, permitting the collection of well-converged statistics. Results: To measure the impact of the spherical-shell geometry and our treatment of boundaries, we evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional stellar evolution calculations, so that our results are focused toward studies exploiting the so-called 321D link. We find that the inclusion in the spherical shell of the boundary between the radiative and convection zones decreases the amplitude of convective velocities in the convection zone. The inclusion of near-surface layers in the spherical shell can increase the amplitude of convective velocities, although the radial structure of the velocity profile established by deep convection is unchanged. The impact of including the near-surface layers depends on the speed and structure of small-scale convection in the near-surface layers. Larger convective velocities in the convection zone result in a commensurate increase in the overshooting layer width and a decrease in the convective turnover time. These results provide support for non-local aspects of convection.

Features in chemical kinetics. III. Attracting subspaces in a hyper-spherical representation of the reactive system

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

Ceccato, Alessandro; Frezzato, Diego, E-mail: diego.frezzato@unipd.it; Nicolini, Paolo

In this work, we deal with general reactive systems involving N species and M elementary reactions under applicability of the mass-action law. Starting from the dynamic variables introduced in two previous works [P. Nicolini and D. Frezzato, J. Chem. Phys. 138(23), 234101 (2013); 138(23), 234102 (2013)], we turn to a new representation in which the system state is specified in a (N × M){sup 2}-dimensional space by a point whose coordinates have physical dimension of inverse-of-time. By adopting hyper-spherical coordinates (a set of dimensionless “angular” variables and a single “radial” one with physical dimension of inverse-of-time) and by examining themore » properties of their evolution law both formally and numerically on model kinetic schemes, we show that the system evolves towards the equilibrium as being attracted by a sequence of fixed subspaces (one at a time) each associated with a compact domain of the concentration space. Thus, we point out that also for general non-linear kinetics there exist fixed “objects” on the global scale, although they are conceived in such an abstract and extended space. Moreover, we propose a link between the persistence of the belonging of a trajectory to such subspaces and the closeness to the slow manifold which would be perceived by looking at the bundling of the trajectories in the concentration space.« less

Numerical relativity in spherical coordinates with the Einstein Toolkit

NASA Astrophysics Data System (ADS)

Mewes, Vassilios; Zlochower, Yosef; Campanelli, Manuela; Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.

2018-04-01

Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes, and accretion disks. While the appearance of coordinate singularities often spoils numerical relativity simulations in spherical coordinates, especially in the absence of any symmetry assumptions, it has recently been demonstrated that these problems can be avoided if the coordinate singularities are handled analytically. This is possible with the help of a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities. In this paper we report on an implementation of this formalism in the Einstein Toolkit. We adapt the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates, to handle spherical coordinates, by providing appropriate boundary conditions at both inner and outer boundaries. We perform numerical simulations for a disturbed Kerr black hole, extract the gravitational wave signal, and demonstrate that the noise in these signals is orders of magnitude smaller when computed on spherical grids rather than Cartesian grids. With the public release of our new Einstein Toolkit thorns, our methods for numerical relativity in spherical coordinates will become available to the entire numerical relativity community.

Acoustic source localization in mixed field using spherical microphone arrays

NASA Astrophysics Data System (ADS)

Huang, Qinghua; Wang, Tong

2014-12-01

Spherical microphone arrays have been used for source localization in three-dimensional space recently. In this paper, a two-stage algorithm is developed to localize mixed far-field and near-field acoustic sources in free-field environment. In the first stage, an array signal model is constructed in the spherical harmonics domain. The recurrent relation of spherical harmonics is independent of far-field and near-field mode strengths. Therefore, it is used to develop spherical estimating signal parameter via rotational invariance technique (ESPRIT)-like approach to estimate directions of arrival (DOAs) for both far-field and near-field sources. In the second stage, based on the estimated DOAs, simple one-dimensional MUSIC spectrum is exploited to distinguish far-field and near-field sources and estimate the ranges of near-field sources. The proposed algorithm can avoid multidimensional search and parameter pairing. Simulation results demonstrate the good performance for localizing far-field sources, or near-field ones, or mixed field sources.

A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates

NASA Astrophysics Data System (ADS)

Läuter, Matthias; Giraldo, Francis X.; Handorf, Dörthe; Dethloff, Klaus

2008-12-01

A global model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation which requires both area (elements) and line (element faces) integrals. Here, we use a Rusanov numerical flux to resolve the discontinuous fluxes at the element faces. A strong stability-preserving third-order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step. The validation of the atmospheric model has been done considering standard tests from Williamson et al. [D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211-224], unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream. A convergence rate of O(Δx) was observed in the model experiments. Furthermore, a numerical experiment is presented, for which the third-order time-integration method limits the model error. Thus, the time step Δt is restricted by both the CFL-condition and accuracy demands. Conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k.

Fast calculation of low altitude disturbing gravity for ballistics

NASA Astrophysics Data System (ADS)

Wang, Jianqiang; Wang, Fanghao; Tian, Shasha

2018-03-01

Fast calculation of disturbing gravity is a key technology in ballistics while spherical cap harmonic(SCH) theory can be used to solve this problem. By using adjusted spherical cap harmonic(ASCH) methods, the spherical cap coordinates are projected into a global coordinates, then the non-integer associated Legendre functions(ALF) of SCH are replaced by integer ALF of spherical harmonics(SH). This new method is called virtual spherical harmonics(VSH) and some numerical experiment were done to test the effect of VSH. The results of earth's gravity model were set as the theoretical observation, and the model of regional gravity field was constructed by the new method. Simulation results show that the approximated errors are less than 5mGal in the low altitude range of the central region. In addition, numerical experiments were conducted to compare the calculation speed of SH model, SCH model and VSH model, and the results show that the calculation speed of the VSH model is raised one order magnitude in a small scope.

Dynamic equations for an isotropic spherical shell using the power series method and surface differential operators

NASA Astrophysics Data System (ADS)

Okhovat, Reza; Boström, Anders

2017-04-01

Dynamic equations for an isotropic spherical shell are derived by using a series expansion technique. The displacement field is split into a scalar (radial) part and a vector (tangential) part. Surface differential operators are introduced to decrease the length of all equations. The starting point is a power series expansion of the displacement components in the thickness coordinate relative to the mid-surface of the shell. By using the expansions of the displacement components, the three-dimensional elastodynamic equations yield a set of recursion relations among the expansion functions that can be used to eliminate all but the four of lowest order and to express higher order expansion functions in terms of those of lowest orders. Applying the boundary conditions on the surfaces of the spherical shell and eliminating all but the four lowest order expansion functions give the shell equations as a power series in the shell thickness. After lengthy manipulations, the final four shell equations are obtained in a relatively compact form which are given to second order in shell thickness explicitly. The eigenfrequencies are compared to exact three-dimensional theory with excellent agreement and to membrane theory.

Coordinate axes, location of origin, and redundancy for the one and two-dimensional discrete Fourier transform

NASA Technical Reports Server (NTRS)

Ioup, G. E.; Ioup, J. W.

1985-01-01

Appendix 4 of the Study of One- and Two-Dimensional Filtering and Deconvolution Algorithms for a Streaming Array Computer discusses coordinate axes, location of origin, and redundancy for the one- and two-dimensional Fourier transform for complex and real data.

Rotational stellar structures based on the Lagrangian variational principle

NASA Astrophysics Data System (ADS)

Yasutake, Nobutoshi; Fujisawa, Kotaro; Yamada, Shoichi

2017-06-01

A new method for multi-dimensional stellar structures is proposed in this study. As for stellar evolution calculations, the Heney method is the defacto standard now, but basically assumed to be spherical symmetric. It is one of the difficulties for deformed stellar-evolution calculations to trace the potentially complex movements of each fluid element. On the other hand, our new method is very suitable to follow such movements, since it is based on the Lagrange coordinate. This scheme is also based on the variational principle, which is adopted to the studies for the pasta structures inside of neutron stars. Our scheme could be a major break through for evolution calculations of any types of deformed stars: proto-planets, proto-stars, and proto-neutron stars, etc.

Generalized transformations and coordinates for static spherically symmetric general relativity

NASA Astrophysics Data System (ADS)

Hill, James M.; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Generalized transformations and coordinates for static spherically symmetric general relativity.

PubMed

Hill, James M; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Generalized transformations and coordinates for static spherically symmetric general relativity

PubMed Central

2018-01-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington–Finkelstein transformation and the Kruskal–Szekeres coordinates. PMID:29765624

Analysis of the nonlinearity of Asian summer monsoon intraseasonal variability using spherical PDFs

NASA Astrophysics Data System (ADS)

Jajcay, Nikola; Hannachi, Abdel

2013-04-01

The Asian summer monsoon (ASM) is a high-dimensional and highly complex phenomenon affecting more than one fifth of the world population. The intraseasonal component of the ASM undergoes periods of active and break phases associated respectively with enhanced and reduced rainfall over the Indian subcontinent and surroundings. In this paper the nonlinear nature of the intraseasonal monsoon variability is investigated using the leading EOFs of ERA-40 sea level pressure reanalyses field over the ASM region. The probability density function is then computed in spherical coordinates using a Epaneshnikov kernel method. Three significant modes are identified. They represent respectively (i) East - West mode with above normal sea level pressure over East China sea and below normal pressure over Himalayas, (ii) mode with above normal sea level pressure over East China sea (without compensating centre of opposite sign as in (i)) and (iii) mode with below normal sea level pressure over East China sea (same as (ii) but with opposite sign). Relationship to large scale flow are also investigated and discussed.

Designing herbicide formulation characteristics to maximize efficacy and minimize rice injury in paddy environments.

PubMed

Cryer, S A; Mann, R K; Erhardt-Zabik, S; Keeney, F N; Handy, P R

2001-06-01

Mathematical descriptors, coupled with experimental observations, are used to quantify differential uptake of an experimental herbicide in Japonica and Indica rice (Oryza sativa, non-target) and barnyardgrass (Echinochloa crus-galli, target). Partitioning, degradation, plant uptake and metabolism are described using mass-balance conservation equations in the form of kinetic approximations. Estimated environmental concentrations, governed by the pesticide formulation, are described using superimposed analytical solutions for the one-dimensional diffusion equation in spherical coordinates and by a finite difference representation of the two-dimensional diffusion equation in Cartesian coordinates. Formulation attributes from granules include active ingredient release rates, particle sizes, pesticide loading, and granule spacing. The diffusion model for pesticide transport is coupled with the compartment model to follow the fate and transport of a pesticide from its initial application location to various environmental matrices of interest. Formulation effects, partitioning and degradation in the various environmental matrices, differential plant uptake and metabolism, and dose-response information for plants are accounted for. This novel model provides a mechanism for selecting formulation delivery systems that optimize specific attributes (such as weed control or the therapeutic index) for risk-assessment procedures. In this report we describe how this methodology was used to explore the factors affecting herbicide efficacy and to define an optimal release rate for a granule formulation.

Sound field reconstruction within an entire cavity by plane wave expansions using a spherical microphone array.

PubMed

Wang, Yan; Chen, Kean

2017-10-01

A spherical microphone array has proved effective in reconstructing an enclosed sound field by a superposition of spherical wave functions in Fourier domain. It allows successful reconstructions surrounding the array, but the accuracy will be degraded at a distance. In order to extend the effective reconstruction to the entire cavity, a plane-wave basis in space domain is used owing to its non-decaying propagating characteristic and compared with the conventional spherical wave function method in a low frequency sound field within a cylindrical cavity. The sensitivity to measurement noise, the effects of the numbers of plane waves, and measurement positions are discussed. Simulations show that under the same measurement conditions, the plane wave function method is superior in terms of reconstruction accuracy and data processing efficiency, that is, the entire sound field imaging can be achieved by only one time calculation instead of translations of local sets of coefficients with respect to every measurement position into a global one. An experiment was conducted inside an aircraft cabin mock-up for validation. Additionally, this method provides an alternative possibility to recover the coefficients of high order spherical wave functions in a global coordinate system without coordinate translations with respect to local origins.

Aspherical Supernovae and Oblique Shock Breakout

NASA Astrophysics Data System (ADS)

Afsariardchi, Niloufar; Matzner, Christopher D.

2017-02-01

In an aspherical supernova explosion, shock emergence is not simultaneous and non-radial flows develop near the stellar surface. Oblique shock breakouts tend to be easily developed in compact progenitors like stripped-envelop core collapse supernovae. According to Matzner et al. (2013), non-spherical explosions develop non-radial flows that alters the observable emission and radiation of a supernova explosion. These flows can limit ejecta speed, change the distribution of matter and heat of the ejecta, suppress the breakout flash, and most importantly engender collisions outside the star. We construct a global numerical FLASH hydrodynamic simulation in a two dimensional spherical coordinate, focusing on the non-relativistic, adiabatic limit in a polytropic envelope to see how these fundamental differences affect the early light curve of core-collapse SNe.

A Numeric Study of the Dependence of the Surface Temperature of Beta-Layered Regions on Absolute Thickness

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

Ebey, Peter S.; Asaki, Thomas J.; Hoffer, James K.

2000-01-15

Beta-layering of deuterium-tritium (D-T) ice in spherical shell geometries is numerically and analytically considered to investigate the relationship between temperature differences that arise because of inner-surface perturbations and the absolute shell thickness. The calculations use dimensions based on a proposed design of an inertial confinement fusion target for use at the National Ignition Facility. The temperature differences are calculated within D-T ice shells of varying total thicknesses, and the temperature differences calculated in three dimensions are compared both to the one-dimensional results and to the expected limits in three dimensions for long- and short-wavelength surface perturbations. The three-dimensional numeric resultsmore » agree well with both the long- and short-wavelength limits; the region of crossover from short- to long-wavelength behavior is mapped out. Temperature differences due to surface perturbations are proportional to D-T layer thickness in one-dimensional systems but not in three-dimensional spherical shells. In spherical shells, surface perturbations of long wavelength give rise to temperature perturbations that are approximately proportional to the total shell thickness, while for short-wavelength perturbations, the temperature differences are inversely related to total shell thickness. In contrast to the one-dimensional result, we find that in three dimensions there is not a general relationship between shell thickness and surface temperature differences.« less

On the efficiency of treating singularities in triatomic variational vibrational computations. The vibrational states of H(+)3 up to dissociation.

PubMed

Szidarovszky, Tamás; Császár, Attila G; Czakó, Gábor

2010-08-01

Several techniques of varying efficiency are investigated, which treat all singularities present in the triatomic vibrational kinetic energy operator given in orthogonal internal coordinates of the two distances-one angle type. The strategies are based on the use of a direct-product basis built from one-dimensional discrete variable representation (DVR) bases corresponding to the two distances and orthogonal Legendre polynomials, or the corresponding Legendre-DVR basis, corresponding to the angle. The use of Legendre functions ensures the efficient treatment of the angular singularity. Matrix elements of the singular radial operators are calculated employing DVRs using the quadrature approximation as well as special DVRs satisfying the boundary conditions and thus allowing for the use of exact DVR expressions. Potential optimized (PO) radial DVRs, based on one-dimensional Hamiltonians with potentials obtained by fixing or relaxing the two non-active coordinates, are also studied. The numerical calculations employed Hermite-DVR, spherical-oscillator-DVR, and Bessel-DVR bases as the primitive radial functions. A new analytical formula is given for the determination of the matrix elements of the singular radial operator using the Bessel-DVR basis. The usually claimed failure of the quadrature approximation in certain singular integrals is revisited in one and three dimensions. It is shown that as long as no potential optimization is carried out the quadrature approximation works almost as well as the exact DVR expressions. If wave functions with finite amplitude at the boundary are to be computed, the basis sets need to meet the required boundary conditions. The present numerical results also confirm that PO-DVRs should be constructed employing relaxed potentials and PO-DVRs can be useful for optimizing quadrature points for calculations applying large coordinate intervals and describing large-amplitude motions. The utility and efficiency of the different algorithms is demonstrated by the computation of converged near-dissociation vibrational energy levels for the H molecular ion.

Casimir interaction between spheres in ( D + 1)-dimensional Minkowski spacetime

NASA Astrophysics Data System (ADS)

Teo, L. P.

2014-05-01

We consider the Casimir interaction between two spheres in ( D + 1)-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar fields. We consider combinations of Dirichlet and Neumann boundary conditions. The TGTG formula of the Casimir interaction energy is derived. The computations of the T matrices of the two spheres are straightforward. To compute the two G matrices, known as translation matrices, which relate the hyper-spherical waves in two spherical coordinate frames differ by a translation, we generalize the operator approach employed in [39]. The result is expressed in terms of an integral over Gegenbauer polynomials. In contrast to the D=3 case, we do not re-express the integral in terms of 3 j-symbols and hyper-spherical waves, which in principle, can be done but does not simplify the formula. Using our expression for the Casimir interaction energy, we derive the large separation and small separation asymptotic expansions of the Casimir interaction energy. In the large separation regime, we find that the Casimir interaction energy is of order L -2 D+3, L -2 D+1 and L -2 D-1 respectively for Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions, where L is the center-to-center distance of the two spheres. In the small separation regime, we confirm that the leading term of the Casimir interaction agrees with the proximity force approximation, which is of order , where d is the distance between the two spheres. Another main result of this work is the analytic computations of the next-to-leading order term in the small separation asymptotic expansion. This term is computed using careful order analysis as well as perturbation method. In the case the radius of one of the sphere goes to infinity, we find that the results agree with the one we derive for sphere-plate configuration. When D=3, we also recover previously known results. We find that when D is large, the ratio of the next-to-leading order term to the leading order term is linear in D, indicating a larger correction at higher dimensions. The methodologies employed in this work and the results obtained can be used to study the one-loop effective action of the system of two spherical objects in the universe.

Methods for characterizing subsurface volatile contaminants using in-situ sensors

DOEpatents

Ho, Clifford K [Albuquerque, NM

2006-02-21

An inverse analysis method for characterizing diffusion of vapor from an underground source of volatile contaminant using data taken by an in-situ sensor. The method uses one-dimensional solutions to the diffusion equation in Cartesian, cylindrical, or spherical coordinates for isotropic and homogenous media. If the effective vapor diffusion coefficient is known, then the distance from the source to the in-situ sensor can be estimated by comparing the shape of the predicted time-dependent vapor concentration response curve to the measured response curve. Alternatively, if the source distance is known, then the effective vapor diffusion coefficient can be estimated using the same inverse analysis method. A triangulation technique can be used with multiple sensors to locate the source in two or three dimensions. The in-situ sensor can contain one or more chemiresistor elements housed in a waterproof enclosure with a gas permeable membrane.

Models for the dynamics of dust-like matter in the self-gravity field: The method of hydrodynamic substitutions

NASA Astrophysics Data System (ADS)

Zhuravlev, V. M.

2017-09-01

Models for the dynamics of a dust-like medium in the self-gravity field are investigated. Solutions of the corresponding problems are constructed by the method of hydrodynamic substitutions generalizing the Cole-Hopf substitutions. The method is extended to multidimensional ideal and viscous fluid flows with cylindrical and spherical symmetries for which exact solutions are constructed. Solutions for the dynamics of self-gravitating dust with arbitrary initial distributions of both fluid density and velocity are constructed using special coordinate transformations. In particular, the problem of cosmological expansion is considered in terms of Newton's gravity theory. Models of a one-dimensional viscous dust fluid flow and some problems of gas hydrodynamics are considered. Examples of exact solutions and their brief analysis are provided.

Spherical Ethylene/Air Diffusion Flames Subject to Concentric DC Electric Field in Microgravity

NASA Technical Reports Server (NTRS)

Yuan, Z. -G.; Hegde, U.; Faeth, G. M.

2001-01-01

It is well known that microgravity conditions, by eliminating buoyant flow, enable many combustion phenomena to be observed that are not possible to observe at normal gravity. One example is the spherical diffusion flame surrounding a porous spherical burner. The present paper demonstrates that by superimposing a spherical electrical field on such a flame, the flame remains spherical so that we can study the interaction between the electric field and flame in a one-dimensional fashion. Flames are susceptible to electric fields that are much weaker than the breakdown field of the flame gases owing to the presence of ions generated in the high temperature flame reaction zone. These ions and the electric current of the moving ions, in turn, significantly change the distribution of the electric field. Thus, to understand the interplay between the electric field and the flame is challenging. Numerous experimental studies of the effect of electric fields on flames have been reported. Unfortunately, they were all involved in complex geometries of both the flow field and the electric field, which hinders detailed study of the phenomena. In a one-dimensional domain, however, the electric field, the flow field, the thermal field and the chemical species field are all co-linear. Thus the problem is greatly simplified and becomes more tractable.

Horizons versus singularities in spherically symmetric space-times

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

Bronnikov, K. A.; Elizalde, E.; Odintsov, S. D.

We discuss different kinds of Killing horizons possible in static, spherically symmetric configurations and recently classified as 'usual', 'naked', and 'truly naked' ones depending on the near-horizon behavior of transverse tidal forces acting on an extended body. We obtain the necessary conditions for the metric to be extensible beyond a horizon in terms of an arbitrary radial coordinate and show that all truly naked horizons, as well as many of those previously characterized as naked and even usual ones, do not admit an extension and therefore must be considered as singularities. Some examples are given, showing which kinds of mattermore » are able to create specific space-times with different kinds of horizons, including truly naked ones. Among them are fluids with negative pressure and scalar fields with a particular behavior of the potential. We also discuss horizons and singularities in Kantowski-Sachs spherically symmetric cosmologies and present horizon regularity conditions in terms of an arbitrary time coordinate and proper (synchronous) time. It turns out that horizons of orders 2 and higher occur in infinite proper times in the past or future, but one-way communication with regions beyond such horizons is still possible.« less

Three dimensional adaptive mesh refinement on a spherical shell for atmospheric models with lagrangian coordinates

NASA Astrophysics Data System (ADS)

Penner, Joyce E.; Andronova, Natalia; Oehmke, Robert C.; Brown, Jonathan; Stout, Quentin F.; Jablonowski, Christiane; van Leer, Bram; Powell, Kenneth G.; Herzog, Michael

2007-07-01

One of the most important advances needed in global climate models is the development of atmospheric General Circulation Models (GCMs) that can reliably treat convection. Such GCMs require high resolution in local convectively active regions, both in the horizontal and vertical directions. During previous research we have developed an Adaptive Mesh Refinement (AMR) dynamical core that can adapt its grid resolution horizontally. Our approach utilizes a finite volume numerical representation of the partial differential equations with floating Lagrangian vertical coordinates and requires resolving dynamical processes on small spatial scales. For the latter it uses a newly developed general-purpose library, which facilitates 3D block-structured AMR on spherical grids. The library manages neighbor information as the blocks adapt, and handles the parallel communication and load balancing, freeing the user to concentrate on the scientific modeling aspects of their code. In particular, this library defines and manages adaptive blocks on the sphere, provides user interfaces for interpolation routines and supports the communication and load-balancing aspects for parallel applications. We have successfully tested the library in a 2-D (longitude-latitude) implementation. During the past year, we have extended the library to treat adaptive mesh refinement in the vertical direction. Preliminary results are discussed. This research project is characterized by an interdisciplinary approach involving atmospheric science, computer science and mathematical/numerical aspects. The work is done in close collaboration between the Atmospheric Science, Computer Science and Aerospace Engineering Departments at the University of Michigan and NOAA GFDL.

Geodetic precession or dragging of inertial frames

NASA Technical Reports Server (NTRS)

Ashby, Neil; Shahid-Saless, Bahman

1989-01-01

In General Relativity, the Principle of General Covariance allows one to describe phenomena by means of any convenient choice of coordinate system. Here, it is shown that the geodetic precession of a gyroscope orbiting a spherically symmetric, nonrotating mass can be recast as a Lense-Thirring frame-dragging effect, in an appropriately chosen coordinate frame whose origin falls freely along with the gyroscope and whose spatial coordinate axes point in fixed directions.

The effects of atmospheric refraction on the accuracy of laser ranging systems

NASA Technical Reports Server (NTRS)

Zanter, D. L.; Gardner, C. S.; Rao, N. N.

1976-01-01

Correction formulas derived by Saastamoinen and Marini, and the ray traces through the refractivity profiles all assume a spherically symmetric refractivity profile. The errors introduced by this assumption were investigated by ray tracing through three-dimensional profiles. The results of this investigation indicate that the difference between ray traces through the spherically symmetric and three-dimensional profiles is approximately three centimeters at 10 deg and decreases to less than one half of a centimeter at 80 deg. If the accuracy desired in future laser ranging systems is less than a few centimeters, Saastamoinen and Marini's formulas must be altered to account for the fact that the refractivity profile is not spherically symmetric.

Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.

PubMed

Yan, Zhenya; Konotop, V V

2009-09-01

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3) space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1975-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear xi lines and by two truncating xi surfaces. The spherical mean is the average of u over a constant xi surface. Conditions on the linear differential operator, L, and on the orthogonal coordinates xi, eta, and zeta are established so that the problem for the determination of the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be reduced to a problem with only one space variable. Conditions are then established so that the spherical mean of the solution in one conical region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes

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

Dias, Goncalo A. S.; Lemos, Jose P. S.; Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa

2008-10-15

The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free {omega} parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{+-}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3), all with a Maxwell term. The Hamiltonian formalismmore » is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P{sub M};Q,P{sub Q}), where M is the mass parameter, which for {omega}<-(3/2) and for {omega}={+-}{infinity} needs a careful renormalization, P{sub M} is the conjugate momenta of M, Q is the charge parameter, and P{sub Q} is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field {phi}. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

New vibration-rotation code for tetraatomic molecules exhibiting wide-amplitude motion: WAVR4

NASA Astrophysics Data System (ADS)

Kozin, Igor N.; Law, Mark M.; Tennyson, Jonathan; Hutson, Jeremy M.

2004-11-01

A general computational method for the accurate calculation of rotationally and vibrationally excited states of tetraatomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. The program offers a choice of coordinate systems based on Radau, Jacobi, diatom-diatom and orthogonal satellite vectors. The method includes all six vibrational dimensions plus three rotational dimensions. Vibration-rotation calculations with reduced dimensionality in the radial degrees of freedom are easily tackled via constraints imposed on the radial coordinates via the input file. Program summaryTitle of program: WAVR4 Catalogue number: ADUN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUN Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: Persons requesting the program must sign the standard CPC nonprofit use license Computer: Developed under Tru64 UNIX, ported to Microsoft Windows and Sun Unix Operating systems under which the program has been tested: Tru64 Unix, Microsoft Windows, Sun Unix Programming language used: Fortran 90 Memory required to execute with typical data: case dependent No. of lines in distributed program, including test data, etc.: 11 937 No. of bytes in distributed program, including test data, etc.: 84 770 Distribution format: tar.gz Nature of physical problem: WAVR4 calculates the bound ro-vibrational levels and wavefunctions of a tetraatomic system using body-fixed coordinates based on generalised orthogonal vectors. Method of solution: The angular coordinates are treated using a finite basis representation (FBR) based on products of spherical harmonics. A discrete variable representation (DVR) [1] based on either Morse-oscillator-like or spherical-oscillator functions [2] is used for the radial coordinates. Matrix elements are computed using an efficient Gaussian quadrature in the angular coordinates and the DVR approximation in the radial coordinates. The solution of the secular problem is carried through a series of intermediate diagonalisations and truncations. Restrictions on the complexity of the problem: (1) The size of the final Hamiltonian matrix that can be practically diagonalised; (2) The DVR approximation for a radial coordinate fails for values of the coordinate near zero—this is remedied only for one radial coordinate by using analytical integration. Typical running time: problem-dependent Unusual features of the program: A user-supplied subroutine to evaluate the potential energy is a program requirement. External routines: BLAS and LAPACK are required. References: [1] J.C. Light, I.P. Hamilton, J.V. Lill, J. Chem. Phys. 92 (1985) 1400. [2] J.R. Henderson, C.R. Le Sueur, J. Tennyson, Comp. Phys. Comm. 75 (1993) 379.

Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

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

Marquette, Ian, E-mail: i.marquette@uq.edu.au; Quesne, Christiane, E-mail: cquesne@ulb.ac.be

2015-06-15

We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformedmore » oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.« less

Three dimensional lithospheric magnetization structures beneath Australia derived by inverse modeling of CHAMP satellite magnetic field model

NASA Astrophysics Data System (ADS)

Du, Jinsong; Chen, Chao; Lesur, Vincent; Li, Yaoguo; Lane, Richard; Liang, Qing; Wang, Haoran

2014-05-01

We present an inversion algorithm for magnetic anomaly data in spherical coordinates to image the three dimensional (3-D) susceptibility distributions in the lithosphere. The method assumes that remanent magnetization is absent and that the magnetic anomalies are solely the result of lateral variations in magnetic susceptibility. To take into account the curvature of the Earth, the 3-D model is comprised of a set of spherical prisms (referred to as tesseroids), each of which has a constant isotropic susceptibility. The inversion method is formulated with a specifically designed model objective function and radial weighting function in spherical coordinates. A Tikhonov regularization technique is used to obtain an optimal solution with data misfit consistent with the estimated error level. Results for regional synthetic models with different magnetized inclinations and declinations are presented to demonstrate the capability of the method to recover large scale lithospheric magnetic structures. We have applied the algoithm to study the lithospheric susceptibility structures in the Australia region using magnetic anomaly data from the GRIMM_L120v0.0 model, which is based on ten years of CHAMP satellite data. As a self-constrained inversion, the maximum depths variation of magnetization layer is estimated first and then incorporated to the three dimensional (3-D) inversion. Results showed that the susceptibility anomalies concentrate in the depth range from 25 km to 45 km, i.e., focused in the lower crust. In addition, the results showed that the susceptibilities in continental lithosphere are higher than those in oceanic lithosphere. The inverted 3-D susceptibility distribution in the region of Australia reveals significant features related to tectonics, surface heat-flux, crustal thickness and Curie isotherm depths. In general, the higher susceptibility anomalies correlate with Precambrian rocks, and the lower susceptibility anomalies correlate with younger orogenic belts, suture zones and modern uplifts. In details, the inverted susceptibility distribution shows differences in the magnetic structures between the eastern and western parts of the Yilgarn Craton, and three lower susceptibility belts from north to south in the Eromanga Basin and the Gawler Craton with high susceptibility that extend to the ocean and then to the west.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction

PubMed Central

Aganj, Iman; Lenglet, Christophe; Sapiro, Guillermo

2015-01-01

By revealing complex fiber structure through the orientation distribution function (ODF), q-ball imaging has recently become a popular reconstruction technique in diffusion-weighted MRI. In this paper, we propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order real and symmetric spherical harmonic basis, the maxima of the two-dimensional ODF lie on an analytically derived one-dimensional space, from which we can detect the ODF maxima. This method reduces the computational complexity of the maxima detection, without compromising the accuracy. We demonstrate the performance of our technique on both artificial and human brain data. PMID:20879302

Dependence of Strain Distribution on In Content in InGaN/GaN Quantum Wires and Spherical Quantum Dots

NASA Astrophysics Data System (ADS)

Sharma, Akant Sagar; Dhar, S.

2018-02-01

The distribution of strain, developed in zero-dimensional quantum spherical dots and one-dimensional cylindrical quantum wires of an InGaN/GaN system is calculated as functions of radius of the structure and indium mole fraction. The strain shows strong dependence on indium mole fraction at small distances from the center. The strain associated with both the structures is found to decrease exponentially with the increase in dot or cylinder radius and increases linearly with indium content.

Nonlinear oscillations of compact stars in the vicinity of the maximum mass configuration

NASA Astrophysics Data System (ADS)

Brillante, A.; Mishustin, I. N.

2015-07-01

We solve the dynamical GR equations for the spherically symmetric evolution of compact stars in the vicinity of the maximum mass, for which instability sets in according to linear perturbation theory. The calculations are done with the analytical Zeldovich-like EOS P=a≤ft(ρ-ρ_0\\right) and with the TM1 parametrisation of the RMF model. The initial configurations for the dynamical calculations are represented by spherical stars with equilibrium density profile, which are perturbed by either i) an artificially added inward velocity field proportional to the radial coordinate, or ii) a rarefaction corresponding to a static and expanded star. These configurations are evolved using a one-dimensional GR hydro code for ideal and barotropic fluids. Depending on the initial conditions we obtain either stable oscillations or the collapse to a black hole. The minimal amplitude of the perturbation, needed to trigger gravitational collapse is evaluated. The approximate independence of this energy on the type of perturbation is pointed out. At the threshold we find type-I critical behaviour for all stellar models considered and discuss the dependence of the time scaling exponent on the baryon mass and EOS.

A microscopy approach for in situ inspection of micro-coordinate measurement machine styli for contamination

NASA Astrophysics Data System (ADS)

Feng, Xiaobing; Pascal, Jonathan; Lawes, Simon

2017-09-01

During the process of measurement using a micro-coordinate measurement machine (µCMM) contamination gradually builds up on the surface of the stylus tip and affects the dimensional accuracy of the measurement. Regular inspection of the stylus for contamination is essential to determine the appropriate cleaning interval and prevent the dimensional error from becoming significant. However, in situ inspection of a µCMM stylus is challenging due to the size, spherical shape, material and surface properties of a typical stylus. To address this challenge, this study evaluates several non-contact measurement technologies for in situ stylus inspection and, based on those findings, proposes a cost-effective microscopy approach. The operational principle is then demonstrated by an automated prototype, coordinated directly by the CMM software MCOSMOS, with an effective threshold of detection as low as 400 nm and a large field of view and depth of field. The level of contamination on the stylus has been found to increase steadily with the number of measurement contacts made. Once excessive contamination is detected on the stylus, measurement should be stopped and a stylus cleaning procedure should be performed to avoid affecting measurement accuracy.

Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

NASA Astrophysics Data System (ADS)

Ivanov, Konstantin L.; Sadovsky, Vladimir M.; Lukzen, Nikita N.

2015-08-01

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical "microreactor," i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the "pole" of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting experimental data for magnetic field effects on RP recombination in confined space and (ii) for describing kinetics of chemical reactions, which occur predominantly on the surfaces of biomembranes, i.e., lipid peroxidation reactions.

Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

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

Ivanov, Konstantin L., E-mail: ivanov@tomo.nsc.ru; Lukzen, Nikita N.; Novosibirsk State University, Pirogova St. 2, Novosibirsk 630090

2015-08-28

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical “microreactor,” i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the “pole” of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression formore » the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting experimental data for magnetic field effects on RP recombination in confined space and (ii) for describing kinetics of chemical reactions, which occur predominantly on the surfaces of biomembranes, i.e., lipid peroxidation reactions.« less

Naked shell singularities on the brane

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

Seahra, Sanjeev S.

By utilizing nonstandard slicings of 5-dimensional Schwarzschild and Schwarzschild-AdS manifolds based on isotropic coordinates, we generate static and spherically-symmetric braneworld spacetimes containing shell-like naked null singularities. For planar slicings, we find that the brane-matter sourcing the solution is a perfect fluid with an exotic equation of state and a pressure singularity where the brane crosses the bulk horizon. From a relativistic point of view, such a singularity is required to maintain matter infinitesimally above the surface of a black hole. From the point of view of the AdS/CFT conjecture, the singular horizon can be seen as one possible quantum correctionmore » to a classical black hole geometry. Various generalizations of planar slicings are also considered for a Ricci-flat bulk, and we find that singular horizons and exotic matter distributions are common features.« less

One-dimensional Cu(II) coordination polymers containing C2h-symmetric 1,1':4',1''-terphenyl-3,3'-dicarboxylate linkers.

PubMed

Kim, Hyun Chul; Gu, Ja Min; Huh, Seong; Yo, Chul Hyun; Kim, Youngmee

2015-10-01

Two new one-dimensional Cu(II) coordination polymers (CPs) containing the C2h-symmetric terphenyl-based dicarboxylate linker 1,1':4',1''-terphenyl-3,3'-dicarboxylate (3,3'-TPDC), namely catena-poly[[bis(dimethylamine-κN)copper(II)]-μ-1,1':4',1''-terphenyl-3,3'-dicarboxylato-κ(4)O,O':O'':O'''] monohydrate], {[Cu(C20H12O4)(C2H7N)2]·H2O}n, (I), and catena-poly[[aquabis(dimethylamine-κN)copper(II)]-μ-1,1':4',1''-terphenyl-3,3'-dicarboxylato-κ(2)O(3):O(3')] monohydrate], {[Cu(C20H12O4)(C2H7N)2(H2O)]·H2O}n, (II), were both obtained from two different methods of preparation: one reaction was performed in the presence of 1,4-diazabicyclo[2.2.2]octane (DABCO) as a potential pillar ligand and the other was carried out in the absence of the DABCO pillar. Both reactions afforded crystals of different colours, i.e. violet plates for (I) and blue needles for (II), both of which were analysed by X-ray crystallography. The 3,3'-TPDC bridging ligands coordinate the Cu(II) ions in asymmetric chelating modes in (I) and in monodenate binding modes in (II), forming one-dimensional chains in each case. Both coordination polymers contain two coordinated dimethylamine ligands in mutually trans positions, and there is an additional aqua ligand in (II). The solvent water molecules are involved in hydrogen bonds between the one-dimensional coordination polymer chains, forming a two-dimensional network in (I) and a three-dimensional network in (II).

Electromagnetic cloaking in higher order spherical cloaks

NASA Astrophysics Data System (ADS)

Sidhwa, H. H.; Aiyar, R. P. R. C.; Kulkarni, S. V.

2017-06-01

The inception of transformation optics has led to the realisation of the invisibility devices for various applications, one of which is spherical cloaking. In this paper, a formulation for a higher-order spherical cloak has been proposed to reduce its physical thickness significantly by introducing a nonlinear relation between the original and transformed coordinate systems and it has been verified using the ray tracing approach. Analysis has been carried out to observe the anomalies in the variation of refractive index for higher order cloaks indicating the presence of poles in the relevant equations. Furthermore, a higher-order spherical cloak with predefined values of the material characteristics on its inner and outer surfaces has been designed for practical application.

On the Exit Boundary Condition for One-Dimensional Calculations of Pulsed Detonation Engine Performance

NASA Technical Reports Server (NTRS)

Wilson, Jack; Paxson, Daniel E.

2002-01-01

In one-dimensional calculations of pulsed detonation engine (PDE) performance, the exit boundary condition is frequently taken to be a constant static pressure. In reality, for an isolated detonation tube, after the detonation wave arrives at the exit plane, there will be a region of high pressure, which will gradually return to ambient pressure as an almost spherical shock wave expands away from the exit, and weakens. Initially, the flow is supersonic, unaffected by external pressure, but later becomes subsonic. Previous authors have accounted for this situation either by assuming the subsonic pressure decay to be a relaxation phenomenon, or by running a two-dimensional calculation first, including a domain external to the detonation tube, and using the resulting exit pressure temporal distribution as the boundary condition for one-dimensional calculations. These calculations show that the increased pressure does affect the PDE performance. In the present work, a simple model of the exit process is used to estimate the pressure decay time. The planar shock wave emerging from the tube is assumed to transform into a spherical shock wave. The initial strength of the spherical shock wave is determined from comparison with experimental results. Its subsequent propagation, and resulting pressure at the tube exit, is given by a numerical blast wave calculation. The model agrees reasonably well with other, limited, results. Finally, the model was used as the exit boundary condition for a one-dimensional calculation of PDE performance to obtain the thrust wall pressure for a hydrogen-air detonation in tubes of length to diameter ratio (L/D) of 4, and 10, as well as for the original, constant pressure boundary condition. The modified boundary condition had no performance impact for values of L/D > 10, and moderate impact for L/D = 4.

Two-dimensional Zn(II) and one-dimensional Co(II) coordination polymers based on benzene-1,4-dicarboxylate and pyridine ligands.

PubMed

Zhou, Li-Juan; Han, Chang-Bao; Wang, Yu-Ling

2016-02-01

Coordination polymers constructed from metal ions and organic ligands have attracted considerable attention owing to their diverse structural topologies and potential applications. Ligands containing carboxylate groups are among the most extensively studied because of their versatile coordination modes. Reactions of benzene-1,4-dicarboxylic acid (H2BDC) and pyridine (py) with Zn(II) or Co(II) yielded two new coordination polymers, namely, poly[(μ4-benzene-1,4-dicarboxylato-κ(4)O:O':O'':O''')(pyridine-κN)zinc(II)], [Zn(C8H4O2)(C5H5N)]n, (I), and catena-poly[aqua(μ3-benzene-1,4-dicarboxylato-κ(3)O:O':O'')bis(pyridine-κN)cobalt(II)], [Co(C8H4O2)(C5H5N)2(H2O)]n, (II). In compound (I), the Zn(II) cation is five-coordinated by four carboxylate O atoms from four BDC(2-) ligands and one pyridine N atom in a distorted square-pyramidal coordination geometry. Four carboxylate groups bridge two Zn(II) ions to form centrosymmetric paddle-wheel-like Zn2(μ2-COO)4 units, which are linked by the benzene rings of the BDC(2-) ligands to generate a two-dimensional layered structure. The two-dimensional layer is extended into a three-dimensional supramolecular structure with the help of π-π stacking interactions between the aromatic rings. Compound (II) has a one-dimensional double-chain structure based on Co2(μ2-COO)2 units. The Co(II) cations are bridged by BDC(2-) ligands and are octahedrally coordinated by three carboxylate O atoms from three BDC(2-) ligands, one water O atom and two pyridine N atoms. Interchain O-H...O hydrogen-bonding interactions link these chains to form a three-dimensional supramolecular architecture.

The effects of electron thermal radiation on laser ablative shock waves from aluminum plasma into ambient air

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

Sai Shiva, S.; Leela, Ch.; Prem Kiran, P., E-mail: premkiranuoh@gmail.com, E-mail: prem@uohyd.ac.in

2016-05-15

The effect of electron thermal radiation on 7 ns laser ablative shock waves from aluminum (Al) plasma into an ambient atmospheric air has been numerically investigated using a one-dimensional, three-temperature (electron, ion, and radiation) radiation hydrodynamic code MULTI. The governing equations in Lagrangian form are solved using an implicit scheme for planar, cylindrical, and spherical geometries. The shockwave velocities (V{sub sw}) obtained numerically are compared with our experimental values obtained over the intensity range of 2.0 × 10{sup 10} to 1.4 × 10{sup 11 }W/cm{sup 2}. It is observed that the numerically obtained V{sub sw} is significantly influenced by the thermal radiation effects which are foundmore » to be dominant in the initial stage up to 2 μs depending on the input laser energy. Also, the results are found to be sensitive to the co-ordinate geometry used in the simulation (planar, cylindrical, and spherical). Moreover, it is revealed that shock wave undergoes geometrical transitions from planar to cylindrical nature and from cylindrical to spherical nature with time during its propagation into an ambient atmospheric air. It is also observed that the spatio-temporal evolution of plasma electron and ion parameters such as temperature, specific energy, pressure, electron number density, and mass density were found to be modified significantly due to the effects of electron thermal radiation.« less

Dimensional control of supramolecular assemblies of diacetylene-derived peptide gemini amphiphile: from spherical micelles to foamlike networks.

PubMed

Jiang, Hao; Ehlers, Martin; Hu, Xiao-Yu; Zellermann, Elio; Schmuck, Carsten

2018-05-22

Peptide amphiphiles capable of assembling into multidimensional nanostructures have attracted much attention over the past decade due to their potential applications in materials science. Herein, a novel diacetylene-derived peptide gemini amphiphile with a fluorenylmethyloxycarbonyl (Fmoc) group at the N-terminus is reported to hierarchically assemble into spherical micelles, one-dimensional nanorods, two-dimensional foamlike networks and lamellae. Solvent polarity shows a remarkable effect on the self-assembled structures by changing the balance of four weak noncovalent interactions (hydrogen-bonding, π-π stacking, hydrophobic interaction, and electrostatic repulsion). We also show the time-evolution not only from spherical micelles to helical nanofibers in aqueous solution, but also from branched wormlike micelles to foamlike networks in methanol solution. In this work, the presence of the Fmoc group plays a key role in the self-assembly process. This work provides an efficient strategy for precise morphological control, aiding the future development in materials science.

Fast Fourier-based deconvolution for three-dimensional acoustic source identification with solid spherical arrays

NASA Astrophysics Data System (ADS)

Yang, Yang; Chu, Zhigang; Shen, Linbang; Ping, Guoli; Xu, Zhongming

2018-07-01

Being capable of demystifying the acoustic source identification result fast, Fourier-based deconvolution has been studied and applied widely for the delay and sum (DAS) beamforming with two-dimensional (2D) planar arrays. It is, however so far, still blank in the context of spherical harmonics beamforming (SHB) with three-dimensional (3D) solid spherical arrays. This paper is motivated to settle this problem. Firstly, for the purpose of determining the effective identification region, the premise of deconvolution, a shift-invariant point spread function (PSF), is analyzed with simulations. To make the premise be satisfied approximately, the opening angle in elevation dimension of the surface of interest should be small, while no restriction is imposed to the azimuth dimension. Then, two kinds of deconvolution theories are built for SHB using the zero and the periodic boundary conditions respectively. Both simulations and experiments demonstrate that the periodic boundary condition is superior to the zero one, and fits the 3D acoustic source identification with solid spherical arrays better. Finally, four periodic boundary condition based deconvolution methods are formulated, and their performance is disclosed both with simulations and experimentally. All the four methods offer enhanced spatial resolution and reduced sidelobe contaminations over SHB. The recovered source strength approximates to the exact one multiplied with a coefficient that is the square of the focus distance divided by the distance from the source to the array center, while the recovered pressure contribution is scarcely affected by the focus distance, always approximating to the exact one.

A one-dimensional zinc(II) coordination polymer with a three-dimensional supramolecular architecture incorporating 1-[(1H-benzimidazol-2-yl)methyl]-1H-tetrazole and adipate.

PubMed

Liu, Chun Li; Huang, Qiu Ying; Meng, Xiang Ru

2016-12-01

The synthesis of coordination polymers or metal-organic frameworks (MOFs) has attracted considerable interest owing to the interesting structures and potential applications of these compounds. It is still a challenge to predict the exact structures and compositions of the final products. A new one-dimensional coordination polymer, catena-poly[[[bis{1-[(1H-benzimidazol-2-yl)methyl]-1H-tetrazole-κN 3 }zinc(II)]-μ-hexane-1,6-dicarboxylato-κ 4 O 1 ,O 1' :O 6 ,O 6' ] monohydrate], {[Zn(C 6 H 8 O 4 )(C 9 H 8 N 6 ) 2 ]·H 2 O} n , has been synthesized by the reaction of Zn(Ac) 2 (Ac is acetate) with 1-[(1H-benzimidazol-2-yl)methyl]-1H-tetrazole (bimt) and adipic acid (H 2 adi) at room temperature. In the polymer, each Zn II ion exhibits an irregular octahedral ZnN 2 O 4 coordination geometry and is coordinated by two N atoms from two symmetry-related bimt ligands and four O atoms from two symmetry-related dianionic adipate ligands. Zn II ions are connected by adipate ligands into a one-dimensional chain which runs parallel to the c axis. The bimt ligands coordinate to the Zn II ions in a monodentate mode on both sides of the main chain. In the crystal, the one-dimensional chains are further connected through N-H...O hydrogen bonds, leading to a three-dimensional supramolecular architecture. In addition, the title polymer exhibits fluorescence, with emissions at 334 and 350 nm in the solid state at room temperature.

Renormalizable Quantum Field Theories in the Large -n Limit

NASA Astrophysics Data System (ADS)

Guruswamy, Sathya

1995-01-01

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

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1974-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Rapid automated superposition of shapes and macromolecular models using spherical harmonics.

PubMed

Konarev, Petr V; Petoukhov, Maxim V; Svergun, Dmitri I

2016-06-01

A rapid algorithm to superimpose macromolecular models in Fourier space is proposed and implemented ( SUPALM ). The method uses a normalized integrated cross-term of the scattering amplitudes as a proximity measure between two three-dimensional objects. The reciprocal-space algorithm allows for direct matching of heterogeneous objects including high- and low-resolution models represented by atomic coordinates, beads or dummy residue chains as well as electron microscopy density maps and inhomogeneous multi-phase models ( e.g. of protein-nucleic acid complexes). Using spherical harmonics for the computation of the amplitudes, the method is up to an order of magnitude faster than the real-space algorithm implemented in SUPCOMB by Kozin & Svergun [ J. Appl. Cryst. (2001 ▸), 34 , 33-41]. The utility of the new method is demonstrated in a number of test cases and compared with the results of SUPCOMB . The spherical harmonics algorithm is best suited for low-resolution shape models, e.g . those provided by solution scattering experiments, but also facilitates a rapid cross-validation against structural models obtained by other methods.

A comparative study of dynamically expanding force-free, constant-alpha magnetic configurations with applications to magnetic clouds

NASA Technical Reports Server (NTRS)

Farrugia, C. J.; Burlaga, L. F.; Osherovich, V. A.; Lepping, R. P.

1992-01-01

We contrast two different solutions of the constant alpha, force-free MHD equation, both of which have been suggested as models for magnetic clouds: a solution in cylindrical coordinates and one in spherical coordinates. In line with the observation that magnetic clouds expand, we generalize these static models and construct their expanding counterparts. We find that expansion introduces in both cases a large asymmetry in the field strength signature which is in the same sense as that seen the the data, i.e. towards the leading edge of the cloud. We then do a least squares fit of the respective models to one-spacecraft data on a magnetic cloud. We find that the fitting routine converges in both cases. However, while purely formally we cannot distinguish between the two models using data from one spacecraft, the field components in the 'spherical' model have features not compatible with data on magnetic clouds.

Towards anti-causal Green's function for three-dimensional sub-diffraction focusing

NASA Astrophysics Data System (ADS)

Ma, Guancong; Fan, Xiying; Ma, Fuyin; de Rosny, Julien; Sheng, Ping; Fink, Mathias

2018-06-01

In causal physics, the causal Green's function describes the radiation of a point source. Its counterpart, the anti-causal Green's function, depicts a spherically converging wave. However, in free space, any converging wave must be followed by a diverging one. Their interference gives rise to the diffraction limit that constrains the smallest possible dimension of a wave's focal spot in free space, which is half the wavelength. Here, we show with three-dimensional acoustic experiments that we can realize a stand-alone anti-causal Green's function in a large portion of space up to a subwavelength distance from the focus point by introducing a near-perfect absorber for spherical waves at the focus. We build this subwavelength absorber based on membrane-type acoustic metamaterial, and experimentally demonstrate focusing of spherical waves beyond the diffraction limit.

Investigating tunneling process of atom exposed in circularly polarized strong-laser field

NASA Astrophysics Data System (ADS)

Yuan, MingHu; Xin, PeiPei; Chu, TianShu; Liu, HongPing

2017-03-01

We propose a method for studying the tunneling process by analyzing the instantaneous ionization rate of a circularly polarized laser. A numerical calculation shows that, for an atom exposed to a long laser pulse, if its initial electronic state wave function is non-spherical symmetric, the delayed phase shift of the ionization rate vs the laser cycle period in real time in the region close to the peak intensity of the laser pulse can be used to probe the tunneling time. In this region, an obvious time delay phase shift of more than 190 attoseconds is observed. Further study shows that the atom has a longer tunneling time in the ionization under a shorter wavelength laser pulse. In our method, a Wigner rotation technique is employed to numerically solve the time-dependent Schrödinger equation of a single-active electron in a three-dimensional spherical coordinate system.

Superlattices assembled through shape-induced directional binding

NASA Astrophysics Data System (ADS)

Lu, Fang; Yager, Kevin G.; Zhang, Yugang; Xin, Huolin; Gang, Oleg

2015-04-01

Organization of spherical particles into lattices is typically driven by packing considerations. Although the addition of directional binding can significantly broaden structural diversity, nanoscale implementation remains challenging. Here we investigate the assembly of clusters and lattices in which anisotropic polyhedral blocks coordinate isotropic spherical nanoparticles via shape-induced directional interactions facilitated by DNA recognition. We show that these polyhedral blocks--cubes and octahedrons--when mixed with spheres, promote the assembly of clusters with architecture determined by polyhedron symmetry. Moreover, three-dimensional binary superlattices are formed when DNA shells accommodate the shape disparity between nanoparticle interfaces. The crystallographic symmetry of assembled lattices is determined by the spatial symmetry of the block's facets, while structural order depends on DNA-tuned interactions and particle size ratio. The presented lattice assembly strategy, exploiting shape for defining the global structure and DNA-mediation locally, opens novel possibilities for by-design fabrication of binary lattices.

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

Lu, Fang; Yager, Kevin G.; Zhang, Yugang

Organization of spherical particles into lattices is typically driven by packing considerations. Although the addition of directional binding can significantly broaden structural diversity, nanoscale implementation remains challenging. Here we investigate the assembly of clusters and lattices in which anisotropic polyhedral blocks coordinate isotropic spherical nanoparticles via shape-induced directional interactions facilitated by DNA recognition. We show that these polyhedral blocks—cubes and octahedrons—when mixed with spheres, promote the assembly of clusters with architecture determined by polyhedron symmetry. Moreover, three-dimensional binary superlattices are formed when DNA shells accommodate the shape disparity between nanoparticle interfaces. The crystallographic symmetry of assembled lattices is determined bymore » the spatial symmetry of the block’s facets, while structural order depends on DNA-tuned interactions and particle size ratio. Lastly, the presented lattice assembly strategy, exploiting shape for defining the global structure and DNA-mediation locally, opens novel possibilities for by-design fabrication of binary lattices.« less

Superlattices assembled through shape-induced directional binding

DOE PAGES

Lu, Fang; Yager, Kevin G.; Zhang, Yugang; ...

2015-04-23

Organization of spherical particles into lattices is typically driven by packing considerations. Although the addition of directional binding can significantly broaden structural diversity, nanoscale implementation remains challenging. Here we investigate the assembly of clusters and lattices in which anisotropic polyhedral blocks coordinate isotropic spherical nanoparticles via shape-induced directional interactions facilitated by DNA recognition. We show that these polyhedral blocks—cubes and octahedrons—when mixed with spheres, promote the assembly of clusters with architecture determined by polyhedron symmetry. Moreover, three-dimensional binary superlattices are formed when DNA shells accommodate the shape disparity between nanoparticle interfaces. The crystallographic symmetry of assembled lattices is determined bymore » the spatial symmetry of the block’s facets, while structural order depends on DNA-tuned interactions and particle size ratio. Lastly, the presented lattice assembly strategy, exploiting shape for defining the global structure and DNA-mediation locally, opens novel possibilities for by-design fabrication of binary lattices.« less

A new approach to spherically symmetric junction surfaces and the matching of FLRW regions

NASA Astrophysics Data System (ADS)

Kirchner, U.

2004-08-01

We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann Lemaître Robertson Walker (FLRW) models. We discuss 'vacuum bubbles' and closed open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time.

Simple model of the indirect compression of targets under conditions close to the national ignition facility at an energy of 1.5 MJ

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

Rozanov, V. B., E-mail: rozanov@sci.lebedev.ru; Vergunova, G. A., E-mail: verg@sci.lebedev.ru

2015-11-15

The possibility of the analysis and interpretation of the reported experiments with the megajoule National Ignition Facility (NIF) laser on the compression of capsules in indirect-irradiation targets by means of the one-dimensional RADIAN program in the spherical geometry has been studied. The problem of the energy balance in a target and the determination of the laser energy that should be used in the spherical model of the target has been considered. The results of action of pulses differing in energy and time profile (“low-foot” and “high-foot” regimes) have been analyzed. The parameters of the compression of targets with a high-densitymore » carbon ablator have been obtained. The results of the simulations are in satisfactory agreement with the measurements and correspond to the range of the observed parameters. The set of compared results can be expanded, in particular, for a more detailed determination of the parameters of a target near the maximum compression of the capsule. The physical foundation of the possibility of using the one-dimensional description is the necessity of the closeness of the last stage of the compression of the capsule to a one-dimensional process. The one-dimensional simulation of the compression of the capsule can be useful in establishing the boundary behind which two-dimensional and three-dimensional simulation should be used.« less

Photonic polymer-blend structures and method for making

DOEpatents

Barnes, Michael D.

2004-06-29

The present invention comprises the formation of photonic polymer-blend structures having tunable optical and mechanical properties. The photonic polymer-blend structures comprise monomer units of spherical microparticles of a polymer-blend material wherein the spherical microparticles have surfaces partially merged with one another in a robust inter-particle bond having a tunable inter-particle separation or bond length sequentially attached in a desired and programmable architecture. The photonic polymer-blend structures of the present invention can be linked by several hundred individual particles sequentially linked to form complex three-dimensional structures or highly ordered two-dimensional arrays of 3D columns with 2D spacing.

HEATING 7. 1 user's manual

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

Childs, K.W.

1991-07-01

HEATING is a FORTRAN program designed to solve steady-state and/or transient heat conduction problems in one-, two-, or three- dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heating generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- and position-dependent. The boundary conditions, which maymore » be surface-to-boundary or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General graybody radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING is variably dimensioned and utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion). The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

A Guided Tour of Mathematical Methods

NASA Astrophysics Data System (ADS)

Snieder, Roel

2009-04-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical co-ordinates; 5. The gradient; 6. The divergence of a vector field; 7. The curl of a vector field; 8. The theorem of Gauss; 9. The theorem of Stokes; 10. The Laplacian; 11. Conservation laws; 12. Scale analysis; 13. Linear algebra; 14. The Dirac delta function; 15. Fourier analysis; 16. Analytic functions; 17. Complex integration; 18. Green's functions: principles; 19. Green's functions: examples; 20. Normal modes; 21. Potential theory; 22. Cartesian tensors; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Variational calculus; 26. Epilogue, on power and knowledge; References.

Development of a high-speed nanoprofiler using normal vector tracing

NASA Astrophysics Data System (ADS)

Kitayama, T.; Matsumura, H.; Usuki, K.; Kojima, T.; Uchikoshi, J.; Higashi, Y.; Endo, K.

2012-09-01

A new high-speed nanoprofiler was developed in this study. This profiler measures normal vectors and their coordinates on the surface of a specimen. Each normal vector and coordinate is determined by making the incident light path and the reflected light path coincident using 5-axis controlled stages. This is ensured by output signal of quadrant photo diode (QPD). From the acquired normal vectors and their coordinates, the three-dimensional shape is calculated by a reconstruction algorithm based on least-squares. In this study, a concave spherical mirror with a 400 mm radius of curvature was measured. As a result, a peak of 30 nm PV was observed at the center of the mirror. Measurement repeatability was 1 nm. In addition, cross-comparison with a Fizeau interferometer was implemented and the results were consistent within 10 nm. In particular, the high spatial frequency profile was highly consistent, and any differences were considered to be caused by systematic errors.

Calculation of three-dimensional compressible laminar and turbulent boundary flows. Three-dimensional compressible boundary layers of reacting gases over realistic configurations

NASA Technical Reports Server (NTRS)

Kendall, R. M.; Bonnett, W. S.; Nardo, C. T.; Abbett, M. J.

1975-01-01

A three-dimensional boundary-layer code was developed for particular application to realistic hypersonic aircraft. It is very general and can be applied to a wide variety of boundary-layer flows. Laminar, transitional, and fully turbulent flows of compressible, reacting gases are efficiently calculated by use of the code. A body-oriented orthogonal coordinate system is used for the calculation and the user has complete freedom in specifying the coordinate system within the restrictions that one coordinate must be normal to the surface and the three coordinates must be mutually orthogonal.

Global isostatic geoid anomalies for plate and boundary layer models of the lithosphere

NASA Technical Reports Server (NTRS)

Hager, B. H.

1981-01-01

Commonly used one dimensional geoid models predict that the isostatic geoid anomaly over old ocean basins for the boundary layer thermal model of the lithosphere is a factor of two greater than that for the plate model. Calculations presented, using the spherical analogues of the plate and boundary layer thermal models, show that for the actual global distribution of plate ages, one dimensional models are not accurate and a spherical, fully three dimensional treatment is necessary. The maximum difference in geoid heights predicted for the two models is only about two meters. The thermal structure of old lithosphere is unlikely to be resolvable using global geoid anomalies. Stripping the effects of plate aging and a hypothetical uniform, 35 km, isostatically-compensated continental crust from the observed geoid emphasizes that the largest-amplitude geoid anomaly is the geoid low of almost 120 m over West Antarctica, a factor of two greater than the low of 60 m over Ceylon.

Magnetic and gravity anomalies in the Americas

NASA Technical Reports Server (NTRS)

Braile, L. W.; Hinze, W. J.; Vonfrese, R. R. B. (Principal Investigator)

1981-01-01

The cleaning and magnetic tape storage of spherical Earth processing programs are reported. These programs include: NVERTSM which inverts total or vector magnetic anomaly data on a distribution of point dipoles in spherical coordinates; SMFLD which utilizes output from NVERTSM to compute total or vector magnetic anomaly fields for a distribution of point dipoles in spherical coordinates; NVERTG; and GFLD. Abstracts are presented for papers dealing with the mapping and modeling of magnetic and gravity anomalies, and with the verification of crustal components in satellite data.

One-dimensional MHD simulations of MTF systems with compact toroid targets and spherical liners

NASA Astrophysics Data System (ADS)

Khalzov, Ivan; Zindler, Ryan; Barsky, Sandra; Delage, Michael; Laberge, Michel

2017-10-01

One-dimensional (1D) MHD code is developed in General Fusion (GF) for coupled plasma-liner simulations in magnetized target fusion (MTF) systems. The main goal of these simulations is to search for optimal parameters of MTF reactor, in which spherical liquid metal liner compresses compact toroid plasma. The code uses Lagrangian description for both liner and plasma. The liner is represented as a set of spherical shells with fixed masses while plasma is discretized as a set of nested tori with circular cross sections and fixed number of particles between them. All physical fields are 1D functions of either spherical (liner) or small toroidal (plasma) radius. Motion of liner and plasma shells is calculated self-consistently based on applied forces and equations of state. Magnetic field is determined by 1D profiles of poloidal and toroidal fluxes - they are advected with shells and diffuse according to local resistivity, this also accounts for flux leakage into the liner. Different plasma transport models are implemented, this allows for comparison with ongoing GF experiments. Fusion power calculation is included into the code. We performed a series of parameter scans in order to establish the underlying dependencies of the MTF system and find the optimal reactor design point.

FPPAC94: A two-dimensional multispecies nonlinear Fokker-Planck package for UNIX systems

NASA Astrophysics Data System (ADS)

Mirin, A. A.; McCoy, M. G.; Tomaschke, G. P.; Killeen, J.

1994-07-01

FPPAC94 solves the complete nonlinear multispecies Fokker-Planck collison operator for a plasma in two-dimensional velocity space. The operator is expressed in terms of spherical coordinates (speed and pitch angle) under the assumption of azimuthal symmetry. Provision is made for additional physics contributions (e.g. rf heating, electric field acceleration). The charged species, referred to as general species, are assumed to be in the presence of an arbitrary number of fixed Maxwellian species. The electrons may be treated either as one of these Maxwellian species or as a general species. Coulomb interactions among all charged species are considered This program is a new version of FPPAC. FPPAC was last published in Computer Physics Communications in 1988. This new version is identical in scope to the previous version. However, it is written in standard Fortran 77 and is able to execute on a variety of Unix systems. The code has been tested on the Cray-C90, HP-755 and Sun Sparc-1. The answers agree on all platforms where the code has been tested. The test problems are the same as those provided in 1988. This version also corrects a bug in the 1988 version.

Applications of Differential Operators in Geodetic Coordinates

NASA Astrophysics Data System (ADS)

Hallam, K. A. T.; Oliveira, V. C., Jr.

2016-12-01

The definition of coordinate systems and frames is an essential step to even start a problem in physical geodesy and geophysics. The commonly used coordinate systems when dealing with problems on (or close to) the surface of the Earth are the geocentric Cartesian coordinates, geocentric spherical coordinates and geodetic coordinates. Transformations between Cartesian and spherical coordinates are widely known and used for several problems. More complex, but not less important, are the transformations between Cartesian and geodetic coordinates. Although most of them utilize an ellipsoidal frame in which the three coordinates are geodetic longitude (λ), geodetic latitude (φ) and the scale factor (u), the latter being a combination of X and Y, not the geometric height (h), the data sets measured on (or close to) the surface of the Earth are given in geodetic coordinates which are usually transformed into Cartesian or spherical coordinates for mathematical developments. It would be useful, however, to preclude coordinate transformations for the subsequent operations. Thus, we derived expressions for the gradient and Laplacian operators in geodetic coordinates in order to make further use on mathematical developments. Results obtained analitically and from numerical simulations validate our expressions. We applied our operators to derive the gravitational field produced by a point mass and used it for representing the regional gravity field in geodetic coordinates. The results obtained with the numerical simulations show that our approach is potentially useful in solving a wide range of problems in physical geodesy and geophysics.

Insensitivity of the octahedral spherical hohlraum to power imbalance, pointing accuracy, and assemblage accuracy

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

Huo, Wen Yi; Zhao, Yiqing; Zheng, Wudi

2014-11-15

The random radiation asymmetry in the octahedral spherical hohlraum [K. Lan et al., Phys. Plasmas 21, 0 10704 (2014)] arising from the power imbalance, pointing accuracy of laser quads, and the assemblage accuracy of capsule is investigated by using the 3-dimensional view factor model. From our study, for the spherical hohlraum, the random radiation asymmetry arising from the power imbalance of the laser quads is about half of that in the cylindrical hohlraum; the random asymmetry arising from the pointing error is about one order lower than that in the cylindrical hohlraum; and the random asymmetry arising from the assemblage errormore » of capsule is about one third of that in the cylindrical hohlraum. Moreover, the random radiation asymmetry in the spherical hohlraum is also less than the amount in the elliptical hohlraum. The results indicate that the spherical hohlraum is more insensitive to the random variations than the cylindrical hohlraum and the elliptical hohlraum. Hence, the spherical hohlraum can relax the requirements to the power imbalance and pointing accuracy of laser facility and the assemblage accuracy of capsule.« less

Euclidean sections of protein conformation space and their implications in dimensionality reduction

PubMed Central

Duan, Mojie; Li, Minghai; Han, Li; Huo, Shuanghong

2014-01-01

Dimensionality reduction is widely used in searching for the intrinsic reaction coordinates for protein conformational changes. We find the dimensionality–reduction methods using the pairwise root–mean–square deviation as the local distance metric face a challenge. We use Isomap as an example to illustrate the problem. We believe that there is an implied assumption for the dimensionality–reduction approaches that aim to preserve the geometric relations between the objects: both the original space and the reduced space have the same kind of geometry, such as Euclidean geometry vs. Euclidean geometry or spherical geometry vs. spherical geometry. When the protein free energy landscape is mapped onto a 2D plane or 3D space, the reduced space is Euclidean, thus the original space should also be Euclidean. For a protein with N atoms, its conformation space is a subset of the 3N-dimensional Euclidean space R3N. We formally define the protein conformation space as the quotient space of R3N by the equivalence relation of rigid motions. Whether the quotient space is Euclidean or not depends on how it is parameterized. When the pairwise root–mean–square deviation is employed as the local distance metric, implicit representations are used for the protein conformation space, leading to no direct correspondence to a Euclidean set. We have demonstrated that an explicit Euclidean-based representation of protein conformation space and the local distance metric associated to it improve the quality of dimensionality reduction in the tetra-peptide and β–hairpin systems. PMID:24913095

Optimization of the dynamic behavior of strongly nonlinear heterogeneous materials

NASA Astrophysics Data System (ADS)

Herbold, Eric B.

New aspects of strongly nonlinear wave and structural phenomena in granular media are developed numerically, theoretically and experimentally. One-dimensional chains of particles and compressed powder composites are the two main types of materials considered here. Typical granular assemblies consist of linearly elastic spheres or layers of masses and effective nonlinear springs in one-dimensional columns for dynamic testing. These materials are highly sensitive to initial and boundary conditions, making them useful for acoustic and shock-mitigating applications. One-dimensional assemblies of spherical particles are examples of strongly nonlinear systems with unique properties. For example, if initially uncompressed, these materials have a sound speed equal to zero (sonic vacuum), supporting strongly nonlinear compression solitary waves with a finite width. Different types of assembled metamaterials will be presented with a discussion of the material's response to static compression. The acoustic diode effect will be presented, which may be useful in shock mitigation applications. Systems with controlled dissipation will also be discussed from an experimental and theoretical standpoint emphasizing the critical viscosity that defines the transition from an oscillatory to monotonous shock profile. The dynamic compression of compressed powder composites may lead to self-organizing mesoscale structures in two and three dimensions. A reactive granular material composed of a compressed mixture of polytetrafluoroethylene (PTFE), tungsten (W) and aluminum (Al) fine-grain powders exhibit this behavior. Quasistatic, Hopkinson bar, and drop-weight experiments show that composite materials with a high porosity and fine metallic particles exhibit a higher strength than less porous mixtures with larger particles, given the same mass fraction of constituents. A two-dimensional Eulerian hydrocode is implemented to investigate the mechanical deformation and failure of the compressed powder samples in simulated drop-weight tests. The calculations indicate that the dynamic formation of mesoscale force chains increase the strength of the sample. This is also apparent in three-dimensional finite element calculations of drop-weight test simulations using LS-Dyna despite a higher granular bulk coordination number, and an increased mobility of individual grains.

A one-dimensional nickel(II) coordination polymer containing 2,6-dipicolinate and dipyrido[3,2-a:2',3'-c]phenazine.

PubMed

Ma, Yi; Zhang, Li-Tian; Wang, Xiao-Fang; He, Yong-Ke; Han, Zheng-Bo

2007-12-01

A new coordination polymer, catena-poly[[(dipyrido[3,2-a:2',3'-c]phenazine-kappa(2)N,N')nickel(II)]-mu-2,6-dipicolinato-kappa(4)O(2),N,O(6):O(2')], [Ni(C7H3NO4)(C18H10N4)]n, exhibits a one-dimensional structure in which 2,6-dipicolinate acts as a bridging ligand interconnecting adjacent nickel(II) centers to form a chain structure. The asymmetric unit contains one Ni(II) center, one dipyrido[3,2-a:2',3'-c]phenazine ligand and one 2,6-dipicolinate ligand. Each Ni(II) center is six-coordinated and surrounded by three N atoms and three O atoms from one dipyrido[3,2-a:2',3'-c]phenazine ligand and two different 2,6-dipicolinate ligands, leading to a distorted octahedral geometry. Adjacent chains are linked by pi-pi stacking interactions and weak interactions to form a three-dimensional supramolecular network.

The Linear Parameters and the Decoupling Matrix for Linearly Coupled Motion in 6 Dimensional Phase Space

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

Parzen, George

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 x 6 matrix, R. R will be called the decoupling matrix. It will be shown that of the 36 elements of the 6 x 6 decoupling matrix R, only 12 elements are independent. This may be contrasted with the results for motion in 4- dimensional phase space, wheremore » R has 4 independent elements. A set of equations is given from which the 12 elements of R can be computed from the one period transfer matrix. This set of equations also allows the linear parameters, the β i,α i, i = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix. An alternative procedure for computing the linear parameters,β i,α i, i = 1, 3, and the 12 independent elements of the decoupling matrix R is also given which depends on computing the eigenvectors of the one period transfer matrix. These results can be used in a tracking program, where the one period transfer matrix can be computed by multiplying the transfer matrices of all the elements in a period, to compute the linear parameters α i and β i, i = 1, 3, and the elements of the decoupling matrix R. The procedure presented here for studying coupled motion in 6-dimensional phase space can also be applied to coupled motion in 4-dimensional phase space, where it may be a useful alternative procedure to the procedure presented by Edwards and Teng. In particular, it gives a simpler programing procedure for computing the beta functions and the emittances for coupled motion in 4-dimensional phase space.« less

The linear parameters and the decoupling matrix for linearly coupled motion in 6 dimensional phase space. Informal report

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

Parzen, G.

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 {times} 6 matrix, R. R will be called the decoupling matrix. It will be shown that of the 36 elements of the 6 {times} 6 decoupling matrix R, only 12 elements are independent. This may be contrasted with the results for motion in 4-dimensional phase space, where Rmore » has 4 independent elements. A set of equations is given from which the 12 elements of R can be computed from the one period transfer matrix. This set of equations also allows the linear parameters, {beta}{sub i}, {alpha}{sub i} = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix. An alternative procedure for computing the linear parameters, the {beta}{sub i}, {alpha}{sub i} i = 1, 3, and the 12 independent elements of the decoupling matrix R is also given which depends on computing the eigenvectors of the one period transfer matrix. These results can be used in a tracking program, where the one period transfer matrix can be computed by multiplying the transfer matrices of all the elements in a period, to compute the linear parameters {alpha}{sub i} and {beta}{sub i}, i = 1, 3, and the elements of the decoupling matrix R. The procedure presented here for studying coupled motion in 6-dimensional phase space can also be applied to coupled motion in 4-dimensional phase space, where it may be a useful alternative procedure to the procedure presented by Edwards and Teng. In particular, it gives a simpler programming procedure for computing the beta functions and the emittances for coupled motion in 4-dimensional phase space.« less

Stereo Imaging Velocimetry

NASA Technical Reports Server (NTRS)

McDowell, Mark (Inventor); Glasgow, Thomas K. (Inventor)

1999-01-01

A system and a method for measuring three-dimensional velocities at a plurality of points in a fluid employing at least two cameras positioned approximately perpendicular to one another. The cameras are calibrated to accurately represent image coordinates in world coordinate system. The two-dimensional views of the cameras are recorded for image processing and centroid coordinate determination. Any overlapping particle clusters are decomposed into constituent centroids. The tracer particles are tracked on a two-dimensional basis and then stereo matched to obtain three-dimensional locations of the particles as a function of time so that velocities can be measured therefrom The stereo imaging velocimetry technique of the present invention provides a full-field. quantitative, three-dimensional map of any optically transparent fluid which is seeded with tracer particles.

One-dimensional arrangement of nanoparticles utilizing the V-groove and cage shaped proteins

NASA Astrophysics Data System (ADS)

Ban, Takahiko; Uenuma, Mutsunori; Migita, Shinji; Okamoto, Naofumi; Ishikawa, Yasuaki; Uraoka, Yukiharu; Yamashita, Ichiro; Yamamoto, Shin-ichi

2017-06-01

The one-dimensional arrangement of nanoparticles (NPs) was performed using a V-groove and ferritins as spherical shell proteins. The V-groove was synthesized by lithography and anisotropic etching of a Si substrate. Ferritin has an outer diameter of 12 nm and an inner diameter of 6 nm, and various inorganic substances can be formed into the cavity. In this study, iron oxide, cobalt oxide, and indium oxide cores were used. The surface potential of ferritin can be changed by genetic modification. Particularly, by using Fer8-K98E, NPs could be arranged one-dimensionally onto the bottom of the V-groove. In addition, we succeeded in selectively forming a one-dimensional array of one layer, two layers, and three layers by changing the protein concentration. This experiment is expected to be applicable to various one-dimensional devices.

Solving the Self-Interaction Problem in Kohn-Sham Density Functional Theory. Application to Atoms

DOE PAGES

Daene, M.; Gonis, A.; Nicholson, D. M.; ...

2014-10-14

Previously, we proposed a computational methodology that addresses the elimination of the self-interaction error from the Kohn–Sham formulation of the density functional theory. We demonstrated how the exchange potential can be obtained, and presented results of calculations for atomic systems up to Kr carried out within a Cartesian coordinate system. In our paper, we provide complete details of this self-interaction free method formulated in spherical coordinates based on the explicit equidensity basis ansatz. We also prove analytically that derivatives obtained using this method satisfy the Virial theorem for spherical orbitals, where the problem can be reduced to one dimension. Wemore » present the results of calculations of ground-state energies of atomic systems throughout the periodic table carried out within the exchange-only mode.« less

Uncertainty propagation in orbital mechanics via tensor decomposition

NASA Astrophysics Data System (ADS)

Sun, Yifei; Kumar, Mrinal

2016-03-01

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker-Planck equation (FPE) is defined on a relatively high dimensional (6-D) state-space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the x-y-z subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors' knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral ("super-fast") convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.

Intelligent Control of a Sensor-Actuator System via Kernelized Least-Squares Policy Iteration

PubMed Central

Liu, Bo; Chen, Sanfeng; Li, Shuai; Liang, Yongsheng

2012-01-01

In this paper a new framework, called Compressive Kernelized Reinforcement Learning (CKRL), for computing near-optimal policies in sequential decision making with uncertainty is proposed via incorporating the non-adaptive data-independent Random Projections and nonparametric Kernelized Least-squares Policy Iteration (KLSPI). Random Projections are a fast, non-adaptive dimensionality reduction framework in which high-dimensionality data is projected onto a random lower-dimension subspace via spherically random rotation and coordination sampling. KLSPI introduce kernel trick into the LSPI framework for Reinforcement Learning, often achieving faster convergence and providing automatic feature selection via various kernel sparsification approaches. In this approach, policies are computed in a low-dimensional subspace generated by projecting the high-dimensional features onto a set of random basis. We first show how Random Projections constitute an efficient sparsification technique and how our method often converges faster than regular LSPI, while at lower computational costs. Theoretical foundation underlying this approach is a fast approximation of Singular Value Decomposition (SVD). Finally, simulation results are exhibited on benchmark MDP domains, which confirm gains both in computation time and in performance in large feature spaces. PMID:22736969

Quantum Entanglement in Optical Lattice Systems

DTIC Science & Technology

2015-02-18

Zitterbewegung oscillation was first predicted by Schroedinger in 1930 for relativistic Dirac electrons where it arises from the interference...magnetic gradient. The gradient affected the Rabi cycling rate, leading to a phase winding along the long axis of the cigar -shaped BEC. While the single...approach is applicable to spherically symmetric, strictly two- dimensional, strictly one-dimensional, cigar -shaped, and pancake-shaped traps and has

Spherical hashing: binary code embedding with hyperspheres.

PubMed

Heo, Jae-Pil; Lee, Youngwoon; He, Junfeng; Chang, Shih-Fu; Yoon, Sung-Eui

2015-11-01

Many binary code embedding schemes have been actively studied recently, since they can provide efficient similarity search, and compact data representations suitable for handling large scale image databases. Existing binary code embedding techniques encode high-dimensional data by using hyperplane-based hashing functions. In this paper we propose a novel hypersphere-based hashing function, spherical hashing, to map more spatially coherent data points into a binary code compared to hyperplane-based hashing functions. We also propose a new binary code distance function, spherical Hamming distance, tailored for our hypersphere-based binary coding scheme, and design an efficient iterative optimization process to achieve both balanced partitioning for each hash function and independence between hashing functions. Furthermore, we generalize spherical hashing to support various similarity measures defined by kernel functions. Our extensive experiments show that our spherical hashing technique significantly outperforms state-of-the-art techniques based on hyperplanes across various benchmarks with sizes ranging from one to 75 million of GIST, BoW and VLAD descriptors. The performance gains are consistent and large, up to 100 percent improvements over the second best method among tested methods. These results confirm the unique merits of using hyperspheres to encode proximity regions in high-dimensional spaces. Finally, our method is intuitive and easy to implement.

Analytical method for analysis of electromagnetic scattering from inhomogeneous spherical structures using duality principles

NASA Astrophysics Data System (ADS)

Kiani, M.; Abdolali, A.; Safari, M.

2018-03-01

In this article, an analytical approach is presented for the analysis of electromagnetic (EM) scattering from radially inhomogeneous spherical structures (RISSs) based on the duality principle. According to the spherical symmetry, similar angular dependencies in all the regions are considered using spherical harmonics. To extract the radial dependency, the system of differential equations of wave propagation toward the inhomogeneity direction is equated with the dual planar ones. A general duality between electromagnetic fields and parameters and scattering parameters of the two structures is introduced. The validity of the proposed approach is verified through a comprehensive example. The presented approach substitutes a complicated problem in spherical coordinate to an easy, well posed, and previously solved problem in planar geometry. This approach is valid for all continuously varying inhomogeneity profiles. One of the major advantages of the proposed method is the capability of studying two general and applicable types of RISSs. As an interesting application, a class of lens antenna based on the physical concept of the gradient refractive index material is introduced. The approach is used to analyze the EM scattering from the structure and validate strong performance of the lens.

A Guided Tour of Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Snieder, Roel; van Wijk, Kasper

2015-05-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical coordinates; 5. Gradient; 6. Divergence of a vector field; 7. Curl of a vector field; 8. Theorem of Gauss; 9. Theorem of Stokes; 10. The Laplacian; 11. Scale analysis; 12. Linear algebra; 13. Dirac delta function; 14. Fourier analysis; 15. Analytic functions; 16. Complex integration; 17. Green's functions: principles; 18. Green's functions: examples; 19. Normal modes; 20. Potential-field theory; 21. Probability and statistics; 22. Inverse problems; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Conservation laws; 26. Cartesian tensors; 27. Variational calculus; 28. Epilogue on power and knowledge.

Closedness of orbits in a space with SU(2) Poisson structure

NASA Astrophysics Data System (ADS)

Fatollahi, Amir H.; Shariati, Ahmad; Khorrami, Mohammad

2014-06-01

The closedness of orbits of central forces is addressed in a three-dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically symmetric potential energies, it is only the Kepler problem for which all bounded orbits are closed. In analogy with the case of the ordinary space, a conserved vector (apart from the angular momentum) is explicitly constructed, which is responsible for the orbits being closed. This is the analog of the Laplace-Runge-Lenz vector. The algebra of the constants of the motion is also worked out.

MR image denoising method for brain surface 3D modeling

NASA Astrophysics Data System (ADS)

Zhao, De-xin; Liu, Peng-jie; Zhang, De-gan

2014-11-01

Three-dimensional (3D) modeling of medical images is a critical part of surgical simulation. In this paper, we focus on the magnetic resonance (MR) images denoising for brain modeling reconstruction, and exploit a practical solution. We attempt to remove the noise existing in the MR imaging signal and preserve the image characteristics. A wavelet-based adaptive curve shrinkage function is presented in spherical coordinates system. The comparative experiments show that the denoising method can preserve better image details and enhance the coefficients of contours. Using these denoised images, the brain 3D visualization is given through surface triangle mesh model, which demonstrates the effectiveness of the proposed method.

Conversion of time-varying Stokes coefficients into mass anomalies at the Earth's surface considering the Earth's oblateness

NASA Astrophysics Data System (ADS)

Ditmar, Pavel

2018-02-01

Time-varying Stokes coefficients estimated from GRACE satellite data are routinely converted into mass anomalies at the Earth's surface with the expression proposed for that purpose by Wahr et al. (J Geophys Res 103(B12):30,205-30,229, 1998). However, the results obtained with it represent mass transport at the spherical surface of 6378 km radius. We show that the accuracy of such conversion may be insufficient, especially if the target area is located in a polar region and the signal-to-noise ratio is high. For instance, the peak values of mean linear trends in 2003-2015 estimated over Greenland and Amundsen Sea embayment of West Antarctica may be underestimated in this way by about 15%. As a solution, we propose an updated expression for the conversion of Stokes coefficients into mass anomalies. This expression is based on the assumptions that: (i) mass transport takes place at the reference ellipsoid and (ii) at each point of interest, the ellipsoidal surface is approximated by the sphere with a radius equal to the current radial distance from the Earth's center ("locally spherical approximation"). The updated expression is nearly as simple as the traditionally used one but reduces the inaccuracies of the conversion procedure by an order of magnitude. In addition, we remind the reader that the conversion expressions are defined in spherical (geocentric) coordinates. We demonstrate that the difference between mass anomalies computed in spherical and ellipsoidal (geodetic) coordinates may not be negligible, so that a conversion of geodetic colatitudes into geocentric ones should not be omitted.

Improvement in airborne position measurements based on an ultrasonic linear-period-modulated wave by 1-bit signal processing

NASA Astrophysics Data System (ADS)

Thong-un, Natee; Hirata, Shinnosuke; Kurosawa, Minoru K.

2015-07-01

In this paper, we describe an expansion of the airborne ultrasonic systems for object localization in the three-dimensional spaces of navigation. A system, which revises the microphone arrangement and algorithm, can expand the object-position measurement from +90° in a previous method up to +180° for both the elevation and azimuth angles. The proposed system consists of a sound source and four acoustical receivers. Moreover, the system is designed to utilize low-cost devices, and low-cost computation relying on 1-bit signal processing is used to support the real-time application on a field-programmable gate array (FPGA). An object location is identified using spherical coordinates. A spherical object, which has a curved surface, is considered a target for this system. The transmit pulse to the target is a linear-period-modulated ultrasonic wave with a chirp rate of 50-20 kHz. Statistical evaluation of this work is the experimental investigation under repeatability.

Combined study of the solar neighbourhood kinematics - Spherical harmonics and Taylor expansions

NASA Astrophysics Data System (ADS)

Hernandez-Pajares, M.; Nunez, J.

1990-08-01

This paper relates two methods of analyzing the kinematic parameters of the local macroscopic motions of the Galaxy: (1) the Ogorodnikov-Milne model (OM) that consists in the three-dimensional Taylor expansion of the mean velocity field, and (2) the two-dimensional spherical harmonic development of the velocity components (SH). The theoretical relations between the SH coefficients and the second-order OM ones for the radial velocity v(r), and the galactic heliocentric components of the velocity U, V, W are presented. Only the hypothesis of separability of the stellar density function of the sample into angular and radial parts is needed. They are applied to 4732 A-M stars included in the Figueras (1986) sample.

Thermodynamics of Newman-Unti-Tamburino charged spaces

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

Mann, Robert; Department of Physics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1; Stelea, Cristian

We discuss and compare at length the results of two methods used recently to describe the thermodynamics of Taub-Newman-Unti-Tamburino (NUT) solutions in a de Sitter background. In the first approach (C approach), one deals with an analytically continued version of the metric while in the second approach (R approach), the discussion is carried out using the unmodified metric with Lorentzian signature. No analytic continuation is performed on the coordinates and/or the parameters that appear in the metric. We find that the results of both these approaches are completely equivalent modulo analytic continuation and we provide the exact prescription that relatesmore » the results in both methods. The extension of these results to the AdS/flat cases aims to give a physical interpretation of the thermodynamics of NUT-charged spacetimes in the Lorentzian sector. We also briefly discuss the higher-dimensional spaces and note that, analogous with the absence of hyperbolic NUTs in AdS backgrounds, there are no spherical Taub-NUT-dS solutions.« less

Precise calculation of the local pressure tensor in Cartesian and spherical coordinates in LAMMPS

NASA Astrophysics Data System (ADS)

Nakamura, Takenobu; Kawamoto, Shuhei; Shinoda, Wataru

2015-05-01

An accurate and efficient algorithm for calculating the 3D pressure field has been developed and implemented in the open-source molecular dynamics package, LAMMPS. Additionally, an algorithm to compute the pressure profile along the radial direction in spherical coordinates has also been implemented. The latter is particularly useful for systems showing a spherical symmetry such as micelles and vesicles. These methods yield precise pressure fields based on the Irving-Kirkwood contour integration and are particularly useful for biomolecular force fields. The present methods are applied to several systems including a buckled membrane and a vesicle.

Total Internal Reflection Ultrasonic Sensor for Detection of Subsurface Flaws: Proof of Concept

DTIC Science & Technology

2010-01-01

34 Tv001 Ve group (ray) velocity of the elastic wave X1, X2, X3 crystallographic coordinates x, y, z Descartes ’ coordinates tied to the transducer y0...TeO2 prism. 1.2.1. Orientation of directions and planes of interest with respect to Descartes ’ and Spherical coordinates. 1.2.2. Reflection of the...spect to Descartes ’ and Spherical coordi- nates. , (1.2.1) lili uuv Γ=ρ 2 where ρ is the crystal density and the symmetrical second rank Christoffel

Cluster of Sound Speed Fields by an Integral Measure

DTIC Science & Technology

2010-06-01

the same cost in time. The increasing the number of sensor depths does not cause execution time to increase. And finally assume that the time required...to be P = Z − ∫ 0 b ∂C(ρ, θ, λ) ∂ρ ∂C(ρ, θ, λ) ∂ρ dρ (2) where (ρ,θ,λ) are the usual geocentric spherical coordinates, and the limits of integration...but using spherical coordinates requires that the horizontal (θ , λ) terms be normalized by the radius. In the case of geocentric coordinates this

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

A numerical and experimental study of three-dimensional liquid sloshing in a rotating spherical container

NASA Technical Reports Server (NTRS)

Chen, Kuo-Huey; Kelecy, Franklyn J.; Pletcher, Richard H.

1992-01-01

A numerical and experimental study of three dimensional liquid sloshing inside a partially-filled spherical container undergoing an orbital rotating motion is described. Solutions of the unsteady, three-dimensional Navier-Stokes equations for the case of a gradual spin-up from rest are compared with experimental data obtained using a rotating test rig fitted with two liquid-filled spherical tanks. Data gathered from several experiments are reduced in terms of a dimensionless free surface height for comparison with transient results from the numerical simulations. The numerical solutions are found to compare favorably with the experimental data.

Volume determination of irregularly-shaped quasi-spherical nanoparticles.

PubMed

Attota, Ravi Kiran; Liu, Eileen Cherry

2016-11-01

Nanoparticles (NPs) are widely used in diverse application areas, such as medicine, engineering, and cosmetics. The size (or volume) of NPs is one of the most important parameters for their successful application. It is relatively straightforward to determine the volume of regular NPs such as spheres and cubes from a one-dimensional or two-dimensional measurement. However, due to the three-dimensional nature of NPs, it is challenging to determine the proper physical size of many types of regularly and irregularly-shaped quasi-spherical NPs at high-throughput using a single tool. Here, we present a relatively simple method that determines a better volume estimate of NPs by combining measurements from their top-down projection areas and peak heights using two tools. The proposed method is significantly faster and more economical than the electron tomography method. We demonstrate the improved accuracy of the combined method over scanning electron microscopy (SEM) or atomic force microscopy (AFM) alone by using modeling, simulations, and measurements. This study also exposes the existence of inherent measurement biases for both SEM and AFM, which usually produce larger measured diameters with SEM than with AFM. However, in some cases SEM measured diameters appear to have less error compared to AFM measured diameters, especially for widely used IS-NPs such as of gold, and silver. The method provides a much needed, proper high-throughput volumetric measurement method useful for many applications. Graphical Abstract The combined method for volume determination of irregularly-shaped quasi-spherical nanoparticles.

Spherical shock waves in general relativity

NASA Astrophysics Data System (ADS)

Nutku, Y.

1991-11-01

We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-N vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-N Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the C0-form of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions.

Deep circulations under simple classes of stratification

NASA Technical Reports Server (NTRS)

Salby, Murry L.

1989-01-01

Deep circulations where the motion field is vertically aligned over one or more scale heights are studied under barotropic and equivalent barotropic stratifications. The study uses two-dimensional equations reduced from the three-dimensional primitive equations in spherical geometry. A mapping is established between the full primitive equations and general shallow water behavior and the correspondence between variables describing deep atmospheric motion and those of shallow water behavior is established.

Spherical harmonic analysis of a harmonic function given on a spheroid

NASA Astrophysics Data System (ADS)

Claessens, S. J.

2016-07-01

A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine-Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine-Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine-Jekeli transformation is numerically more efficient, but the new method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain.

Grid generation in three dimensions by Poisson equations with control of cell size and skewness at boundary surfaces

NASA Technical Reports Server (NTRS)

Sorenson, R. L.; Steger, J. L.

1983-01-01

An algorithm for generating computational grids about arbitrary three-dimensional bodies is developed. The elliptic partial differential equation (PDE) approach developed by Steger and Sorenson and used in the NASA computer program GRAPE is extended from two to three dimensions. Forcing functions which are found automatically by the algorithm give the user the ability to control mesh cell size and skewness at boundary surfaces. This algorithm, as is typical of PDE grid generators, gives smooth grid lines and spacing in the interior of the grid. The method is applied to a rectilinear wind-tunnel case and to two body shapes in spherical coordinates.

Solwnd: A 3D Compressible MHD Code for Solar Wind Studies. Version 1.0: Cartesian Coordinates

NASA Technical Reports Server (NTRS)

Deane, Anil E.

1996-01-01

Solwnd 1.0 is a three-dimensional compressible MHD code written in Fortran for studying the solar wind. Time-dependent boundary conditions are available. The computational algorithm is based on Flux Corrected Transport and the code is based on the existing code of Zalesak and Spicer. The flow considered is that of shear flow with incoming flow that perturbs this base flow. Several test cases corresponding to pressure balanced magnetic structures with velocity shear flow and various inflows including Alfven waves are presented. Version 1.0 of solwnd considers a rectangular Cartesian geometry. Future versions of solwnd will consider a spherical geometry. Some discussions of this issue is presented.

Vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities

NASA Astrophysics Data System (ADS)

Xu, Si-Liu; He, Jun-Rong; Xue, Li; Belić, Milivoj R.

2018-02-01

We demonstrate three-dimensional (3D) vector solitary waves in the coupled (3 + 1)-D nonlinear Gross-Pitaevskii equations with variable nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing novel localized solutions that depend on three modal numbers, l, m, and n. Using the similarity transformation (ST) method in 3D, vector solitary waves are built with the help of a combination of harmonic and trapping potentials, including multipole solutions and necklace rings. In general, the solutions found are stable for low values of the modal numbers; for values larger than 2, the solutions are found to be unstable. Variable nonlinearity allows the utilization of soliton management methods.

On the Structure and Stabilization Mechanisms of Planar and Cylindrical Premixed Flames

NASA Technical Reports Server (NTRS)

Eng, James A.; Zhu, Delin; Law, Chung K.

1993-01-01

The configurational simplicity of the stationary one-dimensional flames renders them intrinsically attractive for fundamental flame structure studies. The possibility and fidelity of studies of such flames on earth, however, have been severely restricted by the unidirectional nature of the gravity vector. To demonstrate these complications, let us first consider the premixed flame. Here a stationary, one-dimensional flame can be established by using the flat-flame burner. We next consider nonpremixed flames. First it may be noted that in an unbounded gravity-free environment, the only stationary one-dimensional flame is the spherical flame. Indeed, this is a major motivation for the study of microgravity droplet combustion, in which the gas-phase processes can be approximated to be quasi-steady because of the significant disparity between the gas and liquid densities for subcritical combustion. In view of the above considerations, an experimental and theoretical program on cylindrical and spherical premixed and nonpremixed flames in microgravity has been initiated. For premixed flames, we are interested in: (1) assessing the heat loss versus flow divergence as the dominant stabilization mechanism; (2) determining the laminar flame speed by using this configuration; and (3) understanding the development of flamefront instability and the effects of the flame curvature on the burning intensity.

Spherical shock waves in general relativity

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

Nutku, Y.

1991-11-15

We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-{ital N} vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-{ital N} Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the {ital C}{sup 0}-formmore » of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions.« less

One-dimensional analysis of supersonic two-stage HVOF process

NASA Astrophysics Data System (ADS)

Katanoda, Hiroshi; Hagi, Junichi; Fukuhara, Minoru

2009-12-01

The one-dimensional calculation of the gas/particle flows of a supersonic two-stage high-velocity oxy-fuel (HVOF) thermal spray process was performed. The internal gas flow was solved by numerically integrating the equations of the quasi-one-dimensional flow including the effects of pipe friction and heat transfer. As for the supersonic jet flow, semi-empirical equations were used to obtain the gas velocity and temperature along the center line. The velocity and temperature of the particle were obtained by an one-way coupling method. The material of the spray particle selected in this study is ultra high molecular weight polyethylene (UHMWPE). The temperature distributions in the spherical UHMWPE particles of 50 and 150µm accelerated and heated by the supersonic gas flow was clarified.

Effect of 3-D heterogeneous-earth on rheology inference of postseismic model following the 2012 Indian Ocean earthquake

NASA Astrophysics Data System (ADS)

Pratama, C.; Ito, T.; Sasajima, R.; Tabei, T.; Kimata, F.; Gunawan, E.; Ohta, Y.; Yamashina, T.; Ismail, N.; Muksin, U.; Maulida, P.; Meilano, I.; Nurdin, I.; Sugiyanto, D.; Efendi, J.

2017-12-01

Postseismic deformation following the 2012 Indian Ocean earthquake has been modeled by several studies (Han et al. 2015, Hu et al. 2016, Masuti et al. 2016). Although each study used different method and dataset, the previous studies constructed a significant difference of earth structure. Han et al. (2015) ignored subducting slab beneath Sumatra while Masuti et al. (2016) neglect sphericity of the earth. Hu et al. (2016) incorporated elastic slab and spherical earth but used uniform rigidity in each layer of the model. As a result, Han et al. (2015) model estimated one order higher Maxwell viscosity than the Hu et al. (2016) and half order lower Kelvin viscosity than the Masuti et al. (2016) model predicted. In the present study, we conduct a quantitative analysis of each heterogeneous geometry and parameter effect on rheology inference. We develop heterogeneous three-dimensional spherical-earth finite element models. We investigate the effect of subducting slab, spherical earth, and three-dimensional earth rigidity on estimated lithosphere-asthenosphere rheology beneath the Indian Ocean. A wide range of viscosity structure from time constant rheology to time dependent rheology was chosen as previous studies have been modeled. In order to evaluate actual displacement, we compared the model to the Global Navigation Satellite System (GNSS) observation. We incorporate the GNSS data from previous studies and introduce new GNSS site as a part of the Indonesian Continuously Operating Reference Stations (InaCORS) located in Sumatra that has not been used in the last analysis. As a preliminary result, we obtained the effect of the spherical earth and elastic slab when we assumed burgers rheology. The model that incorporates the sphericity of the earth needs a one third order lower viscosity than the model that neglects earth curvature. The model that includes elastic slab needs half order lower viscosity than the model that excluding the elastic slab.

The Role of Shabansky Orbits in Compression-Related Electromagnetic Ion Cyclotron Wave Growth (Postprint)

DTIC Science & Technology

2012-03-15

compressing the field. Equation (5) uses a geocentric spherical coordinate system with units of length in Earth radii. It is clear that setting b1 = 0...in a complementary approach to the one used by McCollough et al. [2009]. 3. Anisotropy Arising From Magnetic Field Configuration [21] McCollough et al

Hipparchus' coordinate system

NASA Astrophysics Data System (ADS)

Duke, Dennis W.

2002-07-01

In his "Histoire de l'Astronomie Ancienne" Delambre concludes unequivocally that Hipparchus knew and used a definite system of celestial spherical coordinates, namely the right ascension and declination system that we use today. The basis of Delambre's conclusion was disarmingly simple: he pointed out that in the "Commentary to Aratus" Hipparchus actually quotes the positions of numerous stars directly in right ascension and declination (or more often its complement, polar distance). Nearly two centuries later, in his "A History of Ancient Mathematical Astronomy", Neugebauer not only completely ignores Delambre's conclusion on this issue, but goes further to propose his own, as we shall see quite fanciful, theory that begins "From the Commentary to Aratus, it is quite obvious that at Hipparchus' time a definite system of spherical coordinates for stellar positions did not yet exist." and concludes "...nowhere in Greek astronomy before the catalogue of stars in the Almagest is it attested that orthogonal spherical coordinates are used to determine stellar positions." Today it is clear that Neugebauer's theory is conventionally accepted. It is the purpose of this paper to offer fresh arguments that Delambre was correct.

Analysis of errors introduced by geographic coordinate systems on weather numeric prediction modeling

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

Cao, Yanni; Cervone, Guido; Barkley, Zachary

Most atmospheric models, including the Weather Research and Forecasting (WRF) model, use a spherical geographic coordinate system to internally represent input data and perform computations. However, most geographic information system (GIS) input data used by the models are based on a spheroid datum because it better represents the actual geometry of the earth. WRF and other atmospheric models use these GIS input layers as if they were in a spherical coordinate system without accounting for the difference in datum. When GIS layers are not properly reprojected, latitudinal errors of up to 21 km in the midlatitudes are introduced. Recent studiesmore » have suggested that for very high-resolution applications, the difference in datum in the GIS input data (e.g., terrain land use, orography) should be taken into account. However, the magnitude of errors introduced by the difference in coordinate systems remains unclear. This research quantifies the effect of using a spherical vs. a spheroid datum for the input GIS layers used by WRF to study greenhouse gas transport and dispersion in northeast Pennsylvania.« less

Analysis of errors introduced by geographic coordinate systems on weather numeric prediction modeling

DOE PAGES

Cao, Yanni; Cervone, Guido; Barkley, Zachary; ...

2017-09-19

Most atmospheric models, including the Weather Research and Forecasting (WRF) model, use a spherical geographic coordinate system to internally represent input data and perform computations. However, most geographic information system (GIS) input data used by the models are based on a spheroid datum because it better represents the actual geometry of the earth. WRF and other atmospheric models use these GIS input layers as if they were in a spherical coordinate system without accounting for the difference in datum. When GIS layers are not properly reprojected, latitudinal errors of up to 21 km in the midlatitudes are introduced. Recent studiesmore » have suggested that for very high-resolution applications, the difference in datum in the GIS input data (e.g., terrain land use, orography) should be taken into account. However, the magnitude of errors introduced by the difference in coordinate systems remains unclear. This research quantifies the effect of using a spherical vs. a spheroid datum for the input GIS layers used by WRF to study greenhouse gas transport and dispersion in northeast Pennsylvania.« less

Analysis of errors introduced by geographic coordinate systems on weather numeric prediction modeling

NASA Astrophysics Data System (ADS)

Cao, Yanni; Cervone, Guido; Barkley, Zachary; Lauvaux, Thomas; Deng, Aijun; Taylor, Alan

2017-09-01

Most atmospheric models, including the Weather Research and Forecasting (WRF) model, use a spherical geographic coordinate system to internally represent input data and perform computations. However, most geographic information system (GIS) input data used by the models are based on a spheroid datum because it better represents the actual geometry of the earth. WRF and other atmospheric models use these GIS input layers as if they were in a spherical coordinate system without accounting for the difference in datum. When GIS layers are not properly reprojected, latitudinal errors of up to 21 km in the midlatitudes are introduced. Recent studies have suggested that for very high-resolution applications, the difference in datum in the GIS input data (e.g., terrain land use, orography) should be taken into account. However, the magnitude of errors introduced by the difference in coordinate systems remains unclear. This research quantifies the effect of using a spherical vs. a spheroid datum for the input GIS layers used by WRF to study greenhouse gas transport and dispersion in northeast Pennsylvania.

Resonance energy transfer: The unified theory via vector spherical harmonics

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

Grinter, Roger, E-mail: r.grinter@uea.ac.uk; Jones, Garth A., E-mail: garth.jones@uea.ac.uk

2016-08-21

In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in terms of vector spherical harmonics while Hankel functions are used to define the radial component. This approach alleviates the problem of having to select physically correct solution from non-physical solutions, which seems to be inherentmore » in plane wave derivations. The spherical coordinate system allows one to easily decompose the photon’s fields into longitudinal and transverse components and offers a natural way to analyse near-, intermediate-, and far-zone RET within the context of the relative orientation of the transition dipole moments for the two molecules.« less

Effects of zonal flows on correlation between energy balance and energy conservation associated with nonlinear nonviscous atmospheric dynamics in a thin rotating spherical shell

NASA Astrophysics Data System (ADS)

Ibragimov, Ranis N.

2018-03-01

The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Syntheses, structures, photoluminescence of four dicarboxylate-controlled Zn(II) coordination complexes incorporating flexible 1-(4-pyridylmethyl)-benzimidazole ligand

NASA Astrophysics Data System (ADS)

Hao, Hong-Jun; Du, Ming-Yue; Wang, Dan-Feng; Sun, Cheng-Jie; Wang, Zhan-Hui; Huang, Rong-Bin; Zheng, Lan-Sun

2013-09-01

Four Zn(II) coordination complexes, namely {[Zn(pmbm)2(tpa)]·H2O}n (1), {[Zn(pmbm)(phda)]·2(H2O)}n (2), [Zn(pmbm)(aze)]n (3), {[Zn(pmbm)(1,4-ndc)]·2(CH3OH)}n (4) [pmbm = 1-(4-pyridylmethyl)-benzimidazole, H2tpa = terephthalic acid, H2phda = phenylenediacetic acid, H2aze = azelaic acid, 1,4-ndcH2 = 1,4-naphthalenedicarboxylic acid] have been synthesized by solution phase ultrasonic reactions of Zn(AC)2·2H2O with pmbm and various dicarboxylates ligands under the ammoniacal condition. All the complexes have been characterized by elemental analyses, IR spectra and X-ray diffraction. Complexes 1 and 2 exhibit one-dimensional chains structure and complex 3 and 4 are two-dimensional sheets structure with (4,4) topology. Complexes 1-4 spanning from one-dimensional chains to two-dimensional sheets suggest that dicarboxylates play significant roles in the formation of such coordination architectures. The photoluminescences of the complexes were also investigated in the solid state at room temperature.

Spherical shock-wave propagation in three-dimensional granular packings.

PubMed

Xue, Kun; Bai, Chun-Hua

2011-02-01

We investigate numerically the spherical shock-wave propagation in an open dense granular packing perturbed by the sudden expansion of a spherical intruder in the interior of the pack, focusing on the correlation between geometrical fabrics and propagating properties. The measurements of the temporal and spatial variations in a variety of propagating properties define a consistent serrated wave substructure with characteristic length on the orders of particle diameters. Further inspection of particle packing reveals a well-defined particle layering that persists several particle diameters away from the intruder, although its dominant effects are only within one to two diameters. This interface-induced layering not only exactly coincides with the serrated wave profile, but also highlights the competition between two energy transmission mechanisms involving distinct transport speeds. The alternating dominances between these two mechanisms contribute to the nonlinear wave propagation on the particle scale. Moreover, the proliferation of intricate three-dimensional contact force networks suggests the anisotropic stress transmission, which is found to also arise from the localized packing structure in the vicinity of the intruder.

Accuracy of methods for calculating volumetric wear from coordinate measuring machine data of retrieved metal-on-metal hip joint implants.

PubMed

Lu, Zhen; McKellop, Harry A

2014-03-01

This study compared the accuracy and sensitivity of several numerical methods employing spherical or plane triangles for calculating the volumetric wear of retrieved metal-on-metal hip joint implants from coordinate measuring machine measurements. Five methods, one using spherical triangles and four using plane triangles to represent the bearing and the best-fit surfaces, were assessed and compared on a perfect hemisphere model and a hemi-ellipsoid model (i.e. unworn models), computer-generated wear models and wear-tested femoral balls, with point spacings of 0.5, 1, 2 and 3 mm. The results showed that the algorithm (Method 1) employing spherical triangles to represent the bearing surface and to scale the mesh to the best-fit surfaces produced adequate accuracy for the wear volume with point spacings of 0.5, 1, 2 and 3 mm. The algorithms (Methods 2-4) using plane triangles to represent the bearing surface and to scale the mesh to the best-fit surface also produced accuracies that were comparable to that with spherical triangles. In contrast, if the bearing surface was represented with a mesh of plane triangles and the best-fit surface was taken as a smooth surface without discretization (Method 5), the algorithm produced much lower accuracy with a point spacing of 0.5 mm than Methods 1-4 with a point spacing of 3 mm.

Thermoelastic-plastic flow equations in general coordinates

DOE PAGES

Blaschke, Daniel N.; Preston, Dean L.

2018-03-28

The equations governing the thermoelastic-plastic flow of isotropic solids in the Prandtl- Reuss and small anisotropy approximations in Cartesian coordinates are generalized to arbitrary coordinate systems. In applications the choice of coordinates is dictated by the symmetry of the solid flow. The generally invariant equations are evaluated in spherical, cylindrical (including uniaxial), and both prolate and oblate spheroidal coordinates.

Thermoelastic-plastic flow equations in general coordinates

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

Blaschke, Daniel N.; Preston, Dean L.

The equations governing the thermoelastic-plastic flow of isotropic solids in the Prandtl- Reuss and small anisotropy approximations in Cartesian coordinates are generalized to arbitrary coordinate systems. In applications the choice of coordinates is dictated by the symmetry of the solid flow. The generally invariant equations are evaluated in spherical, cylindrical (including uniaxial), and both prolate and oblate spheroidal coordinates.

One-dimensional array of gold nanoparticles fabricated using biotemplate and its application to fine FET

NASA Astrophysics Data System (ADS)

Ban, Takahiko; Uenuma, Mutsunori; Migita, Shinji; Okamoto, Naofumi; Ishikawa, Yasuaki; Uraoka, Yukiharu; Yamashita, Ichiro; Yamamoto, Shin-ichi

2018-06-01

By synthesizing AuS nanoparticles (NPs) with spherical shell protein (ferritin) and using a V-groove, a one-dimensional array of NPs was formed at the bottom of the V-groove. It has been reported that AuS NPs are converted to Au NPs by UV/ozone treatment. Floating gate memory (FGM) was fabricated by applying this one-dimensional array to V-grooved junctionless (JL) FETs, V-grooved nin-like-type FETs, and pip-like-type FETs, which are fine FETs. In JL-FETs, it is considered that conversion occurred because of good charge storage efficiency, and operation in the opposite direction to normal FGM operation was seen. In the nin-like and pip-like types devices, the same operation as in conventional FGM was shown, and the width of the memory window was about the same size as when one electron entered one NP. The one-dimensional arrangement of the metal NPs used in this study is considered to be applicable to various fields of nanotechnology.

Wavefront-aberration measurement and systematic-error analysis of a high numerical-aperture objective

NASA Astrophysics Data System (ADS)

Liu, Zhixiang; Xing, Tingwen; Jiang, Yadong; Lv, Baobin

2018-02-01

A two-dimensional (2-D) shearing interferometer based on an amplitude chessboard grating was designed to measure the wavefront aberration of a high numerical-aperture (NA) objective. Chessboard gratings offer better diffraction efficiencies and fewer disturbing diffraction orders than traditional cross gratings. The wavefront aberration of the tested objective was retrieved from the shearing interferogram using the Fourier transform and differential Zernike polynomial-fitting methods. Grating manufacturing errors, including the duty-cycle and pattern-deviation errors, were analyzed with the Fourier transform method. Then, according to the relation between the spherical pupil and planar detector coordinates, the influence of the distortion of the pupil coordinates was simulated. Finally, the systematic error attributable to grating alignment errors was deduced through the geometrical ray-tracing method. Experimental results indicate that the measuring repeatability (3σ) of the wavefront aberration of an objective with NA 0.4 was 3.4 mλ. The systematic-error results were consistent with previous analyses. Thus, the correct wavefront aberration can be obtained after calibration.

Droplet Combustion and Soot Formation in Microgravity

NASA Technical Reports Server (NTRS)

Avedisian, C. Thomas

1994-01-01

One of the most complex processes involved in the combustion ot liquid fuels is the formation of soot. A well characterized flow field and simplified flame structure can improve considerably the understanding of soot formation processes. The simplest flame shape to analyze for a droplet is spherical with its associated one-dimensional flow field. It is a fundamental limit and the oldest and most often analyzed configuration of droplet combustion. Spherical symmetry in the droplet burning process will arise when there is no relative motion between the droplet and ambience or uneven heating around the droplet periphery, and buoyancy effects are negligible. The flame and droplet are then concentric with each other and there is no liquid circulation within the droplet. An understanding of the effect of soot on droplet combustion should therefore benefit from this simplified configuration. Soot formed during spherically symmetric droplet combustion, however, has only recently drawn attention and it appears to be one of the few aspects associated with droplet combustion which have not yet been thoroughly investigated. For this review, the broad subject of droplet combustion is narrowed considerably by restricting attention specifically to soot combined with spherically symmetric droplet burning processes that are promoted.

Supramolecular architectures in Co(II) and Cu(II) complexes with thiophene-2-carboxylate and 2-amino-4,6-dimethoxypyrimidine ligands.

PubMed

Karthikeyan, Ammasai; Thomas Muthiah, Packianathan; Perdih, Franc

2016-05-01

The coordination chemistry of mixed-ligand complexes continues to be an active area of research since these compounds have a wide range of applications. Many coordination polymers and metal-organic framworks are emerging as novel functional materials. Aminopyrimidine and its derivatives are flexible ligands with versatile binding and coordination modes which have been proven to be useful in the construction of organic-inorganic hybrid materials and coordination polymers. Thiophenecarboxylic acid, its derivatives and their complexes exhibit pharmacological properties. Cobalt(II) and copper(II) complexes of thiophenecarboxylate have many biological applications, for example, as antifungal and antitumor agents. Two new cobalt(II) and copper(II) complexes incorporating thiophene-2-carboxylate (2-TPC) and 2-amino-4,6-dimethoxypyrimidine (OMP) ligands have been synthesized and characterized by X-ray diffraction studies, namely (2-amino-4,6-dimethoxypyrimidine-κN)aquachlorido(thiophene-2-carboxylato-κO)cobalt(II) monohydrate, [Co(C5H3O2S)Cl(C6H9N3O2)(H2O)]·H2O, (I), and catena-poly[copper(II)-tetrakis(μ-thiophene-2-carboxylato-κ(2)O:O')-copper(II)-(μ-2-amino-4,6-dimethoxypyrimidine-κ(2)N(1):N(3))], [Cu2(C5H3O2S)4(C6H9N3O2)]n, (II). In (I), the Co(II) ion has a distorted tetrahedral coordination environment involving one O atom from a monodentate 2-TPC ligand, one N atom from an OMP ligand, one chloride ligand and one O atom of a water molecule. An additional water molecule is present in the asymmetric unit. The amino group of the coordinated OMP molecule and the coordinated carboxylate O atom of the 2-TPC ligand form an interligand N-H...O hydrogen bond, generating an S(6) ring motif. The pyrimidine molecules also form a base pair [R2(2)(8) motif] via a pair of N-H...N hydrogen bonds. These interactions, together with O-H...O and O-H...Cl hydrogen bonds and π-π stacking interactions, generate a three-dimensional supramolecular architecture. The one-dimensional coordination polymer (II) contains the classical paddle-wheel [Cu2(CH3COO)4(H2O)2] unit, where each carboxylate group of four 2-TPC ligands bridges two square-pyramidally coordinated Cu(II) ions and the apically coordinated OMP ligands bridge the dinuclear copper units. Each dinuclear copper unit has a crystallographic inversion centre, whereas the bridging OMP ligand has crystallographic twofold symmetry. The one-dimensional polymeric chains self-assemble via N-H...O, π-π and C-H...π interactions, generating a three-dimensional supramolecular architecture.

Higher-dimensional gravitational collapse of perfect fluid spherically symmetric spacetime in f(R, T) gravity

NASA Astrophysics Data System (ADS)

Khan, Suhail; Khan, Muhammad Shoaib; Ali, Amjad

2018-04-01

In this paper, our aim is to study (n + 2)-dimensional collapse of perfect fluid spherically symmetric spacetime in the context of f(R, T) gravity. The matching conditions are acquired by considering a spherically symmetric non-static (n + 2)-dimensional metric in the inner region and Schwarzschild (n + 2)-dimensional metric in the outer region of the star. To solve the field equations for above settings in f(R, T) gravity, we choose the stress-energy tensor trace and the Ricci scalar as constants. It is observed that two physical horizons, namely, cosmological and black hole horizons appear as a consequence of this collapse. A singularity is also formed after the birth of both the horizons. It is also observed that the term f(R0, T0) slows down the collapsing process.

Comment on “Error made in reports of main field decay”

NASA Astrophysics Data System (ADS)

IAGA Working Group V-MOD on Geomagnetic Field Modeling,; Maus, Stefan; Macmillan, Susan

2004-09-01

As the International Association of Geomagnetism and Aeronomy (IAGA) Working Group on Geomagnetic Field Modeling (http://www.ngdc.noaa.gov/IAGA/vmod/), responsible for the International Geomagnetic Reference Field (IGRF) [Macmillan et al., 2003], we would like to comment on the Forum article by Wallace H.Campbell (Eos,85(16),20 April 2004). Campbell claims that reports of dipole decay at a special session held at the AGU 2003 Fall Meeting were misleading due to an incorrect choice of the coordinate system for the spherical harmonic analysis (SHA) of the geomagnetic field used for the IGRF the model on which the decay calculation was based.Campbell alleges that the dipole moment of a spherical harmonic expansion depends on the choice of the origin of the coordinate system. In his textbook on geomagnetism, Campbell goes one step further in asserting that, without changing the origin, the process of “tilting the analysis axis to align with the geomagnetic axis…would enhance the dipole term at the expense of the higher multipoles” [Campbell, 2003].

A method of smoothed particle hydrodynamics using spheroidal kernels

NASA Technical Reports Server (NTRS)

Fulbright, Michael S.; Benz, Willy; Davies, Melvyn B.

1995-01-01

We present a new method of three-dimensional smoothed particle hydrodynamics (SPH) designed to model systems dominated by deformation along a preferential axis. These systems cause severe problems for SPH codes using spherical kernels, which are best suited for modeling systems which retain rough spherical symmetry. Our method allows the smoothing length in the direction of the deformation to evolve independently of the smoothing length in the perpendicular plane, resulting in a kernel with a spheroidal shape. As a result the spatial resolution in the direction of deformation is significantly improved. As a test case we present the one-dimensional homologous collapse of a zero-temperature, uniform-density cloud, which serves to demonstrate the advantages of spheroidal kernels. We also present new results on the problem of the tidal disruption of a star by a massive black hole.

Global Resolution of the Physical Vacuum Singularity for Three-Dimensional Isentropic Inviscid Flows with Damping in Spherically Symmetric Motions

NASA Astrophysics Data System (ADS)

Zeng, Huihui

2017-10-01

For the gas-vacuum interface problem with physical singularity and the sound speed being {C^{{1}/{2}}}-Hölder continuous near vacuum boundaries of the isentropic compressible Euler equations with damping, the global existence of smooth solutions and the convergence to Barenblatt self-similar solutions of the corresponding porous media equation are proved in this paper for spherically symmetric motions in three dimensions; this is done by overcoming the analytical difficulties caused by the coordinate's singularity near the center of symmetry, and the physical vacuum singularity to which standard methods of symmetric hyperbolic systems do not apply. Various weights are identified to resolve the singularity near the vacuum boundary and the center of symmetry globally in time. The results obtained here contribute to the theory of global solutions to vacuum boundary problems of compressible inviscid fluids, for which the currently available results are mainly for the local-in-time well-posedness theory, and also to the theory of global smooth solutions of dissipative hyperbolic systems which fail to be strictly hyperbolic.

The coordination chemistry of group 15 element ligand complexes--a developing area.

PubMed

Scheer, Manfred

2008-09-07

A survey of the contemporary challenges of the field of unsubstituted group 15 element ligand complexes (excluding N) is given. The focus of the article is on the coordination chemistry behaviour of such E(n) ligand complexes. This field is subdivided into two areas of reactivity: E(n) ligand complexes with (i) noncoordinated Lewis-acidic cations and (ii) Lewis-acidic coordination compounds containing at least one permanently coordinating ligand. In the latter case, insoluble 1D and 2D polymers respectively are obtained; however, under special conditions soluble, spherical, fullerene-like giant molecules are formed. These nano-sized molecules are up to 2.4 nm in diameter and are able to encapsulate small molecules in their holes. In contrast, the first-mentioned field uses weakly coordinating anions to obtain readily soluble di- and polycationic products. These show depolymerisation tendencies in solution under the formation of oligomer-monomer equilibria and thus reveal dynamic supramolecular aggregation processes.

Optimized formulas for the gravitational field of a tesseroid

NASA Astrophysics Data System (ADS)

Grombein, Thomas; Seitz, Kurt; Heck, Bernhard

2013-07-01

Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton's integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid's potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. Based on this idea, optimized formulas for the gravitational potential of a homogeneous tesseroid and its derivatives up to second-order are elaborated in this paper. These new formulas do not suffer from the polar singularity of the spherical coordinate system and can, therefore, be evaluated for any position on the globe. Since integrals over tesseroid volumes cannot be solved analytically, the numerical evaluation is achieved by means of expanding the integral kernel in a Taylor series with fourth-order error in the spatial coordinates of the integration point. As the structure of the Cartesian integral kernel is substantially simplified, Taylor coefficients can be represented in a compact and computationally attractive form. Thus, the use of the optimized tesseroid formulas particularly benefits from a significant decrease in computation time by about 45 % compared to previously used algorithms. In order to show the computational efficiency and to validate the mathematical derivations, the new tesseroid formulas are applied to two realistic numerical experiments and are compared to previously published tesseroid methods and the conventional prism approach.

Analysis of the curve of Spee and the curve of Wilson in adult Indian population: A three-dimensional measurement study.

PubMed

Surendran, Sowmya Velekkatt; Hussain, Sharmila; Bhoominthan, S; Nayar, Sanjna; Jayesh, Ragavendra

2016-01-01

When reconstructing the occlusal curvatures dentists often use a 4-inch radii arc as a rough standard based on Monson spherical theory. The use of an identical radius for the curve of Spee for all patients may not be appropriate because each patient is individually different. The validity of application of this theory in the Indian population and the present study has been undertaken. This study is an attempt to evaluate the curve of Spee and curve of Wilson in young Indian population using three dimensional analysis. This study compared the radius and the depth of right and left, maxillary and mandibular curves of Spee and the radius of maxillary and mandibular curves of Wilson in males and females. The cusp tips of canines, buccal cusp tips of premolars and molars and palatal/lingual cusp tips of second molars of 60 maxillary and 60 mandibular casts were obtained. Three-dimensional (x, y, z) coordinates of the cusp tips of the molars, premolars, and canines of the right and left sides of the maxilla and mandible were obtained with three dimensional coordinate measuring machine. The radius and the depth of right and left, maxillary and mandibular curves of Spee and the radius of maxillary and mandibular curves of Wilson were measured by means of computer software Metrologic-XG. Pearson's correlation test and Independent t-test were used to test the statistical significance (α=.05). The values of curve of Spee and curve of Wilson in Indian population obtained from this study were higher than the 4 inch (100 mm) radius proposed by Monson. These findings suggest ethnic differences in the radius of curve of Spee and curve of Wilson.

The R.I. Pimenov unified gravitation and electromagnetism field theory as semi-Riemannian geometry

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

Gromov, N. A., E-mail: gromov@dm.komisc.r

2009-05-15

More than forty years ago R.I. Pimenov introduced a new geometry-semi-Riemannian one-as a set of geometrical objects consistent with a fibering pr: M{sub n} {yields} M{sub m}. He suggested the heuristic principle according to which the physically different quantities (meter, second, Coulomb, etc.) are geometrically modelled as space coordinates that are not superposed by automorphisms. As there is only one type of coordinates in Riemannian geometry and only three types of coordinates in pseudo-Riemannian one, a multiple-fibered semi-Riemannian geometry is the most appropriate one for the treatment of more than three different physical quantities as unified geometrical field theory. Semi-Euclideanmore » geometry {sup 3}R{sub 5}{sup 4} with 1-dimensional fiber x{sup 5} and 4-dimensional Minkowski space-time as a base is naturally interpreted as classical electrodynamics. Semi-Riemannian geometry {sup 3}V{sub 5}{sup 4} with the general relativity pseudo-Riemannian space-time {sup 3}V{sub 4}, and 1-dimensional fiber x{sup 5}, responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike Kaluza-Klein theories, where the fifth coordinate appears in nondegenerate Riemannian or pseudo-Riemannian geometry, the theory based on semi-Riemannian geometry is free from defects of the former. In particular, scalar field does not arise.« less

Relativistic scattered-wave theory. II - Normalization and symmetrization. [of Dirac wavefunctions

NASA Technical Reports Server (NTRS)

Yang, C. Y.

1978-01-01

Formalisms for normalization and symmetrization of one-electron Dirac scattered-wave wavefunctions are presented. The normalization integral consists of one-dimensional radial integrals for the spherical regions and an analytic expression for the intersphere region. Symmetrization drastically reduces the size of the secular matrix to be solved. Examples for planar Pb2Se2 and tetrahedral Pd4 are discussed.

One-dimensional ion-beam figuring for grazing-incidence reflective optics

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

Zhou, Lin; Idir, Mourad; Bouet, Nathalie

2016-01-01

One-dimensional ion-beam figuring (1D-IBF) can improve grazing-incidence reflective optics, such as Kirkpatrick–Baez mirrors. 1D-IBF requires only one motion degree of freedom, which reduces equipment complexity, resulting in compact and low-cost IBF instrumentation. Furthermore, 1D-IBF is easy to integrate into a single vacuum system with other fabrication processes, such as a thin-film deposition. The NSLS-II Optical Metrology and Fabrication Group has recently integrated the 1D-IBF function into an existing thin-film deposition system by adding an RF ion source to the system. Using a rectangular grid, a 1D removal function needed to perform 1D-IBF has been produced. In this paper, demonstration experimentsmore » of the 1D-IBF process are presented on one spherical and two plane samples. The final residual errors on both plane samples are less than 1 nm r.m.s. In conclusion, the surface error on the spherical sample has been successfully reduced by a factor of 12. The results show that the 1D-IBF method is an effective method to process high-precision 1D synchrotron optics.« less

The reduction, verification and interpretation of MAGSAT magnetic data over Canada

NASA Technical Reports Server (NTRS)

Coles, R. L. (Principal Investigator); Haines, G. V.; Vanbeek, G. J.; Walker, J. K.; Newitt, L. R.

1982-01-01

Consideration is being given to representing the magnetic field in the area 40 deg N to 83 deg N by means of functions in spherical coordinates. A solution to Laplace's equation for the magnetic potential over a restricted area was found, and programming and testing are currently being carried out. Magnetic anomaly modelling is proceeding. The program SPHERE, which was adapted to function correctly on the Cyber computer, is now operational, for deriving gravity and magnetic models in a spherical coordinate system.

Harwell Subroutine Library. A Catalogue of Subroutines (1973),

DTIC Science & Technology

1973-07-01

up the equations AT Ax = ATb. There may be more than one right-hand size. Remark: If the solution is required see MAO9A. Versions: MAOA ; MAOBAD. Calls...Hermitian MEO8A source decks-modification of OEOIA real gene .’al to Hessenberg sparsity pattern TDO2A MC08A, MCI4A spherical co-ordinates GAOIA real

Spherical 3D isotropic wavelets

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2012-04-01

Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html

Generalized spherical and simplicial coordinates

NASA Astrophysics Data System (ADS)

Richter, Wolf-Dieter

2007-12-01

Elementary trigonometric quantities are defined in l2,p analogously to that in l2,2, the sine and cosine functions are generalized for each p>0 as functions sinp and cosp such that they satisfy the basic equation cosp([phi])p+sinp([phi])p=1. The p-generalized radius coordinate of a point [xi][set membership, variant]Rn is defined for each p>0 as . On combining these quantities, ln,p-spherical coordinates are defined. It is shown that these coordinates are nearly related to ln,p-simplicial coordinates. The Jacobians of these generalized coordinate transformations are derived. Applications and interpretations from analysis deal especially with the definition of a generalized surface content on ln,p-spheres which is nearly related to a modified co-area formula and an extension of Cavalieri's and Torricelli's indivisibeln method, and with differential equations. Applications from probability theory deal especially with a geometric interpretation of the uniform probability distribution on the ln,p-sphere and with the derivation of certain generalized statistical distributions.

A new method to acquire 3-D images of a dental cast

NASA Astrophysics Data System (ADS)

Li, Zhongke; Yi, Yaxing; Zhu, Zhen; Li, Hua; Qin, Yongyuan

2006-01-01

This paper introduced our newly developed method to acquire three-dimensional images of a dental cast. A rotatable table, a laser-knife, a mirror, a CCD camera and a personal computer made up of a three-dimensional data acquiring system. A dental cast is placed on the table; the mirror is installed beside the table; a linear laser is projected to the dental cast; the CCD camera is put up above the dental cast, it can take picture of the dental cast and the shadow in the mirror; while the table rotating, the camera records the shape of the laser streak projected on the dental cast, and transmit the data to the computer. After the table rotated one circuit, the computer processes the data, calculates the three-dimensional coordinates of the dental cast's surface. In data processing procedure, artificial neural networks are enrolled to calibrate the lens distortion, map coordinates form screen coordinate system to world coordinate system. According to the three-dimensional coordinates, the computer reconstructs the stereo image of the dental cast. It is essential for computer-aided diagnosis and treatment planning in orthodontics. In comparison with other systems in service, for example, laser beam three-dimensional scanning system, the characteristic of this three-dimensional data acquiring system: a. celerity, it casts only 1 minute to scan a dental cast; b. compact, the machinery is simple and compact; c. no blind zone, a mirror is introduced ably to reduce blind zone.

A set of alkali and alkaline-earth coordination polymers based on the ligand 2-(1H-benzotriazol-1-yl) acetic acid: Effects the radius of metal ions on structures and properties

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

Wang, Jin-Hua; Tang, Gui-Mei, E-mail: meiguit@163.com; Qin, Ting-Xiao

2014-11-15

Four new metal coordination complexes, namely, [Na(BTA)]{sub n} (1), [K{sub 2}(BTA){sub 2}(μ{sub 2}-H{sub 2}O)]{sub n} (2), and [M(BTA){sub 2}(H{sub 2}O){sub 2}]{sub n} (M=Ca(II) and Sr(II) for 3 and 4, respectively) [BTA=2-(1H-benzotriazol-1-yl) acetic anion], have been obtained under hydrothermal condition, by reacting the different alkali and alkaline-earth metal hydroxides with HBTA. Complexes 1–4 were structurally characterized by X-ray single-crystal diffraction, EA, IR, PXRD, and thermogravimetry analysis (TGA). These complexes display low-dimensional features displaying various two-dimensional (2D) and one-dimensional (1D) coordination motifs. Complex 1 displays a 2D layer with the thickness of 1.5 nm and possesses a topologic structure of a 11more » nodal net with Schläfli symbol of (3{sup 18}). Complex 2 also shows a thick 2D sheet and its topologic structure is a 9 nodes with Schläfli symbol of (3{sup 11}×4{sup 2}). Complexes 3 and 4 possess a 1D linear chain and further stack via hydrogen bonding interactions to generate a three-dimensional supramolecular architecture. These results suggest that both the coordination preferences of the metal ions and the versatile nature of this flexible ligand play a critical role in the final structures. The luminescent spectra show strong emission intensities in complexes 1–4, which display violet photoluminescence. Additionally, ferroelectric, dielectric and nonlinear optic (NLO) second-harmonic generation (SHG) properties of 2 are discussed in detail. - Graphical abstract: A set of alkali and alkaline-earth metal coordination polymers were hydrothermally synthesized by 2-(1H-benzotriazol-1-yl)acetic acid, displaying interesting topologic motifs from two-dimension to one-dimension and specific physical properties. - Highlights: • Alkali and alkaline-earth metal coordination polymers have been obtained. • The ligand 2-(1H-benzotriazol-1-yl)acetic acid has been adopted. • The two-dimensional and one-dimensional structures have been observed. • The properties of second harmonic generation and ferroelectricity for complex 2.« less

Methods and considerations to determine sphere center from terrestrial laser scanner point cloud data

NASA Astrophysics Data System (ADS)

Rachakonda, Prem; Muralikrishnan, Bala; Cournoyer, Luc; Cheok, Geraldine; Lee, Vincent; Shilling, Meghan; Sawyer, Daniel

2017-10-01

The Dimensional Metrology Group at the National Institute of Standards and Technology is performing research to support the development of documentary standards within the ASTM E57 committee. This committee is addressing the point-to-point performance evaluation of a subclass of 3D imaging systems called terrestrial laser scanners (TLSs), which are laser-based and use a spherical coordinate system. This paper discusses the usage of sphere targets for this effort, and methods to minimize the errors due to the determination of their centers. The key contributions of this paper include methods to segment sphere data from a TLS point cloud, and the study of some of the factors that influence the determination of sphere centers.

Mechanisms of the Wurtzite to Rocksalt Transformation in CdSe Nanocrystals

NASA Astrophysics Data System (ADS)

Grünwald, Michael; Rabani, Eran; Dellago, Christoph

2006-06-01

We study the pressure-driven phase transition from the four-coordinate wurtzite to the six-coordinate rocksalt structure in CdSe nanocrystals with molecular dynamics computer simulations. With an ideal gas as the pressure medium, we apply hydrostatic pressure to spherical and faceted nanocrystals ranging in diameter from 25 to 62 Å. In spherical crystals, the main mechanism of the transformation involves the sliding of (100) planes, but depending on the specific surface structure we also observe a second mechanism proceeding through the flattening of (100) planes. In faceted crystals, the transition proceeds via a five-coordinated hexagonal structure, which is stabilized at intermediate pressures due to dominant surface energetics.

A THREE-DIMENSIONAL NUMERICAL SOLUTION FOR THE SHAPE OF A ROTATIONALLY DISTORTED POLYTROPE OF INDEX UNITY

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

Kong, Dali; Zhang, Keke; Schubert, Gerald

2013-02-15

We present a new three-dimensional numerical method for calculating the non-spherical shape and internal structure of a model of a rapidly rotating gaseous body with a polytropic index of unity. The calculation is based on a finite-element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar that is valid only for a slowly rotating gaseous body, we apply it to models of Jupiter and a rapidly rotating, highly flattened star ({alpha} Eridani). In the case of Jupiter, the two-dimensional distributions of density and pressure are determined via a hybridmore » inverse approach by adjusting an a priori unknown coefficient in the equation of state until the model shape matches the observed shape of Jupiter. After obtaining the two-dimensional distribution of density, we then compute the zonal gravity coefficients and the total mass from the non-spherical model that takes full account of rotation-induced shape change. Our non-spherical model with a polytropic index of unity is able to produce the known mass of Jupiter with about 4% accuracy and the zonal gravitational coefficient J {sub 2} of Jupiter with better than 2% accuracy, a reasonable result considering that there is only one parameter in the model. For {alpha} Eridani, we calculate its rotationally distorted shape and internal structure based on the observationally deduced rotation rate and size of the star by using a similar hybrid inverse approach. Our model of the star closely approximates the observed flattening.« less

A new Pb{sup II}(ethylenediaminetetraacetate) coordination polymer with a two-dimensional layer structure

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

Zhao, D., E-mail: iamzd@hpu.edu.cn; Zhang, R. H.; Li, F. F.

2016-12-15

A new Pb{sup II}−edta{sup 4–} coordination polymer, Pb{sub 2}(edta)(H{sub 2}O){sub 0.76} (edta{sup 4–} = ethylenediaminetetraacetate) was synthesized under hydrothermal condition. Single crystal X-ray analysis reveals that it represents a novel two-dimensional (2D) Pb{sup 2+}–edta{sup 4–} layer structure with a (4,8{sup 2})-topology. Each edta{sup 4–} ligand employs its four carboxylate O and two N atoms to chelate one Pb{sup II} atom (hexa-coordinated) and connects five Pb{sup II} atoms (ennea-coordinated) via its four carboxylate groups to form 2D layer framework. Adjacent layers are packed into the overall structure through vander Waals interactions.

On the interpretations of Langevin stochastic equation in different coordinate systems

NASA Astrophysics Data System (ADS)

Martínez, E.; López-Díaz, L.; Torres, L.; Alejos, O.

2004-01-01

The stochastic Langevin Landau-Lifshitz equation is usually utilized in micromagnetics formalism to account for thermal effects. Commonly, two different interpretations of the stochastic integrals can be made: Ito and Stratonovich. In this work, the Langevin-Landau-Lifshitz (LLL) equation is written in both Cartesian and Spherical coordinates. If Spherical coordinates are employed, the noise is additive, and therefore, Ito and Stratonovich solutions are equal. This is not the case when (LLL) equation is written in Cartesian coordinates. In this case, the Langevin equation must be interpreted in the Stratonovich sense in order to reproduce correct statistical results. Nevertheless, the statistics of the numerical results obtained from Euler-Ito and Euler-Stratonovich schemes are equivalent due to the additional numerical constraint imposed in Cartesian system after each time step, which itself assures that the magnitude of the magnetization is preserved.

Tolerance analysis of optical telescopes using coherent addition of wavefront errors

NASA Technical Reports Server (NTRS)

Davenport, J. W.

1982-01-01

A near diffraction-limited telescope requires that tolerance analysis be done on the basis of system wavefront error. One method of analyzing the wavefront error is to represent the wavefront error function in terms of its Zernike polynomial expansion. A Ramsey-Korsch ray trace package, a computer program that simulates the tracing of rays through an optical telescope system, was expanded to include the Zernike polynomial expansion up through the fifth-order spherical term. An option to determine a 3 dimensional plot of the wavefront error function was also included in the Ramsey-Korsch package. Several assimulation runs were analyzed to determine the particular set of coefficients in the Zernike expansion that are effected by various errors such as tilt, decenter and despace. A 3 dimensional plot of each error up through the fifth-order spherical term was also included in the study. Tolerance analysis data are presented.

Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: nonspherical Schwarzschild waves and singularities at null infinity

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Hennig, Jörg

2018-03-01

We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Frauendiener and Hennig (2017 Class. Quantum Grav. 34 045005), to the case of general, nonsymmetric solutions. A key element of our approach is the modern standard representation of spacelike infinity as a cylinder. With a decomposition into spherical harmonics, we reduce the four-dimensional wave equation to a family of two-dimensional equations. These equations can be used to study the behaviour at the cylinder, where the solutions turn out to have, in general, logarithmic singularities at infinitely many orders. We derive regularity conditions that may be imposed on the initial data, in order to avoid the first singular terms. We then demonstrate that the fully pseudospectral time evolution scheme can be applied to this problem leading to a highly accurate numerical reconstruction of the nonsymmetric solutions. We are particularly interested in the behaviour of the solutions at future null infinity, and we numerically show that the singularities spread to null infinity from the critical set, where the cylinder approaches null infinity. The observed numerical behaviour is consistent with similar logarithmic singularities found analytically on the critical set. Finally, we demonstrate that even solutions with singularities at low orders can be obtained with high accuracy by virtue of a coordinate transformation that converts solutions with logarithmic singularities into smooth solutions.

A reappraisal of drug release laws using Monte Carlo simulations: the prevalence of the Weibull function.

PubMed

Kosmidis, Kosmas; Argyrakis, Panos; Macheras, Panos

2003-07-01

To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. A one-dimensional matrix, based on the theoretical assumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three-dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume interactions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different initial particle concentrations. The Higuchi law was verified using the Monte Carlo technique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull function parameters and the specific surface of the system was found. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.

Communication: Coordinate-dependent diffusivity from single molecule trajectories

NASA Astrophysics Data System (ADS)

Berezhkovskii, Alexander M.; Makarov, Dmitrii E.

2017-11-01

Single-molecule observations of biomolecular folding are commonly interpreted using the model of one-dimensional diffusion along a reaction coordinate, with a coordinate-independent diffusion coefficient. Recent analysis, however, suggests that more general models are required to account for single-molecule measurements performed with high temporal resolution. Here, we consider one such generalization: a model where the diffusion coefficient can be an arbitrary function of the reaction coordinate. Assuming Brownian dynamics along this coordinate, we derive an exact expression for the coordinate-dependent diffusivity in terms of the splitting probability within an arbitrarily chosen interval and the mean transition path time between the interval boundaries. This formula can be used to estimate the effective diffusion coefficient along a reaction coordinate directly from single-molecule trajectories.

A fast algorithm for forward-modeling of gravitational fields in spherical coordinates with 3D Gauss-Legendre quadrature

NASA Astrophysics Data System (ADS)

Zhao, G.; Liu, J.; Chen, B.; Guo, R.; Chen, L.

2017-12-01

Forward modeling of gravitational fields at large-scale requires to consider the curvature of the Earth and to evaluate the Newton's volume integral in spherical coordinates. To acquire fast and accurate gravitational effects for subsurface structures, subsurface mass distribution is usually discretized into small spherical prisms (called tesseroids). The gravity fields of tesseroids are generally calculated numerically. One of the commonly used numerical methods is the 3D Gauss-Legendre quadrature (GLQ). However, the traditional GLQ integration suffers from low computational efficiency and relatively poor accuracy when the observation surface is close to the source region. We developed a fast and high accuracy 3D GLQ integration based on the equivalence of kernel matrix, adaptive discretization and parallelization using OpenMP. The equivalence of kernel matrix strategy increases efficiency and reduces memory consumption by calculating and storing the same matrix elements in each kernel matrix just one time. In this method, the adaptive discretization strategy is used to improve the accuracy. The numerical investigations show that the executing time of the proposed method is reduced by two orders of magnitude compared with the traditional method that without these optimized strategies. High accuracy results can also be guaranteed no matter how close the computation points to the source region. In addition, the algorithm dramatically reduces the memory requirement by N times compared with the traditional method, where N is the number of discretization of the source region in the longitudinal direction. It makes the large-scale gravity forward modeling and inversion with a fine discretization possible.

Pulmonary tumor measurements from x-ray computed tomography in one, two, and three dimensions.

PubMed

Villemaire, Lauren; Owrangi, Amir M; Etemad-Rezai, Roya; Wilson, Laura; O'Riordan, Elaine; Keller, Harry; Driscoll, Brandon; Bauman, Glenn; Fenster, Aaron; Parraga, Grace

2011-11-01

We evaluated the accuracy and reproducibility of three-dimensional (3D) measurements of lung phantoms and patient tumors from x-ray computed tomography (CT) and compared these to one-dimensional (1D) and two-dimensional (2D) measurements. CT images of three spherical and three irregularly shaped tumor phantoms were evaluated by three observers who performed five repeated measurements. Additionally, three observers manually segmented 29 patient lung tumors five times each. Follow-up imaging was performed for 23 tumors and response criteria were compared. For a single subject, imaging was performed on nine occasions over 2 years to evaluate multidimensional tumor response. To evaluate measurement accuracy, we compared imaging measurements to ground truth using analysis of variance. For estimates of precision, intraobserver and interobserver coefficients of variation and intraclass correlations (ICC) were used. Linear regression and Pearson correlations were used to evaluate agreement and tumor response was descriptively compared. For spherical shaped phantoms, all measurements were highly accurate, but for irregularly shaped phantoms, only 3D measurements were in high agreement with ground truth measurements. All phantom and patient measurements showed high intra- and interobserver reproducibility (ICC >0.900). Over a 2-year period for a single patient, there was disagreement between tumor response classifications based on 3D measurements and those generated using 1D and 2D measurements. Tumor volume measurements were highly reproducible and accurate for irregular, spherical phantoms and patient tumors with nonuniform dimensions. Response classifications obtained from multidimensional measurements suggest that 3D measurements provide higher sensitivity to tumor response. Copyright © 2011 AUR. Published by Elsevier Inc. All rights reserved.

A new treatment of the albedo radiation pressure in the case of a uniform albedo and of a spherical satellite

NASA Technical Reports Server (NTRS)

Borderies, Nicole; Longaretti, Pierre-Yves

1990-01-01

The purpose of this paper is to present a model for the radiation pressure acceleration of a spherical satellite, due to the radiation reflected by a planet with a uniform albedo. A particular choice of variables allows one to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimensional integrals. Exact analytical expressions are found for the integrals corresponding to the case where the spacecraft does not 'see' the terminator. The other integrals can be computer either numerically, or analytical in an approximate form. The results are compared with those of Lochry (1966). The model is applied to Magellan, a spacecraft orbiting Venus.

Three-dimensional spherical models of convection in the earth's mantle

NASA Technical Reports Server (NTRS)

Bercovici, Dave; Schubert, Gerald; Glatzmaier, Gary A.

1989-01-01

Three-dimensional spherical models of mantle convection in the earth reveal that upwelling cylindrical plumes and downwelling planar sheets are the primary features of mantle circulation. Thus subduction zones and descending sheetlike slabs in the mantle are fundamental characteristics of thermal convection in a spherical shell and are not merely the consequences of the rigidity of the slabs, which are cooler than the surrounding mantle. Cylindrical mantle plumes that cause hot spots such as Hawaii are probably the only form of active upwelling and are therefore not just secondary convective currents separate from the large-scale mantle circulation.

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

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

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

2013-11-21

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

A three-dimensional spatial mapping approach to quantify fine-scale heterogeneity among leaves within canopies1

PubMed Central

Wingfield, Jenna L.; Ruane, Lauren G.; Patterson, Joshua D.

2017-01-01

Premise of the study: The three-dimensional structure of tree canopies creates environmental heterogeneity, which can differentially influence the chemistry, morphology, physiology, and/or phenology of leaves. Previous studies that subdivide canopy leaves into broad categories (i.e., “upper/lower”) fail to capture the differences in microenvironments experienced by leaves throughout the three-dimensional space of a canopy. Methods: We use a three-dimensional spatial mapping approach based on spherical polar coordinates to examine the fine-scale spatial distributions of photosynthetically active radiation (PAR) and the concentration of ultraviolet (UV)-absorbing compounds (A300) among leaves within the canopies of black mangroves (Avicennia germinans). Results: Linear regressions revealed that interior leaves received less PAR and produced fewer UV-absorbing compounds than leaves on the exterior of the canopy. By allocating more UV-absorbing compounds to the leaves on the exterior of the canopy, black mangroves may be maximizing UV-protection while minimizing biosynthesis of UV-absorbing compounds. Discussion: Three-dimensional spatial mapping provides an inexpensive and portable method to detect fine-scale differences in environmental and biological traits within canopies. We used it to understand the relationship between PAR and A300, but the same approach can also be used to identify traits associated with the spatial distribution of herbivores, pollinators, and pathogens. PMID:29188145

One-dimensional radiation-hydrodynamic simulations of imploding spherical plasma liners with detailed equation-of-state modeling

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

Davis, J. S.; Hsu, S. C.; Golovkin, I. E.

2012-10-15

This work extends the one-dimensional radiation-hydrodynamic imploding spherical argon plasma liner simulations of Awe et al.[Phys. Plasmas 18, 072705 (2011)] by using a detailed tabular equation-of-state (EOS) model, whereas Awe et al. used a polytropic EOS model. Results using the tabular EOS model give lower stagnation pressures by a factor of 3.9-8.6 and lower peak ion temperatures compared to the polytropic EOS results. Both local thermodynamic equilibrium (LTE) and non-LTE EOS models were used in this work, giving similar results on stagnation pressure. The lower stagnation pressures using a tabular EOS model are attributed to a reduction in the liner'smore » ability to compress arising from the energy sink introduced by ionization and electron excitation, which are not accounted for in a polytropic EOS model. Variation of the plasma liner species for the same initial liner geometry, mass density, and velocity was also explored using the LTE tabular EOS model, showing that the highest stagnation pressure is achieved with the highest atomic mass species for the constraints imposed.« less

Conserved charges of black holes in Weyl and Einstein-Gauss-Bonnet gravities

NASA Astrophysics Data System (ADS)

Peng, Jun-Jin

2014-11-01

An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge was recently proposed by Kim et al. They achieved this by introducing off-shell Noether currents and potentials. In this paper, we construct the crucial off-shell Noether current by the variation of the Bianchi identity for the expression of EOM, with the help of the property of Killing vector. Our Noether current, which contains an additional term that is just one half of the Lie derivative of a surface term with respect to the Killing vector, takes a different form in comparison with the one in their work. Then we employ the generalized formulation to calculate the quasi-local conserved charges for the most general charged spherically symmetric and the dyonic rotating black holes with AdS asymptotics in four-dimensional conformal Weyl gravity, as well as the charged spherically symmetric black holes in arbitrary dimensional Einstein-Gauss-Bonnet gravity coupled to Maxwell or nonlinear electrodynamics in AdS spacetime. Our results confirm those obtained through other methods in the literature.

The Backscattering Phase Function for a Sphere with a Two-Scale Relief of Rough Surface

NASA Astrophysics Data System (ADS)

Klass, E. V.

2017-12-01

The backscattering of light from spherical surfaces characterized by one and two-scale roughness reliefs has been investigated. The analysis is performed using the three-dimensional Monte-Carlo program POKS-RG (geometrical-optics approximation), which makes it possible to take into account the roughness of objects under study by introducing local geometries of different levels. The geometric module of the program is aimed at describing objects by equations of second-order surfaces. One-scale roughness is set as an ensemble of geometric figures (convex or concave halves of ellipsoids or cones). The two-scale roughness is modeled by convex halves of ellipsoids, with surface containing ellipsoidal pores. It is shown that a spherical surface with one-scale convex inhomogeneities has a flatter backscattering phase function than a surface with concave inhomogeneities (pores). For a sphere with two-scale roughness, the dependence of the backscattering intensity is found to be determined mostly by the lower-level inhomogeneities. The influence of roughness on the dependence of the backscattering from different spatial regions of spherical surface is analyzed.

Strategy for Improved Representation of Magnetospheric Electric Potential Structure on a Polar-Capped Ionosphere

NASA Astrophysics Data System (ADS)

Schulz, M.

2016-12-01

In some simple models of magnetospheric electrodynamics [e.g., Volland, Ann. Géophys., 31, 159-173, 1975], the normal component of the convection electric field is discontinuous across the boundary between closed and open magnetic field lines, and this discontinuity facilitates the formation of auroral arcs there. The requisite discontinuity in E is achieved by making the scalar potential proportional to a positive power (typically 1 or 2) of L on closed field lines and to a negative power (typically -1/2) of L on open (i.e., polar-cap) field lines. This suggests that it may be advantageous to construct more realistic (and thus more complicated) empirical magnetospheric and ionospheric electric-field models from superpositions of mutually orthogonal (or not) vector basis functions having this same analytical property (i.e., discontinuity at L = L*, the boundary surface between closed and open magnetic field lines). The present work offers a few examples of such constructions. A major challenge in this project has been to devise a coordinate system that simplifies the required analytical expansions of electric scalar potentials and accommodates the anti-sunward offset of each polar-cap boundary's centroid with respect to the corresponding magnetic pole. For circular northern and southern polar caps containing equal amounts of magnetic flux, one can imagine a geometrical construction of nested circular (but non-concentric) contours of constant quasi-latitude whose centers converge toward the magnetic poles as the contours themselves approach the magnetic equator. For more general polar-cap shapes and (in any case) to assure mutual orthogonality of respective coordinate surfaces on a spherical ionosphere, a formulation based on harmonic coordinates (expanded from eigen-solutions of the two-dimensional Laplace equation) may be preferable.

A decision support system for map projections of small scale data

USGS Publications Warehouse

Finn, Michael P.; Usery, E. Lynn; Posch, Stephan T.; Seong, Jeong Chang

2004-01-01

The use of commercial geographic information system software to process large raster datasets of terrain elevation, population, land cover, vegetation, soils, temperature, and rainfall requires both projection from spherical coordinates to plane coordinate systems and transformation from one plane system to another. Decision support systems deliver information resulting in knowledge that assists in policies, priorities, or processes. This paper presents an approach to handling the problems of raster dataset projection and transformation through the development of a Web-enabled decision support system to aid users of transformation processes with the selection of appropriate map projections based on data type, areal extent, location, and preservation properties.

The Migration Matrix: Marine Vertebrate Movements in Magnetic Coordinate Space

NASA Astrophysics Data System (ADS)

Horton, T. W.; Holdaway, R. N.; Clapham, P. J.; Zerbini, A. N.; Andriolo, A.; Hays, G. C.; Egevang, C.; Domeier, M. L.; Lucas, N.

2011-12-01

Determining how vertebrates navigate during their long-distance migrations remains one of the most enduring and fundamental challenges of behavioral ecology. It is widely accepted that spatial orientation relative to a reference datum is a fundamental requirement of long-distance return migration between seasonal habitats, and a variety of viable positional and directional orientation cues, including the sun, stars, and magnetic field, have been documented experimentally. However, a fundamental question remains unanswered: Are empirically observed migratory movements compatible with modern theoretical frameworks of spatial orientation? To address this question, we analysed leatherback turtle (Dermochelys coriacea), arctic tern (Sterna paradisaea), humpback whale (Megaptera novaeangliae), and great white shark (Carcharodon carcharias) track maps, frequency distribution diagrams and time-series plots of animal locations in spherical magnetic coordinate space. Our analyses indicates that, although individual migration tracks are spatially and temporally distinct, vertebrate movements are non-randomly distributed in all three spherical magnetic coordinates (i.e. intensity, inclination, and declination). Stop-over locations, migratory destinations, and re-orientation points occur at similar magnetic coordinate locations, relative to tagging areas, in all four species, suggesting that a common system of magnetic orientation likely informs the navigational behaviors of these phylogenetically diverse taxa. Although our analyses demonstrate that the experiment-derived 'magnetic map' goal orientation theoretical framework of animal navigation is compatible with remotely-sensed migration track data, they also indicate that magnetic information is complemented by spatially and temporally contingent celestial stimuli during navigation.

A two-dimensional bilayered Cd(II) coordination polymer with a three-dimensional supramolecular architecture incorporating 1,2-bis(pyridin-4-yl)ethene and 2,2'-(diazenediyl)dibenzoic acid.

PubMed

Liu, Lei-Lei; Zhou, Yan; Li, Ping; Tian, Jiang-Ya

2014-02-01

In poly[[μ2-1,2-bis(pyridin-4-yl)ethene-κ(2)N:N'][μ2-2,2'-(diazenediyl)dibenzoato-κ(3)O,O':O'']cadmium(II)], [Cd(C14H8N2O4)(C12H10N2)]n, the asymmetric unit contains one Cd(II) cation, one 2,2'-(diazenediyl)dibenzoate anion (denoted L(2-)) and one 1,2-bis(pyridin-4-yl)ethene ligand (denoted bpe). Each Cd(II) centre is six-coordinated by four O atoms of bridging/chelating carboxylate groups from three L(2-) ligands and by two N atoms from two bpe ligands, forming a distorted octahedron. The Cd(II) cations are bridged by L(2-) and bpe ligands to give a two-dimensional (4,4) layer. The layers are interlinked through bridging carboxylate O atoms from L(2-) ligands, generating a two-dimensional bilayered structure with a 3(6)4(13)6(2) topology. The bilayered structures are further extended to form a three-dimensional supramolecular architecture via a combination of hydrogen-bonding and aromatic stacking interactions.

Integration of neutron time-of-flight single-crystal Bragg peaks in reciprocal space

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

Schultz, Arthur J; Joergensen, Mads; Wang, Xiaoping

2014-01-01

The intensity of single crystal Bragg peaks obtained by mapping neutron time-of-flight event data into reciprocal space and integrating in various ways are compared. These include spherical integration with a fixed radius, ellipsoid fitting and integrating of the peak intensity and one-dimensional peak profile fitting. In comparison to intensities obtained by integrating in real detector histogram space, the data integrated in reciprocal space results in better agreement factors and more accurate atomic parameters. Furthermore, structure refinement using integrated intensities from one-dimensional profile fitting is demonstrated to be more accurate than simple peak-minus-background integration.

Tonal Interface to MacroMolecules (TIMMol): A Textual and Tonal Tool for Molecular Visualization

ERIC Educational Resources Information Center

Cordes, Timothy J.; Carlson, C. Britt; Forest, Katrina T.

2008-01-01

We developed the three-dimensional visualization software, Tonal Interface to MacroMolecules or TIMMol, for studying atomic coordinates of protein structures. Key features include audio tones indicating x, y, z location, identification of the cursor location in one-dimensional and three-dimensional space, textual output that can be easily linked…

A Three-dimensional Non-spherical Calculation Of The Rotationally Distorted Shape And Internal Structure Of A Model Of Jupiter With A Polytropic Index Of Unity

NASA Astrophysics Data System (ADS)

Zhang, Keke; Kong, D.; Schubert, G.; Anderson, J.

2012-10-01

An accurate calculation of the rotationally distorted shape and internal structure of Jupiter is required to understand the high-precision gravitational field that will be measured by the Juno spacecraft now on its way to Jupiter. We present a three-dimensional non-spherical numerical calculation of the shape and internal structure of a model of Jupiter with a polytropic index of unity. The calculation is based on a finite element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar (1933) that is valid only for a slowly rotating gaseous planet, we apply it to a model of Jupiter whose rapid rotation causes a significant departure from spherical geometry. The two-dimensional distribution of the density and the pressure within Jupiter is then determined via a hybrid inverse approach by matching the a priori unknown coefficient in the equation of state to the observed shape of Jupiter. After obtaining the two-dimensional distribution of Jupiter's density, we then compute the zonal gravity coefficients and the total mass from the non-spherical Jupiter model that takes full account of rotation-induced shape changes. Our non-spherical model with a polytrope of unit index is able to produce the known mass and zonal gravitational coefficients of Jupiter. Chandrasekhar, S. 1933, The equilibrium of distorted polytropes, MNRAS 93, 390

Distributions in Spherical Coordinates with Applications to Classical Electrodynamics

ERIC Educational Resources Information Center

Gsponer, Andre

2007-01-01

A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that all delta functions and their derivatives are automatically generated, and ensures that the Gauss theorem is…

Cylindrical and spherical Akhmediev breather and freak waves in ultracold neutral plasmas

NASA Astrophysics Data System (ADS)

El-Tantawy, S. A.; El-Awady, E. I.

2018-01-01

The properties of cylindrical and spherical ion-acoustic breathers Akhmediev breather and freak waves in strongly coupled ultracold neutral plasmas (UNPs), whose constituents are inertial strongly coupled ions and weakly coupled Maxwellian electrons, are investigated numerically. Using the derivative expansion method, the basic set of fluid equations is reduced to a nonplanar (cylindrical and spherical)/modified nonlinear Schrödinger equation (mNLSE). The analytical solutions of the mNLSE were not possible until now, so their numerical solutions are obtained using the finite difference scheme with the help of the Dirichlet boundary conditions. Moreover, the criteria for the existence and propagation of breathers are discussed in detail. The geometrical effects due to the cylindrical and spherical geometries on the breather profile are studied numerically. It is found that the propagation of the ion-acoustic breathers in one-dimensional planar and nonplanar geometries is very different. Finally, our results may help to manipulate matter breathers experimentally in UNPs.

Ion-acoustic solitons do not exist in cylindrical and spherical geometries

NASA Astrophysics Data System (ADS)

Sheridan, T. E.

2017-09-01

We investigate the time evolution of one-dimensional, compressive, ion acoustic solitary waves for planar, cylindrical, and spherical geometries in a plasma of cold fluid ions and Boltzmann electrons. For cylindrical and spherical geometries, we show that inward (outward) going solitary waves cannot be localized (i.e., always have a tail) since the effect of a unipolar velocity perturbation is to shift ions inward (outward) to smaller (larger) radii, thereby increasing (decreasing) the local ion density. That is, there are no quasi-particle soliton states in the cylindrical and spherical cases. These results are confirmed and expanded using a plasma simulation for the cylindrical case. We initialize the system with an inward propagating planar soliton. We find supersonic solitary waves which increase in speed as they near the origin, while the wave amplitude increases as r-1/2. All solitary waves develop the predicted tail, but for larger amplitudes, the tail is unstable and evolves into an acoustic wave train.

Spherical Coordinate Systems for Streamlining Suited Mobility Analysis

NASA Technical Reports Server (NTRS)

Benson, Elizabeth; Cowley, Matthew; Harvill, Lauren; Rajulu. Sudhakar

2015-01-01

Introduction: When describing human motion, biomechanists generally report joint angles in terms of Euler angle rotation sequences. However, there are known limitations in using this method to describe complex motions such as the shoulder joint during a baseball pitch. Euler angle notation uses a series of three rotations about an axis where each rotation is dependent upon the preceding rotation. As such, the Euler angles need to be regarded as a set to get accurate angle information. Unfortunately, it is often difficult to visualize and understand these complex motion representations. It has been shown that using a spherical coordinate system allows Anthropometry and Biomechanics Facility (ABF) personnel to increase their ability to transmit important human mobility data to engineers, in a format that is readily understandable and directly translatable to their design efforts. Objectives: The goal of this project was to use innovative analysis and visualization techniques to aid in the examination and comprehension of complex motions. Methods: This project consisted of a series of small sub-projects, meant to validate and verify a new method before it was implemented in the ABF's data analysis practices. A mechanical test rig was built and tracked in 3D using an optical motion capture system. Its position and orientation were reported in both Euler and spherical reference systems. In the second phase of the project, the ABF estimated the error inherent in a spherical coordinate system, and evaluated how this error would vary within the reference frame. This stage also involved expanding a kinematic model of the shoulder to include the rest of the joints of the body. The third stage of the project involved creating visualization methods to assist in interpreting motion in a spherical frame. These visualization methods will be incorporated in a tool to evaluate a database of suited mobility data, which is currently in development. Results: Initial results demonstrated that a spherical coordinate system is helpful in describing and visualizing the motion of a space suit. The system is particularly useful in describing the motion of the shoulder, where multiple degrees of freedom can lead to very complex motion paths.

Spherical nonlinear ion-acoustic solitary waves in Titan's atmosphere

NASA Astrophysics Data System (ADS)

Selim, M. M.

2016-03-01

Propagation of spherical nonlinear ion-acoustic solitary waves in positive and negative ion plasmas with superthermal electrons is investigated. The effects of perturbations of the azimuthal and zenith-angle as well as the radial coordinate on the solitary wave profile are reported. The existence domains and the characteristics of the spherical solitary pulses are examined. The solitary excitations are found to be strongly dependent on the plasma parameters; the mass ratio of the positive-to-negative ions, electrons superthermality, and the spherical geometry. The role of superthermal electrons in formation of the spherical nonlinear ion-acoustic solitary excitations for two ion mass groups in Titan's upper atmosphere is investigated.

Air and moisture stable covalently-bonded tin(ii) coordination polymers.

PubMed

de Lima, G M; Walton, R I; Clarkson, G J; Bitzer, R S; Ardisson, J D

2018-06-05

Four covalently-bonded tin(ii) coordination polymers, (1)-(4), were hydrothermally prepared in aqueous alkaline media by the reactions of SnSO4 with 1,2,4,5-benzenetetracarboxylic acid (1), 1,3,5-benzenetricarboxylic acid (2), 4-hydroxypyridine-2,6-dicarboxylic acid (3), and 1,3,5-cyclohexanetricarboxylic acid (4). All products were structurally authenticated by single-crystal X-ray diffraction, and the number of different tin centres and their oxidation states were confirmed by 119Sn Mössbauer spectroscopy. In addition, the comparison between experimental and simulated X-ray powder diffraction patterns confirmed the authenticity of the samples. Our crystallographic results for (1)-(4) show that the Sn(ii) centres are tetracoordinated and exhibit distorted disphenoidal geometries, corroborating the presence of one stereochemically active lone electron pair at each metal site. Products (1) and (2) display bi-dimensional polymeric structures, (3) exhibits a one-dimensional architecture, whereas (4) shows a remarkable three-dimensional coordination network. Hirshfeld surface and supramolecular analyses for the repeating units of (1)-(4) were also performed in order to identify structurally important non-covalent interactions.

Defect in the Joint Spectrum of Hydrogen due to Monodromy.

PubMed

Dullin, Holger R; Waalkens, Holger

2018-01-12

In addition to the well-known case of spherical coordinates, the Schrödinger equation of the hydrogen atom separates in three further coordinate systems. Separating in a particular coordinate system defines a system of three commuting operators. We show that the joint spectrum of the Hamilton operator, the z component of the angular momentum, and an operator involving the z component of the quantum Laplace-Runge-Lenz vector obtained from separation in prolate spheroidal coordinates has quantum monodromy for energies sufficiently close to the ionization threshold. The precise value of the energy above which monodromy is observed depends on the distance of the focus points of the spheroidal coordinates. The presence of monodromy means that one cannot globally assign quantum numbers to the joint spectrum. Whereas the principal quantum number n and the magnetic quantum number m correspond to the Bohr-Sommerfeld quantization of globally defined classical actions a third quantum number cannot be globally defined because the third action is globally multivalued.

Three dimensional radiation fields in free electron lasers using Lienard-Wiechert fields

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

Elias, L.R.; Gallardo, J.

1981-10-28

In a free electron laser a relativistic electron beam is bunched under the action of the ponderomotive potential and is forced to radiate in close phase with the input wave. Until recently, most theories of the FEL have dealt solely with electron beams of infinite transverse dimension radiating only one-dimensional E.M. waves (plane waves). Although these theories describe accurately the dynamics of the electrons during the FEL interaction process, neither the three dimensional nature of the radiated fields nor its non-monochromatic features can be properly studied by them. As a result of this, very important practical issues such as themore » gain per gaussian-spherical optical mode in a free electron laser have not been well addressed, except through a one dimensional field model in which a filling factor describes crudely the coupling of the FEL induced field to the input field.« less

Newton gauge cosmological perturbations for static spherically symmetric modifications of the de Sitter metric

NASA Astrophysics Data System (ADS)

Santa Vélez, Camilo; Enea Romano, Antonio

2018-05-01

Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.

Far Field Boundary Conditions for Underwater Explosions

DTIC Science & Technology

1994-12-22

NSWCDDfTR-94/20 CHAPTER 1 INTRODUCTION A factor controlling the computational resources required to model an underwater explo- sion is the extent of...NSWCDD/TRI-94/20 SPHERICAL SHOCKS The explosion of a spherical TNT charge in a uniform water environment is modeled in spherical coordinates. The TNT is...described using a JWL equation of state while the water is modeled using a modified Tait equation of state.6 The TNT is assumed to combust

CLASSICAL AREAS OF PHENOMENOLOGY: Material parameter equation for rotating elliptical spherical cloaks

NASA Astrophysics Data System (ADS)

Ma, Hua; Qu, Shao-Bo; Xu, Zhuo; Zhang, Jie-Qiu; Wang, Jia-Fu

2009-01-01

By using the coordinate transformation method, we have deduced the material parameter equation for rotating elliptical spherical cloaks and carried out simulation as well. The results indicate that the rotating elliptical spherical cloaking shell, which is made of meta-materials whose permittivity and permeability are governed by the equation deduced in this paper, can achieve perfect invisibility by excluding electromagnetic fields from the internal region without disturbing any external field.

An intersecting chord method for minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error

NASA Astrophysics Data System (ADS)

Liu, Fei; Xu, Guanghua; Zhang, Qing; Liang, Lin; Liu, Dan

2015-11-01

As one of the Geometrical Product Specifications that are widely applied in industrial manufacturing and measurement, sphericity error can synthetically scale a 3D structure and reflects the machining quality of a spherical workpiece. Following increasing demands in the high motion performance of spherical parts, sphericity error is becoming an indispensable component in the evaluation of form error. However, the evaluation of sphericity error is still considered to be a complex mathematical issue, and the related research studies on the development of available models are lacking. In this paper, an intersecting chord method is first proposed to solve the minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error. This new modelling method leverages chord relationships to replace the characteristic points, thereby significantly reducing the computational complexity and improving the computational efficiency. Using the intersecting chords to generate a virtual centre, the reference sphere in two concentric spheres is simplified as a space intersecting structure. The position of the virtual centre on the space intersecting structure is determined by characteristic chords, which may reduce the deviation between the virtual centre and the centre of the reference sphere. In addition,two experiments are used to verify the effectiveness of the proposed method with real datasets from the Cartesian coordinates. The results indicate that the estimated errors are in perfect agreement with those of the published methods. Meanwhile, the computational efficiency is improved. For the evaluation of the sphericity error, the use of high performance computing is a remarkable change.

Orthonormal aberration polynomials for anamorphic optical imaging systems with circular pupils.

PubMed

Mahajan, Virendra N

2012-06-20

In a recent paper, we considered the classical aberrations of an anamorphic optical imaging system with a rectangular pupil, representing the terms of a power series expansion of its aberration function. These aberrations are inherently separable in the Cartesian coordinates (x,y) of a point on the pupil. Accordingly, there is x-defocus and x-coma, y-defocus and y-coma, and so on. We showed that the aberration polynomials orthonormal over the pupil and representing balanced aberrations for such a system are represented by the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point; for example, L(l)(x)L(m)(y), where l and m are positive integers (including zero) and L(l)(x), for example, represents an orthonormal Legendre polynomial of degree l in x. The compound two-dimensional (2D) Legendre polynomials, like the classical aberrations, are thus also inherently separable in the Cartesian coordinates of the pupil point. Moreover, for every orthonormal polynomial L(l)(x)L(m)(y), there is a corresponding orthonormal polynomial L(l)(y)L(m)(x) obtained by interchanging x and y. These polynomials are different from the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil. In this paper, we show that the orthonormal aberration polynomials for an anamorphic system with a circular pupil, obtained by the Gram-Schmidt orthogonalization of the 2D Legendre polynomials, are not separable in the two coordinates. Moreover, for a given polynomial in x and y, there is no corresponding polynomial obtained by interchanging x and y. For example, there are polynomials representing x-defocus, balanced x-coma, and balanced x-spherical aberration, but no corresponding y-aberration polynomials. The missing y-aberration terms are contained in other polynomials. We emphasize that the Zernike circle polynomials, although orthogonal over a circular pupil, are not suitable for an anamorphic system as they do not represent balanced aberrations for such a system.

Three-dimensional Image Reconstruction in J-PET Using Filtered Back-projection Method

NASA Astrophysics Data System (ADS)

Shopa, R. Y.; Klimaszewski, K.; Kowalski, P.; Krzemień, W.; Raczyński, L.; Wiślicki, W.; Białas, P.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Głowacz, B.; Gorgol, M.; Hiesmayr, B.; Jasińska, B.; Kisielewska-Kamińska, D.; Korcyl, G.; Kozik, T.; Krawczyk, N.; Kubicz, E.; Mohammed, M.; Pawlik-Niedźwiecka, M.; Niedźwiecki, S.; Pałka, M.; Rudy, Z.; Sharma, N. G.; Sharma, S.; Silarski, M.; Skurzok, M.; Wieczorek, A.; Zgardzińska, B.; Zieliński, M.; Moskal, P.

We present a method and preliminary results of the image reconstruction in the Jagiellonian PET tomograph. Using GATE (Geant4 Application for Tomographic Emission), interactions of the 511 keV photons with a cylindrical detector were generated. Pairs of such photons, flying back-to-back, originate from e+e- annihilations inside a 1-mm spherical source. Spatial and temporal coordinates of hits were smeared using experimental resolutions of the detector. We incorporated the algorithm of the 3D Filtered Back Projection, implemented in the STIR and TomoPy software packages, which differ in approximation methods. Consistent results for the Point Spread Functions of ~5/7,mm and ~9/20, mm were obtained, using STIR, for transverse and longitudinal directions, respectively, with no time of flight information included.

Quantized vortices and superflow in arbitrary dimensions: structure, energetics and dynamics

NASA Astrophysics Data System (ADS)

Goldbart, Paul M.; Bora, Florin

2009-05-01

The structure and energetics of superflow around quantized vortices, and the motion inherited by these vortices from this superflow, are explored in the general setting of a superfluid in arbitrary dimensions. The vortices may be idealized as objects of codimension 2, such as one-dimensional loops and two-dimensional closed surfaces, respectively, in the cases of three- and four-dimensional superfluidity. By using the analogy between the vortical superflow and Ampère-Maxwell magnetostatics, the equilibrium superflow containing any specified collection of vortices is constructed. The energy of the superflow is found to take on a simple form for vortices that are smooth and asymptotically large, compared with the vortex core size. The motion of vortices is analyzed in general, as well as for the special cases of hyper-spherical and weakly distorted hyper-planar vortices. In all dimensions, vortex motion reflects vortex geometry. In dimension 4 and higher, this includes not only extrinsic but also intrinsic aspects of the vortex shape, which enter via the first and second fundamental forms of classical geometry. For hyper-spherical vortices, which generalize the vortex rings of three-dimensional superfluidity, the energy-momentum relation is determined. Simple scaling arguments recover the essential features of these results, up to numerical and logarithmic factors.

Diffraction peak profiles of surface relaxed spherical nanocrystals

NASA Astrophysics Data System (ADS)

Perez-Demydenko, C.; Scardi, P.

2017-09-01

A model is proposed for surface relaxation of spherical nanocrystals. Besides reproducing the primary effect of changing the average unit cell parameter, the model accounts for the inhomogeneous atomic displacement caused by surface relaxation and its effect on the diffraction line profiles. Based on three parameters with clear physical meanings - extension of the sub-coordination effect, maximum radial displacement due to sub-coordination, and effective hydrostatic pressure - the model also considers elastic anisotropy and provides parametric expressions of the diffraction line profiles directly applicable in data analysis. The model was tested on spherical nanocrystals of several fcc metals, matching atomic positions with those provided by Molecular Dynamics (MD) simulations based on embedded atom potentials. Agreement was also verified between powder diffraction patterns generated by the Debye scattering equation, using atomic positions from MD and the proposed model.

Crystal structure of catena-poly[[aquadi-n-propyl­tin(IV)]-μ-oxalato

PubMed Central

Reichelt, Martin; Reuter, Hans

2014-01-01

The title compound, [Sn(C3H7)2(H2O)(C2O4)]n, represents the first diorganotin(IV) oxalate hydrate to be structurally characterized. The tin(IV) atom of the one-dimensional coordination polymer is located on a twofold rotation axis and is coordinated by two chelating oxalate ligands with two slightly different Sn—O bond lengths of 2.290 (2) and 2.365 (2) Å, two symmetry-related n-propyl groups with a Sn—C bond lengths of 2.127 (3) Å, and a water mol­ecule with a Sn—O bond length of 2.262 (2) Å. The coordination polyhedron around the SnIV atom is a slightly distorted penta­gonal bipyramid with a nearly linear axis between the trans-oriented n-propyl groups [C—Sn—C = 176.8 (1)°]. The bond angles between the oxygen atoms of the equatorial plane range from 70.48 (6)° to 76.12 (8)°. A one-dimensional coordination polymer results from the less asymmetric bilateral coordination of the centrosymmetric oxalate anion, inter­nally reflected by two slightly different C—O bond lengths of 1.248 (3) and 1.254 (3) Å. The chains of the polymer propagate parallel to [001] and are held together by hydrogen bonds between water mol­ecules and oxalate anions of neighboring chains, leading to a two-dimensional network parallel to (100). PMID:25249862

Three-dimensional ghost imaging using acoustic transducer

NASA Astrophysics Data System (ADS)

Zhang, Chi; Guo, Shuxu; Guan, Jian; Cao, Junsheng; Gao, Fengli

2016-06-01

We propose a novel three-dimensional (3D) ghost imaging method using unfocused ultrasonic transducer, where the transducer is used as the bucket detector to collect the total photoacoustic signal intensity from spherical surfaces with different radius circling the transducer. This collected signal is a time sequence corresponding to the optic absorption information on the spherical surfaces, and the values at the same moments in all the sequences are used as the bucket signals to restore the corresponding spherical images, which are assembled as the object 3D reconstruction. Numerical experiments show this method can effectively accomplish the 3D reconstruction and by adding up each sequence on time domain as a bucket signal it can also realize two dimensional (2D) ghost imaging. The influence of the measurement times on the 3D and 2D reconstruction is analyzed with Peak Signal to Noise Ratio (PSNR) as the yardstick, and the transducer as a bucket detector is also discussed.

Classification by Using Multispectral Point Cloud Data

NASA Astrophysics Data System (ADS)

Liao, C. T.; Huang, H. H.

2012-07-01

Remote sensing images are generally recorded in two-dimensional format containing multispectral information. Also, the semantic information is clearly visualized, which ground features can be better recognized and classified via supervised or unsupervised classification methods easily. Nevertheless, the shortcomings of multispectral images are highly depending on light conditions, and classification results lack of three-dimensional semantic information. On the other hand, LiDAR has become a main technology for acquiring high accuracy point cloud data. The advantages of LiDAR are high data acquisition rate, independent of light conditions and can directly produce three-dimensional coordinates. However, comparing with multispectral images, the disadvantage is multispectral information shortage, which remains a challenge in ground feature classification through massive point cloud data. Consequently, by combining the advantages of both LiDAR and multispectral images, point cloud data with three-dimensional coordinates and multispectral information can produce a integrate solution for point cloud classification. Therefore, this research acquires visible light and near infrared images, via close range photogrammetry, by matching images automatically through free online service for multispectral point cloud generation. Then, one can use three-dimensional affine coordinate transformation to compare the data increment. At last, the given threshold of height and color information is set as threshold in classification.

Spherical beamforming for spherical array with impedance surface

NASA Astrophysics Data System (ADS)

Tontiwattanakul, Khemapat

2018-01-01

Spherical microphone array beamforming has been a popular research topic for recent years. Due to their isotropic beam in three dimensional spaces as well as a certain frequency range, the arrays are widely used in many applications such as sound field recording, acoustic beamforming, and noise source localisation. The body of a spherical array is usually considered perfectly rigid. A sound field captured by the sensors on spherical array can be decomposed into a series of spherical harmonics. In noise source localisation, the amplitude density of sound sources is estimated and illustrated by mean of colour maps. In this work, a rigid spherical array covered by fibrous materials is studied via numerical simulation and the performance of the spherical beamforming is discussed.

GGOS and the EOP - the key role of SLR for a stable estimation of highly accurate Earth orientation parameters

NASA Astrophysics Data System (ADS)

Bloßfeld, Mathis; Panzetta, Francesca; Müller, Horst; Gerstl, Michael

2016-04-01

The GGOS vision is to integrate geometric and gravimetric observation techniques to estimate consistent geodetic-geophysical parameters. In order to reach this goal, the common estimation of station coordinates, Stokes coefficients and Earth Orientation Parameters (EOP) is necessary. Satellite Laser Ranging (SLR) provides the ability to study correlations between the different parameter groups since the observed satellite orbit dynamics are sensitive to the above mentioned geodetic parameters. To decrease the correlations, SLR observations to multiple satellites have to be combined. In this paper, we compare the estimated EOP of (i) single satellite SLR solutions and (ii) multi-satellite SLR solutions. Therefore, we jointly estimate station coordinates, EOP, Stokes coefficients and orbit parameters using different satellite constellations. A special focus in this investigation is put on the de-correlation of different geodetic parameter groups due to the combination of SLR observations. Besides SLR observations to spherical satellites (commonly used), we discuss the impact of SLR observations to non-spherical satellites such as, e.g., the JASON-2 satellite. The goal of this study is to discuss the existing parameter interactions and to present a strategy how to obtain reliable estimates of station coordinates, EOP, orbit parameter and Stokes coefficients in one common adjustment. Thereby, the benefits of a multi-satellite SLR solution are evaluated.

Field-Induced and Thermal Electron Currents from Earthed Spherical Emitters

NASA Astrophysics Data System (ADS)

Holgate, J. T.; Coppins, M.

2017-04-01

The theories of electron emission from planar surfaces are well understood, but they are not suitable for describing emission from spherical surfaces; their incorrect application to highly curved, nanometer-scale surfaces can overestimate the emitted current by several orders of magnitude. This inaccuracy is of particular concern for describing modern nanoscale electron sources, which continue to be modeled using the planar equations. In this paper, the field-induced and thermal currents are treated in a unified way to produce Fowler-Nordheim-type and Richardson-Schottky-type equations for the emitted current density from earthed nanoscale spherical surfaces. The limits of applicability of these derived expressions are considered along with the energy spectra of the emitted electrons. Within the relevant limits of validity, these equations are shown to reproduce the results of precise numerical calculations of the emitted current densities. The methods used here are adaptable to other one-dimensional emission problems.

An "adiabatic-hindered-rotor" treatment allows para-H(2) to be treated as if it were spherical.

PubMed

Li, Hui; Roy, Pierre-Nicholas; Le Roy, Robert J

2010-09-14

In para-H(2)-{molecule} interactions, the common assumption that para-H(2) may be treated as a spherical particle is often substantially in error. For example, quantum mechanical eigenvalues on a full four-dimensional (4D) potential energy surface for para H(2)-{linear molecule} species often differ substantially from those calculated from the corresponding two-dimensional (2D) surface obtained by performing a simple spherical average over the relative orientations of the H(2) moiety. However, use of an "adiabatic-hindered-rotor" approximation can yield an effective 2D surface whose spectroscopic properties are an order of magnitude closer to those yielded by a full 4D treatment.

Superintegrability on N-dimensional spaces of constant curvature from so( N + 1) and its contractions

NASA Astrophysics Data System (ADS)

Herranz, F. J.; Ballesteros, Á.

2008-05-01

The Lie—Poisson algebra so( N + 1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the N-dimensional spherical, Euclidean, hyperbolic, Minkowskian, and (anti-)de Sitter spaces. We firstly present a Hamiltonian which is a superposition of an arbitrary central potential with N arbitrary centrifugal terms. Such a system is quasi-maximally superintegrable since this is endowed with 2 N — 3 functionally independent constants of motion (plus the Hamiltonian). Secondly, we identify two maximally superintegrable Hamiltonians by choosing a specific central potential and finding at the same time the remaining integral. The former is the generalization of the Smorodinsky—Winternitz system to the above six spaces, while the latter is a generalization of the Kepler—Coulomb potential, for which the Laplace—Runge—Lenz N vector is also given. All the systems and constants of motion are explicitly expressed in a unified form in terms of ambient and polar coordinates as they are parametrized by two contraction parameters (curvature and signature of the metric).

Low-order modeling of internal heat transfer in biomass particle pyrolysis

DOE PAGES

Wiggins, Gavin M.; Daw, C. Stuart; Ciesielski, Peter N.

2016-05-11

We present a computationally efficient, one-dimensional simulation methodology for biomass particle heating under conditions typical of fast pyrolysis. Our methodology is based on identifying the rate limiting geometric and structural factors for conductive heat transport in biomass particle models with realistic morphology to develop low-order approximations that behave appropriately. Comparisons of transient temperature trends predicted by our one-dimensional method with three-dimensional simulations of woody biomass particles reveal good agreement, if the appropriate equivalent spherical diameter and bulk thermal properties are used. Here, we conclude that, for particle sizes and heating regimes typical of fast pyrolysis, it is possible to simulatemore » biomass particle heating with reasonable accuracy and minimal computational overhead, even when variable size, aspherical shape, anisotropic conductivity, and complex, species-specific internal pore geometry are incorporated.« less

Low-Order Modeling of Internal Heat Transfer in Biomass Particle Pyrolysis

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

Wiggins, Gavin M.; Ciesielski, Peter N.; Daw, C. Stuart

2016-06-16

We present a computationally efficient, one-dimensional simulation methodology for biomass particle heating under conditions typical of fast pyrolysis. Our methodology is based on identifying the rate limiting geometric and structural factors for conductive heat transport in biomass particle models with realistic morphology to develop low-order approximations that behave appropriately. Comparisons of transient temperature trends predicted by our one-dimensional method with three-dimensional simulations of woody biomass particles reveal good agreement, if the appropriate equivalent spherical diameter and bulk thermal properties are used. We conclude that, for particle sizes and heating regimes typical of fast pyrolysis, it is possible to simulate biomassmore » particle heating with reasonable accuracy and minimal computational overhead, even when variable size, aspherical shape, anisotropic conductivity, and complex, species-specific internal pore geometry are incorporated.« less

Hexatic smectic phase with algebraically decaying bond-orientational order

NASA Astrophysics Data System (ADS)

Agosta, Lorenzo; Metere, Alfredo; Dzugutov, Mikhail

2018-05-01

The hexatic phase predicted by the theories of two-dimensional melting is characterized by the power-law decay of the orientational correlations, whereas the in-layer bond orientational order in all the hexatic smectic phases observed so far was found to be long range. We report a hexatic smectic phase where the in-layer bond orientational correlations decay algebraically, in quantitative agreement with the hexatic ordering predicted by the theory for two dimensions. The phase was formed in a molecular dynamics simulation of a one-component system of particles interacting via a spherically symmetric potential. The present results thus demonstrate that the theoretically predicted two-dimensional hexatic order can exist in a three-dimensional system.

High-pressure synthesis and characterization of the first cerium fluoride borate CeB{sub 2}O{sub 4}F

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

Hinteregger, Ernst; Wurst, Klaus; Tribus, Martina

2013-08-15

CeB{sub 2}O{sub 4}F is the first cerium fluoride borate, which is exclusively built up of one-dimensional, infinite chains of condensed trigonal-planar [BO{sub 3}]{sup 3−} groups. This new cerium fluoride borate was synthesized under high-pressure/high-temperature conditions of 0.9 GPa and 1450 °C in a Walker-type multianvil apparatus. The compound crystallizes in the orthorhombic space group Pbca (No. 61) with eight formula units and the lattice parameters a=821.63(5), b=1257.50(9), c=726.71(6) pm, V=750.84(9) Å{sup 3}, R{sub 1}=0.0698, and wR{sub 2}=0.0682 (all data). The structure exhibits a 9+1 coordinated cerium ion, one three-fold coordinated fluoride ion and a one-dimensional chain of [BO{sub 3}]{sup 3−}more » groups. Furthermore, IR spectroscopy, Electron Micro Probe Analysis and temperature-dependent X-ray powder diffraction measurements were performed. - Graphical abstract: A new rare-earth fluoride borate CeB{sub 2}O{sub 4}F could be synthesized under high-pressure/high-temperature conditions of 0.9 °GPa and 1450 °Cin a Walker-type multianvil apparatus. The crystal structure represents a new structure type in the class of rare-earth fluoride borates. The structure exhibits a 9+1 coordinated cerium ion, one three-fold coordinated fluoride ion and a one-dimensional chain of [BO{sub 3}]{sup 3−} groups. A closer view on the ac-plane shows an interesting wave-like modulation of the borate chains. Highlights: • CeB{sub 2}O{sub 4}F is the first fluoride borate exclusively built up of one-dimensional, infinite chains of condensed trigonal-planar [BO{sub 3}]{sup 3−} groups. • CeB{sub 2}O{sub 4}F is the first cerium fluoride borate. • High-pressure conditions were necessary to synthesize CeB{sub 2}O{sub 4}F.« less

Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Denisov, Sergey; Zaburdaev, Vasily; Barkai, Eli

2017-04-01

We consider super-diffusive Lévy walks in d≥slant 2 dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d  >  1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.

ShapeRotator: An R tool for standardized rigid rotations of articulated three-dimensional structures with application for geometric morphometrics.

PubMed

Vidal-García, Marta; Bandara, Lashi; Keogh, J Scott

2018-05-01

The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two-dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark-based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity.

Computational quest for spherical C12B68 fullerenes with "magic" π-electrons and quasi-planar tetra-coordinated carbon.

PubMed

Li, Fengyu; Jiang, De-en; Chen, Zhongfang

2014-02-01

Inspired by the exciting properties of B80 clusters and the novel chemical bonding of planar tetra-coordinated carbon (ptC), we computationally investigated C12B68 clusters by substituting 12 boron atoms to 12 carbon in the B80 framework. Three types of C12B68 configurations, namely core-shell, boron-trapped and fullerene-like, were examined. The fullerene-like C12B68 clusters are featured with multiple quasi-planar tetra-coordinated carbon moieties; though with "magic" (72) number of electrons, they are not highly aromatic due to the limitations of Hirsch's rule for clusters with more than 50 π electrons. These C12B68 fullerenes are not global minima, but the appreciable HOMO-LUMO gaps, spherical aromaticity, and the thermal stability indicate their reasonable stabilities.

Photoacoustic Effect Generated from an Expanding Spherical Source

NASA Astrophysics Data System (ADS)

Bai, Wenyu; Diebold, Gerald J.

2018-02-01

Although the photoacoustic effect is typically generated by amplitude-modulated continuous or pulsed radiation, the form of the wave equation for pressure that governs the generation of sound indicates that optical sources moving in an absorbing fluid can produce sound as well. Here, the characteristics of the acoustic wave produced by a radially symmetric Gaussian source expanding outwardly from the origin are found. The unique feature of the photoacoustic effect from the spherical source is a trailing compressive wave that arises from reflection of an inwardly propagating component of the wave. Similar to the one-dimensional geometry, an unbounded amplification effect is found for the Gaussian source expanding at the sound speed.

Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach

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

Grecu, A. T.; Grecu, D.; Visinescu, Anca

2010-01-21

The modulational (Benjamin-Feir) instability for cylindrical and spherical NLS equations (c/s NLS equations) is studied using a statistical approach (SAMI). A kinetic equation for a two-point correlation function is written and analyzed using the Wigner-Moyal transform. The linear stability of the Fourier transform of the two-point correlation function is studied and an implicit integral form for the dispersion relation is found. This is solved for different expressions of the initial spectrum (delta-spectrum, Lorentzian, Gaussian), and in the case of a Lorentzian spectrum the total growth of the instability is calculated. The similarities and differences with the usual one-dimensional NLS equationmore » are emphasized.« less

On Shocks Driven by High-mass Planets in Radiatively Inefficient Disks. II. Three-dimensional Global Disk Simulations

NASA Astrophysics Data System (ADS)

Lyra, Wladimir; Richert, Alexander J. W.; Boley, Aaron; Turner, Neal; Mac Low, Mordecai-Mark; Okuzumi, Satoshi; Flock, Mario

2016-02-01

Recent high-resolution, near-infrared images of protoplanetary disks have shown that these disks often present spiral features. Spiral arms are among the structures predicted by models of disk-planet interaction and thus it is tempting to suspect that planetary perturbers are responsible for these signatures. However, such interpretation is not free of problems. The observed spirals have large pitch angles, and in at least one case (HD 100546) it appears effectively unpolarized, implying thermal emission of the order of 1000 K (465 ± 40 K at closer inspection). We have recently shown in two-dimensional models that shock dissipation in the supersonic wake of high-mass planets can lead to significant heating if the disk is sufficiently adiabatic. Here we extend this analysis to three dimensions in thermodynamically evolving disks. We use the Pencil Code in spherical coordinates for our models, with a prescription for thermal cooling based on the optical depth of the local vertical gas column. We use a 5MJ planet, and show that shocks in the region around the planet where the Lindblad resonances occur heat the gas to substantially higher temperatures than the ambient gas. The gas is accelerated vertically away from the midplane to form shock bores, and the gas falling back toward the midplane breaks up into a turbulent surf. This turbulence, although localized, has high α values, reaching 0.05 in the inner Lindblad resonance, and 0.1 in the outer one. We find evidence that the disk regions heated up by the shocks become superadiabatic, generating convection far from the planet’s orbit.

Exploring the Free Energy Landscape of Solutes Embedded in Lipid Bilayers.

PubMed

Jämbeck, Joakim P M; Lyubartsev, Alexander P

2013-06-06

Free energy calculations are vital for our understanding of biological processes on an atomistic scale and can offer insight to various mechanisms. However, in some cases, degrees of freedom (DOFs) orthogonal to the reaction coordinate have high energy barriers and/or long equilibration times, which prohibit proper sampling. Here we identify these orthogonal DOFs when studying the transfer of a solute from water to a model membrane. Important DOFs are identified in bulk liquids of different dielectric nature with metadynamics simulations and are used as reaction coordinates for the translocation process, resulting in two- and three-dimensional space of reaction coordinates. The results are in good agreement with experiments and elucidate the pitfalls of using one-dimensional reaction coordinates. The calculations performed here offer the most detailed free energy landscape of solutes embedded in lipid bilayers to date and show that free energy calculations can be used to study complex membrane translocation phenomena.

Theory and application of equivalent transformation relationships between plane wave and spherical wave

NASA Astrophysics Data System (ADS)

Wang, Yao; Yang, Zailin; Zhang, Jianwei; Yang, Yong

2017-10-01

Based on the governing equations and the equivalent models, we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radially inhomogeneous properties. These equivalent relationships can help us to obtain the analytical solutions of the elastodynamic issues in an inhomogeneous medium. The physical essence of the presented equivalent transformations is the equivalent relationships between the geometry and the material properties. It indicates that the spherical wave problem in globular geometry can be transformed into the plane wave problem in the bar with variable property fields, and its inverse transformation is valid as well. Four different examples of wave motion problems in the inhomogeneous media are solved based on the presented equivalent relationships. We obtain two basic analytical solution forms in Examples I and II, investigate the reflection behavior of inhomogeneous half-space in Example III, and exhibit a special inhomogeneity in Example IV, which can keep the traveling spherical wave in constant amplitude. This study implies that our idea makes solving the associated problem easier.

Application of the space-resolving flux detector for radiation measurements from an octahedral-aperture spherical hohlraum

NASA Astrophysics Data System (ADS)

Xie, Xufei; Du, Huabing; Chen, Jinwen; Liu, Shenye; Li, Zhichao; Yang, Dong; Huang, Yunbao; Ren, Kuan; Hou, Lifei; Li, Sanwei; Guo, Liang; Jiang, Xiaohua; Huo, Wenyi; Chen, Yaohua; Ren, Guoli; Lan, Ke; Wang, Feng; Jiang, Shaoen; Ding, Yongkun

2018-06-01

Space-resolving flux detection is an important technique for the diagnostic of the radiation field within the hohlraum in inertial confinement fusion, especially for the radiation field diagnostic in the novel spherical hohlraum with octahedral six laser entrance holes (LEHs), where localized measurements are necessary for the discrimination of the radiation flux from different LEHs. A novel space-resolving flux detector (SRFD) is developed at the SG-III laser facility for the radiation flux measurement in the first campaign of the octahedral spherical hohlraum energetics experiment. The principle and configuration of the SRFD system is introduced. The radiation flux from the wall of a gas-filled octahedral spherical hohlraum is measured for the first time by placing the SRFD system at the equatorial position of the SG-III laser facility, aiming at the hohlraum wall through one of the six LEHs. The absolute radiation flux from the re-emission area on the hohlraum wall is measured, and good consistency is found between the experimental data and the calculated data from a three-dimensional view factor analysis.

ProteinShader: illustrative rendering of macromolecules

PubMed Central

Weber, Joseph R

2009-01-01

Background Cartoon-style illustrative renderings of proteins can help clarify structural features that are obscured by space filling or balls and sticks style models, and recent advances in programmable graphics cards offer many new opportunities for improving illustrative renderings. Results The ProteinShader program, a new tool for macromolecular visualization, uses information from Protein Data Bank files to produce illustrative renderings of proteins that approximate what an artist might create by hand using pen and ink. A combination of Hermite and spherical linear interpolation is used to draw smooth, gradually rotating three-dimensional tubes and ribbons with a repeating pattern of texture coordinates, which allows the application of texture mapping, real-time halftoning, and smooth edge lines. This free platform-independent open-source program is written primarily in Java, but also makes extensive use of the OpenGL Shading Language to modify the graphics pipeline. Conclusion By programming to the graphics processor unit, ProteinShader is able to produce high quality images and illustrative rendering effects in real-time. The main feature that distinguishes ProteinShader from other free molecular visualization tools is its use of texture mapping techniques that allow two-dimensional images to be mapped onto the curved three-dimensional surfaces of ribbons and tubes with minimum distortion of the images. PMID:19331660

Dimensionality reduction of collective motion by principal manifolds

NASA Astrophysics Data System (ADS)

Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.

2015-01-01

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.

Heat transfer evaluation in a plasma core reactor

NASA Technical Reports Server (NTRS)

Smith, D. E.; Smith, T. M.; Stoenescu, M. L.

1976-01-01

Numerical evaluations of heat transfer in a fissioning uranium plasma core reactor cavity, operating with seeded hydrogen propellant, was performed. A two-dimensional analysis is based on an assumed flow pattern and cavity wall heat exchange rate. Various iterative schemes were required by the nature of the radiative field and by the solid seed vaporization. Approximate formulations of the radiative heat flux are generally used, due to the complexity of the solution of a rigorously formulated problem. The present work analyzes the sensitivity of the results with respect to approximations of the radiative field, geometry, seed vaporization coefficients and flow pattern. The results present temperature, heat flux, density and optical depth distributions in the reactor cavity, acceptable simplifying assumptions, and iterative schemes. The present calculations, performed in cartesian and spherical coordinates, are applicable to any most general heat transfer problem.

Towards energy-efficient nonoscillatory forward-in-time integrations on lat-lon grids

NASA Astrophysics Data System (ADS)

Polkowski, Marcin; Piotrowski, Zbigniew; Ryczkowski, Adam

2017-04-01

The design of the next-generation weather prediction models calls for new algorithmic approaches allowing for robust integrations of atmospheric flow over complex orography at sub-km resolutions. These need to be accompanied by efficient implementations exposing multi-level parallelism, capable to run on modern supercomputing architectures. Here we present the recent advances in the energy-efficient implementation of the consistent soundproof/implicit compressible EULAG dynamical core of the COSMO weather prediction framework. Based on the experiences of the atmospheric dwarfs developed within H2020 ESCAPE project, we develop efficient, architecture agnostic implementations of fully three-dimensional MPDATA advection schemes and generalized diffusion operator in curvilinear coordinates and spherical geometry. We compare optimized Fortran implementation with preliminary C++ implementation employing the Gridtools library, allowing for integrations on CPU and GPU while maintaining single source code.

A new general circulation model of Jupiter's atmosphere based on the UKMO Unified Model: Three-dimensional evolution of isolated vortices and zonal jets in mid-latitudes

NASA Astrophysics Data System (ADS)

Yamazaki, Y. H.; Skeet, D. R.; Read, P. L.

2004-04-01

We have been developing a new three-dimensional general circulation model for the stratosphere and troposphere of Jupiter based on the dynamical core of a portable version of the Unified Model of the UK Meteorological Office. Being one of the leading terrestrial GCMs, employed for operational weather forecasting and climate research, the Unified Model has been thoroughly tested and performance tuned for both vector and parallel computers. It is formulated as a generalized form of the standard primitive equations to handle a thick atmosphere, using a scaled pressure as the vertical coordinate. It is able to accurately simulate the dynamics of a three-dimensional fully compressible atmosphere on the whole or a part of a spherical shell at high spatial resolution in all three directions. Using the current version of the GCM, we examine the characteristics of the Jovian winds in idealized configurations based on the observed vertical structure of temperature. Our initial focus is on the evolution of isolated eddies in the mid-latitudes. Following a brief theoretical investigation of the vertical structure of the atmosphere, limited-area cyclic channel domains are used to numerically investigate the nonlinear evolution of the mid-latitude winds. First, the evolution of deep and shallow cyclones and anticyclones are tested in the atmosphere at rest to identify a preferred horizontal and vertical structure of the vortices. Then, the dependency of the migration characteristics of the vortices are investigated against modelling parameters to find that it is most sensitive to the horizontal diffusion. We also examine the hydrodynamical stability of observed subtropical jets in both northern and southern hemispheres in the three-dimensional nonlinear model as initial value problems. In both cases, it was found that the prominent jets are unstable at various scales and that vorteces of various sizes are generated including those comparable to the White Ovals and the Great Red Spot.

Spherical Panoramas for Astrophysical Data Visualization

NASA Astrophysics Data System (ADS)

Kent, Brian R.

2017-05-01

Data immersion has advantages in astrophysical visualization. Complex multi-dimensional data and phase spaces can be explored in a seamless and interactive viewing environment. Putting the user in the data is a first step toward immersive data analysis. We present a technique for creating 360° spherical panoramas with astrophysical data. The three-dimensional software package Blender and the Google Spatial Media module are used together to immerse users in data exploration. Several examples employing these methods exhibit how the technique works using different types of astronomical data.

Modelling sheet-flow sediment transport in wave-bottom boundary layers using discrete-element modelling.

PubMed

Calantoni, Joseph; Holland, K Todd; Drake, Thomas G

2004-09-15

Sediment transport in oscillatory boundary layers is a process that drives coastal geomorphological change. Most formulae for bed-load transport in nearshore regions subsume the smallest-scale physics of the phenomena by parametrizing interactions amongst particles. In contrast, we directly simulate granular physics in the wave-bottom boundary layer using a discrete-element model comprised of a three-dimensional particle phase coupled to a one-dimensional fluid phase via Newton's third law through forces of buoyancy, drag and added mass. The particulate sediment phase is modelled using discrete particles formed to approximate natural grains by overlapping two spheres. Both the size of each sphere and the degree of overlap can be varied for these composite particles to generate a range of non-spherical grains. Simulations of particles having a range of shapes showed that the critical angle--the angle at which a grain pile will fail when tilted slowly from rest--increases from approximately 26 degrees for spherical particles to nearly 39 degrees for highly non-spherical composite particles having a dumbbell shape. Simulations of oscillatory sheet flow were conducted using composite particles with an angle of repose of approximately 33 degrees and a Corey shape factor greater than about 0.8, similar to the properties of beach sand. The results from the sheet-flow simulations with composite particles agreed more closely with laboratory measurements than similar simulations conducted using spherical particles. The findings suggest that particle shape may be an important factor for determining bed-load flux, particularly for larger bed slopes.

On the cross-field diffusion of ions in one- and two-dimensional hybrid simulations of collisionless shocks

NASA Technical Reports Server (NTRS)

Giacalone, Joe

1994-01-01

It can be demonstrated analytically that under certain geometries used in numerical simulations of collisionless shocks in which there is at least one ignorable spatial coordinate, the transport of particles across the magnetic field is essentially zero. This notion is tested using one- and two-dimensional hybrid simulations (kinetic ions/fluid electrons). We find, as the theorem predicts, the particles treated kinetically are tied to the same field line on which they start.

Compression dynamics of quasi-spherical wire arrays with different linear mass profiles

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

Mitrofanov, K. N., E-mail: mitrofan@triniti.ru; Aleksandrov, V. V.; Gritsuk, A. N.

Results of experimental studies of the implosion of quasi-spherical wire (or metalized fiber) arrays are presented. The goal of the experiments was to achieve synchronous three-dimensional compression of the plasma produced in different regions of a quasi-spherical array into its geometrical center. To search for optimal synchronization conditions, quasi-spherical arrays with different initial profiles of the linear mass were used. The following dependences of the linear mass on the poloidal angle were used: m{sub l}(θ) ∝ sin{sup –1}θ and m{sub l}(θ) ∝ sin{sup –2}θ. The compression dynamics of such arrays was compared with that of quasi-spherical arrays without linear massmore » profiling, m{sub l}(θ) = const. To verify the experimental data, the spatiotemporal dynamics of plasma compression in quasi-spherical arrays was studied using various diagnostics. The experiments on three-dimensional implosion of quasi-spherical arrays made it possible to study how the frozen-in magnetic field of the discharge current penetrates into the array. By measuring the magnetic field in the plasma of a quasi-spherical array, information is obtained on the processes of plasma production and formation of plasma flows from the wire/fiber regions with and without an additionally deposited mass. It is found that penetration of the magnetic flux depends on the initial linear mass profile m{sub l}(θ) of the quasi-spherical array. From space-resolved spectral measurements and frame imaging of plasma X-ray emission, information is obtained on the dimensions and shape of the X-ray source formed during the implosion of a quasi-spherical array. The intensity of this source is estimated and compared with that of the Z-pinch formed during the implosion of a cylindrical array.« less

Spherical Coordinate Systems for Streamlining Suited Mobility Analysis

NASA Technical Reports Server (NTRS)

Benson, Elizabeth; Cowley, Matthew S.; Harvill. Lauren; Rajulu, Sudhakar

2014-01-01

When describing human motion, biomechanists generally report joint angles in terms of Euler angle rotation sequences. However, there are known limitations in using this method to describe complex motions such as the shoulder joint during a baseball pitch. Euler angle notation uses a series of three rotations about an axis where each rotation is dependent upon the preceding rotation. As such, the Euler angles need to be regarded as a set to get accurate angle information. Unfortunately, it is often difficult to visualize and understand these complex motion representations. One of our key functions is to help design engineers understand how a human will perform with new designs and all too often traditional use of Euler rotations becomes as much of a hindrance as a help. It is believed that using a spherical coordinate system will allow ABF personnel to more quickly and easily transmit important mobility data to engineers, in a format that is readily understandable and directly translatable to their design efforts. Objectives: The goal of this project is to establish new analysis and visualization techniques to aid in the examination and comprehension of complex motions. Methods: This project consisted of a series of small sub-projects, meant to validate and verify the method before it was implemented in the ABF's data analysis practices. The first stage was a proof of concept, where a mechanical test rig was built and instrumented with an inclinometer, so that its angle from horizontal was known. The test rig was tracked in 3D using an optical motion capture system, and its position and orientation were reported in both Euler and spherical reference systems. The rig was meant to simulate flexion/extension, transverse rotation and abduction/adduction of the human shoulder, but without the variability inherent in human motion. In the second phase of the project, the ABF estimated the error inherent in a spherical coordinate system, and evaluated how this error would vary within the reference frame. This stage also involved expanding a kinematic model of the shoulder, to include the torso, knees, ankle, elbows, wrists and neck. Part of this update included adding a representation of 'roll' about an axis, for upper arm and lower leg rotations. The third stage of the project involved creating visualization methods to assist in interpreting motion in a spherical frame. This visualization method will be incorporated in a tool to evaluate a database of suited mobility data, which is currently in development.

Hydrothermal synthesis and structural characterization of a novel three-dimensional supramolecular framework constructed by zinc salt and pyridine-2,5-dicarboxylate

NASA Astrophysics Data System (ADS)

Wang, Xinlong; Qin, Chao; Wang, Enbo; Hu, Changwen; Xu, Lin

2004-07-01

A novel metal-organic coordination polymer, [Zn(PDB)(H 2O) 2] 4 n (H 2PDB=pyridine-2,5-dicarboxylic acid), has been hydrothermally synthesized and characterized by elemental analysis, IR, TG and single crystal X-ray diffraction. Colorless crystals crystallized in the triclinic system, space group P-1, a=7.0562(14) Å, b=7.38526(15) Å, c=18.4611(4) Å, α=90.01(3)°, β=96.98(3)°, γ=115.67(3)°, V=859.1(3) Å 3, Z=1 and R=0.0334. The structure of the compound exhibits a novel three-dimensional supramolecular network, mainly based on multipoint hydrogen bonds originated from within and outside of a large 24-membered ring. Interestingly, the three-dimensional network consists of one-dimensional parallelogrammic channels in which coordinated water molecules point into the channel wall.

Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation

NASA Astrophysics Data System (ADS)

Adler, Stephen L.; Ramazanoğlu, Fethi M.

2015-12-01

We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action (derived from trace dynamics) that gives an alternative explanation of the origin of "dark energy". We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that: (i) there is no horizon, since g00 is nonvanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar R vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the McVittie Ansatz.

3D inversion of full gravity gradient tensor data in spherical coordinate system using local north-oriented frame

NASA Astrophysics Data System (ADS)

Zhang, Yi; Wu, Yulong; Yan, Jianguo; Wang, Haoran; Rodriguez, J. Alexis P.; Qiu, Yue

2018-04-01

In this paper, we propose an inverse method for full gravity gradient tensor data in the spherical coordinate system. As opposed to the traditional gravity inversion in the Cartesian coordinate system, our proposed method takes the curvature of the Earth, the Moon, or other planets into account, using tesseroid bodies to produce gravity gradient effects in forward modeling. We used both synthetic and observed datasets to test the stability and validity of the proposed method. Our results using synthetic gravity data show that our new method predicts the depth of the density anomalous body efficiently and accurately. Using observed gravity data for the Mare Smythii area on the moon, the density distribution of the crust in this area reveals its geological structure. These results validate the proposed method and potential application for large area data inversion of planetary geological structures.[Figure not available: see fulltext.

Dimensional coordinate measurements: application in characterizing cervical spine motion

NASA Astrophysics Data System (ADS)

Zheng, Weilong; Li, Linan; Wang, Shibin; Wang, Zhiyong; Shi, Nianke; Xue, Yuan

2014-06-01

Cervical spine as a complicated part in the human body, the form of its movement is diverse. The movements of the segments of vertebrae are three-dimensional, and it is reflected in the changes of the angle between two joint and the displacement in different directions. Under normal conditions, cervical can flex, extend, lateral flex and rotate. For there is no relative motion between measuring marks fixed on one segment of cervical vertebra, the cervical vertebrae with three marked points can be seen as a body. Body's motion in space can be decomposed into translational movement and rotational movement around a base point .This study concerns the calculation of dimensional coordinate of the marked points pasted to the human body's cervical spine by an optical method. Afterward, these measures will allow the calculation of motion parameters for every spine segment. For this study, we choose a three-dimensional measurement method based on binocular stereo vision. The object with marked points is placed in front of the CCD camera. Through each shot, we will get there two parallax images taken from different cameras. According to the principle of binocular vision we can be realized three-dimensional measurements. Cameras are erected parallelly. This paper describes the layout of experimental system and a mathematical model to get the coordinates.

Theory and design of compact hybrid microphone arrays on two-dimensional planes for three-dimensional soundfield analysis.

PubMed

Chen, Hanchi; Abhayapala, Thushara D; Zhang, Wen

2015-11-01

Soundfield analysis based on spherical harmonic decomposition has been widely used in various applications; however, a drawback is the three-dimensional geometry of the microphone arrays. In this paper, a method to design two-dimensional planar microphone arrays that are capable of capturing three-dimensional (3D) spatial soundfields is proposed. Through the utilization of both omni-directional and first order microphones, the proposed microphone array is capable of measuring soundfield components that are undetectable to conventional planar omni-directional microphone arrays, thus providing the same functionality as 3D arrays designed for the same purpose. Simulations show that the accuracy of the planar microphone array is comparable to traditional spherical microphone arrays. Due to its compact shape, the proposed microphone array greatly increases the feasibility of 3D soundfield analysis techniques in real-world applications.

A variable-order laminated plate theory based on the variational-asymptotical method

NASA Technical Reports Server (NTRS)

Lee, Bok W.; Sutyrin, Vladislav G.; Hodges, Dewey H.

1993-01-01

The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.

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.

Modelling and precision of the localization of the robotic mobile platforms for constructions with laser tracker and SmartTrack sensor

NASA Astrophysics Data System (ADS)

Dima, M.; Francu, C.

2016-08-01

This paper presents a way to expand the field of use of the laser tracker and SmartTrack sensor localization device used in lately for the localisation of the end effector of the industrial robots to the localization of the mobile construction robots. The research paper presents the equipment along with its characteristics, determines the relationships for the localization coordinates by comparison to the forward kinematics of the industrial robot's spherical arm (positioning mechanism in spherical coordinates) and the orientation mechanism with three revolute axes. In the end of the paper the accuracy of the mobile robot's localization is analysed.

Results of the NIST National Ball Plate Round Robin.

PubMed

Caskey, G W; Phillips, S D; Borchardt, B R

1997-01-01

This report examines the results of the ball plate round robin administered by NIST. The round robin was part of an effort to assess the current state of industry practices for measurements made using coordinate measuring machines. Measurements of a two-dimensional ball plate (240 mm by 240 mm) on 41 coordinate measuring machines were collected and analyzed. Typically, the deviations of the reported X and Y coordinates from the calibrated values were within ± 5 μm, with some coordinate deviations exceeding 20.0 μm. One of the most significant observations from these data was that over 75 % of the participants failed to correctly estimate their measurement error on one or more of the ball plate spheres.

Analysis of the Three-Dimensional Vector FAÇADE Model Created from Photogrammetric Data

NASA Astrophysics Data System (ADS)

Kamnev, I. S.; Seredovich, V. A.

2017-12-01

The results of the accuracy assessment analysis for creation of a three-dimensional vector model of building façade are described. In the framework of the analysis, analytical comparison of three-dimensional vector façade models created by photogrammetric and terrestrial laser scanning data has been done. The three-dimensional model built from TLS point clouds was taken as the reference one. In the course of the experiment, the three-dimensional model to be analyzed was superimposed on the reference one, the coordinates were measured and deviations between the same model points were determined. The accuracy estimation of the three-dimensional model obtained by using non-metric digital camera images was carried out. Identified façade surface areas with the maximum deviations were revealed.

Three-dimensional liquid flattened Luneburg lens with ultra-wide viewing angle and frequency band

NASA Astrophysics Data System (ADS)

Wu, Lingling; Tian, Xiaoyong; Yin, Ming; Li, Dichen; Tang, Yiping

2013-08-01

Traditional Luneburg lens is a dielectric spherical antenna. It can focus the incoming collimated electromagnetic waves on its spherical surface, which causes the incompatibility with the planar feeding and receiving devices. Furthermore, the difficulties in the fabrication process also limited its applications. In this paper, a three-dimensional flattened Luneburg lens with a field-of-view angle up to 180° has been realized based on a liquid medium approach and a 3D-printing process. The fabricated three-dimensional lens showed a broadband transmission characteristic from 12.4 GHz to 18 GHz. The performance of the proposed lens was demonstrated by simulation and experimental results.

Two novel mixed-ligand complexes containing organosulfonate ligands.

PubMed

Li, Mingtian; Huang, Jun; Zhou, Xuan; Fang, Hua; Ding, Liyun

2008-07-01

The structures reported herein, viz. bis(4-aminonaphthalene-1-sulfonato-kappaO)bis(4,5-diazafluoren-9-one-kappa(2)N,N')copper(II), [Cu(C(10)H(8)NO(3)S)(2)(C(11)H(6)N(2)O)(2)], (I), and poly[[[diaquacadmium(II)]-bis(mu-4-aminonaphthalene-1-sulfonato)-kappa(2)O:N;kappa(2)N:O] dihydrate], {[Cd(C(10)H(8)NO(3)S)(2)(H(2)O)(2)].2H(2)O}(n), (II), are rare examples of sulfonate-containing complexes where the anion does not fulfill a passive charge-balancing role, but takes an active part in coordination as a monodentate and/or bridging ligand. Monomeric complex (I) possesses a crystallographic inversion center at the Cu(II) atom, and the asymmetric unit contains one-half of a Cu atom, one complete 4-aminonaphthalene-1-sulfonate (ans) ligand and one 4,5-diazafluoren-9-one (DAFO) ligand. The Cu(II) atom has an elongated distorted octahedral coordination geometry formed by two O atoms from two monodentate ans ligands and by four N atoms from two DAFO molecules. Complex (II) is polymeric and its crystal structure is built up by one-dimensional chains and solvent water molecules. Here also the cation (a Cd(II) atom) lies on a crystallographic inversion center and adopts a slightly distorted octahedral geometry. Each ans anion serves as a bridging ligand linking two Cd(II) atoms into one-dimensional infinite chains along the [010] direction, with each Cd(II) center coordinated by four ans ligands via O and N atoms and by two aqua ligands. In both structures, there are significant pi-pi stacking interactions between adjacent ligands and hydrogen bonds contribute to the formation of two- and three-dimensional networks.

Rotating full- and reduced-dimensional quantum chemical models of molecules

NASA Astrophysics Data System (ADS)

Fábri, Csaba; Mátyus, Edit; Császár, Attila G.

2011-02-01

A flexible protocol, applicable to semirigid as well as floppy polyatomic systems, is developed for the variational solution of the rotational-vibrational Schrödinger equation. The kinetic energy operator is expressed in terms of curvilinear coordinates, describing the internal motion, and rotational coordinates, characterizing the orientation of the frame fixed to the nonrigid body. Although the analytic form of the kinetic energy operator might be very complex, it does not need to be known a priori within this scheme as it is constructed automatically and numerically whenever needed. The internal coordinates can be chosen to best represent the system of interest and the body-fixed frame is not restricted to an embedding defined with respect to a single reference geometry. The features of the technique mentioned make it especially well suited to treat large-amplitude nuclear motions. Reduced-dimensional rovibrational models can be defined straightforwardly by introducing constraints on the generalized coordinates. In order to demonstrate the flexibility of the protocol and the associated computer code, the inversion-tunneling of the ammonia (14NH3) molecule is studied using one, two, three, four, and six active vibrational degrees of freedom, within both vibrational and rovibrational variational computations. For example, the one-dimensional inversion-tunneling model of ammonia is considered also for nonzero rotational angular momenta. It turns out to be difficult to significantly improve upon this simple model. Rotational-vibrational energy levels are presented for rotational angular momentum quantum numbers J = 0, 1, 2, 3, and 4.

A review of recent advances in the spherical harmonics expansion method for semiconductor device simulation.

PubMed

Rupp, K; Jungemann, C; Hong, S-M; Bina, M; Grasser, T; Jüngel, A

The Boltzmann transport equation is commonly considered to be the best semi-classical description of carrier transport in semiconductors, providing precise information about the distribution of carriers with respect to time (one dimension), location (three dimensions), and momentum (three dimensions). However, numerical solutions for the seven-dimensional carrier distribution functions are very demanding. The most common solution approach is the stochastic Monte Carlo method, because the gigabytes of memory requirements of deterministic direct solution approaches has not been available until recently. As a remedy, the higher accuracy provided by solutions of the Boltzmann transport equation is often exchanged for lower computational expense by using simpler models based on macroscopic quantities such as carrier density and mean carrier velocity. Recent developments for the deterministic spherical harmonics expansion method have reduced the computational cost for solving the Boltzmann transport equation, enabling the computation of carrier distribution functions even for spatially three-dimensional device simulations within minutes to hours. We summarize recent progress for the spherical harmonics expansion method and show that small currents, reasonable execution times, and rare events such as low-frequency noise, which are all hard or even impossible to simulate with the established Monte Carlo method, can be handled in a straight-forward manner. The applicability of the method for important practical applications is demonstrated for noise simulation, small-signal analysis, hot-carrier degradation, and avalanche breakdown.

Magnetohydrodynamic Simulations of Black Hole Accretion Flows Using PATCHWORK, a Multi-Patch, multi-code approach

NASA Astrophysics Data System (ADS)

Avara, Mark J.; Noble, Scott; Shiokawa, Hotaka; Cheng, Roseanne; Campanelli, Manuela; Krolik, Julian H.

2017-08-01

A multi-patch approach to numerical simulations of black hole accretion flows allows one to robustly match numerical grid shape and equations solved to the natural structure of the physical system. For instance, a cartesian gridded patch can be used to cover coordinate singularities on a spherical-polar grid, increasing computational efficiency and better capturing the physical system through natural symmetries. We will present early tests, initial applications, and first results from the new MHD implementation of the PATCHWORK framework.

Spherical harmonics analysis of surface density fluctuations of spherical ionic SDS and nonionic C12E8 micelles: A molecular dynamics study

NASA Astrophysics Data System (ADS)

Yoshii, Noriyuki; Nimura, Yuki; Fujimoto, Kazushi; Okazaki, Susumu

2017-07-01

The surface structure and its fluctuation of spherical micelles were investigated using a series of density correlation functions newly defined by spherical harmonics and Legendre polynomials based on the molecular dynamics calculations. To investigate the influence of head-group charges on the micelle surface structure, ionic sodium dodecyl sulfate and nonionic octaethyleneglycol monododecylether (C12E8) micelles were investigated as model systems. Large-scale density fluctuations were observed for both micelles in the calculated surface static structure factor. The area compressibility of the micelle surface evaluated by the surface static structure factor was tens-of-times larger than a typical value of a lipid membrane surface. The structural relaxation time, which was evaluated from the surface intermediate scattering function, indicates that the relaxation mechanism of the long-range surface structure can be well described by the hydrostatic approximation. The density fluctuation on the two-dimensional micelle surface has similar characteristics to that of three-dimensional fluids near the critical point.

Spherical harmonics analysis of surface density fluctuations of spherical ionic SDS and nonionic C12E8 micelles: A molecular dynamics study.

PubMed

Yoshii, Noriyuki; Nimura, Yuki; Fujimoto, Kazushi; Okazaki, Susumu

2017-07-21

The surface structure and its fluctuation of spherical micelles were investigated using a series of density correlation functions newly defined by spherical harmonics and Legendre polynomials based on the molecular dynamics calculations. To investigate the influence of head-group charges on the micelle surface structure, ionic sodium dodecyl sulfate and nonionic octaethyleneglycol monododecylether (C 12 E 8 ) micelles were investigated as model systems. Large-scale density fluctuations were observed for both micelles in the calculated surface static structure factor. The area compressibility of the micelle surface evaluated by the surface static structure factor was tens-of-times larger than a typical value of a lipid membrane surface. The structural relaxation time, which was evaluated from the surface intermediate scattering function, indicates that the relaxation mechanism of the long-range surface structure can be well described by the hydrostatic approximation. The density fluctuation on the two-dimensional micelle surface has similar characteristics to that of three-dimensional fluids near the critical point.

Synthesis, structural characterization and antitumor activity of a Ca(II) coordination polymer based on 4-formyl-1,3-benzenedisulfonate-2-furoic acid hydrazide ligands

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

Tai, Xi-Shi, E-mail: taixs@wfu.edu.cn; Wang, Xin

2017-03-15

A new Ca(II) coordination polymer, ([CaL(H{sub 2}O){sub 4}] · (H{sub 2}O){sub 4}){sub n} (L = 4-formyl-1,3-benzenedisulfonate-2-furoic acid hydrazide) has been prepared by one-pot synthesis method. And it was characterized by elemental analysis, IR and thermal analysis. The result of X-ray single-crystal diffraction analysis shows that the Ca(II) complex molecules form one-dimensional chain structure by the bridging oxygen atoms. The anti-tumor activity of L ligand and the Ca(II) coordination polymer has also been studied.

Large radius of curvature measurement based on virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer.

PubMed

Yang, Zhongming; Wang, Kailiang; Cheng, Jinlong; Gao, Zhishan; Yuan, Qun

2016-06-10

We have proposed a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer to measure the large radius of curvature for a spherical surface. In a quadratic polar coordinate system, linear carrier testing Newton rings interferogram and virtual Newton rings interferogram form the moiré fringes. It is possible to retrieve the wavefront difference data between the testing and standard spherical surface from the moiré fringes after low-pass filtering. Based on the wavefront difference data, we deduced a precise formula to calculate the radius of curvature in the quadratic polar coordinate system. We calculated the retrace error in the nonnull interferometer using the multi-configuration model of the nonnull interferometric system in ZEMAX. Our experimental results indicate that the measurement accuracy is better than 0.18% for a spherical mirror with a radius of curvature of 41,400 mm.

The Inflatable Poster

NASA Astrophysics Data System (ADS)

Tackley, P. J.

2004-12-01

Inflatable devices are frequently used in advertising in order to grab the attention of consumers: one sees, for example, 20 foot tall inflatable drink containers, inflatable cell phones, inflatable bubble gum packets, as well as blimps wafting majestically over major sports events. More usefully, inflatable representations of scientifically-interesting items are widely available, including astronauts, space shuttles, dinosaurs and globes and can help to build and inspire the interest of the general public, and in particular children, in such ideas. How can such concepts be adapted to improve poster presentations? Possibility one is to use relevant existing commercially-available inflatables to dress the poster: skeletons, astronauts, globes and so forth. More exciting is to develop custom inflatables that represent three-dimensional renderings of objects that the poster is describing. Examples of individual objects might be an inflatable slab, inflatable avalanche, inflatable plume, or it's larger cousin, the 10 foot high inflatable superplume or 20 foot high inflatable megaplume. More elaborately, inflatables might represent isosurfaces in three-dimensional spherical convection, although other fabrication methods may be more suitable. More simply, inflatable spheres could be imprinted with the planform of convection, geoid, or other spherical fields of geophysical interest. Finally, it should be possible to put an entire poster on an inflatable object, possibly small ones (balloons) to hand out. A major concern, however, is that the presenter may use such techniques to inflate their scientific findings, or to present overblown ideas.

Large gyres as a shallow-water asymptotic solution of Euler's equation in spherical coordinates

NASA Astrophysics Data System (ADS)

Constantin, A.; Johnson, R. S.

2017-04-01

Starting from the Euler equation expressed in a rotating frame in spherical coordinates, coupled with the equation of mass conservation and the appropriate boundary conditions, a thin-layer (i.e. shallow water) asymptotic approximation is developed. The analysis is driven by a single, overarching assumption based on the smallness of one parameter: the ratio of the average depth of the oceans to the radius of the Earth. Consistent with this, the magnitude of the vertical velocity component through the layer is necessarily much smaller than the horizontal components along the layer. A choice of the size of this speed ratio is made, which corresponds, roughly, to the observational data for gyres; thus the problem is characterized by, and reduced to an analysis based on, a single small parameter. The nonlinear leading-order problem retains all the rotational contributions of the moving frame, describing motion in a thin spherical shell. There are many solutions of this system, corresponding to different vorticities, all described by a novel vorticity equation: this couples the vorticity generated by the spin of the Earth with the underlying vorticity due to the movement of the oceans. Some explicit solutions are obtained, which exhibit gyre-like flows of any size; indeed, the technique developed here allows for many different choices of the flow field and of any suitable free-surface profile. We comment briefly on the next order problem, which provides the structure through the layer. Some observations about the new vorticity equation are given, and a brief indication of how these results can be extended is offered.

Spherically symmetric conformal gravity and ''gravitational bubbles''

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

Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru

2016-01-01

The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ''gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-timesmore » (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ''nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.« less

Electrostatic similarity of proteins: Application of three dimensional spherical harmonic decomposition

PubMed Central

Długosz, Maciej; Trylska, Joanna

2008-01-01

We present a method for describing and comparing global electrostatic properties of biomolecules based on the spherical harmonic decomposition of electrostatic potential data. Unlike other approaches our method does not require any prior three dimensional structural alignment. The electrostatic potential, given as a volumetric data set from a numerical solution of the Poisson or Poisson–Boltzmann equation, is represented with descriptors that are rotation invariant. The method can be applied to large and structurally diverse sets of biomolecules enabling to cluster them according to their electrostatic features. PMID:18624502

Spherical Model Integrating Academic Competence with Social Adjustment and Psychopathology.

ERIC Educational Resources Information Center

Schaefer, Earl S.; And Others

This study replicates and elaborates a three-dimensional, spherical model that integrates research findings concerning social and emotional behavior, psychopathology, and academic competence. Kindergarten teachers completed an extensive set of rating scales on 100 children, including the Classroom Behavior Inventory and the Child Adaptive Behavior…

A complete set of two-dimensional harmonic vortices on a spherical surface

NASA Astrophysics Data System (ADS)

Esparza, Christian; Rendón, Pablo Luis; Ley Koo, Eugenio

2018-03-01

The solutions of the Euler equations on a spherical surface are constructed, starting from a vector velocity potential A in the radial direction and with a two-dimensional spherical harmonic variation of order m and well-defined parity under \\varphi \\mapsto -\\varphi . The solutions are well-behaved on the entire surface and continuous at the position of a parallel circle θ ={θ }0, where the vorticity is shown to be harmonically distributed. The velocity field is evaluated as the curl of the vector potential: it is shown that the velocity is divergenceless and distributed on the spherical surface. Its polar components at the parallel circle are shown to be continuous, confirming its divergenceless nature, while its azimuthal components are discontinuous at the circle, and their discontinuity is a measure of the vorticity in the radial direction. A closed form for the velocity field lines is also obtained in terms of fixed values of the scalar harmonic function associated with the vector potential. Additionally, the connections of the solutions on a spherical surface with their circular, elliptic and bipolar counterparts on the equatorial plane are implemented via stereographic projections.

Multielectron-Transfer-based Rechargeable Energy Storage of Two-Dimensional Coordination Frameworks with Non-Innocent Ligands.

PubMed

Wada, Keisuke; Sakaushi, Ken; Sasaki, Sono; Nishihara, Hiroshi

2018-04-19

The metallically conductive bis(diimino)nickel framework (NiDI), an emerging class of metal-organic framework (MOF) analogues consisting of two-dimensional (2D) coordination networks, was found to have an energy storage principle that uses both cation and anion insertion. This principle gives high energy led by a multielectron transfer reaction: Its specific capacity is one of the highest among MOF-based cathode materials in rechargeable energy storage devices, with stable cycling performance up to 300 cycles. This mechanism was studied by a wide spectrum of electrochemical techniques combined with density-functional calculations. This work shows that a rationally designed material system of conductive 2D coordination networks can be promising electrode materials for many types of energy devices. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

The point explosion with radiation transport

NASA Astrophysics Data System (ADS)

Lin, Zhiwei; Zhang, Lu; Kuang, Longyu; Jiang, Shaoen

2017-10-01

Some amount of energy is released instantaneously at the origin to generate simultaneously a spherical radiative heat wave and a spherical shock wave in the point explosion with radiation transport, which is a complicated problem due to the competition between these two waves. The point explosion problem possesses self-similar solutions when only hydrodynamic motion or only heat conduction is considered, which are Sedov solution and Barenblatt solution respectively. The point explosion problem wherein both physical mechanisms of hydrodynamic motion and heat conduction are included has been studied by P. Reinicke and A.I. Shestakov. In this talk we numerically investigate the point explosion problem wherein both physical mechanisms of hydrodynamic motion and radiation transport are taken into account. The radiation transport equation in one dimensional spherical geometry has to be solved for this problem since the ambient medium is optically thin with respect to the initially extremely high temperature at the origin. The numerical results reveal a high compression of medium and a bi-peak structure of density, which are further theoretically analyzed at the end.

Flyby Characterization of Lower-Degree Spherical Harmonics Around Small Bodies

NASA Technical Reports Server (NTRS)

Takahashi, Yu; Broschart, Stephen; Lantoine, Gregory

2014-01-01

Interest in studying small bodies has grown significantly in the last two decades, and there are a number of past, present, and future missions. These small body missions challenge navigators with significantly different kinds of problems than the planets and moons do. The small bodies' shape is often irregular and their gravitational field significantly weak, which make the designing of a stable orbit a complex dynamical problem. In the initial phase of spacecraft rendezvous with a small body, the determination of the gravitational parameter and lower-degree spherical harmonics are of crucial importance for safe navigation purposes. This motivates studying how well one can determine the total mass and lower-degree spherical harmonics in a relatively short time in the initial phase of the spacecraft rendezvous via flybys. A quick turnaround for the gravity data is of high value since it will facilitate the subsequent mission design of the main scientific observation campaign. We will present how one can approach the problem to determine a desirable flyby geometry for a general small body. We will work in the non-dimensional formulation since it will generalize our results across different size/mass bodies and the rotation rate for a specific combination of gravitational coefficients.

The derivative-free Fourier shell identity for photoacoustics.

PubMed

Baddour, Natalie

2016-01-01

In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.

A finite element solution algorithm for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

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

2-and 1-D coordination polymers of Dy(III) and Ho(III) with near infrared and visible luminescence by efficient charge-transfer antenna ligand

NASA Astrophysics Data System (ADS)

Oylumluoglu, Gorkem; Coban, Mustafa Burak; Kocak, Cagdas; Aygun, Muhittin; Kara, Hulya

2017-10-01

Two new lanthanide-based coordination complexes, [Dy(2-stp).2(H2O)]n (1) and {[Ho(2-stp).3(H2O)]·(H2O)}n (2) [2-stp = 2-sulfoterephthalic acid] were synthesized by hydrothermal reaction and characterized by elemental analysis, UV, IR, single crystal X-ray diffraction and solid state photoluminescence. DyIII and HoIII atoms are eight-coordinated and adopt a distorted square-antiprismatic geometry in complexes 1 and 2, respectively. In compound 1, Dy atoms are coordinated by four bridging 2-stp ligands forming two-dimensional (2D) layer, while Ho atoms by three bridging 2-stp ligands creating one dimensional (1D) double chains in 2. In addition, complexes 1 and 2 display in the solid state and at room temperature an intense yellow emission, respectively; this photoluminescence is achieved by an indirect process (antenna effect). The excellent luminescent performances make these complexes very good candidates for potential luminescence materials.

Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments.

PubMed

Choi, Ji Yeh; Hwang, Heungsun; Timmerman, Marieke E

2018-03-01

Parallel factor analysis (PARAFAC) is a useful multivariate method for decomposing three-way data that consist of three different types of entities simultaneously. This method estimates trilinear components, each of which is a low-dimensional representation of a set of entities, often called a mode, to explain the maximum variance of the data. Functional PARAFAC permits the entities in different modes to be smooth functions or curves, varying over a continuum, rather than a collection of unconnected responses. The existing functional PARAFAC methods handle functions of a one-dimensional argument (e.g., time) only. In this paper, we propose a new extension of functional PARAFAC for handling three-way data whose responses are sequenced along both a two-dimensional domain (e.g., a plane with x- and y-axis coordinates) and a one-dimensional argument. Technically, the proposed method combines PARAFAC with basis function expansion approximations, using a set of piecewise quadratic finite element basis functions for estimating two-dimensional smooth functions and a set of one-dimensional basis functions for estimating one-dimensional smooth functions. In a simulation study, the proposed method appeared to outperform the conventional PARAFAC. We apply the method to EEG data to demonstrate its empirical usefulness.

Characterization of MOSFET Dosimeter Angular Response Using a Spherical Phantom for Fluoroscopic Dosimetry.

PubMed

Wang, Chu; Hill, Kevin; Yoshizumi, Terry

2016-01-01

Metal-Oxide Semiconductor Field-Effect Transistor (MOSFET) dosimeters, placed in anthropomorphic phantoms, are a standard method for organ dosimetry in medical x-ray imaging applications. However, many x-ray applications, particularly fluoroscopy procedures, use variable projection angles. During dosimetry, the MOSFET detector active area may not always be perpendicular to the x-ray beam. The goal of this study was to characterize the dosimeter's angular response in the fluoroscopic irradiation involved in pediatric cardiac catheterization procedures, during which a considerable amount of fluoroscopic x-ray irradiation is often applied from various projection angles. A biological x-ray irradiator was used to simulate the beam quality of a biplane fluoroscopy imaging system. A custom-designed acrylic spherical scatter phantom was fabricated to measure dosimeter response (in mV) in two rotational axes, axial (ψ) and normal-to-axial (θ), in 30° increments, as well as four common oblique angles used in cardiac catheterization: a) 90° Left Anterior Oblique (LAO); b) 70° LAO/ 20° Cranial; c) 20° LAO/ 15° Cranial; and d) 30° Right Anterior Oblique (RAO). All results were normalized to the angle where the dosimeter epoxy is perpendicular to the beam or the Posterior-Anterior projection angle in the clinical setup. The relative response in the axial rotation was isotropic (within ± 10% deviation); that in the normal-to-axial rotation was isotropic in all angles except the ψ = 270° angle, where the relative response was 83 ± 9%. No significant deviation in detector response was observed in the four common oblique angles, with their relative responses being: a) 102 ± 3%; b) 90 ± 3%; c) 92 ± 3%; and d) 95 ± 3%, respectively. These angular correction factors will be used in future dosimetry studies for fluoroscopy. The spherical phantom may be useful for other applications, as it allows the measurement of dosimeter response in virtually all angles in the 3-dimensional spherical coordinates.

Rapid Optimal SPH Particle Distributions in Spherical Geometries For Creating Astrophysical Initial Conditions

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

Raskin, Cody; Owen, J. Michael

Creating spherical initial conditions in smoothed particle hydrodynamics simulations that are spherically conformal is a difficult task. Here in this paper, we describe two algorithmic methods for evenly distributing points on surfaces that when paired can be used to build three-dimensional spherical objects with optimal equipartition of volume between particles, commensurate with an arbitrary radial density function. We demonstrate the efficacy of our method against stretched lattice arrangements on the metrics of hydrodynamic stability, spherical conformity, and the harmonic power distribution of gravitational settling oscillations. We further demonstrate how our method is highly optimized for simulating multi-material spheres, such asmore » planets with core–mantle boundaries.« less

Rapid Optimal SPH Particle Distributions in Spherical Geometries For Creating Astrophysical Initial Conditions

DOE PAGES

Raskin, Cody; Owen, J. Michael

2016-03-24

Creating spherical initial conditions in smoothed particle hydrodynamics simulations that are spherically conformal is a difficult task. Here in this paper, we describe two algorithmic methods for evenly distributing points on surfaces that when paired can be used to build three-dimensional spherical objects with optimal equipartition of volume between particles, commensurate with an arbitrary radial density function. We demonstrate the efficacy of our method against stretched lattice arrangements on the metrics of hydrodynamic stability, spherical conformity, and the harmonic power distribution of gravitational settling oscillations. We further demonstrate how our method is highly optimized for simulating multi-material spheres, such asmore » planets with core–mantle boundaries.« less

RAPID OPTIMAL SPH PARTICLE DISTRIBUTIONS IN SPHERICAL GEOMETRIES FOR CREATING ASTROPHYSICAL INITIAL CONDITIONS

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

Raskin, Cody; Owen, J. Michael

2016-04-01

Creating spherical initial conditions in smoothed particle hydrodynamics simulations that are spherically conformal is a difficult task. Here, we describe two algorithmic methods for evenly distributing points on surfaces that when paired can be used to build three-dimensional spherical objects with optimal equipartition of volume between particles, commensurate with an arbitrary radial density function. We demonstrate the efficacy of our method against stretched lattice arrangements on the metrics of hydrodynamic stability, spherical conformity, and the harmonic power distribution of gravitational settling oscillations. We further demonstrate how our method is highly optimized for simulating multi-material spheres, such as planets with core–mantlemore » boundaries.« less

A Gaussian quadrature method for total energy analysis in electronic state calculations

NASA Astrophysics Data System (ADS)

Fukushima, Kimichika

This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2.

Structure and Dynamics of the Solar Corona

NASA Technical Reports Server (NTRS)

Schnack, D. D.

1994-01-01

Advanced computational techniques were used to study solar coronal heating and coronal mass ejections. A three dimensional, time dependent resistive magnetohydrodynamic code was used to study the dynamic response of a model corona to continuous, slow, random magnetic footpoint displacements in the photosphere. Three dimensional numerical simulations of the response of the corona to simple smooth braiding flows in the photosphere were calculated to illustrate and understand the spontaneous formation of current filaments. Two dimensional steady state helmet streamer configurations were obtained by determining the time asymptotic state of the interaction of an initially one dimensinal transponic solar wind with a spherical potential dipole field. The disruption of the steady state helmet streamer configuration was studied as a response to shearing of the magnetic footpoints of the closed field lines under the helmet.

Dimensional reduction of a general advection–diffusion equation in 2D channels

NASA Astrophysics Data System (ADS)

Kalinay, Pavol; Slanina, František

2018-06-01

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.

Calcium Coordination Solids for pH-Triggered Release of Olsalazine

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

Levine, Dana J.; Gonzalez, Miguel I.; Legendre, Christina M.

Here, calcium coordination solids were synthesized and evaluated for delivery of olsalazine (H 4olz), an anti-inflammatory compound used for treatment of ulcerative colitis. The materials include one-dimensional Ca(H 2olz)•4H 2O chains, two-dimensional Ca(H 2olz)•2H 2O sheets, and a three-dimensional metal-organic framework Ca(H 2olz)•2DMF (DMF= N,N-dimethylformamide). The framework undergoes structural changes in response to solvent, forming a dense Ca(H 2olz) phase when exposed to aqueous HCl. The compounds Ca(H 2olz)•xH 2O (x=0, 2, 4) were each pressed into pellets and exposed to simulated gastrointestinal fluids to mimic the passage of a pill from the acidic stomach to the pH-neutral intestines. Allmore » three calcium materials exhibited a delayed release of olsalazine relative to Na 2(H 2olz), the commercial formulation, illustrating how formulation of a drug within an extended coordination solid can serve to tune its solubility and performance.« less

Calcium Coordination Solids for pH-Triggered Release of Olsalazine

DOE PAGES

Levine, Dana J.; Gonzalez, Miguel I.; Legendre, Christina M.; ...

2017-09-12

Here, calcium coordination solids were synthesized and evaluated for delivery of olsalazine (H 4olz), an anti-inflammatory compound used for treatment of ulcerative colitis. The materials include one-dimensional Ca(H 2olz)•4H 2O chains, two-dimensional Ca(H 2olz)•2H 2O sheets, and a three-dimensional metal-organic framework Ca(H 2olz)•2DMF (DMF= N,N-dimethylformamide). The framework undergoes structural changes in response to solvent, forming a dense Ca(H 2olz) phase when exposed to aqueous HCl. The compounds Ca(H 2olz)•xH 2O (x=0, 2, 4) were each pressed into pellets and exposed to simulated gastrointestinal fluids to mimic the passage of a pill from the acidic stomach to the pH-neutral intestines. Allmore » three calcium materials exhibited a delayed release of olsalazine relative to Na 2(H 2olz), the commercial formulation, illustrating how formulation of a drug within an extended coordination solid can serve to tune its solubility and performance.« less

Pseudo-spectral methods applied to gravitational collapse.

NASA Astrophysics Data System (ADS)

Bonazzola, S.; Marck, J.-A.

The authors present codes for solving Newtonian gravitational collapse in spherical coordinates for the spherical, axial and true 3 D cases. The pseudo-spectral techniques are used. All quantities are expanded in Chebychev or Legendre polynomials or Fourier series for the periodic parts. The codes are able to handle in a rigorous way the pseudo-singularities τ = 0 and θ = 0, π. Illustrative results for each of the three cases are given.

Photoluminescent lead(II) coordination polymers stabilised by bifunctional organoarsonate ligands

NASA Astrophysics Data System (ADS)

Lin, Jian-Di; Onet, Camelia I.; Schmitt, Wolfgang

2015-04-01

Four lead(II) coordination polymers were isolated under hydro(solvo)thermal conditions. The applied synthetic methodology takes advantage of the coordination behaviour of a new bifunctional organoarsonate ligand, 4-(1, 2, 4-triazol-4-yl)phenylarsonic acid (H2TPAA) and involves the variation of lead(II) reactants, metal/ligand mole ratios, and solvents. The constitutional composition of the four lead(II) coordination polymers can be formulated as [Pb2(TPAA)(HTPAA)(NO3)]·6H2O (1), [Pb2(TPAA)(HTPAA)2]·DMF·0.5H2O (DMF = N, N-Dimethylformamide) (2), [Pb2Cl2(TPAA)H2O] (3), and [Pb3Cl(TPAA)(HTPAA)2H2O]Cl (4). The compounds were characterized by single-crystal and powder x-ray diffraction techniques, thermogravimetric analyses, infra-red spectroscopy, and elemental analyses. Single-crystal x-ray diffraction reveals that 1 and 2 represent two-dimensional (2D) layered structures whilst 3 and 4 form three-dimensional (3D) frameworks. The structures of 1, 2, and 4 contain one-dimensional (1D) {PbII/AsO3} substructures, while 3 is composed of 2D {PbII/AsO3} arrays. Besides their interesting topologies, 1-4 all exhibit photoluminescence properties in the solid state at room temperature.

Geometric Calibration of Full Spherical Panoramic Ricoh-Theta Camera

NASA Astrophysics Data System (ADS)

Aghayari, S.; Saadatseresht, M.; Omidalizarandi, M.; Neumann, I.

2017-05-01

A novel calibration process of RICOH-THETA, full-view fisheye camera, is proposed which has numerous applications as a low cost sensor in different disciplines such as photogrammetry, robotic and machine vision and so on. Ricoh Company developed this camera in 2014 that consists of two lenses and is able to capture the whole surrounding environment in one shot. In this research, each lens is calibrated separately and interior/relative orientation parameters (IOPs and ROPs) of the camera are determined on the basis of designed calibration network on the central and side images captured by the aforementioned lenses. Accordingly, designed calibration network is considered as a free distortion grid and applied to the measured control points in the image space as correction terms by means of bilinear interpolation. By performing corresponding corrections, image coordinates are transformed to the unit sphere as an intermediate space between object space and image space in the form of spherical coordinates. Afterwards, IOPs and EOPs of each lens are determined separately through statistical bundle adjustment procedure based on collinearity condition equations. Subsequently, ROPs of two lenses is computed from both EOPs. Our experiments show that by applying 3*3 free distortion grid, image measurements residuals diminish from 1.5 to 0.25 degrees on aforementioned unit sphere.

Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition

NASA Astrophysics Data System (ADS)

Volegov, P. L.; Danly, C. R.; Fittinghoff, D.; Geppert-Kleinrath, V.; Grim, G.; Merrill, F. E.; Wilde, C. H.

2017-11-01

Neutron, gamma-ray, and x-ray imaging are important diagnostic tools at the National Ignition Facility (NIF) for measuring the two-dimensional (2D) size and shape of the neutron producing region, for probing the remaining ablator and measuring the extent of the DT plasmas during the stagnation phase of Inertial Confinement Fusion implosions. Due to the difficulty and expense of building these imagers, at most only a few two-dimensional projections images will be available to reconstruct the three-dimensional (3D) sources. In this paper, we present a technique that has been developed for the 3D reconstruction of neutron, gamma-ray, and x-ray sources from a minimal number of 2D projections using spherical harmonics decomposition. We present the detailed algorithms used for this characterization and the results of reconstructed sources from experimental neutron and x-ray data collected at OMEGA and NIF.

The consequences of two distinct reaction coordinates in the decomposition of the ethylamine cation conformers

NASA Astrophysics Data System (ADS)

Petersen, Allan C.; Sølling, Theis I.

2018-06-01

The ethylamine cation CH3CH2NH2+ is shown to loose CH3 accompanied by a bimodal kinetic energy release. CH3CH2NH2+ exists in two conformeric forms, which are computationally shown to be distinct minima. The barrier separating the conformers is modest compared to the energy requirement for dissociation, and the conformers are so easily interconverted that the reactions take place from a mixture of the two conformers in equilibrium. However, once a reaction begins it is conformer-specific. The reaction from one conformational origin takes place by simple cleavage along a one-dimensional reaction coordinate, whereas reaction from the other origin is by a complex reaction mechanism with a two- or possibly three-dimensional reaction coordinate. Reaction by the former mechanism is a statistical process associated with a low kinetic energy release (KER), while the latter is non-statistical giving rise to a very low KER. The experimental result is a composite signal due to the superposition of two simple Gaussians, each corresponding to their respective KER.

A three-dimensional model of Tangential YORP

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

Golubov, O.; Scheeres, D. J.; Krugly, Yu. N., E-mail: golubov@astron.kharkov.ua

2014-10-10

Tangential YORP, or TYORP, has recently been demonstrated to be an important factor in the evolution of an asteroid's rotation state. It is complementary to normal YORP, or NYORP, which used to be considered previously. While NYORP is produced by non-symmetry in the large-scale geometry of an asteroid, TYORP is due to heat conductivity in stones on the surface of the asteroid. To date, TYORP has been studied only in a simplified one-dimensional model, substituting stones with high long walls. This article for the first time considers TYORP in a realistic three-dimensional model, also including shadowing and self-illumination effects viamore » ray tracing. TYORP is simulated for spherical stones lying on regolith. The model includes only five free parameters and the dependence of the TYORP on each of them is studied. The TYORP torque appears to be smaller than previous estimates from the one-dimensional model, but is still comparable to the NYORP torques. These results can be used to estimate TYORP of different asteroids and also as a basis for more sophisticated models of TYORP.« less

A Structure-Based Distance Metric for High-Dimensional Space Exploration with Multi-Dimensional Scaling

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

Lee, Hyun Jung; McDonnell, Kevin T.; Zelenyuk, Alla

2014-03-01

Although the Euclidean distance does well in measuring data distances within high-dimensional clusters, it does poorly when it comes to gauging inter-cluster distances. This significantly impacts the quality of global, low-dimensional space embedding procedures such as the popular multi-dimensional scaling (MDS) where one can often observe non-intuitive layouts. We were inspired by the perceptual processes evoked in the method of parallel coordinates which enables users to visually aggregate the data by the patterns the polylines exhibit across the dimension axes. We call the path of such a polyline its structure and suggest a metric that captures this structure directly inmore » high-dimensional space. This allows us to better gauge the distances of spatially distant data constellations and so achieve data aggregations in MDS plots that are more cognizant of existing high-dimensional structure similarities. Our MDS plots also exhibit similar visual relationships as the method of parallel coordinates which is often used alongside to visualize the high-dimensional data in raw form. We then cast our metric into a bi-scale framework which distinguishes far-distances from near-distances. The coarser scale uses the structural similarity metric to separate data aggregates obtained by prior classification or clustering, while the finer scale employs the appropriate Euclidean distance.« less

An integral condition for core-collapse supernova explosions

DOE PAGES

Murphy, Jeremiah W.; Dolence, Joshua C.

2017-01-10

Here, we derive an integral condition for core-collapse supernova (CCSN) explosions and use it to construct a new diagnostic of explodability. The fundamental challenge in CCSN theory is to explain how a stalled accretion shock revives to explode a star. In this manuscript, we assume that the shock revival is initiated by the delayed-neutrino mechanism and derive an integral condition for spherically symmetric shock expansion, v s > 0. One of the most useful one-dimensional explosion conditions is the neutrino luminosity and mass-accretion rate (more » $${L}_{\

One-dimensional cuts through multidimensional potential-energy surfaces by tunable x rays

NASA Astrophysics Data System (ADS)

Eckert, Sebastian; da Cruz, Vinícius Vaz; Gel'mukhanov, Faris; Ertan, Emelie; Ignatova, Nina; Polyutov, Sergey; Couto, Rafael C.; Fondell, Mattis; Dantz, Marcus; Kennedy, Brian; Schmitt, Thorsten; Pietzsch, Annette; Odelius, Michael; Föhlisch, Alexander

2018-05-01

The concept of the potential-energy surface (PES) and directional reaction coordinates is the backbone of our description of chemical reaction mechanisms. Although the eigenenergies of the nuclear Hamiltonian uniquely link a PES to its spectrum, this information is in general experimentally inaccessible in large polyatomic systems. This is due to (near) degenerate rovibrational levels across the parameter space of all degrees of freedom, which effectively forms a pseudospectrum given by the centers of gravity of groups of close-lying vibrational levels. We show here that resonant inelastic x-ray scattering (RIXS) constitutes an ideal probe for revealing one-dimensional cuts through the ground-state PES of molecular systems, even far away from the equilibrium geometry, where the independent-mode picture is broken. We strictly link the center of gravity of close-lying vibrational peaks in RIXS to a pseudospectrum which is shown to coincide with the eigenvalues of an effective one-dimensional Hamiltonian along the propagation coordinate of the core-excited wave packet. This concept, combined with directional and site selectivity of the core-excited states, allows us to experimentally extract cuts through the ground-state PES along three complementary directions for the showcase H2O molecule.

Matrix elements of vibration kinetic energy operator of tetrahedral molecules in non-orthogonal-dependent coordinates

NASA Astrophysics Data System (ADS)

Protasevich, Alexander E.; Nikitin, Andrei V.

2018-01-01

In this work, we propose an algorithm for calculating the matrix elements of the kinetic energy operator for tetrahedral molecules. This algorithm uses the dependent six-angle coordinates (6A) and takes into account the full symmetry of molecules. Unlike A.V. Nikitin, M. Rey, and Vl. G. Tyuterev who operate with the kinetic energy operator only in Radau orthogonal coordinates, we consider a general case. The matrix elements are shown to be a sum of products of one-dimensional integrals.

The linear sizes tolerances and fits system modernization

NASA Astrophysics Data System (ADS)

Glukhov, V. I.; Grinevich, V. A.; Shalay, V. V.

2018-04-01

The study is carried out on the urgent topic for technical products quality providing in the tolerancing process of the component parts. The aim of the paper is to develop alternatives for improving the system linear sizes tolerances and dimensional fits in the international standard ISO 286-1. The tasks of the work are, firstly, to classify as linear sizes the elements additionally linear coordinating sizes that determine the detail elements location and, secondly, to justify the basic deviation of the tolerance interval for the element's linear size. The geometrical modeling method of real details elements, the analytical and experimental methods are used in the research. It is shown that the linear coordinates are the dimensional basis of the elements linear sizes. To standardize the accuracy of linear coordinating sizes in all accuracy classes, it is sufficient to select in the standardized tolerance system only one tolerance interval with symmetrical deviations: Js for internal dimensional elements (holes) and js for external elements (shafts). The main deviation of this coordinating tolerance is the average zero deviation, which coincides with the nominal value of the coordinating size. Other intervals of the tolerance system are remained for normalizing the accuracy of the elements linear sizes with a fundamental change in the basic deviation of all tolerance intervals is the maximum deviation corresponding to the limit of the element material: EI is the lower tolerance for the of the internal elements (holes) sizes and es is the upper tolerance deviation for the outer elements (shafts) sizes. It is the sizes of the material maximum that are involved in the of the dimensional elements mating of the shafts and holes and determine the fits type.

Bragg x-ray optics for imaging spectroscopy of plasma microsources.

PubMed

Pikuz, T A; Ya Faenov, A; Pikuz, S A; Romanova, V M; Shelkovenko, T A

1995-01-01

Bragg x-ray optics based on crystals with transmission and reflection properties bent on cylindrical or spherical surfaces are discussed. Applications of such optics for obtaining one- and two-dimensional monochromatic images of different plasma sources in the wide spectral range 1-20 Å are described. Samples of spectra obtained with spectral resolution of up to λ/Δλ ~ 10,000 and spatial resolution of up to 18 μm are presented.

General Wahlquist metrics in all dimensions

NASA Astrophysics Data System (ADS)

Hinoue, Kazuki; Houri, Tsuyoshi; Rugina, Christina; Yasui, Yukinori

2014-07-01

It is shown that the Wahlquist metric, which is a stationary, axially symmetric perfect fluid solution with ρ +3p=const, admits a rank-2 generalized closed conformal Killing-Yano tensor with a skew-symmetric torsion. Taking advantage of the presence of such a tensor, we obtain a higher-dimensional generalization of the Wahlquist metric in arbitrary dimensions, including a family of vacuum black hole solutions with spherical horizon topology such as Schwarzschild-Tangherlini, Myers-Perry and higher-dimensional Kerr-NUT-(A)dS metrics and a family of static, spherically symmetric perfect fluid solutions in higher dimensions.

The motion of a cloud of solid spherical particles falling in a cellular flow field at low Stokes number

NASA Astrophysics Data System (ADS)

Marchetti, Benjamin; Bergougnoux, Laurence; Guazzelli, Elisabeth

2017-11-01

We present a jointed experimental and numerical study examining the influence of vortical structures on the settling of a cloud of solid spherical particles under the action of gravity at low Stokes numbers. The two-dimensional model experiment uses electro-convection to generate a two-dimensional array of controlled vortices which mimics a simplified vortical flow. Particle image-velocimetry and tracking are used to examine the motion of the cloud within this vortical flow. The cloud motion is compared to the predictions of a two-way-coupling numerical simulation.

Absolute judgment for one- and two-dimensional stimuli embedded in Gaussian noise

NASA Technical Reports Server (NTRS)

Kvalseth, T. O.

1977-01-01

This study examines the effect on human performance of adding Gaussian noise or disturbance to the stimuli in absolute judgment tasks involving both one- and two-dimensional stimuli. For each selected stimulus value (both an X-value and a Y-value were generated in the two-dimensional case), 10 values (or 10 pairs of values in the two-dimensional case) were generated from a zero-mean Gaussian variate, added to the selected stimulus value and then served as the coordinate values for the 10 points that were displayed sequentially on a CRT. The results show that human performance, in terms of the information transmitted and rms error as functions of stimulus uncertainty, was significantly reduced as the noise variance increased.

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

A Computational Investigation of Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Chao, B. H.; Sunderland, P. B.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2007-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, and residence time. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with residence times longer than 200 ms were found to have temperatures near 1190 K where C/O = 0.6, whereas flames with shorter residence times required increased temperatures. Acetylene was found to be a reasonable surrogate for soot precursor species in these flames, having peak mole fractions of about 0.01.

Effects of C/O Ratio and Temperature on Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Sunderland, P. B.; Chao, B. H.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2008-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, residence time and scalar dissipation rate. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with scalar dissipation rate lower than 2/s were found to have temperatures near 1400 K where C/O = 0.51, whereas flames with greater scalar dissipation rate required increased temperatures. This finding was valid across a broad range of fuel and oxidizer compositions and convection directions.

Nonlinear nature of composite structure induced by the interaction of nonplanar solitons in a nonextensive plasma

NASA Astrophysics Data System (ADS)

Han, Jiu-Ning; Luo, Jun-Hua; Liu, Zhen-Lai; Shi, Jun; Xiang, Gen-Xiang; Li, Jun-Xiu

2015-06-01

The nonlinear properties of composite structure induced by the head-on collision of electron-acoustic solitons in a general plasma composed of cold fluid electrons, hot nonextensive distributed electron, and stationary ions are studied. We have made a detailed investigation on the time-evolution process of this merged wave structure. It is found that the structure survives during some time interval, and there are obviously different for the properties of the composite structures which are induced in cylindrical and spherical geometries. Moreover, it is shown that there are both positive and negative phase shifts for each colliding soliton after the interaction. For fixed plasma parameters, the soliton received the largest phase shift in spherical geometry, followed by the cylindrical and one-dimensional planar geometries.

A series of three-dimensional lanthanide coordination polymers with rutile and unprecedented rutile-related topologies.

PubMed

Qin, Chao; Wang, Xin-Long; Wang, En-Bo; Su, Zhong-Min

2005-10-03

The complexes of formulas Ln(pydc)(Hpydc) (Ln = Sm (1), Eu (2), Gd (3); H2pydc = pyridine-2,5-dicarboxylic acid) and Ln(pydc)(bc)(H2O) (Ln = Sm (4), Gd (5); Hbc = benzenecarboxylic acid) have been synthesized under hydrothermal conditions and characterized by elemental analysis, IR, TG analysis, and single-crystal X-ray diffraction. Compounds 1-3 are isomorphous and crystallize in the orthorhombic system, space group Pbcn. Their final three-dimensional racemic frameworks can be considered as being constructed by helix-linked scalelike sheets. Compounds 4 and 5 are isostructural and crystallize in the monoclinic system, space group P2(1)/c. pydc ligands bridge dinuclear lanthanide centers to form the three-dimensional frameworks featuring hexagonal channels along the a-axis that are occupied by one-end-coordinated bc ligands. From the topological point of view, the five three-dimensional nets are binodal with six- and three-connected nodes, the former of which exhibit a rutile-related (4.6(2))(2)(4(2).6(9).8(4)) topology that is unprecedented within coordination frames, and the latter two species display a distorted rutile (4.6(2))(2)(4(2).6(10).8(3)) topology. Furthermore, the luminescent properties of 2 were studied.

A Generalization of the Spherical Inversion

ERIC Educational Resources Information Center

Ramírez, José L.; Rubiano, Gustavo N.

2017-01-01

In the present article, we introduce a generalization of the spherical inversion. In particular, we define an inversion with respect to an ellipsoid, and prove several properties of this new transformation. The inversion in an ellipsoid is the generalization of the elliptic inversion to the three-dimensional space. We also study the inverse images…

A study in three-dimensional chaotic dynamics: Granular flow and transport in a bi-axial spherical tumbler

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

Christov, Ivan C.; Lueptow, Richard M.; Ottino, Julio M.

We study three-dimensional (3D) chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial “blinking” tumbler). The flow is essentially quasi-two-dimensional in any vertical slice of the sphere during rotation about a single axis, and we provide an explicit exact solution to the model in this case. Hence, the cross-sectional flow can be represented by a twist map, allowing us to express the 3D flow as a linked twist map (LTM). We prove that if the rates of rotation about each axis are equal, then (inmore » the absence of stochasticity) particle trajectories are restricted to two-dimensional (2D) surfaces consisting of a portion of a hemispherical shell closed by a “cap''; if the rotation rates are unequal, then particles can leave the surface they start on and traverse a volume of the tumbler. The period-one structures of the governing LTM are examined in detail: analytical expressions are provided for the location of period-one curves, their extent into the bulk of the granular material, and their dependence on the protocol parameters (rates and durations of rotations). Exploiting the restriction of trajectories to 2D surfaces in the case of equal rotation rates about the axes, a method is proposed for identifying and constructing 3D Kolmogorov--Arnold--Moser (KAM) tubes around the normally elliptic period-one curves. The invariant manifold structure arising from the normally hyperbolic period-one curves is also examined. When the motion is restricted to 2D surfaces, the structure of manifolds of the hyperbolic points in the bulk differs from that corresponding to hyperbolic points in the flowing layer. Each is reminiscent of a template provided by a non-integrable perturbation to a Hamiltonian system, though the governing LTM is not. This highlights the novel 3D chaotic behaviors observed in this model dynamical system.« less

A study in three-dimensional chaotic dynamics: Granular flow and transport in a bi-axial spherical tumbler

DOE PAGES

Christov, Ivan C.; Lueptow, Richard M.; Ottino, Julio M.; ...

2014-05-22

We study three-dimensional (3D) chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial “blinking” tumbler). The flow is essentially quasi-two-dimensional in any vertical slice of the sphere during rotation about a single axis, and we provide an explicit exact solution to the model in this case. Hence, the cross-sectional flow can be represented by a twist map, allowing us to express the 3D flow as a linked twist map (LTM). We prove that if the rates of rotation about each axis are equal, then (inmore » the absence of stochasticity) particle trajectories are restricted to two-dimensional (2D) surfaces consisting of a portion of a hemispherical shell closed by a “cap''; if the rotation rates are unequal, then particles can leave the surface they start on and traverse a volume of the tumbler. The period-one structures of the governing LTM are examined in detail: analytical expressions are provided for the location of period-one curves, their extent into the bulk of the granular material, and their dependence on the protocol parameters (rates and durations of rotations). Exploiting the restriction of trajectories to 2D surfaces in the case of equal rotation rates about the axes, a method is proposed for identifying and constructing 3D Kolmogorov--Arnold--Moser (KAM) tubes around the normally elliptic period-one curves. The invariant manifold structure arising from the normally hyperbolic period-one curves is also examined. When the motion is restricted to 2D surfaces, the structure of manifolds of the hyperbolic points in the bulk differs from that corresponding to hyperbolic points in the flowing layer. Each is reminiscent of a template provided by a non-integrable perturbation to a Hamiltonian system, though the governing LTM is not. This highlights the novel 3D chaotic behaviors observed in this model dynamical system.« less

Discontinuous Galerkin Method with Numerical Roe Flux for Spherical Shallow Water Equations

NASA Astrophysics Data System (ADS)

Yi, T.; Choi, S.; Kang, S.

2013-12-01

In developing the dynamic core of a numerical weather prediction model with discontinuous Galerkin method, a numerical flux at the boundaries of grid elements plays a vital role since it preserves the local conservation properties and has a significant impact on the accuracy and stability of numerical solutions. Due to these reasons, we developed the numerical Roe flux based on an approximate Riemann problem for spherical shallow water equations in Cartesian coordinates [1] to find out its stability and accuracy. In order to compare the performance with its counterpart flux, we used the Lax-Friedrichs flux, which has been used in many dynamic cores such as NUMA [1], CAM-DG [2] and MCore [3] because of its simplicity. The Lax-Friedrichs flux is implemented by a flux difference between left and right states plus the maximum characteristic wave speed across the boundaries of elements. It has been shown that the Lax-Friedrichs flux with the finite volume method is more dissipative and unstable than other numerical fluxes such as HLLC, AUSM+ and Roe. The Roe flux implemented in this study is based on the decomposition of flux difference over the element boundaries where the nonlinear equations are linearized. It is rarely used in dynamic cores due to its complexity and thus computational expensiveness. To compare the stability and accuracy of the Roe flux with the Lax-Friedrichs, two- and three-dimensional test cases are performed on a plane and cubed-sphere, respectively, with various numbers of element and polynomial order. For the two-dimensional case, the Gaussian bell is simulated on the plane with two different numbers of elements at the fixed polynomial orders. In three-dimensional cases on the cubed-sphere, we performed the test cases of a zonal flow over an isolated mountain and a Rossby-Haurwitz wave, of which initial conditions are the same as those of Williamson [4]. This study presented that the Roe flux with the discontinuous Galerkin method is less dissipative and has stronger numerical stability than the Lax-Friedrichs. Reference 1. 2002, Giraldo, F.X., Hesthaven, J.S. and Warburton, T., "Nodal High-Order Discontinous Galerkin Methods for the Spherical Shallow Water Equations," Journal of Computational Physics, Vol.181, pp.499-525. 2. 2005, Nair, R.D., Thomas, S.J. and Loft, R.D., "A Discontinuous Galerkin Transport Scheme on the Cubed Sphere," Monthly Weather Review, Vol.133, pp.814-828. 3. 2010, Ullrich, P.A., Jablonowski, C. and Leer, van B., "High-Order Finite-Volume Methods for the Shallow-Water Equations on the Sphere," Journal of Computational Physics, Vol.229, pp.6104-6134. 4. 1992, Williamson, D.L., Drake, J.B., Hack, J., Jacob, R. and Swartztrauber, P.N., "A Standard Test Set for Numerical Approximations to the Shallow Water Equations in Spherical Geometry," Journal of Computational Physics, Vol.102, pp.211-224.

A novel stereotactic frame for real PET-guided biopsies: A preclinical proof-of-concept.

PubMed

Cortes-Rodicio, J; Sanchez-Merino, G; Garcia-Fidalgo, M A; Tobalina-Larrea, I

2017-09-01

To design, build and test a stereotactic device that allows PET image-guided biopsies to be performed. An initial prototype consisting of four main pieces, one of which contains radioactive markers to make it visible in the PET images, was built using a 3D printer. Once the device is mounted, a spherical coordinate system is built with the entrance needle point in the skin as the origin of coordinates. Two in-house software programs, namely getCoord.ijm, which obtains the spherical coordinates of the tumour tissue to be biopsied, and getNeedle.ijm, which virtualizes the inner needle tip once the puncture has taken place, were written. This prototype was tested on an FDG-doped phantom to characterize both the accuracy of the system and the procedure time. Up to 11 complete biopsy procedures were conducted. The mean total procedure time was less than 20min, which is less than the procedure time of conventional standard CT-guided biopsies. The overall accuracy of the system was found to be 5.0±1.3mm, which outperforms the criterion used in routine clinical practice when targeting tumours with a diameter of 10mm. A stereotactic frame to conduct real PET image-guided biopsies has been designed and built. A proof-of-concept was performed to characterize the system. The procedure time and accuracy of the system were found to meet the current needs of physicians performing biopsies. Copyright © 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Sheet-like assemblies of spherical particles with point-symmetrical patches.

PubMed

Mani, Ethayaraja; Sanz, Eduardo; Roy, Soumyajit; Dijkstra, Marjolein; Groenewold, Jan; Kegel, Willem K

2012-04-14

We report a computational study on the spontaneous self-assembly of spherical particles into two-dimensional crystals. The experimental observation of such structures stabilized by spherical objects appeared paradoxical so far. We implement patchy interactions with the patches point-symmetrically (icosahedral and cubic) arranged on the surface of the particle. In these conditions, preference for self-assembly into sheet-like structures is observed. We explain our findings in terms of the inherent symmetry of the patches and the competition between binding energy and vibrational entropy. The simulation results explain why hollow spherical shells observed in some Keplerate-type polyoxometalates (POM) appear. Our results also provide an explanation for the experimentally observed layer-by-layer growth of apoferritin--a quasi-spherical protein.

Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball.

PubMed

Adhikari, S K

2017-11-22

We study spontaneous symmetry breaking (SSB), Josephson oscillation, and self-trapping in a stable, mobile, three-dimensional matter-wave spherical quantum ball self-bound by attractive two-body and repulsive three-body interactions. The SSB is realized by a parity-symmetric (a) one-dimensional (1D) double-well potential or (b) a 1D Gaussian potential, both along the z axis and no potential along the x and y axes. In the presence of each of these potentials, the symmetric ground state dynamically evolves into a doubly-degenerate SSB ground state. If the SSB ground state in the double well, predominantly located in the first well (z > 0), is given a small displacement, the quantum ball oscillates with a self-trapping in the first well. For a medium displacement one encounters an asymmetric Josephson oscillation. The asymmetric oscillation is a consequence of SSB. The study is performed by a variational and a numerical solution of a non-linear mean-field model with 1D parity-symmetric perturbations.

Dynamical ion transfer between coupled Coulomb crystals in a double-well potential.

PubMed

Klumpp, Andrea; Zampetaki, Alexandra; Schmelcher, Peter

2017-09-01

We investigate the nonequilibrium dynamics of coupled Coulomb crystals of different sizes trapped in a double well potential. The dynamics is induced by an instantaneous quench of the potential barrier separating the two crystals. Due to the intra- and intercrystal Coulomb interactions and the asymmetric population of the potential wells, we observe a complex reordering of ions within the two crystals as well as ion transfer processes from one well to the other. The study and analysis of the latter processes constitutes the main focus of this work. In particular, we examine the dependence of the observed ion transfers on the quench amplitude performing an analysis for different crystalline configurations ranging from one-dimensional ion chains via two-dimensional zigzag chains and ring structures to three-dimensional spherical structures. Such an analysis provides us with the means to extract the general principles governing the ion transfer dynamics and we gain some insight on the structural disorder caused by the quench of the barrier height.

Titan impacts and escape

NASA Astrophysics Data System (ADS)

Korycansky, D. G.; Zahnle, Kevin J.

2011-01-01

We report on hydrodynamic calculations of impacts of large (multi-kilometer) objects on Saturn's moon Titan. We assess escape from Titan, and evaluate the hypothesis that escaping ejecta blackened the leading hemisphere of Iapetus and peppered the surface of Hyperion. We carried out two- and three-dimensional simulations of impactors ranging in size from 4 to 100 km diameter, impact velocities between 7 and 15 km s -1, and impact angles from 0° to 75° from the vertical. We used the ZEUSMP2 hydrocode for the calculations. Simulations were made using three different geometries: three-dimensional Cartesian, two-dimensional axisymmetric spherical polar, and two-dimensional plane polar. Three-dimensional Cartesian geometry calculations were carried out over a limited domain (e.g. 240 km on a side for an impactor of size di = 10 km), and the results compared to ones with the same parameters done by Artemieva and Lunine (2005); in general the comparison was good. Being computationally less demanding, two-dimensional calculations were possible for much larger domains, covering global regions of the satellite (from 800 km below Titan's surface to the exobase altitude 1700 km above the surface). Axisymmetric spherical polar calculations were carried out for vertical impacts. Two-dimensional plane-polar geometry calculations were made for both vertical and oblique impacts. In general, calculations among all three geometries gave consistent results. Our basic result is that the amount of escaping material is less than or approximately equal to the impactor mass even for the most favorable cases. Amounts of escaping material scaled most strongly as a function of velocity, with high-velocity impacts generating the largest amount, as expected. Dependence of the relative amount of escaping mass fesc = mesc/ Mi on impactor diameter di was weak. Oblique impacts (impact angle θi > 45°) were more effective than vertical or near-vertical impacts; ratios of mesc/ Mi ˜ 1-2 were found in the simulations.

Analysis of Uncertainty in a Middle-Cost Device for 3D Measurements in BIM Perspective

PubMed Central

Sánchez, Alonso; Naranjo, José-Manuel; Jiménez, Antonio; González, Alfonso

2016-01-01

Medium-cost devices equipped with sensors are being developed to get 3D measurements. Some allow for generating geometric models and point clouds. Nevertheless, the accuracy of these measurements should be evaluated, taking into account the requirements of the Building Information Model (BIM). This paper analyzes the uncertainty in outdoor/indoor three-dimensional coordinate measures and point clouds (using Spherical Accuracy Standard (SAS) methods) for Eyes Map, a medium-cost tablet manufactured by e-Capture Research & Development Company, Mérida, Spain. To achieve it, in outdoor tests, by means of this device, the coordinates of targets were measured from 1 to 6 m and cloud points were obtained. Subsequently, these were compared to the coordinates of the same targets measured by a Total Station. The Euclidean average distance error was 0.005–0.027 m for measurements by Photogrammetry and 0.013–0.021 m for the point clouds. All of them satisfy the tolerance for point cloud acquisition (0.051 m) according to the BIM Guide for 3D Imaging (General Services Administration); similar results are obtained in the indoor tests, with values of 0.022 m. In this paper, we establish the optimal distances for the observations in both, Photogrammetry and 3D Photomodeling modes (outdoor) and point out some working conditions to avoid in indoor environments. Finally, the authors discuss some recommendations for improving the performance and working methods of the device. PMID:27669245

Pickett angles and Cremer-Pople coordinates as collective variables for the enhanced sampling of six-membered ring conformations

NASA Astrophysics Data System (ADS)

Sega, M.; Autieri, E.; Pederiva, F.

2011-01-01

Although completely equivalent for the description of puckered ring conformers, the two popular coordinates sets of Strauss-Pickett dihedral angles and Cremer-Pople spherical coordinates are shown to have contrasting features when employed as collective variables in free-energy calculations with accelerated sampling techniques. Results from a 100 ns molecular dynamics simulation at conformational equilibrium and from combined metadynamics/umbrella sampling calculations of glucose are exploited to elucidate these differences.

Self-consistent description of the SHFB equations for 112Sn

NASA Astrophysics Data System (ADS)

Ghafouri, M.; Sadeghi, H.; Torkiha, M.

2018-03-01

The Hartree-Fock (HF) method is an excellent approximation of the closed shell magic nuclei. Pair correlation is essential for the description of open shell nuclei and has been derived for even-even, odd-odd and even-odd nuclei. These effects are reported by Hartree-Fock with BCS (HFBCS) or Hartree-Fock-Bogolyubov (HFB). These issues have been investigated, especially in the nuclear charts, and such studies have been compared with the observed information. We compute observations such as total binding energy, charge radius, densities, separation energies, pairing gaps and potential energy surfaces for neutrons and protons, and compare them with experimental data and the result of the spherical codes. In spherical even-even neutron-rich nuclei are considered in the Skyrme-Hartree-Fock-Bogolyubov (SHFB) method with density-dependent pairing interaction. Zero-range density-dependent interactions is used in the pairing channel. We solve SHF or SHFB equations in the spatial coordinates with spherical symmetry for tin isotopes such as 112Sn. The numerical accuracy of solving equations in the coordinate space is much greater than the fundamental extensions, which yields almost precise results.

Wide-Angle Multistatic Synthetic Aperture Radar: Focused Image Formation and Aliasing Artifact Mitigation

DTIC Science & Technology

2005-07-01

Progress in Applied Computational Electro- magnetics. ACES, Syracuse, NY, 2004. 91. Mahafza, Bassem R. Radar Systems Analysis and Design Using MATLAB...Figure Page 4.5. RCS chamber coordinate system . . . . . . . . . . . . . . . . . 88 4.6. AFIT’s RCS Chamber...4.11. Frequency domain schematic of RCS data collection . . . . . . 98 4.12. Spherical coordinate system for RCS data calibration . . . . . . 102 4.13

Data analytics and parallel-coordinate materials property charts

NASA Astrophysics Data System (ADS)

Rickman, Jeffrey M.

2018-01-01

It is often advantageous to display material properties relationships in the form of charts that highlight important correlations and thereby enhance our understanding of materials behavior and facilitate materials selection. Unfortunately, in many cases, these correlations are highly multidimensional in nature, and one typically employs low-dimensional cross-sections of the property space to convey some aspects of these relationships. To overcome some of these difficulties, in this work we employ methods of data analytics in conjunction with a visualization strategy, known as parallel coordinates, to represent better multidimensional materials data and to extract useful relationships among properties. We illustrate the utility of this approach by the construction and systematic analysis of multidimensional materials properties charts for metallic and ceramic systems. These charts simplify the description of high-dimensional geometry, enable dimensional reduction and the identification of significant property correlations and underline distinctions among different materials classes.

Three-dimensional structure of Erwinia carotovora L-asparaginase

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

Kislitsyn, Yu. A.; Kravchenko, O. V.; Nikonov, S. V.

2006-10-15

Three-dimensional structure of Erwinia carotovora L-asparaginase, which has antitumor activity and is used for the treatment of acute lymphoblastic leukemia, was solved at 3 A resolution and refined to R{sub cryst} = 20% and R{sub free} = 28%. Crystals of recombinant Erwinia carotovora L-asparaginase were grown by the hanging-drop vapor-diffusion method from protein solutions in a HEPES buffer (pH 6.5) and PEG MME 5000 solutions in a cacodylate buffer (pH 6.5) as the precipitant. Three-dimensional X-ray diffraction data were collected up to 3 A resolution from one crystal at room temperature. The structure was solved by the molecular replacement methodmore » using the coordinates of Erwinia chrysanthemi L-asparaginase as the starting model. The coordinates refined with the use of the CNS program package were deposited in the Protein Data Bank (PDB code 1ZCF)« less

Three-Dimensional Spherical Models of Convection in the Earth's Mantle.

PubMed

Bercovici, D; Schubert, G; Glatzmaier, G A

1989-05-26

Three-dimensional, spherical models of mantle convection in the earth reveal that upwelling cylindrical plumes and downwelling planar sheets are the primary features of mantle circulation. Thus, subduction zones and descending sheetlike slabs in the mantle are fundamental characteristics of thermal convection in a spherical shell and are not merely the consequences of the rigidity of the slabs, which are cooler than the surrounding mantle. Cylindrical mantle plumes that cause hotspots such as Hawaii are probably the only form of active upwelling and are therefore not just secondary convective currents separate from the large-scale mantle circulation. Active sheetlike upwellings that could be associated with mid-ocean ridges did not develop in the model simulations, a result that is in agreement with evidence suggesting that ridges are passive phenomena resulting from the tearing of surface plates by the pull of descending slabs.

Extreme fluctuations in stochastic network coordination with time delays

NASA Astrophysics Data System (ADS)

Hunt, D.; Molnár, F.; Szymanski, B. K.; Korniss, G.

2015-12-01

We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network. We then obtain the scaling behavior of the extreme fluctuations with system size, as well as the distribution of the extremes on complex networks, and compare them to those on regular one-dimensional lattices. For large complex networks, when the delay is not too close to the critical one, fluctuations at the nodes effectively decouple, and the limit distributions converge to the Fisher-Tippett-Gumbel density. In contrast, fluctuations in low-dimensional spatial graphs are strongly correlated, and the limit distribution of the extremes is the Airy density. Finally, we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes.

Single-shot three-dimensional reconstruction based on structured light line pattern

NASA Astrophysics Data System (ADS)

Wang, ZhenZhou; Yang, YongMing

2018-07-01

Reconstruction of the object by single-shot is of great importance in many applications, in which the object is moving or its shape is non-rigid and changes irregularly. In this paper, we propose a single-shot structured light 3D imaging technique that calculates the phase map from the distorted line pattern. This technique makes use of the image processing techniques to segment and cluster the projected structured light line pattern from one single captured image. The coordinates of the clustered lines are extracted to form a low-resolution phase matrix which is then transformed to full-resolution phase map by spline interpolation. The 3D shape of the object is computed from the full-resolution phase map and the 2D camera coordinates. Experimental results show that the proposed method was able to reconstruct the three-dimensional shape of the object robustly from one single image.

On mass transport in magmatic porosity waves

NASA Astrophysics Data System (ADS)

Jordan, J.; Hesse, M. A.; Rudge, J. F.

2017-12-01

Geochemical analyses of oceanic basalts indicate the mantle is lithologically heterogenous and subject to partial melting. Here we show that porosity waves-which arise naturally in models of buoyancy driven melt migration-transport mass and preserve geochemical signatures, at least partially. Prior studies of tracer transport in one dimensional porosity waves conclude that porosity waves do not transfer mass. However, it is well known that one-dimensional porosity waves are unstable in two and three dimensions and break up into sets of cylindrical or spherical porosity waves. We show that tracer transport in higher dimensional porosity waves is dramatically different than in one dimension. Lateral melt focusing into these high porosity regions leads to melt recirculating in the center of the wave. Melt focusing and recirculation are not resolvable in one dimension where no sustained transport is observed in numerical experiments of solitary porosity waves. In two and three dimensions, the recirculating melt is separated from the background melt-flow field by a circular or spherical dividing streamline and transported with the phase velocity of the porosity wave. The amount of melt focusing that occurs within any given porosity wave, and thus, the extent of the dividing streamline, and resultant volume of transported melt is extremely sensitive to the selection of porosity-permeability and porosity-rheology relationships. Therefore, we present a regime diagram spanning common parameterizations that illustrates the minimum amplitude and phase velocity required for a solitary porosity wave to transport mass as a function of material properties and common parameters used in magma dynamics and mid-ocean ridge models. The realization that solitary waves are capable of sustaining melt transport may require the reinterpretation of previous studies. For example, transport in porosity waves may allow melts that originated from the partial melting of fertile heterogeneities to retain their incompatible trace element signatures as they rise through the mantle. Porosity waves may also provide a mechanism for mixing melts derived from heterogeneities with ambient melts derived from different depths in the mantle.

Analytical Solutions for Radiative Transfer: Implications for Giant Planet Formation by Disk Instability

NASA Astrophysics Data System (ADS)

Boss, Alan P.

2009-03-01

The disk instability mechanism for giant planet formation is based on the formation of clumps in a marginally gravitationally unstable protoplanetary disk, which must lose thermal energy through a combination of convection and radiative cooling if they are to survive and contract to become giant protoplanets. While there is good observational support for forming at least some giant planets by disk instability, the mechanism has become theoretically contentious, with different three-dimensional radiative hydrodynamics codes often yielding different results. Rigorous code testing is required to make further progress. Here we present two new analytical solutions for radiative transfer in spherical coordinates, suitable for testing the code employed in all of the Boss disk instability calculations. The testing shows that the Boss code radiative transfer routines do an excellent job of relaxing to and maintaining the analytical results for the radial temperature and radiative flux profiles for a spherical cloud with high or moderate optical depths, including the transition from optically thick to optically thin regions. These radial test results are independent of whether the Eddington approximation, diffusion approximation, or flux-limited diffusion approximation routines are employed. The Boss code does an equally excellent job of relaxing to and maintaining the analytical results for the vertical (θ) temperature and radiative flux profiles for a disk with a height proportional to the radial distance. These tests strongly support the disk instability mechanism for forming giant planets.

Novel bimetallic thiocyanate-bridged Cu(II)-Hg(II) compounds—synthesis, X-Ray studies and magnetic properties

NASA Astrophysics Data System (ADS)

Machura, B.; Świtlicka, A.; Zwoliński, P.; Mroziński, J.; Kalińska, B.; Kruszynski, R.

2013-01-01

Seven novel heterobimetallic Cu/Hg polymers based on thiocyanate bridges have been synthesised and characterised by means of IR, EPR, magnetic measurements and single crystal X-Ray. Three of them, [Cu(pzH)4Hg(SCN)4]n (1) [Cu(indH)4Hg(SCN)4]n (2) and [Cu(ampy)2Hg(SCN)4]n (3), have one-dimensional coordination structure. Two compounds [Cu(pzH)2Hg(SCN)4]n (4) and [Cu(abzimH)Hg(SCN)4]n (5) form two-dimensional nets, whereas the complexes [Cu(pyCN)2Hg(SCN)4]n (6) and [Cu(pyCH(OH)(OMe))2Hg(SCN)4]n (7) are three-dimensional coordination polymers. The chains of 1 are connected by the intermolecular N-H•••N hydrogen bonds to the three dimensional net. In 2 the N-H•••S hydrogen bonds link the polymeric chains to the two dimensional layer extending along crystallographic (0 0 1) plane. The polymeric chains of compound 3 are joined by the intermolecular N-H•••N and N-H•••S hydrogen bonds to the three dimensional net. The polymeric layers of 4 are connected by the intermolecular N-H•••N hydrogen bonds to the three dimensional net.

Interference effects in phased beam tracing using exact half-space solutions.

PubMed

Boucher, Matthew A; Pluymers, Bert; Desmet, Wim

2016-12-01

Geometrical acoustics provides a correct solution to the wave equation for rectangular rooms with rigid boundaries and is an accurate approximation at high frequencies with nearly hard walls. When interference effects are important, phased geometrical acoustics is employed in order to account for phase shifts due to propagation and reflection. Error increases, however, with more absorption, complex impedance values, grazing incidence, smaller volumes and lower frequencies. Replacing the plane wave reflection coefficient with a spherical one reduces the error but results in slower convergence. Frequency-dependent stopping criteria are then applied to avoid calculating higher order reflections for frequencies that have already converged. Exact half-space solutions are used to derive two additional spherical wave reflection coefficients: (i) the Sommerfeld integral, consisting of a plane wave decomposition of a point source and (ii) a line of image sources located at complex coordinates. Phased beam tracing using exact half-space solutions agrees well with the finite element method for rectangular rooms with absorbing boundaries, at low frequencies and for rooms with different aspect ratios. Results are accurate even for long source-to-receiver distances. Finally, the crossover frequency between the plane and spherical wave reflection coefficients is discussed.

Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments.

PubMed

Kevrekidis, P G; Wang, Wenlong; Carretero-González, R; Frantzeskakis, D J

2017-06-16

Consider a lower-dimensional solitonic structure embedded in a higher-dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark soliton in 2D space, a spherical shell soliton in 3D space, etc. By extending the Landau dynamics approach [Phys. Rev. Lett. 93, 240403 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.240403], we show that it is possible to capture the transverse dynamical modes (the "Kelvin modes") of the undulation of this "soliton filament" within the higher-dimensional space. These are the transverse stability or instability modes and are the ones potentially responsible for the breakup of the soliton into structures such as vortices, vortex rings, etc. We present the theory and case examples in 2D and 3D, corroborating the results by numerical stability and dynamical computations.

Parsimonious description for predicting high-dimensional dynamics

PubMed Central

Hirata, Yoshito; Takeuchi, Tomoya; Horai, Shunsuke; Suzuki, Hideyuki; Aihara, Kazuyuki

2015-01-01

When we observe a system, we often cannot observe all its variables and may have some of its limited measurements. Under such a circumstance, delay coordinates, vectors made of successive measurements, are useful to reconstruct the states of the whole system. Although the method of delay coordinates is theoretically supported for high-dimensional dynamical systems, practically there is a limitation because the calculation for higher-dimensional delay coordinates becomes more expensive. Here, we propose a parsimonious description of virtually infinite-dimensional delay coordinates by evaluating their distances with exponentially decaying weights. This description enables us to predict the future values of the measurements faster because we can reuse the calculated distances, and more accurately because the description naturally reduces the bias of the classical delay coordinates toward the stable directions. We demonstrate the proposed method with toy models of the atmosphere and real datasets related to renewable energy. PMID:26510518

How should spin-weighted spherical functions be defined?

NASA Astrophysics Data System (ADS)

Boyle, Michael

2016-09-01

Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the normal to the sphere. These component functions are usually presented as functions on the sphere itself, but this requires an implicit choice of distinguished tangent vectors with which to contract. Thus, we may more accurately say that spin-weighted spherical functions are functions of both a point on the sphere and a choice of frame in the tangent space at that point. The distinction becomes extremely important when transforming the coordinates in which these functions are expressed, because the implicit choice of frame will also transform. Here, it is proposed that spin-weighted spherical functions should be treated as functions on the spin or rotation groups, which simultaneously tracks the point on the sphere and the choice of tangent frame by rotating elements of an orthonormal basis. In practice, the functions simply take a quaternion argument and produce a complex value. This approach more cleanly reflects the geometry involved, and allows for a more elegant description of the behavior of spin-weighted functions. In this form, the spin-weighted spherical harmonics have simple expressions as elements of the Wigner 𝔇 representations, and transformations under rotation are simple. Two variants of the angular-momentum operator are defined directly in terms of the spin group; one is the standard angular-momentum operator L, while the other is shown to be related to the spin-raising operator ð.

Large exchange anisotropy in quasi-one-dimensional spin-1/2 fluoride antiferromagnets with a d (z2)1 ground state

NASA Astrophysics Data System (ADS)

Kurzydłowski, D.; Grochala, W.

2017-10-01

Hybrid density functional calculations are performed for a variety of systems containing d9 ions (C u2 + and A g2 + ) and exhibiting quasi-one-dimensional magnetic properties. In particular, we study fluorides containing these ions in a rarely encountered compressed octahedral coordination that forces the unpaired electron into the local d (z2) orbital. We predict that such systems should exhibit exchange anisotropies surpassing that of S r2Cu O3 , one of the best realizations of a one-dimensional system known to date. In particular, we predict that the interchain coupling in the A g2 + -containing [AgF ] [B F4 ] system should be nearly four orders of magnitude smaller than the intrachain interaction. Our results indicate that quasi-one-dimensional spin-1/2 systems containing chains with spin sites in the d (z2)1 local ground state could constitute a versatile model for testing modern theories of quantum many-body physics in the solid state.

New water soluble heterometallic complex showing unpredicted coordination modes of EDTA

NASA Astrophysics Data System (ADS)

Mudsainiyan, R. K.; Jassal, A. K.; Chawla, S. K.

2015-10-01

A mesoporous 3D polymeric complex (I) having formula {[Zr(IV)O-μ3-(EDTA)Fe(III)OH]·H2O}n has been crystallized and characterized by various techniques. Single-crystal X-ray diffraction analysis revealed that complex (I) crystallized in chiral monoclinic space group Cc (space group no. 9) with unexpected coordination modes of EDTA and mixture of two transition metal ions. In this complex, the coordination number of Zr(IV) ion is seven where four carboxylate oxygen atoms, two nitrogen atoms, one oxide atom are coordinating with Zr(IV). Fe(III) is four coordinated and its coordination environment is composed of three different carboxylic oxygen atoms from three different EDTA and one oxygen atom of -OH group. The structure consists of 4-c and 16-c (2-nodal) net with new topology and point symbol for net is (336·454·530)·(36). TGA study and XRPD pattern showed that the coordination polymer is quite stable even after losing water molecule and -OH ion. Quenching behavior in fluorescence of ligand is observed by complexation with transition metal ions is due to n-π* transition. The SEM micrograph shows the morphology of complex (I) exhibits spherical shape with size ranging from 50 to 280 nm. The minimum N2 (SBET=8.7693 m2/g) and a maximum amount of H2 (high surface area=1044.86 m2/g (STP)) could be adsorbed at 77 K. From DLS study, zeta potential is calculated i.e. -7.94 shows the negative charges on the surface of complex. Hirshfeld surface analysis and fingerprint plots revealed influence of weak or non bonding interactions in crystal packing of complex.

The curious case of large-N expansions on a (pseudo)sphere

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

Polyakov, Alexander M.; Saleem, Zain H.; Stokes, James

We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand-Dikiy equations.

The curious case of large-N expansions on a (pseudo)sphere

DOE PAGES

Polyakov, Alexander M.; Saleem, Zain H.; Stokes, James

2015-02-03

We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand-Dikiy equations.

Computation at a coordinate singularity

NASA Astrophysics Data System (ADS)

Prusa, Joseph M.

2018-05-01

Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold - that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. In this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held-Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ∼ 20% faster in wall clock time than the control-resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar singularity are observed to increase with grid resolution. In contrast, test simulations demonstrate robust polar behavior independent of grid resolution.

Computer numerically controlled (CNC) aspheric shaping with toroidal Wheels (Abstract Only)

NASA Astrophysics Data System (ADS)

Ketelsen, D.; Kittrell, W. C.; Kuhn, W. M.; Parks, R. E.; Lamb, George L.; Baker, Lynn

1987-01-01

Contouring with computer numerically controlled (CNC) machines can be accomplished with several different tool geometries and coordinated machine axes. To minimize the number of coordinated axes for nonsymmetric work to three, it is common practice to use a spherically shaped tool such as a ball-end mill. However, to minimize grooving due to the feed and ball radius, it is desirable to use a long ball radius, but there is clearly a practical limit to ball diameter with the spherical tool. We have found that the use of commercially available toroidal wheels permits long effective cutting radii, which in turn improve finish and minimize grooving for a set feed. In addition, toroidal wheels are easier than spherical wheels to center accurately. Cutting parameters are also easier to control because the feed rate past the tool does not change as the slope of the work changes. The drawback to the toroidal wheel is the more complex calculation of the tool path. Of course, once the algorithm is worked out, the tool path is as easily calculated as for a spherical tool. We have performed two experiments with the Large Optical Generator (LOG) that were ideally suited to three-axis contouring--surfaces that have no axis of rotational symmetry. By oscillating the cutting head horizontally or vertically (in addition to the motions required to generate the power of the surface) , and carefully coordinating those motions with table rotation, the mostly astigmatic departure for these surfaces is produced. The first experiment was a pair of reflector molds that together correct the spherical aberration of the Arecibo radio telescope. The larger of these was 5 m in diameter and had a 12 cm departure from the best-fit sphere. The second experiment was the generation of a purely astigmatic surface to demonstrate the feasibility of producing axially symmetric asphe.rics while mounted and rotated about any off-axis point. Measurements of the latter (the first experiment had relatively loose tolerances) indicate an accuracy only 3 or 4 times that achieved by conventional two-axis contouring (10 AM as opposed to 3 pm rms) The successful completion of these projects demonstrates the successful application of three-axis contouring with the LOG. Toroidal cutters have also solved many of the drawbacks of spherical wheels. Work remains to be done in improving machine response and decreasing the contribution of backlash errors.

Optical Forces on Non-Spherical Nanoparticles Trapped by Optical Waveguides

NASA Astrophysics Data System (ADS)

Hasan Ahmed, Dewan; Sung, Hyung Jin

2011-07-01

Numerical simulations of a solid-core polymer waveguide structure were performed to calculate the trapping efficiencies of particles with nanoscale dimensions smaller than the wavelength of the trapping beam. A three-dimensional (3-D) finite element method was employed to calculate the electromagnetic field. The inlet and outlet boundary conditions were obtained using an eigenvalue solver to determine the guided and evanescent mode profiles. The Maxwell stress tensor was considered for the calculation of the transverse and downward trapping efficiencies. A particle at the center of the waveguide showed minimal transverse trapping efficiency and maximal downward trapping efficiency. This trend gradually reversed as the particle moved away from the center of the waveguide. Particles with larger surface areas exhibited higher trapping efficiencies and tended to be trapped near the waveguide. Particles displaced from the wave input tended to be trapped at the waveguide surface. Simulation of an ellipsoidal particle showed that the orientation of the major axis along the waveguide's lateral z-coordinate significantly influenced the trapping efficiency. The particle dimensions along the z-coordinate were more critical than the gap distance (vertical displacement from the floor of the waveguide) between the ellipsoid particle and the waveguide. The present model was validated using the available results reported in the literature for different trapping efficiencies.

A finite element method for solving the shallow water equations on the sphere

NASA Astrophysics Data System (ADS)

Comblen, Richard; Legrand, Sébastien; Deleersnijder, Eric; Legat, Vincent

Within the framework of ocean general circulation modeling, the present paper describes an efficient way to discretize partial differential equations on curved surfaces by means of the finite element method on triangular meshes. Our approach benefits from the inherent flexibility of the finite element method. The key idea consists in a dialog between a local coordinate system defined for each element in which integration takes place, and a nodal coordinate system in which all local contributions related to a vectorial degree of freedom are assembled. Since each element of the mesh and each degree of freedom are treated in the same way, the so-called pole singularity issue is fully circumvented. Applied to the shallow water equations expressed in primitive variables, this new approach has been validated against the standard test set defined by [Williamson, D.L., Drake, J.B., Hack, J.J., Jakob, R., Swarztrauber, P.N., 1992. A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics 102, 211-224]. Optimal rates of convergence for the P1NC-P1 finite element pair are obtained, for both global and local quantities of interest. Finally, the approach can be extended to three-dimensional thin-layer flows in a straightforward manner.

One- and two-dimensional divalent copper coordination polymers based on kinked organodiimine and long flexible aliphatic dicarboxylate ligands

NASA Astrophysics Data System (ADS)

Mallika Krishnan, Subhashree; Supkowski, Ronald M.; LaDuca, Robert L.

2008-11-01

Hydrothermal synthesis under acidic conditions has afforded a pair of divalent copper coordination polymers containing the kinked dipodal tethering organodiimine 4,4'-dipyridylamine (dpa) and flexible long-chain aliphatic dicarboxylate ligands. The new materials were characterized by single crystal X-ray structure determination, infrared spectroscopy, and thermogravimetric analysis. [CuCl(suberate) 0.5(dpa)] ( 1) manifests 1-D ladder-like motifs aggregated into 3-D through hydrogen bonding and copper-mediated supramolecular interactions. Extension of the aliphatic chain within the dicarboxylate ligand by one methylene unit resulted in {[Cu(azelate)(dpa)(H 2O)] · 3H 2O} ( 2), a (4,4) rhomboid grid 2-D coordination polymer encapsulating acyclic water molecule trimers.

A statistical formulation of one-dimensional electron fluid turbulence

NASA Technical Reports Server (NTRS)

Fyfe, D.; Montgomery, D.

1977-01-01

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Non-dissipative equilibrium canonical distributions are determined in a phase space whose co-ordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to k to the negative second power for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.

A set of alkali and alkaline-earth coordination polymers based on the ligand 2-(1H-benzotriazol-1-yl) acetic acid: Effects the radius of metal ions on structures and properties

NASA Astrophysics Data System (ADS)

Wang, Jin-Hua; Tang, Gui-Mei; Qin, Ting-Xiao; Yan, Shi-Chen; Wang, Yong-Tao; Cui, Yue-Zhi; Weng Ng, Seik

2014-11-01

Four new metal coordination complexes, namely, [Na(BTA)]n (1), [K2(BTA)2(μ2-H2O)]n (2), and [M(BTA)2(H2O)2]n (M=Ca(II) and Sr(II) for 3 and 4, respectively) [BTA=2-(1H-benzotriazol-1-yl) acetic anion], have been obtained under hydrothermal condition, by reacting the different alkali and alkaline-earth metal hydroxides with HBTA. Complexes 1-4 were structurally characterized by X-ray single-crystal diffraction, EA, IR, PXRD, and thermogravimetry analysis (TGA). These complexes display low-dimensional features displaying various two-dimensional (2D) and one-dimensional (1D) coordination motifs. Complex 1 displays a 2D layer with the thickness of 1.5 nm and possesses a topologic structure of a 11 nodal net with Schläfli symbol of {318}. Complex 2 also shows a thick 2D sheet and its topologic structure is a 9 nodes with Schläfli symbol of {311×42}. Complexes 3 and 4 possess a 1D linear chain and further stack via hydrogen bonding interactions to generate a three-dimensional supramolecular architecture. These results suggest that both the coordination preferences of the metal ions and the versatile nature of this flexible ligand play a critical role in the final structures. The luminescent spectra show strong emission intensities in complexes 1-4, which display violet photoluminescence. Additionally, ferroelectric, dielectric and nonlinear optic (NLO) second-harmonic generation (SHG) properties of 2 are discussed in detail.

Simulation and experimental research on spherical dome by 3D laser forming of square feet

NASA Astrophysics Data System (ADS)

Yang, Lijun; Wang, Yang

2007-01-01

Laser forming is a technique of using the energy from a laser beam to modify and adjust the curvature of sheet metals or hard materials. 2-dimensional laser forming can reasonably accurately control bend angles with various materials. To advance this process further for realistic forming applications in a manufacturing industry, it is necessary to consider larger scale controlled 3-dimensional laser forming. However, this is a different situation for 3-dimensional laser forming. The work presented in this paper uses the spider scanning path to form the thin square sheet to spherical dome by laser forming. The explicit dynamic analysis on 3-dimentional laser forming is shown in the article. On the base of temperature gradient mechanism of 2-dimensional laser forming, depending on the geometry and the thermo-physical properties of stainless steel lCrl8Ni9Ti, develop the mechanism of laser forming of thin square sheet to the spherical dome. This paper discusses the interaction between moving laser beam and sheet, the temperature field on the sheet, and the step transition of stress and deformation in laser forming. In order to give the verification on the results of simulation, the correlative experiment has progressed with Lumonics JK7O2H Nd:YAG laser. The results of experiments are in accord with the simulation.

Two-component dark-bright solitons in three-dimensional atomic Bose-Einstein condensates.

PubMed

Wang, Wenlong; Kevrekidis, P G

2017-03-01

In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3D) form. Motivated by earlier studies of dark-bright solitons in the 1D case, we explore the stability of these structures in their fully 3D form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal wave forms that are more robust. Finally, using the SO(2) symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.

Real time three dimensional sensing system

DOEpatents

Gordon, S.J.

1996-12-31

The invention is a three dimensional sensing system which utilizes two flexibly located cameras for receiving and recording visual information with respect to a sensed object illuminated by a series of light planes. Each pixel of each image is converted to a digital word and the words are grouped into stripes, each stripe comprising contiguous pixels. One pixel of each stripe in one image is selected and an epi-polar line of that point is drawn in the other image. The three dimensional coordinate of each selected point is determined by determining the point on said epi-polar line which also lies on a stripe in the second image and which is closest to a known light plane. 7 figs.

Real time three dimensional sensing system

DOEpatents

Gordon, Steven J.

1996-01-01

The invention is a three dimensional sensing system which utilizes two flexibly located cameras for receiving and recording visual information with respect to a sensed object illuminated by a series of light planes. Each pixel of each image is converted to a digital word and the words are grouped into stripes, each stripe comprising contiguous pixels. One pixel of each stripe in one image is selected and an epi-polar line of that point is drawn in the other image. The three dimensional coordinate of each selected point is determined by determining the point on said epi-polar line which also lies on a stripe in the second image and which is closest to a known light plane.

Trajectory specification for high capacity air traffic control

NASA Technical Reports Server (NTRS)

Paielli, Russell A. (Inventor)

2010-01-01

Method and system for analyzing and processing information on one or more aircraft flight paths, using a four-dimensional coordinate system including three Cartesian or equivalent coordinates (x, y, z) and a fourth coordinate .delta. that corresponds to a distance estimated along a reference flight path to a nearest reference path location corresponding to a present location of the aircraft. Use of the coordinate .delta., rather than elapsed time t, avoids coupling of along-track error into aircraft altitude and reduces effects of errors on an aircraft landing site. Along-track, cross-track and/or altitude errors are estimated and compared with a permitted error bounding space surrounding the reference flight path.

A self-learning algorithm for biased molecular dynamics

PubMed Central

Tribello, Gareth A.; Ceriotti, Michele; Parrinello, Michele

2010-01-01

A new self-learning algorithm for accelerated dynamics, reconnaissance metadynamics, is proposed that is able to work with a very large number of collective coordinates. Acceleration of the dynamics is achieved by constructing a bias potential in terms of a patchwork of one-dimensional, locally valid collective coordinates. These collective coordinates are obtained from trajectory analyses so that they adapt to any new features encountered during the simulation. We show how this methodology can be used to enhance sampling in real chemical systems citing examples both from the physics of clusters and from the biological sciences. PMID:20876135

Synthesis, crystal structures and luminescent properties of two 4 d-4 f Ln-Ag heterometallic coordination polymers based on anion template

NASA Astrophysics Data System (ADS)

Fan, Le-Qing; Chen, Yuan; Wu, Ji-Huai; Huang, Yun-Fang

2011-04-01

Two new 4 d-4 f Ln-Ag heterometallic coordination polymers, {[ Ln3Ag 5(IN) 10(H 2O) 7]·4(ClO 4)·4(H 2O)} n ( Ln=Eu ( 1) and Sm ( 2), HIN=isonicotinic acid), have been synthesized under hydrothermal conditions by reactions of Ln2O 3, AgNO 3, HIN and HClO 4, and characterized by elemental analysis, IR, thermal analysis and single-crystal X-ray diffraction. It is proved that HClO 4 not only adjusts the pH value of the reaction mixture, but also acts as anion template. The structure determination reveals that 1 and 2 are isostructural and feature a novel two-dimensional (2D) layered hetrometallic structure constructed from one-dimensional Ln-carboxylate chains and pillared Ag(IN) 2 units. The 2D layers are further interlinked through Ag⋯Ag and Ag⋯O(ClO 4-) multiple weak interactions, which form a rare Ag-ClO 4 ribbon in lanthanide-transition metal coordination polymers, to give rise to a three-dimensional supramolecular architecture. Moreover, the luminescent properties of these two compounds have also been investigated at room temperature.

Neuromodulation and Synaptic Plasticity for the Control of Fast Periodic Movement: Energy Efficiency in Coupled Compliant Joints via PCA.

PubMed

Stratmann, Philipp; Lakatos, Dominic; Albu-Schäffer, Alin

2016-01-01

There are multiple indications that the nervous system of animals tunes muscle output to exploit natural dynamics of the elastic locomotor system and the environment. This is an advantageous strategy especially in fast periodic movements, since the elastic elements store energy and increase energy efficiency and movement speed. Experimental evidence suggests that coordination among joints involves proprioceptive input and neuromodulatory influence originating in the brain stem. However, the neural strategies underlying the coordination of fast periodic movements remain poorly understood. Based on robotics control theory, we suggest that the nervous system implements a mechanism to accomplish coordination between joints by a linear coordinate transformation from the multi-dimensional space representing proprioceptive input at the joint level into a one-dimensional controller space. In this one-dimensional subspace, the movements of a whole limb can be driven by a single oscillating unit as simple as a reflex interneuron. The output of the oscillating unit is transformed back to joint space via the same transformation. The transformation weights correspond to the dominant principal component of the movement. In this study, we propose a biologically plausible neural network to exemplify that the central nervous system (CNS) may encode our controller design. Using theoretical considerations and computer simulations, we demonstrate that spike-timing-dependent plasticity (STDP) for the input mapping and serotonergic neuromodulation for the output mapping can extract the dominant principal component of sensory signals. Our simulations show that our network can reliably control mechanical systems of different complexity and increase the energy efficiency of ongoing cyclic movements. The proposed network is simple and consistent with previous biologic experiments. Thus, our controller could serve as a candidate to describe the neural control of fast, energy-efficient, periodic movements involving multiple coupled joints.

Neuromodulation and Synaptic Plasticity for the Control of Fast Periodic Movement: Energy Efficiency in Coupled Compliant Joints via PCA

PubMed Central

Stratmann, Philipp; Lakatos, Dominic; Albu-Schäffer, Alin

2016-01-01

There are multiple indications that the nervous system of animals tunes muscle output to exploit natural dynamics of the elastic locomotor system and the environment. This is an advantageous strategy especially in fast periodic movements, since the elastic elements store energy and increase energy efficiency and movement speed. Experimental evidence suggests that coordination among joints involves proprioceptive input and neuromodulatory influence originating in the brain stem. However, the neural strategies underlying the coordination of fast periodic movements remain poorly understood. Based on robotics control theory, we suggest that the nervous system implements a mechanism to accomplish coordination between joints by a linear coordinate transformation from the multi-dimensional space representing proprioceptive input at the joint level into a one-dimensional controller space. In this one-dimensional subspace, the movements of a whole limb can be driven by a single oscillating unit as simple as a reflex interneuron. The output of the oscillating unit is transformed back to joint space via the same transformation. The transformation weights correspond to the dominant principal component of the movement. In this study, we propose a biologically plausible neural network to exemplify that the central nervous system (CNS) may encode our controller design. Using theoretical considerations and computer simulations, we demonstrate that spike-timing-dependent plasticity (STDP) for the input mapping and serotonergic neuromodulation for the output mapping can extract the dominant principal component of sensory signals. Our simulations show that our network can reliably control mechanical systems of different complexity and increase the energy efficiency of ongoing cyclic movements. The proposed network is simple and consistent with previous biologic experiments. Thus, our controller could serve as a candidate to describe the neural control of fast, energy-efficient, periodic movements involving multiple coupled joints. PMID:27014051

Di-μ3-chlorido-tetra-μ2-chlorido-dichloridobis(dimethyl­formamide-κO)hexa­kis­(1H-imidazole-κN 3)tetra­cadmium

PubMed Central

Zhu, Run-Qiang

2011-01-01

The centrosymmetric mol­ecule of the title complex, [Cd4Cl8(C3H4N2)6(C3H7NO)2], contains four CdII atoms, six imidazole, two dimethyl­formamide and eight chloride ligands. The structure shows a novel chloride-bridged tetra­nuclear cadmium quasi-cubane cluster. The coordination geometry of all CdII atoms is distorted octa­hedral, with the two metal atoms in the asymmetric unit in different coordination environments. One of the Cd2+ ions is coordinated by five Cl− ions and by one N atom from an imidazole ligand, while the second is coordinated by three chloride ligands, two N atoms from two imidazole ligands and one O atom from a dimethyl­formamide mol­ecule. Inter­molecular N—H⋯Cl hydrogen bonds link the mol­ecules into a two-dimensional polymeric structure parallel to the ab plane. PMID:22058708

Theory of confined states of positronium in spherical and circular quantum dots with Kane’s dispersion law

PubMed Central

2013-01-01

Confined states of a positronium (Ps) in the spherical and circular quantum dots (QDs) are theoretically investigated in two size quantization regimes: strong and weak. Two-band approximation of Kane’s dispersion law and parabolic dispersion law of charge carriers are considered. It is shown that electron-positron pair instability is a consequence of dimensionality reduction, not of the size quantization. The binding energies for the Ps in circular and spherical QDs are calculated. The Ps formation dependence on the QD radius is studied. PMID:23826867

Three-dimensional ray tracing in spherical and elliptical generalized Luneburg lenses for application in the human eye lens.

PubMed

Gómez-Correa, J E; Coello, V; Garza-Rivera, A; Puente, N P; Chávez-Cerda, S

2016-03-10

Ray tracing in spherical Luneburg lenses has always been represented in 2D. All propagation planes in a 3D spherical Luneburg lens generate the same ray tracing, due to its radial symmetry. A geometry without radial symmetry generates a different ray tracing. For this reason, a new ray tracing method in 3D through spherical and elliptical Luneburg lenses using 2D methods is proposed. The physics of the propagation is shown here, which allows us to make a ray tracing associated with a vortex beam. A 3D ray tracing in a composite modified Luneburg lens that represents the human eye lens is also presented.

A two-dimensional ZnII coordination polymer constructed from benzene-1,2,3-tricarboxylic acid and N,N'-bis[(pyridin-4-yl)methylidene]hydrazine.

PubMed

Wang, Xiangfei; Yang, Fang; Tang, Meng; Yuan, Limin; Liu, Wenlong

2015-07-01

The hydrothermal synthesis of the novel complex poly[aqua(μ4-benzene-1,2,3-tricarboxylato)[μ2-4,4'-(hydrazine-1,2-diylidenedimethanylylidene)dipyridine](μ3-hydroxido)dizinc(II)], [Zn(C9H3O6)(OH)(C12H10N4)(H2O)]n, is described. The benzene-1,2,3-tricarboxylate ligand connects neighbouring Zn4(OH)2 secondary building units (SBUs) producing an infinite one-dimensional chain. Adjacent one-dimensional chains are connected by the N,N'-bis[(pyridin-4-yl)methylidene]hydrazine ligand, forming a two-dimensional layered structure. Adjacent layers are stacked to generate a three-dimensional supramolecular architecture via O-H...O hydrogen-bond interactions. The thermal stability of this complex is described and the complex also appears to have potential for application as a luminescent material.

Time-dependent corona models - Scaling laws

NASA Technical Reports Server (NTRS)

Korevaar, P.; Martens, P. C. H.

1989-01-01

Scaling laws are derived for the one-dimensional time-dependent Euler equations that describe the evolution of a spherically symmetric stellar atmosphere. With these scaling laws the results of the time-dependent calculations by Korevaar (1989) obtained for one star are applicable over the whole Hertzsprung-Russell diagram and even to elliptic galaxies. The scaling is exact for stars with the same M/R-ratio and a good approximation for stars with a different M/R-ratio. The global relaxation oscillation found by Korevaar (1989) is scaled to main sequence stars, a solar coronal hole, cool giants and elliptic galaxies.

The Nature of Bonding in Bulk Tellurium Composed of One-Dimensional Helical Chains.

PubMed

Yi, Seho; Zhu, Zhili; Cai, Xiaolin; Jia, Yu; Cho, Jun-Hyung

2018-05-07

Bulk tellurium (Te) is composed of one-dimensional (1D) helical chains which have been considered to be coupled by van der Waals (vdW) interactions. However, on the basis of first-principles density functional theory calculations, we here propose a different bonding nature between neighboring chains: i.e., helical chains made of normal covalent bonds are connected together by coordinate covalent bonds. It is revealed that the lone pairs of electrons of Te atoms participate in forming coordinate covalent bonds between neighboring chains, where each Te atom behaves as both an electron donor to neighboring chains and an electron acceptor from neighboring chains. This ligand-metal-like bonding nature in bulk Te results in the same order of bulk moduli along the directions parallel and perpendicular to the chains, contrasting with the large anisotropy of bulk moduli in vdW crystals. We further find that the electron effective masses parallel and perpendicular to the chains are almost the same as each other, consistent with the observed nearly isotropic electrical resistivity. It is thus demonstrated that the normal/coordinate covalent bonds parallel/perpendicular to the chains in bulk Te lead to a minor anisotropy in structural and transport properties.

1D cyanide complexes with 2-pyridinemethanol: Synthesis, crystal structures and spectroscopic properties

NASA Astrophysics Data System (ADS)

Sayın, Elvan; Kürkçüoğlu, Güneş Süheyla; Yeşilel, Okan Zafer; Hökelek, Tuncer

2015-12-01

Two new one-dimensional coordination polymers, [Cu(hmpH)2Pd(μ-CN)2(CN)2]n (1) and [Cu(hmpH)2Pt(μ-CN)2(CN)2]n (2), (hmpH = 2-pyridinemethanol), have been synthesized and characterized by vibrational (FT-IR and Raman) spectroscopy, single crystal X-ray diffraction, thermal and elemental analyses techniques. Single crystal X-ray diffraction analysis indicates that complexes 1 and 2 are isomorphous and isostructural, and crystallize in the triclinic system and P-1 space group. The Pd(II) or Pt(II) ions are four coordinated with four cyanide-carbon atoms in a square planar geometry. Cu(II) ion displays a distorted octahedral coordination by two N-atoms and two O-atoms of hmpH ligands, two bridging cyanide groups. In one dimensional structure of the complexes, [M(CN)4]2- (M = Pd(II) or Pt(II)) anions and [Cu(hmpH)2]2+ cations are linked via bridging cyanide ligands. In the complexes, the presence of intramolecular C-H⋯M (M = Pd(II) or Pt(II)) interactions with distance values of 3.00-2.95 Å are established, respectively.

One dimensional coordination polymers: Synthesis, crystal structures and spectroscopic properties

NASA Astrophysics Data System (ADS)

Karaağaç, Dursun; Kürkçüoğlu, Güneş Süheyla; Şenyel, Mustafa; Şahin, Onur

2016-11-01

Two new one dimensional (1D) cyanide complexes, namely [M(4-aepy)2(H2O)2][Pt(CN)4], (4-aepy = 4-(2-aminoethyl)pyridine M = Cu(II) (1) or Zn(II) (2)), have been synthesized and characterized by vibrational (FT-IR and Raman) spectroscopy, single crystal X-ray diffraction, thermal and elemental analyses techniques. The crystallographic analyses reveal that 1 and 2 are isomorphous and isostructural, and crystallize in the monoclinic system and C2 space group. The Pt(II) ions are coordinated by four cyanide-carbon atoms in the square-planar geometry and the [Pt(CN)4]2- ions act as a counter ion. The M(II) ions display an N4O2 coordination sphere with a distorted octahedral geometry, the nitrogen donors belonging to four molecules of the organic 4-aepy that act as unidentate ligands and two oxygen atoms from aqua ligands. The crystal structures of 1 and 2 are similar each other and linked via intermolecular hydrogen bonding, Pt⋯π interactions to form 3D supramolecular network. Vibration assignments of all the observed bands are given and the spectral features also supported to the crystal structures of the complexes.

pH-specific hydrothermal assembly of binary and ternary Pb(II)-(O,N-carboxylic acid) metal organic framework compounds: correlation of aqueous solution speciation with variable dimensionality solid-state lattice architecture and spectroscopic signatures.

PubMed

Gabriel, C; Perikli, M; Raptopoulou, C P; Terzis, A; Psycharis, V; Mateescu, C; Jakusch, T; Kiss, T; Bertmer, M; Salifoglou, A

2012-09-03

Hydrothermal pH-specific reactivity in the binary/ternary systems of Pb(II) with the carboxylic acids N-hydroxyethyl-iminodiacetic acid (Heida), 1,3-diamino-2-hydroxypropane-N,N,N',N'-tetraacetic acid (Dpot), and 1,10-phenanthroline (Phen) afforded the new well-defined crystalline compounds [Pb(Heida)](n)·nH(2)O(1), [Pb(Phen)(Heida)]·4H(2)O(2), and [Pb(3)(NO(3))(Dpot)](n)(3). All compounds were characterized by elemental analysis, FT-IR, solution or/and solid-state NMR, and single-crystal X-ray diffraction. The structures in 1-2 reveal the presence of a Pb(II) center coordinated to one Heida ligand, with 1 exhibiting a two-dimensional (2D) lattice extending to a three-dimensional (3D) one through H-bonding interactions. The concurrent aqueous speciation study of the binary Pb(II)-Heida system projects species complementing the synthetic efforts, thereby lending credence to a global structural speciation strategy in investigating binary/ternary Pb(II)-Heida/Phen systems. The involvement of Phen in 2 projects the significance of nature and reactivity potential of N-aromatic chelators, disrupting the binary lattice in 1 and influencing the nature of the ultimately arising ternary 3D lattice. 3 is a ternary coordination polymer, where Pb(II)-Dpot coordination leads to a 2D metal-organic-framework material with unique architecture. The collective physicochemical properties of 1-3 formulate the salient features of variable dimensionality metal-organic-framework lattices in binary/ternary Pb(II)-(hydroxy-carboxylate) structures, based on which new Pb(II) materials with distinct architecture and spectroscopic signature can be rationally designed and pursued synthetically.

Synthesis, structure and topological analysis of glycine templated highly stable cadmium sulfate framework: A New Lewis Acid catalyst

NASA Astrophysics Data System (ADS)

Paul, Avijit Kumar

2018-04-01

One new open-framework two-dimensional layer, [Cd(NH3CH2COO)(SO4)], I, has been synthesized using amino acid as templating agent. Single crystal structural analysis shows that the compound crystallizes in monoclinic cell with non-centrosymmetric space group P21, a = 4.9513(1) Å, b = 7.9763(2) Å, c = 8.0967(2) Å, β = 105.917(1)° and V = 307.504(12) Å3. The compound has connectivity between the Cd-centers and the sulfate units forming a two-dimensional layer structure. Sulfate unit is coordinated to metal center with η3, μ4 mode possessing a coordination free oxygen atom. The zwitterionic form of glycine molecule is present in the structure bridging with two metal centers through μ2-mode by carboxylate oxygens. The topological analysis reveals that the two-dimensional network is formed with a novel 4- and 6-connected binodal net of (32,42,52)(34,44,54,63) topology. Although one end of the glycine molecule is free from coordination, the structure is highly stable up to 350 °C. Strong N-H⋯ O hydrogen bonding interactions play an important role in the stabilization and formation of three-dimensional supramolecular structure. The cyanosilylation of imines using the present compounds as heterogeneous catalyst indicates good catalytic behavior. The present study illustrates the usefulness of the amino acid for the structure building in less studied sulfate based framework materials as well as designing of new heterogeneous catalysts for the broad application. The compound has also been characterized through elemental analysis, PXRD, IR, SEM and TG-DT studies.

Three-dimensional presentation of the earth and planets in classrooms and science centers with a spherical screen

NASA Astrophysics Data System (ADS)

Saito, A.; Tsugawa, T.; Odagi, Y.; Nishi, N.; Miyazaki, S.; Ichikawa, H.

2012-12-01

Educational programs have been developed for the earth and planetary science using a three-dimensional presentation system of the Earth and planets with a spherical screen. They have been used in classrooms of universities, high schools, elementary schools, and science centers. Two-dimensional map is a standard tool to present the data of the Earth and planets. However the distortion of the shape is inevitable especially for the map of wide areas. Three-dimensional presentation of the Earth, such as globes, is an only way to avoid this distortion. There are several projects to present the earth and planetary science results in three-dimension digitally, such as Science on a sphere (SOS) by NOAA, and Geo-cosmos by the National Museum of Emerging Science and Innovation (Miraikan), Japan. These projects are relatively large-scale in instruments and cost, and difficult to use in classrooms and small-scale science centers. Therefore we developed a portable, scalable and affordable system of the three-dimensional presentation of the Earth and planets, Dagik Earth. This system uses a spherical screen and a PC projector. Several educational programs have been developed using Dagik Earth under collaboration of the researchers of the earth and planetary science and science education, school teachers, and curators of science centers, and used in schools and museums in Japan, Taiwan and other countries. It helps learners to achieve the proper cognition of the shape and size of the phenomena on the Earth and planets. Current status and future development of the project will be introduced in the presentation.

Synthesis and structure of cesium complexes of nitrilotris(methylenephosphonic) acid [Cs-μ6-NH(CH2PO3)3H4] and [Cs2-μ10-NH(CH2PO3H)3] · H2O

NASA Astrophysics Data System (ADS)

Somov, N. V.; Chausov, F. F.; Zakirov, R. M.

2017-07-01

3D coordination polymers cesium nitrilotris(methylenephosphonate) and dicesium nitrilotris( methylenephosphonate) are synthesized and their crystal structure is determined. In the crystal of [Cs-μ6-NH(CH2PO3)3H4] (space group P, Z = 2), cesium atoms occupy two crystallographically inequivalent positions with c.n. = 10 and c.n. = 14. The phosphonate ligand plays the bridging function; its denticity is nine. The crystal packing consists of alternating layers of Cs atoms in different environments with layers of ligand molecules between them. A ligand is bound to three Cs atoms of one layer and three Cs atoms of another layer. In the crystal of [Cs2-μ10-NH(CH2PO3H)3] · H2O (space group P, Z = 2), the complex has a dimeric structure: the bridging phosphonate ligand coordinates Cs to form a three-dimensional Cs4O6 cluster. The denticity of the ligand is equal to nine; the coordination numbers of cesium atoms are seven and nine. Two-dimensional corrugated layers of Cs4O6 clusters lie in the (002) plane, and layers of ligand molecules are located between them. Each ligand molecule coordinates eight Cs atoms of one layer and two Cs atoms of the neighboring layer.

Orthogonality of spherical harmonic coefficients

NASA Astrophysics Data System (ADS)

McLeod, M. G.

1980-08-01

Orthogonality relations are obtained for the spherical harmonic coefficients of functions defined on the surface of a sphere. Following a brief discussion of the orthogonality of Fourier series coefficients, consideration is given to the values averaged over all orientations of the coordinate system of the spherical harmonic coefficients of a function defined on the surface of a sphere that can be expressed in terms of Legendre polynomials for the special case where the function is the sum of two delta functions located at two different points on the sphere, and for the case of an essentially arbitrary function. It is noted that the orthogonality relations derived have found applications in statistical studies of the geomagnetic field.

Simulating The Prompt Electromagnetic Pulse In 3D Using Vector Spherical Harmonics

NASA Astrophysics Data System (ADS)

Friedman, Alex; Cohen, Bruce I.; Eng, Chester D.; Farmer, William A.; Grote, David P.; Kruger, Hans W.; Larson, David J.

2017-10-01

We describe a new, efficient code for simulating the prompt electromagnetic pulse. In SHEMP (``Spherical Harmonic EMP''), we extend to 3-D the methods pioneered in C. Longmire's CHAP code. The geomagnetic field and air density are consistent with CHAP's assumed spherical symmetry only for narrow domains of influence about the line of sight, limiting validity to very early times. Also, we seek to model inherently 3-D situations. In CHAP and our own CHAP-lite, the independent coordinates are r (the distance from the source) and τ = t-r/c; the pulse varies slowly with r at fixed τ, so a coarse radial grid suffices. We add non-spherically-symmetric physics via a vector spherical harmonic decomposition. For each (l,m) harmonic, the radial equation is similar to that in CHAP and CHAP-lite. We present our methodology and results on model problems. This work was performed under the auspices of the U.S. DOE by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)

NASA Astrophysics Data System (ADS)

Lee, Jin

2014-05-01

The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.

Linear perturbations of a Schwarzschild blackhole by thin disc - convergence

NASA Astrophysics Data System (ADS)

Čížek, P.; Semerák, O.

2012-07-01

In order to find the perturbation of a Schwarzschild space-time due to a rotating thin disc, we try to adjust the method used by [4] in the case of perturbation by a one-dimensional ring. This involves solution of stationary axisymmetric Einstein's equations in terms of spherical-harmonic expansions whose convergence however turned out questionable in numerical examples. Here we show, analytically, that the series are almost everywhere convergent, but in some regions the convergence is not absolute.

Finding a spherically symmetric cosmology from observations in observational coordinates — advantages and challenges

NASA Astrophysics Data System (ADS)

Araújo, M. E.; Stoeger, W. R.

2011-07-01

One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions — without, for instance, assuming that the universe is almost Friedmann-Lemaître-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lemaître-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework, in which the radial coordinate y is null (light-like) and measured down the past light cone of the observer. In this paper we investigate the stability of solutions, and the use of data in the OC field equations including their time evolution — i.e. our procedure is not restricted to our past light cone — and compare both approaches with respect to the singularity problem at the maximum of the angular-diameter distance, the stability of solutions, and the use of data in the field equations. We also compare the two approaches with regard to determining the cosmological constant Λ. This allows a more detailed account and assessment of the OC integration procedure, and enables a comparison of the relative advantages of the two equivalent solution frameworks. Both formulations and integration procedures should, in principle, lead to the same results. However, as we show in this paper, the OC procedure manifests certain advantages, particularly in the avoidance of coordinate singularities at the maximum of the angular-diameter distance, and in the stability of the solutions obtained. This particular feature is what allows us to do the best fitting of the data to smooth data functions and the possibility of constructing analytic solutions to the field equations. Smoothed data functions enable us to include properties that data must have within the model.

Three-dimensional global MHD modeling of a coronal mass ejection interacting with the solar wind

NASA Astrophysics Data System (ADS)

An, J.; Inoue, S.; Magara, T.; Lee, H.; Kang, J.; Hayashi, K.; Tanaka, T.; Den, M.

2013-12-01

We developed a three-dimensional (3D) magnetohydrodynamic (MHD) code to reproduce the structure of the solar wind, the propagation of a coronal mass ejection (CME), and the interaction between them. This MHD code is based on the finite volume method and total diminishing (TVD) scheme with an unstructured grid system. In particular, this grid system can avoid the singularity at the north and south poles and relax tight CFL conditions around the poles, both of which would arise in the spherical coordinate system (Tanaka 1995). In this study, we constructed a model of the solar wind driven by the physical values at 50 solar radii obtained from the MHD tomographic method (Hayashi et al. 2003) where an interplanetary scintillation (IPS) observational data is used. By comparing the result to the observational data obtained from the near-Earth OMNI dataset, we confirmed that our simulation reproduces the velocity, temperature and density profiles obtained from the near-Earth OMNI dataset. We then insert a spheromak-type CME (Kataoka et al. 2009) into our solar-wind model and investigate the propagation process of the CME interacting with the solar wind. In particular, we discuss how the magnetic twist accumulated in a CME affects the CME-solar wind interaction.

Formation of Gd coordination polymer with 1D chains mediated by Bronsted acidic ionic liquids

NASA Astrophysics Data System (ADS)

Luo, Qianqian; Han, Ying; Lin, Hechun; Zhang, Yuanyuan; Duan, Chungang; Peng, Hui

2017-03-01

One dimensional coordination polymer Gd[(SO4)(NO3)(C2H6SO)2] (1) is prepared through the mediation of Bronsted acid ionic liquid, which crystallized in the monoclinic space of C2/c. In this polymer, adjacent Gd atoms are linked by two SO42- ions to generate a 1-D chain, and all oxygen atoms in SO42- groups are connected to three nearest Gd atoms in μ3:η1:η1:η2 fashion. Gd, S and N from SO42- and NO3- are precisely coplanar. The planar is coordinated by a pair of DMSO molecules, which is parallel and linked by hydrogen bonding to form a three-dimensional supramolecular network. Magnetic susceptibility measurement of 1 reveals weak antiferromagnetic interactions between the Gd (III) ions. It exhibits relatively large magneto-caloric effect with -ΔSm=28.8 J Kg-1 K-1 for ΔH=7 T.

Meter-Scale 3-D Models of the Martian Surface from Combining MOC and MOLA Data

NASA Technical Reports Server (NTRS)

Soderblom, Laurence A.; Kirk, Randolph L.

2003-01-01

We have extended our previous efforts to derive through controlled photoclinometry, accurate, calibrated, high-resolution topographic models of the martian surface. The process involves combining MGS MOLA topographic profiles and MGS MOC Narrow Angle images. The earlier work utilized, along with a particular MOC NA image, the MOLA topographic profile that was acquired simultaneously, in order to derive photometric and scattering properties of the surface and atmosphere so as to force the low spatial frequencies of a one-dimensional MOC photoclinometric model to match the MOLA profile. Both that work and the new results reported here depend heavily on successful efforts to: 1) refine the radiometric calibration of MOC NA; 2) register the MOC to MOLA coordinate systems and refine the pointing; and 3) provide the ability to project into a common coordinate system, simultaneously acquired MOC and MOLA with a single set of SPICE kernels utilizing the USGS ISIS cartographic image processing tools. The approach described in this paper extends the MOC-MOLA integration and cross-calibration procedures from one-dimensional profiles to full two-dimensional photoclinometry and image simulations. Included are methods to account for low-frequency albedo variations within the scene.

Scaling effects in direct shear tests

USGS Publications Warehouse

Orlando, A.D.; Hanes, D.M.; Shen, H.H.

2009-01-01

Laboratory experiments of the direct shear test were performed on spherical particles of different materials and diameters. Results of the bulk friction vs. non-dimensional shear displacement are presented as a function of the non-dimensional particle diameter. Simulations of the direct shear test were performed using the Discrete Element Method (DEM). The simulation results show Considerable differences with the physical experiments. Particle level material properties, such as the coefficients of static friction, restitution and rolling friction need to be known a priori in order to guarantee that the simulation results are an accurate representation of the physical phenomenon. Furthermore, laboratory results show a clear size dependency on the results, with smaller particles having a higher bulk friction than larger ones. ?? 2009 American Institute of Physics.

Simulation and Analysis of Converging Shock Wave Test Problems

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

Ramsey, Scott D.; Shashkov, Mikhail J.

2012-06-21

Results and analysis pertaining to the simulation of the Guderley converging shock wave test problem (and associated code verification hydrodynamics test problems involving converging shock waves) in the LANL ASC radiation-hydrodynamics code xRAGE are presented. One-dimensional (1D) spherical and two-dimensional (2D) axi-symmetric geometric setups are utilized and evaluated in this study, as is an instantiation of the xRAGE adaptive mesh refinement capability. For the 2D simulations, a 'Surrogate Guderley' test problem is developed and used to obviate subtleties inherent to the true Guderley solution's initialization on a square grid, while still maintaining a high degree of fidelity to the originalmore » problem, and minimally straining the general credibility of associated analysis and conclusions.« less

One-dimensional reduction of viscous jets. II. Applications

NASA Astrophysics Data System (ADS)

Pitrou, Cyril

2018-04-01

In a companion paper [Phys. Rev. E 97, 043115 (2018), 10.1103/PhysRevE.97.043115], a formalism allowing to describe viscous fibers as one-dimensional objects was developed. We apply it to the special case of a viscous fluid torus. This allows to highlight the differences with the basic viscous string model and with its viscous rod model extension. In particular, an elliptic deformation of the torus section appears because of surface tension effects, and this cannot be described by viscous string nor viscous rod models. Furthermore, we study the Rayleigh-Plateau instability for periodic deformations around the perfect torus, and we show that the instability is not sufficient to lead to the torus breakup in several droplets before it collapses to a single spherical drop. Conversely, a rotating torus is dynamically attracted toward a stationary solution, around which the instability can develop freely and split the torus in multiple droplets.

Transmittance properties of one dimensional ternary nanocomposite photonic crystals

NASA Astrophysics Data System (ADS)

Elsayed, Hussein A.

2018-03-01

In the present work, we have theoretically investigated the transmittance characteristics of one dimensional ternary photonic crystals that containing a nanocomposite layer. The nanocomposite layer was designed from metallic nanoparticles of (Ag) in a transparent matrix of a dielectric material (MgF2). The numerical results are obtained based on the theoretical modeling of the characteristic matrix method and Maxwell-Garnett model. The investigated results demonstrate the significant effect of the volume fraction of the nanoparticles on the effective permittivity of the nanocomposite material as well as the transmission characteristics of our design. Moreover, the roles played by other parameters such as the thickness of the nanocomposite layer, the permittivity of the host dielectric material and the spherical radius of the nanoparticles are included her. The proposed structure could be promising for many applications such as THz optical filters, reflectors and optical switches.

A polar-drive shock-ignition design for the National Ignition Facilitya)

NASA Astrophysics Data System (ADS)

Anderson, K. S.; Betti, R.; McKenty, P. W.; Collins, T. J. B.; Hohenberger, M.; Theobald, W.; Craxton, R. S.; Delettrez, J. A.; Lafon, M.; Marozas, J. A.; Nora, R.; Skupsky, S.; Shvydky, A.

2013-05-01

Shock ignition [R. Betti et al., Phys. Rev. Lett. 98, 155001 (2007)] is being pursued as a viable option to achieve ignition on the National Ignition Facility (NIF). Shock-ignition target designs use a high-intensity laser spike at the end of a low-adiabat assembly pulse to launch a spherically convergent strong shock to ignite the hot spot of an imploding capsule. A shock-ignition target design for the NIF is presented. One-dimensional simulations indicate an ignition threshold factor of 4.1 with a gain of 58. A polar-drive beam-pointing configuration for shock-ignition experiments on the NIF at 750 kJ is proposed. The capsule design is shown to be robust to the various one- and two-dimensional effects and nonuniformities anticipated on the NIF. The target is predicted to ignite with a gain of 38 when including all anticipated levels of nonuniformity and system uncertainty.

Recommended coordinate systems for thin spherocylindrical lenses.

PubMed

Deal, F C; Toop, J

1993-05-01

Because the set of thin spherocylindrical lenses forms a vector space, any such lens can be expressed in terms of its cartesian coordinates with respect to whatever set of basis lenses we may choose. Two types of cartesian coordinate systems have become prominent, those having coordinates associated with the lens power matrix and those having coordinates associated with the Humphrey Vision Analyzer. This paper emphasizes the value of a particular cartesian coordinate system of the latter type, and the cylindrical coordinate system related to it, by showing how it can simplify the trigonometry of adding lenses and how it preserves symmetry in depicting the sets of all spherical lenses, all Jackson crossed-cylinders, and all cylindrical lenses. It also discusses appropriate coordinates for keeping statistics on lenses and shows that an easy extension of the lens vector space to include general optical systems is not possible.

Constructing a Teleseismic Tomographic Image of Taiwan using BATS Recordings

NASA Astrophysics Data System (ADS)

Krajewski, J.; Roecker, S.

2005-12-01

Taiwan is an evolving arc-continent collision located at a complicated part of the plate boundary between the Eurasian and Philippine Sea plates. To better understand the role of the upper mantle in the dynamics of this collision, we reviewed 4 years of data from the Broadband Array in Taiwan for Seismology (BATS) in Taiwan to construct a teleseismic dataset for tomographic imaging of the subsurface of the island. From an initial selection of approximately 300 events, we used waveform correlation to generate a dataset of 4500 relative arrival times. To calculate accurate travel times in three dimensional wavespeed models over the large lateral distances in our model (~800 km), we solve the eikonal equation directly in a spherical coordinate system. We reduce the influence of smearing of crustal heterogeneity into the deeper mantle, we fix the upper 30 km to a previously determined P wavespeed model for the region. Initial resolution tests suggest a spatial limit on the order of 40 km.

Hawking radiation from dilatonic black holes via anomalies

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

Jiang Qingquan; Cai Xu; Wu Shuangqing

2007-03-15

Recently, Hawking radiation from a Schwarzschild-type black hole via a gravitational anomaly at the horizon has been derived by Robinson and Wilczek. Their result shows that, in order to demand general coordinate covariance at the quantum level to hold in the effective theory, the flux of the energy-momentum tensor required to cancel the gravitational anomaly at the horizon of the black hole is exactly equal to that of (1+1)-dimensional blackbody radiation at the Hawking temperature. In this paper, we attempt to apply the analysis to derive Hawking radiation from the event horizons of static, spherically symmetric dilatonic black holes withmore » arbitrary coupling constant {alpha}, and that from the rotating Kaluza-Klein ({alpha}={radical}(3)) as well as the Kerr-Sen ({alpha}=1) black holes via an anomalous point of view. Our results support Robinson and Wilczek's opinion. In addition, the properties of the obtained physical quantities near the extreme limit are qualitatively discussed.« less

Local sensory control of a dexterous end effector

NASA Technical Reports Server (NTRS)

Pinto, Victor H.; Everett, Louis J.; Driels, Morris

1990-01-01

A numerical scheme was developed to solve the inverse kinematics for a user-defined manipulator. The scheme was based on a nonlinear least-squares technique which determines the joint variables by minimizing the difference between the target end effector pose and the actual end effector pose. The scheme was adapted to a dexterous hand in which the joints are either prismatic or revolute and the fingers are considered open kinematic chains. Feasible solutions were obtained using a three-fingered dexterous hand. An algorithm to estimate the position and orientation of a pre-grasped object was also developed. The algorithm was based on triangulation using an ideal sensor and a spherical object model. By choosing the object to be a sphere, only the position of the object frame was important. Based on these simplifications, a minimum of three sensors are needed to find the position of a sphere. A two dimensional example to determine the position of a circle coordinate frame using a two-fingered dexterous hand was presented.

A model-based 3D phase unwrapping algorithm using Gegenbauer polynomials.

PubMed

Langley, Jason; Zhao, Qun

2009-09-07

The application of a two-dimensional (2D) phase unwrapping algorithm to a three-dimensional (3D) phase map may result in an unwrapped phase map that is discontinuous in the direction normal to the unwrapped plane. This work investigates the problem of phase unwrapping for 3D phase maps. The phase map is modeled as a product of three one-dimensional Gegenbauer polynomials. The orthogonality of Gegenbauer polynomials and their derivatives on the interval [-1, 1] are exploited to calculate the expansion coefficients. The algorithm was implemented using two well-known Gegenbauer polynomials: Chebyshev polynomials of the first kind and Legendre polynomials. Both implementations of the phase unwrapping algorithm were tested on 3D datasets acquired from a magnetic resonance imaging (MRI) scanner. The first dataset was acquired from a homogeneous spherical phantom. The second dataset was acquired using the same spherical phantom but magnetic field inhomogeneities were introduced by an external coil placed adjacent to the phantom, which provided an additional burden to the phase unwrapping algorithm. Then Gaussian noise was added to generate a low signal-to-noise ratio dataset. The third dataset was acquired from the brain of a human volunteer. The results showed that Chebyshev implementation and the Legendre implementation of the phase unwrapping algorithm give similar results on the 3D datasets. Both implementations of the phase unwrapping algorithm compare well to PRELUDE 3D, 3D phase unwrapping software well recognized for functional MRI.

There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator

PubMed Central

2011-01-01

Background Epithelial folding is a common morphogenetic process during the development of multicellular organisms. In metazoans, the biological and biomechanical processes that underlie such three-dimensional (3D) developmental events are usually complex and difficult to investigate. Spheroidal green algae of the genus Volvox are uniquely suited as model systems for studying the basic principles of epithelial folding. Volvox embryos begin life inside out and then must turn their spherical cell monolayer outside in to achieve their adult configuration; this process is called 'inversion.' There are two fundamentally different sequences of inversion processes in Volvocaceae: type A and type B. Type A inversion is well studied, but not much is known about type B inversion. How does the embryo of a typical type B inverter, V. globator, turn itself inside out? Results In this study, we investigated the type B inversion of V. globator embryos and focused on the major movement patterns of the cellular monolayer, cell shape changes and changes in the localization of cytoplasmic bridges (CBs) connecting the cells. Isolated intact, sectioned and fragmented embryos were analyzed throughout the inversion process using light microscopy, confocal laser scanning microscopy, scanning electron microscopy and transmission electron microscopy techniques. We generated 3D models of the identified cell shapes, including the localizations of CBs. We show how concerted cell-shape changes and concerted changes in the position of cells relative to the CB system cause cell layer movements and turn the spherical cell monolayer inside out. The type B inversion of V. globator is compared to the type A inversion in V. carteri. Conclusions Concerted, spatially and temporally coordinated changes in cellular shapes in conjunction with concerted migration of cells relative to the CB system are the causes of type B inversion in V. globator. Despite significant similarities between type A and type B inverters, differences exist in almost all details of the inversion process, suggesting analogous inversion processes that arose through parallel evolution. Based on our results and due to the cellular biomechanical implications of the involved tensile and compressive forces, we developed a global mechanistic scenario that predicts epithelial folding during embryonic inversion in V. globator. PMID:22206406

Gravitational Anomalies Caused by Zonal Winds in Jupiter

NASA Astrophysics Data System (ADS)

Schubert, G.; Kong, D.; Zhang, K.

2012-12-01

We present an accurate three-dimensional non-spherical numerical calculation of the gravitational anomalies caused by zonal winds in Jupiter. The calculation is based on a three-dimensional finite element method and accounts for the full effect of significant departure from spherical geometry caused by rapid rotation. Since the speeds of Jupiter's zonal winds are much smaller than that of its rigid-body rotation, our numerical calculation is carried out in two stages. First, we compute the non-spherical distributions of density and pressure at the equilibrium within Jupiter via a hybrid inverse approach by determining an a priori unknown coefficient in the polytropic equation of state that results in a match to the observed shape of Jupiter. Second, by assuming that Jupiter's zonal winds extend throughout the interior along cylinders parallel to the rotation axis, we compute gravitational anomalies produced by the wind-related density anomalies, providing an upper bound to the gravitational anomalies caused by the Jovian zonal winds.

Assembly of the most topologically regular two-dimensional micro and nanocrystals with spherical, conical, and tubular shapes

NASA Astrophysics Data System (ADS)

Roshal, D. S.; Konevtsova, O. V.; Myasnikova, A. E.; Rochal, S. B.

2016-11-01

We consider how to control the extension of curvature-induced defects in the hexagonal order covering different curved surfaces. In these frames we propose a physical mechanism for improving structures of two-dimensional spherical colloidal crystals (SCCs). For any SCC comprising of about 300 or less particles the mechanism transforms all extended topological defects (ETDs) in the hexagonal order into the point disclinations. Perfecting the structure is carried out by successive cycles of the particle implantation and subsequent relaxation of the crystal. The mechanism is potentially suitable for obtaining colloidosomes with better selective permeability. Our approach enables modeling the most topologically regular tubular and conical two-dimensional nanocrystals including various possible polymorphic forms of the HIV viral capsid. Different HIV-like shells with an arbitrary number of structural units (SUs) and desired geometrical parameters are easily formed. Faceting of the obtained structures is performed by minimizing the suggested elastic energy.

Shell-crossing in quasi-one-dimensional flow

NASA Astrophysics Data System (ADS)

Rampf, Cornelius; Frisch, Uriel

2017-10-01

Blow-up of solutions for the cosmological fluid equations, often dubbed shell-crossing or orbit crossing, denotes the breakdown of the single-stream regime of the cold-dark-matter fluid. At this instant, the velocity becomes multi-valued and the density singular. Shell-crossing is well understood in one dimension (1D), but not in higher dimensions. This paper is about quasi-one-dimensional (Q1D) flow that depends on all three coordinates but differs only slightly from a strictly 1D flow, thereby allowing a perturbative treatment of shell-crossing using the Euler-Poisson equations written in Lagrangian coordinates. The signature of shell-crossing is then just the vanishing of the Jacobian of the Lagrangian map, a regular perturbation problem. In essence, the problem of the first shell-crossing, which is highly singular in Eulerian coordinates, has been desingularized by switching to Lagrangian coordinates, and can then be handled by perturbation theory. Here, all-order recursion relations are obtained for the time-Taylor coefficients of the displacement field, and it is shown that the Taylor series has an infinite radius of convergence. This allows the determination of the time and location of the first shell-crossing, which is generically shown to be taking place earlier than for the unperturbed 1D flow. The time variable used for these statements is not the cosmic time t but the linear growth time τ ˜ t2/3. For simplicity, calculations are restricted to an Einstein-de Sitter universe in the Newtonian approximation, and tailored initial data are used. However it is straightforward to relax these limitations, if needed.

Novel bipyridinyl oxadiazole-based metal coordination complexes: High efficient and green synthesis of 3,4-dihydropyrimidin-2(1H)-ones through the Biginelli reactions

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

Wang, Jin-Hua; Zhang, E.; Tang, Gui-Mei, E-mail: meiguit@163.com

2016-09-15

Three new metal coordination complexes, namely, [Co(BPO){sub 2}(H{sub 2}O){sub 4}](BS){sub 2}(H{sub 2}O){sub 2} (1), [Co(BPO){sub 2}(H{sub 2}O){sub 4}](ABS){sub 2}(H{sub 2}O){sub 2} (2), [Co(BPO){sub 2}(H{sub 2}O){sub 4}](MBS){sub 2}(H{sub 2}O){sub 2} (3) [BPO=2,5-di(pyridin-4-yl)-1,3,4-oxadiazole, BS=benzenesulphonate, ABS=4-aminobenzenesulphonate, MBS=4-methylbenzenesulphonate] were obtained under hydrothermal conditions. Complexes 1–3 were structurally characterized by single-crystal X-ray diffraction, powder X-ray diffraction, IR and thermogravimetric analyses (TGA). All of them display a zero-dimensional motif, in which strong intermolecular hydrogen bonding interactions (O–H···O/N) and packing interactions (C–H···π and π···π) make them achieve a three-dimensional supramolecular architecture. The primary catalytic results of these three complexes show that high efficiency for the green synthesismore » of a variety of 3,4-dihydropyrimidin-2(1H)-ones was observed under solvent free conditions through Biginelli reactions. The present catalytic protocols exhibit advantages such as excellent yield, easy isolation, eco-friendly conditions, and short reaction time. - Graphical abstract: Three new metal coordination complexes with bipyridinyl-oxadiazole were obtained under hydrothermal conditions, which display a zero-dimensional motif, and show high efficiency for the green synthesis of a variety of 3,4-dihydropyrimidin-2(1H)-ones under solvent free conditions through Biginelli reactions. The present catalytic protocols exhibit advantages such as excellent yield, easy isolation, eco-friendly conditions, and short reaction time. Display Omitted.« less

Synthesis and structures of ligand-dominated one-dimensional silver(I)–bis(pyridylmethyl)amine coordination chains

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

Lin, Hung-Jui; Liu, Yu-Chiao; Tseng, Yu-Jui

2016-10-15

Reactants slow diffusion of Ag(I) salts with 3,4′-bis(pyridylmethyl)amine (3,4′-bpma), an unsymmetric bis-pyridyl ligand equipped with a non-innocent amine backbone, afforded polymeric coordination adducts 1–5 having a general formula ([Ag(3,4′-bpma)(solv)]X){sub n} (solv = H{sub 2}O, CH{sub 3}OH, and none; X= CF{sub 3}CO{sub 2}{sup –}, BF{sub 4}{sup –}, ClO{sub 4}{sup –}, CF{sub 3}SO{sub 3}{sup –}, and SbF{sub 6}{sup –}). Single-crystal X-ray diffraction (SCXRD) analyses reveal that colorless crystals of Ag(I) coordination polymers (CPs) 1–5 have very similar one-dimensional (1D) non-flat chain structures, which are preferentially depicted as a “zipper-like” rather than a ladder-like or a double-stranded chain topologies. The 3,4′-bpma ligand inmore » these Ag(I) CPs displays a μ{sub 3}-bridging mode with a gauche–trans (1,4, and 5) and a trans–trans (2 and 3) conformations. Noteworthy, anions do not show strong influence on structural modulation of Ag(I) CPs in the solid state, but really affect CP conformations and packing fashions, indicative of a ligand-dominated assembly process for such a Ag(I)–3,4′-bpma system. Thermal stabilities and solid-state photoluminescence properties of crystalline materials 1–5 were investigated. - Graphical abstract: This work has addressed five ligand-dominated Ag(I)–3,4′-bpma polymeric adducts, which show similar one-dimensional non-flat chain structures depicting a “zipper-like” topology rather than a ladder-like or a double-stranded chain structures.« less

Co-assembly of Zn(SPh){sub 2} and organic linkers into helical and zig-zag polymer chains

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

Liu Yi; Yu Lingmin; Loo, Say Chye Joachim

2012-07-15

Two novel one-dimensional coordination polymers, single helicate [Zn(SPh){sub 2}(TPyTA)(EG)]{sub n} (EG=ethylene glycol) (1) and zig-zag structure [Zn(SPh){sub 2}(BPyVB)]{sub n} (2), were synthesized under solvothermal conditions at 150 Degree-Sign C or room temperature by the co-assembly of Zn(SPh){sub 2} and organic linkers such as 2,4,6-tri(4-pyridyl)-1,3,5-triazine (TPyTA) and 1,3-bis(trans-4-pyridylvinyl)benzene (BPyVB). X-ray crystallography study reveals that both polymers 1 and 2 crystallize in space group P2{sub 1}/c of the monoclinic system. The solid-state UV-vis absorption spectra show that 1 and 2 have maxium absorption onsets at 400 nm and 420 nm, respectively. TGA analysis indicates that 1 and 2 are stable up tomore » 110 Degree-Sign C and 210 Degree-Sign C. - Graphical abstract: Two novel one-dimensional coordination polymers, single helicate [Zn(SPh){sub 2}(TPyTA)(EG)]{sub n} (1) and zig-zag structure [Zn(SPh){sub 2}(BPyVB)]{sub n} (2), were synthesized. Solid-state UV-vis absorptions show that 1 and 2 have maxium absorption onsets at 400 nm and 420 nm, respectively. TGA analysis indicates that 1 and 2 are stable up to 110 Degree-Sign C and 210 Degree-Sign C. Highlights: Black-Right-Pointing-Pointer Two novel one-dimensional coordination polymers have been synthesized. Black-Right-Pointing-Pointer TPyTA results in helical structures in 1 while BPyVB leads to zig-zag chains in 2. Black-Right-Pointing-Pointer Solid-state UV-vis absorption spectra and TGA analysis of the title polymers were studied.« less

Particle paths and phase plane for time-dependent similarity solutions of the one-dimensional Vlasov-Maxwell equations

NASA Technical Reports Server (NTRS)

Roberts, Dana Aaron; Abraham-Shrauner, Barbara

1987-01-01

The phase trajectories of particles in a plasma described by the one-dimensional Vlasov-Maxwell equations are determined qualitatively, analyzing exact general similarity solutions for the cases of temporally damped and growing (sinusoidal or localized) electric fields. The results of numerical integration in both untransformed and Lie-group point-transformed coordinates are presented in extensive graphs and characterized in detail. The implications of the present analysis for the stability of BGK equilibria are explored, and the existence of nonlinear solutions arbitrarily close to and significantly different from the BGK solutions is demonstrated.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Numerical solutions of 3-dimensional Navier-Stokes equations for closed bluff-bodies

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallelepiped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDc VPS 32 computer. The codes are written in 32-bit (half word) FORTRAN, which provides an approximate factor of two decreasing in computational time and doubles the memory size compared to the 54-bit word size.

The Combination of Spherical Photogrammetry and UAV for 3D Modeling

NASA Astrophysics Data System (ADS)

Ihsanudin, T.; Affriani, A. R.

2017-12-01

The complete of 3D models required the object that was recorded from both side and top. If the object recorded from above, then the object from the side can not be covered, and if the objects recorded from the side, it can not be covered from the top. Recording of objects from the side using spherical photogrammetry method and from the top using UAV method. The merge of both models using a conform transformation, by bringing the spherical photogrammetry coordinates system to the UAV model. The object of this research is Ratu Boko temple, Sleman, Yogyakarta. The spherical photogrammetry recording was performed by rotating the camera in 360° angle on the entire area of the temple. The area consists of 12 stations. The UAV method uses a drone with flight attitude of 20 meters. The merge of the both models produced the completeness of the temple model from the top and side.

Bromidotetra-kis-(2-ethyl-1H-imidazole-κN (3))copper(II) bromide.

PubMed

Godlewska, Sylwia; Kelm, Harald; Krüger, Hans-Jörg; Dołęga, Anna

2012-12-01

The Cu(II) ion in the title mol-ecular salt, [CuBr(C5H8N2)4]Br, is coordinated in a square-pyramidal geometry by four N atoms of imidazole ligands and one bromide anion in the apical position. In the crystal, the ions are linked by N-H⋯Br hydrogen bonds involving both the coordinating and the free bromide species as acceptors. A C-H⋯Br inter-action is also observed. Overall, a three-dimensional network results.

Modeling of the spatial state of the ionosphere using regular definitions of the VTEC identifier at the network of continuously operating GNSS stations of Ukraine

NASA Astrophysics Data System (ADS)

Yankiv-Vitkovska, Liubov; Dzhuman, Bogdan

2017-04-01

Due to the wide application of global navigation satellite systems (GNSS), the development of the modern GNSS infrastructure moved the monitoring of the Earth's ionosphere to a new methodological and technological level. The peculiarity of such monitoring is that it allows conducting different experimental studies including the study of the ionosphere directly while using the existing networks of reference GNSS stations intended for solving other problems. The application of the modern GNSS infrastructure is another innovative step in the ionospheric studies as such networks allow to conduct measurements continuously over time in any place. This is used during the monitoring of the ionosphere and allows studying the global and regional phenomena in the ionosphere in real time. Application of a network of continuously operating reference stations to determine numerical characteristics of the Earth's ionosphere allows creating an effective technology to monitor the ionosphere regionally. This technology is intended to solve both scientific problems concerning the space weather, and practical tasks such as providing coordinates of the geodetic level accuracy. For continuously operating reference GNSS stations, the results of the determined ionization identifier TEC (Total Electron Content). On the one hand, this data reflects the state of the ionosphere during the observation; on the other hand, it is a substantial tool for accuracy improvement and reliable determination of coordinates of the observation place. Thus, it was decided to solve a problem of restoring the spatial position of the ionospheric state or its ionization field according to the regular definitions of the TEC identifier, i.e. VTEC (Vertical TEC). The description below shows one of the possible solutions that is based on the spherical cap harmonic analysis method for modeling VTEC parameter. This method involves transformation of the initial data to a spherical cap and construction of model using associated Legendre functions of integer order but not necessarily of integer degree. Such functions form two orthogonal systems of functions on the spherical cap. The method was tested for network of permanent stations ZAKPOS.

Gray and multigroup radiation transport models for two-dimensional binary stochastic media using effective opacities

DOE PAGES

Olson, Gordon L.

2015-09-24

One-dimensional models for the transport of radiation through binary stochastic media do not work in multi-dimensions. In addition, authors have attempted to modify or extend the 1D models to work in multidimensions without success. Analytic one-dimensional models are successful in 1D only when assuming greatly simplified physics. State of the art theories for stochastic media radiation transport do not address multi-dimensions and temperature-dependent physics coefficients. Here, the concept of effective opacities and effective heat capacities is found to well represent the ensemble averaged transport solutions in cases with gray or multigroup temperature-dependent opacities and constant or temperature-dependent heat capacities. Inmore » every case analyzed here, effective physics coefficients fit the transport solutions over a useful range of parameter space. The transport equation is solved with the spherical harmonics method with angle orders of n=1 and 5. Although the details depend on what order of solution is used, the general results are similar, independent of angular order.« less

Gray and multigroup radiation transport models for two-dimensional binary stochastic media using effective opacities

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

Olson, Gordon L.

One-dimensional models for the transport of radiation through binary stochastic media do not work in multi-dimensions. In addition, authors have attempted to modify or extend the 1D models to work in multidimensions without success. Analytic one-dimensional models are successful in 1D only when assuming greatly simplified physics. State of the art theories for stochastic media radiation transport do not address multi-dimensions and temperature-dependent physics coefficients. Here, the concept of effective opacities and effective heat capacities is found to well represent the ensemble averaged transport solutions in cases with gray or multigroup temperature-dependent opacities and constant or temperature-dependent heat capacities. Inmore » every case analyzed here, effective physics coefficients fit the transport solutions over a useful range of parameter space. The transport equation is solved with the spherical harmonics method with angle orders of n=1 and 5. Although the details depend on what order of solution is used, the general results are similar, independent of angular order.« less

Geometric interpretation of four-wave mixing

NASA Astrophysics Data System (ADS)

Ott, J. R.; Steffensen, H.; Rottwitt, K.; McKinstrie, C. J.

2013-10-01

The nonlinear phenomenon of four-wave mixing (FWM) is investigated using a method, where, without the need of calculus, both phase and amplitudes of the mixing fields are visualized simultaneously, giving a complete overview of the FWM dynamics. This is done by introducing a set of Stokes-like coordinates of the electric fields, which reduce the FWM dynamics to a closed two-dimensional surface, similar to the Bloch sphere of quantum electrodynamics or the Pointcaré sphere in polarization dynamics. The coordinates are chosen so as to use the gauge invariance symmetries of the FWM equations which also give the conservation of action flux known as the Manley-Rowe relations. This reduces the dynamics of FWM to the one-dimensional intersection between the closed two-dimensional surface and the phase-plane given by the conserved Hamiltonian. The analysis is advantageous for visualizing phase-dependent FWM phenomena which are found in a large variety of nonlinear systems and even in various optical communication schemes.

Analysis of the Effect of UTI-UTC to High Precision Orbit

NASA Astrophysics Data System (ADS)

Shin, Dongseok; Kwak, Sunghee; Kim, Tag-Gon

1999-12-01

As the spatial resolution of remote sensing satellites becomes higher, very accurate determination of the position of a LEO (Low Earth Orbit) satellite is demanding more than ever. Non-symmetric Earth gravity is the major perturbation force to LEO satellites. Since the orbit propagation is performed in the celestial frame while Earth gravity is defined in the terrestrial frame, it is required to convert the coordinates of the satellite from one to the other accurately. Unless the coordinate conversion between the two frames is performed accurately the orbit propagation calculates incorrect Earth gravitational force at a specific time instant, and hence, causes errors in orbit prediction. The coordinate conversion between the two frames involves precession, nutation, Earth rotation and polar motion. Among these factors, unpredictability and uncertainty of Earth rotation, called UTI-UTC, is the largest error source. In this paper, the effect of UTI-UTC on the accuracy of the LEO propagation is introduced, tested and analzed. Considering the maximum unpredictability of UTI-UTC, 0.9 seconds, the meaningful order of non-spherical Earth harmonic functions is derived.

Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media.

PubMed

Pan, De-Bei; Gao, Xiang; Feng, Xia; Pan, Jun-Ting; Zhang, Hong

2016-02-24

Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves.

A new Schwarzschild optical system for two-dimensional EUV imaging of MRX plasmas

NASA Astrophysics Data System (ADS)

Bolgert, P.; Bitter, M.; Efthimion, P.; Hill, K. W.; Ji, H.; Myers, C. E.; Yamada, M.; Yoo, J.; Zweben, S.

2013-10-01

This poster describes the design and construction of a new Schwarzschild optical system for two-dimensional EUV imaging of plasmas. This optical system consists of two concentric spherical mirrors with radii R1 and R2, and is designed to operate with certain angles of incidence θ1 and θ2. The special feature of this system resides in the fact that all the rays passing through the system are tangential to a third concentric circle; it assures that the condition for Bragg reflection is simultaneously fulfilled at each point on the two reflecting surfaces if the spherical mirrors are replaced by spherical multi-layer structures. A prototype of this imaging system will be implemented in the Magnetic Reconnection Experiment (MRX) at PPPL to obtain two-dimensional EUV images of the plasma in the energy range from 18 to 62 eV; the relative intensity of the emitted radiation in this energy range was determined from survey measurements with a photodiode. It is thought that the radiation at these energies is due to Bremsstrahlung and line emission caused by suprathermal electrons. This research is supported by DoE Contract Number DE-AC02-09CH11466 and by the Center for Magnetic Self-Organization (CMSO).

Conversion of the magnetic field measured in three components on the magnetic sensor body's random coordinate system into three components on geographical coordinate system through quaternion rotation.

NASA Astrophysics Data System (ADS)

LIM, M.; PARK, Y.; Jung, H.; SHIN, Y.; Rim, H.; PARK, C.

2017-12-01

To measure all components of a physical property, for example the magnetic field, is more useful than to measure its magnitude only in interpretation and application thereafter. To convert the physical property measured in 3 components on a random coordinate system, for example on moving magnetic sensor body's coordinate system, into 3 components on a fixed coordinate system, for example on geographical coordinate system, by the rotations of coordinate system around Euler angles for example, we should have the attitude values of the sensor body in time series, which could be acquired by an INS-GNSS system of which the axes are installed coincident with those of the sensor body. But if we want to install some magnetic sensors in array at sea floor but without attitude acquisition facility of the magnetic sensors and to monitor the variation of magnetic fields in time, we should have also some way to estimate the relation between the geographical coordinate system and each sensor body's coordinate system by comparison of the vectors only measured on both coordinate systems on the assumption that the directions of the measured magnetic field on both coordinate systems are the same. For that estimation, we have at least 3 ways. The first one is to calculate 3 Euler angles phi, theta, psi from the equation Vgeograph = Rx(phi) Ry(theta) Rz(psi) Vrandom, where Vgeograph is the vector on geographical coordinate system etc. and Rx(phi) is the rotation matrix around the x axis by the angle phi etc. The second one is to calculate the difference of inclination and declination between the 2 vectors on spherical coordinate system. The third one, used by us for this study, is to calculate the angle of rotation along a great circle around the rotation axis, and the direction of the rotation axis. We installed no. 1 and no. 2 FVM-400 fluxgate magnetometers in array near Cheongyang Geomagnetic Observatory (IAGA code CYG) and acquired time series of magnetic fields for CYG and for the two magnetometers. Once the angle of rotation and the direction of the rotation axis for each couple of CYG and no. 1 and of CYG and no. 2 estimated, we rotated the measured time series of vectors using quaternion rotation to get 3 time series of magnetic fields all on geographical coordinate system, which were used for tracing the moving magnetic bodies along time in that area.

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong

2014-02-01

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. Copyright © 2013 Elsevier B.V. All rights reserved.

How wet should be the reaction coordinate for ligand unbinding?

PubMed

Tiwary, Pratyush; Berne, B J

2016-08-07

We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)], to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Using SGOOP with under-sampled biased simulations, we predict that water plays a distinct role in the reaction coordinate for unbinding in the case when the ligand is sterically constrained to move along an axis of symmetry. This prediction is validated through extensive calculations of the unbinding times through metadynamics and by comparison through detailed balance with unbiased molecular dynamics estimate of the binding time. However when the steric constraint is removed, we find that the role of water in the reaction coordinate diminishes. Here instead SGOOP identifies a good one-dimensional RC involving various motional degrees of freedom.

How wet should be the reaction coordinate for ligand unbinding?

NASA Astrophysics Data System (ADS)

Tiwary, Pratyush; Berne, B. J.

2016-08-01

We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)], to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Using SGOOP with under-sampled biased simulations, we predict that water plays a distinct role in the reaction coordinate for unbinding in the case when the ligand is sterically constrained to move along an axis of symmetry. This prediction is validated through extensive calculations of the unbinding times through metadynamics and by comparison through detailed balance with unbiased molecular dynamics estimate of the binding time. However when the steric constraint is removed, we find that the role of water in the reaction coordinate diminishes. Here instead SGOOP identifies a good one-dimensional RC involving various motional degrees of freedom.

How wet should be the reaction coordinate for ligand unbinding?

PubMed Central

Tiwary, Pratyush; Berne, B. J.

2016-01-01

We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)], to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Using SGOOP with under-sampled biased simulations, we predict that water plays a distinct role in the reaction coordinate for unbinding in the case when the ligand is sterically constrained to move along an axis of symmetry. This prediction is validated through extensive calculations of the unbinding times through metadynamics and by comparison through detailed balance with unbiased molecular dynamics estimate of the binding time. However when the steric constraint is removed, we find that the role of water in the reaction coordinate diminishes. Here instead SGOOP identifies a good one-dimensional RC involving various motional degrees of freedom. PMID:27497545

Effect of acoustic coupling on power-law flame acceleration in spherical confinement

NASA Astrophysics Data System (ADS)

Akkerman, V'yacheslav; Law, Chung K.

2013-01-01

A model describing acoustically-generated parametric instability in a spherical chamber is developed for quasi-one-dimensional, low-Mach number flames. We demonstrate how sound waves generated by a centrally-ignited, outwardly-propagating accelerating flamefront can be incorporated into an existing theory of self-similar flame acceleration in free space [V. Akkerman, C. K. Law, and V. Bychkov, "Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering," Phys. Rev. E 83, 026305 (2011)], 10.1103/PhysRevE.83.026305. Being reflected from the chamber wall, flame-generated acoustics interact with the flamefront and the attendant hydrodynamic flamefront cellular instability. This in turn affects the subsequent flame morphology and propagation speed. It is shown that the acoustics modify the power-law flame acceleration, concomitantly facilitating or inhibiting the transition to detonation in confinement, which allows reconciliation of a discrepancy in experimental measurements of different groups.

Poly[tetra­aqua­(μ6-9,10-dioxo-9,10-dihydro­anthracene-1,4,5,8-tetra­carboxyl­ato)dimanganese(II)

PubMed Central

Xu, Rui; Liu, Jian-Lan

2012-01-01

The title complex, [Mn2(C18H4O10)(H2O)4]n, was synthesized from manganese(II) chloride tetra­hydrate and 9,10-dioxo-9,10-dihydro­anthracene-1,4,5,8-tetra­carb­oxy­lic acid (H4AQTC) in water. The anthraquinone unit is located about a crystallographic center of inversion. Each asymmetric unit therefore contains one MnII atom, two water ligands and one half AQTC4− anion. The MnII atom is coordinated in a distorted octa­hedral geometry by four O atoms from three AQTC4− ligands and two water O atoms. Two of the carboxyl­ate groups coordinate one MnII atom in a chelating mode, whereas the others each coordinate two MnII atoms. Each AQTC4− tetra-anion therefore coordinates six different MnII ions and, as a result, a three-dimensional coordination polymer is formed. O—H⋯O hydrogen bonds, some of them bifurcated, between water ligands and neighboring water or anthraquinone ligands are observed in the crystal structure. PMID:22807779

Sound Source Localization Using Non-Conformal Surface Sound Field Transformation Based on Spherical Harmonic Wave Decomposition

PubMed Central

Zhang, Lanyue; Ding, Dandan; Yang, Desen; Wang, Jia; Shi, Jie

2017-01-01

Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on generalized Fourier transform. When the sound source is on the cylindrical surface, it is difficult to locate by using spherical surface conformal transform. The non-conformal sound field transformation by making a transfer matrix based on spherical harmonic wave decomposition is proposed in this paper, which can achieve the transformation of a spherical surface into a cylindrical surface by using spherical array data. The theoretical expressions of the proposed method are deduced, and the performance of the method is simulated. Moreover, the experiment of sound source localization by using a spherical array with randomly and uniformly distributed elements is carried out. Results show that the non-conformal surface sound field transformation from a spherical surface to a cylindrical surface is realized by using the proposed method. The localization deviation is around 0.01 m, and the resolution is around 0.3 m. The application of the spherical array is extended, and the localization ability of the spherical array is improved. PMID:28489065

Trading spaces: building three-dimensional nets from two-dimensional tilings

PubMed Central

Castle, Toen; Evans, Myfanwy E.; Hyde, Stephen T.; Ramsden, Stuart; Robins, Vanessa

2012-01-01

We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic (S2), Euclidean (E2) and hyperbolic (H2) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions. PMID:24098839

Studies of Flame Structure in Microgravity

NASA Technical Reports Server (NTRS)

Law, C. K.; Sung, C. J.; Zhu, D. L.

1997-01-01

The present research endeavor is concerned with gaining fundamental understanding of the configuration, structure, and dynamics of laminar premixed and diffusion flames under conditions of negligible effects of gravity. Of particular interest is the potential to establish and hence study the properties of spherically- and cylindrically-symmetric flames and their response to external forces not related to gravity. For example, in an earlier experimental study of the burner-stabilized cylindrical premixed flames, the possibility of flame stabilization through flow divergence was established, while the resulting one-dimensional, adiabatic, stretchless flame also allowed an accurate means of determining the laminar flame speeds of combustible mixtures. We have recently extended our studies of the flame structure in microgravity along the following directions: (1) Analysis of the dynamics of spherical premixed flames; (2) Analysis of the spreading of cylindrical diffusion flames; (3) Experimental observation of an interesting dual luminous zone structure of a steady-state, microbuoyancy, spherical diffusion flame of air burning in a hydrogen/methane mixture environment, and its subsequent quantification through computational simulation with detailed chemistry and transport; (4) Experimental quantification of the unsteady growth of a spherical diffusion flame; and (5) Computational simulation of stretched, diffusionally-imbalanced premixed flames near and beyond the conventional limits of flammability, and the substantiation of the concept of extended limits of flammability. Motivation and results of these investigations are individually discussed.

Nada: A new code for studying self-gravitating tori around black holes

NASA Astrophysics Data System (ADS)

Montero, Pedro J.; Font, José A.; Shibata, Masaru

2008-09-01

We present a new two-dimensional numerical code called Nada designed to solve the full Einstein equations coupled to the general relativistic hydrodynamics equations. The code is mainly intended for studies of self-gravitating accretion disks (or tori) around black holes, although it is also suitable for regular spacetimes. Concerning technical aspects the Einstein equations are formulated and solved in the code using a formulation of the standard 3+1 Arnowitt-Deser-Misner canonical formalism system, the so-called Baumgarte-Shapiro Shibata-Nakamura approach. A key feature of the code is that derivative terms in the spacetime evolution equations are computed using a fourth-order centered finite difference approximation in conjunction with the Cartoon method to impose the axisymmetry condition under Cartesian coordinates (the choice in Nada), and the puncture/moving puncture approach to carry out black hole evolutions. Correspondingly, the general relativistic hydrodynamics equations are written in flux-conservative form and solved with high-resolution, shock-capturing schemes. We perform and discuss a number of tests to assess the accuracy and expected convergence of the code, namely, (single) black hole evolutions, shock tubes, and evolutions of both spherical and rotating relativistic stars in equilibrium, the gravitational collapse of a spherical relativistic star leading to the formation of a black hole. In addition, paving the way for specific applications of the code, we also present results from fully general relativistic numerical simulations of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium.

Honeycomb-shaped coordination polymers based on the self-assembly of long flexible ligands and alkaline-earth ions

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

Lian, Chen; Liu, Liu; Guo, Xu

2016-01-15

Two novel coordination polymers, namely, [Ca(NCP){sub 2}]{sub ∞} (I) and [Sr(NCP){sub 2}]{sub ∞} (II) were synthesized under hydrothermal conditions based on 2-(4-carboxyphenyl)imidazo(4,5-f)-(1,10)phenanthroline (HNCP) and characterized by elemental analysis, infrared spectrometry, X-ray powder diffraction and single crystal X-ray diffraction. Findings indicate that I and II are isomorphous and isostructural, containing the unit of M(NCP{sup −}){sub 4} (M=Ca(II) and Sr(II)), based on which to assemble into three-dimensional (3D) porous 4-fold interpenetration honeycomb-shaped neutral coordination polymers (CPs). Between the adjacent lamellar structures in I and II, there exist π–π interactions between the pyridine rings belonging to phenanthroline of NCP{sup −} which stabilize themore » frameworks. Both I and II display stronger fluorescence emissions as well as high thermal stability. - Graphical abstract: One-dimensional nanotubular channels with the cross dimension of 37.1959(20)×23.6141(11)Å{sup 2} in the three-dimensional honeycomb-shaped coordination network of II are observed. The topological analysis of II indicates that there exists a typical diamond framework possessing large adamantanoid cages, which containing four cyclohexane-shaped patterns in chair conformations. - Highlights: • Two isomorphous and isostructural coordination polymers based on flexible ligand and two alkaline-earth metal salts have been synthesized and characterized. • Structural analysis indicates that I and II are assembled into 3D porous honeycomb-shaped metal-organic frameworks. • Both I and II display stronger fluorescence emissions and higher thermal stability.« less

Syntheses, structures and properties of four Cd(II) coordination polymers induced by the pH regulator

NASA Astrophysics Data System (ADS)

Xu, Yun; Ding, Fang; Liu, Dong; Yang, Pei-Pei; Zhu, Li-Li

2018-03-01

Four new coordination polymers [Cd2(CHDC)2(APYZ)(H2O)2](H2O) (1), [Cd(HCHDC)2(APYZ) (H2O)] (2), [Cd2(CHDC)2(PYZ)(H2O)2](H2O) (3), and [Cd(HCHDC)2(PYZ)(H2O)] (4) (H2CHDC = 1,4-cyclohexanedicarboxylic acid, APYZ = 2-aminopyrazine, PYZ = pyrazine) have been synthesized under the hydrothermal conditions by changing the pH regulator and the N-containing ligands. The pH regulator impacted on the degree of deprotonation of the 1,4-cyclohexanedicarboxylic acid ligand and resulted in the formation of the two pairs of different networks. Polymers 1 and 3 crystallize in monoclinic, space group P21/c, exhibit two dimensional 63 net, which further formed three-dimensional supramolecular structure by the Csbnd H⋯O hydrogen bond interactions. While polymers 2 and 4 possess one dimensional chain structures and further link into two dimensional layered supramolecular structures by intermolecular hydrogen bonding interactions. From all three conformers of H2CHDC, e,a-cis is consistently present in the Cd coordination polymers. Furthermore, photoluminescence properties of four polymers are also investigated, the luminescent intensity of polymer 1 (or 2) with amino group in pyrazine is dramatically stronger than that of the similar structure of polymer 3 (or 4) without amino group in pyrazine, the results shown that the presence of the amino group from 2-aminopyrazine play a key role in increasing the luminescence properties.

Computer simulation of plasma and N-body problems

NASA Technical Reports Server (NTRS)

Harries, W. L.; Miller, J. B.

1975-01-01

The following FORTRAN language computer codes are presented: (1) efficient two- and three-dimensional central force potential solvers; (2) a three-dimensional simulator of an isolated galaxy which incorporates the potential solver; (3) a two-dimensional particle-in-cell simulator of the Jeans instability in an infinite self-gravitating compressible gas; and (4) a two-dimensional particle-in-cell simulator of a rotating self-gravitating compressible gaseous system of which rectangular coordinate and superior polar coordinate versions were written.

Methodology for evaluate the form deviations for formula one nose car

NASA Astrophysics Data System (ADS)

Bere, Paul; Neamtu, Calin

2014-06-01

The paper presents a measuring strategy for a Formula One car using a Coordinate Measuring Machine (CMM) and a 3D laser scanning devices. The measurement procedures outlined the dimensional deviation of the CAD model and prototype made of composite material. The authors present two methods for the determination of symmetry for components of a Formula One car based on measuring and 3D scanning.

The Electrochemical Behavior of Dispersions of Spherical Ultramicroelectrodes.

DTIC Science & Technology

1986-07-30

means of bipolar electrolyses with dispersions. Polarization equations are predicted for highly simplified models based on the concept of the mixture...three-dimensional electrodes. Bipolar electrolyses on dispersions of spherical particles have been proposed and the behavior of such electrodes in the...photodecomposition of water (e.g. see (32-41)). It should be noted that the size range of the particles which will be most frequently used in dispersion

Novel bimetallic thiocyanate-bridged Cu(II)-Hg(II) compounds-synthesis, X-Ray studies and magnetic properties

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

Machura, B., E-mail: basia@ich.us.edu.pl; Switlicka, A.; Zwolinski, P.

2013-01-15

Seven novel heterobimetallic Cu/Hg polymers based on thiocyanate bridges have been synthesised and characterised by means of IR, EPR, magnetic measurements and single crystal X-Ray. Three of them, [Cu(pzH){sub 4}Hg(SCN){sub 4}]{sub n} (1) [Cu(indH){sub 4}Hg(SCN){sub 4}]{sub n} (2) and [Cu(ampy){sub 2}Hg(SCN){sub 4}]{sub n} (3), have one-dimensional coordination structure. Two compounds [Cu(pzH){sub 2}Hg(SCN){sub 4}]{sub n} (4) and [Cu(abzimH)Hg(SCN){sub 4}]{sub n} (5) form two-dimensional nets, whereas the complexes [Cu(pyCN){sub 2}Hg(SCN){sub 4}]{sub n} (6) and [Cu(pyCH(OH)(OMe)){sub 2}Hg(SCN){sub 4}]{sub n} (7) are three-dimensional coordination polymers. The chains of 1 are connected by the intermolecular N-H Bullet Bullet Bullet N hydrogen bonds to the threemore » dimensional net. In 2 the N-H Bullet Bullet Bullet S hydrogen bonds link the polymeric chains to the two dimensional layer extending along crystallographic (0 0 1) plane. The polymeric chains of compound 3 are joined by the intermolecular N-H Bullet Bullet Bullet N and N-H Bullet Bullet Bullet S hydrogen bonds to the three dimensional net. The polymeric layers of 4 are connected by the intermolecular N-H Bullet Bullet Bullet N hydrogen bonds to the three dimensional net. - Graphical abstract: Novel bimetallic thiocyanate-bridged Cu(II)-Hg(II) compound-synthesis,X-Ray studies and magnetic properties. Highlights: Black-Right-Pointing-Pointer Novel heterobimetallic Cu/Hg coordination polymers were synthesised. Black-Right-Pointing-Pointer The multidimensional structures have been proved by single X-ray analysIs. Black-Right-Pointing-Pointer A variation in the crystalline architectures was observed depending on auxiliary ligands. Black-Right-Pointing-Pointer Magnetic measurements indicate weak exchange interaction between Cu(II) in the crystal lattices below 10 K.« less

Speed and pressure recording in three-dimensional flow

NASA Technical Reports Server (NTRS)

Krisam, F

1932-01-01

Van der Megge Zijnen's spherical Pitot tube with its 5 test holes insures a simultaneous record of static pressure and magnitude and direction of velocity in three-dimensional flow. The report treats the method as well as the range of application of this Pitot in the light of modern knowledge on flow around spheres.

Reply to Comment on ‘The motion of an arbitrarily rotating spherical projectile and its application to ball games’

NASA Astrophysics Data System (ADS)

Robinson, Garry; Robinson, Ian

2014-06-01

Jensen (2014 Phys. Scr. 89 067001) presents arguments that the expressions that we have used in our recent paper (Robinson and Robinson 2013 Phys. Scr. 88 018101) for the lift force and possibly the drag force acting on a rotating spherical projectile are dimensionally incorrect and therefore cannot be valid. We acknowledge that the alternative equations suggested by Jensen are dimensionally correct, and may well be borne out by future experimental results. However, we demonstrate that our equations are in fact also dimensionally correct, the key concept being that of having the appropriate dimensions for the multiplying constants, an extensively used practice with experimentally determined laws. After a detailed discussion of the situation, a simple illustrative example of Hooke's law for the restoring force, F, due to a mass attached to a spring displaced by a distance x from its equilibrium position is presented, where the spring constant, k, has such units as to render the equation dimensionally correct. Finally we discuss the implications of some relevant existing experimental results for the lift force.

Painleve-gullstrand-type Coordinates for the Five-dimensional Myers-Perry Black Hole

NASA Technical Reports Server (NTRS)

Finch, Tehani Kahi

2013-01-01

The Painleve-Gullstrand coordinates provide a convenient framework for presenting the Schwarzschild geometry because of their flat constant-time hypersurfaces, and the fact that they are free of coordinate singularities outside r=0. Generalizations of Painlev´e-Gullstrand coordinates suitable for the Kerr geometry have been presented by Doran and Nat´ario. These coordinate systems feature a time coordinate identical to the proper time of zero-angular-momentum observers that are dropped from infinity. Here, the methods of Doran and Nat´ario are extended to the five-dimensional rotating black hole found by Myers and Perry. The result is a new formulation of the Myers-Perry metric. The properties and physical significance of these new coordinates are discussed.

Statistical validation of brain tumor shape approximation via spherical harmonics for image-guided neurosurgery.

PubMed

Goldberg-Zimring, Daniel; Talos, Ion-Florin; Bhagwat, Jui G; Haker, Steven J; Black, Peter M; Zou, Kelly H

2005-04-01

Surgical planning now routinely uses both two-dimensional (2D) and three-dimensional (3D) models that integrate data from multiple imaging modalities, each highlighting one or more aspects of morphology or function. We performed a preliminary evaluation of the use of spherical harmonics (SH) in approximating the 3D shape and estimating the volume of brain tumors of varying characteristics. Magnetic resonance (MR) images from five patients with brain tumors were selected randomly from our MR-guided neurosurgical practice. Standardized mean square reconstruction errors (SMSRE) by tumor volume were measured. Validation metrics for comparing performances of the SH method against segmented contours (SC) were the dice similarity coefficient (DSC) and standardized Euclidean distance (SED) measure. Tumor volume range was 22,413-85,189 mm3, and range of number of vertices in triangulated models was 3674-6544. At SH approximations with degree of at least 30, SMSRE were within 1.66 x 10(-5) mm(-1). Summary measures yielded a DSC range of 0.89-0.99 (pooled median, 0.97 and significantly >0.7; P < .001) and an SED range of 0.0002-0.0028 (pooled median, 0.0005). 3D shapes of tumors may be approximated by using SH for neurosurgical applications.

Two-fluid and magnetohydrodynamic modelling of magnetic reconnection in the MAST spherical tokamak and the solar corona

NASA Astrophysics Data System (ADS)

Browning, P. K.; Cardnell, S.; Evans, M.; Arese Lucini, F.; Lukin, V. S.; McClements, K. G.; Stanier, A.

2016-01-01

Twisted magnetic flux ropes are ubiquitous in laboratory and astrophysical plasmas, and the merging of such flux ropes through magnetic reconnection is an important mechanism for restructuring magnetic fields and releasing free magnetic energy. The merging-compression scenario is one possible start-up scheme for spherical tokamaks, which has been used on the Mega Amp Spherical Tokamak (MAST). Two current-carrying plasma rings or flux ropes approach each due to mutual attraction, forming a current sheet and subsequently merge through magnetic reconnection into a single plasma torus, with substantial plasma heating. Two-dimensional resistive and Hall-magnetohydrodynamic simulations of this process are reported, including a strong guide field. A model of the merging based on helicity-conserving relaxation to a minimum energy state is also presented, extending previous work to tight-aspect-ratio toroidal geometry. This model leads to a prediction of the final state of the merging, in good agreement with simulations and experiment, as well as the average temperature rise. A relaxation model of reconnection between two or more flux ropes in the solar corona is also described, allowing for different senses of twist, and the implications for heating of the solar corona are discussed.

A Numerical Gamma-Ray Burst Simulation Using Three-Dimensional Relativistic Hydrodynamics: The Transition from Spherical to Jet-like Expansion

NASA Technical Reports Server (NTRS)

Cannizzo, John K.; Gehrels, Neil; Vishniac, Ethan T.

2003-01-01

Utilizing 3D relativistic hydrodynamical calculations, we have examined the evolution of an expanding relativistic blob of gas intended to be representative of a jet associated with ejecta from an extremely energetic event such as a hypernova, that produces a gamma-ray burst (Aloy et al. 2000; Tan, Matzner, & McKee 2001; MacFadyen, Woosley, & Heger 2001, Zhang, Woosley, & Heger 2003, Zhang, Woosley, & MacFadyen 2003). Since these are the first such calculations applied to the blob during the time in which the afterglow radiation is produced, we have purposely kept them simple in an effort to concentrate on the most fundamental aspects of the physics. We restrict our attention to the transition from spherical to jetlike expansion that occurs during the time that the Lorentz factor becomes less than the reciprocal of the jet spreading angle. We have not yet attached specific numbers to our results. From the SRHD equations, one sees that the relevant quantities are the ratios of pressure to density, and of distance to time. If we specify either one of these two sets of numbers, the other one is also determined.

An Alternative Lunar Ephemeris Model for On-Board Flight Software Use

NASA Technical Reports Server (NTRS)

Simpson, David G.

1998-01-01

In calculating the position vector of the Moon in on-board flight software, one often begins by using a series expansion to calculate the ecliptic latitude and longitude of the Moon, referred to the mean ecliptic and equinox of date. One then performs a reduction for precession, followed by a rotation of the position vector from the ecliptic plane to the equator, and a transformation from spherical to Cartesian coordinates before finally arriving at the desired result: equatorial J2000 Cartesian components of the lunar position vector. An alternative method is developed here in which the equatorial J2000 Cartesian components of the lunar position vector are calculated directly by a series expansion, saving valuable on-board computer resources.

A Method for Computing Three-Dimensional Viscous Flows over an Ogival Body at Angle of Attack

DTIC Science & Technology

1976-02-01

the ogival body problems; however, some gen- erality is still maintained by considering coordinate systems that are generated from any two ...transformation. We shall assume that the covariant derivative is the natural one derivable from the metric. This is known as the Levi - Civita connection (Ref...MV..»^^.^ R76-91202^-8 I A Method for Computing Three-Dimensional Viscoua Flows Over an Ogival Body at Angle of Attack TABLE OF CONTENTS

Extended Applicability of the Spherical-Harmonic and Point-Mass Modeling of the Gravity Field,

DTIC Science & Technology

1980-02-01

the metric in spherical coordinates {X,F, rl reads ds2 = r2cos 2j dX2 + r 2d 2 + dr2 yielding the metric tensor and the associated metric tensor: {grs...leading to (3.52) would have required considerably more space if the tensor approach to this problem had been avoided, whether for pedagogical or other...useful, especially from the pedagogical point of view, since it addresses itself to large audiences and exposes the treated subject in great depth. On

Crystal structure of poly[di­aqua­bis­(μ5-benzene-1,3-di­carboxyl­ato)(N,N-di­methyl­formamide)­cadmium(II)disodium(I)

PubMed Central

Sangsawang, Matimon; Chainok, Kittipong; Wannarit, Nanthawat

2017-01-01

The title compound, [CdNa2(C8H4O4)2(C3H7NO)(H2O)2]n or [CdNa2(1,3-bdc)2(DMF)(H2O)2]n, is a new CdII–NaI heterobimetallic coordination polymer. The asymmetric unit consists of one CdII atom, two NaI atoms, two 1,3-bdc ligands, two coordinated water mol­ecules and one coordinated DMF mol­ecule. The CdII atom exhibits a seven-coordinate geometry, while the NaI atoms can be considered to be penta­coordinate. The metal ions and their symmetry-related equivalents are connected via chelating–bridging carboxyl­ate groups of the 1,3-bdc ligands to generate a three-dimensional framework. In the crystal, there are classical O—H⋯O hydrogen bonds involving the coordinated water mol­ecules and the 1,3-bdc carboxyl­ate groups and π–π stacking between the benzene rings of the 1,3-bdc ligands present within the frameworks. PMID:29152332

Three-dimensional finite element modelling of muscle forces during mastication.

PubMed

Röhrle, Oliver; Pullan, Andrew J

2007-01-01

This paper presents a three-dimensional finite element model of human mastication. Specifically, an anatomically realistic model of the masseter muscles and associated bones is used to investigate the dynamics of chewing. A motion capture system is used to track the jaw motion of a subject chewing standard foods. The three-dimensional nonlinear deformation of the masseter muscles are calculated via the finite element method, using the jaw motion data as boundary conditions. Motion-driven muscle activation patterns and a transversely isotropic material law, defined in a muscle-fibre coordinate system, are used in the calculations. Time-force relationships are presented and analysed with respect to different tasks during mastication, e.g. opening, closing, and biting, and are also compared to a more traditional one-dimensional model. The results strongly suggest that, due to the complex arrangement of muscle force directions, modelling skeletal muscles as conventional one-dimensional lines of action might introduce a significant source of error.

Trisodium citrate, Na 3 (C 6 H 5 O 7 )

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

Rammohan, Alagappa; Kaduk, James A.

2016-05-10

The crystal structure of anhydrous trisodium citrate, Na 3(C 6H 5O 7), has been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional theory (DFT). There are two independent five-coordinate Na +and one six-coordinate Na +cations in the asymmetric unit. The [NaO 5] and [NaO 6] polyhedra share edges and corners to form a three-dimensional framework. There are channels parallel to theaandbaxes in which the remainder of the citrate anions reside. The only hydrogen bonds are an intramolecular one between the hydroxy group and one of the terminal carboxylate O atoms and an intermolecular onemore » between a methylene group and the hydroxyl O atom.« less

Poly[diaqua­tris­(μ4-1,3-phenyl­enediacetato)­dineodymium(III)

PubMed Central

Gao, Zhu-Qing; Lv, Dong-Yu; Li, Hong-Ji; Gu, Jin-Zhong

2011-01-01

In the title coordination polymer, [Nd2(C10H8O4)3(H2O)2]n, each of the two NdIII ions is nine-coordinated by eight O atoms from six different 2,2′-(m-phenyl­ene)diacetate (pda) bivalent anions and by one O atom from a water mol­ecule, forming a distorted tricapped trigonal–prismatic coordination geometry. Eight NdIII ions and 12 pda ligands form a large [Nd8(pda)12] ring, and four NdIII ions and six pda ligands form a small [Nd4(pda)6] ring. These rings are further connected by the coordination inter­actions of pda ligands and NdIII, generating a three-dimensional supra­molecular framework. PMID:21522305

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

NASA Astrophysics Data System (ADS)

Troisi, Antonio

2017-03-01

Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f( R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R)=f_0R^n the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions.

A Microfluidic Route to Breaking Chiral Symmetry: Theory and Experiment

NASA Astrophysics Data System (ADS)

Ocko, Samuel; Adams, Laura

A robust route for the biased production of single handed chiral structures has been found in generating non-spherical, multi-component double emulsions using glass microfluidic devices. The specific type of handedness is determined by the final packing geometry of four different inner drops inside an ultra-thin sheath of oil. Before the three dimensional chiral structures are formed, the quasi-one dimensional chain of four inner drops re-arranges in two dimensions into either checkerboard or stripe patterns. We derive an analytical model predicting which pattern is more likely and assembles in the least amount of time. Moreover, our model accurately predicts our experimental results and is based on local bending dynamics, rather than global surface energy minimization. We gratefully acknowledge Professors D. Weitz and L. Mahadevan's support.

The forward modelling and analysis of magnetic field on the East Asia area using tesseroids

NASA Astrophysics Data System (ADS)

Chen, Z.; Meng, X.; Xu, G.

2017-12-01

As the progress of airborne and satellite magnetic survey, high-resolution magnetic data could be measured at different scale. In order to test and improve the accuracy of the existing crustal model, the forward modeling method is usually used to simulate the magnetic field of the lithosphere. Traditional models to forward modelling the magnetic field are based on the Cartesian coordinate system, and are always used to calculate the magnetic field of the local and small area. However, the Cartesian coordinate system is not an ideal choice for calculating the magnetic field of the global or continental area at the height of the satellite and Earth's curvature cannot be ignored in this situation. The spherical element (called tesseroids) can be used as a model element in the spherical coordinate system to solve this problem. On the basis of studying the principle of this forward method, we focus the selection of data source and the mechanism of adaptive integration. Then we calculate the magnetic anomaly data of East Asia area based on the model Crust1.0. The results presented the crustal susceptibility distribution, which was well consistent with the basic tectonic features in the study area.

Simple Analytic Expressions for the Magnetic Field of a Circular Current Loop

NASA Technical Reports Server (NTRS)

Simpson, James C.; Lane, John E.; Immer, Christopher D.; Youngquist, Robert C.

2001-01-01

Analytic expressions for the magnetic induction (magnetic flux density, B) of a simple planar circular current loop have been published in Cartesian and cylindrical coordinates [1,2], and are also known implicitly in spherical coordinates [3]. In this paper, we present explicit analytic expressions for B and its spatial derivatives in Cartesian, cylindrical, and spherical coordinates for a filamentary current loop. These results were obtained with extensive use of Mathematica "TM" and are exact throughout all space outside of the conductor. The field expressions reduce to the well-known limiting cases and satisfy V · B = 0 and V x B = 0 outside the conductor. These results are general and applicable to any model using filamentary circular current loops. Solenoids of arbitrary size may be easily modeled by approximating the total magnetic induction as the sum of those for the individual loops. The inclusion of the spatial derivatives expands their utility to magnetohydrodynamics where the derivatives are required. The equations can be coded into any high-level programming language. It is necessary to numerically evaluate complete elliptic integrals of the first and second kind, but this capability is now available with most programming packages.

Black hole perturbation under a 2 +2 decomposition in the action

NASA Astrophysics Data System (ADS)

Ripley, Justin L.; Yagi, Kent

2018-01-01

Black hole perturbation theory is useful for studying the stability of black holes and calculating ringdown gravitational waves after the collision of two black holes. Most previous calculations were carried out at the level of the field equations instead of the action. In this work, we compute the Einstein-Hilbert action to quadratic order in linear metric perturbations about a spherically symmetric vacuum background in Regge-Wheeler gauge. Using a 2 +2 splitting of spacetime, we expand the metric perturbations into a sum over scalar, vector, and tensor spherical harmonics, and dimensionally reduce the action to two dimensions by integrating over the two sphere. We find that the axial perturbation degree of freedom is described by a two-dimensional massive vector action, and that the polar perturbation degree of freedom is described by a two-dimensional dilaton massive gravity action. Varying the dimensionally reduced actions, we rederive covariant and gauge-invariant master equations for the axial and polar degrees of freedom. Thus, the two-dimensional massive vector and massive gravity actions we derive by dimensionally reducing the perturbed Einstein-Hilbert action describe the dynamics of a well-studied physical system: the metric perturbations of a static black hole. The 2 +2 formalism we present can be generalized to m +n -dimensional spacetime splittings, which may be useful in more generic situations, such as expanding metric perturbations in higher dimensional gravity. We provide a self-contained presentation of m +n formalism for vacuum spacetime splittings.

Two novel zinc(II) coordination polymers constructed from in situ amidation ligands

NASA Astrophysics Data System (ADS)

Yu, Xiao-Yang; Fu, Yao; Fu, Jian-Tao; Xu, Jia-Ning; Luo, Ya-Nan; Yang, Yan-Yan; Qu, Xiao-Shu; Zhang, Jing; Lu, Shu-Lai

2018-04-01

Two novel coordination compounds, [Zn(Hbimh) (H2O)]·H2O (1) and [Zn(Hbimh)]·(4,4ʹ-bpy)0.5 (2) (H3bimh = benzimidazole-5,6-hydrazide, 4,4ʹ-bpy = 4,4ʹ-bipyridine), have been prepared from the hydrothermal in situ amidation cyclization reactions of H3bimdc (H3bimdc = benzimidazole-5,6-dicarboxylic acid) and hydrazine hydrate (N2H4·H2O). Compound 1 exhibits a one-dimensional (1D) hexagon channel structure. Compound 2 is a three-dimensional (3D) framework structure, with 4,4ʹ-bpy fill the channels. We also obtained the ligand H3bimh. The compounds were characterized by IR, PXRD, TGA and elemental analysis. The fluorescence properties in the solid state at room temperature were also investigated.

Deadlock-free class routes for collective communications embedded in a multi-dimensional torus network

DOEpatents

Chen, Dong; Eisley, Noel A.; Steinmacher-Burow, Burkhard; Heidelberger, Philip

2013-01-29

A computer implemented method and a system for routing data packets in a multi-dimensional computer network. The method comprises routing a data packet among nodes along one dimension towards a root node, each node having input and output communication links, said root node not having any outgoing uplinks, and determining at each node if the data packet has reached a predefined coordinate for the dimension or an edge of the subrectangle for the dimension, and if the data packet has reached the predefined coordinate for the dimension or the edge of the subrectangle for the dimension, determining if the data packet has reached the root node, and if the data packet has not reached the root node, routing the data packet among nodes along another dimension towards the root node.

Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface

NASA Astrophysics Data System (ADS)

Wang, Yimin; Braams, Bastiaan J.; Bowman, Joel M.; Carter, Stuart; Tew, David P.

2008-06-01

Quantum calculations of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcal/mol, in excellent agreement with the reported ab initio value. Model one-dimensional and ``exact'' full-dimensional calculations of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calculated using the unbiased ``fixed-node'' diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm-1 in Cartesian coordinates and 22.6 cm-1 in normal coordinates, with an uncertainty of 2-3 cm-1. This splitting is also calculated based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calculation gives a tunneling splitting of 21-22 cm-1. The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm-1. These calculated tunneling splittings agree with each other to within less than the standard uncertainties obtained with the DMC method used, which are between 2 and 3 cm-1, and agree well with the experimental values of 21.6 and 2.9 cm-1 for the H and D transfer, respectively.

Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface.

PubMed

Wang, Yimin; Braams, Bastiaan J; Bowman, Joel M; Carter, Stuart; Tew, David P

2008-06-14

Quantum calculations of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcalmol, in excellent agreement with the reported ab initio value. Model one-dimensional and "exact" full-dimensional calculations of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calculated using the unbiased "fixed-node" diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm(-1) in Cartesian coordinates and 22.6 cm(-1) in normal coordinates, with an uncertainty of 2-3 cm(-1). This splitting is also calculated based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calculation gives a tunneling splitting of 21-22 cm(-1). The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm(-1). These calculated tunneling splittings agree with each other to within less than the standard uncertainties obtained with the DMC method used, which are between 2 and 3 cm(-1), and agree well with the experimental values of 21.6 and 2.9 cm(-1) for the H and D transfer, respectively.

On numerical solution of the Schrödinger equation: the shooting method revisited

NASA Astrophysics Data System (ADS)

Indjin, D.; Todorović, G.; Milanović, V.; Ikonić, Z.

1995-09-01

An alternative formulation of the "shooting" method for a numerical solution of the Schrödinger equation is described for cases of general asymmetric one-dimensional potential (planar geometry), and spherically symmetric potential. The method relies on matching the asymptotic wavefunctions and the potential core region wavefunctions, in course of finding bound states energies. It is demonstrated in the examples of Morse and Kratzer potentials, where a high accuracy of the calculated eigenvalues is found, together with a considerable saving of the computation time.

Guidance of microswimmers by wall and flow: Thigmotaxis and rheotaxis of unsteady squirmers in two and three dimensions

NASA Astrophysics Data System (ADS)

Ishimoto, Kenta

2017-10-01

The motions of an unsteady circular-disk squirmer and a spherical squirmer have been investigated in the presence of a no-slip infinite wall and a background shear flow in order to clarify the similarities and differences between two- and three-dimensional motions. Despite the similar bifurcation structure of the dynamical system, the stability of the fixed points differs due to the Hamiltonian structure of the disk squirmer. Once the unsteady oscillating surface velocity profile is considered, the disk squirmer can behave in a chaotic manner and cease to be confined in a near-wall region. In contrast, in an unsteady spherical squirmer, the dynamics is well attracted by a stable fixed point. Additional wall contact interactions lead to stable fixed points for the disk squirmer, and, in turn, the surface entrapment of the disk squirmer can be stabilized, regardless of the existence of the background flow. Finally, we consider spherical motion under a background flow. The separated time scales of the surface entrapment (thigmotaxis) and the turning toward the flow direction (rheotaxis) enable us to reduce the dynamics to two-dimensional phase space, and simple weather-vane mechanics can predict squirmer rheotaxis. The analogous structure of the phase plane with the wall contact in two and three dimensions implies that the two-dimensional disk swimmer successfully captures the nonlinear interactions, and thus two-dimensional approximation could be useful in designing microfluidic devices for the guidance of microswimmers and for clarifying the locomotions in a complex geometry.

One-dimensional velocity model of the Middle Kura Depresion from local earthquakes data of Azerbaijan

NASA Astrophysics Data System (ADS)

Yetirmishli, G. C.; Kazimova, S. E.; Kazimov, I. E.

2011-09-01

We present the method for determining the velocity model of the Earth's crust and the parameters of earthquakes in the Middle Kura Depression from the data of network telemetry in Azerbaijan. Application of this method allowed us to recalculate the main parameters of the hypocenters of the earthquake, to compute the corrections to the arrival times of P and S waves at the observation station, and to significantly improve the accuracy in determining the coordinates of the earthquakes. The model was constructed using the VELEST program, which calculates one-dimensional minimal velocity models from the travel times of seismic waves.

The Minkowski metric in non-inertial observer radar coordinates

NASA Astrophysics Data System (ADS)

Minguzzi, E.

2005-12-01

We give a closed expression for the Minkowski (1+1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform experiments in spacetime without making reference to inertial frames. To clarify the relation between inertial and non-inertial observers the coordinate transformation between radar and inertial coordinates also is given. We show that every conformally flat coordinate system can be regarded as the radar coordinate system of a suitable observer for a suitable parametrization of the observer worldline. Therefore, the coordinate transformation between arbitrarily moving observers is a conformal transformation and conformally invariant (1+1)-dimensional theories lead to the same physics for all observers, independently of their relative motion.

Fish Tank Optics.

ERIC Educational Resources Information Center

McCausland, Stuart; Allard, Brian

1997-01-01

Describes procedures for a demonstration of the focal length of spherical lenses and mirrors using an aquarium, a flashlight, and nondairy creamer. Enables nonquantitative three-dimensional observation of these phenomena. (DDR)

Three-dimensional cinematography with control object of unknown shape.

PubMed

Dapena, J; Harman, E A; Miller, J A

1982-01-01

A technique for reconstruction of three-dimensional (3D) motion which involves a simple filming procedure but allows the deduction of coordinates in large object volumes was developed. Internal camera parameters are calculated from measurements of the film images of two calibrated crosses while external camera parameters are calculated from the film images of points in a control object of unknown shape but at least one known length. The control object, which includes the volume in which the activity is to take place, is formed by a series of poles placed at unknown locations, each carrying two targets. From the internal and external camera parameters, and from locations of the images of point in the films of the two cameras, 3D coordinates of the point can be calculated. Root mean square errors of the three coordinates of points in a large object volume (5m x 5m x 1.5m) were 15 mm, 13 mm, 13 mm and 6 mm, and relative errors in lengths averaged 0.5%, 0.7% and 0.5%, respectively.

Bromidotetra­kis­(2-ethyl-1H-imidazole-κN 3)copper(II) bromide

PubMed Central

Godlewska, Sylwia; Kelm, Harald; Krüger, Hans-Jörg; Dołęga, Anna

2012-01-01

The CuII ion in the title mol­ecular salt, [CuBr(C5H8N2)4]Br, is coordinated in a square-pyramidal geometry by four N atoms of imidazole ligands and one bromide anion in the apical position. In the crystal, the ions are linked by N—H⋯Br hydrogen bonds involving both the coordinating and the free bromide species as acceptors. A C—H⋯Br inter­action is also observed. Overall, a three-dimensional network results. PMID:23468738

High Accuracy, Two-Dimensional Read-Out in Multiwire Proportional Chambers

DOE R&D Accomplishments Database

Charpak, G.; Sauli, F.

1973-02-14

In most applications of proportional chambers, especially in high-energy physics, separate chambers are used for measuring different coordinates. In general one coordinate is obtained by recording the pulses from the anode wires around which avalanches have grown. Several methods have been imagined for obtaining the position of an avalanche along a wire. In this article a method is proposed which leads to the same range of accuracies and may be preferred in some cases. The problem of accurate measurements for large-size chamber is also discussed.

Black holes, hidden symmetries, and complete integrability

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2017-11-01

The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-(A)dS black hole spacetimes. We start with discussion of the Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a "seed object" which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

Black holes, hidden symmetries, and complete integrability.

PubMed

Frolov, Valeri P; Krtouš, Pavel; Kubizňák, David

2017-01-01

The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-(A)dS black hole spacetimes. We start with discussion of the Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a "seed object" which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

Black String and Velocity Frame Dragging

NASA Astrophysics Data System (ADS)

Lee, Jungjai; Kim, Hyeong-Chan

We investigate velocity frame dragging with the boosted Schwarzschild black string solution and the boosted Kaluza-Klein bubble solution, in which a translational symmetry along the boosted z-coordinate is implemented. The velocity frame dragging effect can be nullified by the motion of an observer using the boost symmetry along the z-coordinate if it is not compact. However, in spacetime with the compact z-coordinate, we show that the effect cannot be removed since the compactification breaks the global Lorentz boost symmetry. As a result, the comoving velocity depends on r and the momentum parameter along the z-coordinate becomes an observer independent characteristic quantity of the black string and bubble solutions. The dragging induces a spherical ergo-region around the black string.

Deflection of light to second order: A tool for illustrating principles of general relativity

NASA Astrophysics Data System (ADS)

Bodenner, Jeremiah; Will, Clifford M.

2003-08-01

We calculate the deflection of light by a spherically symmetric body in general relativity, to second order in the quantity GM/dc2, where M is the mass of the body and d is a measure of the distance of closest approach of the ray. Using three different coordinate systems for the Schwarzschild metric we show that the answers for the deflection, while the same at order GM/dc2, differ at order (GM/dc2)2. We demonstrate that all three expressions are really the same by expressing them in terms of measurable, coordinate-independent quantities. These results provide concrete illustrations of the meaning of coordinates and coordinate invariance, which may be useful in teaching general relativity.

Research on the method of improving the accuracy of CMM (coordinate measuring machine) testing aspheric surface

NASA Astrophysics Data System (ADS)

Cong, Wang; Xu, Lingdi; Li, Ang

2017-10-01

Large aspheric surface which have the deviation with spherical surface are being used widely in various of optical systems. Compared with spherical surface, Large aspheric surfaces have lots of advantages, such as improving image quality, correcting aberration, expanding field of view, increasing the effective distance and make the optical system compact, lightweight. Especially, with the rapid development of space optics, space sensor resolution is required higher and viewing angle is requred larger. Aspheric surface will become one of the essential components in the optical system. After finishing Aspheric coarse Grinding surface profile error is about Tens of microns[1].In order to achieve the final requirement of surface accuracy,the aspheric surface must be quickly modified, high precision testing is the basement of rapid convergence of the surface error . There many methods on aspheric surface detection[2], Geometric ray detection, hartmann detection, ronchi text, knifeedge method, direct profile test, interferometry, while all of them have their disadvantage[6]. In recent years the measure of the aspheric surface become one of the import factors which are restricting the aspheric surface processing development. A two meter caliber industrial CMM coordinate measuring machine is avaiable, but it has many drawbacks such as large detection error and low repeatability precision in the measurement of aspheric surface coarse grinding , which seriously affects the convergence efficiency during the aspherical mirror processing. To solve those problems, this paper presents an effective error control, calibration and removal method by calibration mirror position of the real-time monitoring and other effective means of error control, calibration and removal by probe correction and the measurement mode selection method to measure the point distribution program development. This method verified by real engineer examples, this method increases the original industrial-grade coordinate system nominal measurement accuracy PV value of 7 microns to 4microns, Which effectively improves the grinding efficiency of aspheric mirrors and verifies the correctness of the method. This paper also investigates the error detection and operation control method, the error calibration of the CMM and the random error calibration of the CMM .

Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media

PubMed Central

Pan, De-Bei; Gao, Xiang; Feng, Xia; Pan, Jun-Ting; Zhang, Hong

2016-01-01

Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves. PMID:26905367

A calculus based on a q-deformed Heisenberg algebra

DOE PAGES

Cerchiai, B. L.; Hinterding, R.; Madore, J.; ...

1999-04-27

We show how one can construct a differential calculus over an algebra where position variables $x$ and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by cursive Greek chi and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on thismore » derivative differential forms and an exterior differential calculus can be constructed.« less

A method of indirect registration of the coordinates of condylar points with a six-degree-of-freedom jaw tracker.

PubMed

Huang, B Y; Durrant, C J; Johnson, C W L; Murray, G M

2002-06-30

Previous studies have indicated that the location of a condylar point can significantly influence its trajectory. The aim of this investigation was to develop a method of registering the location of radiographically defined condylar points in the coordinate system of a six-degree-of-freedom jaw-tracking device and to determine the accuracy of this method by using a perspex model in one experiment and a dry skull in another. A direct measurement ('the gold standard') of condylar point coordinates in the coordinate system of JAWS3D was done using a three-dimensional (3D) digitizer (MicroScribe-3DX). The indirect measurement used a distributed fiducial marker as the interface between the coordinate system of MicroScribe-3DX (which was used to register the fiducial marker and the JAWS3D coordinate system) and the coordinate system of the CT scans (used to define condyle anatomy and the relation with the fiducial marker). The coordinates of condylar points could then be calculated in the coordinate system of JAWS3D. The results showed that the indirect method could register condylar point coordinates on either side to an accuracy of approximately 0.5 mm.

Path description of coordinate-space amplitudes

NASA Astrophysics Data System (ADS)

Erdoǧan, Ozan; Sterman, George

2017-06-01

We develop a coordinate version of light-cone-ordered perturbation theory, for general time-ordered products of fields, by carrying out integrals over one light-cone coordinate for each interaction vertex. The resulting expressions depend on the lengths of paths, measured in the same light-cone coordinate. Each path is associated with a denominator equal to a "light-cone deficit," analogous to the "energy deficits" of momentum-space time- or light-cone-ordered perturbation theory. In effect, the role played by intermediate states in momentum space is played by paths between external fields in coordinate space. We derive a class of identities satisfied by coordinate diagrams, from which their imaginary parts can be derived. Using scalar QED as an example, we show how the eikonal approximation arises naturally when the external points in a Green function approach the light cone, and we give applications to products of Wilson lines. Although much of our discussion is directed at massless fields in four dimensions, we extend the formalism to massive fields and dimensional regularization.

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

NASA Technical Reports Server (NTRS)

Podhorodeski, R. P.; Fenton, R. G.; Goldenberg, A. A.

1989-01-01

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Hamiltonian 3-D Ray Tracing in the Oceanic Waveguide on the Ellipsoidal Earth

DTIC Science & Technology

1990-12-01

equivalent to Eq. (B 1). I The ionosphere has a uniform refractive index (the isovelocity acoustic analogue) in this con- Using the ray invariant (the...spherical coordinates in NOAA’s 3-D ray tracer HARPO, are adapted to ellipsoidal coordinates in the oceanic waveguide. The ensuing modified HARPO is used to...objective of this modeling is to extract the predictable part of the travel-time trend and fluctua- tions along several long paths that will be used to

Toward an Increased Understanding of the Singularity Expansion Method.

DTIC Science & Technology

1980-12-01

distribution unlimited. DTIC AIR-FORCE WEAPONS LABORATORY ELECTE Air Force Systems Command SJUL 16 18 OmKirtland Air Force Base, NM 87117 S B 82 07...EMP community. This report does not address the applications of the method to EMP system effects, rather we elaborate on the contribution of SEM to an...IL (10) E S where SL =Lim far [GVOE - OEGr2 sinO d~do (11) 15 .1 with 0, , and r being spherical coordinates defined in a coordinate system having

Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography.

PubMed

Johnson, R S

2018-01-28

This review makes a case for describing many of the flows observed in our oceans, simply based on the Euler equation, with (piecewise) constant density and with suitable boundary conditions. The analyses start from the Euler and mass conservation equations, expressed in a rotating, spherical coordinate system (but the f -plane and β -plane approximations are also mentioned); five examples are discussed. For three of them, a suitable non-dimensionalization is introduced, and a single small parameter is identified in each case. These three examples lead straightforwardly and directly to new results for: waves on the Pacific Equatorial Undercurrent (EUC) with a thermocline (in the f -plane); a nonlinear, three-dimensional model for EUC-type flows (in the β -plane); and a detailed model for large gyres. The other two examples are exact solutions of the complete system: a flow which corresponds to the underlying structure of the Pacific EUC; and a flow based on the necessary requirement to use a non-conservative body force, which produces the type of flow observed in the Antarctic Circumpolar Current. (All these examples have been discussed in detail in the references cited.) This review concludes with a few comments on how these solutions can be extended and expanded.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

Test-retest assessment of cortical activation induced by repetitive transcranial magnetic stimulation with brain atlas-guided optical topography

NASA Astrophysics Data System (ADS)

Tian, Fenghua; Kozel, F. Andrew; Yennu, Amarnath; Croarkin, Paul E.; McClintock, Shawn M.; Mapes, Kimberly S.; Husain, Mustafa M.; Liu, Hanli

2012-11-01

Repetitive transcranial magnetic stimulation (rTMS) is a technology that stimulates neurons with rapidly changing magnetic pulses with demonstrated therapeutic applications for various neuropsychiatric disorders. Functional near-infrared spectroscopy (fNIRS) is a suitable tool to assess rTMS-evoked brain responses without interference from the magnetic or electric fields generated by the TMS coil. We have previously reported a channel-wise study of combined rTMS/fNIRS on the motor and prefrontal cortices, showing a robust decrease of oxygenated hemoglobin concentration (Δ[HbO2]) at the sites of 1-Hz rTMS and the contralateral brain regions. However, the reliability of this putative clinical tool is unknown. In this study, we develop a rapid optical topography approach to spatially characterize the rTMS-evoked hemodynamic responses on a standard brain atlas. A hemispherical approximation of the brain is employed to convert the three-dimensional topography on the complex brain surface to a two-dimensional topography in the spherical coordinate system. The test-retest reliability of the combined rTMS/fNIRS is assessed using repeated measurements performed two to three days apart. The results demonstrate that the Δ[HbO2] amplitudes have moderate-to-high reliability at the group level; and the spatial patterns of the topographic images have high reproducibility in size and a moderate degree of overlap at the individual level.

Simulations of four-dimensional simplicial quantum gravity as dynamical triangulation

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

Agishtein, M.E.; Migdal, A.A.

1992-04-20

In this paper, Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. The authors studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: the authors reached about 5 {times} 10{sup 4} simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reachmore » the second order phase transition point, where the correlation length grows to infinity. The authors varied the gravitational constant, and they found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). The authors studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths.« less

One Dimensional Coordination Polymer of Zn(II) for Developing Multifunctional Nanoparticles.

PubMed

Agarwal, Rashmi A

2017-10-16

A variety of nanoparticles (NPs) including Ag, Au, Pd, Cr and mixed Cu/Fe have been synthesized in a non-activated (without solvent removal) one dimensional coordination polymer (CP) of Zn(II) via two different mechanisms, acid formation and redox activity of the framework. Main driving force to grow these NPs within the cavities of CP is the presence of free oxygens of one of the monodentate carboxylate groups of BDC ligand. These free oxygens act as anchoring sites for the metal ions of the metal precursors. Chemical and physical characteristics of the NPs within the framework have been evaluated by the high resolution transmission electron microscopic (HRTEM) images. Excluding Ag(0) and Pd(0) other NPs are present as combinations of their elemental as well as oxide forms (Au/Au 2 O 3 , Cr/Cr 2 O 3 /CrO 2 and Cu/Cu 2 O, Fe/FeO). Synthesized Ag NPs within the framework show remarkable antibacterial efficacy at extremely low concentrations. Ag, Au and Cu/Fe NPs show ferromagnetic properties within the framework at room temperature. This polymer has potential to sequester highly toxic Cr(VI) to non toxic Cr(0), Cr(III) and Cr(IV) species.

Generalizations of the Toda molecule

NASA Astrophysics Data System (ADS)

Van Velthoven, W. P. G.; Bais, F. A.

1986-12-01

Finite-energy monopole solutions are constructed for the self-dual equations with spherical symmetry in an arbitrary integer graded Lie algebra. The constraint of spherical symmetry in a complex noncoordinate basis leads to a dimensional reduction. The resulting two-dimensional ( r, t) equations are of second order and furnish new generalizations of the Toda molecule equations. These are then solved by a technique which is due to Leznov and Saveliev. For time-independent solutions a further reduction is made, leading to an ansatz for all SU(2) embeddings of the Lie algebra. The regularity condition at the origin for the solutions, needed to ensure finite energy, is also solved for a special class of nonmaximal embeddings. Explicit solutions are given for the groups SU(2), SO(4), Sp(4) and SU(4).

Exact Green's functions for a Brownian particle reversibly binding to a fixed target in a finite, two-dimensional, circular domain

NASA Astrophysics Data System (ADS)

Kalay, Ziya

2012-06-01

Despite the apparent need to study reversible reactions between molecules confined to a two-dimensional space such as the cell membrane, exact Green’s functions for this case have not been reported. Here we present exact analytical Green’s functions for a Brownian particle reversibly reacting with a fixed reaction center in a finite two-dimensional circular region with reflecting or absorbing boundaries, considering either a spherically symmetric initial distribution or a particle that is initially bound. We show that Green’s function can be used to predict the effect of measurement uncertainties on the outcome of single-particle/molecule-tracking experiments in which molecular interactions are investigated. Hence, we bridge the gap between previously known solutions in one dimension (Agmon 1984 J. Chem. Phys. 81 2811) and three dimensions (Kim and Shin 1999 Phys. Rev. Lett. 82 1578), and provide an example of how the knowledge of Green’s function can be used to predict experimentally accessible quantities.

Area law microstate entropy from criticality and spherical symmetry

NASA Astrophysics Data System (ADS)

Dvali, Gia

2018-05-01

It is often assumed that the area law of microstate entropy and the holography are intrinsic properties exclusively of the gravitational systems, such as black holes. We construct a nongravitational model that exhibits an entropy that scales as area of a sphere of one dimension less. It is represented by a nonrelativistic bosonic field living on a d -dimensional sphere of radius R and experiencing an angular-momentum-dependent attractive interaction. We show that the system possesses a quantum critical point with the emergent gapless modes. Their number is equal to the area of a d -1 -dimensional sphere of the same radius R . These gapless modes create an exponentially large number of degenerate microstates with the corresponding microstate entropy given by the area of the same d -1 -dimensional sphere. Thanks to a double-scaling limit, the counting of the entropy and of the number of the gapless modes is made exact. The phenomenon takes place for arbitrary number of dimensions and can be viewed as a version of holography.

Wave Phenomena in Reaction-Diffusion Systems

NASA Astrophysics Data System (ADS)

Steinbock, Oliver; Engel, Harald

2013-12-01

Pattern formation in excitable and oscillatory reaction-diffusion systems provides intriguing examples for the emergence of macroscopic order from molecular reaction events and Brownian motion. Here we review recent results on several aspects of excitation waves including anomalous dispersion, vortex pinning, and three-dimensional scroll waves. Anomalies in the speed-wavelength dependence of pulse trains include nonmonotonic behavior, bistability, and velocity gaps. We further report on the hysteresis effects during the pinning-depinning transition of twodimensional spiral waves. The pinning of three-dimensional scroll waves shows even richer dynamic complexity, partly due to the possibility of geometric and topological mismatches between the unexcitable, pinning heterogeneities and the one-dimensional rotation backbone of the vortex. As examples we present results on the pinning of scroll rings to spherical, C-shaped, and genus-2-type heterogeneities. We also review the main results of several experimental studies employing the Belousov-Zhabotinsky reaction and briefly discuss the biomedical relevance of this research especially in the context of cardiology.

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

DOE PAGES

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; ...

2016-08-04

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computationalmore » cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.« less

Well-balanced compressible cut-cell simulation of atmospheric flow.

PubMed

Klein, R; Bates, K R; Nikiforakis, N

2009-11-28

Cut-cell meshes present an attractive alternative to terrain-following coordinates for the representation of topography within atmospheric flow simulations, particularly in regions of steep topographic gradients. In this paper, we present an explicit two-dimensional method for the numerical solution on such meshes of atmospheric flow equations including gravitational sources. This method is fully conservative and allows for time steps determined by the regular grid spacing, avoiding potential stability issues due to arbitrarily small boundary cells. We believe that the scheme is unique in that it is developed within a dimensionally split framework, in which each coordinate direction in the flow is solved independently at each time step. Other notable features of the scheme are: (i) its conceptual and practical simplicity, (ii) its flexibility with regard to the one-dimensional flux approximation scheme employed, and (iii) the well-balancing of the gravitational sources allowing for stable simulation of near-hydrostatic flows. The presented method is applied to a selection of test problems including buoyant bubble rise interacting with geometry and lee-wave generation due to topography.

Two novel copper(II) complexes constructed from dicarboxylate ligands with different spacer lengths and 2-phenylimidazo[4,5- f]1,10-phenanthroline (PIP): Synthesis, structures and properties

NASA Astrophysics Data System (ADS)

Wang, X.-L.; Chen, Yongqiang; Liu, Guocheng; Lin, Hongyan; Zhang, Jinxia

2009-09-01

Two novel metal-organic coordination polymers [Cu(PIP)(bpea)(H 2O)]·H 2O ( 1) and [Cu(PIP)(1,4-bdc)] ( 2) have been obtained from hydrothermal reaction of copper(II) with the mixed ligands [biphenylethene-4,4'-dicarboxylic acid (bpea) for 1, benzene-1,4-dicarboxylic acid (1,4-H 2bdc) for 2, and 2-phenylimidazo[4,5- f]1,10-phenanthroline (PIP)]. Both complexes have been structurally characterized by elemental analyses, IR and single-crystal X-ray diffraction analyses. Structural analyses reveal that complex 1 possesses infinite one-dimensional zigzag chain, 2 exhibits a two-dimensional (4,4) network, both of which are extended into three-dimensional supramolecular network by weak interactions. The different structures of the title complexes illustrate the influence of the flexibility (the spacer length of carboxyl groups and the structural rigidity of the spacer) of organic dicarboxylate ligands on the formation of such coordination architectures. Moreover, the thermal properties and the voltammetric behavior of complexes 1 and 2 have been reported.

On the localisation of four-dimensional brane-world black holes: II. The general case

NASA Astrophysics Data System (ADS)

Kanti, P.; Pappas, N.; Pappas, T.

2016-01-01

We perform a comprehensive analysis of a number of scalar field theories in an attempt to find analytically five-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the five-dimensional metric tensor that allows for a time-dependent, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen energy-momentum tensor which is non-isotropic in five dimensions, solutions that have the form of a Schwarzschild-(anti)de Sitter or Reissner-Nordstrom type of solution do emerge. However, the resulting profile of the mass function along the bulk coordinate, when allowed, is not the correct one for eliminating bulk singularities.

Synthesis and Characterization Hierarchical Three-Dimensional TiO2 Structure via Hydrothermal Method

NASA Astrophysics Data System (ADS)

Syuhada, N.; Yuliarto, B.; Nugraha

2018-05-01

TiO2 is one of the most potential candidates due to its fascinating properties for multi-discipline fields. One dimensional nanostructure TiO2 such as nanotube and nanorods has been widely used for many devices technology. Compare with one-dimensional nanostructure TiO2; the hierarchical TiO2 has not been widely applied. Three dimensional TiO2 play a promising role for application in many different fields such as photovoltaics, photocatalytic and a gas sensor. Herein, we report that the hierarchically structures TiO2 have been successfully obtained by the one-pot Hydrothermal process. The growth mechanism of Titania was controlled by Titanium (IV) isopropoxide (TTIP). Ethylene glycol (EG). Hydrochloric acid (HCl). Hexadecyltrimethylammonium bromide (CTAB) molar ratio. TTIP was used as titanium source and CTAB as a soft template. The molar ratio of TTIP. EG. HCl. CTAB was 0.1:0.2:0.4:0.001. Those samples were synthesized using the hydrothermal method at 180 °C for 20 h. The purpose of this work was focused on investigating morphology, crystallite size, crystalline phase, and particle size. The properties of these materials were characterized by XRay Diffraction, Energy Dispersive Spectroscopy and Scanning Electron Microscope. It was found all particles exhibited unique spherical morphology which arranged by nanorods and good distribution nanoparticle. The Average size of the sphere has range 1 µm to 3 µm with diameter nanorods 60 nm to 100 nm. The TiO2 spheres were constructed of interconnected nanorods and formed a three dimensional (3D) porous framework. XRD analysis confirmed that sample consisted of pure rutile crystal structure with crystallite size was 50 nm, and EDS revealed an elemental content of Ti 61.03 % and O 38.97 %.

A panning DLT procedure for three-dimensional videography.

PubMed

Yu, B; Koh, T J; Hay, J G

1993-06-01

The direct linear transformation (DLT) method [Abdel-Aziz and Karara, APS Symposium on Photogrammetry. American Society of Photogrammetry, Falls Church, VA (1971)] is widely used in biomechanics to obtain three-dimensional space coordinates from film and video records. This method has some major shortcomings when used to analyze events which take place over large areas. To overcome these shortcomings, a three-dimensional data collection method based on the DLT method, and making use of panning cameras, was developed. Several small single control volumes were combined to construct a large total control volume. For each single control volume, a regression equation (calibration equation) is developed to express each of the 11 DLT parameters as a function of camera orientation, so that the DLT parameters can then be estimated from arbitrary camera orientations. Once the DLT parameters are known for at least two cameras, and the associated two-dimensional film or video coordinates of the event are obtained, the desired three-dimensional space coordinates can be computed. In a laboratory test, five single control volumes (in a total control volume of 24.40 x 2.44 x 2.44 m3) were used to test the effect of the position of the single control volume on the accuracy of the computed three dimensional space coordinates. Linear and quadratic calibration equations were used to test the effect of the order of the equation on the accuracy of the computed three dimensional space coordinates. For four of the five single control volumes tested, the mean resultant errors associated with the use of the linear calibration equation were significantly larger than those associated with the use of the quadratic calibration equation. The position of the single control volume had no significant effect on the mean resultant errors in computed three dimensional coordinates when the quadratic calibration equation was used. Under the same data collection conditions, the mean resultant errors in the computed three dimensional coordinates associated with the panning and stationary DLT methods were 17 and 22 mm, respectively. The major advantages of the panning DLT method lie in the large image sizes obtained and in the ease with which the data can be collected. The method also has potential for use in a wide variety of contexts. The major shortcoming of the method is the large amount of digitizing necessary to calibrate the total control volume. Adaptations of the method to reduce the amount of digitizing required are being explored.

Low-dimensional quantum magnetism in Cu (NCS) 2: A molecular framework material

NASA Astrophysics Data System (ADS)

Cliffe, Matthew J.; Lee, Jeongjae; Paddison, Joseph A. M.; Schott, Sam; Mukherjee, Paromita; Gaultois, Michael W.; Manuel, Pascal; Sirringhaus, Henning; Dutton, Siân E.; Grey, Clare P.

2018-04-01

Low-dimensional magnetic materials with spin-1/2 moments can host a range of exotic magnetic phenomena due to the intrinsic importance of quantum fluctuations to their behavior. Here, we report the structure, magnetic structure, and magnetic properties of copper ii thiocyanate, Cu(NCS ) 2, a one-dimensional coordination polymer which displays low-dimensional quantum magnetism. Magnetic susceptibility, electron paramagnetic resonance spectroscopy, 13C magic-angle spinning nuclear magnetic resonance spectroscopy, and density functional theory investigations indicate that Cu(NCS ) 2 behaves as a two-dimensional array of weakly coupled antiferromagnetic spin chains [J2=133 (1 ) K , α =J1/J2=0.08 ] . Powder neutron-diffraction measurements confirm that Cu(NCS ) 2 orders as a commensurate antiferromagnet below TN=12 K , with a strongly reduced ordered moment (0.3 μB ) due to quantum fluctuations.

Fully automated measuring setup for tactile coordinate measuring machine for three dimensional measurement of freeform eyeglass frames

NASA Astrophysics Data System (ADS)

Rückwardt, M.; Göpfert, A.; Correns, M.; Schellhorn, M.; Linß, G.

2010-07-01

Coordinate measuring machines are high precession all-rounder in three dimensional measuring. Therefore the versatility of parameters and expandability of additionally hardware is very comprehensive. Consequently you need much expert knowledge of the user and mostly a lot of advanced information about the measuring object. In this paper a coordinate measuring machine and a specialized measuring machine are compared at the example of the measuring of eyeglass frames. For this case of three dimensional measuring challenges the main focus is divided into metrological and economical aspects. At first there is shown a fully automated method for tactile measuring of this abstract form. At second there is shown a comparison of the metrological characteristics of a coordinate measuring machine and a tracer for eyeglass frames. The result is in favour to the coordinate measuring machine. It was not surprising in these aspects. At last there is shown a comparison of the machine in front of the economical aspects.

Synthesis of Spherical Carbon Nitride-Based Polymer Composites by Continuous Aerosol-Photopolymerization with Efficient Light Harvesting.

PubMed

Poostforooshan, Jalal; Badiei, Alireza; Kolahdouz, Mohammadreza; Weber, Alfred P

2016-08-24

Here we report a novel, facile, and sustainable approach for the preparation of spherical submicrometer carbon nitride-based polymer composites by a continuous aerosol-photopolymerization process. In this regard, spherical mesoporous carbon nitride (SMCN) nanoparticles were initially prepared via a nanocasting approach using spray-drying synthesized spherical mesoporous silica (SMS) nanoparticles as hard templates. In addition to experimental characterization, the effect of porosity on the light absorption enhancement and consequently the generation rate of electron-hole pairs inside the SMCN was simulated using a three-dimensional finite difference time-domain (FDTD) method. To produce the carbon nitride-based polymer composite, SMCN nanoparticles exhibit excellent performance in photopolymerization of butyl acrylate (PBuA) monomer in the presence of n-methyldiethanolamine (MDEA) as a co-initiator in a continuous aerosol-based process. In this one-pot synthesis, SMCN nanoparticles act not only as photoinitiators but at the same time as fillers and templates. The average aerosol residence time in the photoreactor is about 90 s. The presented aerosol-photopolymerization process avoids the need for solvent and surfactant, operates at room temperature, and, more importantly, is suitable to produce the spherical composite with hydrophobic polymers. Furthermore, we simulated the condition of SMCN nanoparticles during illumination in the gas phase process, which can freely rotate. The results demonstrated that the hole (h(+)) density is almost equally distributed in the whole part of the SMCN nanoparticles due to their rotation, leading to efficient light harvesting and more homogeneous photoreaction. The combination of the outstanding features of environmentally friendly SMCN, photopolymerization, and aerosol processing might open new avenues, especially in green chemistry, to produce novel polymer composites with multifunctional properties.

Decoherence and Determinism in a One-Dimensional Cloud-Chamber Model

NASA Astrophysics Data System (ADS)

Sparenberg, Jean-Marc; Gaspard, David

2018-03-01

The hypothesis (Sparenberg et al. in EPJ Web Conf 58:01016, [1]. https://doi.org/10.1051/epjconf/20135801016) that the particular linear tracks appearing in the measurement of a spherically-emitting radioactive source in a cloud chamber are determined by the (random) positions of atoms or molecules inside the chamber is further explored in the framework of a recently established one-dimensional model (Carlone et al. Comm Comput Phys 18:247, [2]. https://doi.org/10.4208/cicp.270814.311214a). In this model, meshes of localized spins 1/2 play the role of the cloud-chamber atoms and the spherical wave is replaced by a linear superposition of two wave packets moving from the origin to the left and to the right, evolving deterministically according to the Schrödinger equation. We first revisit these results using a time-dependent approach, where the wave packets impinge on a symmetric two-sided detector. We discuss the evolution of the wave function in the configuration space and stress the interest of a non-symmetric detector in a quantum-measurement perspective. Next we use a time-independent approach to study the scattering of a plane wave on a single-sided detector. Preliminary results are obtained, analytically for the single-spin case and numerically for up to 8 spins. They show that the spin-excitation probabilities are sometimes very sensitive to the parameters of the model, which corroborates the idea that the measurement result could be determined by the atom positions. The possible origin of decoherence and entropy increase in future models is finally discussed.

Strong ferromagnetic exchange interaction under ambient pressure in BaFe 2 S 3

DOE PAGES

Wang, Meng; Jin, S. J.; Yi, Ming; ...

2017-02-03

Inelastic neutron scattering measurements have been performed to investigate the spin waves of the quasi-one-dimensional antiferromagnetic ladder compound BaFe 2 S 3 , where a superconducting transition was observed under pressure [H. Takahashi et al., Nat. Mater. 14, 1008 (2015); T. Yamauchi et al., Phys. Rev. Lett. 115, 246402 (2015)]. By fitting the spherically averaged experimental data collected on a powder sample to a Heisenberg Hamiltonian, we find that the one-dimensional antiferromagnetic ladder exhibits a strong nearest-neighbor ferromagnetic exchange interaction (SJ R = - 71 ± 4 meV) along the rung direction, an antiferromagnetic SJ L = 49 ± 3more » meV along the leg direction, and a ferromagnetic SJ 2 = - 15 ± 2 meV along the diagonal direction. Finally, our data demonstrate that the antiferromagnetic spin excitations are a common characteristic for the iron-based superconductors, while specific relative values for the exchange interactions do not appear to be unique for the parent states of the superconducting materials.« less

Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for multiparticles in quantum field theories

NASA Astrophysics Data System (ADS)

Aoki, Sinya; Ishii, Noriyoshi; Doi, Takumi; Ikeda, Yoichi; Inoue, Takashi

2013-07-01

We derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than two particles in quantum field theories. To deal with n particles in the center-of-mass frame coherently, we introduce the Jacobi coordinates of n particles and then combine their 3(n-1) coordinates into the one spherical coordinate in D=3(n-1) dimensions. We parametrize the on-shell T matrix for n scalar particles at low energy using the unitarity constraint of the S matrix. We then express asymptotic behaviors of the NBS wave function for n particles at low energy in terms of parameters of the T matrix and show that the NBS wave function carries information of the T matrix such as phase shifts and mixing angles of the n-particle system in its own asymptotic behavior, so that the NBS wave function can be considered as the scattering wave of n particles in quantum mechanics. This property is one of the essential ingredients of the HAL QCD scheme to define “potential” from the NBS wave function in quantum field theories such as QCD. Our results, together with an extension to systems with spin 1/2 particles, justify the HAL QCD’s definition of potentials for three or more nucleons (or baryons) in terms of the NBS wave functions.

Dual fermionic variables and renormalization group approach to junctions of strongly interacting quantum wires

NASA Astrophysics Data System (ADS)

Giuliano, Domenico; Nava, Andrea

2015-09-01

Making a combined use of bosonization and fermionization techniques, we build nonlocal transformations between dual fermion operators, describing junctions of strongly interacting spinful one-dimensional quantum wires. Our approach allows for trading strongly interacting (in the original coordinates) fermionic Hamiltonians for weakly interacting (in the dual coordinates) ones. It enables us to generalize to the strongly interacting regime the fermionic renormalization group approach to weakly interacting junctions. As a result, on one hand, we are able to pertinently complement the information about the phase diagram of the junction obtained within the bosonization approach; on the other hand, we map out the full crossover of the conductance tensors between any two fixed points in the phase diagram connected by a renormalization group trajectory.

Closed Analytic Solution for the Potential and Equations of Motion in the Presence of a Gravitating Oblate Spheroid

NASA Astrophysics Data System (ADS)

Atkinson, William

2008-10-01

A closed analytic solution for the potential due to a gravitating solid oblate spheroid, derived in oblate spheroidal coordinates in this paper, is shown to be much simpler than those obtained either in cylindrical coordinates (MacMillan) or in spherical coordinates (McCullough). The derivation in oblate spheroidal coordinates is also much simpler to follow than those of the MacMillan or McCullough. The potential solution is applied in exacting a closed solution for the equations of motion for an object rolling on the surface of the spheroid subjected only to the gravitational force component tangential to the surface of the spheroid. The exact solution was made possible by the fact that the force can be represented as separable functions of the coordinates only in oblate spheroidal coordinates. The derivation is a good demonstration of the use of curvilinear coordinates to problems in classical mechanics, potential theory, and mathematical physics for both undergraduate and graduate students.

Visualizing curved spacetime

NASA Astrophysics Data System (ADS)

Jonsson, Rickard M.

2005-03-01

I present a way to visualize the concept of curved spacetime. The result is a curved surface with local coordinate systems (Minkowski systems) living on it, giving the local directions of space and time. Relative to these systems, special relativity holds. The method can be used to visualize gravitational time dilation, the horizon of black holes, and cosmological models. The idea underlying the illustrations is first to specify a field of timelike four-velocities uμ. Then, at every point, one performs a coordinate transformation to a local Minkowski system comoving with the given four-velocity. In the local system, the sign of the spatial part of the metric is flipped to create a new metric of Euclidean signature. The new positive definite metric, called the absolute metric, can be covariantly related to the original Lorentzian metric. For the special case of a two-dimensional original metric, the absolute metric may be embedded in three-dimensional Euclidean space as a curved surface.

Three-dimensional transformation optics for arbitrary coordinate systems: transforming conductive materials and boundaries.

PubMed

Kazemzadeh, Mohammad-Rahim; Alighanbari, Abbas

2018-04-16

A three-dimensional transformation optics method, leading to homogeneous materials, applicable to any non-Cartesian coordinate systems or waveguides/objects of arbitrary cross-sections is presented. Both the conductive boundary and internal material of the desired device is determined by the proposed formulation. The method is applicable to a wide range of waveguide, radiation, and cloaking problems, and is demonstrated for circular waveguide couplers and an external cloak. An advantage of the present method is that the material properties are simplified by appropriately selecting the conductive boundaries. For instance, a right-angle circular waveguide bend is presented which uses only one homogenous material. Also, transformation of conductive materials and boundaries are studied. The conditions in which the transformed boundaries remain conductive are discussed. In addition, it is demonstrated that negative infinite conductivity can be replaced with positive conductivity, without affecting the field outside the conductive boundary. It is also observed that a negative finite conductivity can be replaced with a positive one, by accepting some small errors. The general mathematical procedure and formulation for calculating the parametric surface equations of the conductive peripheries are presented.

Shear wave induced resonance elastography of spherical masses with polarized torsional waves

NASA Astrophysics Data System (ADS)

Hadj Henni, Anis; Schmitt, Cédric; Trop, Isabelle; Cloutier, Guy

2012-03-01

Shear wave induced resonance (SWIR) is a technique for dynamic ultrasound elastography of confined mechanical inclusions. It was developed for breast tumor imaging and tissue characterization. This method relies on the polarization of torsional shear waves modeled with the Helmholtz equation in spherical coordinates. To validate modeling, an invitro set-up was used to measure and image the first three eigenfrequencies and eigenmodes of a soft sphere. A preliminary invivo SWIR measurement on a breast fibroadenoma is also reported. Results revealed the potential of SWIR elastography to detect and mechanically characterize breast lesions for early cancer detection.

Shear wave induced resonance elastography of spherical masses with polarized torsional waves.

PubMed

Henni, Anis Hadj; Schmitt, Cédric; Trop, Isabelle; Cloutier, Guy

2012-03-26

Shear Wave Induced Resonance (SWIR) is a technique for dynamic ultrasound elastography of confined mechanical inclusions. It was developed for breast tumor imaging and tissue characterization. This method relies on the polarization of torsional shear waves modeled with the Helmholtz equation in spherical coordinates. To validate modeling, an in vitro set-up was used to measure and image the first three eigenfrequencies and eigenmodes of a soft sphere. A preliminary in vivo SWIR measurement on a breast fibroadenoma is also reported. Results revealed the potential of SWIR elastography to detect and mechanically characterize breast lesions for early cancer detection.

PERFECTLY MATCHED LAYERS FOR ELASTIC WAVES IN CYLINDRICAL AND SPHERICAL COORDINATES. (R825225)

EPA Science Inventory

The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

Retinal image contrast obtained by a model eye with combined correction of chromatic and spherical aberrations

PubMed Central

Ohnuma, Kazuhiko; Kayanuma, Hiroyuki; Lawu, Tjundewo; Negishi, Kazuno; Yamaguchi, Takefumi; Noda, Toru

2011-01-01

Correcting spherical and chromatic aberrations in vitro in human eyes provides substantial visual acuity and contrast sensitivity improvements. We found the same improvement in the retinal images using a model eye with/without correction of longitudinal chromatic aberrations (LCAs) and spherical aberrations (SAs). The model eye included an intraocular lens (IOL) and artificial cornea with human ocular LCAs and average human SAs. The optotypes were illuminated using a D65 light source, and the images were obtained using two-dimensional luminance colorimeter. The contrast improvement from the SA correction was higher than the LCA correction, indicating the benefit of an aspheric achromatic IOL. PMID:21698008

Geometry induced phase transitions in magnetic spherical shell

NASA Astrophysics Data System (ADS)

Sloika, Mykola I.; Sheka, Denis D.; Kravchuk, Volodymyr P.; Pylypovskyi, Oleksandr V.; Gaididei, Yuri

2017-12-01

Equilibrium magnetization states in spherical shells of a magnetically soft ferromagnet form two out-of-surface vortices with codirectionally magnetized vortex cores at the sphere poles: (i) a whirligig state with the in-surface magnetization oriented along parallels is typical for thick shells; (ii) a three dimensional onion state with the in-surface meridional direction of the magnetization is realized in thin shells. The geometry of spherical shell prohibits an existence of spatially homogeneous magnetization distribution, even in the case of small sample radii. By varying geometrical parameters a continuous phase transition between the whirligig and onion states takes place. The detailed analytical description of the phase diagram is well confirmed by micromagnetic simulations.

Conformal Yano-Killing Tensors for Space-times with Cosmological Constant

NASA Astrophysics Data System (ADS)

Czajka, P.; Jezierski, J.

We present a new method for constructing conformal Yano-Killing tensors in five-di\\-men\\-sio\\-nal Anti-de Sitter space-time. The found tensors are represented in two different coordinate systems. We also discuss, in terms of CYK tensors, global charges which are well defined for asymptotically (five-dimensional) Anti-de Sitter space-time. Additionally in Appendix we present our own derivation of conformal Killing one-forms in four-dimensional Anti-de Sitter space-time as an application of the Theorem presented in the paper.

Multi-domain boundary element method for axi-symmetric layered linear acoustic systems

NASA Astrophysics Data System (ADS)

Reiter, Paul; Ziegelwanger, Harald

2017-12-01

Homogeneous porous materials like rock wool or synthetic foam are the main tool for acoustic absorption. The conventional absorbing structure for sound-proofing consists of one or multiple absorbers placed in front of a rigid wall, with or without air-gaps in between. Various models exist to describe these so called multi-layered acoustic systems mathematically for incoming plane waves. However, there is no efficient method to calculate the sound field in a half space above a multi layered acoustic system for an incoming spherical wave. In this work, an axi-symmetric multi-domain boundary element method (BEM) for absorbing multi layered acoustic systems and incoming spherical waves is introduced. In the proposed BEM formulation, a complex wave number is used to model absorbing materials as a fluid and a coordinate transformation is introduced which simplifies singular integrals of the conventional BEM to non-singular radial and angular integrals. The radial and angular part are integrated analytically and numerically, respectively. The output of the method can be interpreted as a numerical half space Green's function for grounds consisting of layered materials.

An analytical and experimental study of the behavior of semi-infinite metal targets under hypervelocity impact

NASA Technical Reports Server (NTRS)

Chakrapani, B.; Rand, J. L.

1971-01-01

The material strength and strain rate effects associated with the hypervelocity impact problem were considered. A yield criterion involving the second and third invariants of the stress deviator and a strain rate sensitive constitutive equation were developed. The part of total deformation which represents change in shape is attributable to the stress deviator. Constitutive equation is a means for analytically describing the mechanical response of a continuum under study. The accuracy of the yield criterion was verified utilizing the published two and three dimensional experimental data. The constants associated with the constitutive equation were determined from one dimensional quasistatic and dynamic experiments. Hypervelocity impact experiments were conducted on semi-infinite targets of 1100 aluminum, 6061 aluminum alloy, mild steel, and commercially pure lead using spherically shaped and normally incident pyrex projectiles.

Characterizing the Three-Dimensional Structure of Block Copolymers via Sequential Infiltration Synthesis and Scanning Transmission Electron Tomography

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

Segal-Peretz, Tamar; Winterstein, Jonathan; Doxastakis, Manolis

Understanding and controlling the three-dimensional structure of block copolymer (BCP) thin films is critical for utilizing these materials for sub-20 nm nanopatterning in semiconductor devices, as well as in membranes and solar cell applications. Combining an atomic layer deposition (ALD) based technique for enhancing the contrast of BCPs in transmission electron microscopy (TEM) together with scanning TEM (STEM) tomography reveals and characterizes the three-dimensional structures of poly(styrene-block-methyl methacrylate) (PS-b-PMMA) thin films with great clarity. Sequential infiltration synthesis (SIS), a block-selective technique for growing inorganic materials in BCPs films in ALD, and an emerging tool for enhancing the etch contrast ofmore » BCPs, was harnessed to significantly enhance the high-angle scattering from the polar domains of BCP films in the TEM. The power of combining SIS and STEM tomography for three dimensional (3D) characterization of BCPs films was demonstrated with the following cases: self-assembled cylindrical, lamellar, and spherical PS-PMMA thin films. In all cases, STEM tomography has revealed 3D structures that were hidden underneath the surface, including: 1) the 3D structure of defects in cylindrical and lamellar phases, 2) non-perpendicular 3D surface of grain boundaries in the cylindrical phase, and 3) the 3D arrangement of spheres in body centered cubic (BCC) and hexagonal closed pack (HCP) morphologies in the spherical phase. The 3D data of the spherical morphologies was compared to coarse-grained simulations and assisted in validating the simulations’ parameters. STEM tomography of SIS-treated BCP films enables the characterization of the exact structure used for pattern transfer, and can lead to better understating of the physics which is utilized in BCP lithography.« less

An analytically solvable three-body break-up model problem in hyperspherical coordinates

NASA Astrophysics Data System (ADS)

Ancarani, L. U.; Gasaneo, G.; Mitnik, D. M.

2012-10-01

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behavior. Since the coordinates' coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.

Development of a new EMP code at LANL

NASA Astrophysics Data System (ADS)

Colman, J. J.; Roussel-Dupré, R. A.; Symbalisty, E. M.; Triplett, L. A.; Travis, B. J.

2006-05-01

A new code for modeling the generation of an electromagnetic pulse (EMP) by a nuclear explosion in the atmosphere is being developed. The source of the EMP is the Compton current produced by the prompt radiation (γ-rays, X-rays, and neutrons) of the detonation. As a first step in building a multi- dimensional EMP code we have written three kinetic codes, Plume, Swarm, and Rad. Plume models the transport of energetic electrons in air. The Plume code solves the relativistic Fokker-Planck equation over a specified energy range that can include ~ 3 keV to 50 MeV and computes the resulting electron distribution function at each cell in a two dimensional spatial grid. The energetic electrons are allowed to transport, scatter, and experience Coulombic drag. Swarm models the transport of lower energy electrons in air, spanning 0.005 eV to 30 keV. The swarm code performs a full 2-D solution to the Boltzmann equation for electrons in the presence of an applied electric field. Over this energy range the relevant processes to be tracked are elastic scattering, three body attachment, two body attachment, rotational excitation, vibrational excitation, electronic excitation, and ionization. All of these occur due to collisions between the electrons and neutral bodies in air. The Rad code solves the full radiation transfer equation in the energy range of 1 keV to 100 MeV. It includes effects of photo-absorption, Compton scattering, and pair-production. All of these codes employ a spherical coordinate system in momentum space and a cylindrical coordinate system in configuration space. The "z" axis of the momentum and configuration spaces is assumed to be parallel and we are currently also assuming complete spatial symmetry around the "z" axis. Benchmarking for each of these codes will be discussed as well as the way forward towards an integrated modern EMP code.

Modelling studies in aqueous solution of lanthanide (III) chelates designed for nuclear magnetic resonance biomedical applications

NASA Astrophysics Data System (ADS)

Henriques, E. S.; Geraldes, C. F. G. C.; Ramos, M. J.

Molecular dynamics simulations and complementary modelling studies have been carried out for the [Gd(DOTA)·(H2O)]- and [Tm(DOTP)]5- chelates in aqueous media, to provide a better understanding of several structural and dynamical properties of these versatile nuclear magnetic resonance (NMR) probes, including coordination shells and corresponding water exchange mechanisms, and interactions of these complexes with alkali metal ions. This knowledge is of key importance in the areas of 1H relaxation and shift reagents for NMR applications in medical diagnosis. A new refinement of our own previously developed set of parameters for these Ln(III) chelates has been used, and is reported here. Calculations of water mean residence times suggest a reassessment of the characterization of the chelates' second coordination shell, one where the simple spherical distribution model is discarded in favour of a more detailed approach. Na+ probe interaction maps are in good agreement with the available site location predictions derived from 23Na NMR shifts.

Pearson's random walk in the space of the CMB phases: Evidence for parity asymmetry

NASA Astrophysics Data System (ADS)

Hansen, M.; Frejsel, A. M.; Kim, J.; Naselsky, P.; Nesti, F.

2011-05-01

The temperature fluctuations of the cosmic microwave background (CMB) are supposed to be distributed randomly in both magnitude and phase, following to the simplest model of inflation. In this paper, we look at the odd and even multipoles of the spherical harmonic decomposition of the CMB, and the different characteristics of these, giving rise to a parity asymmetry. We compare the even and odd multipoles in the CMB power spectrum, and also the even and odd mean angles. We find for the multipoles of the power spectrum that there is power excess in odd multipoles, compared to even ones, meaning that we have a parity asymmetry. Further, for the phases, we present a random walk for the mean angles, and find a significant separation for even/odd mean angles, especially so for galactic coordinates. This is further tested and confirmed with a directional parity test, comparing the parity asymmetry in galactic and ecliptic coordinates.

Conformal mapping and bound states in bent waveguides

NASA Astrophysics Data System (ADS)

Sadurní, E.; Schleich, W. P.

2010-12-01

Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending. The problem can be reduced to a one-dimensional matrix Schroedinger equation using two descriptions: oblique modes and conformal coordinates. We use a corner-corrected WKB formalism to find the energies of the one-dimensional problem. It is shown that the presence of bound states is an effect due to the boundary alone, with no classical counterpart for this geometry. The conformal description proves to be simpler, as the coupling of transversal modes is not essential in this case.

Acoustic wave simulation using an overset grid for the global monitoring system

NASA Astrophysics Data System (ADS)

Kushida, N.; Le Bras, R.

2017-12-01

The International Monitoring System of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) has been monitoring hydro-acoustic and infrasound waves over the globe. Because of the complex natures of the oceans and the atmosphere, computer simulation can play an important role in understanding the observed signals. In this regard, methods which depend on partial differential equations and require minimum modelling, are preferable. So far, to our best knowledge, acoustic wave propagation simulations based on partial differential equations on such a large scale have not been performed (pp 147 - 161 of ref [1], [2]). The main difficulties in building such simulation codes are: (1) considering the inhomogeneity of medium including background flows, (2) high aspect ratio of computational domain, (3) stability during long time integration. To overcome these difficulties, we employ a two-dimensional finite different (FDM) scheme on spherical coordinates with the Yin-Yang overset grid[3] solving the governing equation of acoustic waves introduces by Ostashev et. al.[4]. The comparison with real recording examples in hydro-acoustic will be presented at the conference. [1] Paul C. Etter: Underwater Acoustic Modeling and Simulation, Fourth Edition, CRC Press, 2013. [2] LIAN WANG et. al.: REVIEW OF UNDERWATER ACOUSTIC PROPAGATION MODELS, NPL Report AC 12, 2014. [3] A. Kageyama and T. Sato: "Yin-Yang grid": An overset grid in spherical geometry, Geochem. Geophys. Geosyst., 5, Q09005, 2004. [4] Vladimir E. Ostashev et. al: Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation, Acoustical Society of America. DOI: 10.1121/1.1841531, 2005.

Photogrammetry research for FAST eleven-meter reflector panel surface shape measurement

NASA Astrophysics Data System (ADS)

Zhou, Rongwei; Zhu, Lichun; Li, Weimin; Hu, Jingwen; Zhai, Xuebing

2010-10-01

In order to design and manufacture the Five-hundred-meter Aperture Spherical Radio Telescope (FAST) active reflector measuring equipment, measurement on each reflector panel surface shape was presented, static measurement of the whole neutral spherical network of nodes was performed, real-time dynamic measurement at the cable network dynamic deformation was undertaken. In the implementation process of the FAST, reflector panel surface shape detection was completed before eleven-meter reflector panel installation. Binocular vision system was constructed based on the method of binocular stereo vision in machine vision, eleven-meter reflector panel surface shape was measured with photogrammetry method. Cameras were calibrated with the feature points. Under the linearity camera model, the lighting spot array was used as calibration standard pattern, and the intrinsic and extrinsic parameters were acquired. The images were collected for digital image processing and analyzing with two cameras, feature points were extracted with the detection algorithm of characteristic points, and those characteristic points were matched based on epipolar constraint method. Three-dimensional reconstruction coordinates of feature points were analyzed and reflective panel surface shape structure was established by curve and surface fitting method. The error of reflector panel surface shape was calculated to realize automatic measurement on reflector panel surface shape. The results show that unit reflector panel surface inspection accuracy was 2.30mm, within the standard deviation error of 5.00mm. Compared with the requirement of reflector panel machining precision, photogrammetry has fine precision and operation feasibility on eleven-meter reflector panel surface shape measurement for FAST.

Simulations of Lateral Transport and Dropout Structure of Energetic Particles from Impulsive Solar Flares

NASA Astrophysics Data System (ADS)

Tooprakai, P.; Seripienlert, A.; Ruffolo, D.; Chuychai, P.; Matthaeus, W. H.

2016-11-01

We simulate trajectories of energetic particles from impulsive solar flares for 2D+slab models of magnetic turbulence in spherical geometry to study dropout features, I.e., sharp, repeated changes in the particle density. Among random-phase realizations of two-dimensional (2D) turbulence, a spherical harmonic expansion can generate homogeneous turbulence over a sphere, but a 2D fast Fourier transform (FFT) locally mapped onto the lateral coordinates in the region of interest is much faster computationally, and we show that the results are qualitatively similar. We then use the 2D FFT field as input to a 2D MHD simulation, which dynamically generates realistic features of turbulence such as coherent structures. The magnetic field lines and particles spread non-diffusively (ballistically) to a patchy distribution reaching up to 25° from the injection longitude and latitude at r ˜ 1 au. This dropout pattern in field line trajectories has sharper features in the case of the more realistic 2D MHD model, in better qualitative agreement with observations. The initial dropout pattern in particle trajectories is relatively insensitive to particle energy, though the energy affects the pattern’s evolution with time. We make predictions for future observations of solar particles near the Sun (e.g., at 0.25 au), for which we expect a sharp pulse of outgoing particles along the dropout pattern, followed by backscattering that first remains close to the dropout pattern and later exhibits cross-field transport to a distribution that is more diffusive, yet mostly contained within the dropout pattern found at greater distances.

Three-dimensional iron(ii) porous coordination polymer exhibiting carbon dioxide-dependent spin crossover.

PubMed

Shin, Jong Won; Jeong, Ah Rim; Jeoung, Sungeun; Moon, Hoi Ri; Komatsumaru, Yuki; Hayami, Shinya; Moon, Dohyun; Min, Kil Sik

2018-04-24

We report a three-dimensional Fe(ii) porous coordination polymer that exhibits a spin crossover temperature change following CO2 sorption (though not N2 sorption). Furthermore, single crystals of the desolvated polymer with CO2 molecules at three different temperatures were characterised by X-ray crystallography.

Superfast assembly and synthesis of gold nanostructures using nanosecond low-temperature compression via magnetic pulsed power

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

Li, Binsong; Bian, Kaifu; Lane, J. Matthew D.

Gold nanostructured materials exhibit important size- and shape-dependent properties that enable a wide variety of applications in photocatalysis, nanoelectronics and phototherapy. Here we show the use of superfast dynamic compression to synthesize extended gold nanostructures, such as nanorods, nanowires and nanosheets, with nanosecond coalescence times. Using a pulsed power generator, we ramp compress spherical gold nanoparticle arrays to pressures of tens of GPa, demonstrating pressure-driven assembly beyond the quasi-static regime of the diamond anvil cell. Our dynamic magnetic ramp compression approach produces smooth, shockless (that is, isentropic) one-dimensional loading with low-temperature states suitable for nanostructure synthesis. Transmission electron microscopy clearlymore » establishes that various gold architectures are formed through compressive mesoscale coalescences of spherical gold nanoparticles, which is further confirmed by in-situ synchrotron X-ray studies and large-scale simulation. As a result, this nanofabrication approach applies magnetically driven uniaxial ramp compression to mimic established embossing and imprinting processes, but at ultra-short (nanosecond) timescales.« less

Superfast assembly and synthesis of gold nanostructures using nanosecond low-temperature compression via magnetic pulsed power

DOE PAGES

Li, Binsong; Bian, Kaifu; Lane, J. Matthew D.; ...

2017-03-16

Gold nanostructured materials exhibit important size- and shape-dependent properties that enable a wide variety of applications in photocatalysis, nanoelectronics and phototherapy. Here we show the use of superfast dynamic compression to synthesize extended gold nanostructures, such as nanorods, nanowires and nanosheets, with nanosecond coalescence times. Using a pulsed power generator, we ramp compress spherical gold nanoparticle arrays to pressures of tens of GPa, demonstrating pressure-driven assembly beyond the quasi-static regime of the diamond anvil cell. Our dynamic magnetic ramp compression approach produces smooth, shockless (that is, isentropic) one-dimensional loading with low-temperature states suitable for nanostructure synthesis. Transmission electron microscopy clearlymore » establishes that various gold architectures are formed through compressive mesoscale coalescences of spherical gold nanoparticles, which is further confirmed by in-situ synchrotron X-ray studies and large-scale simulation. As a result, this nanofabrication approach applies magnetically driven uniaxial ramp compression to mimic established embossing and imprinting processes, but at ultra-short (nanosecond) timescales.« less

Superfast assembly and synthesis of gold nanostructures using nanosecond low-temperature compression via magnetic pulsed power

NASA Astrophysics Data System (ADS)

Li, Binsong; Bian, Kaifu; Lane, J. Matthew D.; Salerno, K. Michael; Grest, Gary S.; Ao, Tommy; Hickman, Randy; Wise, Jack; Wang, Zhongwu; Fan, Hongyou

2017-03-01

Gold nanostructured materials exhibit important size- and shape-dependent properties that enable a wide variety of applications in photocatalysis, nanoelectronics and phototherapy. Here we show the use of superfast dynamic compression to synthesize extended gold nanostructures, such as nanorods, nanowires and nanosheets, with nanosecond coalescence times. Using a pulsed power generator, we ramp compress spherical gold nanoparticle arrays to pressures of tens of GPa, demonstrating pressure-driven assembly beyond the quasi-static regime of the diamond anvil cell. Our dynamic magnetic ramp compression approach produces smooth, shockless (that is, isentropic) one-dimensional loading with low-temperature states suitable for nanostructure synthesis. Transmission electron microscopy clearly establishes that various gold architectures are formed through compressive mesoscale coalescences of spherical gold nanoparticles, which is further confirmed by in-situ synchrotron X-ray studies and large-scale simulation. This nanofabrication approach applies magnetically driven uniaxial ramp compression to mimic established embossing and imprinting processes, but at ultra-short (nanosecond) timescales.

Superfast assembly and synthesis of gold nanostructures using nanosecond low-temperature compression via magnetic pulsed power.

PubMed

Li, Binsong; Bian, Kaifu; Lane, J Matthew D; Salerno, K Michael; Grest, Gary S; Ao, Tommy; Hickman, Randy; Wise, Jack; Wang, Zhongwu; Fan, Hongyou

2017-03-16

Gold nanostructured materials exhibit important size- and shape-dependent properties that enable a wide variety of applications in photocatalysis, nanoelectronics and phototherapy. Here we show the use of superfast dynamic compression to synthesize extended gold nanostructures, such as nanorods, nanowires and nanosheets, with nanosecond coalescence times. Using a pulsed power generator, we ramp compress spherical gold nanoparticle arrays to pressures of tens of GPa, demonstrating pressure-driven assembly beyond the quasi-static regime of the diamond anvil cell. Our dynamic magnetic ramp compression approach produces smooth, shockless (that is, isentropic) one-dimensional loading with low-temperature states suitable for nanostructure synthesis. Transmission electron microscopy clearly establishes that various gold architectures are formed through compressive mesoscale coalescences of spherical gold nanoparticles, which is further confirmed by in-situ synchrotron X-ray studies and large-scale simulation. This nanofabrication approach applies magnetically driven uniaxial ramp compression to mimic established embossing and imprinting processes, but at ultra-short (nanosecond) timescales.

Superfast assembly and synthesis of gold nanostructures using nanosecond low-temperature compression via magnetic pulsed power

PubMed Central

Li, Binsong; Bian, Kaifu; Lane, J. Matthew D.; Salerno, K. Michael; Grest, Gary S.; Ao, Tommy; Hickman, Randy; Wise, Jack; Wang, Zhongwu; Fan, Hongyou

2017-01-01

Gold nanostructured materials exhibit important size- and shape-dependent properties that enable a wide variety of applications in photocatalysis, nanoelectronics and phototherapy. Here we show the use of superfast dynamic compression to synthesize extended gold nanostructures, such as nanorods, nanowires and nanosheets, with nanosecond coalescence times. Using a pulsed power generator, we ramp compress spherical gold nanoparticle arrays to pressures of tens of GPa, demonstrating pressure-driven assembly beyond the quasi-static regime of the diamond anvil cell. Our dynamic magnetic ramp compression approach produces smooth, shockless (that is, isentropic) one-dimensional loading with low-temperature states suitable for nanostructure synthesis. Transmission electron microscopy clearly establishes that various gold architectures are formed through compressive mesoscale coalescences of spherical gold nanoparticles, which is further confirmed by in-situ synchrotron X-ray studies and large-scale simulation. This nanofabrication approach applies magnetically driven uniaxial ramp compression to mimic established embossing and imprinting processes, but at ultra-short (nanosecond) timescales. PMID:28300067

Magnetic structure of the swedenborgite CaBa (Co3Fe ) O7 derived by unpolarized neutron diffraction and spherical neutron polarimetry

NASA Astrophysics Data System (ADS)

Qureshi, N.; Díaz, M. T. Fernández; Chapon, L. C.; Senyshyn, A.; Schweika, W.; Valldor, M.

2018-02-01

We present a study that combines polarized and unpolarized neutrons to derive the magnetic structure of the swedenborgite compound CaBa (Co3Fe ) O7. Integrated intensities from a standard neutron diffraction experiment and polarization matrices from spherical neutron polarimetry have been simultaneously analyzed revealing a complex order, which differs from the usual spin configurations on a kagome lattice. We find that the magnetic structure is well described by a combination of two one-dimensional representations corresponding to the magnetic superspace symmetry P 21' , and it consists of spins rotating around an axis close to the [110] direction. Due to the propagation vector q =(1/3 00 ) , this modulation has cycloidal and helicoidal character rendering this system a potential multiferroic. The resulting spin configuration can be mapped onto the classical √{3 }×√{3 } structure of a kagome lattice, and it indicates an important interplay between the kagome and the triangular layers of the crystal structure.