New method to design stellarator coils without the winding surface

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

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao

Finding an easy-to-build coils set has been a critical issue for stellarator design for decades. Conventional approaches assume a toroidal 'winding' surface, but a poorly chosen winding surface can unnecessarily constrain the coil optimization algorithm, This article presents a new method to design coils for stellarators. Each discrete coil is represented as an arbitrary, closed, one-dimensional curve embedded in three-dimensional space. A target function to be minimized that includes both physical requirements and engineering constraints is constructed. The derivatives of the target function with respect to the parameters describing the coil geometries and currents are calculated analytically. A numerical code,more » named flexible optimized coils using space curves (FOCUS), has been developed. Furthermore, applications to a simple stellarator configuration, W7-X and LHD vacuum fields are presented.« less

Strings in bubbling geometries and dual Wilson loop correlators

NASA Astrophysics Data System (ADS)

Aguilera-Damia, Jeremías; Correa, Diego H.; Fucito, Francesco; Giraldo-Rivera, Victor I.; Morales, Jose F.; Pando Zayas, Leopoldo A.

2017-12-01

We consider a fundamental string in a bubbling geometry of arbitrary genus dual to a half-supersymmetric Wilson loop in a general large representation R of the SU( N) gauge group in N=4 Supersymmetric Yang-Mills. We demonstrate, under some mild conditions, that the minimum value of the string classical action for a bubbling geometry of arbitrary genus precisely matches the correlator of a Wilson loop in the fundamental representation and one in a general large representation. We work out the case in which the large representation is given by a rectangular Young tableau, corresponding to a genus one bubbling geometry, explicitly. We also present explicit results in the field theory for a correlator of two Wilson loops: a large one in an arbitrary representation and a "small" one in the fundamental, totally symmetric or totally antisymmetric representation.

Strings in bubbling geometries and dual Wilson loop correlators

DOE PAGES

Aguilera-Damia, Jeremias; Correa, Diego H.; Fucito, Francesco; ...

2017-12-20

We consider a fundamental string in a bubbling geometry of arbitrary genus dual to a half-supersymmetric Wilson loop in a general large representation R of the SU(N) gauge group in N = 4 Supersymmetric Yang-Mills. We demonstrate, under some mild conditions, that the minimum value of the string classical action for a bubbling geometry of arbitrary genus precisely matches the correlator of a Wilson loop in the fundamental representation and one in a general large representation. We work out the case in which the large representation is given by a rectangular Young tableau, corresponding to a genus one bubbling geometry,more » explicitly. Lastly, we also present explicit results in the field theory for a correlator of two Wilson loops: a large one in an arbitrary representation and a “small” one in the fundamental, totally symmetric or totally antisymmetric representation.« less

Strings in bubbling geometries and dual Wilson loop correlators

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

Aguilera-Damia, Jeremias; Correa, Diego H.; Fucito, Francesco

We consider a fundamental string in a bubbling geometry of arbitrary genus dual to a half-supersymmetric Wilson loop in a general large representation R of the SU(N) gauge group in N = 4 Supersymmetric Yang-Mills. We demonstrate, under some mild conditions, that the minimum value of the string classical action for a bubbling geometry of arbitrary genus precisely matches the correlator of a Wilson loop in the fundamental representation and one in a general large representation. We work out the case in which the large representation is given by a rectangular Young tableau, corresponding to a genus one bubbling geometry,more » explicitly. Lastly, we also present explicit results in the field theory for a correlator of two Wilson loops: a large one in an arbitrary representation and a “small” one in the fundamental, totally symmetric or totally antisymmetric representation.« less

The Use of Langmuir Probes in Non-Maxwellian Space Plasmas

NASA Technical Reports Server (NTRS)

Hoegy, Walter R.; Brace, Larry H.

1998-01-01

Disturbance of the Maxwellian plasma may occur in the vicinity of a spacecraft due to photoemission, interactions between the spacecraft and thermospheric gases, or electron emissions from other devices on the spacecraft. Significant non-maxwellian plasma distributions may also occur in nature as a mixture of ionospheric and magnetospheric plasmas or secondaries produced by photoionization in the thermosphere or auroral precipitation. The general formulas for current collection (volt-ampere curves) by planar, cylindrical, and spherical Langmuir probes in isotropic and anisotropic non-maxwellian plasmas are examined. Examples are given of how one may identify and remove the non-maxwellian components in the Langmuir probe current to permit the ionospheric parameters to be determined. Theoretical volt-ampere curves presented for typical examples of non-maxwellian distributions include: two-temperature plasmas and a thermal plasma with an energetic electron beam. If the non-ionospheric electrons are Maxwellian at a temperature distinct from that of the ionosphere electrons, the volt-ampere curves can be fitted directly to obtain the temperatures and densities of both electron components without resorting to differenting the current. For an arbitrary isotropic distribution, the current for retarded particles is shown to be identical for the three geometries. For anisotropic distributions, the three probe geometries are not equally suited for measuring the ionospheric electron temperature and density or for determining the distribution function in the presence of non-maxwellian back-round electrons.

Covariant effective action for a Galilean invariant quantum Hall system

NASA Astrophysics Data System (ADS)

Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.

2016-09-01

We construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of curved Galilean spacetimes, including torsion and a gravitational field, allowing us to study charge, energy, stress and mass currents within a unified framework. A shift symmetry specific to single constituent theories constraints the effective action to couple to an effective background gauge field and spin connection that is solved for by a self-consistent equation, providing a manifestly covariant extension of Hoyos and Son's improvement terms to arbitrary order in m.

Newton-Cartan gravity and torsion

NASA Astrophysics Data System (ADS)

Bergshoeff, Eric; Chatzistavrakidis, Athanasios; Romano, Luca; Rosseel, Jan

2017-10-01

We compare the gauging of the Bargmann algebra, for the case of arbitrary torsion, with the result that one obtains from a null-reduction of General Relativity. Whereas the two procedures lead to the same result for Newton-Cartan geometry with arbitrary torsion, the null-reduction of the Einstein equations necessarily leads to Newton-Cartan gravity with zero torsion. We show, for three space-time dimensions, how Newton-Cartan gravity with arbitrary torsion can be obtained by starting from a Schrödinger field theory with dynamical exponent z = 2 for a complex compensating scalar and next coupling this field theory to a z = 2 Schrödinger geometry with arbitrary torsion. The latter theory can be obtained from either a gauging of the Schrödinger algebra, for arbitrary torsion, or from a null-reduction of conformal gravity.

Dynamics of the Rydberg state population of slow highly charged ions impinging a solid surface at arbitrary collision geometry

NASA Astrophysics Data System (ADS)

Nedeljković, N. N.; Majkić, M. D.; Božanić, D. K.; Dojčilović, R. J.

2016-06-01

We consider the population dynamics of the intermediate Rydberg states of highly charged ions (core charge Z\\gg 1, principal quantum number {n}{{A}}\\gg 1) interacting with solid surfaces at arbitrary collision geometry. The recently developed resonant two-state vector model for the grazing incidence (2012 J. Phys. B: At. Mol. Opt. Phys. 45 215202) is extended to the quasi-resonant case and arbitrary angle of incidence. According to the model, the population probabilities depend both on the projectile parallel and perpendicular velocity components, in a complementary way. A cascade neutralization process for {{{Xe}}}Z+ ions, for Z=15{--}45, interacting with a conductive-surface is considered by taking into account the population dynamics. For an arbitrary collision geometry and given range of ionic velocities, a micro-staircase model for the simultaneous calculation of the kinetic energy gain and the charge state of the ion in front of the surface is proposed. The relevance of the obtained results for the explanation of the formation of nanostructures on solid surfaces by slow highly charged ions for normal incidence geometry is briefly discussed.

(2+1)-dimensional stars

NASA Astrophysics Data System (ADS)

Lubo, M.; Rooman, M.; Spindel, Ph.

1999-02-01

We investigate, in the framework of (2+1)-dimensional gravity, stationary rotationally symmetric gravitational sources of the perfect fluid type, embedded in a space of an arbitrary cosmological constant. We show that the matching conditions between the interior and exterior geometries imply restrictions on the physical parameters of the solutions. In particular, imposing finite sources and the absence of closed timelike curves privileges negative values of the cosmological constant, yielding exterior vacuum geometries of rotating black hole type. In the special case of static sources, we prove the complete integrability of the field equations and show that the sources' masses are bounded from above and, for a vanishing cosmological constant, generally equal to 1. We also discuss and illustrate the stationary configurations by explicitly solving the field equations for constant mass-energy densities. If the pressure vanishes, we recover as interior geometries Gödel-like metrics defined on causally well behaved domains, but with unphysical values of the mass to angular momentum ratio. The introduction of pressure in the sources cures the latter problem and leads to physically more relevant models.

Nonreciprocal lasing in topological cavities of arbitrary geometries

NASA Astrophysics Data System (ADS)

Bahari, Babak; Ndao, Abdoulaye; Vallini, Felipe; El Amili, Abdelkrim; Fainman, Yeshaiahu; Kanté, Boubacar

2017-11-01

Resonant cavities are essential building blocks governing many wave-based phenomena, but their geometry and reciprocity fundamentally limit the integration of optical devices. We report, at telecommunication wavelengths, geometry-independent and integrated nonreciprocal topological cavities that couple stimulated emission from one-way photonic edge states to a selected waveguide output with an isolation ratio in excess of 10 decibels. Nonreciprocity originates from unidirectional edge states at the boundary between photonic structures with distinct topological invariants. Our experimental demonstration of lasing from topological cavities provides the opportunity to develop complex topological circuitry of arbitrary geometries for the integrated and robust generation and transport of photons in classical and quantum regimes.

Accurate Solution of Multi-Region Continuum Biomolecule Electrostatic Problems Using the Linearized Poisson-Boltzmann Equation with Curved Boundary Elements

PubMed Central

Altman, Michael D.; Bardhan, Jaydeep P.; White, Jacob K.; Tidor, Bruce

2009-01-01

We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson–Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Finally, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as non-rigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry, such as charge optimization or component analysis, can be computed to high accuracy using the presented BEM approach, in compute times comparable to traditional finite-difference methods. PMID:18567005

Three-dimensional curved grid finite-difference modelling for non-planar rupture dynamics

NASA Astrophysics Data System (ADS)

Zhang, Zhenguo; Zhang, Wei; Chen, Xiaofei

2014-11-01

In this study, we present a new method for simulating the 3-D dynamic rupture process occurring on a non-planar fault. The method is based on the curved-grid finite-difference method (CG-FDM) proposed by Zhang & Chen and Zhang et al. to simulate the propagation of seismic waves in media with arbitrary irregular surface topography. While keeping the advantages of conventional FDM, that is computational efficiency and easy implementation, the CG-FDM also is flexible in modelling the complex fault model by using general curvilinear grids, and thus is able to model the rupture dynamics of a fault with complex geometry, such as oblique dipping fault, non-planar fault, fault with step-over, fault branching, even if irregular topography exists. The accuracy and robustness of this new method have been validated by comparing with the previous results of Day et al., and benchmarks for rupture dynamics simulations. Finally, two simulations of rupture dynamics with complex fault geometry, that is a non-planar fault and a fault rupturing a free surface with topography, are presented. A very interesting phenomenon was observed that topography can weaken the tendency for supershear transition to occur when rupture breaks out at a free surface. Undoubtedly, this new method provides an effective, at least an alternative, tool to simulate the rupture dynamics of a complex non-planar fault, and can be applied to model the rupture dynamics of a real earthquake with complex geometry.

Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge.

PubMed

Xuan, Xiangchun; Li, Dongqing

2005-09-01

General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale varpi defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz-Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Omega defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.

Noninertial Multirelativity

NASA Astrophysics Data System (ADS)

Smarandache, Florentin

2012-10-01

We firstly propose an extension of Einstein's thought experiment with atomic clocks of the Special Theory of Relativity: considering non-constant accelerations and arbitrary 3D-curves for both a particle's speed and trajectory inside the rocket and respectively the rocket's speed and trajectory. And secondly we propose as research multiple reference frames F1, F2, , Fn moving on respectively arbitrary 3D-curves C1, C2, , Cn with respectively arbitrary non-constant accelerations a1, a2, , an and respectively initial velocities v1, v2, , vn. The reference frame Fi is moving with a nonconstant acceleration ai and initial velocity vi on a 3D-curve Ci with respect to another reference frame Fi+1 (where 1 <= i <= n-1).

Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques

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

Rodriguez, Alejandro; Ibanescu, Mihai; Joannopoulos, J. D.

2007-09-15

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustratemore » our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising nonmonotonic ''lateral'' force from the walls.« less

Visualizing the Zero-Potential Line of Bipolar Electrodes with Arbitrary Geometry.

PubMed

Li, Meng; Liu, Shasha; Jiang, Yingyan; Wang, Wei

2018-06-05

In a typical bipolar electrochemistry (BPE) configuration, voltage applied between the two driving electrodes induced a potential drop through solution filled in the microchannel, resulting in an interfacial potential difference between solution and BPE varied along the BPE. In the present work, we employed a recently developed plasmonic imaging technique to map the distribution of surface potential of bipolar electrodes with various geometries including round, triangle, hexagon, star, and rhombus shapes under the nonfaradaic charging process, from which the line of zero potential (LZP) was visualized and determined. We further investigated the dependence of LZP on electrode geometry and the distribution of external electric field and explained the experimental results with a charge balance mechanism. The triangular and star-shaped BPEs show quite different LZP features from the other ones with symmetrical geometry. These experimentally obtained potential distributions are all in good agreement with electromagnetic simulations. Finally, the line of zero overpotential (LZO) of the triangular-shaped BPE under faradaic reactions were investigated. The results confirm the shift of LZO when faradaic reactions occurred at the corresponding ends of BPE. The present work demonstrates the first experimental capability to map the potential distribution of BPE with arbitrary geometry under an arbitrary driving field. It is anticipated to help the design and optimization on the geometry of electrodes and microchannels with implications for boosting their applications in chemical sensing and materials synthesis.

Aspects géométriques et intégrables des modèles de matrices aléatoires

NASA Astrophysics Data System (ADS)

Marchal, Olivier

2010-12-01

This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of integrable systems. The variety of these applications shows why matrix models are important from a mathematical point of view. First, the thesis will focus on the study of the merging of two intervals of the eigenvalues density near a singular point. Specifically, we will show why this special limit gives universal equations from the Painlevé II hierarchy of integrable systems theory. Then, following the approach of (bi) orthogonal polynomials introduced by Mehta to compute partition functions, we will find Riemann-Hilbert and isomonodromic problems connected to matrix models, making the link with the theory of Jimbo, Miwa and Ueno. In particular, we will describe how the hermitian two-matrix models provide a degenerate case of Jimbo-Miwa-Ueno's theory that we will generalize in this context. Furthermore, the loop equations method, with its central notions of spectral curve and topological expansion, will lead to the symplectic invariants of algebraic geometry recently proposed by Eynard and Orantin. This last point will be generalized to the case of non-hermitian matrix models (arbitrary beta) paving the way to "quantum algebraic geometry" and to the generalization of symplectic invariants to "quantum curves". Finally, this set up will be applied to combinatorics in the context of topological string theory, with the explicit computation of an hermitian random matrix model enumerating the Gromov-Witten invariants of a toric Calabi-Yau threefold.

Propagation of waves from an arbitrary shaped surface-A generalization of the Fresnel diffraction integral

NASA Astrophysics Data System (ADS)

Feshchenko, R. M.; Vinogradov, A. V.; Artyukov, I. A.

2018-04-01

Using the method of Laplace transform the field amplitude in the paraxial approximation is found in the two-dimensional free space using initial values of the amplitude specified on an arbitrary shaped monotonic curve. The obtained amplitude depends on one a priori unknown function, which can be found from a Volterra first kind integral equation. In a special case of field amplitude specified on a concave parabolic curve the exact solution is derived. Both solutions can be used to study the light propagation from arbitrary surfaces including grazing incidence X-ray mirrors. They can find applications in the analysis of coherent imaging problems of X-ray optics, in phase retrieval algorithms as well as in inverse problems in the cases when the initial field amplitude is sought on a curved surface.

Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains.

PubMed

Nash, Rupert W; Carver, Hywel B; Bernabeu, Miguel O; Hetherington, James; Groen, Derek; Krüger, Timm; Coveney, Peter V

2014-02-01

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002); Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001); Junk and Yang, Phys. Rev. E 72, 066701 (2005)] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

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

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

DOE PAGES

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai; ...

2017-06-29

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

Experiments with BECs in a Painted Potential: Atom SQUID, Matter Wave Bessel Beams, and Matter Wave Circuits

NASA Astrophysics Data System (ADS)

Boshier, Malcolm; Ryu, Changhyun; Blackburn, Paul; Blinova, Alina; Henderson, Kevin

2014-05-01

The painted potential is a time-averaged optical dipole potential which is able to create arbitrary and dynamic two dimensional potentials for Bose Einstein condensates (BECs). This poster reports three recent experiments using this technique. First, we have realized the dc atom SQUID geometry of a BEC in a toroidal trap with two Josephson junctions. We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. Second, we have used free expansion of a rotating toroidal BEC to create matter wave Bessel beams, which are of interest because perfect Bessel beams (plane waves with amplitude profiles described by Bessel functions) propagate without diffraction. Third, we have realized the basic circuit elements necessary to create complex matter wave circuits. We launch BECs at arbitrary velocity along straight waveguides, propagate them around curved waveguides and stadium-shaped waveguide traps, and split them coherently at y-junctions that can also act as switches. Supported by LANL/LDRD.

Ductile-Phase-Toughened Tungsten for Plasma-Facing Materials

NASA Astrophysics Data System (ADS)

Cunningham, Kevin Hawkins

A variety of processing approaches were employed to fabricate ductile-phase-toughened (DPT) tungsten (W) composites. Mechanical testing and analytical modeling were used to guide composite development. This work provides a basis for further development of W composites to be used in structural divertor components of future fusion reactors. W wire was tested in tension, showing significant ductility and strength. Coatings of copper (Cu) or tungsten carbide (WC) were applied to the W wire via electrodeposition and carburization, respectively. Composites were fabricated using spark plasma sintering (SPS) to consolidate W powders together with each type of coated W wire. DPT behavior, e.g. crack arrest and crack bridging, was not observed in three-point bend testing of the sintered composites. A laminate was fabricated by hot pressing W and Cu foils together with W wires, and subsequently tested in tension. This laminate was bonded via hot pressing to thick W plate as a reinforcing layer, and the composite was tested in three-point bending. Crack arrest was observed along with some fiber pullout, but significant transverse cracking in the W plate confounded further fracture toughness analysis. The fracture toughness of thin W plate was measured in three-point bending. W plates were brazed with Cu foils to form a laminate. Crack arrest and crack bridging were observed in three-point bend tests of the laminate, and fracture resistance curves were successfully calculated for this DPT composite. An analytical model of crack bridging was developed using the basis described by Chao in previous work by the group. The model uses the specimen geometry, matrix properties, and the stress-displacement function of a ductile reinforcement ("bridging law") to calculate the fracture resistance curve (R-curve) and load-displacement curve (P-D curve) for any test specimen geometry. The code was also implemented to estimate the bridging law of an arbitrary composite using R-curve data. Finally, a parametric study was performed to quantitatively determine the necessary mechanical properties of useful toughening reinforcements for a DPT W composite. The analytical model has a broad applicability for any DPT material.

Online shaft encoder geometry compensation for arbitrary shaft speed profiles using Bayesian regression

NASA Astrophysics Data System (ADS)

Diamond, D. H.; Heyns, P. S.; Oberholster, A. J.

2016-12-01

The measurement of instantaneous angular speed is being increasingly investigated for its use in a wide range of condition monitoring and prognostic applications. Central to many measurement techniques are incremental shaft encoders recording the arrival times of shaft angular increments. The conventional approach to processing these signals assumes that the angular increments are equidistant. This assumption is generally incorrect when working with toothed wheels and especially zebra tape encoders and has been shown to introduce errors in the estimated shaft speed. There are some proposed methods in the literature that aim to compensate for this geometric irregularity. Some of the methods require the shaft speed to be perfectly constant for calibration, something rarely achieved in practice. Other methods assume the shaft speed to be nearly constant with minor deviations. Therefore existing methods cannot calibrate the entire shaft encoder geometry for arbitrary shaft speeds. The present article presents a method to calculate the shaft encoder geometry for arbitrary shaft speed profiles. The method uses Bayesian linear regression to calculate the encoder increment distances. The method is derived and then tested against simulated and laboratory experiments. The results indicate that the proposed method is capable of accurately determining the shaft encoder geometry for any shaft speed profile.

Lattice Boltzmann Method for 3-D Flows with Curved Boundary

NASA Technical Reports Server (NTRS)

Mei, Renwei; Shyy, Wei; Yu, Dazhi; Luo, Li-Shi

2002-01-01

In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamics applications of the lattice, Boltzmann equation (LBE): (1) Computational stability and accuracy of different lattice Boltzmann models and (2) the treatment of the boundary conditions on curved solid boundaries and their 3-D implementations. Three athermal 3-D LBE models (D3QI5, D3Ql9, and D3Q27) are studied and compared in terms of efficiency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hanel and Met et al. in 2-D is extended to and implemented for 3-D. The convergence, stability, and computational efficiency of the 3-D LBE models with the boundary treatment for curved boundaries were tested in simulations of four 3-D flows: (1) Fully developed flows in a square duct, (2) flow in a 3-D lid-driven cavity, (3) fully developed flows in a circular pipe, and (4) a uniform flow over a sphere. We found that while the fifteen-velocity 3-D (D3Ql5) model is more prone to numerical instability and the D3Q27 is more computationally intensive, the 63Q19 model provides a balance between computational reliability and efficiency. Through numerical simulations, we demonstrated that the boundary treatment for 3-D arbitrary curved geometry has second-order accuracy and possesses satisfactory stability characteristics.

Covariant electrodynamics in linear media: Optical metric

NASA Astrophysics Data System (ADS)

Thompson, Robert T.

2018-03-01

While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance—form invariance under general coordinate transformations, including between accelerating frames—that led to general relativity. Several lines of inquiry over the past two decades, notably the development of metamaterial-based transformation optics, has spurred a greater interest in the role of geometry and space-time covariance for electrodynamics in ponderable media. I develop a generally covariant, coordinate-free framework for electrodynamics in general dielectric media residing in curved background space-times. In particular, I derive a relation for the spatial medium parameters measured by an arbitrary timelike observer. In terms of those medium parameters I derive an explicit expression for the pseudo-Finslerian optical metric of birefringent media and show how it reduces to a pseudo-Riemannian optical metric for nonbirefringent media. This formulation provides a basis for a unified approach to ray and congruence tracing through media in curved space-times that may smoothly vary among positively refracting, negatively refracting, and vacuum.

A spectral-Tchebychev solution for three-dimensional dynamics of curved beams under mixed boundary conditions

NASA Astrophysics Data System (ADS)

Bediz, Bekir; Aksoy, Serdar

2018-01-01

This paper presents the application of the spectral-Tchebychev (ST) technique for solution of three-dimensional dynamics of curved beams/structures having variable and arbitrary cross-section under mixed boundary conditions. To accurately capture the vibrational behavior of curved structures, a three-dimensional (3D) solution approach is required since these structures generally exhibit coupled motions. In this study, the integral boundary value problem (IBVP) governing the dynamics of the curved structures is found using extended Hamilton's principle where the strain energy is expressed using 3D linear elasticity equation. To solve the IBVP numerically, the 3D spectral Tchebychev (3D-ST) approach is used. To evaluate the integral and derivative operations defined by the IBVP and to render the complex geometry into an equivalent straight beam with rectangular cross-section, a series of coordinate transformations are applied. To validate and assess the performance of the presented solution approach, two case studies are performed: (i) curved beam with rectangular cross-section, (ii) curved and pretwisted beam with airfoil cross-section. In both cases, the results (natural frequencies and mode shapes) are also found using a finite element (FE) solution approach. It is shown that the difference in predicted natural frequencies are less than 1%, and the mode shapes are in excellent agreement based on the modal assurance criteria (MAC) analyses; however, the presented spectral-Tchebychev solution approach significantly reduces the computational burden. Therefore, it can be concluded that the presented solution approach can capture the 3D vibrational behavior of curved beams as accurately as an FE solution, but for a fraction of the computational cost.

A linear shock cell model for jets of arbitrary exit geometry

NASA Technical Reports Server (NTRS)

Morris, P. J.; Bhat, T. R. S.; Chen, G.

1989-01-01

The shock cell structures of single supersonic non-ideally expanded jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. This formulation enables the calculations to be performed only on the vortex sheet. This permits the efficient and convenient study of complicated jet geometries. Results are given for circular, elliptic and rectangular jets and the results are compared with analysis and experiment. The agreement between the predictions and measurements is very good but depends on the assumptions made to predict the geometry of the fully expanded jet. A finite diffference technique is used to examine the effect of finite mixing layer thickness for a single jet. The finite thickness of the mixing layer is found to decrease the shock spacing by approximately 20 percent over the length of the jet potential core.

Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains

NASA Astrophysics Data System (ADS)

Nash, Rupert W.; Carver, Hywel B.; Bernabeu, Miguel O.; Hetherington, James; Groen, Derek; Krüger, Timm; Coveney, Peter V.

2014-02-01

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002), 10.1063/1.1471914; Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001), 10.1063/1.1399290; Junk and Yang, Phys. Rev. E 72, 066701 (2005), 10.1103/PhysRevE.72.066701] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

Dynamic mapping of conical intersection seams: A general method for incorporating the geometric phase in adiabatic dynamics in polyatomic systems

NASA Astrophysics Data System (ADS)

Xie, Changjian; Malbon, Christopher L.; Yarkony, David R.; Guo, Hua

2017-07-01

The incorporation of the geometric phase in single-state adiabatic dynamics near a conical intersection (CI) seam has so far been restricted to molecular systems with high symmetry or simple model Hamiltonians. This is due to the fact that the ab initio determined derivative coupling (DC) in a multi-dimensional space is not curl-free, thus making its line integral path dependent. In a recent work [C. L. Malbon et al., J. Chem. Phys. 145, 234111 (2016)], we proposed a new and general approach based on an ab initio determined diabatic representation consisting of only two electronic states, in which the DC is completely removable, so that its line integral is path independent in the simply connected domains that exclude the CI seam. Then with the CIs included, the line integral of the single-valued DC can be used to construct the complex geometry-dependent phase needed to exactly eliminate the double-valued character of the real-valued adiabatic electronic wavefunction. This geometry-dependent phase gives rise to a vector potential which, when included in the adiabatic representation, rigorously accounts for the geometric phase in a system with an arbitrary locus of the CI seam and an arbitrary number of internal coordinates. In this work, we demonstrate this approach in a three-dimensional treatment of the tunneling facilitated dissociation of the S1 state of phenol, which is affected by a Cs symmetry allowed but otherwise accidental seam of CI. Here, since the space is three-dimensional rather than two-dimensional, the seam is a curve rather than a point. The nodal structure of the ground state vibronic wavefunction is shown to map out the seam of CI.

Time Domain Version of the Uniform Geometrical Theory of Diffraction

NASA Astrophysics Data System (ADS)

Rousseau, Paul R.

1995-01-01

A time domain (TD) version of the uniform geometrical theory of diffraction which is referred to as the TD-UTD is developed to analyze the transient electromagnetic scattering from perfectly conducting objects that are large in terms of pulse width. In particular, the scattering from a perfectly conducting arbitrary curved wedge and an arbitrary smooth convex surface are treated in detail. Note that the canonical geometries of a circular cylinder and a sphere are special cases of the arbitrary smooth convex surface. These TD -UTD solutions are obtained in the form of relatively simple analytical expressions valid for early to intermediate times. The geometries treated here can be used to build up a transient solution to more complex radiating objects via space-time localization, in exactly the same way as is done by invoking spatial localization properties in the frequency domain UTD. The TD-UTD provides the response due to an excitation of a general astigmatic impulsive wavefront with any polarization. This generalized impulse response may then be convolved with other excitation time pulses, to find even more general solutions due to other excitation pulses. Since the TD-UTD uses the same rays as the frequency domain UTD, it provides a simple picture for transient radiation or scattering and is therefore just as physically appealing as the frequency domain UTD. The formulation of an analytic time transform (ATT), which produces an analytic time signal given a frequency response function, is given here. This ATT is used because it provides a very efficient method of inverting the asymptotic high frequency UTD representations to obtain the corresponding TD-UTD expressions even when there are special UTD transition functions which may not be well behaved at the low frequencies; also, using the ATT avoids the difficulties associated with the inversion of UTD ray fields that traverse line or smooth caustics. Another useful aspect of the ATT is the ability to perform an efficient convolution with a broad class of excitation pulse functions, where the frequency response of the excitation function must be expressed as a summation of complex exponential functions.

Algebro-geometric approach for a centrally extended Uq[sl(2|2)] R-matrix

NASA Astrophysics Data System (ADS)

Martins, M. J.

2017-04-01

In this paper we investigate the algebraic geometric nature of a solution of the Yang-Baxter equation based on the quantum deformation of the centrally extended sl (2 | 2) superalgebra proposed by Beisert and Koroteev [1]. We derive an alternative representation for the R-matrix in which the matrix elements are given in terms of rational functions depending on weights sited on a degree six surface. For generic gauge the weights geometry are governed by a genus one ruled surface while for a symmetric gauge choice the weights lie instead on a genus five curve. We have written down the polynomial identities satisfied by the R-matrix entries needed to uncover the corresponding geometric properties. For arbitrary gauge the R-matrix geometry is argued to be birational to the direct product CP1 ×CP1 × A where A is an Abelian surface. For the symmetric gauge we present evidences that the geometric content is that of a surface of general type lying on the so-called Severi line with irregularity two and geometric genus nine. We discuss potential geometric degenerations when the two free couplings are restricted to certain one-dimensional subspaces.

Acoustic emission source location in composite structure by Voronoi construction using geodesic curve evolution.

PubMed

Gangadharan, R; Prasanna, G; Bhat, M R; Murthy, C R L; Gopalakrishnan, S

2009-11-01

Conventional analytical/numerical methods employing triangulation technique are suitable for locating acoustic emission (AE) source in a planar structure without structural discontinuities. But these methods cannot be extended to structures with complicated geometry, and, also, the problem gets compounded if the material of the structure is anisotropic warranting complex analytical velocity models. A geodesic approach using Voronoi construction is proposed in this work to locate the AE source in a composite structure. The approach is based on the fact that the wave takes minimum energy path to travel from the source to any other point in the connected domain. The geodesics are computed on the meshed surface of the structure using graph theory based on Dijkstra's algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first intersection point of these waves, one can get the AE source location. In this work, the geodesic approach is shown more suitable for a practicable source location solution in a composite structure with arbitrary surface containing finite discontinuities. Experiments have been conducted on composite plate specimens of simple and complex geometry to validate this method.

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces.

PubMed

Hornikx, Maarten; Dragna, Didier

2015-07-01

The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions

NASA Astrophysics Data System (ADS)

Demirchian, Hovhannes; Nersessian, Armen; Sadeghian, Saeedeh; Sheikh-Jabbari, M. M.

2018-05-01

We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed by Hakobyan et al. [Phys. Lett. B 772, 586 (2017)., 10.1016/j.physletb.2017.07.028]. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals and discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider a near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.

Electrode-shaping for the excitation and detection of permitted arbitrary modes in arbitrary geometries in piezoelectric resonators.

PubMed

Pulskamp, Jeffrey S; Bedair, Sarah S; Polcawich, Ronald G; Smith, Gabriel L; Martin, Joel; Power, Brian; Bhave, Sunil A

2012-05-01

This paper reports theoretical analysis and experimental results on a numerical electrode shaping design technique that permits the excitation of arbitrary modes in arbitrary geometries for piezoelectric resonators, for those modes permitted to exist by the nonzero piezoelectric coefficients and electrode configuration. The technique directly determines optimal electrode shapes by assessing the local suitability of excitation and detection electrode placement on two-port resonators without the need for iterative numerical techniques. The technique is demonstrated in 61 different electrode designs in lead zirconate titanate (PZT) thin film on silicon RF micro electro-mechanical system (MEMS) plate, beam, ring, and disc resonators for out-of-plane flexural and various contour modes up to 200 MHz. The average squared effective electromechanical coupling factor for the designs was 0.54%, approximately equivalent to the theoretical maximum value of 0.53% for a fully electroded length-extensional mode beam resonator comprised of the same composite. The average improvement in S(21) for the electrode-shaped designs was 14.6 dB with a maximum improvement of 44.3 dB. Through this piezoelectric electrodeshaping technique, 95% of the designs showed a reduction in insertion loss.

Universal inverse design of surfaces with thin nematic elastomer sheets.

PubMed

Aharoni, Hillel; Xia, Yu; Zhang, Xinyue; Kamien, Randall D; Yang, Shu

2018-06-21

Programmable shape-shifting materials can take different physical forms to achieve multifunctionality in a dynamic and controllable manner. Although morphing a shape from 2D to 3D via programmed inhomogeneous local deformations has been demonstrated in various ways, the inverse problem-finding how to program a sheet in order for it to take an arbitrary desired 3D shape-is much harder yet critical to realize specific functions. Here, we address this inverse problem in thin liquid crystal elastomer (LCE) sheets, where the shape is preprogrammed by precise and local control of the molecular orientation of the liquid crystal monomers. We show how blueprints for arbitrary surface geometries can be generated using approximate numerical methods and how local extrinsic curvatures can be generated to assist in properly converting these geometries into shapes. Backed by faithfully alignable and rapidly lockable LCE chemistry, we precisely embed our designs in LCE sheets using advanced top-down microfabrication techniques. We thus successfully produce flat sheets that, upon thermal activation, take an arbitrary desired shape, such as a face. The general design principles presented here for creating an arbitrary 3D shape will allow for exploration of unmet needs in flexible electronics, metamaterials, aerospace and medical devices, and more.

Selective Mode Focusing in a Plate of Arbitrary Shape Applying Time Reversal Mirrors

DOE PAGES

Payan, Cedric; Remillieux, Marcel C.; Bas, Pierre-Yves Le; ...

2017-11-01

In this study, a time reversal mirror is used to remotely focus symmetric or antisymmetric modes in a plate of arbitrary shape without the need of precise knowledge about material properties and geometry. The addition or subtraction of the forward motions recorded by two laser beams located on both sides of the plate allows, respectively, to focus a symmetric or an antisymmetric mode. The concept is validated using experimental and numerical analysis on an aluminum plate of complex machined geometry which exhibits various thicknesses as well as a bi-materials zone. Finally, the limitations and possible ways to overcome them aremore » then presented.« less

Fast immersed interface Poisson solver for 3D unbounded problems around arbitrary geometries

NASA Astrophysics Data System (ADS)

Gillis, T.; Winckelmans, G.; Chatelain, P.

2018-02-01

We present a fast and efficient Fourier-based solver for the Poisson problem around an arbitrary geometry in an unbounded 3D domain. This solver merges two rewarding approaches, the lattice Green's function method and the immersed interface method, using the Sherman-Morrison-Woodbury decomposition formula. The method is intended to be second order up to the boundary. This is verified on two potential flow benchmarks. We also further analyse the iterative process and the convergence behavior of the proposed algorithm. The method is applicable to a wide range of problems involving a Poisson equation around inner bodies, which goes well beyond the present validation on potential flows.

Selective Mode Focusing in a Plate of Arbitrary Shape Applying Time Reversal Mirrors

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

Payan, Cedric; Remillieux, Marcel C.; Bas, Pierre-Yves Le

In this study, a time reversal mirror is used to remotely focus symmetric or antisymmetric modes in a plate of arbitrary shape without the need of precise knowledge about material properties and geometry. The addition or subtraction of the forward motions recorded by two laser beams located on both sides of the plate allows, respectively, to focus a symmetric or an antisymmetric mode. The concept is validated using experimental and numerical analysis on an aluminum plate of complex machined geometry which exhibits various thicknesses as well as a bi-materials zone. Finally, the limitations and possible ways to overcome them aremore » then presented.« less

Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)

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

Dolbow, John; Zhang, Ziyu; Spencer, Benjamin

Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside ofmore » the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.« less

Accuracy-preserving source term quadrature for third-order edge-based discretization

NASA Astrophysics Data System (ADS)

Nishikawa, Hiroaki; Liu, Yi

2017-09-01

In this paper, we derive a family of source term quadrature formulas for preserving third-order accuracy of the node-centered edge-based discretization for conservation laws with source terms on arbitrary simplex grids. A three-parameter family of source term quadrature formulas is derived, and as a subset, a one-parameter family of economical formulas is identified that does not require second derivatives of the source term. Among the economical formulas, a unique formula is then derived that does not require gradients of the source term at neighbor nodes, thus leading to a significantly smaller discretization stencil for source terms. All the formulas derived in this paper do not require a boundary closure, and therefore can be directly applied at boundary nodes. Numerical results are presented to demonstrate third-order accuracy at interior and boundary nodes for one-dimensional grids and linear triangular/tetrahedral grids over straight and curved geometries.

Equivalent-circuit model for stacked slot-based 2D periodic arrays of arbitrary geometry for broadband analysis

NASA Astrophysics Data System (ADS)

Astorino, Maria Denise; Frezza, Fabrizio; Tedeschi, Nicola

2018-03-01

The analysis of the transmission and reflection spectra of stacked slot-based 2D periodic structures of arbitrary geometry and the ability to devise and control their electromagnetic responses have been a matter of extensive research for many decades. The purpose of this paper is to develop an equivalent Π circuit model based on the transmission-line theory and Floquet harmonic interactions, for broadband and short longitudinal period analysis. The proposed circuit model overcomes the limits of identical and symmetrical configurations imposed by the even/odd excitation approach, exploiting both the circuit topology of a single 2D periodic array of apertures and the ABCD matrix formalism. The transmission spectra obtained through the equivalent-circuit model have been validated by comparison with full-wave simulations carried out with a finite-element commercial electromagnetic solver. This allowed for a physical insight into the spectral and angular responses of multilayer devices with arbitrary aperture shapes, guaranteeing a noticeable saving of computational resources.

Representation of Ice Geometry by Parametric Functions: Construction of Approximating NURBS Curves and Quantification of Ice Roughness--Year 1: Approximating NURBS Curves

NASA Technical Reports Server (NTRS)

Dill, Loren H.; Choo, Yung K. (Technical Monitor)

2004-01-01

Software was developed to construct approximating NURBS curves for iced airfoil geometries. Users specify a tolerance that determines the extent to which the approximating curve follows the rough ice. The user can therefore smooth the ice geometry in a controlled manner, thereby enabling the generation of grids suitable for numerical aerodynamic simulations. Ultimately, this ability to smooth the ice geometry will permit studies of the effects of smoothing upon the aerodynamics of iced airfoils. The software was applied to several different types of iced airfoil data collected in the Icing Research Tunnel at NASA Glenn Research Center, and in all cases was found to efficiently generate suitable approximating NURBS curves. This method is an improvement over the current "control point formulation" of Smaggice (v.1.2). In this report, we present the relevant theory of approximating NURBS curves and discuss typical results of the software.

Geometry of Thin Nematic Elastomer Sheets

NASA Astrophysics Data System (ADS)

Aharoni, Hillel; Sharon, Eran; Kupferman, Raz

A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this talk we describe the intrinsic geometry of such a sheet, and derive an expression for the metric induced by general smooth nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry. We provide an explicit analytical recipe for constructing any surface of revolution using this method. We demonstrate how the design of an arbitrary 2D geometry is accessible using approximate numerical methods.

Beam shaping of laser diode radiation by waveguides with arbitrary cladding geometry written with fs-laser radiation.

PubMed

Beckmann, Dennis; Schnitzler, Daniel; Schaefer, Dagmar; Gottmann, Jens; Kelbassa, Ingomar

2011-12-05

Waveguides with arbitrary cross sections are written in the volume of Al(2)O(3)-crystals using tightly focused femtosecond laser radiation. Utilizing a scanning system with large numerical aperture, complex cladding geometries are realized with a precision around 0.5 µm and a scanning speed up to 100 mm/s. Individual beam and mode shaping of laser diode radiation is demonstrated by varying the design of the waveguide cladding. The influence of the writing parameters on the waveguide properties are investigated resulting in a numerical aperture of the waveguides in the range of 0.1. This direct laser writing technique enables optical devices which could possibly replace bulky beam shaping setups with an integrated solution.

Influence of geometry variations on the gravitational focusing of timelike geodesic congruences

NASA Astrophysics Data System (ADS)

Seriu, Masafumi

2015-10-01

We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard Raychaudhuri-type equations due to the geodesic shifts and an equation describing the geodesic shifts due to the geometry variations. In this framework, the geometry variations, which can be chosen arbitrarily, serve as probes to investigate the gravitational contraction processes from various angles. We apply the obtained framework to the case of conformal geometry variations, characterized by an arbitrary function f (x ), and see that the formulas get simplified to a great extent. We investigate the response of the convergence properties of geodesics in the latest phase of gravitational contractions by restricting the class of conformal geometry variations to the one satisfying the strong energy condition. We then find out that in the final stage, f and D .D f control the overall contraction behavior and that the contraction rate gets larger when f is negative and |f | is so large as to overwhelm |D .D f |. (Here D .D is the Laplacian operator on the spatial hypersurfaces orthogonal to the geodesic congruence in concern.) To get more concrete insights, we also apply the framework to the time-reversed Friedmann-Robertson-Walker model as the simplest case of the singularity formations.

Diffusion from a line source

NASA Technical Reports Server (NTRS)

Burns, R. E.

1973-01-01

The problem with predicting pollutant diffusion from a line source of arbitrary geometry is treated. The concentration at the line source may be arbitrarily varied with time. Special attention is given to the meteorological inputs which act as boundary conditions for the problem, and a mixing layer of arbitrary depth is assumed. Numerical application of the derived theory indicates the combinations of meteorological parameters that may be expected to result in high pollution concentrations.

A coordinate free description of magnetohydrostatic equilibria

NASA Technical Reports Server (NTRS)

Martens, P. C. H.

1986-01-01

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

Efficient Modeling of Gravity Fields Caused by Sources with Arbitrary Geometry and Arbitrary Density Distribution

NASA Astrophysics Data System (ADS)

Wu, Leyuan

2018-01-01

We present a brief review of gravity forward algorithms in Cartesian coordinate system, including both space-domain and Fourier-domain approaches, after which we introduce a truly general and efficient algorithm, namely the convolution-type Gauss fast Fourier transform (Conv-Gauss-FFT) algorithm, for 2D and 3D modeling of gravity potential and its derivatives due to sources with arbitrary geometry and arbitrary density distribution which are defined either by discrete or by continuous functions. The Conv-Gauss-FFT algorithm is based on the combined use of a hybrid rectangle-Gaussian grid and the fast Fourier transform (FFT) algorithm. Since the gravity forward problem in Cartesian coordinate system can be expressed as continuous convolution-type integrals, we first approximate the continuous convolution by a weighted sum of a series of shifted discrete convolutions, and then each shifted discrete convolution, which is essentially a Toeplitz system, is calculated efficiently and accurately by combining circulant embedding with the FFT algorithm. Synthetic and real model tests show that the Conv-Gauss-FFT algorithm can obtain high-precision forward results very efficiently for almost any practical model, and it works especially well for complex 3D models when gravity fields on large 3D regular grids are needed.

Estimated bankfull discharge for selected Michigan rivers and regional hydraulic geometry curves for estimating bankfull characteristics in southern Michigan rivers

USGS Publications Warehouse

Rachol, Cynthia M.; Boley-Morse, Kristine

2009-01-01

Regional hydraulic geometry curves are power-function equations that relate riffle dimensions and bankfull discharge to drainage-basin size. They are defined by data collected through surveys conducted at stable stream reaches and can be used to aid watershed managers, design engineers, and others involved in determination of the best course of action for an unstable stream. Hydraulic geometry curves provide a mechanism through which comparisons can be made between riffle dimensions collected at an unstable stream to those collected at stable streams within the same region. In 2005, a study was initiated to delineate regional hydraulic geometry curves for Michigan. After in-office review of 343 U.S. Geological Survey streamgaging stations and an extensive field reconnaissance effort, 44 stable reaches were selected for this study. Detailed surveys that included cross-sectional and longitudinal profiles and pebble counts were conducted at selected streamgages, which were distributed throughout Michigan. By use of survey data from riffle cross sections and water-surface slope, bankfull discharge was estimated and compared to flood-recurrence intervals using regional flood equations. This comparison shows that bankfull discharges in Michigan recur more frequently than every 2 years. Regional hydraulic geometry curves were developed rather than statewide curves owing to large differences in factors that control channel geometry across the State. However, after the data were subdivided according to ecoregions, it was determined that there were enough data to delineate regional hydraulic geometry curves only for the Southern Lower Michigan Ecoregion. For this ecoregion, geometry curve equations and their coefficients of determination are: Width = 8.19 x DA0.44; R2 = 0.69, Depth = 0.67 x DA0.27; R2 = 0.28, Area = 4.38 x DA0.74; R2 = 0.59, where DA is the drainage area and R2 is the coefficient of determination. By use of discharge estimates for the Southern Lower Michigan Ecoregion, a bankfull discharge curve was delineated. The corresponding equation and its coefficient of determination are: Discharge = 4.05 x DA0.95; R2 = 0.60

Three-bead steering microswimmers

NASA Astrophysics Data System (ADS)

Rizvi, Mohd Suhail; Farutin, Alexander; Misbah, Chaouqi

2018-02-01

The self-propelled microswimmers have recently attracted considerable attention as model systems for biological cell migration as well as artificial micromachines. A simple and well-studied microswimmer model consists of three identical spherical beads joined by two springs in a linear fashion with active oscillatory forces being applied on the beads to generate self-propulsion. We have extended this linear microswimmer configuration to a triangular geometry where the three beads are connected by three identical springs in an equilateral triangular manner. The active forces acting on each spring can lead to autonomous steering motion; i.e., allowing the swimmer to move along arbitrary paths. We explore the microswimmer dynamics analytically and pinpoint its rich character depending on the nature of the active forces. The microswimmers can translate along a straight trajectory, rotate at a fixed location, as well as perform a simultaneous translation and rotation resulting in complex curved trajectories. The sinusoidal active forces on the three springs of the microswimmer contain naturally four operating parameters which are more than required for the steering motion. We identify the minimal operating parameters which are essential for the motion of the microswimmer along any given arbitrary trajectory. Therefore, along with providing insights into the mechanics of the complex motion of the natural and artificial microswimmers, the triangular three-bead microswimmer can be utilized as a model for targeted drug delivery systems and autonomous underwater vehicles where intricate trajectories are involved.

Projecting diffusion along the normal bundle of a plane curve

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

Valero-Valdés, Carlos; Herrera-Guzmán, Rafael

2014-05-15

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

User's guide for a computer program for calculating the zero-lift wave drag of complex aircraft configurations

NASA Technical Reports Server (NTRS)

Craidon, C. B.

1983-01-01

A computer program was developed to extend the geometry input capabilities of previous versions of a supersonic zero lift wave drag computer program. The arbitrary geometry input description is flexible enough to describe almost any complex aircraft concept, so that highly accurate wave drag analysis can now be performed because complex geometries can be represented accurately and do not have to be modified to meet the requirements of a restricted input format.

A dummy cell immersed boundary method for incompressible turbulence simulations over dirty geometries

NASA Astrophysics Data System (ADS)

Onishi, Keiji; Tsubokura, Makoto

2016-11-01

A methodology to eliminate the manual work required for correcting the surface imperfections of computer-aided-design (CAD) data, will be proposed. Such a technique is indispensable for CFD analysis of industrial applications involving complex geometries. The CAD geometry is degenerated into cell-oriented values based on Cartesian grid. This enables the parallel pre-processing as well as the ability to handle 'dirty' CAD data that has gaps, overlaps, or sharp edges without necessitating any fixes. An arbitrary boundary representation is used with a dummy-cell technique based on immersed boundary (IB) method. To model the IB, a forcing term is directly imposed at arbitrary ghost cells by linear interpolation of the momentum. The mass conservation is satisfied in the approximate domain that covers fluid region except the wall including cells. Attempts to Satisfy mass conservation in the wall containing cells leads to pressure oscillations near the IB. The consequence of this approximation will be discussed through fundamental study of an LES based channel flow simulation, and high Reynolds number flow around a sphere. And, an analysis comparing our results with wind tunnel experiments of flow around a full-vehicle geometry will also be presented.

A dose assessment method for arbitrary geometries with virtual reality in the nuclear facilities decommissioning

NASA Astrophysics Data System (ADS)

Chao, Nan; Liu, Yong-kuo; Xia, Hong; Ayodeji, Abiodun; Bai, Lu

2018-03-01

During the decommissioning of nuclear facilities, a large number of cutting and demolition activities are performed, which results in a frequent change in the structure and produce many irregular objects. In order to assess dose rates during the cutting and demolition process, a flexible dose assessment method for arbitrary geometries and radiation sources was proposed based on virtual reality technology and Point-Kernel method. The initial geometry is designed with the three-dimensional computer-aided design tools. An approximate model is built automatically in the process of geometric modeling via three procedures namely: space division, rough modeling of the body and fine modeling of the surface, all in combination with collision detection of virtual reality technology. Then point kernels are generated by sampling within the approximate model, and when the material and radiometric attributes are inputted, dose rates can be calculated with the Point-Kernel method. To account for radiation scattering effects, buildup factors are calculated with the Geometric-Progression formula in the fitting function. The effectiveness and accuracy of the proposed method was verified by means of simulations using different geometries and the dose rate results were compared with that derived from CIDEC code, MCNP code and experimental measurements.

Elastic stability of laminated, flat and curved, long rectangular plates subjected to combined inplane loads

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Tamekuni, M.; Baker, L. L.

1974-01-01

A method is presented to predict theoretical buckling loads of long, rectangular flat and curved laminated plates with arbitrary orientation of orthotropic axes each lamina. The plate is subjected to combined inplane normal and shear loads. Arbitrary boundary conditions may be stipulated along the longitudinal sides of the plate. In the absence of inplane shear loads and extensional-shear coupling, the analysis is also applicable to finite length plates. Numerical results are presented for curved laminated composite plates with boundary conditions and subjected to various loadings. These results indicate some of the complexities involved in the numerical solution of the analysis for general laminates. The results also show that the reduced bending stiffness approximation when applied to buckling problems could lead to considerable error in some cases and therefore must be used with caution.

Casimir-Lifshitz interaction between dielectrics of arbitrary geometry: A dielectric contrast perturbation theory

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

Golestanian, Ramin

2009-07-15

The general theory of electromagnetic-fluctuation-induced interactions in dielectric bodies as formulated by Dzyaloshinskii, Lifshitz, and Pitaevskii is rewritten as a perturbation theory in terms of the spatial contrast in (imaginary) frequency dependent dielectric function. The formulation can be used to calculate the Casimir-Lifshitz forces for dielectric objects of arbitrary geometry, as a perturbative expansion in the dielectric contrast, and could thus complement the existing theories that use perturbation in geometrical features. We find that expansion in dielectric contrast recasts the resulting Lifshitz energy into a sum of the different many-body contributions. The limit of validity and convergence properties of themore » perturbation theory is discussed using the example of parallel semi-infinite objects for which the exact result is known.« less

Photon escape probabilities in a semi-infinite plane-parallel medium. [from electron plasma surrounding galactic X-ray sources

NASA Technical Reports Server (NTRS)

Williams, A. C.; Elsner, R. F.; Weisskopf, M. C.; Darbro, W.

1984-01-01

It is shown in this work how to obtain the probabilities of photons escaping from a cold electron plasma environment after having undergone an arbitrary number of scatterings. This is done by retaining the exact differential cross section for Thomson scattering as opposed to using its polarization and angle averaged form. The results are given in the form of recursion relations. The geometry used is the semi-infinite plane-parallel geometry witlh a photon source located on a plane at an arbitrary optical depth below the surface. Analytical expressions are given for the probabilities which are accurate over a wide range of initial optical depth. These results can be used to model compact X-ray galactic sources which are surrounded by an electron-rich plasma.

Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials.

PubMed

Rodriguez, Alejandro W; Ilic, Ognjen; Bermel, Peter; Celanovic, Ivan; Joannopoulos, John D; Soljačić, Marin; Johnson, Steven G

2011-09-09

We demonstrate the possibility of achieving enhanced frequency-selective near-field radiative heat transfer between patterned (photonic-crystal) slabs at designable frequencies and separations, exploiting a general numerical approach for computing heat transfer in arbitrary geometries and materials based on the finite-difference time-domain method. Our simulations reveal a tradeoff between selectivity and near-field enhancement as the slab-slab separation decreases, with the patterned heat transfer eventually reducing to the unpatterned result multiplied by a fill factor (described by a standard proximity approximation). We also find that heat transfer can be further enhanced at selective frequencies when the slabs are brought into a glide-symmetric configuration, a consequence of the degeneracies associated with the nonsymmorphic symmetry group.

A Monte Carlo modeling on charging effect for structures with arbitrary geometries

NASA Astrophysics Data System (ADS)

Li, C.; Mao, S. F.; Zou, Y. B.; Li, Yong Gang; Zhang, P.; Li, H. M.; Ding, Z. J.

2018-04-01

Insulating materials usually suffer charging effects when irradiated by charged particles. In this paper, we present a Monte Carlo study on the charging effect caused by electron beam irradiation for sample structures with any complex geometry. When transporting in an insulating solid, electrons encounter elastic and inelastic scattering events; the Mott cross section and a Lorentz-type dielectric function are respectively employed to describe such scatterings. In addition, the band gap and the electron–long optical phonon interaction are taken into account. The electronic excitation in inelastic scattering causes generation of electron–hole pairs; these negative and positive charges establish an inner electric field, which in turn induces the drift of charges to be trapped by impurities, defects, vacancies etc in the solid, where the distributions of trapping sites are assumed to have uniform density. Under charging conditions, the inner electric field distorts electron trajectories, and the surface electric potential dynamically alters secondary electron emission. We present, in this work, an iterative modeling method for a self-consistent calculation of electric potential; the method has advantages in treating any structure with arbitrary complex geometry, in comparison with the image charge method—which is limited to a quite simple boundary geometry. Our modeling is based on: the combination of the finite triangle mesh method for an arbitrary geometry construction; a self-consistent method for the spatial potential calculation; and a full dynamic description for the motion of deposited charges. Example calculations have been done to simulate secondary electron yield of SiO2 for a semi-infinite solid, the charging for a heterostructure of SiO2 film grown on an Au substrate, and SEM imaging of a SiO2 line structure with rough surfaces and SiO2 nanoparticles with irregular shapes. The simulations have explored interesting interlaced charge layer distribution underneath the nanoparticle surface and the mechanism by which it is produced.

Subsurface solute transport with one-, two-, and three-dimensional arbitrary shape sources

NASA Astrophysics Data System (ADS)

Chen, Kewei; Zhan, Hongbin; Zhou, Renjie

2016-07-01

Solutions with one-, two-, and three-dimensional arbitrary shape source geometries will be very helpful tools for investigating a variety of contaminant transport problems in the geological media. This study proposed a general method to develop new solutions for solute transport in a saturated, homogeneous aquifer (confined or unconfined) with a constant, unilateral groundwater flow velocity. Several typical source geometries, such as arbitrary line sources, vertical and horizontal patch sources, circular and volumetric sources, were considered. The sources can sit on the upper or lower aquifer boundary to simulate light non-aqueous-phase-liquids (LNAPLs) or dense non-aqueous-phase-liquids (DNAPLs), respectively, or can be located anywhere inside the aquifer. The developed new solutions were tested against previous benchmark solutions under special circumstances and were shown to be robust and accurate. Such solutions can also be used as a starting point for the inverse problem of source zone and source geometry identification in the future. The following findings can be obtained from analyzing the solutions. The source geometry, including shape and orientation, generally played an important role for the concentration profile through the entire transport process. When comparing the inclined line sources with the horizontal line sources, the concentration contours expanded considerably along the vertical direction, and shrank considerably along the groundwater flow direction. A planar source sitting on the upper aquifer boundary (such as a LNAPL pool) would lead to significantly different concentration profiles compared to a planar source positioned in a vertical plane perpendicular to the flow direction. For a volumetric source, its dimension along the groundwater flow direction became less important compared to its other two dimensions.

3D automatic Cartesian grid generation for Euler flows

NASA Technical Reports Server (NTRS)

Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.

1993-01-01

We describe a Cartesian grid strategy for the study of three dimensional inviscid flows about arbitrary geometries that uses both conventional and CAD/CAM surface geometry databases. Initial applications of the technique are presented. The elimination of the body-fitted constraint allows the grid generation process to be automated, significantly reducing the time and effort required to develop suitable computational grids for inviscid flowfield simulations.

Adaptive Meshing of Ship Air-Wake Flowfields

DTIC Science & Technology

2014-10-21

performs cut- cell operations at geometry boundaries. A second-order spatial finite-volume scheme has been incorporated with explicit first order...The cells intersected by the geometry are handled using the “cut- cell ” approach, which is basically creating arbitrary polyhedral elements with...appropriate surface boundary conditions. Any cells completely outside the computational domain are tagged external and not solved in the flow solution

Advanced DPSM approach for modeling ultrasonic wave scattering in an arbitrary geometry

NASA Astrophysics Data System (ADS)

Yadav, Susheel K.; Banerjee, Sourav; Kundu, Tribikram

2011-04-01

Several techniques are used to diagnose structural damages. In the ultrasonic technique structures are tested by analyzing ultrasonic signals scattered by damages. The interpretation of these signals requires a good understanding of the interaction between ultrasonic waves and structures. Therefore, researchers need analytical or numerical techniques to have a clear understanding of the interaction between ultrasonic waves and structural damage. However, modeling of wave scattering phenomenon by conventional numerical techniques such as finite element method requires very fine mesh at high frequencies necessitating heavy computational power. Distributed point source method (DPSM) is a newly developed robust mesh free technique to simulate ultrasonic, electrostatic and electromagnetic fields. In most of the previous studies the DPSM technique has been applied to model two dimensional surface geometries and simple three dimensional scatterer geometries. It was difficult to perform the analysis for complex three dimensional geometries. This technique has been extended to model wave scattering in an arbitrary geometry. In this paper a channel section idealized as a thin solid plate with several rivet holes is formulated. The simulation has been carried out with and without cracks near the rivet holes. Further, a comparison study has been also carried out to characterize the crack. A computer code has been developed in C for modeling the ultrasonic field in a solid plate with and without cracks near the rivet holes.

Turbine blade profile design method based on Bezier curves

NASA Astrophysics Data System (ADS)

Alexeev, R. A.; Tishchenko, V. A.; Gribin, V. G.; Gavrilov, I. Yu.

2017-11-01

In this paper, the technique of two-dimensional parametric blade profile design is presented. Bezier curves are used to create the profile geometry. The main feature of the proposed method is an adaptive approach of curve fitting to given geometric conditions. Calculation of the profile shape is produced by multi-dimensional minimization method with a number of restrictions imposed on the blade geometry.The proposed method has been used to describe parametric geometry of known blade profile. Then the baseline geometry was modified by varying some parameters of the blade. The numerical calculation of obtained designs has been carried out. The results of calculations have shown the efficiency of chosen approach.

Acoustic field of a wedge-shaped section of a spherical cap transducer

NASA Astrophysics Data System (ADS)

Ketterling, Jeffrey A.

2003-12-01

The acoustic pressure field at an arbitrary point in space is derived for a wedge-shaped section of a spherical cap transducer using the spatial impulse response (SIR) method. For a spherical surface centered at the origin, a wedge shape is created by taking cuts in the X-Y and X-Z planes and removing the smallest surface component. Analytic expressions are derived for the SIR based on spatial location. The expressions utilize the SIR solutions for a spherical cap transducer [Arditi et al., Ultrason. Imaging 3, 37-61 (1981)] with additional terms added to account for the reduced surface area of the wedge. Results from the numerical model are compared to experimental measurements from a wedge transducer with an 8-cm outer diameter and 9-cm geometric focus. The experimental and theoretical -3-dB beamwidths agreed to within 10%+/-5%. The SIR model for a wedge-shaped transducer is easily extended to other spherically curved transducer geometries that consist of combinations of wedge sections and spherical caps.

Acoustic field of a wedge-shaped section of a spherical cap transducer.

PubMed

Ketterling, Jeffrey A

2003-12-01

The acoustic pressure field at an arbitrary point in space is derived for a wedge-shaped section of a spherical cap transducer using the spatial impulse response (SIR) method. For a spherical surface centered at the origin, a wedge shape is created by taking cuts in the X-Y and X-Z planes and removing the smallest surface component. Analytic expressions are derived for the SIR based on spatial location. The expressions utilize the SIR solutions for a spherical cap transducer [Arditi et al., Ultrason. Imaging 3, 37-61 (1981)] with additional terms added to account for the reduced surface area of the wedge. Results from the numerical model are compared to experimental measurements from a wedge transducer with an 8-cm outer diameter and 9-cm geometric focus. The experimental and theoretical -3-dB beamwidths agreed to within 10% +/- 5%. The SIR model for a wedge-shaped transducer is easily extended to other spherically curved transducer geometries that consist of combinations of wedge sections and spherical caps.

New approach for absolute fluence distribution calculations in Monte Carlo simulations of light propagation in turbid media

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

Böcklin, Christoph, E-mail: boecklic@ethz.ch; Baumann, Dirk; Fröhlich, Jürg

A novel way to attain three dimensional fluence rate maps from Monte-Carlo simulations of photon propagation is presented in this work. The propagation of light in a turbid medium is described by the radiative transfer equation and formulated in terms of radiance. For many applications, particularly in biomedical optics, the fluence rate is a more useful quantity and directly derived from the radiance by integrating over all directions. Contrary to the usual way which calculates the fluence rate from absorbed photon power, the fluence rate in this work is directly calculated from the photon packet trajectory. The voxel based algorithmmore » works in arbitrary geometries and material distributions. It is shown that the new algorithm is more efficient and also works in materials with a low or even zero absorption coefficient. The capabilities of the new algorithm are demonstrated on a curved layered structure, where a non-scattering, non-absorbing layer is sandwiched between two highly scattering layers.« less

Three-dimensional analytical model for the spatial variation of the foreshock electron distribution function - Systematics and comparisons with ISEE observations

NASA Technical Reports Server (NTRS)

Fitzenreiter, R. J.; Scudder, J. D.; Klimas, A. J.

1990-01-01

A model which is consistent with the solar wind and shock surface boundary conditions for the foreshock electron distribution in the absence of wave-particle effects is formulated for an arbitrary location behind the magnetic tangent to the earth's bow shock. Variations of the gyrophase-averaged velocity distribution are compared and contrasted with in situ ISEE observations. It is found that magnetic mirroring of solar wind electrons is the most important process by which nonmonotonic reduced electron distributions in the foreshock are produced. Leakage of particles from the magnetosheath is shown to be relatively unimportant in determining reduced distributions that are nonmonotonic. The two-dimensional distribution function off the magnetic field direction is the crucial contribution in producing reduced distributions which have beams. The time scale for modification of the electron velocity distribution in velocity space can be significantly influenced by steady state spatial gradients in the background imposed by the curved shock geometry.

Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.

Geometry Control System for Exploratory Shape Optimization Applied to High-Fidelity Aerodynamic Design of Unconventional Aircraft

NASA Astrophysics Data System (ADS)

Gagnon, Hugo

This thesis represents a step forward to bring geometry parameterization and control on par with the disciplinary analyses involved in shape optimization, particularly high-fidelity aerodynamic shape optimization. Central to the proposed methodology is the non-uniform rational B-spline, used here to develop a new geometry generator and geometry control system applicable to the aerodynamic design of both conventional and unconventional aircraft. The geometry generator adopts a component-based approach, where any number of predefined but modifiable (parametric) wing, fuselage, junction, etc., components can be arbitrarily assembled to generate the outer mold line of aircraft geometry. A unique Python-based user interface incorporating an interactive OpenGL windowing system is proposed. Together, these tools allow for the generation of high-quality, C2 continuous (or higher), and customized aircraft geometry with fast turnaround. The geometry control system tightly integrates shape parameterization with volume mesh movement using a two-level free-form deformation approach. The framework is augmented with axial curves, which are shown to be flexible and efficient at parameterizing wing systems of arbitrary topology. A key aspect of this methodology is that very large shape deformations can be achieved with only a few, intuitive control parameters. Shape deformation consumes a few tenths of a second on a single processor and surface sensitivities are machine accurate. The geometry control system is implemented within an existing aerodynamic optimizer comprising a flow solver for the Euler equations and a sequential quadratic programming optimizer. Gradients are evaluated exactly with discrete-adjoint variables. The algorithm is first validated by recovering an elliptical lift distribution on a rectangular wing, and then demonstrated through the exploratory shape optimization of a three-pronged feathered winglet leading to a span efficiency of 1.22 under a height-to-span ratio constraint of 0.1. Finally, unconventional aircraft configurations sized for a regional mission are compared against a conventional baseline. Each aircraft is optimized by varying wing section and wing planform (excluding span) under lift and trim constraints at a single operating point. Based on inviscid pressure drag, the box-wing, C-tip blended-wing-body, and braced-wing configurations considered here are respectively 22%, 25%, and 45% more efficient than the tube-and-wing configuration.

Fabrication of longitudinally arbitrary shaped fiber tapers

NASA Astrophysics Data System (ADS)

Nold, J.; Plötner, M.; Böhme, S.; Sattler, B.; deVries, O.; Schreiber, T.; Eberhardt, R.; Tünnermann, A.

2018-02-01

We present our current results on the fabrication of arbitrary shaped fiber tapers on our tapering rig using a CO2-laser as heat source. Single mode excitation of multimode fibers as well as changing the fiber geometry in an LPG-like fashion is presented. It is shown that this setup allows for reproducible fabrication of single-mode excitation tapers to extract the fundamental mode (M2 < 1.1) from a 30 μm core having an NA of 0.09.

Refringence, field theory and normal modes

NASA Astrophysics Data System (ADS)

Barceló, Carlos; Liberati, Stefano; Visser, Matt

2002-06-01

In a previous paper [Barceló C et al 2001 Class. Quantum Grav. 18 3595-610 (Preprint gr-qc/0104001)] we have shown that the occurrence of curved spacetime 'effective Lorentzian geometries' is a generic result of linearizing an arbitrary classical field theory around some nontrivial background configuration. This observation explains the ubiquitous nature of the 'analogue models' for general relativity that have recently been developed based on condensed matter physics. In the simple (single scalar field) situation analysed in our previous paper, there is a single unique effective metric; more complicated situations can lead to bi-metric and multi-metric theories. In the present paper we will investigate the conditions required to keep the situation under control and compatible with experiment - either by enforcing a unique effective metric (as would be required to be strictly compatible with the Einstein equivalence principle), or at the worst by arranging things so that there are multiple metrics that are all 'close' to each other (in order to be compatible with the Eötvös experiment). The algebraically most general situation leads to a physical model whose mathematical description requires an extension of the usual notion of Finsler geometry to a Lorentzian-signature pseudo-Finsler geometry; while this is possibly of some interest in its own right, this particular case does not seem to be immediately relevant for either particle physics or gravitation. The key result is that wide classes of theories lend themselves to an effective metric description. This observation provides further evidence that the notion of 'analogue gravity' is rather generic.

Hybrid space-airborne bistatic SAR geometric resolutions

NASA Astrophysics Data System (ADS)

Moccia, Antonio; Renga, Alfredo

2009-09-01

Performance analysis of Bistatic Synthetic Aperture Radar (SAR) characterized by arbitrary geometric configurations is usually complex and time-consuming since system impulse response has to be evaluated by bistatic SAR processing. This approach does not allow derivation of general equations regulating the behaviour of image resolutions with varying the observation geometry. It is well known that for an arbitrary configuration of bistatic SAR there are not perpendicular range and azimuth directions, but the capability to produce an image is not prevented as it depends only on the possibility to generate image pixels from time delay and Doppler measurements. However, even if separately range and Doppler resolutions are good, bistatic SAR geometries can exist in which imaging capabilities are very poor when range and Doppler directions become locally parallel. The present paper aims to derive analytical tools for calculating the geometric resolutions of arbitrary configuration of bistatic SAR. The method has been applied to a hybrid bistatic Synthetic Aperture Radar formed by a spaceborne illuminator and a receiving-only airborne forward-looking Synthetic Aperture Radar (F-SAR). It can take advantage of the spaceborne illuminator to dodge the limitations of monostatic FSAR. Basic modeling and best illumination conditions have been detailed in the paper.

Morse Monte Carlo Radiation Transport Code System

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

Emmett, M.B.

1975-02-01

The report contains sections containing descriptions of the MORSE and PICTURE codes, input descriptions, sample problems, deviations of the physical equations and explanations of the various error messages. The MORSE code is a multipurpose neutron and gamma-ray transport Monte Carlo code. Time dependence for both shielding and criticality problems is provided. General three-dimensional geometry may be used with an albedo option available at any material surface. The PICTURE code provide aid in preparing correct input data for the combinatorial geometry package CG. It provides a printed view of arbitrary two-dimensional slices through the geometry. By inspecting these pictures one maymore » determine if the geometry specified by the input cards is indeed the desired geometry. 23 refs. (WRF)« less

Border and surface tracing--theoretical foundations.

PubMed

Brimkov, Valentin E; Klette, Reinhard

2008-04-01

In this paper we define and study digital manifolds of arbitrary dimension, and provide (in particular)a general theoretical basis for curve or surface tracing in picture analysis. The studies involve properties such as one-dimensionality of digital curves and (n-1)-dimensionality of digital hypersurfaces that makes them discrete analogs of corresponding notions in continuous topology. The presented approach is fully based on the concept of adjacency relation and complements the concept of dimension as common in combinatorial topology. This work appears to be the first one on digital manifolds based ona graph-theoretical definition of dimension. In particular, in the n-dimensional digital space, a digital curve is a one-dimensional object and a digital hypersurface is an (n-1)-dimensional object, as it is in the case of curves and hypersurfaces in the Euclidean space. Relying on the obtained properties of digital hypersurfaces, we propose a uniform approach for studying good pairs defined by separations and obtain a classification of good pairs in arbitrary dimension. We also discuss possible applications of the presented definitions and results.

Gamma-Ray Pulsar Light Curves in Offset Polar Cap Geometry

NASA Technical Reports Server (NTRS)

Harding, Alice K.; DeCesar, Megan; Miller, M. Coleman

2011-01-01

Recent studies have shown that gamma-ray pulsar light curves are very sensitive to the geometry of the pulsar magnetic field. Pulsar magnetic field geometries, such as the retarded vacuum dipole and force-free magnetospheres, used to model high-energy light curves have distorted polar caps that are offset from the magnetic axis in the direction opposite to rotation. Since this effect is due to the sweepback of field lines near the light cylinder, offset polar caps are a generic property of pulsar magnetospheres and their effects should be included in gamma-ray pulsar light curve modeling. In slot gap models (having two-pole caustic geometry), the offset polar caps cause a strong azimuthal asymmetry of the particle acceleration around the magnetic axis. We have studied the effect of the offset polar caps in both retarded vacuum dipole and force-free geometry on the model high-energy pulse profile. We find that. corn pared to the profile:-; derived from :-;ymmetric caps, the flux in the pulse peaks, which are caustics formed along the trailing magnetic field lines. increases significantly relative to the off-peak emission. formed along leading field lines. The enhanced contrast produces greatly improved slot gap model fits to Fermi pulsar light curves like Vela, which show very little off-peak emIssIon.

Users manual for the NASA Lewis three-dimensional ice accretion code (LEWICE 3D)

NASA Technical Reports Server (NTRS)

Bidwell, Colin S.; Potapczuk, Mark G.

1993-01-01

A description of the methodology, the algorithms, and the input and output data along with an example case for the NASA Lewis 3D ice accretion code (LEWICE3D) has been produced. The manual has been designed to help the user understand the capabilities, the methodologies, and the use of the code. The LEWICE3D code is a conglomeration of several codes for the purpose of calculating ice shapes on three-dimensional external surfaces. A three-dimensional external flow panel code is incorporated which has the capability of calculating flow about arbitrary 3D lifting and nonlifting bodies with external flow. A fourth order Runge-Kutta integration scheme is used to calculate arbitrary streamlines. An Adams type predictor-corrector trajectory integration scheme has been included to calculate arbitrary trajectories. Schemes for calculating tangent trajectories, collection efficiencies, and concentration factors for arbitrary regions of interest for single droplets or droplet distributions have been incorporated. A LEWICE 2D based heat transfer algorithm can be used to calculate ice accretions along surface streamlines. A geometry modification scheme is incorporated which calculates the new geometry based on the ice accretions generated at each section of interest. The three-dimensional ice accretion calculation is based on the LEWICE 2D calculation. Both codes calculate the flow, pressure distribution, and collection efficiency distribution along surface streamlines. For both codes the heat transfer calculation is divided into two regions, one above the stagnation point and one below the stagnation point, and solved for each region assuming a flat plate with pressure distribution. Water is assumed to follow the surface streamlines, hence starting at the stagnation zone any water that is not frozen out at a control volume is assumed to run back into the next control volume. After the amount of frozen water at each control volume has been calculated the geometry is modified by adding the ice at each control volume in the surface normal direction.

High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities

NASA Astrophysics Data System (ADS)

Britt, Darrell Steven, Jr.

Problems of time-harmonic wave propagation arise in important fields of study such as geological surveying, radar detection/evasion, and aircraft design. These often involve highfrequency waves, which demand high-order methods to mitigate the dispersion error. We propose a high-order method for computing solutions to the variable-coefficient inhomogeneous Helmholtz equation in two dimensions on domains bounded by piecewise smooth curves of arbitrary shape with a finite number of boundary singularities at known locations. We utilize compact finite difference (FD) schemes on regular structured grids to achieve highorder accuracy due to their efficiency and simplicity, as well as the capability to approximate variable-coefficient differential operators. In this work, a 4th-order compact FD scheme for the variable-coefficient Helmholtz equation on a Cartesian grid in 2D is derived and tested. The well known limitation of finite differences is that they lose accuracy when the boundary curve does not coincide with the discretization grid, which is a severe restriction on the geometry of the computational domain. Therefore, the algorithm presented in this work combines high-order FD schemes with the method of difference potentials (DP), which retains the efficiency of FD while allowing for boundary shapes that are not aligned with the grid without sacrificing the accuracy of the FD scheme. Additionally, the theory of DP allows for the universal treatment of the boundary conditions. One of the significant contributions of this work is the development of an implementation that accommodates general boundary conditions (BCs). In particular, Robin BCs with discontinuous coefficients are studied, for which we introduce a piecewise parameterization of the boundary curve. Problems with discontinuities in the boundary data itself are also studied. We observe that the design convergence rate suffers whenever the solution loses regularity due to the boundary conditions. This is because the FD scheme is only consistent for classical solutions of the PDE. For this reason, we implement the method of singularity subtraction as a means for restoring the design accuracy of the scheme in the presence of singularities at the boundary. While this method is well studied for low order methods and for problems in which singularities arise from the geometry (e.g., corners), we adapt it to our high-order scheme for curved boundaries via a conformal mapping and show that it can also be used to restore accuracy when the singularity arises from the BCs rather than the geometry. Altogether, the proposed methodology for 2D boundary value problems is computationally efficient, easily handles a wide class of boundary conditions and boundary shapes that are not aligned with the discretization grid, and requires little modification for solving new problems.

Volume growth and puncture repair in conformal geometry

NASA Astrophysics Data System (ADS)

Eastwood, Michael G.; Gover, A. Rod

2018-04-01

Suppose M is a compact Riemannian manifold and p ∈ M an arbitrary point. We employ estimates on the volume growth around p to prove that the only conformal compactification of M ∖ { p } is M itself.

Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

Calculation methods for turbulent duct flows are generalized for ducts with arbitrary cross-sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered. These procedures enable the prediction of both the turbulence-driven secondary flow and the anisotropy of the Reynolds stresses, in contrast to some of the earlier calculation methods. Model predictions are compared to experimental data for developed flow in triangular duct, trapezoidal duct and a rod-bundle geometry. The correct trends are predicted, and the quantitative agreement is mostly fair. The simpler variant of the algebraic stress model procured better agreement with the measured data.

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

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

Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg; Zhou, Yu

2016-07-15

Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonantmore » frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.« less

Free-form geometric modeling by integrating parametric and implicit PDEs.

PubMed

Du, Haixia; Qin, Hong

2007-01-01

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit trivariate PDEs to define geometric solid models containing both geometric information and intensity distribution subject to flexible boundary conditions. The integrated formulation of second-order or fourth-order elliptic PDEs permits designers to manipulate PDE objects of complex geometry and/or arbitrary topology through direct sculpting and free-form modeling. We developed a PDE-based geometric modeling system for shape design and manipulation of PDE objects. The integration of implicit PDEs with parametric geometry offers more general and arbitrary shape blending and free-form modeling for objects with intensity attributes than pure geometric models.

Virtual reality based adaptive dose assessment method for arbitrary geometries in nuclear facility decommissioning.

PubMed

Liu, Yong-Kuo; Chao, Nan; Xia, Hong; Peng, Min-Jun; Ayodeji, Abiodun

2018-05-17

This paper presents an improved and efficient virtual reality-based adaptive dose assessment method (VRBAM) applicable to the cutting and dismantling tasks in nuclear facility decommissioning. The method combines the modeling strength of virtual reality with the flexibility of adaptive technology. The initial geometry is designed with the three-dimensional computer-aided design tools, and a hybrid model composed of cuboids and a point-cloud is generated automatically according to the virtual model of the object. In order to improve the efficiency of dose calculation while retaining accuracy, the hybrid model is converted to a weighted point-cloud model, and the point kernels are generated by adaptively simplifying the weighted point-cloud model according to the detector position, an approach that is suitable for arbitrary geometries. The dose rates are calculated with the Point-Kernel method. To account for radiation scattering effects, buildup factors are calculated with the Geometric-Progression formula in the fitting function. The geometric modeling capability of VRBAM was verified by simulating basic geometries, which included a convex surface, a concave surface, a flat surface and their combination. The simulation results show that the VRBAM is more flexible and superior to other approaches in modeling complex geometries. In this paper, the computation time and dose rate results obtained from the proposed method were also compared with those obtained using the MCNP code and an earlier virtual reality-based method (VRBM) developed by the same authors. © 2018 IOP Publishing Ltd.

Analysis of high-aspect-ratio jet-flap wings of arbitrary geometry

NASA Technical Reports Server (NTRS)

Lissaman, P. B. S.

1973-01-01

An analytical technique to compute the performance of an arbitrary jet-flapped wing is developed. The solution technique is based on the method of Maskell and Spence in which the well-known lifting-line approach is coupled with an auxiliary equation providing the extra function needed in jet-flap theory. The present method is generalized to handle straight, uncambered wings of arbitrary planform, twist, and blowing (including unsymmetrical cases). An analytical procedure is developed for continuous variations in the above geometric data with special functions to exactly treat discontinuities in any of the geometric and blowing data. A rational theory for the effect of finite wing thickness is introduced as well as simplified concepts of effective aspect ratio for rapid estimation of performance.

Wave Field Synthesis of moving sources with arbitrary trajectory and velocity profile.

PubMed

Firtha, Gergely; Fiala, Péter

2017-08-01

The sound field synthesis of moving sound sources is of great importance when dynamic virtual sound scenes are to be reconstructed. Previous solutions considered only virtual sources moving uniformly along a straight trajectory, synthesized employing a linear loudspeaker array. This article presents the synthesis of point sources following an arbitrary trajectory. Under high-frequency assumptions 2.5D Wave Field Synthesis driving functions are derived for arbitrary shaped secondary source contours by adapting the stationary phase approximation to the dynamic description of sources in motion. It is explained how a referencing function should be chosen in order to optimize the amplitude of synthesis on an arbitrary receiver curve. Finally, a finite difference implementation scheme is considered, making the presented approach suitable for real-time applications.

Geometrical optimization of the transmission and dispersion properties of arrayed waveguide gratings using two stigmatic point mountings.

PubMed

Muñoz, P; Pastor, D; Capmany, J; Martínez, A

2003-09-22

In this paper, the procedure to optimize flat-top Arrayed Waveguide Grating (AWG) devices in terms of transmission and dispersion properties is presented. The systematic procedure consists on the stigmatization and minimization of the Light Path Function (LPF) used in classic planar spectrograph theory. The resulting geometry arrangement for the Arrayed Waveguides (AW) and the Output Waveguides (OW) is not the classical Rowland mounting, but an arbitrary geometry arrangement. Simulation using previous published enhanced modeling show how this geometry reduces the passband ripple, asymmetry and dispersion, in a design example.

SABRINA - an interactive geometry modeler for MCNP

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

West, J.T.; Murphy, J.

One of the most difficult tasks when analyzing a complex three-dimensional system with Monte Carlo is geometry model development. SABRINA attempts to make the modeling process more user-friendly and less of an obstacle. It accepts both combinatorial solid bodies and MCNP surfaces and produces MCNP cells. The model development process in SABRINA is highly interactive and gives the user immediate feedback on errors. Users can view their geometry from arbitrary perspectives while the model is under development and interactively find and correct modeling errors. An example of a SABRINA display is shown. It represents a complex three-dimensional shape.

Optimization of magnet end-winding geometry

NASA Astrophysics Data System (ADS)

Reusch, Michael F.; Weissenburger, Donald W.; Nearing, James C.

1994-03-01

A simple, almost entirely analytic, method for the optimization of stress-reduced magnet-end winding paths for ribbon-like superconducting cable is presented. This technique is based on characterization of these paths as developable surfaces, i.e., surfaces whose intrinsic geometry is flat. The method is applicable to winding mandrels of arbitrary geometry. Computational searches for optimal winding paths are easily implemented via the technique. Its application to the end configuration of cylindrical Superconducting Super Collider (SSC)-type magnets is discussed. The method may be useful for other engineering problems involving the placement of thin sheets of material.

Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

USGS Publications Warehouse

Dudley, Robert W.

2004-01-01

Hydraulic-geometry relations (curves) were derived for 15 sites on 12 rivers in coastal and central Maine on the basis of site-specific (at-a-station) hydraulic-geometry relations and hydraulic models. At-a-station hydraulic-geometry curves, expressed as well-established power functions, describe the relations between channel geometry, velocity, and flow at a given point on a river. The derived at-a-station hydraulic-geometry curves indicate that, on average, a given increase in flow at a given river cross section in the study area will be nearly equally conveyed by increases in velocity and channel cross-sectional area. Regional curves describing the bankfull streamflow and associated channel geometry as functions of drainage area were derived for use in stream-channel assessment and restoration projects specific to coastal and central Maine. Regional hydraulic-geometry curves were derived by combining hydraulic-geometry information for 15 river cross sections using bankfull flow as the common reference streamflow. The exponents of the derived regional hydraulic-geometry relations indicate that, in the downstream direction, most of the conveyance of increasing contribution of flow is accommodated by an increase in cross-sectional area?with about 50 percent of the increase in flow accommodated by an increase in channel width, and 32 percent by an increase in depth. The remaining 18 percent is accommodated by an increase in streamflow velocity. On an annual-peak-series basis, results of this study indicate that the occurrence of bankfull streamflow for rivers in Maine is more frequent than the 1.5-year streamflow. On a flow-duration basis, bankfull streamflow for rivers in coastal and central Maine is equaled or exceeded approximately 8.1 percent of the time on mean?or about 30 days a year. Bankfull streamflow is roughly three times that of the mean annual streamflow for the sites investigated in this study. Regional climate, snowmelt hydrology, and glacial geology may play important roles in dictating the magnitude and frequency of occurrence of bankfull streamflows observed for rivers in coastal and central Maine.

On Pythagoras Theorem for Products of Spectral Triples

NASA Astrophysics Data System (ADS)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

Unsteady density-current equations for highly curved terrain

NASA Technical Reports Server (NTRS)

Sivakumaran, N. S.; Dressler, R. F.

1989-01-01

New nonlinear partial differential equations containing terrain curvature and its rate of change are derived that describe the flow of an atmospheric density current. Unlike the classical hydraulic-type equations for density currents, the new equations are valid for two-dimensional, gradually varied flow over highly curved terrain, hence suitable for computing unsteady (or steady) flows over arbitrary mountain/valley profiles. The model assumes the atmosphere above the density current exerts a known arbitrary variable pressure upon the unknown interface. Later this is specialized to the varying hydrostatic pressure of the atmosphere above. The new equations yield the variable velocity distribution, the interface position, and the pressure distribution that contains a centrifugal component, often significantly larger than its hydrostatic component. These partial differential equations are hyperbolic, and the characteristic equations and characteristic directions are derived. Using these to form a characteristic mesh, a hypothetical unsteady curved-flow problem is calculated, not based upon observed data, merely as an example to illustrate the simplicity of their application to unsteady flows over mountains.

Algebraic invariant curves of plane polynomial differential systems

NASA Astrophysics Data System (ADS)

Tsygvintsev, Alexei

2001-01-01

We consider a plane polynomial vector field P(x,y) dx + Q(x,y) dy of degree m>1. With each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential ω = dx/P = dy/Q. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate has already been found by Cerveau and Lins Neto in a different way.

Enhancements to the Tonge-Ramesh Ceramic Failure Model for Use in Eulerian Simulations

DTIC Science & Technology

2016-09-14

ability to project an arbitrary trial stress (σtr) onto the quasi -static yield surface (providing the value for σqs). Once the projection onto the quasi ...Model Evaluation Methods 4.1 Geometry from Prior Experiments There are experimental data from 2 research groups on penetration of confined boron carbide...by high-density, long-rod projectiles.21,22 Based on these prior ex- periments, the following 3 experimental geometries were identified to test the

f(R) theories of gravity with coupling between matter and geometry in autonomous system

NASA Astrophysics Data System (ADS)

Wang, Jun; Gui, Ruoyu; Qiu, Wenjun

2018-03-01

In this paper, a general approach has been introduced to investigate f(R) theories of gravity with coupling between matter and geometry via autonomous system, where there is no need to specify the arbitrary function of the scalar curvature. By this way, we find the general condition for the cosmic accelerated expansion. Moreover, in order to exemplify how to use our method to study specific cases, we applied it to three different models.

BUCLAP2

NASA Technical Reports Server (NTRS)

Halstead, D. W.; Tripp, L. L.; Tamekuni, M.; Baker, L. L.; Viswanathan, A. V.

1976-01-01

Program is used to predict buckling of rectangular flat and curved laminated plates subjected to in-plane normal and shearing loads, with each lamina composed of orthotropic material with arbitrary orientation of orthotropic axes.

Calculation of the aerodynamic loading of swept and unswept flexible wings of arbitrary stiffness

NASA Technical Reports Server (NTRS)

Diederich, Franklin W

1950-01-01

A method is presented for calculating the aerodynamic loading, the divergence speed, and certain stability derivatives of swept and unswept wings and tail surfaces of arbitrary stiffness. Provision is made for using either stiffness curves and root rotation constants or structural influence coefficients in the analysis. Computing forms, tables of numerical constants required in the analysis, and an illustrative example are included to facilitate calculations by means of the method.

A complete characterization of relativistic uniform acceleration

NASA Astrophysics Data System (ADS)

Scarr, Tzvi; Friedman, Yaakov

2017-05-01

We use the Frenet frame to define and completely characterize “uniform acceleration” in flat spacetime. We extend the definition to arbitrary curved spacetime and provide an example in Schwarzschild spacetime.

Numerical Solution of the Three-Dimensional Navier-Stokes Equation.

DTIC Science & Technology

1982-03-01

compressible, viscous fluid in an arbitrary geometry. We wish to use a grid generating scheme so we assume that the geometry of the physical problem given in...bian J of the mapping are provided. (For work on grid generating schemes see [4], [5] or [6).) Hence we must solve the following system of equations...these limitations the data structure used in the ILLIAC code is to partition the grid into 8 x 8 x 8 blocks. A row of these blocks in a given

Vapor ingestion in a cylindrical tank with a concave elliptical bottom

NASA Technical Reports Server (NTRS)

Klavins, A.

1974-01-01

An approximate analytical technique is presented for estimating the liquid residual in a tank of arbitrary geometry due to vapor ingestion at any drain rate and acceleration level. The bulk liquid depth at incipient pull-through is defined in terms of the Weber and Bond numbers and two functions that describe the fluid velocity field and free surface shape appropriate to the tank geometry. Numerical results are obtained for the Centaur LH2 tank using limiting approximations to these functions.

Gamma-Ray Pulsar Light Curves in Vacuum and Force-Free Geometry

NASA Technical Reports Server (NTRS)

Harding, Alice K.; DeCesar, Megan E.; Miller, M. Coleman; Kalapotharakos, Constantinos; Contopoulos, Ioannis

2011-01-01

Recent studies have shown that gamma-ray pulsar light curves are very sensitive to the geometry of the pulsar magnetic field. Pulsar magnetic field geometries, such as the retarded vacuum dipole and force-free magnetospheres have distorted polar caps that are offset from the magnetic axis in the direction opposite to rotation. Since this effect is due to the sweepback of field lines near the light cylinder, offset polar caps are a generic property of pulsar magnetospheres and their effects should be included in gamma-ray pulsar light curve modeling. In slot gap models (having two-pole caustic geometry), the offset polar caps cause a strong azimuthal asymmetry of the particle acceleration around the magnetic axis. We have studied the effect of the offset polar caps in both retarded vacuum dipole and force-free geometry on the model high-energy pulse profiles. We find that, compared to the profiles derived from symmetric caps, the flux in the pulse peaks, which are caustics formed along the trailing magnetic field lines, increases significantly relative to the off-peak emission, formed along leading field lines. The enhanced contrast produces improved slot gap model fits to Fermi pulsar light curves like Vela, with vacuum dipole fits being more favorable.

Numerical and experimental study of curved and planar frequency selective surfaces with arbitrary illumination. M.S. Thesis - Maryland Univ., 1989

NASA Technical Reports Server (NTRS)

Caroglanian, Armen

1991-01-01

A frequency selective surface (FSS) composed of apertures in a metallic sheet is known as the inductive FSS. The infinite inductive FSS theory is derived and the aperture fields are solved by a spectral domain formulation with method of moments solution. Both full domain and subsectional basis functions are studied. A locally planar technique (LPT) is used to determine the forward scattered field from a generally shaped inductive FSS with arbitrary illumination.

Ideal solar cell equation in the presence of photon recycling

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

Lan, Dongchen, E-mail: d.lan@unsw.edu.au; Green, Martin A., E-mail: m.green@unsw.edu.au

Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included.

Conformal dual-band near-perfectly absorbing mid-infrared metamaterial coating.

PubMed

Jiang, Zhi Hao; Yun, Seokho; Toor, Fatima; Werner, Douglas H; Mayer, Theresa S

2011-06-28

Metamaterials offer a new approach to create surface coatings with highly customizable electromagnetic absorption from the microwave to the optical regimes. Thus far, efficient metamaterial absorbers have been demonstrated at microwave frequencies, with recent efforts aimed at much shorter terahertz and infrared wavelengths. The present infrared absorbers have been constructed from arrays of nanoscale metal resonators with simple circular or cross-shaped geometries, which provide a single band response. In this paper, we demonstrate a conformal metamaterial absorber with a narrow band, polarization-independent absorptivity of >90% over a wide ±50° angular range centered at mid-infrared wavelengths of 3.3 and 3.9 μm. The highly efficient dual-band metamaterial was realized by using a genetic algorithm to identify an array of H-shaped nanoresonators with an effective electric and magnetic response that maximizes absorption in each wavelength band when patterned on a flexible Kapton and Au thin film substrate stack. This conformal metamaterial absorber maintains its absorption properties when integrated onto curved surfaces of arbitrary materials, making it attractive for advanced coatings that suppress the infrared reflection from the protected surface.

Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems.

PubMed

Fall, Mandiaye; Boutami, Salim; Glière, Alain; Stout, Brian; Hazart, Jerome

2013-06-01

A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.

New Computational Approach to Electron Transport in Irregular Graphene Nanostructures

NASA Astrophysics Data System (ADS)

Mason, Douglas; Heller, Eric; Prendergast, David; Neaton, Jeffrey

2009-03-01

For novel graphene devices of nanoscale-to-macroscopic scale, many aspects of their transport properties are not easily understood due to difficulties in fabricating devices with regular edges. Here we develop a framework to efficiently calculate and potentially screen electronic transport properties of arbitrary nanoscale graphene device structures. A generalization of the established recursive Green's function method is presented, providing access to arbitrary device and lead geometries with substantial computer-time savings. Using single-orbital nearest-neighbor tight-binding models and the Green's function-Landauer scattering formalism, we will explore the transmission function of irregular two-dimensional graphene-based nanostructures with arbitrary lead orientation. Prepared by LBNL under contract DE-AC02-05CH11231 and supported by the U.S. Dept. of Energy Computer Science Graduate Fellowship under grant DE-FG02-97ER25308.

Fast RBF OGr for solving PDEs on arbitrary surfaces

NASA Astrophysics Data System (ADS)

Piret, Cécile; Dunn, Jarrett

2016-10-01

The Radial Basis Functions Orthogonal Gradients method (RBF-OGr) was introduced in [1] to discretize differential operators defined on arbitrary manifolds defined only by a point cloud. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent complex geometries in any spatial dimension. A large limitation of the RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this paper, we apply the RBF-Finite Difference (RBF-FD) technique to the RBF-OGr method for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami operator. This method can be applied to solving PDEs on arbitrary surfaces embedded in ℛ3. We illustrate the accuracy of our new method by solving the heat equation on the unit sphere.

Charged defects in two-dimensional semiconductors of arbitrary thickness and geometry: Formulation and application to few-layer black phosphorus

NASA Astrophysics Data System (ADS)

Wang, Dan; Han, Dong; Li, Xian-Bin; Chen, Nian-Ke; West, Damien; Meunier, Vincent; Zhang, Shengbai; Sun, Hong-Bo

2017-10-01

Energy evaluation of charged defects is tremendously important in two-dimensional (2D) semiconductors for the industrialization of 2D electronic devices because of its close relation with the corresponding type of conductivity and its strength. Although the method to calculate the energy of charged defects in single-layer one-atom-thick systems of equilateral unit-cell geometry has recently been proposed, few-layer 2D semiconductors are more common in device applications. As it turns out, one may not apply the one-layer formalism to multilayer cases without jeopardizing accuracy. Here, we generalize the approach to 2D systems of arbitrary cell geometry and thickness and use few-layer black phosphorus to illustrate how defect properties, mainly group-VI substitutional impurities, are affected. Within the framework of density functional theory, we show that substitutional Te (T eP) is the best candidate for n -type doping, and as the thickness increases, the ionization energy is found to decrease monotonically from 0.67 eV (monolayer) to 0.47 eV (bilayer) and further to 0.33 eV (trilayer). Although these results show the ineffectiveness of the dielectric screening at the monolayer limit, they also show how it evolves with increasing thickness whereby setting a new direction for the design of 2D electronics. The proposed method here is generally suitable to all the 2D materials regardless of their thickness and geometry.

Hydrogels for engineering: normalization of swelling due to arbitrary stimulus

NASA Astrophysics Data System (ADS)

Ehrenhofer, Adrian; Wallmersperger, Thomas

2017-04-01

In engineering, materials are chosen from databases: Engineers orient on specific parameters such as Young's modulus, yield stress or thermal expansion coefficients for a desired application. For hydrogels, the choice of materials is rather tedious since no generalized material parameters are currently available to quantify the swelling behavior. The normalization of swelling, which we present in the current work, allows an easy comparison of different hydrogel materials. Thus, for a specific application like a sensor or an actuator, an adequate material can be chosen. In the current work, we present the process of normalization and provide a course of action for the data analysis. Special challenges for hydrogels like hysteresis, conditional multi-sensitivity and anisotropic swelling are addressed. Then, the Temperature Expansion Model is shortly described and applied. Using the derived normalized swelling curves, a nonlinear expansion coefficient ß(F) is derived. The derived material behavior is used in an analytical model to predict the bending behavior of a beam made of thermo-responsive hydrogel material under an anisotropic temperature load. A bending behavior of the beam can be observed and the impact of other geometry and material parameters can be investigated. To overcome the limitations of the one-dimensional beam theory, the material behavior and geometry can be implemented in Finite Element analysis tools. Thus, novel applications for hydrogels in various fields can be envisioned, designed and tested. This can lead to a wider use of smart materials in sensor or actuator devices even by engineers without chemical background.

Transition to Turbulence in curved pipe

NASA Astrophysics Data System (ADS)

Hashemi, Amirreza; Loth, Francis

2014-11-01

Studies have shown that transitional turbulence in a curved pipe is delayed significantly compared with straight pipes. These analytical, numerical and experimental studies employed a helical geometry that is infinitely long such that the effect of the inlet and outlet can be neglected. The present study examined transition to turbulence in a finite curved pipe with a straight inlet/outlet and a 180 degrees curved pipe with a constant radius of curvature and diameter (D). We have employed the large scale direct numerical simulation (DNS) by using the spectral element method, nek5000, to simulate the flow field within curved pipe geometry with different curvature radii and Reynolds numbers to determine the point of the transition to turbulence. Long extensions for the inlet (5D) and outlet (20D) were used to diminish the effect of the boundary conditions. Our numerical results for radius of curvatures of 1.5D and 5D show transition turbulence is near Re = 3000. This is delayed compared with a straight pipe (Re = 2200) but still less that observed for helical geometries (Reynolds number less than 5000). Our research aims to describe the critical Reynolds number for transition to turbulence for a finite curved pipe at various curvature radii.

Pulsar Emission Geometry and Accelerating Field Strength

NASA Technical Reports Server (NTRS)

DeCesar, Megan E.; Harding, Alice K.; Miller, M. Coleman; Kalapotharakos, Constantinos; Parent, Damien

2012-01-01

The high-quality Fermi LAT observations of gamma-ray pulsars have opened a new window to understanding the generation mechanisms of high-energy emission from these systems, The high statistics allow for careful modeling of the light curve features as well as for phase resolved spectral modeling. We modeled the LAT light curves of the Vela and CTA I pulsars with simulated high-energy light curves generated from geometrical representations of the outer gap and slot gap emission models. within the vacuum retarded dipole and force-free fields. A Markov Chain Monte Carlo maximum likelihood method was used to explore the phase space of the magnetic inclination angle, viewing angle. maximum emission radius, and gap width. We also used the measured spectral cutoff energies to estimate the accelerating parallel electric field dependence on radius. under the assumptions that the high-energy emission is dominated by curvature radiation and the geometry (radius of emission and minimum radius of curvature of the magnetic field lines) is determined by the best fitting light curves for each model. We find that light curves from the vacuum field more closely match the observed light curves and multiwavelength constraints, and that the calculated parallel electric field can place additional constraints on the emission geometry

Watt steam governor stability

NASA Astrophysics Data System (ADS)

Denny, Mark

2002-05-01

The physics of the fly-ball governor, introduced to regulate the speed of steam engines, is here analysed anew. The original analysis is generalized to arbitrary governor geometry. The well-known stability criterion for the linearized system breaks down for large excursions from equilibrium; we show approximately how this criterion changes.

Computational Systems for Multidisciplinary Applications

NASA Technical Reports Server (NTRS)

Soni, Bharat; Haupt, Tomasz; Koomullil, Roy; Luke, Edward; Thompson, David

2002-01-01

In this paper, we briefly describe our efforts to develop complex simulation systems. We focus first on four key infrastructure items: enterprise computational services, simulation synthesis, geometry modeling and mesh generation, and a fluid flow solver for arbitrary meshes. We conclude by presenting three diverse applications developed using these technologies.

Elasticity Solution of an Adhesively Bonded Cover Plate of Various Geometries

NASA Technical Reports Server (NTRS)

Aksel, G. N.; Erdogan, F.

1985-01-01

The plane strain of adhesively bonded structures consisting of two different isotropic adherends is considered. By expressing the x-y components of the displacements in terms of Fourier integrals and using the corresponding boundary and continuity conditions, the integral equations for the general problem are obtained and solved numerically by applying Gauss-Chebyshev integration scheme. The shear and the normal stresses in the adhesive are calculated for various geometries and material properties for a stiffened plate under uniaxial tension. Numerical results involving the stress intensity factors and the strain energy release rate are presented. The closed-form expressions for the Fredholm kernels are provided to obtain the solution for an arbitrary geometry and material properties. For the general geometry, the contribution of the normal stress is quite significant, while for symmetric geometries, the shear stress is dominant, the normal stress vanishes if the adherends are of the same material and the same thickness.

Bankfull-channel geometry and discharge curves for the Rocky Mountains Hydrologic Region in Wyoming

USGS Publications Warehouse

Foster, Katharine

2012-01-01

Regional curves relate bankfull-channel geometry and bankfull discharge to drainage area in regions with similar runoff characteristics and are used to estimate the bankfull discharge and bankfull-channel geometry when the drainage area of a stream is known. One-variable, ordinary least-squares regressions relating bankfull discharge, cross-sectional area, bankfull width, and bankfull mean depth to drainage area were developed from data collected at 35 streamgages in or near Wyoming. Watersheds draining to these streamgages are within the Rocky Mountains Hydrologic Region of Wyoming and neighboring states.

Analysis of diffusion in curved surfaces and its application to tubular membranes

PubMed Central

Klaus, Colin James Stockdale; Raghunathan, Krishnan; DiBenedetto, Emmanuele; Kenworthy, Anne K.

2016-01-01

Diffusion of particles in curved surfaces is inherently complex compared with diffusion in a flat membrane, owing to the nonplanarity of the surface. The consequence of such nonplanar geometry on diffusion is poorly understood but is highly relevant in the case of cell membranes, which often adopt complex geometries. To address this question, we developed a new finite element approach to model diffusion on curved membrane surfaces based on solutions to Fick’s law of diffusion and used this to study the effects of geometry on the entry of surface-bound particles into tubules by diffusion. We show that variations in tubule radius and length can distinctly alter diffusion gradients in tubules over biologically relevant timescales. In addition, we show that tubular structures tend to retain concentration gradients for a longer time compared with a comparable flat surface. These findings indicate that sorting of particles along the surfaces of tubules can arise simply as a geometric consequence of the curvature without any specific contribution from the membrane environment. Our studies provide a framework for modeling diffusion in curved surfaces and suggest that biological regulation can emerge purely from membrane geometry. PMID:27733625

A geometry package for generation of input data for a three-dimensional potential-flow program

NASA Technical Reports Server (NTRS)

Halsey, N. D.; Hess, J. L.

1978-01-01

The preparation of geometric data for input to three-dimensional potential flow programs was automated and simplified by a geometry package incorporated into the NASA Langley version of the 3-D lifting potential flow program. Input to the computer program for the geometry package consists of a very sparse set of coordinate data, often with an order of magnitude of fewer points than required for the actual potential flow calculations. Isolated components, such as wings, fuselages, etc. are paneled automatically, using one of several possible element distribution algorithms. Curves of intersection between components are calculated, using a hybrid curve-fit/surface-fit approach. Intersecting components are repaneled so that adjacent elements on either side of the intersection curves line up in a satisfactory manner for the potential-flow calculations. Many cases may be run completely (from input, through the geometry package, and through the flow calculations) without interruption. Use of the package significantly reduces the time and expense involved in making three-dimensional potential flow calculations.

Strip Yield Model Numerical Application to Different Geometries and Loading Conditions

NASA Technical Reports Server (NTRS)

Hatamleh, Omar; Forman, Royce; Shivakumar, Venkataraman; Lyons, Jed

2006-01-01

A new numerical method based on the strip-yield analysis approach was developed for calculating the Crack Tip Opening Displacement (CTOD). This approach can be applied for different crack configurations having infinite and finite geometries, and arbitrary applied loading conditions. The new technique adapts the boundary element / dislocation density method to obtain crack-face opening displacements at any point on a crack, and succeeds by obtaining requisite values as a series of definite integrals, the functional parts of each being evaluated exactly in a closed form.

Automated Geometry assisted PEC for electron beam direct write nanolithography

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

Ocola, Leonidas E.; Gosztola, David J.; Rosenmann, Daniel

Nanoscale geometry assisted proximity effect correction (NanoPEC) is demonstrated to improve PEC for nanoscale structures over standard PEC, in terms of feature sharpness for sub-100 nm structures. The method was implemented onto an existing commercially available PEC software. Plasmonic arrays of crosses were fabricated using regular PEC and NanoPEC, and optical absorbance was measured. Results confirm that the improved sharpness of the structures leads to increased sharpness in the optical absorbance spectrum features. We also demonstrated that this method of PEC is applicable to arbitrary shaped structures beyond crosses.

General Relativity Exactly Described by Use of Newton's Laws within a Curved Geometry

NASA Astrophysics Data System (ADS)

Savickas, David

2014-03-01

The connection between general relativity and Newtonian mechanics is shown to be much closer than generally recognized. When Newton's second law is written in a curved geometry by using the physical components of a vector as defined in tensor calculus, and by replacing distance within the momentum's velocity by the vector metric ds in a curved geometry, the second law can then be easily shown to be exactly identical to the geodesic equation of motion occurring in general relativity. By using a time whose vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be separated into two equations one of which is a curved three-dimensional equation of motion and the other is an equation for energy. For the gravitational field of an isolated particle, they yield the Schwarzschild equations. They can be used to describe gravitation for any array of masses for which the Newtonian gravitational potential is known, and is applied here to describe motion in the gravitational field of a thin mass-rod.

Harmonic oscillations of a longitudinal shear infinite hollow cylinder arbitrary cross-section with a tunnel crack

NASA Astrophysics Data System (ADS)

Kyrylova, O. I.; Popov, V. G.

2018-04-01

An effective analytical-numerical method for determining the dynamic stresses in a hollow cylindrical body of arbitrary cross-section with a tunnel crack under antiplane strain conditions is proposed. The method allows separately solving the integral equations on the crack faces and satisfying the boundary conditions on the body boundaries. It provides a convenient numerical scheme. Approximate formulas for calculating the dynamic stress intensity factors in a neighborhood of the crack are obtained and the influence of the crack geometry and wave number on these quantities is investigated, especially from the point of view of the resonance existence.

Rarefied gas flow through two-dimensional nozzles

NASA Technical Reports Server (NTRS)

De Witt, Kenneth J.; Jeng, Duen-Ren; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

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

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Analysis of optimisation method for a two-stroke piston ring using the Finite Element Method and the Simulated Annealing Method

NASA Astrophysics Data System (ADS)

Kaliszewski, M.; Mazuro, P.

2016-09-01

Simulated Annealing Method of optimisation for the sealing piston ring geometry is tested. The aim of optimisation is to develop ring geometry which would exert demanded pressure on a cylinder just while being bended to fit the cylinder. Method of FEM analysis of an arbitrary piston ring geometry is applied in an ANSYS software. The demanded pressure function (basing on formulae presented by A. Iskra) as well as objective function are introduced. Geometry definition constructed by polynomials in radial coordinate system is delivered and discussed. Possible application of Simulated Annealing Method in a piston ring optimisation task is proposed and visualised. Difficulties leading to possible lack of convergence of optimisation are presented. An example of an unsuccessful optimisation performed in APDL is discussed. Possible line of further optimisation improvement is proposed.

Effects of fatigue on driving performance under different roadway geometries: a simulator study.

PubMed

Du, Hongji; Zhao, Xiaohua; Zhang, Xingjian; Zhang, Yunlong; Rong, Jian

2015-01-01

This article examines the effects of fatigue on driving performance under different roadway geometries using a driving simulator. Twenty-four participants each completed a driving scenario twice: while alert and while experiencing fatigue. The driving scenario was composed of straight road segments and curves; there were 6 curves with 3 radius values (i.e., 200, 500, and 800 m) and 2 turning directions (i.e., left and right). Analysis was conducted on driving performance measures such as longitudinal speed, steering wheel movements, and lateral position. RESULTS confirmed that decremental changes in driving performance due to fatigue varied among road conditions. On straight segments, drivers' abilities to steer and maintain lane position were impaired, whereas on curves we found decremental changes in the quality of longitudinal speed as well as steering control and keeping the vehicle in the lane. Moreover, the effects of fatigue on driving performance were relative to the radius and direction of the curve. Fatigue impaired drivers' abilities to control the steering wheel, and the impairment proved more obvious on curves. The degree varied significantly as the curve radius changed. Drivers tended to drive closer to the right side due to fatigue, and the impairment in maintaining lane position became more obvious as the right-turn curve radius decreased. Driver fatigue has detrimental effects on driving performance, and the effects differ under different roadway geometries.

Influence of sweeping detonation-wave loading on damage evolution during spallation loading of tantalum in both a planar and curved geometry

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

Gray, George Thompson III; Hull, Lawrence Mark; Livescu, Veronica

Widespread research over the past five decades has provided a wealth of experimental data and insight concerning the shock hardening, damage evolution, and the spallation response of materials subjected to square-topped shock-wave loading profiles. However, fewer quantitative studies have been conducted on the effect of direct, in-contact, high explosive (HE)-driven Taylor wave (unsupported shocks) loading on the shock hardening, damage evolution, or spallation response of materials. Systematic studies quantifying the effect of sweeping-detonation wave loading are yet sparser. In this study, the damage evolution and spallation response of Ta is shown to be critically dependent on the peak shock stress,more » the geometry of the sample (flat or curved plate geometry), and the shock obliquity during sweeping-detonation-wave shock loading. Sweepingwave loading in the flat-plate geometry is observed to: a) yield a lower spall strength than previously documented for 1-D supported-shock-wave loading, b) exhibit increased shock hardening as a function of increasing obliquity, and c) lead to an increased incidence of deformation twin formation with increasing shock obliquity. Sweeping-wave loading of a 10 cm radius curved Ta plate is observed to: a) lead to an increase in the shear stress as a function of increasing obliquity, b) display a more developed level of damage evolution, extensive voids and coalescence, and lower spall strength with obliquity in the curved plate than seen in the flat-plate sweeping-detonation wave loading for an equivalent HE loading, and c) no increased propensity for deformation twin formation with increasing obliquity as seen in the flat-plate geometry. The overall observations comparing and contrasting the flat versus curved sweeping-wave spall experiments with 1D loaded spallation behavior suggests a coupled influence of obliquity and geometry on dynamic shock-induced damage evolution and spall strength. Coupled experimental and modeling research to quantify the combined effects of sweeping-wave loading with increasingly complex sample geometries on the shockwave response of materials is clearly crucial to providing the basis for developing and thereafter validation of predictive modeling capability.« less

A Numerical Method for Calculating Stellar Occultation Light Curves from an Arbitrary Atmospheric Model

NASA Technical Reports Server (NTRS)

Chamberlain, D. M.; Elliot, J. L.

1997-01-01

We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmosphere with an arbitrary atmospheric model that has spherical symmetry. This improved speed makes least-squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10(exp -4) of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a l/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal model. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors of no more than 10(exp -4), with the largest errors occurring in small planets. These errors are well below the precision of the best stellar occultation data available. Fits to noisy data had formal errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for the most accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.

Geometry effect on electrokinetic flow and ionic conductance in pH-regulated nanochannels

NASA Astrophysics Data System (ADS)

Sadeghi, Morteza; Saidi, Mohammad Hassan; Moosavi, Ali; Sadeghi, Arman

2017-12-01

Semi-analytical solutions are obtained for the electrical potential, electroosmotic velocity, ionic conductance, and surface physicochemical properties associated with long pH-regulated nanochannels of arbitrary but constant cross-sectional area. The effects of electric double layer overlap, multiple ionic species, and surface association/dissociation reactions are all taken into account, assuming low surface potentials. The method of analysis includes series solutions which the pertinent coefficients are obtained by applying the wall boundary conditions using either of the least-squares or point matching techniques. Although the procedure is general enough to be applied to almost any arbitrary cross section, nine nanogeometries including polygonal, trapezoidal, double-trapezoidal, rectangular, elliptical, semi-elliptical, isosceles triangular, rhombic, and isotropically etched profiles are selected for presentation. For the special case of an elliptic cross section, full analytical solutions are also obtained utilizing the Mathieu functions. We show that the geometrical configuration plays a key role in determination of the ionic conductance, surface charge density, electrical potential and velocity fields, and proton enhancement. In this respect, the net electric charge and convective ionic conductance are higher for channels of larger perimeter to area ratio, whereas the opposite is true for the average surface charge density and mean velocity; the geometry impact on the two latest ones, however, vanishes if the background salt concentration is high enough. Moreover, we demonstrate that considering a constant surface potential equal to the average charge-regulated potential provides sufficiently accurate results for smooth geometries such as an ellipse at medium-high aspect ratios but leads to significant errors for geometries having narrow corners such as a triangle.

Skin Effect Modeling in Conductors of Arbitrary Shape Through a Surface Admittance Operator and the Contour Integral Method

NASA Astrophysics Data System (ADS)

Patel, Utkarsh R.; Triverio, Piero

2016-09-01

An accurate modeling of skin effect inside conductors is of capital importance to solve transmission line and scattering problems. This paper presents a surface-based formulation to model skin effect in conductors of arbitrary cross section, and compute the per-unit-length impedance of a multiconductor transmission line. The proposed formulation is based on the Dirichlet-Neumann operator that relates the longitudinal electric field to the tangential magnetic field on the boundary of a conductor. We demonstrate how the surface operator can be obtained through the contour integral method for conductors of arbitrary shape. The proposed algorithm is simple to implement, efficient, and can handle arbitrary cross-sections, which is a main advantage over the existing approach based on eigenfunctions, which is available only for canonical conductor's shapes. The versatility of the method is illustrated through a diverse set of examples, which includes transmission lines with trapezoidal, curved, and V-shaped conductors. Numerical results demonstrate the accuracy, versatility, and efficiency of the proposed technique.

The effect of chevron alignment signs on driver performance on horizontal curves with different roadway geometries.

PubMed

Zhao, Xiaohua; Wu, Yiping; Rong, Jian; Ma, Jianming

2015-02-01

To develop a practicable and clear guideline for implementing Chevrons on China's highways, it is necessary to understand the effect of Chevrons on driving performance in different roadway geometries. Using a driving simulator, this study tests the effect of China's Chevrons on vehicle speed and lane position on two-lane rural highway horizontal curves with different roadway geometries. The results showed a significant effect of Chevrons on speed reduction, and this function was not significantly affected by curve radius but was statistically affected by curve direction. The speed reduction caused by Chevrons was also significant at the approach of curve, middle of curve and point of tangent. The 85th percentile speed was also markedly lower when Chevrons were present. We also found a significant effect of Chevrons in encouraging participants to drive the vehicle with a more proper lane position at the first half of curves; and this function was slightly affected by curve radius. Meanwhile, the effect of Chevrons on keeping drivers staying in a more stable lane position was also statistically significant at the second half of curves. In sharp curves, the function of Chevrons to make drivers keep a stable lane position was lost. Besides, the impact of curve direction on the function of Chevrons on lane position was always present, and drivers would drive slightly away from Chevrons. Regardless of the curve radius, China's Chevrons at horizontal curves provide an advance warning, speed control and lane position guide for traffic on the nearside of Chevrons. Besides, combing with the function of Chevrons on preventing excessive speed and the benefit to make drivers keep a more proper lane position, China's Chevrons appear to be of great benefit to reduce crashes (e.g., run-off-road) in curves. Copyright © 2014 Elsevier Ltd. All rights reserved.

DEVELOPING A METHOD TO IDENTIFY HORIZONTAL CURVE SEGMENTS WITH HIGH CRASH OCCURRENCES USING THE HAF ALGORITHM

DOT National Transportation Integrated Search

2018-04-01

Crashes occur every day on Utahs highways. Curves can be particularly dangerous as they require driver focus due to potentially unseen hazards. Often, crashes occur on curves due to poor curve geometry, a lack of warning signs, or poor surface con...

Execution of deep dipole geoelectrical soundings in areas of geothermal interest. Final report

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

Patella, D.

It is suggested that deep geoelectrical problems may be resolved by carrying out dipole soundings in the field and applying a quantitative interpretation in the Schlumberger domain. The 'transformation' of original field dipole sounding curves into equivalent Schlumberger curves is outlined for the cases of layered structures and arbitrary underground structures. Theoretical apparent resistivity curves are derived for soundings over bidimensional structures. Following a summary of the geological features of the Travale-Radicondoli geothermal area of Italy, the dipole sounding method employed for this field study and the means of collecting and analyzing the data, are outlined.

General heat kernel coefficients for massless free spin-3/2 Rarita-Schwinger field

NASA Astrophysics Data System (ADS)

Karan, Sudip; Kumar, Shashank; Panda, Binata

2018-04-01

We review the general heat kernel method for the Dirac spinor field as an elementary example in any arbitrary background. We, then compute the first three Seeley-DeWitt coefficients for the massless free spin-3/2 Rarita-Schwinger field without imposing any limitations on the background geometry.

Geometry and the Physics of Seasons

ERIC Educational Resources Information Center

Khavrus, Vyacheslav; Shelevytsky, Ihor

2012-01-01

By means of a simple mathematical model recently developed by the authors (2010 "Phys. Educ." 45 641), the passage of the seasons on the Earth is simulated for arbitrary latitudes, taking into account sunlight attenuation in the atmosphere. The method developed can be used to predict a realistic value of the solar energy input (insolation) that…

Parallel SOR methods with a parabolic-diffusion acceleration technique for solving an unstructured-grid Poisson equation on 3D arbitrary geometries

NASA Astrophysics Data System (ADS)

Zapata, M. A. Uh; Van Bang, D. Pham; Nguyen, K. D.

2016-05-01

This paper presents a parallel algorithm for the finite-volume discretisation of the Poisson equation on three-dimensional arbitrary geometries. The proposed method is formulated by using a 2D horizontal block domain decomposition and interprocessor data communication techniques with message passing interface. The horizontal unstructured-grid cells are reordered according to the neighbouring relations and decomposed into blocks using a load-balanced distribution to give all processors an equal amount of elements. In this algorithm, two parallel successive over-relaxation methods are presented: a multi-colour ordering technique for unstructured grids based on distributed memory and a block method using reordering index following similar ideas of the partitioning for structured grids. In all cases, the parallel algorithms are implemented with a combination of an acceleration iterative solver. This solver is based on a parabolic-diffusion equation introduced to obtain faster solutions of the linear systems arising from the discretisation. Numerical results are given to evaluate the performances of the methods showing speedups better than linear.

Effect of Loop Geometry on TEM Response Over Layered Earth

NASA Astrophysics Data System (ADS)

Qi, Youzheng; Huang, Ling; Wu, Xin; Fang, Guangyou; Yu, Gang

2014-09-01

A large horizontal loop located on the ground or carried by an aircraft are the most common sources of the transient electromagnetic method. Although topographical factors or airplane outlines make the loop of arbitrary shape, magnetic sources are generally represented as a magnetic dipole or a circular loop, which may bring about significant errors in the calculated response. In this paper, we present a method for calculating the response of a loop of arbitrary shape (for which the description can be obtained by different methods, including GPS localization) in air or on the surface of a stratified earth. The principle of reciprocity is firstly used to exchange the functions of the transmitting loop and the dipole receiver, then the response of a vertical or a horizontal magnetic dipole is calculated beforehand, and finally the line integral of the second kind is employed to get the transient response. Analytical analysis and comparisons depict that our work got very good results in many situations. Synthetic and field examples are given in the end to show the effect of loop geometry and how our method improves the precision of the EM response.

Analytic Reflected Lightcurves for Exoplanets

NASA Astrophysics Data System (ADS)

Haggard, Hal M.; Cowan, Nicolas B.

2018-04-01

The disk-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motion coupled with an inhomogeneous albedo map. We have previously derived analytic reflected lightcurves for spherical harmonic albedo maps in the special case of a synchronously-rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard 2013). In this letter, we present analytic reflected lightcurves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points (δ-maps), and spherical harmonics (Y_l^m-maps). In particular, we use Wigner D-matrices to express an harmonic lightcurve for an arbitrary viewing geometry as a non-linear combination of harmonic lightcurves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected lightcurves, as well as fast calculation of lightcurves for mapping exoplanets based on time-resolved photometry. To these ends we make available Exoplanet Analytic Reflected Lightcurves (EARL), a simple open-source code that allows rapid computation of reflected lightcurves.

Micromaths: Removing Euclid from the Shackles.

ERIC Educational Resources Information Center

Oldknow, Adrian

2000-01-01

Attempts to lay the groundwork for a study of curves produced as loci using dynamic geometry. Provides some sketches of ways Cabri may be used to enhance the teaching of geometry with particular reference to synthetic plane Euclidean geometry, locus, and the conics. (Contains 26 references.) (ASK)

A generalized reconstruction framework for unconventional PET systems

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

Mathews, Aswin John, E-mail: amathews@wustl.edu; Li, Ke; O’Sullivan, Joseph A.

2015-08-15

Purpose: Quantitative estimation of the radionuclide activity concentration in positron emission tomography (PET) requires precise modeling of PET physics. The authors are focused on designing unconventional PET geometries for specific applications. This work reports the creation of a generalized reconstruction framework, capable of reconstructing tomographic PET data for systems that use right cuboidal detector elements positioned at arbitrary geometry using a regular Cartesian grid of image voxels. Methods: The authors report on a variety of design choices and optimization for the creation of the generalized framework. The image reconstruction algorithm is maximum likelihood-expectation–maximization. System geometry can be specified using amore » simple script. Given the geometry, a symmetry seeking algorithm finds existing symmetry in the geometry with respect to the image grid to improve the memory usage/speed. Normalization is approached from a geometry independent perspective. The system matrix is computed using the Siddon’s algorithm and subcrystal approach. The program is parallelized through open multiprocessing and message passing interface libraries. A wide variety of systems can be modeled using the framework. This is made possible by modeling the underlying physics and data correction, while generalizing the geometry dependent features. Results: Application of the framework for three novel PET systems, each designed for a specific application, is presented to demonstrate the robustness of the framework in modeling PET systems of unconventional geometry. Three PET systems of unconventional geometry are studied. (1) Virtual-pinhole half-ring insert integrated into Biograph-40: although the insert device improves image quality over conventional whole-body scanner, the image quality varies depending on the position of the insert and the object. (2) Virtual-pinhole flat-panel insert integrated into Biograph-40: preliminary results from an investigation into a modular flat-panel insert are presented. (3) Plant PET system: a reconfigurable PET system for imaging plants, with resolution of greater than 3.3 mm, is shown. Using the automated symmetry seeking algorithm, the authors achieved a compression ratio of the storage and memory requirement by a factor of approximately 50 for the half-ring and flat-panel systems. For plant PET system, the compression ratio is approximately five. The ratio depends on the level of symmetry that exists in different geometries. Conclusions: This work brings the field closer to arbitrary geometry reconstruction. A generalized reconstruction framework can be used to validate multiple hypotheses and the effort required to investigate each system is reduced. Memory usage/speed can be improved with certain optimizations.« less

A generalized reconstruction framework for unconventional PET systems.

PubMed

Mathews, Aswin John; Li, Ke; Komarov, Sergey; Wang, Qiang; Ravindranath, Bosky; O'Sullivan, Joseph A; Tai, Yuan-Chuan

2015-08-01

Quantitative estimation of the radionuclide activity concentration in positron emission tomography (PET) requires precise modeling of PET physics. The authors are focused on designing unconventional PET geometries for specific applications. This work reports the creation of a generalized reconstruction framework, capable of reconstructing tomographic PET data for systems that use right cuboidal detector elements positioned at arbitrary geometry using a regular Cartesian grid of image voxels. The authors report on a variety of design choices and optimization for the creation of the generalized framework. The image reconstruction algorithm is maximum likelihood-expectation-maximization. System geometry can be specified using a simple script. Given the geometry, a symmetry seeking algorithm finds existing symmetry in the geometry with respect to the image grid to improve the memory usage/speed. Normalization is approached from a geometry independent perspective. The system matrix is computed using the Siddon's algorithm and subcrystal approach. The program is parallelized through open multiprocessing and message passing interface libraries. A wide variety of systems can be modeled using the framework. This is made possible by modeling the underlying physics and data correction, while generalizing the geometry dependent features. Application of the framework for three novel PET systems, each designed for a specific application, is presented to demonstrate the robustness of the framework in modeling PET systems of unconventional geometry. Three PET systems of unconventional geometry are studied. (1) Virtual-pinhole half-ring insert integrated into Biograph-40: although the insert device improves image quality over conventional whole-body scanner, the image quality varies depending on the position of the insert and the object. (2) Virtual-pinhole flat-panel insert integrated into Biograph-40: preliminary results from an investigation into a modular flat-panel insert are presented. (3) Plant PET system: a reconfigurable PET system for imaging plants, with resolution of greater than 3.3 mm, is shown. Using the automated symmetry seeking algorithm, the authors achieved a compression ratio of the storage and memory requirement by a factor of approximately 50 for the half-ring and flat-panel systems. For plant PET system, the compression ratio is approximately five. The ratio depends on the level of symmetry that exists in different geometries. This work brings the field closer to arbitrary geometry reconstruction. A generalized reconstruction framework can be used to validate multiple hypotheses and the effort required to investigate each system is reduced. Memory usage/speed can be improved with certain optimizations.

A generalized reconstruction framework for unconventional PET systems

PubMed Central

Mathews, Aswin John; Li, Ke; Komarov, Sergey; Wang, Qiang; Ravindranath, Bosky; O’Sullivan, Joseph A.; Tai, Yuan-Chuan

2015-01-01

Purpose: Quantitative estimation of the radionuclide activity concentration in positron emission tomography (PET) requires precise modeling of PET physics. The authors are focused on designing unconventional PET geometries for specific applications. This work reports the creation of a generalized reconstruction framework, capable of reconstructing tomographic PET data for systems that use right cuboidal detector elements positioned at arbitrary geometry using a regular Cartesian grid of image voxels. Methods: The authors report on a variety of design choices and optimization for the creation of the generalized framework. The image reconstruction algorithm is maximum likelihood-expectation–maximization. System geometry can be specified using a simple script. Given the geometry, a symmetry seeking algorithm finds existing symmetry in the geometry with respect to the image grid to improve the memory usage/speed. Normalization is approached from a geometry independent perspective. The system matrix is computed using the Siddon’s algorithm and subcrystal approach. The program is parallelized through open multiprocessing and message passing interface libraries. A wide variety of systems can be modeled using the framework. This is made possible by modeling the underlying physics and data correction, while generalizing the geometry dependent features. Results: Application of the framework for three novel PET systems, each designed for a specific application, is presented to demonstrate the robustness of the framework in modeling PET systems of unconventional geometry. Three PET systems of unconventional geometry are studied. (1) Virtual-pinhole half-ring insert integrated into Biograph-40: although the insert device improves image quality over conventional whole-body scanner, the image quality varies depending on the position of the insert and the object. (2) Virtual-pinhole flat-panel insert integrated into Biograph-40: preliminary results from an investigation into a modular flat-panel insert are presented. (3) Plant PET system: a reconfigurable PET system for imaging plants, with resolution of greater than 3.3 mm, is shown. Using the automated symmetry seeking algorithm, the authors achieved a compression ratio of the storage and memory requirement by a factor of approximately 50 for the half-ring and flat-panel systems. For plant PET system, the compression ratio is approximately five. The ratio depends on the level of symmetry that exists in different geometries. Conclusions: This work brings the field closer to arbitrary geometry reconstruction. A generalized reconstruction framework can be used to validate multiple hypotheses and the effort required to investigate each system is reduced. Memory usage/speed can be improved with certain optimizations. PMID:26233187

Exp(1076) Shades of Black: Aspects of Black Hole Microstates

NASA Astrophysics Data System (ADS)

Vasilakis, Orestis

In this thesis we examine smooth supergravity solutions known as "microstate geometries". These solutions have neither a horizon, nor a singularity, yet they have the same asymptotic structure and conserved charges as black holes. Specifically we study supersymmetric and extremal non-supersymmetric solutions. The goal of this program is to construct enough microstates to account for the correct scaling behavior of the black hole entropy with respect to the charges within the supergravity approximation. For supersymmetric systems that are ⅛-BPS, microstate geometries account so far only for Q5/4 of the total entropy S ˜ Q3/2, while for non-supersymmetric systems the known microstate geometries are sporadic. For the supersymmetric case we construct solutions with three and four charges. Five-dimensional systems with three and four charges are ⅛-BPS. Thus they admit macroscopic horizons making the supergravity approximation valid. For the three-charge case we present some steps towards the construction of the superstratum, a microstate geometry depending on arbitrary functions of two variables, which is expected to provide the necessary entropy for this class of solutions. Specifically we construct multiple concentric solutions with three electric and two dipole magnetic charges which depend on arbitrary functions of two variables and examine their properties. These solutions have no KKM charge and thus are singular. For the four-charge case we construct microstate geometries by extending results available in the literature for three charges. We find smooth solutions in terms of bubbled geometries with ambipolar Gibbons-Hawking base space and by constructing the relevant supertubes. In the non-supersymmetric case we work with a three-charge system of extremal black holes known as almost-BPS, which provides a controlled way of breaking sypersymmetry. By using supertubes we construct the first systematic example of a family of almost-BPS microstate geometries and examine the moduli space of solutions. Furthermore by using brane probe analysis we show that, despite the breaking of supersymmetry, almost-BPS solutions receive no quantum corrections and thus must be subject to some kind of non-renormalization theorem.

Experimental Determination of the HPGe Spectrometer Efficiency Calibration Curves for Various Sample Geometry for Gamma Energy from 50 keV to 2000 keV

NASA Astrophysics Data System (ADS)

Saat, Ahmad; Hamzah, Zaini; Yusop, Mohammad Fariz; Zainal, Muhd Amiruddin

2010-07-01

Detection efficiency of a gamma-ray spectrometry system is dependent upon among others, energy, sample and detector geometry, volume and density of the samples. In the present study the efficiency calibration curves of newly acquired (August 2008) HPGe gamma-ray spectrometry system was carried out for four sample container geometries, namely Marinelli beaker, disc, cylindrical beaker and vial, normally used for activity determination of gamma-ray from environmental samples. Calibration standards were prepared by using known amount of analytical grade uranium trioxide ore, homogenized in plain flour into the respective containers. The ore produces gamma-rays of energy ranging from 53 keV to 1001 keV. Analytical grade potassium chloride were prepared to determine detection efficiency of 1460 keV gamma-ray emitted by potassium isotope K-40. Plots of detection efficiency against gamma-ray energy for the four sample geometries were found to fit smoothly to a general form of ɛ = AΕa+BΕb, where ɛ is efficiency, Ε is energy in keV, A, B, a and b are constants that are dependent on the sample geometries. All calibration curves showed the presence of a "knee" at about 180 keV. Comparison between the four geometries showed that the efficiency of Marinelli beaker is higher than cylindrical beaker and vial, while cylindrical disk showed the lowest.

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

NASA Astrophysics Data System (ADS)

Hill, Peter; Shanahan, Brendan; Dudson, Ben

2017-04-01

We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q → ∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions. The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined. We also demonstrate the feasibility of using the FCI approach in no n-axisymmetric configurations for a simple diffusion model in a "straight stellarator" magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius. The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

GEMPAK: An arbitrary aircraft geometry generator

NASA Technical Reports Server (NTRS)

Stack, S. H.; Edwards, C. L. W.; Small, W. J.

1977-01-01

A computer program, GEMPAK, has been developed to aid in the generation of detailed configuration geometry. The program was written to allow the user as much flexibility as possible in his choices of configurations and the detail of description desired and at the same time keep input requirements and program turnaround and cost to a minimum. The program consists of routines that generate fuselage and planar-surface (winglike) geometry and a routine that will determine the true intersection of all components with the fuselage. This paper describes the methods by which the various geometries are generated and provides input description with sample input and output. Also included are descriptions of the primary program variables and functions performed by the various routines. The FORTRAN program GEMPAK has been used extensively in conjunction with interfaces to several aerodynamic and plotting computer programs and has proven to be an effective aid in the preliminary design phase of aircraft configurations.

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

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

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro

2017-04-01

We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Theoretical antisymmetric span loading for wings of arbitrary plan form at subsonic speeds

NASA Technical Reports Server (NTRS)

Deyoung, John

1951-01-01

A simplified lifting-surface theory that includes effects of compressibility and spanwise variation of section lift-curve slope is used to provide charts with which antisymmetric loading due to arbitrary antisymmetric angle of attack can be found for wings having symmetric plan forms with a constant spanwise sweep angle of the quarter-chord line. Consideration is given to the flexible wing in roll. Aerodynamic characteristics due to rolling, deflected ailerons, and sideslip of wings with dihedral are considered. Solutions are presented for straight-tapered wings for a range of swept plan forms.

Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries

NASA Astrophysics Data System (ADS)

Savickas, David

2015-04-01

General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).

Calculation of three-dimensional compressible laminar and turbulent boundary layers. Calculation of three-dimensional compressible boundary layers on arbitrary wings

NASA Technical Reports Server (NTRS)

Cebeci, T.; Kaups, K.; Ramsey, J.; Moser, A.

1975-01-01

A very general method for calculating compressible three-dimensional laminar and turbulent boundary layers on arbitrary wings is described. The method utilizes a nonorthogonal coordinate system for the boundary-layer calculations and includes a geometry package that represents the wing analytically. In the calculations all the geometric parameters of the coordinate system are accounted for. The Reynolds shear-stress terms are modeled by an eddy-viscosity formulation developed by Cebeci. The governing equations are solved by a very efficient two-point finite-difference method used earlier by Keller and Cebeci for two-dimensional flows and later by Cebeci for three-dimensional flows.

Low-frequency quadrupole impedance of undulators and wigglers

DOE PAGES

Blednykh, A.; Bassi, G.; Hidaka, Y.; ...

2016-10-25

An analytical expression of the low-frequency quadrupole impedance for undulators and wigglers is derived and benchmarked against beam-based impedance measurements done at the 3 GeV NSLS-II storage ring. The adopted theoretical model, valid for an arbitrary number of electromagnetic layers with parallel geometry, allows to calculate the quadrupole impedance for arbitrary values of the magnetic permeability μ r. Here, in the comparison of the analytical results with the measurements for variable magnet gaps, two limit cases of the permeability have been studied: the case of perfect magnets (μ r → ∞), and the case in which the magnets are fullymore » saturated (μ r = 1).« less

Extreme scale multi-physics simulations of the tsunamigenic 2004 Sumatra megathrust earthquake

NASA Astrophysics Data System (ADS)

Ulrich, T.; Gabriel, A. A.; Madden, E. H.; Wollherr, S.; Uphoff, C.; Rettenberger, S.; Bader, M.

2017-12-01

SeisSol (www.seissol.org) is an open-source software package based on an arbitrary high-order derivative Discontinuous Galerkin method (ADER-DG). It solves spontaneous dynamic rupture propagation on pre-existing fault interfaces according to non-linear friction laws, coupled to seismic wave propagation with high-order accuracy in space and time (minimal dispersion errors). SeisSol exploits unstructured meshes to account for complex geometries, e.g. high resolution topography and bathymetry, 3D subsurface structure, and fault networks. We present the up-to-date largest (1500 km of faults) and longest (500 s) dynamic rupture simulation modeling the 2004 Sumatra-Andaman earthquake. We demonstrate the need for end-to-end-optimization and petascale performance of scientific software to realize realistic simulations on the extreme scales of subduction zone earthquakes: Considering the full complexity of subduction zone geometries leads inevitably to huge differences in element sizes. The main code improvements include a cache-aware wave propagation scheme and optimizations of the dynamic rupture kernels using code generation. In addition, a novel clustered local-time-stepping scheme for dynamic rupture has been established. Finally, asynchronous output has been implemented to overlap I/O and compute time. We resolve the frictional sliding process on the curved mega-thrust and a system of splay faults, as well as the seismic wave field and seafloor displacement with frequency content up to 2.2 Hz. We validate the scenario by geodetic, seismological and tsunami observations. The resulting rupture dynamics shed new light on the activation and importance of splay faults.

Further Evidence in Support of the Universal Nilpotent Grammatical Computational Paradigm of Quantum Physics

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

Marcer, Peter J.; Rowlands, Peter

2010-12-22

Further evidence is presented in favour of the computational paradigm, conceived and constructed by Rowlands and Diaz, as detailed in Rowlands' book Zero to Infinity (2007), and in particular the authors' paper 'The Grammatical Universe: the Laws of Thermodynamics and Quantum Entanglement'. The paradigm, which has isomorphic group and algebraic quantum mechanical language interpretations, not only predicts the well-established facts of quantum physics, the periodic table, chemistry / valence and of molecular biology, whose understanding it extends; it also provides an elegant, simple solution to the unresolved quantum measurement problem. In this fundamental paradigm, all the computational constructs / predictionsmore » that emerge, follow from the simple fact, that, as in quantum mechanics, the wave function is defined only up to an arbitrary fixed phase. This fixed phase provides a simple physical understanding of the quantum vacuum in quantum field theory, where only relative phases, known to be able to encode 3+1 relativistic space-time geometries, can be measured. It is the arbitrary fixed measurement standard, against which everything that follows is to be measured, even though the standard itself cannot be, since nothing exists against which to measure it. The standard, as an arbitrary fixed reference phase, functions as the holographic basis for a self-organized universal quantum process of emergent novel fermion states of matter where, following each emergence, the arbitrary standard is re-fixed anew so as to provide a complete history / holographic record or hologram of the current fixed past, advancing an unending irreversible evolution, such as is the evidence of our senses. The fermion states, in accord with the Pauli exclusion principle, each correspond to a unique nilpotent symbol in the infinite alphabet (which specifies the grammar in this nilpotent universal computational rewrite system (NUCRS) paradigm); and the alphabet, as Hill and Rowlands hypothesize on substantial evidence [26], includes that of the RNA / DNA genetic code and, as holographic phase encodings / holograms, the 4D geometries of all living systems as self-organised grammatical computational rewrite machines / machinery. Human brains, natural grammatical (written symbol) languages, 4D geometric self-awareness and a totally new emergent property of matter, human consciousness, can thus with some measure of confidence be postulated as further genetic consequences which follow from this self-organizing fundamental rewrite NUCRS construction. For it, like natural language, possesses a semantics and not just a syntax, where the initial symbol, i.e. the arbitrary fixed phase measurement standard, is able to function as the template for the blueprints of the emergent 4D relativistic real and virtual geometries to come, in a 'from the Self Creation to the creation of the human self' computational rewrite process evolution.« less

Further Evidence in Support of the Universal Nilpotent Grammatical Computational Paradigm of Quantum Physics

NASA Astrophysics Data System (ADS)

Marcer, Peter J.; Rowlands, Peter

2010-12-01

Further evidence is presented in favour of the computational paradigm, conceived and constructed by Rowlands and Diaz, as detailed in Rowlands' book Zero to Infinity (2007) [2], and in particular the authors' paper `The Grammatical Universe: the Laws of Thermodynamics and Quantum Entanglement' [1]. The paradigm, which has isomorphic group and algebraic quantum mechanical language interpretations, not only predicts the well-established facts of quantum physics, the periodic table, chemistry / valence and of molecular biology, whose understanding it extends; it also provides an elegant, simple solution to the unresolved quantum measurement problem. In this fundamental paradigm, all the computational constructs / predictions that emerge, follow from the simple fact, that, as in quantum mechanics, the wave function is defined only up to an arbitrary fixed phase. This fixed phase provides a simple physical understanding of the quantum vacuum in quantum field theory, where only relative phases, known to be able to encode 3+1 relativistic space-time geometries, can be measured. It is the arbitrary fixed measurement standard, against which everything that follows is to be measured, even though the standard itself cannot be, since nothing exists against which to measure it. The standard, as an arbitrary fixed reference phase, functions as the holographic basis for a self-organized universal quantum process of emergent novel fermion states of matter where, following each emergence, the arbitrary standard is re-fixed anew so as to provide a complete history / holographic record or hologram of the current fixed past, advancing an unending irreversible evolution, such as is the evidence of our senses. The fermion states, in accord with the Pauli exclusion principle, each correspond to a unique nilpotent symbol in the infinite alphabet (which specifies the grammar in this nilpotent universal computational rewrite system (NUCRS) paradigm); and the alphabet, as Hill and Rowlands hypothesize on substantial evidence [26], includes that of the RNA / DNA genetic code and, as holographic phase encodings / holograms, the 4D geometries of all living systems as self-organised grammatical computational rewrite machines / machinery. Human brains, natural grammatical (written symbol) languages, 4D geometric self-awareness and a totally new emergent property of matter, human consciousness, can thus with some measure of confidence be postulated as further genetic consequences which follow from this self-organizing fundamental rewrite NUCRS construction. For it, like natural language, possesses a semantics and not just a syntax, where the initial symbol, i.e. the arbitrary fixed phase measurement standard, is able to function as the template for the blueprints of the emergent 4D relativistic real and virtual geometries to come, in a `from the Self Creation to the creation of the human self' computational rewrite process evolution.

VNAP2: A Computer Program for Computation of Two-dimensional, Time-dependent, Compressible, Turbulent Flow

NASA Technical Reports Server (NTRS)

Cline, M. C.

1981-01-01

A computer program, VNAP2, for calculating turbulent (as well as laminar and inviscid), steady, and unsteady flow is presented. It solves the two dimensional, time dependent, compressible Navier-Stokes equations. The turbulence is modeled with either an algebraic mixing length model, a one equation model, or the Jones-Launder two equation model. The geometry may be a single or a dual flowing stream. The interior grid points are computed using the unsplit MacCormack scheme. Two options to speed up the calculations for high Reynolds number flows are included. The boundary grid points are computed using a reference plane characteristic scheme with the viscous terms treated as source functions. An explicit artificial viscosity is included for shock computations. The fluid is assumed to be a perfect gas. The flow boundaries may be arbitrary curved solid walls, inflow/outflow boundaries, or free jet envelopes. Typical problems that can be solved concern nozzles, inlets, jet powered afterbodies, airfoils, and free jet expansions. The accuracy and efficiency of the program are shown by calculations of several inviscid and turbulent flows. The program and its use are described completely, and six sample cases and a code listing are included.

Curved focusing crystals for hard X-ray astronomy

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

Ferrari, C., E-mail: ferrari@imem.cnr.it; Buffagni, E.; Bonnini, E.

A lens made by a properly arranged array of crystals can be used to focus x-rays of energy ranging from 30 to 500 keV for x-ray astronomy. Mosaic or curved crystals can be employed as x-ray optical elements. In this work self standing curved focusing Si and GaAs crystals in which the lattice bending is induced by a controlled damaging process on one side of planar crystals are characterized. Diffraction profiles in Laue geometry have been measured in crystals at x-ray energies E = 17, 59 and 120 keV. An enhancement of diffraction efficiency is found in asymmetric geometries.

Bellows flow-induced vibrations

NASA Technical Reports Server (NTRS)

Tygielski, P. J.; Smyly, H. M.; Gerlach, C. R.

1983-01-01

The bellows flow excitation mechanism and results of comprehensive test program are summarized. The analytical model for predicting bellows flow induced stress is refined. The model includes the effects of an upstream elbow, arbitrary geometry, and multiple piles. A refined computer code for predicting flow induced stress is described which allows life prediction if a material S-N diagram is available.

Workshops on using the GPS method to determine curve advisory speeds.

DOT National Transportation Integrated Search

2009-12-01

Curve warning signs are intended to improve curve safety by alerting the driver to a change in : geometry that may not be apparent or expected. However, several research projects conducted in the last 20 : years have consistently shown that drivers a...

49 CFR 213.59 - Elevation of curved track; runoff.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 49 Transportation 4 2011-10-01 2011-10-01 false Elevation of curved track; runoff. 213.59 Section 213.59 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL RAILROAD ADMINISTRATION, DEPARTMENT OF TRANSPORTATION TRACK SAFETY STANDARDS Track Geometry § 213.59 Elevation of curved...

SPIDERMAN: Fast code to simulate secondary transits and phase curves

NASA Astrophysics Data System (ADS)

Louden, Tom; Kreidberg, Laura

2017-11-01

SPIDERMAN calculates exoplanet phase curves and secondary eclipses with arbitrary surface brightness distributions in two dimensions. The code uses a geometrical algorithm to solve exactly the area of sections of the disc of the planet that are occulted by the star. Approximately 1000 models can be generated per second in typical use, which makes making Markov Chain Monte Carlo analyses practicable. The code is modular and allows comparison of the effect of multiple different brightness distributions for a dataset.

UTM: Universal Transit Modeller

NASA Astrophysics Data System (ADS)

Deeg, Hans J.

2014-12-01

The Universal Transit Modeller (UTM) is a light-curve simulator for all kinds of transiting or eclipsing configurations between arbitrary numbers of several types of objects, which may be stars, planets, planetary moons, and planetary rings. A separate fitting program, UFIT (Universal Fitter) is part of the UTM distribution and may be used to derive best fits to light-curves for any set of continuously variable parameters. UTM/UFIT is written in IDL code and its source is released in the public domain under the GNU General Public License.

Waveform fitting and geometry analysis for full-waveform lidar feature extraction

NASA Astrophysics Data System (ADS)

Tsai, Fuan; Lai, Jhe-Syuan; Cheng, Yi-Hsiu

2016-10-01

This paper presents a systematic approach that integrates spline curve fitting and geometry analysis to extract full-waveform LiDAR features for land-cover classification. The cubic smoothing spline algorithm is used to fit the waveform curve of the received LiDAR signals. After that, the local peak locations of the waveform curve are detected using a second derivative method. According to the detected local peak locations, commonly used full-waveform features such as full width at half maximum (FWHM) and amplitude can then be obtained. In addition, the number of peaks, time difference between the first and last peaks, and the average amplitude are also considered as features of LiDAR waveforms with multiple returns. Based on the waveform geometry, dynamic time-warping (DTW) is applied to measure the waveform similarity. The sum of the absolute amplitude differences that remain after time-warping can be used as a similarity feature in a classification procedure. An airborne full-waveform LiDAR data set was used to test the performance of the developed feature extraction method for land-cover classification. Experimental results indicate that the developed spline curve- fitting algorithm and geometry analysis can extract helpful full-waveform LiDAR features to produce better land-cover classification than conventional LiDAR data and feature extraction methods. In particular, the multiple-return features and the dynamic time-warping index can improve the classification results significantly.

Free vibration of rectangular plates with a small initial curvature

NASA Technical Reports Server (NTRS)

Adeniji-Fashola, A. A.; Oyediran, A. A.

1988-01-01

The method of matched asymptotic expansions is used to solve the transverse free vibration of a slightly curved, thin rectangular plate. Analytical results for natural frequencies and mode shapes are presented in the limit when the dimensionless bending rigidity, epsilon, is small compared with in-plane forces. Results for different boundary conditions are obtained when the initial deflection is: (1) a polynomial in both directions, and (2) the product of a polynomial and a trigonometric function, and arbitrary. For the arbitrary initial deflection case, the Fourier series technique is used to define the initial deflection. The results obtained show that the natural frequencies of vibration of slightly curved plates are coincident with those of perfectly flat, prestressed rectangular plates. However, the eigenmodes are very different from those of initially flat prestressed rectangular plates. The total deflection is found to be the sum of the initial deflection, the deflection resulting from the solution of the flat plate problem, and the deflection resulting from the static problem.

FIDDLE: A Computer Code for Finite Difference Development of Linear Elasticity in Generalized Curvilinear Coordinates

NASA Technical Reports Server (NTRS)

Kaul, Upender K.

2005-01-01

A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.

3D freeform printing of silk fibroin.

PubMed

Rodriguez, Maria J; Dixon, Thomas A; Cohen, Eliad; Huang, Wenwen; Omenetto, Fiorenzo G; Kaplan, David L

2018-04-15

Freeform fabrication has emerged as a key direction in printing biologically-relevant materials and structures. With this emerging technology, complex structures with microscale resolution can be created in arbitrary geometries and without the limitations found in traditional bottom-up or top-down additive manufacturing methods. Recent advances in freeform printing have used the physical properties of microparticle-based granular gels as a medium for the submerged extrusion of bioinks. However, most of these techniques require post-processing or crosslinking for the removal of the printed structures (Miller et al., 2015; Jin et al., 2016) [1,2]. In this communication, we introduce a novel method for the one-step gelation of silk fibroin within a suspension of synthetic nanoclay (Laponite) and polyethylene glycol (PEG). Silk fibroin has been used as a biopolymer for bioprinting in several contexts, but chemical or enzymatic additives or bulking agents are needed to stabilize 3D structures. Our method requires no post-processing of printed structures and allows for in situ physical crosslinking of pure aqueous silk fibroin into arbitrary geometries produced through freeform 3D printing. 3D bioprinting has emerged as a technology that can produce biologically relevant structures in defined geometries with microscale resolution. Techniques for fabrication of free-standing structures by printing into granular gel media has been demonstrated previously, however, these methods require crosslinking agents and post-processing steps on printed structures. Our method utilizes one-step gelation of silk fibroin within a suspension of synthetic nanoclay (Laponite), with no need for additional crosslinking compounds or post processing of the material. This new method allows for in situ physical crosslinking of pure aqueous silk fibroin into defined geometries produced through freeform 3D printing. Copyright © 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Development of bankfull hydraulic geometry relationships for the physiographic divisions of the United States

USDA-ARS?s Scientific Manuscript database

Bankfull hydraulic geometry relationships are used to estimate channel dimensions for stream flow simulation models, which require channel geometry data as input parameters. Often, one nationwide curve is used across the entire U.S. (e.g. in SWAT), even though studies have shown that the use of reg...

Computational Geometry and Computer-Aided Design

NASA Technical Reports Server (NTRS)

Fay, T. H. (Compiler); Shoosmith, J. N. (Compiler)

1985-01-01

Extended abstracts of papers addressing the analysis, representation, and synthesis of shape information are presented. Curves and shape control, grid generation and contouring, solid modelling, surfaces, and curve intersection are specifically addressed.

QPOs from Random X-ray Bursts around Rotating Black Holes

NASA Technical Reports Server (NTRS)

Kukumura, Keigo; Kazanas, Demosthenes; Stephenson, Gordon

2009-01-01

We continue our earlier studies of quasi-periodic oscillations (QPOs) in the power spectra of accreting, rapidly-rotating black holes that originate from the geometric 'light echoes' of X-ray flares occurring within the black hole ergosphere. Our present work extends our previous treatment to three-dimensional photon emission and orbits to allow for arbitrary latitudes in the positions of the distant observers and the X-ray sources in place of the mainly equatorial positions and photon orbits of the earlier consideration. Following the trajectories of a large number of photons we calculate the response functions of a given geometry and use them to produce model light curves which we subsequently analyze to compute their power spectra and autocorrelation functions. In the case of an optically-thin environment, relevant to advection-dominated accretion flows, we consistently find QPOs at frequencies of order of approximately kHz for stellar-mass black hole candidates while order of approximately mHz for typical active galactic nuclei (approximately equal to 10(exp 7) solar mass) for a wide range of viewing angles (30 degrees to 80 degrees) from X-ray sources predominantly concentrated toward the equator within the ergosphere. As in out previous treatment, here too, the QPO signal is produced by the frame-dragging of the photons by the rapidly-rotating black hole, which results in photon 'bunches' separated by constant time-lags, the result of multiple photon orbits around the hole. Our model predicts for various source/observer configurations the robust presence of a new class of QPOs, which is inevitably generic to curved spacetime structure in rotating black hole systems.

An examination of the shrinking-core model of sub-micron aluminum combustion

NASA Astrophysics Data System (ADS)

Buckmaster, John; Jackson, Thomas L.

2013-04-01

We revisit the shrinking-core model of sub-micron aluminum combustion with particular attention to the mass flux balance at the reaction front which necessarily leads to a displacement velocity of the alumina shell surrounding the liquid aluminum. For the planar problem this displacement simply leads to an equal displacement of the entire alumina layer, and therefore a straightforward mathematical framework can be constructed. In this way we are able to construct a single curve which defines the burn time for arbitrary values of the diffusion coefficient of O atoms, the reaction rate, the characteristic length of the combustion field, and the O atom mass concentration within the alumina provided that it is much smaller than the aluminum density. This demonstrates a transition between a 'd 2-t' law for fast chemistry and a 'd-t' law for slow chemistry. For the spherical geometry, the one of physical interest, the outward displacement velocity creates not a simple displacement, but a stress field which, when examined within the framework of linear elasticity, strongly suggests the creation of internal cracking. We note that if the molten aluminum is pushed into these cracks by the high internal pressure characteristic of the stress field, its surface, where reaction occurs, could be fractal in nature and affect the fundamental nature of the burning law. Indeed, if this ingredient is added to the planar model, a single curve for the burn time can again be derived, and this describes a transition from a 'd 2-t' law to a 'd ν-t' law, where 0<ν<1.

Regional Curves of Bankfull Channel Geometry for Non-Urban Streams in the Piedmont Physiographic Province, Virginia

USGS Publications Warehouse

Lotspeich, R. Russell

2009-01-01

Natural-channel design involves constructing a stream channel with the dimensions, slope, and plan-view pattern that would be expected to transport water and sediment and yet maintain habitat and aesthetics consistent with unimpaired stream segments, or reaches. Regression relations for bankfull stream characteristics based on drainage area, referred to as 'regional curves,' are used in natural stream channel design to verify field determinations of bankfull discharge and stream channel characteristics. One-variable, ordinary least-squares regressions relating bankfull discharge, bankfull cross-sectional area, bankfull width, bankfull mean depth, and bankfull slope to drainage area were developed on the basis of data collected at 17 streamflow-gaging stations in rural areas with less than 20 percent urban land cover within the basin area (non-urban areas) of the Piedmont Physiographic Province in Virginia. These regional curves can be used to estimate the bankfull discharge and bankfull channel geometry when the drainage area of a watershed is known. Data collected included bankfull cross-sectional geometry, flood-plain geometry, and longitudinal profile data. In addition, particle-size distributions of streambed material were determined, and data on basin characteristics were compiled for each reach. Field data were analyzed to determine bankfull cross-sectional area, bankfull width, bankfull mean depth, bankfull discharge, bankfull channel slope, and D50 and D84 particle sizes at each site. The bankfull geometry from the 17 sites surveyed during this study represents the average of two riffle cross sections for each site. Regional curves developed for the 17 sites had coefficient of determination (R2) values of 0.950 for bankfull cross-sectional area, 0.913 for bankfull width, 0.915 for bankfull mean depth, 0.949 for bankfull discharge, and 0.497 for bankfull channel slope. The regional curves represent conditions for streams with defined channels and bankfull features in the Piedmont Physiographic Province in Virginia with drainage areas ranging from 0.29 to 111 square miles. All sites included in the development of the regional curves were located on streams with current or historical U.S. Geological Survey streamflow-gaging stations. These curves can be used to verify bankfull features identified in the field and bankfull stage for ungaged streams in non-urban areas.

High-Speed Laser Image Analysis of Plume Angles for Pressurised Metered Dose Inhalers: The Effect of Nozzle Geometry.

PubMed

Chen, Yang; Young, Paul M; Murphy, Seamus; Fletcher, David F; Long, Edward; Lewis, David; Church, Tanya; Traini, Daniela

2017-04-01

The aim of this study is to investigate aerosol plume geometries of pressurised metered dose inhalers (pMDIs) using a high-speed laser image system with different actuator nozzle materials and designs. Actuators made from aluminium, PET and PTFE were manufactured with four different nozzle designs: cone, flat, curved cone and curved flat. Plume angles and spans generated using the designed actuator nozzles with four solution-based pMDI formulations were imaged using Oxford Lasers EnVision system and analysed using EnVision Patternate software. Reduced plume angles for all actuator materials and nozzle designs were observed with pMDI formulations containing drug with high co-solvent concentration (ethanol) due to the reduced vapour pressure. Significantly higher plume angles were observed with the PTFE flat nozzle across all formulations, which could be a result of the nozzle geometry and material's hydrophobicity. The plume geometry of pMDI aerosols can be influenced by the vapour pressure of the formulation, nozzle geometries and actuator material physiochemical properties.

Two-Phase Annular Flow in Helical Coil Flow Channels in a Reduced Gravity Environment

NASA Technical Reports Server (NTRS)

Keshock, Edward G.; Lin, Chin S.

1996-01-01

A brief review of both single- and two-phase flow studies in curved and coiled flow geometries is first presented. Some of the complexities of two-phase liquid-vapor flow in curved and coiled geometries are discussed, and serve as an introduction to the advantages of observing such flows under a low-gravity environment. The studies proposed -- annular two-phase air-water flow in helical coil flow channels are described. Objectives of the studies are summarized.

Practical quality control tools for curves and surfaces

NASA Technical Reports Server (NTRS)

Small, Scott G.

1992-01-01

Curves (geometry) and surfaces created by Computer Aided Geometric Design systems in the engineering environment must satisfy two basic quality criteria: the geometric shape must have the desired engineering properties; and the objects must be parameterized in a way which does not cause computational difficulty for geometric processing and engineering analysis. Interactive techniques are described which are in use at Boeing to evaluate the quality of aircraft geometry prior to Computational Fluid Dynamic analysis, including newly developed methods for examining surface parameterization and its effects.

On the role of tip curvature on flapping plates.

PubMed

Martin, Nathan; Gharib, Morteza

2018-01-09

During the flapping motion of a fish's tail, the caudal fin exhibits antero-posterior bending and dorso-ventral bending, the latter of which is referred to as chord-wise bending herein. The impact of chord-wise tip curvature on the hydrodynamic forces for flapping plates is investigated to explore potential mechanisms to improve the maneuverability or the performance of autonomous underwater vehicles. First, actuated chord-wise tip curvature is explored. Comparison of rigid curved geometries to a rigid flat plate as a baseline suggests that an increased curvature decreases the generated forces. An actuated plate with a dynamic tip curvature is created to illustrate a modulation of this decrease in forces. Second, the impact of curvature is isolated using curved plates with an identical planform area. Comparison of rigid curved geometries as a baseline corroborates the result that an increased curvature decreases the generated forces, with the exception that presenting a concave geometry into the flow increases the thrust and the efficiency. A passively-actuated plate is designed to capitalize on this effect by presenting a concave geometry into the flow throughout the cycle. The dynamically and passively actuated plates show potential to improve the maneuverability and the efficiency of autonomous underwater vehicles, respectively.

A dissipative particle dynamics method for arbitrarily complex geometries

NASA Astrophysics Data System (ADS)

Li, Zhen; Bian, Xin; Tang, Yu-Hang; Karniadakis, George Em

2018-02-01

Dissipative particle dynamics (DPD) is an effective Lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to relatively simple geometries. Here, we formulate a local detection method for DPD involving arbitrarily shaped geometric three-dimensional domains. By introducing an indicator variable of boundary volume fraction (BVF) for each fluid particle, the boundary of arbitrary-shape objects is detected on-the-fly for the moving fluid particles using only the local particle configuration. Therefore, this approach eliminates the need of an analytical description of the boundary and geometry of objects in DPD simulations and makes it possible to load the geometry of a system directly from experimental images or computer-aided designs/drawings. More specifically, the BVF of a fluid particle is defined by the weighted summation over its neighboring particles within a cutoff distance. Wall penetration is inferred from the value of the BVF and prevented by a predictor-corrector algorithm. The no-slip boundary condition is achieved by employing effective dissipative coefficients for liquid-solid interactions. Quantitative evaluations of the new method are performed for the plane Poiseuille flow, the plane Couette flow and the Wannier flow in a cylindrical domain and compared with their corresponding analytical solutions and (high-order) spectral element solution of the Navier-Stokes equations. We verify that the proposed method yields correct no-slip boundary conditions for velocity and generates negligible fluctuations of density and temperature in the vicinity of the wall surface. Moreover, we construct a very complex 3D geometry - the "Brown Pacman" microfluidic device - to explicitly demonstrate how to construct a DPD system with complex geometry directly from loading a graphical image. Subsequently, we simulate the flow of a surfactant solution through this complex microfluidic device using the new method. Its effectiveness is demonstrated by examining the rich dynamics of surfactant micelles, which are flowing around multiple small cylinders and stenotic regions in the microfluidic device without wall penetration. In addition to stationary arbitrary-shape objects, the new method is particularly useful for problems involving moving and deformable boundaries, because it only uses local information of neighboring particles and satisfies the desired boundary conditions on-the-fly.

Langevin Equation on Fractal Curves

NASA Astrophysics Data System (ADS)

Satin, Seema; Gangal, A. D.

2016-07-01

We analyze random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, plays an important role in this analysis. A Langevin equation with a particular model of noise is proposed and solved using techniques of the Fα-Calculus.

In vivo proton dosimetry using a MOSFET detector in an anthropomorphic phantom with tissue inhomogeneity.

PubMed

Kohno, Ryosuke; Hotta, Kenji; Matsubara, Kana; Nishioka, Shie; Matsuura, Taeko; Kawashima, Mitsuhiko

2012-03-08

When in vivo proton dosimetry is performed with a metal-oxide semiconductor field-effect transistor (MOSFET) detector, the response of the detector depends strongly on the linear energy transfer. The present study reports a practical method to correct the MOSFET response for linear energy transfer dependence by using a simplified Monte Carlo dose calculation method (SMC). A depth-output curve for a mono-energetic proton beam in polyethylene was measured with the MOSFET detector. This curve was used to calculate MOSFET output distributions with the SMC (SMC(MOSFET)). The SMC(MOSFET) output value at an arbitrary point was compared with the value obtained by the conventional SMC(PPIC), which calculates proton dose distributions by using the depth-dose curve determined by a parallel-plate ionization chamber (PPIC). The ratio of the two values was used to calculate the correction factor of the MOSFET response at an arbitrary point. The dose obtained by the MOSFET detector was determined from the product of the correction factor and the MOSFET raw dose. When in vivo proton dosimetry was performed with the MOSFET detector in an anthropomorphic phantom, the corrected MOSFET doses agreed with the SMC(PPIC) results within the measurement error. To our knowledge, this is the first report of successful in vivo proton dosimetry with a MOSFET detector.

Maxis-A rezoning and remapping code in two dimensional cylindrical geometry

NASA Astrophysics Data System (ADS)

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

2018-06-01

This paper presents the new version of our code Maxis (Lin et al., 2011). Maxis is a local rezoning and remapping code in two dimensional cylindrical geometry, which can be employed to address the grid distortion problem of unstructured meshes. The new version of Maxis is mostly programmed in the C language which considerably improves its computational efficiency with respect to the former Matlab version. A new algorithm for determining the intersection of two arbitrary convex polygons is also incorporated into the new version. Some additional linking functions are further provided in the new version for the purpose of combining Maxis and MULTI2D.

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

DOE PAGES

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; ...

2017-01-03

In this paper, we present a consistent implicit incompressible smoothed particle hydrodynamics (I 2SPH) discretization of Navier–Stokes, Poisson–Boltzmann, and advection–diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent I 2SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. Lastly, the new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Calculation of the lateral control of swept and unswept flexible wings of arbitrary stiffness

NASA Technical Reports Server (NTRS)

Diederich, Franklin W

1951-01-01

A method similar to that of NACA rep. 1000 is presented for calculating the effectiveness and the reversal speed of lateral-control devices on swept and unswept wings of arbitrary stiffness. Provision is made for using either stiffness curves and root-rotation constants or structural influence coefficients in the analysis. Computing forms and an illustrative example are included to facilitate calculations by means of the method. The effectiveness of conventional aileron configurations and the margin against aileron reversal are shown to be relatively low for swept wings at all speeds and for all wing plan forms at supersonic speeds.

Iterated Hamiltonian type systems and applications

NASA Astrophysics Data System (ADS)

Tiba, Dan

2018-04-01

We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.

Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons

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

Elizalde, E.; Odintsov, S. D.; Institucio Catalana de Recerca i Estudis Avanccats

2009-03-15

We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a (D+1)-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other. For Robinmore » boundary conditions, the Casimir forces can be either attractive or repulsive, depending on the Robin coefficients and the separation between the plates, what is actually remarkable and useful. Indeed, we demonstrate the existence of an equilibrium point for the interplate distance, which is stabilized due to the Casimir force, and show that stability is enhanced by the presence of the extra dimensions. Applications of these properties in braneworld models are discussed. Finally, the corresponding results are generalized to the geometry of a piston of arbitrary cross section.« less

A Fictitious Domain Method for Resolving the Interaction of Blood Flow with Clot Growth

NASA Astrophysics Data System (ADS)

Mukherjee, Debanjan; Shadden, Shawn

2016-11-01

Thrombosis and thrombo-embolism cause a range of diseases including heart attack and stroke. Closer understanding of clot and blood flow mechanics provides valuable insights on the etiology, diagnosis, and treatment of thrombotic diseases. Such mechanics are complicated, however, by the discrete and multi-scale phenomena underlying thrombosis, and the complex interactions of unsteady, pulsatile hemodynamics with a clot of arbitrary shape and microstructure. We have developed a computational technique, based on a fictitious domain based finite element method, to study these interactions. The method can resolve arbitrary clot geometries, and dynamically couple fluid flow with static or growing clot boundaries. Macroscopic thrombus-hemodynamics interactions were investigated within idealized vessel geometries representative of the common carotid artery, with realistic unsteady flow profiles as inputs. The method was also employed successfully to resolve micro-scale interactions using a model driven by in-vivo morphology data. The results provide insights into the flow structures and hemodynamic loading around an arbitrarily grown clot at arterial length-scales, as well as flow and transport within the interstices of platelet aggregates composing the clot. The work was supported by AHA Award No: 16POST27500023.

FDD Massive MIMO Channel Estimation With Arbitrary 2D-Array Geometry

NASA Astrophysics Data System (ADS)

Dai, Jisheng; Liu, An; Lau, Vincent K. N.

2018-05-01

This paper addresses the problem of downlink channel estimation in frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. The existing methods usually exploit hidden sparsity under a discrete Fourier transform (DFT) basis to estimate the cdownlink channel. However, there are at least two shortcomings of these DFT-based methods: 1) they are applicable to uniform linear arrays (ULAs) only, since the DFT basis requires a special structure of ULAs, and 2) they always suffer from a performance loss due to the leakage of energy over some DFT bins. To deal with the above shortcomings, we introduce an off-grid model for downlink channel sparse representation with arbitrary 2D-array antenna geometry, and propose an efficient sparse Bayesian learning (SBL) approach for the sparse channel recovery and off-grid refinement. The main idea of the proposed off-grid method is to consider the sampled grid points as adjustable parameters. Utilizing an in-exact block majorization-minimization (MM) algorithm, the grid points are refined iteratively to minimize the off-grid gap. Finally, we further extend the solution to uplink-aided channel estimation by exploiting the angular reciprocity between downlink and uplink channels, which brings enhanced recovery performance.

Numerical Modeling of Electromagnetic Radiation Within a Particulate Medium.

NASA Astrophysics Data System (ADS)

Noe Dobrea, E. Z.

2017-12-01

Numerical modeling of electromagnetic radiation with a particulate medium. Understanding the effect of particulate media and coatings on electromagnetic radiation is key to understanding the effects of multiple scattering on the spectra of geologic materials. Multiple radiative transfer theories have been developed that provide a good approximation to these effects [1,2]. However, approximations regarding particle size, distribution, shape, and other parameters need to be made and in some cases, the theory is limited to specific geometries [2]. In this work, we seek to develop an numerical radiative transfer algorithm to simulate the passage of light through a particulate medium. The code allows arbitrary particle size distributions (uniform, bimodal, trimodal, composition dependent), compositions, and viewing geometries, as well as arbitrary coating thicknesses and compositions. Here, we report on the the status of our model and present comparisons of model predictions with the spectra of well-characterize minerals and mixtures. Future work will include particle size-dependent effects of diffraction as well as particle emittance due to fluorescence and Raman excitation. [1] Hapke, B. (2012). Theory of reflectance and emittance spectroscopy. Cambridge University Press, 2nd edition, 528 p. [2] Shkuratov et al. (1999) Icarus 137

An exact solution for axial flow in cylindrically symmetric, steady-state detonation in polytropic explosive with an arbitrary rate of decomposition

NASA Astrophysics Data System (ADS)

Cowperthwaite, M.

1994-03-01

Methods of differential geometry and Bernoulli's equation, written as B=0, are used to develop a new approach for constructing an exact solution for axial flow in a classical, two-dimensional, ZND detonation wave in a polytropic explosive with an arbitrary rate of decomposition. This geometric approach is fundamentally different from the traditional approaches to this axial flow problem formulated by Wood and Kirkwood (WK) and Fickett and Davis (FD), and gives equations for the axial particle velocity (u), the sound speed (c), the pressure (p), and the density (ρ), that are expressed in terms of the detonation velocity (D), the extent of decomposition (λ), the polytropic index (K), and two nonideal parameters ɛ3 and ɛ1, and reduce to the equations for steady-state, one-dimensional detonation as ɛ3 and ɛ1 approach zero. In contrast to the FD approach, the equations for u and c are obtained from first integrals of a tangent vector à on (u,c,λ) space, and the invariant condition, ÃB=aB=0, bypasses the FD eigenvalue problem by defining ɛ3 in terms of the detonation velocity deficit D/D∞ and K. In contrast to the WK approach, the equations for p and ρ are obtained from equations expressing the conservation of axial momentum and energy. Because the equations for these flow variables are derived without using the conservation of mass, the axial radial particle velocity gradient (war) associated with the flow can be obtained from the continuity equation without making approximations. The relationship between ɛ1 and ɛ3 that closes the solution is obtained from equations expressing constraints imposed on the axial flow at the shock front by the axial and radial momentum equations, the curved shock and the decomposition rate law, and a particular solution is constructed from the ɛ1-ɛ3 relationship determined by a prescribed rate law and value of K. Properties of particular solutions are presented to provide a better understanding of two-dimensional detonation, and a new axial condition for detonation failure is used to show that detonation failure can occur before the curve relating D/D∞ to the axial radius of curvature of the shock (Sa) becomes infinite.

Geometry and physics

PubMed Central

Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel

2010-01-01

We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740

Surface fitting three-dimensional bodies

NASA Technical Reports Server (NTRS)

Dejarnette, F. R.

1974-01-01

The geometry of general three-dimensional bodies is generated from coordinates of points in several cross sections. Since these points may not be smooth, they are divided into segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction by fitting parametric cubic-spline curves through coordinate points which define the conic sections in the cross-sectional planes. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines and slopes at selected points. Slopes may be continuous or discontinuous and finite or infinite. After a satisfactory surface fit has been obtained, cards may be punched with the data necessary to form a geometry subroutine package for use in other computer programs. At any position on the body, coordinates, slopes and second partial derivatives are calculated. The method is applied to a blunted 70 deg delta wing, and it was found to generate the geometry very well.

Effect of discharge duct geometry on centrifugal fan performance and noise emission

NASA Astrophysics Data System (ADS)

Nelson, David A.; Butrymowicz, William; Thomas, Christopher

2005-09-01

Non-ideal inlet and discharge duct geometries can cause significant changes to both the aerodynamic performance (``fan curve'') and specific sound power emission of a fan. A proper understanding of actual installed performance, as well as a good estimate of the system backpressure curve, is critical to achieving flow and acoustic goals as well as other criteria such as power consumption, mass and volume. To this end a battery of ISO 10302 tests was performed on a blower assembly which supports the Advanced Animal Habitat, being developed by ORBITEC for deployment on the International Space Station. The blower assembly consists of (4) identical centrifugal fans that, amongst themselves and across two prototypes, incorporated several discharge geometries. The inlet geometries were identical in all cases. Thus by comparing the dimensionless pressure-flow and noise emission characteristics across the cases, significant insight into the nature and potential magnitude of these effects is gained.

Geometric engineering on flops of length two

NASA Astrophysics Data System (ADS)

Collinucci, Andrés; Fazzi, Marco; Valandro, Roberto

2018-04-01

Type IIA on the conifold is a prototype example for engineering QED with one charged hypermultiplet. The geometry admits a flop of length one. In this paper, we study the next generation of geometric engineering on singular geometries, namely flops of length two such as Laufer's example, which we affectionately think of as the conifold 2.0. Type IIA on the latter geometry gives QED with higher-charge states. In type IIB, even a single D3-probe gives rise to a nonabelian quiver gauge theory. We study this class of geometries explicitly by leveraging their quiver description, showing how to parametrize the exceptional curve, how to see the flop transition, and how to find the noncompact divisors intersecting the curve. With a view towards F-theory applications, we show how these divisors contribute to the enhancement of the Mordell-Weil group of the local elliptic fibration defined by Laufer's example.

Analysis of diffusion in curved surfaces and its application to tubular membranes.

PubMed

Klaus, Colin James Stockdale; Raghunathan, Krishnan; DiBenedetto, Emmanuele; Kenworthy, Anne K

2016-12-01

Diffusion of particles in curved surfaces is inherently complex compared with diffusion in a flat membrane, owing to the nonplanarity of the surface. The consequence of such nonplanar geometry on diffusion is poorly understood but is highly relevant in the case of cell membranes, which often adopt complex geometries. To address this question, we developed a new finite element approach to model diffusion on curved membrane surfaces based on solutions to Fick's law of diffusion and used this to study the effects of geometry on the entry of surface-bound particles into tubules by diffusion. We show that variations in tubule radius and length can distinctly alter diffusion gradients in tubules over biologically relevant timescales. In addition, we show that tubular structures tend to retain concentration gradients for a longer time compared with a comparable flat surface. These findings indicate that sorting of particles along the surfaces of tubules can arise simply as a geometric consequence of the curvature without any specific contribution from the membrane environment. Our studies provide a framework for modeling diffusion in curved surfaces and suggest that biological regulation can emerge purely from membrane geometry. © 2016 Klaus, Raghunathan, et al. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

UTM, a universal simulator for lightcurves of transiting systems

NASA Astrophysics Data System (ADS)

Deeg, Hans

2009-02-01

The Universal Transit Modeller (UTM) is a light-curve simulator for all kinds of transiting or eclipsing configurations between arbitrary numbers of several types of objects, which may be stars, planets, planetary moons, and planetary rings. Applications of UTM to date have been mainly in the generation of light-curves for the testing of detection algorithms. For the preparation of such test for the Corot Mission, a special version has been used to generate multicolour light-curves in Corot's passbands. A separate fitting program, UFIT (Universal Fitter) is part of the UTM distribution and may be used to derive best fits to light-curves for any set of continuously variable parameters. UTM/UFIT is written in IDL code and its source is released in the public domain under the GNU General Public License.

Specimen geometry effects on graphite/PMR-15 composites during thermo-oxidative aging

NASA Technical Reports Server (NTRS)

Bowles, K. J.; Meyers, A.

1986-01-01

Studies were conducted to establish the effects of specimen geometry on the thermo-oxidative stability and the mechanical properties retention of unidirectional Celion 12000 graphite fiber reinforced PMR-15 polyimide composites. Weight loss, flexural strength and interlaminar shear strength are measured at isothermal aging times as long as 1639 hr at a temperature of 316 C for three different specimen geometries. It is found that the three different types of specimen surfaces exhibit different values of weight loss/unit area. The mechanical properties retention is also found to be dependent on geometry for these composites. The interlaminar shear strength decreases significantly over the complete range of aging times. The flexural strength retention starts showing geometric dependency after about 1000 hr of aging at 316C. Weight loss fluxes, associated with the three different types of exposed surfaces, are calculated and used to develop an empirical mathematical model for predicting the weight loss behavior of unidirectional composites of arbitrary geometries. Data are presented comparing experimentally determined weight loss with weight loss values predicted using the empirical model.

Specimen geometry effects on graphite/PMR-15 composites during thermo-oxidative aging

NASA Technical Reports Server (NTRS)

Bowles, K. J.; Meyers, A.

1986-01-01

Studies were conducted to establish the effects of specimen geometry on the thermo-oxidative stability and the mechanical properties retention of unidirectional Celion 12000 graphite fiber reinforced PMR-15 polyimide composites. Weight loss, flexural strength and interlaminar shear strength are measured at isothermal aging times as long as 1639 hr at a temperature of 316 C for three different specimen geometries. It is found that the three different types of specimen surfaces exhibit different values of weight loss/unit area. The mechanical properties retention is also found to be dependent on geometry for these composites. The interlaminar shear strength decreases significantly over the complete range of aging times. The flexural strength retention starts showing geometric dependency after about 1000 hr of aging at 316 C. Weight loss fluxes, associated with the three different types of exposed surfaces, are calculated and used to develop an empirical mathematical model for predicting the weight loss behavior of unidirectional composites of arbitrary geometries. Data are presented comparing experimentally determined weight loss with weight loss values predicted using the empirical model.

Convex Curved Crystal Spectograph for Pulsed Plasma Sources.

DTIC Science & Technology

The geometry of a convex curved crystal spectrograph as applied to pulsed plasma sources is presented. Also presented are data from the dense plasma focus with particular emphasis on the absolute intensity of line radiations.

An integral equation-based numerical solver for Taylor states in toroidal geometries

NASA Astrophysics Data System (ADS)

O'Neil, Michael; Cerfon, Antoine J.

2018-04-01

We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1991-01-01

A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes.

Fully Automated Single-Zone Elliptic Grid Generation for Mars Science Laboratory (MSL) Aeroshell and Canopy Geometries

NASA Technical Reports Server (NTRS)

kaul, Upender K.

2008-01-01

A procedure for generating smooth uniformly clustered single-zone grids using enhanced elliptic grid generation has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy. The procedure obviates the need for generating multizone grids for such geometries, as reported in the literature. This has been possible because the enhanced elliptic grid generator automatically generates clustered grids without manual prescription of decay parameters needed with the conventional approach. In fact, these decay parameters are calculated as decay functions as part of the solution, and they are not constant over a given boundary. Since these decay functions vary over a given boundary, orthogonal grids near any arbitrary boundary can be clustered automatically without having to break up the boundaries and the corresponding interior domains into various zones for grid generation.

The Triangle: a Multiprocessor Architecture for Fast Curve and Surface Generation.

DTIC Science & Technology

1987-08-01

design , curves and surfaces, graphics hardware. 20...curves, B-splines, computer-aided geometric design ; curves and sur- faces, graphics hardware. (k 12). -/ .... This work was supported in part by the...34 Electronic Design , October 30, 1986. 21. M. A. Penna and R. R. Patterson, Projective Geometry and its Applications to Computer Graphics , Prentice-Hall, Englewood Cliffs, N.J., 1985. 70,e, 41100vr -~ ~ - -- --

LOCAL ORTHOGONAL CUTTING METHOD FOR COMPUTING MEDIAL CURVES AND ITS BIOMEDICAL APPLICATIONS

PubMed Central

Einstein, Daniel R.; Dyedov, Vladimir

2010-01-01

Medial curves have a wide range of applications in geometric modeling and analysis (such as shape matching) and biomedical engineering (such as morphometry and computer assisted surgery). The computation of medial curves poses significant challenges, both in terms of theoretical analysis and practical efficiency and reliability. In this paper, we propose a definition and analysis of medial curves and also describe an efficient and robust method called local orthogonal cutting (LOC) for computing medial curves. Our approach is based on three key concepts: a local orthogonal decomposition of objects into substructures, a differential geometry concept called the interior center of curvature (ICC), and integrated stability and consistency tests. These concepts lend themselves to robust numerical techniques and result in an algorithm that is efficient and noise resistant. We illustrate the effectiveness and robustness of our approach with some highly complex, large-scale, noisy biomedical geometries derived from medical images, including lung airways and blood vessels. We also present comparisons of our method with some existing methods. PMID:20628546

Complete spectrum of long operators in Script N = 4 SYM at one loop

NASA Astrophysics Data System (ADS)

Beisert, Niklas; Kazakov, Vladimir A.; Sakai, Kazuhiro; Zarembo, Konstantin

2005-07-01

We construct the complete spectral curve for an arbitrary local operator, including fermions and covariant derivatives, of one-loop Script N = 4 gauge theory in the thermodynamic limit. This curve perfectly reproduces the Frolov-Tseytlin limit of the full spectral curve of classical strings on AdS5 × S5 derived in [64]. To complete the comparison we introduce stacks, novel bound states of roots of different flavors which arise in the thermodynamic limit of the corresponding Bethe ansatz equations. We furthermore show the equivalence of various types of Bethe equations for the underlying fraktur sfraktur u(2,2|4) superalgebra, in particular of the type ``Beauty'' and ``Beast''.

Similarity recognition of online data curves based on dynamic spatial time warping for the estimation of lithium-ion battery capacity

NASA Astrophysics Data System (ADS)

Tao, Laifa; Lu, Chen; Noktehdan, Azadeh

2015-10-01

Battery capacity estimation is a significant recent challenge given the complex physical and chemical processes that occur within batteries and the restrictions on the accessibility of capacity degradation data. In this study, we describe an approach called dynamic spatial time warping, which is used to determine the similarities of two arbitrary curves. Unlike classical dynamic time warping methods, this approach can maintain the invariance of curve similarity to the rotations and translations of curves, which is vital in curve similarity search. Moreover, it utilizes the online charging or discharging data that are easily collected and do not require special assumptions. The accuracy of this approach is verified using NASA battery datasets. Results suggest that the proposed approach provides a highly accurate means of estimating battery capacity at less time cost than traditional dynamic time warping methods do for different individuals and under various operating conditions.

Non-lightlike ruled surfaces with constant curvatures in Minkowski 3-space

NASA Astrophysics Data System (ADS)

Ali, Ahmad Tawfik

We study the non-lightlike ruled surfaces in Minkowski 3-space with non-lightlike base curve c(s) =∫(αt + βn + γb)ds, where t, n, b are the tangent, principal normal and binormal vectors of an arbitrary timelike curve Γ(s). Some important results of flat, minimal, II-minimal and II-flat non-lightlike ruled surfaces are studied. Finally, the following interesting theorem is proved: the only non-zero constant mean curvature (CMC) non-lightlike ruled surface is developable timelike ruled surface generated by binormal vector.

An angular biasing method using arbitrary convex polyhedra for Monte Carlo radiation transport calculations

DOE PAGES

Kulesza, Joel A.; Solomon, Clell J.; Kiedrowski, Brian C.

2018-01-02

This paper presents a new method for performing angular biasing in Monte Carlo radiation transport codes using arbitrary convex polyhedra to define regions of interest toward which to project particles (DXTRAN regions). The method is derived and is implemented using axis-aligned right parallelepipeds (AARPPs) and arbitrary convex polyhedra. Attention is also paid to possible numerical complications and areas for future refinement. A series of test problems are executed with void, purely absorbing, purely scattering, and 50% absorbing/50% scattering materials. For all test problems tally results using AARPP and polyhedral DXTRAN regions agree with analog and/or spherical DXTRAN results within statisticalmore » uncertainties. In cases with significant scattering the figure of merit (FOM) using AARPP or polyhedral DXTRAN regions is lower than with spherical regions despite the ability to closely fit the tally region. This is because spherical DXTRAN processing is computationally less expensive than AARPP or polyhedral DXTRAN processing. Thus, it is recommended that the speed of spherical regions be considered versus the ability to closely fit the tally region with an AARPP or arbitrary polyhedral region. It is also recommended that short calculations be made prior to final calculations to compare the FOM for the various DXTRAN geometries because of the influence of the scattering behavior.« less

(2+1)-dimensional spacetimes containing closed timelike curves

NASA Astrophysics Data System (ADS)

Headrick, Matthew P.; Gott, J. Richard, III

1994-12-01

We investigate the global geometries of (2+1)-dimensional spacetimes as characterized by the transformations undergone by tangent spaces upon parallel transport around closed curves. We critically discuss the use of the term ``total energy-momentum'' as a label for such parallel-transport transformations, pointing out several problems with it. We then investigate parallel-transport transformations in the known (2+1)-dimensional spacetimes containing closed timelike curves (CTC's), and introduce a few new such spacetimes. Using the more specific concept of the holonomy of a closed curve, applicable in simply connected spacetimes, we emphasize that Gott's two-particle CTC-containing spacetime does not have a tachyonic geometry. Finally, we prove the following modified version of Kabat's conjecture: if a CTC is deformable to spacelike or null infinity while remaining a CTC, then its parallel-transport transformation cannot be a rotation; therefore its holonomy, if defined, cannot be a rotation other than through a multiple of 2π.

Analysis of electrophoresis performance

NASA Technical Reports Server (NTRS)

Roberts, Glyn O.

1988-01-01

A flexible efficient computer code is being developed to simulate electrophoretic separation phenomena, in either a cylindrical or a rectangular geometry. The code will computer the evolution in time of the concentrations of an arbitrary number of chemical species, and of the temperature, pH distribution, conductivity, electric field, and fluid motion. Use of nonuniform meshes and fast accurate implicit time-stepping will yield accurate answers at economical cost.

Introduction to Solar Motion Geometry on the Basis of a Simple Model

ERIC Educational Resources Information Center

Khavrus, Vyacheslav; Shelevytsky, Ihor

2010-01-01

By means of a simple mathematical model developed by the authors, the apparent movement of the Sun can be studied for arbitrary latitudes. Using this model, it is easy to gain insight into various phenomena, such as the passage of the seasons, dependences of position and time of sunrise or sunset on a specific day of year, day duration for…

Distributed feedback imprinted electrospun fiber lasers.

PubMed

Persano, Luana; Camposeo, Andrea; Del Carro, Pompilio; Fasano, Vito; Moffa, Maria; Manco, Rita; D'Agostino, Stefania; Pisignano, Dario

2014-10-01

Imprinted, distributed feedback lasers are demonstrated on individual, active electrospun polymer nanofibers. In addition to advantages related to miniaturization, optical confinement and grating nanopatterning lead to a significant threshold reduction compared to conventional thin-film lasers. The possibility of imprinting arbitrary photonic crystal geometries on electrospun lasing nanofibers opens new opportunities for realizing optical circuits and chips. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The scattering variety

NASA Astrophysics Data System (ADS)

He, Yang-Hui; Matti, Cyril; Sun, Chuang

2014-10-01

The so-called Scattering Equations which govern the kinematics of the scattering of massless particles in arbitrary dimensions have recently been cast into a system of homogeneous polynomials. We study these as affine and projective geometries which we call Scattering Varieties by analyzing such properties as Hilbert series, Euler characteristic and singularities. Interestingly, we find structures such as affine Calabi-Yau threefolds as well as singular K3 and Fano varieties.

Geometric Model for a Parametric Study of the Blended-Wing-Body Airplane

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne; Smith, Robert E.; Sadrehaghighi, Ideen; Wiese, Micharl R.

1996-01-01

A parametric model is presented for the blended-wing-body airplane, one concept being proposed for the next generation of large subsonic transports. The model is defined in terms of a small set of parameters which facilitates analysis and optimization during the conceptual design process. The model is generated from a preliminary CAD geometry. From this geometry, airfoil cross sections are cut at selected locations and fitted with analytic curves. The airfoils are then used as boundaries for surfaces defined as the solution of partial differential equations. Both the airfoil curves and the surfaces are generated with free parameters selected to give a good representation of the original geometry. The original surface is compared with the parametric model, and solutions of the Euler equations for compressible flow are computed for both geometries. The parametric model is a good approximation of the CAD model and the computed solutions are qualitatively similar. An optimal NURBS approximation is constructed and can be used by a CAD model for further refinement or modification of the original geometry.

Indirect dark matter signatures in the cosmic dark ages. II. Ionization, heating, and photon production from arbitrary energy injections

NASA Astrophysics Data System (ADS)

Slatyer, Tracy R.

2016-01-01

Any injection of electromagnetically interacting particles during the cosmic dark ages will lead to increased ionization, heating, production of Lyman-α photons and distortions to the energy spectrum of the cosmic microwave background, with potentially observable consequences. In this paper we describe numerical results for the low-energy electrons and photons produced by the cooling of particles injected at energies from keV to multi-TeV scales, at arbitrary injection redshifts (but focusing on the post-recombination epoch). We use these data, combined with existing calculations modeling the cooling of these low-energy particles, to estimate the resulting contributions to ionization, excitation and heating of the gas, and production of low-energy photons below the threshold for excitation and ionization. We compute corrected deposition-efficiency curves for annihilating dark matter, and demonstrate how to compute equivalent curves for arbitrary energy-injection histories. These calculations provide the necessary inputs for the limits on dark matter annihilation presented in the accompanying paper I, but also have potential applications in the context of dark matter decay or deexcitation, decay of other metastable species, or similar energy injections from new physics. We make our full results publicly available at http://nebel.rc.fas.harvard.edu/epsilon, to facilitate further independent studies. In particular, we provide the full low-energy electron and photon spectra, to allow matching onto more detailed codes that describe the cooling of such particles at low energies.

Curved Saccade Trajectories Reveal Conflicting Predictions in Associative Learning

ERIC Educational Resources Information Center

Koenig, Stephan; Lachnit, Harald

2011-01-01

We report how the trajectories of saccadic eye movements are affected by memory interference acquired during associative learning. Human participants learned to perform saccadic choice responses based on the presentation of arbitrary central cues A, B, AC, BC, AX, BY, X, and Y that were trained to predict the appearance of a peripheral target…

Prediction of error rates in dose-imprinted memories on board CRRES by two different methods. [Combined Release and Radiation Effects Satellite

NASA Technical Reports Server (NTRS)

Brucker, G. J.; Stassinopoulos, E. G.

1991-01-01

An analysis of the expected space radiation effects on the single event upset (SEU) properties of CMOS/bulk memories onboard the Combined Release and Radiation Effects Satellite (CRRES) is presented. Dose-imprint data from ground test irradiations of identical devices are applied to the predictions of cosmic-ray-induced space upset rates in the memories onboard the spacecraft. The calculations take into account the effect of total dose on the SEU sensitivity of the devices as the dose accumulates in orbit. Estimates of error rates, which involved an arbitrary selection of a single pair of threshold linear energy transfer (LET) and asymptotic cross-section values, were compared to the results of an integration over the cross-section curves versus LET. The integration gave lower upset rates than the use of the selected values of the SEU parameters. Since the integration approach is more accurate and eliminates the need for an arbitrary definition of threshold LET and asymptotic cross section, it is recommended for all error rate predictions where experimental sigma-versus-LET curves are available.

Evaluation of a transient, simultaneous, arbitrary Lagrange-Euler based multi-physics method for simulating the mitral heart valve.

PubMed

Espino, Daniel M; Shepherd, Duncan E T; Hukins, David W L

2014-01-01

A transient multi-physics model of the mitral heart valve has been developed, which allows simultaneous calculation of fluid flow and structural deformation. A recently developed contact method has been applied to enable simulation of systole (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the mitral valve within the heart walls in two dimensions. Only the mitral valve undergoes deformation. A moving arbitrary Lagrange-Euler mesh is used to allow true fluid-structure interaction (FSI). The FSI model requires blood flow to induce valve closure by inducing strains in the region of 10-20%. Model predictions were found to be consistent with existing literature and will undergo further development.

Passive orientation apparatus

DOEpatents

Spletzer, Barry L.; Fischer, Gary J.; Martinez, Michael A.

2001-01-01

An apparatus that can return a payload to a known orientation after unknown motion, without requiring external power or complex mechanical systems. The apparatus comprises a faceted cage that causes the system to rest in a stable position and orientation after arbitrary motion. A gimbal is mounted with the faceted cage and holds the payload, allowing the payload to move relative to the stable faceted cage. The payload is thereby placed in a known orientation by the interaction of gravity with the geometry of the faceted cage, the mass of the system, and the motion of the payload and gimbal. No additional energy, control, or mechanical actuation is required. The apparatus is suitable for use in applications requiring positioning of a payload to a known orientation after arbitrary or uncontrolled motion, including remote sensing and mobile robot applications.

Direct S -matrix calculation for diffractive structures and metasurfaces

NASA Astrophysics Data System (ADS)

Shcherbakov, Alexey A.; Stebunov, Yury V.; Baidin, Denis F.; Kämpfe, Thomas; Jourlin, Yves

2018-06-01

The paper presents a derivation of analytical components of S matrices for arbitrary planar diffractive structures and metasurfaces in the Fourier domain. The attained general formulas for S -matrix components can be applied within both formulations in the Cartesian and curvilinear metric. A numerical method based on these results can benefit from all previous improvements of the Fourier domain methods. In addition, we provide expressions for S -matrix calculation in the case of periodically corrugated layers of two-dimensional materials, which are valid for arbitrary corrugation depth-to-period ratios. As an example, the derived equations are used to simulate resonant grating excitation of graphene plasmons and the impact of a silica interlayer on corresponding reflection curves.

Resistive-force theory for mesh-like superhydrophobic surfaces

NASA Astrophysics Data System (ADS)

Schnitzer, Ory; Yariv, Ehud

2018-03-01

A common realization of superhydrophobic surfaces makes use of a mesh-like geometry, where pockets of air are trapped in a periodic array of holes in a no-slip solid substrate. We consider the small-solid-fraction limit where the ribs of the mesh are narrow. In this limit, we obtain a simple leading-order approximation for the slip-length tensor of an arbitrary mesh geometry. This approximation scales as the solid-fraction logarithm, as anticipated by Ybert et al. [Phys. Fluids 19, 123601 (2007), 10.1063/1.2815730]; in the special case of a square mesh it agrees with the analytical results obtained by Davis and Lauga [Phys. Fluids 21, 113101 (2009), 10.1063/1.3250947].

Transonic flow analysis for rotors. Part 2: Three-dimensional, unsteady, full-potential calculation

NASA Technical Reports Server (NTRS)

Chang, I. C.

1985-01-01

A numerical method is presented for calculating the three-dimensional unsteady, transonic flow past a helicopter rotor blade of arbitrary geometry. The method solves the full-potential equations in a blade-fixed frame of reference by a time-marching implicit scheme. At the far-field, a set of first-order radiation conditions is imposed, thus minimizing the reflection of outgoing wavelets from computational boundaries. Computed results are presented to highlight radial flow effects in three dimensions, to compare surface pressure distributions to quasi-steady predictions, and to predict the flow field on a swept-tip blade. The results agree well with experimental data for both straight- and swept-tip blade geometries.

A General Computational Approach for Magnetohydrodynamic Flows Using the CFX Code: Buoyant Flow Through a Vertical Square Channel

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

Di Piazza, Ivan; Buehler, Leo

2000-09-15

The buoyancy-driven magnetoconvection in the cross section of an infinitely long vertical square duct is investigated numerically using the CFX code package. The implementation of a magnetohydrodynamic (MHD) problem in CFX is discussed, with particular reference to the Lorentz forces and the electric potential boundary conditions for arbitrary electrical conductivity of the walls. The method proposed is general and applies to arbitrary geometries with an arbitrary orientation of the magnetic field. Results for fully developed flow under various thermal boundary conditions are compared with asymptotic analytical solutions. The comparison shows that the asymptotic analysis is confirmed for highly conducting wallsmore » as high velocity jets occur at the side walls. For weakly conducting walls, the side layers become more conducting than the side walls, and strong electric currents flow within these layers parallel to the magnetic field. As a consequence, the velocity jets are suppressed, and the core solution is only corrected by the viscous forces near the wall. The implementation of MHD in CFX is achieved.« less

Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas for arbitrary magnetic fields

NASA Astrophysics Data System (ADS)

Chacon, Luis; Del-Castillo-Negrete, Diego; Hauck, Cory

2012-10-01

Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (χ/χ˜10^10 in fusion plasmas). Recently, a Lagrangian Green's function approach, developed for the purely parallel transport case,footnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011)^,footnotetextD. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, 19, 056112 (2012) has been extended to the anisotropic transport case in the tokamak-ordering limit with constant density.footnotetextL. Chac'on, D. del-Castillo-Negrete, C. Hauck, JCP, submitted (2012) An operator-split algorithm is proposed that allows one to treat Eulerian and Lagrangian components separately. The approach is shown to feature bounded numerical errors for arbitrary χ/χ ratios, which renders it asymptotic-preserving. In this poster, we will present the generalization of the Lagrangian approach to arbitrary magnetic fields. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.

Quantum to classical transition in quantum field theory

NASA Astrophysics Data System (ADS)

Lombardo, Fernando C.

1998-12-01

We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalar-tensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the Einstein-Langevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.

Coil optimisation for transcranial magnetic stimulation in realistic head geometry.

PubMed

Koponen, Lari M; Nieminen, Jaakko O; Mutanen, Tuomas P; Stenroos, Matti; Ilmoniemi, Risto J

Transcranial magnetic stimulation (TMS) allows focal, non-invasive stimulation of the cortex. A TMS pulse is inherently weakly coupled to the cortex; thus, magnetic stimulation requires both high current and high voltage to reach sufficient intensity. These requirements limit, for example, the maximum repetition rate and the maximum number of consecutive pulses with the same coil due to the rise of its temperature. To develop methods to optimise, design, and manufacture energy-efficient TMS coils in realistic head geometry with an arbitrary overall coil shape. We derive a semi-analytical integration scheme for computing the magnetic field energy of an arbitrary surface current distribution, compute the electric field induced by this distribution with a boundary element method, and optimise a TMS coil for focal stimulation. Additionally, we introduce a method for manufacturing such a coil by using Litz wire and a coil former machined from polyvinyl chloride. We designed, manufactured, and validated an optimised TMS coil and applied it to brain stimulation. Our simulations indicate that this coil requires less than half the power of a commercial figure-of-eight coil, with a 41% reduction due to the optimised winding geometry and a partial contribution due to our thinner coil former and reduced conductor height. With the optimised coil, the resting motor threshold of abductor pollicis brevis was reached with the capacitor voltage below 600 V and peak current below 3000 A. The described method allows designing practical TMS coils that have considerably higher efficiency than conventional figure-of-eight coils. Copyright © 2017 Elsevier Inc. All rights reserved.

Resonant ultrasound spectroscopy for materials with high damping and samples of arbitrary geometry

DOE PAGES

Remillieux, Marcel C.; Ulrich, T. J.; Payan, Cédric; ...

2015-07-23

This paper describes resonant ultrasound spectroscopy (RUS) as a powerful and established technique for measuring elastic constants of a material with general anisotropy. The first step of this technique consists of extracting resonance frequencies and damping from the vibrational frequency spectrum measured on a sample with free boundary conditions. An inversion technique is then used to retrieve the elastic tensor from the measured resonance frequencies. As originally developed, RUS has been mostly applicable to (i) materials with small damping such that the resonances of the sample are well separated and (ii) samples with simple geometries for which analytical solutions exist.more » In this paper, these limitations are addressed with a new RUS approach adapted to materials with high damping and samples of arbitrary geometry. Resonances are extracted by fitting a sum of exponentially damped sinusoids to the measured frequency spectrum. The inversion of the elastic tensor is achieved with a genetic algorithm, which allows searching for a global minimum within a discrete and relatively wide solution space. First, the accuracy of the proposed approach is evaluated against numerical data simulated for samples with isotropic symmetry and transversely isotropic symmetry. Subsequently, the applicability of the approach is demonstrated using experimental data collected on a composite structure consisting of a cylindrical sample of Berea sandstone glued to a large piezoelectric disk. In the proposed experiments, RUS is further enhanced by the use of a 3-D laser vibrometer allowing the visualization of most of the modes in the frequency band studied.« less

Stability of horizontal viscous fluid layers in a vertical arbitrary time periodic electric field

NASA Astrophysics Data System (ADS)

Bandopadhyay, Aditya; Hardt, Steffen

2017-12-01

The stability of a horizontal interface between two viscous fluids, one of which is conducting and the other is dielectric, acted upon by a vertical time-periodic electric field is considered theoretically. The two fluids are bounded by electrodes separated by a finite distance. For an applied ac electric field, the unstable interface deforms in a time periodic manner, owing to the time dependent Maxwell stress, and is characterized by the oscillation frequency which may or may not be the same as the frequency of the ac electric field. The stability curve, which relates the critical voltage, manifested through the Mason number—the ratio of normal electric stress and viscous stress, and the instability wavenumber at the onset of the instability, is obtained by means of the Floquet theory for a general arbitrary time periodic electric field. The limit of vanishing viscosities is shown to be in excellent agreement with the marginal stability curves predicted by means of a Mathieu equation. The influence of finite viscosity and electrode separation is discussed in relation to the ideal case of inviscid fluids. The methodology to obtain the marginal stability curves developed here is applicable to any arbitrary but time periodic signal, as demonstrated for the case of a signal with two different frequencies, and four different frequencies with a dc offset. The mode coupling in the interfacial normal stress leads to appearance of harmonic and subharmonic modes, characterized by the frequency of the oscillating interface at an integral or half-integral multiple of the applied frequency, respectively. This is in contrast to the application of a voltage with a single frequency which always leads to a harmonic mode oscillation of the interface. Whether a harmonic or subharmonic mode is the most unstable one depends on details of the excitation signal.

Shape-matching soft mechanical metamaterials.

PubMed

Mirzaali, M J; Janbaz, S; Strano, M; Vergani, L; Zadpoor, A A

2018-01-17

Architectured materials with rationally designed geometries could be used to create mechanical metamaterials with unprecedented or rare properties and functionalities. Here, we introduce "shape-matching" metamaterials where the geometry of cellular structures comprising auxetic and conventional unit cells is designed so as to achieve a pre-defined shape upon deformation. We used computational models to forward-map the space of planar shapes to the space of geometrical designs. The validity of the underlying computational models was first demonstrated by comparing their predictions with experimental observations on specimens fabricated with indirect additive manufacturing. The forward-maps were then used to devise the geometry of cellular structures that approximate the arbitrary shapes described by random Fourier's series. Finally, we show that the presented metamaterials could match the contours of three real objects including a scapula model, a pumpkin, and a Delft Blue pottery piece. Shape-matching materials have potential applications in soft robotics and wearable (medical) devices.

Accelerating execution of the integrated TIGER series Monte Carlo radiation transport codes

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

Smith, L.M.; Hochstedler, R.D.

1997-02-01

Execution of the integrated TIGER series (ITS) of coupled electron/photon Monte Carlo radiation transport codes has been accelerated by modifying the FORTRAN source code for more efficient computation. Each member code of ITS was benchmarked and profiled with a specific test case that directed the acceleration effort toward the most computationally intensive subroutines. Techniques for accelerating these subroutines included replacing linear search algorithms with binary versions, replacing the pseudo-random number generator, reducing program memory allocation, and proofing the input files for geometrical redundancies. All techniques produced identical or statistically similar results to the original code. Final benchmark timing of themore » accelerated code resulted in speed-up factors of 2.00 for TIGER (the one-dimensional slab geometry code), 1.74 for CYLTRAN (the two-dimensional cylindrical geometry code), and 1.90 for ACCEPT (the arbitrary three-dimensional geometry code).« less

In vivo proton dosimetry using a MOSFET detector in an anthropomorphic phantom with tissue inhomogeneity

PubMed Central

Hotta, Kenji; Matsubara, Kana; Nishioka, Shie; Matsuura, Taeko; Kawashima, Mitsuhiko

2012-01-01

When in vivo proton dosimetry is performed with a metal‐oxide semiconductor field‐effect transistor (MOSFET) detector, the response of the detector depends strongly on the linear energy transfer. The present study reports a practical method to correct the MOSFET response for linear energy transfer dependence by using a simplified Monte Carlo dose calculation method (SMC). A depth‐output curve for a mono‐energetic proton beam in polyethylene was measured with the MOSFET detector. This curve was used to calculate MOSFET output distributions with the SMC (SMCMOSFET). The SMCMOSFET output value at an arbitrary point was compared with the value obtained by the conventional SMCPPIC, which calculates proton dose distributions by using the depth‐dose curve determined by a parallel‐plate ionization chamber (PPIC). The ratio of the two values was used to calculate the correction factor of the MOSFET response at an arbitrary point. The dose obtained by the MOSFET detector was determined from the product of the correction factor and the MOSFET raw dose. When in vivo proton dosimetry was performed with the MOSFET detector in an anthropomorphic phantom, the corrected MOSFET doses agreed with the SMCPPIC results within the measurement error. To our knowledge, this is the first report of successful in vivo proton dosimetry with a MOSFET detector. PACS number: 87.56.‐v PMID:22402385

Regional Curve Development and Use in Stream Restoration and Hydrologic Assessment in High Gradient Headwater Streams

EPA Pesticide Factsheets

Introduction to Regional Curves including; regressions relating bankfull channelcharacteristics to drainage area, providing estimates of bankfull discharge and channel geometry, validating the selection of the bankfull channel as determined in the field

Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time

NASA Astrophysics Data System (ADS)

Noble, J. H.; Jentschura, U. D.

2016-03-01

We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

A general strategy for hybrid thin film fabrication and transfer onto arbitrary substrates.

PubMed

Zhang, Yong; Magan, John J; Blau, Werner J

2014-04-28

The development of thin film-based structures/devices often requires thin films to be transferred onto arbitrary substrates/surfaces. Controllable and non-destructive transfer method, although highly desired, remains quite challenging. Here we report a general method for fabrication and transfer of hybrid (ultra)thin films. The proposed solution-based in-situ transfer method shows not only its robust ability for thin film transfer onto arbitrary substrates but also its highly controlled and non-destructive characteristic. With a hole structure as the support, fully-stretched free-standing thin film is prepared. The successful transfer to a curved surface demonstrates the possibility for production of thin film-coated complex optical components. Ultrathin (35 nm) hybrid film transferred onto PET (50 μm thick) shows high transparency (>90% in visible range), conductivity (1.54 × 10(4) S/m), and flexibility (radius of curvature down to mm scale). The reported transfer method would provide a powerful route towards complex thin film-based structures/devices.

A General Strategy for Hybrid Thin Film Fabrication and Transfer onto Arbitrary Substrates

PubMed Central

Zhang, Yong; Magan, John J.; Blau, Werner J.

2014-01-01

The development of thin film-based structures/devices often requires thin films to be transferred onto arbitrary substrates/surfaces. Controllable and non-destructive transfer method, although highly desired, remains quite challenging. Here we report a general method for fabrication and transfer of hybrid (ultra)thin films. The proposed solution-based in-situ transfer method shows not only its robust ability for thin film transfer onto arbitrary substrates but also its highly controlled and non-destructive characteristic. With a hole structure as the support, fully-stretched free-standing thin film is prepared. The successful transfer to a curved surface demonstrates the possibility for production of thin film-coated complex optical components. Ultrathin (35 nm) hybrid film transferred onto PET (50 μm thick) shows high transparency (>90% in visible range), conductivity (1.54 × 104 S/m), and flexibility (radius of curvature down to mm scale). The reported transfer method would provide a powerful route towards complex thin film-based structures/devices. PMID:24769689

Discrete Jordan curve theorem

NASA Astrophysics Data System (ADS)

Chen, Li

1999-09-01

According to a general definition of discrete curves, surfaces, and manifolds (Li Chen, 'Generalized discrete object tracking algorithms and implementations, ' In Melter, Wu, and Latecki ed, Vision Geometry VI, SPIE Vol. 3168, pp 184 - 195, 1997.). This paper focuses on the Jordan curve theorem in 2D discrete spaces. The Jordan curve theorem says that a (simply) closed curve separates a simply connected surface into two components. Based on the definition of discrete surfaces, we give three reasonable definitions of simply connected spaces. Theoretically, these three definition shall be equivalent. We have proved the Jordan curve theorem under the third definition of simply connected spaces. The Jordan theorem shows the relationship among an object, its boundary, and its outside area. In continuous space, the boundary of an mD manifold is an (m - 1)D manifold. The similar result does apply to regular discrete manifolds. The concept of a new regular nD-cell is developed based on the regular surface point in 2D, and well-composed objects in 2D and 3D given by Latecki (L. Latecki, '3D well-composed pictures,' In Melter, Wu, and Latecki ed, Vision Geometry IV, SPIE Vol 2573, pp 196 - 203, 1995.).

Radar Cross Section Prediction for Coated Perfect Conductors with Arbitrary Geometries.

DTIC Science & Technology

1986-01-01

equivalent electric and magnetic surface currents as the desired unknowns. Triangular patch modelling is ap- plied to the boundary surfaces. The method of...matrix inversion for the unknown surface current coefficients. Huygens’ principle is again applied to calculate the scattered electric field produced...differential equations with the equivalent electric and magnetic surface currents as the desired unknowns. Triangular patch modelling is ap- plied to the

Development and application of a method for predicting rotor free wake positions and resulting rotor blade air loads. Volume 1: Model and results

NASA Technical Reports Server (NTRS)

Sadler, S. G.

1971-01-01

Rotor wake geometries are predicted by a process similar to the startup of a rotor in a free stream. An array of discrete trailing and shed vortices is generated with vortex strengths corresponding to stepwise radial and azimuthal blade circulations. The array of shed and trailing vortices is limited to an arbitrary number of azimuthal steps behind each blade. The remainder of the wake model of each blade is an arbitrary number of trailing vortices. Vortex element end points were allowed to be transported by the resultant velocity of the free stream and vortex-induced velocities. Wake geometry, wake flow, and wake-induced velocity influence coefficients are generated by this program for use in the blade loads portion of the calculations. Blade loads computations include the effects of nonuniform inflow due to a free wake, nonlinear airfoil characteristics, and response of flexible blades to the applied loads. Computed wake flows and blade loads are compared with experimentally measured data. Predicted blade loads, response and shears and moments are obtained for a model rotor system having two independent rotors. The effects of advance ratio, vertical separation of rotors, different blade radius ratios, and different azimuthal spacing of the blades of one rotor with respect to the other are investigated.

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.

Three-dimensional light-tissue interaction models for bioluminescence tomography

NASA Astrophysics Data System (ADS)

Côté, D.; Allard, M.; Henkelman, R. M.; Vitkin, I. A.

2005-09-01

Many diagnostic and therapeutic approaches in medical physics today take advantage of the unique properties of light and its interaction with tissues. Because light scatters in tissue, our ability to develop these techniques depends critically on our knowledge of the distribution of light in tissue. Solutions to the diffusion equation can provide such information, but often lack the flexibility required for more general problems that involve, for instance, inhomogeneous optical properties, light polarization, arbitrary three-dimensional geometries, or arbitrary scattering. Monte Carlo techniques, which statistically sample the light distribution in tissue, offer a better alternative to analytical models. First, we discuss our implementation of a validated three-dimensional polarization-sensitive Monte Carlo algorithm and demonstrate its generality with respect to the geometry and scattering models it can treat. Second, we apply our model to bioluminescence tomography. After appropriate genetic modifications to cell lines, bioluminescence can be used as an indicator of cell activity, and is often used to study tumour growth and treatment in animal models. However, the amount of light escaping the animal is strongly dependent on the position and size of the tumour. Using forward models and structural data from magnetic resonance imaging, we show how the models can help to determine the location and size of tumour made of bioluminescent cancer cells in the brain of a mouse.

Multilayer integral method for simulation of eddy currents in thin volumes of arbitrary geometry produced by MRI gradient coils.

PubMed

Sanchez Lopez, Hector; Freschi, Fabio; Trakic, Adnan; Smith, Elliot; Herbert, Jeremy; Fuentes, Miguel; Wilson, Stephen; Liu, Limei; Repetto, Maurizio; Crozier, Stuart

2014-05-01

This article aims to present a fast, efficient and accurate multi-layer integral method (MIM) for the evaluation of complex spatiotemporal eddy currents in nonmagnetic and thin volumes of irregular geometries induced by arbitrary arrangements of gradient coils. The volume of interest is divided into a number of layers, wherein the thickness of each layer is assumed to be smaller than the skin depth and where one of the linear dimensions is much smaller than the remaining two dimensions. The diffusion equation of the current density is solved both in time-harmonic and transient domain. The experimentally measured magnetic fields produced by the coil and the induced eddy currents as well as the corresponding time-decay constants were in close agreement with the results produced by the MIM. Relevant parameters such as power loss and force induced by the eddy currents in a split cryostat were simulated using the MIM. The proposed method is capable of accurately simulating the current diffusion process inside thin volumes, such as the magnet cryostat. The method permits the priori-calculation of optimal pre-emphasis parameters. The MIM enables unified designs of gradient coil-magnet structures for an optimal mitigation of deleterious eddy current effects. Copyright © 2013 Wiley Periodicals, Inc.

Local Orthogonal Cutting Method for Computing Medial Curves and Its Biomedical Applications

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

Jiao, Xiangmin; Einstein, Daniel R.; Dyedov, Volodymyr

2010-03-24

Medial curves have a wide range of applications in geometric modeling and analysis (such as shape matching) and biomedical engineering (such as morphometry and computer assisted surgery). The computation of medial curves poses significant challenges, both in terms of theoretical analysis and practical efficiency and reliability. In this paper, we propose a definition and analysis of medial curves and also describe an efficient and robust method for computing medial curves. Our approach is based on three key concepts: a local orthogonal decomposition of objects into substructures, a differential geometry concept called the interior center of curvature (ICC), and integrated stabilitymore » and consistency tests. These concepts lend themselves to robust numerical techniques including eigenvalue analysis, weighted least squares approximations, and numerical minimization, resulting in an algorithm that is efficient and noise resistant. We illustrate the effectiveness and robustness of our approach with some highly complex, large-scale, noisy biomedical geometries derived from medical images, including lung airways and blood vessels. We also present comparisons of our method with some existing methods.« less

Development and presentation of a roadway and roadside design course : final report, December 2009.

DOT National Transportation Integrated Search

2009-12-01

The overall goal of this course is to provide training in the elements of geometric highway : design. Specific course objectives are: : To review the geometry of horizontal and vertical alignment including simple circular : curves, compound curve...

Origin of the Uinta recess, Sevier fold thrust belt, Utah: influence of basin architecture on fold thrust belt geometry

NASA Astrophysics Data System (ADS)

Paulsen, Timothy; Marshak, Stephen

1999-11-01

Structural trends in the Sevier fold-thrust belt define a pronounced concave-to-the-foreland map-view curve, the Uinta recess, in north-central Utah. This recess separates two convex-to-the-foreland curves, the Provo salient on the south and the Wyoming salient on the north. The two limbs of the recess comprise transverse zones (fault zones at a high-angle to the regional trend of the orogen) that border the flanks of the east-west-trending Uinta/Cottonwood arch. Our structural analysis indicates that the transverse zones formed during the Sevier orogeny, and that they differ markedly from each other in structural style. The Charleston transverse zone (CTZ), on the south side of the arch, initiated as a complex sinistral strike-slip fault system that defines the abrupt northern boundary of the Provo salient. The Mount Raymond transverse zone (MRTZ), on the north side of the arch, represents the region in which the southeast-verging southern limb of the gently curving Wyoming salient was tilted northwards during the Laramide phase of uplift of the Uinta/Cottonwood arch. In effect, the MRTZ represents an oblique cross section through a thrust belt. The contrasting architecture of these transverse zones demonstrates how pre-deformation basin geometry influences the geometry of a fold-thrust belt. Analysis of isopach maps indicates that, at the time the Sevier fold-thrust belt formed, the area just north of the present site of the Uinta/Cottonwood arch was a basement high, with a gently dipping north flank, and a steeply dipping south flank. Thus, predeformational sediment thickened abruptly to the south of the high and thickened gradually to the north of the high. As illustrated by sandbox models, the distance that a fold-thrust belt propagates into the foreland depends on the thickness of the sedimentary layer being deformed, so the shape of the salient mimics the longitudinal cross-sectional shape of the sedimentary basin. Where basins taper gradually along strike, the thrust belt curves gently, but where basins taper abruptly along strike, the thrust belt curves so tightly that it disarticulates and becomes bounded laterally by a strike-slip accommodation zone. The geometry of the Uinta recess provides a field example of this concept. Differential movement of Sevier thrusts led to formation of gradually curving thrusts on the north side of the high, because of the gradual slope of the high's north flank, but led to the along-strike disarticulation of thrusts on the south side of the high, because of the steep slope of the high's south flank. In effect, therefore, thrust belt map-view geometry provides insight into predeformational basin geometry.

Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry

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

Huang, Lei; Xue, Junpeng; Gao, Bo

2017-06-14

There are wide applications for zonal reconstruction methods in slope-based metrology due to its good capability of reconstructing the local details on surface profile. It was noticed in the literature that large reconstruction errors occur when using zonal reconstruction methods designed for rectangular geometry to process slopes in a quadrilateral geometry, which is a more general geometry with phase measuring deflectometry. In this paper, we present a new idea for the zonal methods for quadrilateral geometry. Instead of employing the intermediate slopes to set up height-slope equations, we consider the height increment as a more general connector to establish themore » height-slope relations for least-squares regression. The classical zonal methods and interpolation-assisted zonal methods are compared with our proposal. Results of both simulation and experiment demonstrate the effectiveness of the proposed idea. In implementation, the modification on the classical zonal methods is addressed. Finally, the new methods preserve many good aspects of the classical ones, such as the ability to handle a large incomplete slope dataset in an arbitrary aperture, and the low computational complexity comparable with the classical zonal method. Of course, the accuracy of the new methods is much higher when integrating the slopes in quadrilateral geometry.« less

Computing observables in curved multifield models of inflation—A guide (with code) to the transport method

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

Dias, Mafalda; Seery, David; Frazer, Jonathan, E-mail: m.dias@sussex.ac.uk, E-mail: j.frazer@sussex.ac.uk, E-mail: a.liddle@sussex.ac.uk

We describe how to apply the transport method to compute inflationary observables in a broad range of multiple-field models. The method is efficient and encompasses scenarios with curved field-space metrics, violations of slow-roll conditions and turns of the trajectory in field space. It can be used for an arbitrary mass spectrum, including massive modes and models with quasi-single-field dynamics. In this note we focus on practical issues. It is accompanied by a Mathematica code which can be used to explore suitable models, or as a basis for further development.

GOATS - Orbitology Component

NASA Technical Reports Server (NTRS)

Haber, Benjamin M.; Green, Joseph J.

2010-01-01

The GOATS Orbitology Component software was developed to specifically address the concerns presented by orbit analysis tools that are often written as stand-alone applications. These applications do not easily interface with standard JPL first-principles analysis tools, and have a steep learning curve due to their complicated nature. This toolset is written as a series of MATLAB functions, allowing seamless integration into existing JPL optical systems engineering modeling and analysis modules. The functions are completely open, and allow for advanced users to delve into and modify the underlying physics being modeled. Additionally, this software module fills an analysis gap, allowing for quick, high-level mission analysis trades without the need for detailed and complicated orbit analysis using commercial stand-alone tools. This software consists of a series of MATLAB functions to provide for geometric orbit-related analysis. This includes propagation of orbits to varying levels of generalization. In the simplest case, geosynchronous orbits can be modeled by specifying a subset of three orbit elements. The next case is a circular orbit, which can be specified by a subset of four orbit elements. The most general case is an arbitrary elliptical orbit specified by all six orbit elements. These orbits are all solved geometrically, under the basic problem of an object in circular (or elliptical) orbit around a rotating spheroid. The orbit functions output time series ground tracks, which serve as the basis for more detailed orbit analysis. This software module also includes functions to track the positions of the Sun, Moon, and arbitrary celestial bodies specified by right ascension and declination. Also included are functions to calculate line-of-sight geometries to ground-based targets, angular rotations and decompositions, and other line-of-site calculations. The toolset allows for the rapid execution of orbit trade studies at the level of detail required for the early stage of mission concept development.

Proficiency Standards and Cut-Scores for Language Proficiency Tests.

ERIC Educational Resources Information Center

Moy, Raymond H.

1984-01-01

Discusses the problems associated with "grading on a curve," the approach often used for standard setting on language proficiency tests. Proposes four main steps presented in the setting of a non-arbitrary cut-score. These steps not only establish a proficiency standard checked by external criteria, but also check to see that the test covers the…

Positive geometries and canonical forms

NASA Astrophysics Data System (ADS)

Arkani-Hamed, Nima; Bai, Yuntao; Lam, Thomas

2017-11-01

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. The structures seen in the physical setting of the Amplituhedron are both rigid and rich enough to motivate an investigation of the notions of "positive geometries" and their associated "canonical forms" as objects of study in their own right, in a more general mathematical setting. In this paper we take the first steps in this direction. We begin by giving a precise definition of positive geometries and canonical forms, and introduce two general methods for finding forms for more complicated positive geometries from simpler ones — via "triangulation" on the one hand, and "push-forward" maps between geometries on the other. We present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties, both for the simplest "simplex-like" geometries and the richer "polytope-like" ones. We also illustrate a number of strategies for computing canonical forms for large classes of positive geometries, ranging from a direct determination exploiting knowledge of zeros and poles, to the use of the general triangulation and push-forward methods, to the representation of the form as volume integrals over dual geometries and contour integrals over auxiliary spaces. These methods yield interesting representations for the canonical forms of wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

The 124Sb activity standardization by gamma spectrometry for medical applications

NASA Astrophysics Data System (ADS)

de Almeida, M. C. M.; Iwahara, A.; Delgado, J. U.; Poledna, R.; da Silva, R. L.

2010-07-01

This work describes a metrological activity determination of 124Sb, which can be used as radiotracer, applying gamma spectrometry methods with hyper pure germanium detector and efficiency curves. This isotope with good activity and high radionuclidic purity is employed in the form of meglumine antimoniate (Glucantime) or sodium stibogluconate (Pentostam) to treat leishmaniasis. 124Sb is also applied in animal organ distribution studies to solve some questions in pharmacology. 124Sb decays by β-emission and it produces several photons (X and gamma rays) with energy varying from 27 to 2700 keV. Efficiency curves to measure point 124Sb solid sources were obtained from a 166mHo standard that is a multi-gamma reference source. These curves depend on radiation energy, sample geometry, photon attenuation, dead time and sample-detector position. Results for activity determination of 124Sb samples using efficiency curves and a high purity coaxial germanium detector were consistent in different counting geometries. Also uncertainties of about 2% ( k=2) were obtained.

Strategies Toward Automation of Overset Structured Surface Grid Generation

NASA Technical Reports Server (NTRS)

Chan, William M.

2017-01-01

An outline of a strategy for automation of overset structured surface grid generation on complex geometries is described. The starting point of the process consists of an unstructured surface triangulation representation of the geometry derived from a native CAD, STEP, or IGES definition, and a set of discretized surface curves that captures all geometric features of interest. The procedure for surface grid generation is decomposed into an algebraic meshing step, a hyperbolic meshing step, and a gap-filling step. This paper will focus primarily on the high-level plan with details on the algebraic step. The algorithmic procedure for the algebraic step involves analyzing the topology of the network of surface curves, distributing grid points appropriately on these curves, identifying domains bounded by four curves that can be meshed algebraically, concatenating the resulting grids into fewer patches, and extending appropriate boundaries of the concatenated grids to provide proper overlap. Results are presented for grids created on various aerospace vehicle components.

Inverse Diffusion Curves Using Shape Optimization.

PubMed

Zhao, Shuang; Durand, Fredo; Zheng, Changxi

2018-07-01

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

Emergent gauge field for a chiral bound state on curved surface

NASA Astrophysics Data System (ADS)

Shi, Zhe-Yu; Zhai, Hui

2017-09-01

Emergent physics is one of the most important concepts in modern physics, and one of the most intriguing examples is the emergent gauge field. Here we show that a gauge field emerges for a chiral bound state formed by two attractively interacting particles on a curved surface. We demonstrate explicitly that the center-of-mass wave function of such a deeply bound state is monopole harmonic instead of spherical harmonic, which means that the bound state experiences a magnetic monopole at the center of the sphere. This emergent gauge field is due to the coupling between the center-of-mass and the relative motion on a curved surface, and our results can be generalized to an arbitrary curved surface. This result establishes an intriguing connection between the space curvature and gauge field, and paves an alternative way to engineer a topological state with space curvature, and may be observed in a cold atom system.

Fabrication of anodic aluminium oxide templates on curved surfaces.

PubMed

Yin, Aijun; Guico, Rodney S; Xu, Jimmy

2007-01-24

Aluminium anodization provides a simple and inexpensive way to obtain nanoporous templates with uniform and controllable pore diameters and periods over a wide range. Moreover, one of the interesting possibilities afforded by the anodization process is that the anodization can take place on arbitrary surfaces, such as curved surfaces, which has not yet been well studied or applied in nanofabrication. In this paper, we characterize the anodization of Al films on silicon substrates with a curved top surface. The structures of the resultant anodic aluminium oxide (AAO) films are examined by scanning electron microscopy. Unique features including cessation, bending, and branching of pore channels are observed in the curved area. Possible growth mechanisms are proposed, which can also contribute to the understanding of the self-organization mechanism in the formation of porous AAO membranes. The new structures may open new opportunities in optical, electronic and electrochemical applications.

An efficient method to compute microlensed light curves for point sources

NASA Technical Reports Server (NTRS)

Witt, Hans J.

1993-01-01

We present a method to compute microlensed light curves for point sources. This method has the general advantage that all microimages contributing to the light curve are found. While a source moves along a straight line, all micro images are located either on the primary image track or on the secondary image tracks (loops). The primary image track extends from - infinity to + infinity and is made of many sequents which are continuously connected. All the secondary image tracks (loops) begin and end on the lensing point masses. The method can be applied to any microlensing situation with point masses in the deflector plane, even for the overcritical case and surface densities close to the critical. Furthermore, we present general rules to evaluate the light curve for a straight track arbitrary placed in the caustic network of a sample of many point masses.

Residual zonal flows in tokamaks and stellarators at arbitrary wavelengths

NASA Astrophysics Data System (ADS)

Monreal, Pedro; Calvo, Iván; Sánchez, Edilberto; Parra, Félix I.; Bustos, Andrés; Könies, Axel; Kleiber, Ralf; Görler, Tobias

2016-04-01

In the linear collisionless limit, a zonal potential perturbation in a toroidal plasma relaxes, in general, to a non-zero residual value. Expressions for the residual value in tokamak and stellarator geometries, and for arbitrary wavelengths, are derived. These expressions involve averages over the lowest order particle trajectories, that typically cannot be evaluated analytically. In this work, an efficient numerical method for the evaluation of such expressions is reported. It is shown that this method is faster than direct gyrokinetic simulations performed with the Gene and EUTERPE codes. Calculations of the residual value in stellarators are provided for much shorter wavelengths than previously available in the literature. Electrons must be treated kinetically in stellarators because, unlike in tokamaks, kinetic electrons modify the residual value even at long wavelengths. This effect, that had already been predicted theoretically, is confirmed by gyrokinetic simulations.

Shielded resistive electromagnets of arbitrary surface geometry using the boundary element method and a minimum energy constraint.

PubMed

Harris, Chad T; Haw, Dustin W; Handler, William B; Chronik, Blaine A

2013-09-01

Eddy currents are generated in MR by the use of rapidly switched electromagnets, resulting in time varying and spatially varying magnetic fields that must be either minimized or corrected. This problem is further complicated when non-cylindrical insert magnets are used for specialized applications. Interruption of the coupling between an insert coil and the MR system is typically accomplished using active magnetic shielding. A new method of actively shielding insert gradient and shim coils of any surface geometry by use of the boundary element method for coil design with a minimum energy constraint is presented. This method was applied to shield x- and z-gradient coils for two separate cases: a traditional cylindrical primary gradient with cylindrical shield and, to demonstrate its versatility in surface geometry, the same cylindrical primary gradients with a rectangular box-shaped shield. For the cylindrical case this method produced shields that agreed with analytic solutions. For the second case, the rectangular box-shaped shields demonstrated very good shielding characteristics despite having a different geometry than the primary coils. Copyright © 2013 Elsevier Inc. All rights reserved.

SDM - A geodetic inversion code incorporating with layered crust structure and curved fault geometry

NASA Astrophysics Data System (ADS)

Wang, Rongjiang; Diao, Faqi; Hoechner, Andreas

2013-04-01

Currently, inversion of geodetic data for earthquake fault ruptures is most based on a uniform half-space earth model because of its closed-form Green's functions. However, the layered structure of the crust can significantly affect the inversion results. The other effect, which is often neglected, is related to the curved fault geometry. Especially, fault planes of most mega thrust earthquakes vary their dip angle with depth from a few to several tens of degrees. Also the strike directions of many large earthquakes are variable. For simplicity, such curved fault geometry is usually approximated to several connected rectangular segments, leading to an artificial loss of the slip resolution and data fit. In this presentation, we introduce a free FORTRAN code incorporating with the layered crust structure and curved fault geometry in a user-friendly way. The name SDM stands for Steepest Descent Method, an iterative algorithm used for the constrained least-squares optimization. The new code can be used for joint inversion of different datasets, which may include systematic offsets, as most geodetic data are obtained from relative measurements. These offsets are treated as unknowns to be determined simultaneously with the slip unknowns. In addition, a-priori and physical constraints are considered. The a-priori constraint includes the upper limit of the slip amplitude and the variation range of the slip direction (rake angle) defined by the user. The physical constraint is needed to obtain a smooth slip model, which is realized through a smoothing term to be minimized with the misfit to data. In difference to most previous inversion codes, the smoothing can be optionally applied to slip or stress-drop. The code works with an input file, a well-documented example of which is provided with the source code. Application examples are demonstrated.

Robot computer problem solving system

NASA Technical Reports Server (NTRS)

Merriam, E. W.; Becker, J. D.

1973-01-01

A robot computer problem solving system which represents a robot exploration vehicle in a simulated Mars environment is described. The model exhibits changes and improvements made on a previously designed robot in a city environment. The Martian environment is modeled in Cartesian coordinates; objects are scattered about a plane; arbitrary restrictions on the robot's vision have been removed; and the robot's path contains arbitrary curves. New environmental features, particularly the visual occlusion of objects by other objects, were added to the model. Two different algorithms were developed for computing occlusion. Movement and vision capabilities of the robot were established in the Mars environment, using LISP/FORTRAN interface for computational efficiency. The graphical display program was redesigned to reflect the change to the Mars-like environment.

Elastic buckling analysis for composite stiffened panels and other structures subjected to biaxial inplane loads

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Tamekuni, M.

1973-01-01

An exact linear analysis method is presented for predicting buckling of structures with arbitrary uniform cross section. The structure is idealized as an assemblage of laminated plate-strip elements, curved and planar, and beam elements. Element edges normal to the longitudinal axes are assumed to be simply supported. Arbitrary boundary conditions may be specified on any external longitudinal edge of plate-strip elements. The structure or selected elements may be loaded in any desired combination of inplane transverse compression or tension side load and axial compression load. The analysis simultaneously considers all possible modes of instability and is applicable for the buckling of laminated composite structures. Numerical results correlate well with the results of previous analysis methods.

Efficiency of Magnetic to Kinetic Energy Conversion in a Monopole Magnetosphere

NASA Astrophysics Data System (ADS)

Tchekhovskoy, Alexander; McKinney, Jonathan C.; Narayan, Ramesh

2009-07-01

Unconfined relativistic outflows from rotating, magnetized compact objects are often well modeled by assuming that the field geometry is approximately a split-monopole at large radii. Earlier work has indicated that such an unconfined flow has an inefficient conversion of magnetic energy to kinetic energy. This has led to the conclusion that ideal magnetohydrodynamical (MHD) processes fail to explain observations of, e.g., the Crab pulsar wind at large radii where energy conversion appears efficient. In addition, as a model for astrophysical jets, the monopole field geometry has been abandoned in favor of externally confined jets since the latter appeared to be generically more efficient jet accelerators. We perform time-dependent axisymmetric relativistic MHD simulations in order to find steady-state solutions for a wind from a compact object endowed with a monopole field geometry. Our simulations follow the outflow for 10 orders of magnitude in distance from the compact object, which is large enough to study both the initial "acceleration zone" of the magnetized wind as well as the asymptotic "coasting zone." We obtain the surprising result that acceleration is actually efficient in the polar region, which develops a jet despite not being confined by an external medium. Our models contain jets that have sufficient energy to account for moderately energetic long and short gamma-ray burst (GRB) events (~1051-1052 erg), collimate into narrow opening angles (opening half-angle θ j ≈ 0.03 rad), become matter-dominated at large radii (electromagnetic energy flux per unit matter energy flux σ < 1), and move at ultrarelativistic Lorentz factors (γ j ~ 200 for our fiducial model). The simulated jets have γ j θ j ~ 5-15, so they are in principle capable of generating "achromatic jet breaks" in GRB afterglow light curves. By defining a "causality surface" beyond which the jet cannot communicate with a generalized "magnetic nozzle" near the axis of rotation, we obtain approximate analytical solutions for the Lorentz factor that fit the numerical solutions well. This allows us to extend our results to monopole wind models with arbitrary magnetization. Overall, our results demonstrate that the production of ultrarelativistic jets is a more robust process than previously thought.

Compatible, total energy conserving and symmetry preserving arbitrary Lagrangian-Eulerian hydrodynamics in 2D rz - Cylindrical coordinates

NASA Astrophysics Data System (ADS)

Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail

2014-07-01

We present a new discretization for 2D arbitrary Lagrangian-Eulerian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic Lagrangian hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the Lagrangian equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its “Cartesian” form with a special definition of “planar” masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of “planar” subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; formulated for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for Lagrangian equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary Lagrangian-Eulerian algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a local constrained-optimization-based approach for each zone to find the subzonal mass fluxes. In this paper we give a systematic and complete description of the algorithm for the axisymmetric case and provide justification for our approach. The ALE algorithm conserves total energy on arbitrary meshes and preserves symmetry when remapping from one equiangular polar mesh to another. The principal contributions of this part of the paper are the extension of this algorithm to general polygonal meshes and 2D rz geometry with requirement of symmetry preservation on special meshes. We present numerical examples that demonstrate the robustness of the new ALE method on a variety of grids and test problems including polygonal meshes and some realistic experiments. We confirm the importance of conservation of total energy for correctly modeling shock waves.

Ewald method for polytropic potentials in arbitrary dimensionality

NASA Astrophysics Data System (ADS)

Osychenko, O. N.; Astrakharchik, G. E.; Boronat, J.

2012-02-01

The Ewald summation technique is generalized to power-law 1/| r | k potentials in three-, two- and one-dimensional geometries with explicit formulae for all the components of the sums. The cases of short-range, long-range and 'marginal' interactions are treated separately. The jellium model, as a particular case of a charge-neutral system, is discussed and the explicit forms of the Ewald sums for such a system are presented. A generalized form of the Ewald sums for a non-cubic (non-square) simulation cell for three- (two-) dimensional geometry is obtained and its possible field of application is discussed. A procedure for the optimization of the involved parameters in actual simulations is developed and an example of its application is presented.

Method for determining optimal supercell representation of interfaces

NASA Astrophysics Data System (ADS)

Stradi, Daniele; Jelver, Line; Smidstrup, Søren; Stokbro, Kurt

2017-05-01

The geometry and structure of an interface ultimately determines the behavior of devices at the nanoscale. We present a generic method to determine the possible lattice matches between two arbitrary surfaces and to calculate the strain of the corresponding matched interface. We apply this method to explore two relevant classes of interfaces for which accurate structural measurements of the interface are available: (i) the interface between pentacene crystals and the (1 1 1) surface of gold, and (ii) the interface between the semiconductor indium-arsenide and aluminum. For both systems, we demonstrate that the presented method predicts interface geometries in good agreement with those measured experimentally, which present nontrivial matching characteristics and would be difficult to guess without relying on automated structure-searching methods.

Generalizing the extensibility of a dynamic geometry software

NASA Astrophysics Data System (ADS)

Herceg, Đorđe; Radaković, Davorka; Herceg, Dejana

2012-09-01

Plug-and-play visual components in a Dynamic Geometry Software (DGS) enable development of visually attractive, rich and highly interactive dynamic drawings. We are developing SLGeometry, a DGS that contains a custom programming language, a computer algebra system (CAS engine) and a graphics subsystem. The basic extensibility framework on SLGeometry supports dynamic addition of new functions from attribute annotated classes that implement runtime metadata registration in code. We present a general plug-in framework for dynamic importing of arbitrary Silverlight user interface (UI) controls into SLGeometry at runtime. The CAS engine maintains a metadata storage that describes each imported visual component and enables two-way communication between the expressions stored in the engine and the UI controls on the screen.

Plasma shaping effects on tokamak scrape-off layer turbulence

NASA Astrophysics Data System (ADS)

Riva, Fabio; Lanti, Emmanuel; Jolliet, Sébastien; Ricci, Paolo

2017-03-01

The impact of plasma shaping on tokamak scrape-off layer (SOL) turbulence is investigated. The drift-reduced Braginskii equations are written for arbitrary magnetic geometries, and an analytical equilibrium model is used to introduce the dependence of turbulence equations on tokamak inverse aspect ratio (ε ), Shafranov’s shift (Δ), elongation (κ), and triangularity (δ). A linear study of plasma shaping effects on the growth rate of resistive ballooning modes (RBMs) and resistive drift waves (RDWs) reveals that RBMs are strongly stabilized by elongation and negative triangularity, while RDWs are only slightly stabilized in non-circular magnetic geometries. Assuming that the linear instabilities saturate due to nonlinear local flattening of the plasma gradient, the equilibrium gradient pressure length {L}p=-{p}e/{{\

Monte Carlo simulation of portal dosimetry on a rectilinear voxel geometry: a variable gantry angle solution.

PubMed

Chin, P W; Spezi, E; Lewis, D G

2003-08-21

A software solution has been developed to carry out Monte Carlo simulations of portal dosimetry using the BEAMnrc/DOSXYZnrc code at oblique gantry angles. The solution is based on an integrated phantom, whereby the effect of incident beam obliquity was included using geometric transformations. Geometric transformations are accurate within +/- 1 mm and +/- 1 degrees with respect to exact values calculated using trigonometry. An application in portal image prediction of an inhomogeneous phantom demonstrated good agreement with measured data, where the root-mean-square of the difference was under 2% within the field. Thus, we achieved a dose model framework capable of handling arbitrary gantry angles, voxel-by-voxel phantom description and realistic particle transport throughout the geometry.

Light Curve Simulation Using Spacecraft CAD Models and Empirical Material Spectral BRDFS

NASA Astrophysics Data System (ADS)

Willison, A.; Bedard, D.

This paper presents a Matlab-based light curve simulation software package that uses computer-aided design (CAD) models of spacecraft and the spectral bidirectional reflectance distribution function (sBRDF) of their homogenous surface materials. It represents the overall optical reflectance of objects as a sBRDF, a spectrometric quantity, obtainable during an optical ground truth experiment. The broadband bidirectional reflectance distribution function (BRDF), the basis of a broadband light curve, is produced by integrating the sBRDF over the optical wavelength range. Colour-filtered BRDFs, the basis of colour-filtered light curves, are produced by first multiplying the sBRDF by colour filters, and integrating the products. The software package's validity is established through comparison of simulated reflectance spectra and broadband light curves with those measured of the CanX-1 Engineering Model (EM) nanosatellite, collected during an optical ground truth experiment. It is currently being extended to simulate light curves of spacecraft in Earth orbit, using spacecraft Two-Line-Element (TLE) sets, yaw/pitch/roll angles, and observer coordinates. Measured light curves of the NEOSSat spacecraft will be used to validate simulated quantities. The sBRDF was chosen to represent material reflectance as it is spectrometric and a function of illumination and observation geometry. Homogeneous material sBRDFs were obtained using a goniospectrometer for a range of illumination and observation geometries, collected in a controlled environment. The materials analyzed include aluminum alloy, two types of triple-junction photovoltaic (TJPV) cell, white paint, and multi-layer insulation (MLI). Interpolation and extrapolation methods were used to determine the sBRDF for all possible illumination and observation geometries not measured in the laboratory, resulting in empirical look-up tables. These look-up tables are referenced when calculating the overall sBRDF of objects, where the contribution of each facet is proportionally integrated.

Extensions and Adjuncts to the BRL-COMGEOM Program

DTIC Science & Technology

1974-08-01

m MAGIC Code, GIFT Code, Computer Simulation, Target Description, Geometric Modeling Techniques, Vulnerability Analysis 20...Arbitrary Quadric Surf ace.. 0Oo „<>. 7 III. BRITL: A GEOMETRY PREPROCESSOR PROGRAM FOR INPUT TO THE GIFT SYSTEM „ 0 18 A. Introduction <, „. ° 18 B...the BRL- GIFT code. The tasks completed under this contract and described in the report are: Ao The addition to the list of available body types

Multipath modeling for aeronautical communications.

NASA Technical Reports Server (NTRS)

Painter, J. H.; Gupta, S. C.; Wilson, L. R.

1973-01-01

One of the fundamental technical problems in aeronautical digital communications is that of multipath propagation between aircraft and ground terminal. This paper examines in detail a model of the received multipath signal that is useful for application of modern detection and estimation theories. The model treats arbitrary modulation and covers the selective and nonselective cases. The necessarily nonstationary statistics of the received signal are determined from the link geometry and the surface roughness parameters via a Kirchhoff solution.

NASA Ames potential flow analysis (POTFAN) geometry program (POTGEM), version 1

NASA Technical Reports Server (NTRS)

Medan, R. T.; Bullock, R. B.

1976-01-01

A computer program known as POTGEM is reported which has been developed as an independent segment of a three-dimensional linearized, potential flow analysis system and which is used to generate a panel point description of arbitrary, three-dimensional bodies from convenient engineering descriptions consisting of equations and/or tables. Due to the independent, modular nature of the program, it may be used to generate corner points for other computer programs.

A new unified approach to analyze wing-body-tail configurations with control surfaces in steady, oscillatory and fully unsteady, subsonic and supersonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.; Morino, L.

1975-01-01

A general formulation for the analysis of steady and unsteady, subsonic and supersonic potential aerodynamics for arbitrary complex geometries is presented. The theoretical formulation, the numerical procedure, and numerical results are included. In particular, generalized forces for fully unsteady (complex frequency) aerodynamics for an AGARD coplanar wing-tail interfering configuration in both subsonic and supersonic flows are considered.

Republication of: Relativistic cosmology

NASA Astrophysics Data System (ADS)

Ellis, George F. R.

2009-03-01

This is a republication of a paper by G.F.R. Ellis first published in Proceedings of the International School of Physics: General Relativity and Cosmology, 1971, in which he formulated the framework for relativistic cosmology with an arbitrary background geometry. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. The paper is accompanied by a Golden Oldie Editorial comprising an editorial note written by Bill Stoeger and Ellis’ brief autobiography.

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

PubMed Central

Seyler, Sean L.; Kumar, Avishek; Thorpe, M. F.; Beckstein, Oliver

2015-01-01

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example, showed that the geometry-based FRODA occasionally sampled the pathway space of force field-based DIMS MD. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions. PMID:26488417

Weak form implementation of the semi-analytical finite element (SAFE) method for a variety of elastodynamic waveguides

NASA Astrophysics Data System (ADS)

Hakoda, Christopher; Lissenden, Clifford; Rose, Joseph L.

2018-04-01

Dispersion curves are essential to any guided wave NDE project. The Semi-Analytical Finite Element (SAFE) method has significantly increased the ease by which these curves can be calculated. However, due to misconceptions regarding theory and fragmentation based on different finite-element software, the theory has stagnated, and adoption by researchers who are new to the field has been slow. This paper focuses on the relationship between the SAFE formulation and finite element theory, and the implementation of the SAFE method in a weak form for plates, pipes, layered waveguides/composites, curved waveguides, and arbitrary cross-sections is shown. The benefits of the weak form are briefly described, as is implementation in open-source and commercial finite element software.

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

Shang, Yu; Yu, Guoqiang, E-mail: guoqiang.yu@uky.edu

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD{sub B}). The purpose of this study is to extend the capability of the Nth-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different typesmore » of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD{sub B} in the brain layer with a step decrement of 10% while maintaining αD{sub B} values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order (N ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The Nth-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.« less

A Nth-order linear algorithm for extracting diffuse correlation spectroscopy blood flow indices in heterogeneous tissues.

PubMed

Shang, Yu; Yu, Guoqiang

2014-09-29

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a N th-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD B ). The purpose of this study is to extend the capability of the N th-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different types of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD B in the brain layer with a step decrement of 10% while maintaining αD B values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order ( N  ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The N th-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.

Identifying Blocks Formed by Curbed Fractures Using Exact Arithmetic

NASA Astrophysics Data System (ADS)

Zheng, Y.; Xia, L.; Yu, Q.; Zhang, X.

2015-12-01

Identifying blocks formed by fractures is important in rock engineering. Most studies assume the fractures to be perfect planar whereas curved fractures are rarely considered. However, large fractures observed in the field are often curved. This paper presents a new method for identifying rock blocks formed by both curved and planar fractures based on the element-block-assembling approach. The curved and planar fractures are represented as triangle meshes and planar discs, respectively. In the beginning of the identification method, the intersection segments between different triangle meshes are calculated and the intersected triangles are re-meshed to construct a piecewise linear complex (PLC). Then, the modeling domain is divided into tetrahedral subdomains under the constraint of the PLC and these subdomains are further decomposed into element blocks by extended planar fractures. Finally, the element blocks are combined and the subdomains are assembled to form complex blocks. The combination of two subdomains is skipped if and only if the common facet lies on a curved fracture. In this study, the exact arithmetic is used to handle the computational errors, which may threat the robustness of the block identification program when the degenerated cases are encountered. Specifically, a real number is represented as the ratio between two integers and the basic arithmetic such as addition, subtraction, multiplication and division between different real numbers can be performed exactly if an arbitrary precision integer package is used. In this way, the exact construction of blocks can be achieved without introducing computational errors. Several analytical examples are given in this paper and the results show effectiveness of this method in handling arbitrary shaped blocks. Moreover, there is no limitation on the number of blocks in a block system. The results also show (suggest) that the degenerated cases can be handled without affecting the robustness of the identification program.

Field of view of limitations in see-through HMD using geometric waveguides.

PubMed

DeHoog, Edward; Holmstedt, Jason; Aye, Tin

2016-08-01

Geometric waveguides are being integrated into head-mounted display (HMD) systems, where having see-through capability in a compact, lightweight form factor is required. We developed methods for determining the field of view (FOV) of such waveguide HMD systems and have analytically derived the FOV for waveguides using planar and curved geometries. By using real ray-tracing methods, we are able to show how the geometry and index of refraction of the waveguide, as well as the properties of the coupling optics, impact the FOV. Use of this analysis allows one to determine the maximum theoretical FOV of a planar or curved waveguide-based system.

Local-area simulations of rotating compressible convection and associated mean flows

NASA Technical Reports Server (NTRS)

Hurlburt, Neal E.; Brummell, N. H.; Toomre, Juri

1995-01-01

The dynamics of compressible convection within a curved local segment of a rotating spherical shell are considered in relation to the turbulent redistribution of angular momentum within the solar convection zone. Current supercomputers permit fully turbulent flows to be considered within the restricted geometry of local area models. By considering motions in a curvilinear geometry in which the Coriolos parameters vary with latitude, Rossby waves which couple with the turbulent convection are thought of as being possible. Simulations of rotating convection are presented in such a curved local segment of a spherical shell using a newly developed, sixth-order accurate code based on compact finite differences.

Revised text for TxDOT manual procedures for establishing speed zones, chapter 5, section 2.

DOT National Transportation Integrated Search

2010-02-01

Warning signs are intended to improve curve safety by alerting the driver to a change in : geometry that may not be apparent or expected. These signs notify drivers of the change : through the use of one or more of the curve warning signs identified ...

Turtle Escapes the Plane: Some Advanced Turtle Geometry. Artificial Intelligence Memo Number 348.

ERIC Educational Resources Information Center

diSessa, Andy

The LOGO Turtles, originally developed at the Massachusetts Institute of Technology Artificial Intelligence Laboratory for teaching concepts in elementary geometry to primary-age children, can also be used in teaching higher-level mathematics. In the exercises described here, the turtle was programed to traverse curved surfaces. Both geometric and…

Development and comparison of multiple regression models to predict bankfull channel dimensions for use in hydrologic models

USDA-ARS?s Scientific Manuscript database

Bankfull hydraulic geometry relationships are used to estimate channel dimensions for streamflow simulation models, which require channel geometry data as input parameters. Often, one nationwide curve is used across the entire United States (U.S.) (e.g., in Soil and Water Assessment Tool), even tho...

Integral geometry and holography

DOE PAGES

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

2015-10-27

We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS 3/CFT 2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length ofmore » any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS 3 whose kinematic space is two-dimensional de Sitter space.« less

Image Understanding Proceedings of a Workshop Held at Washington, DC, April 23, 1981

DTIC Science & Technology

1981-04-01

quantities on the projection plane. constituent velocities, the problem can and should No 3D geometry is involved. Also 3utlined is a be studied on its own...illuniiration, aspects of object geometry , and the data) have occurred. This means that our reasoning can no6production of illumination diasoptinuities by...interpretation distinct classes: those ct~used by disco,.tinuities in the of image curves (also known as intensity discontinuities or geometry of an

Approach to solution of coupled heat transfer problem on the surface of hypersonic vehicle of arbitrary shape

NASA Astrophysics Data System (ADS)

Bocharov, A. N.; Bityurin, V. A.; Golovin, N. N.; Evstigneev, N. M.; Petrovskiy, V. P.; Ryabkov, O. I.; Teplyakov, I. O.; Shustov, A. A.; Solomonov, Yu S.; Fortov, V. E.

2016-11-01

In this paper, an approach to solve conjugate heat- and mass-transfer problems is considered to be applied to hypersonic vehicle surface of arbitrary shape. The approach under developing should satisfy the following demands. (i) The surface of the body of interest may have arbitrary geometrical shape. (ii) The shape of the body can change during calculation. (iii) The flight characteristics may vary in a wide range, specifically flight altitude, free-stream Mach number, angle-of-attack, etc. (iv) The approach should be realized with using the high-performance-computing (HPC) technologies. The approach is based on coupled solution of 3D unsteady hypersonic flow equations and 3D unsteady heat conductance problem for the thick wall. Iterative process is applied to account for ablation of wall material and, consequently, mass injection from the surface and changes in the surface shape. While iterations, unstructured computational grids both in the flow region and within the wall interior are adapted to the current geometry and flow conditions. The flow computations are done on HPC platform and are most time-consuming part of the whole problem, while heat conductance problem can be solved on many kinds of computers.

An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells

DOE PAGES

Diot, Steven; François, Marianne M.

2015-10-22

In this study, we are interested in an interface reconstruction method for 3D arbitrary convex cells that could be used in multi-material flow simulations for instance. We assume that the interface is represented by a plane whose normal vector is known and we focus on the volume-matching step that consists in finding the plane constant so that it splits the cell according to a given volume fraction. We follow the same approach as in the recent authors' publication for 2D arbitrary convex cells in planar and axisymmetrical geometries, namely we derive an analytical formula for the volume of the specificmore » prismatoids obtained when decomposing the cell using the planes that are parallel to the interface and passing through all the cell nodes. This formula is used to bracket the interface plane constant such that the volume-matching problem is rewritten in a single prismatoid in which the same formula is used to find the final solution. Finally, the proposed method is tested against an important number of reproducible configurations and shown to be at least five times faster.« less

Static properties of hydrostatic thrust gas bearings with curved surfaces.

NASA Technical Reports Server (NTRS)

Rehsteiner, F. H.; Cannon, R. H., Jr.

1971-01-01

The classical treatment of circular, hydrostatic, orifice-regulated thrust gas bearings, in which perfectly plane bearing plates are assumed, is extended to include axisymmetric, but otherwise arbitrary, plate profiles. Plate curvature has a strong influence on bearing load capability, static stiffness, tilting stiffness, and side force per unit misalignment angle. By a suitable combination of gas inlet impedance and concave plate profile, the static stiffness can be made almost constant over a wide load range, and to remain positive at the closure load. Extensive measurements performed with convex and concave plates agree with theory to within the experimental error throughout and demonstrate the practical feasibility of using curved plates.

A synthetic method of solar spectrum based on LED

NASA Astrophysics Data System (ADS)

Wang, Ji-qiang; Su, Shi; Zhang, Guo-yu; Zhang, Jian

2017-10-01

A synthetic method of solar spectrum which based on the spectral characteristics of the solar spectrum and LED, and the principle of arbitrary spectral synthesis was studied by using 14 kinds of LED with different central wavelengths.The LED and solar spectrum data were selected by Origin Software firstly, then calculated the total number of LED for each center band by the transformation relation between brightness and illumination and Least Squares Curve Fit in Matlab.Finally, the spectrum curve of AM1.5 standard solar spectrum was obtained. The results met the technical indexes of the solar spectrum matching with ±20% and the solar constant with >0.5.

Higher spin conformal geometry in three dimensions and prepotentials for higher spin gauge fields

NASA Astrophysics Data System (ADS)

Henneaux, Marc; Hörtner, Sergio; Leonard, Amaury

2016-01-01

We study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish a number of its properties that turn out to be key in solving in terms of prepotentials the constraint equations of the Hamiltonian (3 + 1) formulation of four-dimensional higher spin gauge fields. The prepotentials are shown to exhibit higher spin conformal symmetry. Just as for spins 1 and 2, they provide a remarkably simple, manifestly duality invariant formulation of the theory. While the higher spin conformal geometry is developed for arbitrary bosonic spin, we explicitly perform the Hamiltonian analysis and derive the solution of the constraints only in the illustrative case of spin 3. In a separate publication, the Hamiltonian analysis in terms of prepotentials is extended to all bosonic higher spins using the conformal tools of this paper, and the same emergence of higher spin conformal symmetry is confirmed.

Thermal stability of black holes with arbitrary hairs

NASA Astrophysics Data System (ADS)

Sinha, Aloke Kumar

2018-02-01

We have derived the criteria for thermal stability of charged rotating black holes, for horizon areas that are large relative to the Planck area (in these dimensions). In this paper, we generalized it for black holes with arbitrary hairs. The derivation uses results of loop quantum gravity and equilibrium statistical mechanics of the grand canonical ensemble and there is no explicit use of classical spacetime geometry at all in this analysis. The assumption is that the mass of the black hole is a function of its horizon area and all the hairs. Our stability criteria are then tested in detail against some specific black holes, whose metrics provide us with explicit relations for the dependence of the mass on the area and other hairs of the black holes. This enables us to predict which of these black holes are expected to be thermally unstable under Hawking radiation.

A Computational Framework to Control Verification and Robustness Analysis

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2010-01-01

This paper presents a methodology for evaluating the robustness of a controller based on its ability to satisfy the design requirements. The framework proposed is generic since it allows for high-fidelity models, arbitrary control structures and arbitrary functional dependencies between the requirements and the uncertain parameters. The cornerstone of this contribution is the ability to bound the region of the uncertain parameter space where the degradation in closed-loop performance remains acceptable. The size of this bounding set, whose geometry can be prescribed according to deterministic or probabilistic uncertainty models, is a measure of robustness. The robustness metrics proposed herein are the parametric safety margin, the reliability index, the failure probability and upper bounds to this probability. The performance observed at the control verification setting, where the assumptions and approximations used for control design may no longer hold, will fully determine the proposed control assessment.

Routing of individual polymers in designed patterns

NASA Astrophysics Data System (ADS)

Knudsen, Jakob Bach; Liu, Lei; Bank Kodal, Anne Louise; Madsen, Mikael; Li, Qiang; Song, Jie; Woehrstein, Johannes B.; Wickham, Shelley F. J.; Strauss, Maximilian T.; Schueder, Florian; Vinther, Jesper; Krissanaprasit, Abhichart; Gudnason, Daniel; Smith, Anton Allen Abbotsford; Ogaki, Ryosuke; Zelikin, Alexander N.; Besenbacher, Flemming; Birkedal, Victoria; Yin, Peng; Shih, William M.; Jungmann, Ralf; Dong, Mingdong; Gothelf, Kurt V.

2015-10-01

Synthetic polymers are ubiquitous in the modern world, but our ability to exert control over the molecular conformation of individual polymers is very limited. In particular, although the programmable self-assembly of oligonucleotides and proteins into artificial nanostructures has been demonstrated, we currently lack the tools to handle other types of synthetic polymers individually and thus the ability to utilize and study their single-molecule properties. Here we show that synthetic polymer wires containing short oligonucleotides that extend from each repeat can be made to assemble into arbitrary routings. The wires, which can be more than 200 nm in length, are soft and bendable, and the DNA strands allow individual polymers to self-assemble into predesigned routings on both two- and three-dimensional DNA origami templates. The polymers are conjugated and potentially conducting, and could therefore be used to create molecular-scale electronic or optical wires in arbitrary geometries.

Time-reversal MUSIC imaging of extended targets.

PubMed

Marengo, Edwin A; Gruber, Fred K; Simonetti, Francesco

2007-08-01

This paper develops, within a general framework that is applicable to rather arbitrary electromagnetic and acoustic remote sensing systems, a theory of time-reversal "MUltiple Signal Classification" (MUSIC)-based imaging of extended (nonpoint-like) scatterers (targets). The general analysis applies to arbitrary remote sensing geometry and sheds light onto how the singular system of the scattering matrix relates to the geometrical and propagation characteristics of the entire transmitter-target-receiver system and how to use this effect for imaging. All the developments are derived within exact scattering theory which includes multiple scattering effects. The derived time-reversal MUSIC methods include both interior sampling, as well as exterior sampling (or enclosure) approaches. For presentation simplicity, particular attention is given to the time-harmonic case where the informational wave modes employed for target interrogation are purely spatial, but the corresponding generalization to broadband fields is also given. This paper includes computer simulations illustrating the derived theory and algorithms.

Induced drag ideal efficiency factor of arbitrary lateral-vertical wing forms

NASA Technical Reports Server (NTRS)

Deyoung, J.

1980-01-01

A relatively simple equation is presented for estimating the induced drag ideal efficiency factor e for arbitrary cross sectional wing forms. This equation is based on eight basic but varied wing configurations which have exact solutions. The e function which relates the basic wings is developed statistically and is a continuous function of configuration geometry. The basic wing configurations include boxwings shaped as a rectangle, ellipse, and diamond; the V-wing; end-plate wing; 90 degree cruciform; circle dumbbell; and biplane. Example applications of the e equations are made to many wing forms such as wings with struts which form partial span rectangle dumbbell wings; bowtie, cruciform, winglet, and fan wings; and multiwings. Derivations are presented in the appendices of exact closed form solutions found of e for the V-wing and 90 degree cruciform wing and for an asymptotic solution for multiwings.

Chrono: A Parallel Physics Library for Rigid-Body, Flexible-Body, and Fluid Dynamics

DTIC Science & Technology

2013-08-01

big data. Chrono::Render is capable of using 320 cores and is built around Pixar’s RenderMan. All these components combine to produce Chrono, a multi...rather small collection of rigid and/or deformable bodies of complex geometry (hourglass wall, wheel, track shoe, excava- tor blade, dipper ), and a...motivated by the scope of arbitrary data sets and the potentially immense scene complexity that results from big data; REYES, the underlying architecture

Tensors and Differential Geometry Applied to Analytic and Numerical Coordinate Generation

DTIC Science & Technology

1981-01-01

or surfaces. Since the writing of the first memoir on the subject of tensor analysis by Ricci and Levi - Civita [11 in 1901 some very significant...available in the standard texts, such as, Levi - Civita [2], Weatherburn [3), McConnell [41, Eisenhart [51, [6], Tolman [7], Graustein [8], Synge and...Equations (216) have been used in Ref. [29] to compute the coordinates for arbitrary shaped two -dimensional bodies . §7. Miscellaneous Derivations. In this

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

DTIC Science & Technology

1992-09-11

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

Non-linear flow law of rockglacier creep determined from geomorphological observations: A case study from the Murtèl rockglacier (Engadin, SE Switzerland)

NASA Astrophysics Data System (ADS)

Frehner, Marcel; Amschwand, Dominik; Gärtner-Roer, Isabelle

2016-04-01

Rockglaciers consist of unconsolidated rock fragments (silt/sand-rock boulders) with interstitial ice; hence their creep behavior (i.e., rheology) may deviate from the simple and well-known flow-laws for pure ice. Here we constrain the non-linear viscous flow law that governs rockglacier creep based on geomorphological observations. We use the Murtèl rockglacier (upper Engadin valley, SE Switzerland) as a case study, for which high-resolution digital elevation models (DEM), time-lapse borehole deformation data, and geophysical soundings exist that reveal the exterior and interior architecture and dynamics of the landform. Rockglaciers often feature a prominent furrow-and-ridge topography. For the Murtèl rockglacier, Frehner et al. (2015) reproduced the wavelength, amplitude, and distribution of the furrow-and-ridge morphology using a linear viscous (Newtonian) flow model. Arenson et al. (2002) presented borehole deformation data, which highlight the basal shear zone at about 30 m depth and a curved deformation profile above the shear zone. Similarly, the furrow-and-ridge morphology also exhibits a curved geometry in map view. Hence, the surface morphology and the borehole deformation data together describe a curved 3D geometry, which is close to, but not quite parabolic. We use a high-resolution DEM to quantify the curved geometry of the Murtèl furrow-and-ridge morphology. We then calculate theoretical 3D flow geometries using different non-linear viscous flow laws. By comparing them to the measured curved 3D geometry (i.e., both surface morphology and borehole deformation data), we can determine the most adequate flow-law that fits the natural data best. Linear viscous models result in perfectly parabolic flow geometries; non-linear creep leads to localized deformation at the sides and bottom of the rockglacier while the deformation in the interior and top are less intense. In other words, non-linear creep results in non-parabolic flow geometries. Both the linear (power-law exponent, n=1) and strongly non-linear models (n=10) do not match the measured data well. However, the moderately non-linear models (n=2-3) match the data quite well indicating that the creep of the Murtèl rockglacier is governed by a moderately non-linear viscous flow law with a power-law exponent close to the one of pure ice. Our results are crucial for improving existing numerical models of rockglacier flow that currently use simplified (i.e., linear viscous) flow-laws. References: Arenson L., Hoelzle M., and Springman S., 2002: Borehole deformation measurements and internal structure of some rock glaciers in Switzerland, Permafrost and Periglacial Processes 13, 117-135. Frehner M., Ling A.H.M., and Gärtner-Roer I., 2015: Furrow-and-ridge morphology on rockglaciers explained by gravity-driven buckle folding: A case study from the Murtèl rockglacier (Switzerland), Permafrost and Periglacial Processes 26, 57-66.

Adaptive acoustic energy delivery to near and far fields using foldable, tessellated star transducers

NASA Astrophysics Data System (ADS)

Zou, Chengzhe; Harne, Ryan L.

2017-05-01

Methods of guiding acoustic energy arbitrarily through space have long relied on digital controls to meet performance needs. Yet, more recent attention to adaptive structures with unique spatial configurations has motivated mechanical signal processing (MSP) concepts that may not be subjected to the same functional and performance limitations as digital acoustic beamforming counterparts. The periodicity of repeatable structural reconfiguration enabled by origami-inspired tessellated architectures turns attention to foldable platforms as frameworks for MSP development. This research harnesses principles of MSP to study a tessellated, star-shaped acoustic transducer constituent that provides on-demand control of acoustic energy guiding via folding-induced shape reconfiguration. An analytical framework is established to probe the roles of mechanical and acoustic geometry on the far field directivity and near field focusing of sound energy. Following validation by experiments and verification by simulations, parametric studies are undertaken to uncover relations between constituent topology and acoustic energy delivery to arbitrary points in the free field. The adaptations enabled by folding of the star-shaped transducer reveal capability for restricting sound energy to angular regions in the far field while also introducing means to modulate sound energy by three orders-of-magnitude to locations near to the transducer surface. In addition, the modeling philosophy devised here provides a valuable approach to solve general sound radiation problems for foldable, tessellated acoustic transducer constituents of arbitrary geometry.

Delamination stresses in semicircular laminated composite bars

NASA Technical Reports Server (NTRS)

Ko, William L.

1988-01-01

Using anisotropic elasticity theory, delamination stresses in a semicircular laminated composite curved bar subjected to end forces and end moments were calculated, and their radial locations determined. A family of design curves was presented, showing variation of the intensity of delamination stresses and their radial locations with different geometry and different degrees of anisotropy of the curved bar. The effect of anisotropy on the location of peak delamination stress was found to be small.

Magnetism in curved geometries

NASA Astrophysics Data System (ADS)

Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys

2016-09-01

Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.

Predicting top-of-atmosphere radiance for arbitrary viewing geometries from the visible to thermal infrared: generalization to arbitrary average scene temperatures

NASA Astrophysics Data System (ADS)

Florio, Christopher J.; Cota, Steve A.; Gaffney, Stephanie K.

2010-08-01

In a companion paper presented at this conference we described how The Aerospace Corporation's Parameterized Image Chain Analysis & Simulation SOftware (PICASSO) may be used in conjunction with a limited number of runs of AFRL's MODTRAN4 radiative transfer code, to quickly predict the top-of-atmosphere (TOA) radiance received in the visible through midwave IR (MWIR) by an earth viewing sensor, for any arbitrary combination of solar and sensor elevation angles. The method is particularly useful for large-scale scene simulations where each pixel could have a unique value of reflectance/emissivity and temperature, making the run-time required for direct prediction via MODTRAN4 prohibitive. In order to be self-consistent, the method described requires an atmospheric model (defined, at a minimum, as a set of vertical temperature, pressure and water vapor profiles) that is consistent with the average scene temperature. MODTRAN4 provides only six model atmospheres, ranging from sub-arctic winter to tropical conditions - too few to cover with sufficient temperature resolution the full range of average scene temperatures that might be of interest. Model atmospheres consistent with intermediate temperature values can be difficult to come by, and in any event, their use would be too cumbersome for use in trade studies involving a large number of average scene temperatures. In this paper we describe and assess a method for predicting TOA radiance for any arbitrary average scene temperature, starting from only a limited number of model atmospheres.

Debonding Stress Concentrations in a Pressurized Lobed Sandwich-Walled Generic Cryogenic Tank

NASA Technical Reports Server (NTRS)

Ko, William L.

2004-01-01

A finite-element stress analysis has been conducted on a lobed composite sandwich tank subjected to internal pressure and cryogenic cooling. The lobed geometry consists of two obtuse circular walls joined together with a common flat wall. Under internal pressure and cryogenic cooling, this type of lobed tank wall will experience open-mode (a process in which the honeycomb is stretched in the depth direction) and shear stress concentrations at the junctures where curved wall changes into flat wall (known as a curve-flat juncture). Open-mode and shear stress concentrations occur in the honeycomb core at the curve-flat junctures and could cause debonding failure. The levels of contributions from internal pressure and temperature loading to the open-mode and shear debonding failure are compared. The lobed fuel tank with honeycomb sandwich walls has been found to be a structurally unsound geometry because of very low debonding failure strengths. The debonding failure problem could be eliminated if the honeycomb core at the curve-flat juncture is replaced with a solid core.

Conjugate heat and mass transfer in the lattice Boltzmann equation method.

PubMed

Li, Like; Chen, Chen; Mei, Renwei; Klausner, James F

2014-04-01

An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer in porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved interfaces, the present treatment yields second-order accurate interior and interfacial temperatures (concentrations) and first-order accurate interfacial heat (mass) flux. An increase of order of convergence by one degree is obtained for each of these three quantities compared with the half-lattice division scheme. The surface-averaged Sherwood numbers computed in test (iv) agree well with published results.

Conjugate heat and mass transfer in the lattice Boltzmann equation method

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

Li, LK; Chen, C; Mei, RW

2014-04-22

An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer inmore » porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved interfaces, the present treatment yields second-order accurate interior and interfacial temperatures (concentrations) and first-order accurate interfacial heat (mass) flux. An increase of order of convergence by one degree is obtained for each of these three quantities compared with the half-lattice division scheme. The surface-averaged Sherwood numbers computed in test (iv) agree well with published results.« less

Pfirsch–Schlüter neoclassical heavy impurity transport in a rotating plasma

DOE PAGES

Belli, Emily A.; Candy, Jefferey M.; Angioni, C.

2014-11-07

In this paper, we extend previous analytic theories for the neoclassical transport of a trace heavy impurity in a rotating plasma in the Pfirsch-Schl¨uter regime. The complete diffusive and convective components of the ambipolar particle flux are derived. The solution is valid for arbitrary impurity charge and impurity Mach number and for general geometry. Inclusion of finite main ion temperature gradient effects is shown in the small ion Mach number limit. A simple interpolation formula is derived for the case of high impurity charge and circular geometry. While an enhancement of the diffusion coefficient is found for order one impuritymore » Mach number, a reduction due to the rotation-driven poloidal asymmetry in the density occurs for very large Mach number.« less

A program to compute three-dimensional subsonic unsteady aerodynamic characteristics using the doublet lattice method, L216 (DUBFLEX). Volume 2: Supplemental system design and maintenance document

NASA Technical Reports Server (NTRS)

Harrison, B. A.; Richard, M.

1979-01-01

The information necessary for execution of the digital computer program L216 on the CDC 6600 is described. L216 characteristics are based on the doublet lattice method. Arbitrary aerodynamic configurations may be represented with combinations of nonplanar lifting surfaces composed of finite constant pressure panel elements, and axially summetric slender bodies composed of constant pressure line elements. Program input consists of configuration geometry, aerodynamic parameters, and modal data; output includes element geometry, pressure difference distributions, integrated aerodynamic coefficients, stability derivatives, generalized aerodynamic forces, and aerodynamic influence coefficient matrices. Optionally, modal data may be input on magnetic field (tape or disk), and certain geometric and aerodynamic output may be saved for subsequent use.

Local surface curvature analysis based on reflection estimation

NASA Astrophysics Data System (ADS)

Lu, Qinglin; Laligant, Olivier; Fauvet, Eric; Zakharova, Anastasia

2015-07-01

In this paper, we propose a novel reflection based method to estimate the local orientation of a specular surface. For a calibrated scene with a fixed light band, the band is reflected by the surface to the image plane of a camera. Then the local geometry between the surface and reflected band is estimated. Firstly, in order to find the relationship relying the object position, the object surface orientation and the band reflection, we study the fundamental theory of the geometry between a specular mirror surface and a band source. Then we extend our approach to the spherical surface with arbitrary curvature. Experiments are conducted with mirror surface and spherical surface. Results show that our method is able to obtain the local surface orientation merely by measuring the displacement and the form of the reflection.

A calculation procedure for viscous flow in turbomachines, volume 2

NASA Technical Reports Server (NTRS)

Khalil, J.; Tabakoff, W.

1980-01-01

Turbulent flow within turbomachines having arbitrary blade geometries is examined. Effects of turbulence are modeled using two equations, one expressing the development of the turbulence kinetic energy and the other its dissipation rate. To account for complicated blade geometries, the flow equations are formulated in terms of a nonorthogonal boundary fitted coordinate system. The analysis is applied to a radial inflow turbine. The solution obtained indicates the severity of the complex interaction mechanism that occurs between the different flow regimes (i.e., boundary layers, recirculating eddies, separation zones, etc.). Comparison with nonviscous flow solutions tend to justify strongly the inadequacy of using the latter with standard boundary layer techniques to obtain viscous flow details within turbomachine rotors. Capabilities and limitations of the present method of analysis are discussed.

Modelling the phase curve and occultation of WASP-43b with SPIDERMAN

NASA Astrophysics Data System (ADS)

Louden, Tom

2017-06-01

Presenting SPIDERMAN, a fast code for calculating exoplanet phase curves and secondary eclipses with arbitrary two dimensional surface brightness distributions. SPIDERMAN uses an exact geometric algorithm to calculate the area of sub-regions of the planet that are occulted by the star, with no loss in numerical precision. The speed of this calculation makes it possible to run MCMCs to marginalise effectively over the underlying parameters controlling the brightness distribution of exoplanets. The code is fully open source and available over Github. We apply the code to the phase curve of WASP-43b using an analytical surface brightness distribution, and find an excellent fit to the data. We are able to place direct constraints on the physics of heat transport in the atmosphere, such as the ratio between advective and radiative timescales at different altitudes.

A general method of aquitard control of flow for arbitrary orientation of wells in Aquitard- Aquifer-Aquitard System (AAA)

NASA Astrophysics Data System (ADS)

Zhan, H.; Sun, D.

2006-12-01

Aquitards are low permeable sedimentary layers that often serve as interfaces through which recharge, contaminants, and nutrients from the vadose zone enter aquifers. Aquitards are capable of storing water, yet lack of ability to transmit water. Hydrologists have recognized the importance of aquitards on subsurface flow and transport for many decades. However, for various reasons, studies of aquitards have received much less attention than that of the aquifers for many years. In this study, we have investigated the effects of aquitard on drawdown caused by arbitrary orientation of well pumping in an aquitard-aquifer-aquitard system. Pumping well could be partial penetrating vertical well, horizontal well or slanted well at arbitrary angles to horizontal plane. We have derived the solutions for six cases with various combinations of water table, aquitard, aquifer, aquitard, and bedrocks. Previous study treated the leakage from aquitard-aquifer mass flux as a volumetric source/sink term in the governing equation of flow in the aquifer. In this study, new semi-analytical solutions are acquired for the aquitard-aquifer-aquitard system via rigorous mass conservation laws. Flows in aquitard and aquifer are treated as separate systems which are linked through the continuity of flux and head at the aquitard-aquifer boundary. This general solution is applicable to both water table aquifer and leaky-confined aquifer. Examples illustrate the effect of aquitard properties at different well configurations. The results will be used to generate type curves for various situations. The results of this paper are useful for parameter identification and water resource management. Keywords: Aquitard-Aquifer-Aquitard; Pumping Well, Slanted Well, Horizontal well, Type curves.

Parametric design and gridding through relational geometry

NASA Technical Reports Server (NTRS)

Letcher, John S., Jr.; Shook, D. Michael

1995-01-01

Relational Geometric Synthesis (RGS) is a new logical framework for building up precise definitions of complex geometric models from points, curves, surfaces and solids. RGS achieves unprecedented design flexibility by supporting a rich variety of useful curve and surface entities. During the design process, many qualitative and quantitative relationships between elementary objects may be captured and retained in a data structure equivalent to a directed graph, such that they can be utilized for automatically updating the complete model geometry following changes in the shape or location of an underlying object. Capture of relationships enables many new possibilities for parametric variations and optimization. Examples are given of panelization applications for submarines, sailing yachts, offshore structures, and propellers.

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. III. Twist Number Method

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

Guo, Y.; Pariat, E.; Moraitis, K.

We study the writhe, twist, and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov–Démoulin equilibrium solution, non-force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger–Prior formula, which is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twistmore » multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.« less

Intelligent Patching of Conceptual Geometry for CFD Analysis

NASA Technical Reports Server (NTRS)

Li, Wu

2010-01-01

The iPatch computer code for intelligently patching surface grids was developed to convert conceptual geometry to computational fluid dynamics (CFD) geometry (see figure). It automatically uses bicubic B-splines to extrapolate (if necessary) each surface in a conceptual geometry so that all the independently defined geometric components (such as wing and fuselage) can be intersected to form a watertight CFD geometry. The software also computes the intersection curves of surface patches at any resolution (up to 10.4 accuracy) specified by the user, and it writes the B-spline surface patches, and the corresponding boundary points, for the watertight CFD geometry in the format that can be directly used by the grid generation tool VGRID. iPatch requires that input geometry be in PLOT3D format where each component surface is defined by a rectangular grid {(x(i,j), y(i,j), z(i,j)):1less than or equal to i less than or equal to m, 1 less than or equal to j less than or equal to n} that represents a smooth B-spline surface. All surfaces in the PLOT3D file conceptually represent a watertight geometry of components of an aircraft on the half-space y greater than or equal to 0. Overlapping surfaces are not allowed, but could be fixed by a utility code "fixp3d". The fixp3d utility code first finds the two grid lines on the two surface grids that are closest to each other in Hausdorff distance (a metric to measure the discrepancies of two sets); then uses one of the grid lines as the transition line, extending grid lines on one grid to the other grid to form a merged grid. Any two connecting surfaces shall have a "visually" common boundary curve, or can be described by an intersection relationship defined in a geometry specification file. The intersection of two surfaces can be at a conceptual level. However, the intersection is directional (along either i or j index direction), and each intersecting grid line (or its spine extrapolation) on the first surface should intersect the second surface. No two intersection relationships will result in a common intersection point of three surfaces. The output files of iPatch are IGES, d3m, and mapbc files that define the CFD geometry in VGRID format. The IGES file gives the NURBS definition of the outer mold line in the geometry. The d3m file defines how the outer mold line is broken into surface patches whose boundary curves are defined by points. The mapbc file specifies what the boundary condition is on each patch and the corresponding NURBS surface definition of each non-planar patch in the IGES file.

A spectral element method with adaptive segmentation for accurately simulating extracellular electrical stimulation of neurons.

PubMed

Eiber, Calvin D; Dokos, Socrates; Lovell, Nigel H; Suaning, Gregg J

2017-05-01

The capacity to quickly and accurately simulate extracellular stimulation of neurons is essential to the design of next-generation neural prostheses. Existing platforms for simulating neurons are largely based on finite-difference techniques; due to the complex geometries involved, the more powerful spectral or differential quadrature techniques cannot be applied directly. This paper presents a mathematical basis for the application of a spectral element method to the problem of simulating the extracellular stimulation of retinal neurons, which is readily extensible to neural fibers of any kind. The activating function formalism is extended to arbitrary neuron geometries, and a segmentation method to guarantee an appropriate choice of collocation points is presented. Differential quadrature may then be applied to efficiently solve the resulting cable equations. The capacity for this model to simulate action potentials propagating through branching structures and to predict minimum extracellular stimulation thresholds for individual neurons is demonstrated. The presented model is validated against published values for extracellular stimulation threshold and conduction velocity for realistic physiological parameter values. This model suggests that convoluted axon geometries are more readily activated by extracellular stimulation than linear axon geometries, which may have ramifications for the design of neural prostheses.

Three-dimensional spatially curved local Bessel beams generated by metasurface

NASA Astrophysics Data System (ADS)

Liu, Dawei; Wu, Jiawen; Cheng, Bo; Li, Hongliang

2018-03-01

We propose a reflective metasurface based on an artificial admittance modulation surface to generate three-dimensional spatially curved beams. The phase acquisition utilized to modulate this sinusoidally varying surface admittance combines the enveloping theory of differential geometry and the method for producing two-dimensional Bessel beams. The metasurface is fabricated, and the comparison between the full-wave simulations and experimental results demonstrates good performance of three-dimensional spatially curved beams generated by the metasurface.

Isentropic fluid dynamics in a curved pipe

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Holden, Helge

2016-10-01

In this paper we study isentropic flow in a curved pipe. We focus on the consequences of the geometry of the pipe on the dynamics of the flow. More precisely, we present the solution of the general Cauchy problem for isentropic fluid flow in an arbitrarily curved, piecewise smooth pipe. We consider initial data in the subsonic regime, with small total variation about a stationary solution. The proof relies on the front-tracking method and is based on [1].

Traction curves for the decohesion of covalent crystals

NASA Astrophysics Data System (ADS)

Enrique, Raúl A.; Van der Ven, Anton

2017-01-01

We study, by first principles, the energy versus separation curves for the cleavage of a family of covalent crystals with the diamond and zincblende structure. We find that there is universality in the curves for different materials which is chemistry independent but specific to the geometry of the particular cleavage plane. Since these curves do not strictly follow the universal binding energy relationship (UBER), we present a derivation of an extension to this relationship that includes non-linear force terms. This extended form of UBER allows for a flexible and practical mathematical description of decohesion curves that can be applied to the quantification of cohesive zone models.

Transformation of localized necking of strain space into stress space for advanced high strength steel sheet

NASA Astrophysics Data System (ADS)

Nakwattanaset, Aeksuwat; Suranuntchai, Surasak

2018-03-01

Normally, Forming Limit Curves (FLCs) can’t explain for shear fracture better than Damage Curve, this article aims to show the experimental of Forming Limit Curve (FLC) for Advanced High Strength Steel (AHSS) sheets grade JAC780Y with the Nakazima forming test and tensile tests of different sample geometries. From these results, the Forming Limit Curve (strain space) was transformed to damage curve (stress space) between plastic strain and stress triaxiality. Therefore, Stress space transformed using by Hill-48 and von-Mises yield function. This article shows that two of these yield criterions can use in the transformation.

Optimal savings and the value of population.

PubMed

Arrow, Kenneth J; Bensoussan, Alain; Feng, Qi; Sethi, Suresh P

2007-11-20

We study a model of economic growth in which an exogenously changing population enters in the objective function under total utilitarianism and into the state dynamics as the labor input to the production function. We consider an arbitrary population growth until it reaches a critical level (resp. saturation level) at which point it starts growing exponentially (resp. it stops growing altogether). This requires population as well as capital as state variables. By letting the population variable serve as the surrogate of time, we are still able to depict the optimal path and its convergence to the long-run equilibrium on a two-dimensional phase diagram. The phase diagram consists of a transient curve that reaches the classical curve associated with a positive exponential growth at the time the population reaches the critical level. In the case of an asymptotic population saturation, we expect the transient curve to approach the equilibrium as the population approaches its saturation level. Finally, we characterize the approaches to the classical curve and to the equilibrium.

Optimal savings and the value of population

PubMed Central

Arrow, Kenneth J.; Bensoussan, Alain; Feng, Qi; Sethi, Suresh P.

2007-01-01

We study a model of economic growth in which an exogenously changing population enters in the objective function under total utilitarianism and into the state dynamics as the labor input to the production function. We consider an arbitrary population growth until it reaches a critical level (resp. saturation level) at which point it starts growing exponentially (resp. it stops growing altogether). This requires population as well as capital as state variables. By letting the population variable serve as the surrogate of time, we are still able to depict the optimal path and its convergence to the long-run equilibrium on a two-dimensional phase diagram. The phase diagram consists of a transient curve that reaches the classical curve associated with a positive exponential growth at the time the population reaches the critical level. In the case of an asymptotic population saturation, we expect the transient curve to approach the equilibrium as the population approaches its saturation level. Finally, we characterize the approaches to the classical curve and to the equilibrium. PMID:17984059

Simplified fatigue life analysis for traction drive contacts

NASA Technical Reports Server (NTRS)

Rohn, D. A.; Loewenthal, S. H.; Coy, J. J.

1980-01-01

A simplified fatigue life analysis for traction drive contacts of arbitrary geometry is presented. The analysis is based on the Lundberg-Palmgren theory used for rolling-element bearings. The effects of torque, element size, speed, contact ellipse ratio, and the influence of traction coefficient are shown. The analysis shows that within the limits of the available traction coefficient, traction contacts exhibit longest life at high speeds. Multiple, load-sharing roller arrangements have an advantageous effect on system life, torque capacity, power-to-weight ratio and size.

Free drainage of aqueous foams: Container shape effects on capillarity and vertical gradients

NASA Astrophysics Data System (ADS)

Saint-Jalmes, A.; Vera, M. U.; Durian, D. J.

2000-06-01

The standard drainage equation applies only to foam columns of constant cross-sectional area. Here, we generalize to include the effects of arbitrary container shape and develop an exact solution for an exponential, "Eiffel Tower", sample. This geometry largely eliminates vertical wetness gradients, and hence capillary effects, and should permit a clean test of dissipation mechanisms. Agreement with experiment is not achieved at late times, however, highlighting the importance of both boundary conditions and coarsening.

A hybrid framework for coupling arbitrary summation-by-parts schemes on general meshes

NASA Astrophysics Data System (ADS)

Lundquist, Tomas; Malan, Arnaud; Nordström, Jan

2018-06-01

We develop a general interface procedure to couple both structured and unstructured parts of a hybrid mesh in a non-collocated, multi-block fashion. The target is to gain optimal computational efficiency in fluid dynamics simulations involving complex geometries. While guaranteeing stability, the proposed procedure is optimized for accuracy and requires minimal algorithmic modifications to already existing schemes. Initial numerical investigations confirm considerable efficiency gains compared to non-hybrid calculations of up to an order of magnitude.

Entropy in Spacetime and Topological Hair

NASA Astrophysics Data System (ADS)

Hyun, Young-Hwan; Kim, Yoonbai

2018-01-01

Global topological soliton of the hedgehog ansatz is added to de Sitter spacetime in arbitrary dimensions larger than three, and then thermodynamic law is checked at the cosmological horizon. All geometric and thermodynamic quantities are varied in the presence of a long-range interacting matter distribution with negative pressure, however the entropy-area relation is satisfied in the exact form. Its geometry involves deficit solid angle but maintains a single horizon which allows unique temperature normalization, different from the case of Schwarzschild-de Sitter spacetime.

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The main goals are the development, validation, and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems. A solution method that combines a finite volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

Condition of Mechanical Equilibrium at the Phase Interface with Arbitrary Geometry

NASA Astrophysics Data System (ADS)

Zubkov, V. V.; Zubkova, A. V.

2017-09-01

The authors produced an expression for the mechanical equilibrium condition at the phase interface within the force definition of surface tension. This equilibrium condition is the most general one from the mathematical standpoint and takes into account the three-dimensional aspect of surface tension. Furthermore, the formula produced allows describing equilibrium on the fractal surface of the interface. The authors used the fractional integral model of fractal distribution and took the fractional order integrals over Euclidean space instead of integrating over the fractal set.

General wave optics propagation scaling law.

PubMed

Shakir, Sami A; Dolash, Thomas M; Spencer, Mark; Berdine, Richard; Cargill, Daniel S; Carreras, Richard

2016-12-01

A general far-field wave propagation scaling law is developed. The formulation is simple but predicts diffraction peak irradiance accurately in the far field, regardless of the near-field beam type or geometry, including laser arrays. We also introduce the concept of the equivalent uniform circular beam that generates a far-field peak irradiance and power-in-the-bucket that are the same as an arbitrary laser source. Applications to clipped Gaussian beams with an obscuration, both as a single beam and as an array of beams, are shown.

Nanomanufacturing of 2D Transition Metal Dichalcogenide Materials Using Self-Assembled DNA Nanotubes.

PubMed

Choi, Jungwook; Chen, Haorong; Li, Feiran; Yang, Lingming; Kim, Steve S; Naik, Rajesh R; Ye, Peide D; Choi, Jong Hyun

2015-11-04

2D transition metal dichalcogenides (TMDCs) are nanomanufactured using a generalized strategy with self-assembled DNA nanotubes. DNA nanotubes of various lengths serve as lithographic etch masks for the dry etching of TMDCs. The nanostructured TMDCs are studied by atomic force microscopy, photoluminescence, and Raman spectroscopy. This parallel approach can be used to manufacture 2D TMDC nanostructures of arbitrary geometries with molecular-scale precision. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Geometry of quantum state manifolds generated by the Lie algebra operators

NASA Astrophysics Data System (ADS)

Kuzmak, A. R.

2018-03-01

The Fubini-Study metric of quantum state manifold generated by the operators which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the manifold generated by the so(3) Lie algebra operators. Using these results, we calculate the Fubini-Study metrics of state manifolds generated by the position and momentum operators. Also the metrics of quantum state manifolds generated by some spin systems are obtained. Finally, we generalize this problem for operators of an arbitrary Lie algebra.

A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Hu, Changqing; Shu, Chi-Wang

1998-01-01

In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

Equiangular Surfaces, Self-Similar Surfaces, and the Geometry of Seashells

ERIC Educational Resources Information Center

Boyadzhiev, Khristo N.

2007-01-01

Logarithmic spirals are among the most fascinating curves in the plane, being the only curves that are equiangular, and the only ones that are self-similar. In this article, we show that in three dimensions, these two properties are independent. Although there are surfaces that have both properties, there are some that are equiangular, but not…

Geometry of Quantum Computation with Qudits

PubMed Central

Luo, Ming-Xing; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-01-01

The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(dn). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound. PMID:24509710

Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow

NASA Astrophysics Data System (ADS)

Bhateja, Ashish; Khakhar, Devang V.

2018-06-01

We consider the rheology of steady two-dimensional granular flows, in different geometries, using discrete element method-based simulations of soft spheres. The flow classification parameter (ψ ), which defines the local flow type (ranging from pure rotation to simple shear to pure extension), varies spatially, to a significant extent, in the flows. We find that the material behaves as a generalized Newtonian fluid. The μ -I scaling proposed by Jop et al. [Nature (London) 441, 727 (2006), 10.1038/nature04801] is found to be valid in both two-dimensional and unidirectional flows, as observed in previous studies; however, the data for each flow geometry fall on a different curve. The results for the two-dimensional silo flow indicate that the viscosity does not depend directly on the flow type parameter, ψ . We find that the scaling based on "granular fluidity" [Zhang and Kamrin, Phys. Rev. Lett. 118, 058001 (2017), 10.1103/PhysRevLett.118.058001] gives good collapse of the data to a single curve for all the geometries. The data for the variation of the solid faction with inertial number show a reasonable collapse for the different geometries.

THE EFFECT OF GRAVITATION ON THE POLARIZATION STATE OF A LIGHT RAY

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

Ghosh, Tanay; Sen, A. K.

In the present work, detailed calculations have been carried out on the rotation of the polarization vector of an electromagnetic wave due to the presence of a gravitational field of a rotating body. This has been done using the general expression of Maxwell’s equation in curved spacetime. Considering the far-field approximation (i.e., the impact parameter is greater than the Schwarzschild radius and rotation parameter), the amount of rotation of the polarization vector as a function of impact parameter has been obtained for a rotating body (considering Kerr geometry). The present work shows that the rotation of the polarization vector cannotmore » be observed in the case of Schwarzschild geometry. This work also calculates the rotational effect when considering prograde and retrograde orbits for the light ray. Although the present work demonstrates the effect of rotation of the polarization vector, it confirms that there would be no net polarization of an electromagnetic wave due to the curved spacetime geometry in a Kerr field.« less

Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Boyd, Joshua; Buick, James M.; Green, Simon

2007-09-01

The lattice Boltzmann method is modified to allow the simulation of non-Newtonian shear-dependent viscosity models. Casson and Carreau-Yasuda non-Newtonian blood viscosity models are implemented and are used to compare two-dimensional Newtonian and non-Newtonian flows in the context of simple steady flow and oscillatory flow in straight and curved pipe geometries. It is found that compared to analogous Newtonian flows, both the Casson and Carreau-Yasuda flows exhibit significant differences in the steady flow situation. In the straight pipe oscillatory flows, both models exhibit differences in velocity and shear, with the largest differences occurring at low Reynolds and Womersley numbers. Larger differences occur for the Casson model. In the curved pipe Carreau-Yasuda model, moderate differences are observed in the velocities in the central regions of the geometries, and the largest shear rate differences are observed near the geometry walls. These differences may be important for the study of atherosclerotic progression.

Nine-degrees-of-freedom flexmap for a cone-beam computed tomography imaging device with independently movable source and detector.

PubMed

Keuschnigg, Peter; Kellner, Daniel; Fritscher, Karl; Zechner, Andrea; Mayer, Ulrich; Huber, Philipp; Sedlmayer, Felix; Deutschmann, Heinz; Steininger, Philipp

2017-01-01

Couch-mounted cone-beam computed tomography (CBCT) imaging devices with independently rotatable x-ray source and flat-panel detector arms for acquisitions of arbitrary regions of interest (ROI) have recently been introduced in image-guided radiotherapy (IGRT). This work analyzes mechanical limitations and gravity-induced effects influencing the geometric accuracy of images acquired with arbitrary angular constellations of source and detector in nonisocentric trajectories, which is considered essential for IGRT. In order to compensate for geometric inaccuracies of this modality, a 9-degrees-of-freedom (9-DOF) flexmap correction approach is presented, focusing especially on the separability of the flexmap parameters of the independently movable components of the device. The 9-DOF comprise a 3D translation of the x-ray source focal spot, a 3D translation of the flat-panel's active area center and three Euler-rotations of the detector's row and column vectors. The flexmap parameters are expressed with respect to the angular position of each of the devices arms. Estimation of the parameters is performed, using a CT-based structure set of a table-mounted, cylindrical ball-bearing phantom. Digitally reconstructed radiograph (DRR) patches are derived from the structure set followed by local 2D in-plane registration and subsequent 3D transform estimation by nonlinear regression with outlier detection. Flexmap parameter evaluations for the factory-calibrated system in clockwise and counter-clockwise rotation direction have shown only minor differences for the overall set of flexmap parameters. High short-term reproducibility of the flexmap parameters has been confirmed by experiments over 10 acquisitions for both directions, resulting in standard deviation values of ≤0.183 mm for translational components and ≤0.0219 deg for rotational components, respectively. A comparison of isocentric and nonisocentric flexmap evaluations showed that the mean differences of the parameter curves reside within their standard deviations, confirming the ability of the proposed calibration method to handle both types of trajectories equally well. Reconstructions of 0.1 mm and 0.25 mm steel wires showed similar results for the isocentric and nonisocentric cases. The full-width at half maximum (FWHM) measure indicates an average improvement of the calibrated reconstruction of 85% over the uncalibrated reconstruction. The contrast of the point spread function (PSF) improved by 310% on average over all experiments. Moreover, a reduced amount of artifacts visible in nonisocentric reconstructions of a head phantom and a line-pair phantom has been achieved by separate application of the 9-DOF flexmap on the geometry described by the independently moving source arm and detector arm. Using a 9-DOF flexmap approach for correcting the geometry of projections acquired with a device capable of independent movements of the source and panel arms has been shown to be essential for IGRT use cases such as CBCT reconstruction and 2D/3D registration tasks. The proposed pipeline is able to create flexmap curves which are easy to interpret, useful for mechanical description of the device and repetitive quality assurance as well as system-level preventive maintenance. Application of the flexmap has shown improvements of image quality for planar imaging and volumetric imaging which is crucial for patient alignment accuracy. © 2016 American Association of Physicists in Medicine.

Function follows form: combining nanoimprint and inkjet printing

NASA Astrophysics Data System (ADS)

Muehlberger, M.; Haslinger, M. J.; Kurzmann, J.; Ikeda, M.; Fuchsbauer, A.; Faury, T.; Koepplmayr, T.; Ausserhuber, H.; Kastner, J.; Woegerer, C.; Fechtig, D.

2017-06-01

We are investigating the possibilities and the technical requirements to do nanopatterning on arbitrary curved surfaces. This is done considering the opportunities and possibilities of additive manufacturing. One of the key elements is the necessity to deposit material in well-defined areas of various complex 3D objects. In order to achieve this we are developing a robot-based inkjet printing. We report on our progress with this respect and also on our efforts to perform nanoimprinting on curved, possibly 3D-printed objects using materials that can be deposited by inkjet printing. In the framework of this article, we provide an overview over our current status, the challenges and an outlook.

The 1-loop effective potential for the Standard Model in curved spacetime

NASA Astrophysics Data System (ADS)

Markkanen, Tommi; Nurmi, Sami; Rajantie, Arttu; Stopyra, Stephen

2018-06-01

The renormalisation group improved Standard Model effective potential in an arbitrary curved spacetime is computed to one loop order in perturbation theory. The loop corrections are computed in the ultraviolet limit, which makes them independent of the choice of the vacuum state and allows the derivation of the complete set of β-functions. The potential depends on the spacetime curvature through the direct non-minimal Higgs-curvature coupling, curvature contributions to the loop diagrams, and through the curvature dependence of the renormalisation scale. Together, these lead to significant curvature dependence, which needs to be taken into account in cosmological applications, which is demonstrated with the example of vacuum stability in de Sitter space.

Wavelet-based fMRI analysis: 3-D denoising, signal separation, and validation metrics

PubMed Central

Khullar, Siddharth; Michael, Andrew; Correa, Nicolle; Adali, Tulay; Baum, Stefi A.; Calhoun, Vince D.

2010-01-01

We present a novel integrated wavelet-domain based framework (w-ICA) for 3-D de-noising functional magnetic resonance imaging (fMRI) data followed by source separation analysis using independent component analysis (ICA) in the wavelet domain. We propose the idea of a 3-D wavelet-based multi-directional de-noising scheme where each volume in a 4-D fMRI data set is sub-sampled using the axial, sagittal and coronal geometries to obtain three different slice-by-slice representations of the same data. The filtered intensity value of an arbitrary voxel is computed as an expected value of the de-noised wavelet coefficients corresponding to the three viewing geometries for each sub-band. This results in a robust set of de-noised wavelet coefficients for each voxel. Given the decorrelated nature of these de-noised wavelet coefficients; it is possible to obtain more accurate source estimates using ICA in the wavelet domain. The contributions of this work can be realized as two modules. First, the analysis module where we combine a new 3-D wavelet denoising approach with better signal separation properties of ICA in the wavelet domain, to yield an activation component that corresponds closely to the true underlying signal and is maximally independent with respect to other components. Second, we propose and describe two novel shape metrics for post-ICA comparisons between activation regions obtained through different frameworks. We verified our method using simulated as well as real fMRI data and compared our results against the conventional scheme (Gaussian smoothing + spatial ICA: s-ICA). The results show significant improvements based on two important features: (1) preservation of shape of the activation region (shape metrics) and (2) receiver operating characteristic (ROC) curves. It was observed that the proposed framework was able to preserve the actual activation shape in a consistent manner even for very high noise levels in addition to significant reduction in false positives voxels. PMID:21034833

Geometric Continuity: A Parametrization Independent Measure of Continuity for Computer Aided Geometric Design

DTIC Science & Technology

1985-08-01

in a. typography system, the surface of a. ship hull, or the skin of a.n airplane. To define objects such as these, higher order curve a.nd surface...rate). Thus, a parametrization contains infor- mation about the geometry (the shape or image of the curve), the orientation, and the rate. Figure 2.3...2.3. Each of the curves above has the same image ; they only differ in orientation and rate. Orientation is indicated by arrowheads and rate is

Development of optically pumped DBR-free semiconductor disk lasers (Conference Presentation)

NASA Astrophysics Data System (ADS)

Yang, Zhou; Albrecht, Alexander R.; Cederberg, Jeffrey G.; Sheik-Bahae, Mansoor

2017-03-01

Semiconductor disk lasers (SDLs) are attractive for applications requiring good beam quality, wavelength versatility, and high output powers. Typical SDLs utilize the active mirror geometry, where a semiconductor DBR is integrated with the active region by growth or post-growth bonding. This imposes restrictions for the SDL design, like material system choice, thermal management, and effective gain bandwidth. In DBR-free geometry, these restrictions can be alleviated. An integrated gain model predicts DBR-free geometry with twice the gain bandwidth of typical SDLs, which has been experimentally verified with active regions near 1 μm and 1.15 μm. The lift-off and bonding technique enables the integration of semiconductor active regions with arbitrary high quality substrates, allowing novel monolithic geometries. Bonding an active region onto a straight side of a commercial fused silica right angle prism, and attaching a high reflectivity mirror onto the hypotenuse side, with quasi CW pumping at 780 nm, lasing operation was achieved at 1037 nm with 0.2 mW average power at 1.6 mW average pump power. Laser dynamics show that thermal lens generation in the active region bottlenecks the laser efficiency. Investigations on total internal reflection based monolithic ring cavities are ongoing. These geometries would allow the intracavity integration of 2D materials or other passive absorbers, which could be relevant for stable mode locking. Unlike typical monolithic microchip SDLs, with the evanescent wave coupling technique, these monolithic geometries allow variable coupling efficiency.

Efficient geometry optimization by Hellmann-Feynman forces with the anti-Hermitian contracted Schrödinger equation

NASA Astrophysics Data System (ADS)

Foley, Jonathan J.; Mazziotti, David A.

2010-10-01

An efficient method for geometry optimization based on solving the anti-Hermitian contracted Schrödinger equation (ACSE) is presented. We formulate a reduced version of the Hellmann-Feynman theorem (HFT) in terms of the two-electron reduced Hamiltonian operator and the two-electron reduced density matrix (2-RDM). The HFT offers a considerable reduction in computational cost over methods which rely on numerical derivatives. While previous geometry optimizations with numerical gradients required 2M evaluations of the ACSE where M is the number of nuclear degrees of freedom, the HFT requires only a single ACSE calculation of the 2-RDM per gradient. Synthesizing geometry optimization techniques with recent extensions of the ACSE theory to arbitrary electronic and spin states provides an important suite of tools for accurately determining equilibrium and transition-state structures of ground- and excited-state molecules in closed- and open-shell configurations. The ability of the ACSE to balance single- and multi-reference correlation is particularly advantageous in the determination of excited-state geometries where the electronic configurations differ greatly from the ground-state reference. Applications are made to closed-shell molecules N2, CO, H2O, the open-shell molecules B2 and CH, and the excited state molecules N2, B2, and BH. We also study the HCN ↔ HNC isomerization and the geometry optimization of hydroxyurea, a molecule which has a significant role in the treatment of sickle-cell anaemia.

Movement Timing and Invariance Arise from Several Geometries

PubMed Central

Bennequin, Daniel; Fuchs, Ronit; Berthoz, Alain; Flash, Tamar

2009-01-01

Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations. PMID:19593380

Magnetism in curved geometries

DOE PAGES

Streubel, Robert; Fischer, Peter; Kronast, Florian; ...

2016-08-17

Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. Asmore » a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. Finally, these recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.« less

Magnetism in curved geometries

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

Streubel, Robert; Fischer, Peter; Kronast, Florian

Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. Asmore » a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. Finally, these recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.« less

Self-consistent field theory simulations of polymers on arbitrary domains

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

Ouaknin, Gaddiel, E-mail: gaddielouaknin@umail.ucsb.edu; Laachi, Nabil; Delaney, Kris

2016-12-15

We introduce a framework for simulating the mesoscale self-assembly of block copolymers in arbitrary confined geometries subject to Neumann boundary conditions. We employ a hybrid finite difference/volume approach to discretize the mean-field equations on an irregular domain represented implicitly by a level-set function. The numerical treatment of the Neumann boundary conditions is sharp, i.e. it avoids an artificial smearing in the irregular domain boundary. This strategy enables the study of self-assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface. In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refinemore » the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain. This approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement. Finally, in the case of regular periodic domains, where pseudo-spectral approaches are superior to finite differences in terms of CPU time and accuracy, we use the adaptive strategy to store chain propagators, reducing the memory footprint without loss of accuracy in computed physical observables.« less

Replicating the benefits of Deutschian closed timelike curves without breaking causality

NASA Astrophysics Data System (ADS)

Yuan, Xiao; Assad, Syed M.; Thompson, Jayne; Haw, Jing Yan; Vedral, Vlatko; Ralph, Timothy C.; Lam, Ping Koy; Weedbrook, Christian; Gu, Mile

2015-11-01

In general relativity, closed timelike curves can break causality with remarkable and unsettling consequences. At the classical level, they induce causal paradoxes disturbing enough to motivate conjectures that explicitly prevent their existence. At the quantum level such problems can be resolved through the Deutschian formalism, however this induces radical benefits—from cloning unknown quantum states to solving problems intractable to quantum computers. Instinctively, one expects these benefits to vanish if causality is respected. Here we show that in harnessing entanglement, we can efficiently solve NP-complete problems and clone arbitrary quantum states—even when all time-travelling systems are completely isolated from the past. Thus, the many defining benefits of Deutschian closed timelike curves can still be harnessed, even when causality is preserved. Our results unveil a subtle interplay between entanglement and general relativity, and significantly improve the potential of probing the radical effects that may exist at the interface between relativity and quantum theory.

Retrieving spin textures on curved magnetic thin films with full-field soft X-ray microscopies

DOE PAGES

Streubel, Robert; Kronast, Florian; Fischer, Peter; ...

2015-07-03

X-ray tomography is a well-established technique to characterize 3D structures in material sciences and biology; its magnetic analogue—magnetic X-ray tomography—is yet to be developed. We demonstrate the visualization and reconstruction of magnetic domain structures in a 3D curved magnetic thin films with tubular shape by means of full-field soft X-ray microscopies. In the 3D arrangement of the magnetization is retrieved from a set of 2D projections by analysing the evolution of the magnetic contrast with varying projection angle. By using reconstruction algorithms to analyse the angular evolution of 2D projections provides quantitative information about domain patterns and magnetic coupling phenomenamore » between windings of azimuthally and radially magnetized tubular objects. In conclusion, the present approach represents a first milestone towards visualizing magnetization textures of 3D curved thin films with virtually arbitrary shape.« less

Retrieving spin textures on curved magnetic thin films with full-field soft X-ray microscopies

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

Streubel, Robert; Kronast, Florian; Fischer, Peter

X-ray tomography is a well-established technique to characterize 3D structures in material sciences and biology; its magnetic analogue—magnetic X-ray tomography—is yet to be developed. We demonstrate the visualization and reconstruction of magnetic domain structures in a 3D curved magnetic thin films with tubular shape by means of full-field soft X-ray microscopies. In the 3D arrangement of the magnetization is retrieved from a set of 2D projections by analysing the evolution of the magnetic contrast with varying projection angle. By using reconstruction algorithms to analyse the angular evolution of 2D projections provides quantitative information about domain patterns and magnetic coupling phenomenamore » between windings of azimuthally and radially magnetized tubular objects. In conclusion, the present approach represents a first milestone towards visualizing magnetization textures of 3D curved thin films with virtually arbitrary shape.« less

HD 47755, a new eclipsing binary

NASA Technical Reports Server (NTRS)

Koch, R. H.; Bradstreet, D. H.; Hrivnak, B. J.; Pfeiffer, R. J.; Perry, P. M.

1986-01-01

The IUE spectra of the close binary star HD 47755 have been examined in order to determine its geometry, chemical composition, and light curve. UBV fluxes in the spectra, when dereddened for E(B-V) = 0.09 yield an effective temperature of 16,500 K. The ratio of the mean radii of the stars is found to agree well with an old blueband spectrophotometric value. Eclipses in the binary have been observed and a complex green light curve is derived. It is suggested that the wind from at least one of the components of HD 47755 is the source of the complexity in the light curve. The geometry of the HD 47755 is compared to that of V 641 Mon, A definite cluster member of NGC 2264. The interstellar line spectrum is found to be similar to that of V 641 Mon and the column densities for a few interstellar ions are given in a table. Evaluation of the nonastrometric evidence indicates that HD 47755 is also a member of NGC 2264.

An Interlaminar Tensile Strength Specimen

NASA Technical Reports Server (NTRS)

Martin, Roderick H.; Jackson, Wade C.

1993-01-01

This paper describes a technique to determine interlaminar tensile strength, sigma(sub 3c), of a fiber reinforced composite material using a curved beam. The specimen was a unidirectional curved beam, bent 90 deg, with straight arms. Attached to each arm was a hinged loading mechanism that was held by the grips of a tension testing machine. Geometry effects of the specimen, including the effects of loading arm length, inner radius, thickness, and width, were studied. The data sets fell into two categories: low strength corresponding to a macroscopic flaw related failure and high strength corresponding to a microscopic flaw related failure. From the data available, the specimen width and loading arm length had little effect on sigma(sub 3c). The inner radius was not expected to have a significant effect on sigma(sub 3c), but this conclusion could not be confirmed because of differences in laminate quality for each curve geometry. The thicker specimens had the lowest value of sigma(sub 3c) because of poor laminate quality.

Spin-curvature interaction from curved Dirac equation: Application to single-wall carbon nanotubes

NASA Astrophysics Data System (ADS)

Zhang, Kai; Zhang, Erhu; Chen, Huawei; Zhang, Shengli

2017-06-01

The spin-curvature interaction (SCI) and its effects are investigated based on curved Dirac equation. Through the low-energy approximation of curved Dirac equation, the Hamiltonian of SCI is obtained and depends on the geometry and spinor structure of manifold. We find that the curvature can be considered as field strength and couples with spin through Zeeman-like term. Then, we use dimension reduction to derive the local Hamiltonian of SCI for cylinder surface, which implies that the effective Hamiltonian of single-wall carbon nanotubes results from the geometry and spinor structure of lattice and includes two types of interactions: one does not break any symmetries of the lattice and only shifts the Dirac points for all nanotubes, while the other one does and opens the gaps except for armchair nanotubes. At last, analytical expressions of the band gaps and the shifts of their positions induced by curvature are given for metallic nanotubes. These results agree well with experiments and can be verified experimentally.

Dynamics and density distribution of strongly confined noninteracting nonaligning self-propelled particles in a nonconvex boundary

NASA Astrophysics Data System (ADS)

Fily, Yaouen; Baskaran, Aparna; Hagan, Michael F.

2015-01-01

We study the dynamics of nonaligning, noninteracting self-propelled particles confined to a box in two dimensions. In the strong confinement limit, when the persistence length of the active particles is much larger than the size of the box, particles stay on the boundary and align with the local boundary normal. It is then possible to derive the steady-state density on the boundary for arbitrary box shapes. In nonconvex boxes, the nonuniqueness of the boundary normal results in hysteretic dynamics and the density is nonlocal, i.e., it depends on the global geometry of the box. These findings establish a general connection between the geometry of a confining box and the behavior of an ideal active gas it confines, thus providing a powerful tool to understand and design such confinements.

Multimode Acoustic Research

NASA Technical Reports Server (NTRS)

Barmatz, M.

1985-01-01

There is a need for high temperature containerless processing facilities that can efficiently position and manipulate molten samples in the reduced gravity environment of space. The goal of the research is to develop sophisticated high temperature manipulation capabilities such as selection of arbitrary axes rotation and rapid sample cooling. This program will investigate new classes of acoustic levitation in rectangular, cylindrical and spherical geometries. The program tasks include calculating theoretical expressions of the acoustic forces in these geometries for the excitation of up to three acoustic modes (multimodes). These calculations are used to: (1) determine those acoustic modes that produce stable levitation, (2) isolate the levitation and rotation capabilities to produce more than one axis of rotation, and (3) develop methods to translate samples down long tube cylindrical chambers. Experimental levitators will then be constructed to verify the stable levitation and rotation predictions of the models.

On genera of curves from high-loop generalized unitarity cuts

NASA Astrophysics Data System (ADS)

Huang, Rijun; Zhang, Yang

2013-04-01

Generalized unitarity cut of a Feynman diagram generates an algebraic system of polynomial equations. At high-loop levels, these equations may define a complex curve or a (hyper-)surface with complicated topology. We study the curve cases, i.e., a 4-dimensional L-loop diagram with (4 L-1) cuts. The topology of a complex curve is classified by its genus. Hence in this paper, we use computational algebraic geometry to calculate the genera of curves from two and three-loop unitarity cuts. The global structure of degenerate on-shell equations under some specific kinematic configurations is also sketched. The genus information can also be used to judge if a unitary cut solution could be rationally parameterized.

A high-order multi-zone cut-stencil method for numerical simulations of high-speed flows over complex geometries

NASA Astrophysics Data System (ADS)

Greene, Patrick T.; Eldredge, Jeff D.; Zhong, Xiaolin; Kim, John

2016-07-01

In this paper, we present a method for performing uniformly high-order direct numerical simulations of high-speed flows over arbitrary geometries. The method was developed with the goal of simulating and studying the effects of complex isolated roughness elements on the stability of hypersonic boundary layers. The simulations are carried out on Cartesian grids with the geometries imposed by a third-order cut-stencil method. A fifth-order hybrid weighted essentially non-oscillatory scheme was implemented to capture any steep gradients in the flow created by the geometries and a third-order Runge-Kutta method is used for time advancement. A multi-zone refinement method was also utilized to provide extra resolution at locations with expected complex physics. The combination results in a globally fourth-order scheme in space and third order in time. Results confirming the method's high order of convergence are shown. Two-dimensional and three-dimensional test cases are presented and show good agreement with previous results. A simulation of Mach 3 flow over the logo of the Ubuntu Linux distribution is shown to demonstrate the method's capabilities for handling complex geometries. Results for Mach 6 wall-bounded flow over a three-dimensional cylindrical roughness element are also presented. The results demonstrate that the method is a promising tool for the study of hypersonic roughness-induced transition.

A multiprojection noncontact fluorescence tomography setup for imaging arbitrary geometries

NASA Astrophysics Data System (ADS)

Meyer, H.; Garofalakis, A.; Zacharakis, G.; Economou, E. N.; Mamalaki, C.; Kioussis, D.; Ntziachristos, V.; Ripoll, J.

2005-04-01

Optical imaging and tomography in tissues can facilitate the quantitative study of several important chromophores and fluorophores in-vivo. Due to this fact, there has been great interest in developing imaging systems offering quantitative information on the location and concentration of chromophores and fluorescent probes. However, most imaging systems currently used in research make use of fiber technology for delivery and detection, which restricts the size of the photon collecting arrays leading to insufficient spatial sampling and field of view. To enable large data sets and full 360o angular measurements, we developed a novel imaging system that enables 3D imaging of fluorescent signals in bodies of arbitrary shapes in a non-contact geometry in combination with a 3D surface reconstruction algorithm. The system consists of a rotating subject holder and a lens coupled Charge Coupled Device (CCD) camera in combination with a fiber coupled laser scanning device. An Argon ion laser is used as the source and different filters are used for the detection of various fluorophores or fluorescing proteins. With this new setup a large measurements dataset can be achieved while the use of inversion models give a high capacity for quantitative 3D reconstruction of fluorochrome distributions as well as high spatial resolution. The system is currently being tested in the observation of the distribution of Green Fluorescent Protein (GFP) expressing T-lymphocytes in order to study the function of the immune system in a murine model.

Noncommutative Geometry of the Moyal Plane: Translation Isometries, Connes' Distance on Coherent States, Pythagoras Equality

NASA Astrophysics Data System (ADS)

Martinetti, Pierre; Tomassini, Luca

2013-10-01

We study the metric aspect of the Moyal plane from Connes' noncommutative geometry point of view. First, we compute Connes' spectral distance associated with the natural isometric action of on the algebra of the Moyal plane . We show that the distance between any state of and any of its translated states is precisely the amplitude of the translation. As a consequence, we obtain the spectral distance between coherent states of the quantum harmonic oscillator as the Euclidean distance on the plane. We investigate the classical limit, showing that the set of coherent states equipped with Connes' spectral distance tends towards the Euclidean plane as the parameter of deformation goes to zero. The extension of these results to the action of the symplectic group is also discussed, with particular emphasis on the orbits of coherent states under rotations. Second, we compute the spectral distance in the double Moyal plane, intended as the product of (the minimal unitization of) by . We show that on the set of states obtained by translation of an arbitrary state of , this distance is given by the Pythagoras theorem. On the way, we prove some Pythagoras inequalities for the product of arbitrary unital and non-degenerate spectral triples. Applied to the Doplicher- Fredenhagen-Roberts model of quantum spacetime [DFR], these two theorems show that Connes' spectral distance and the DFR quantum length coincide on the set of states of optimal localization.

Glucose and insulin do not decrease in a dose-dependent manner after increasing doses of mixed fibers that are consumed in muffins for breakfast.

PubMed

Willis, Holly J; Thomas, William; Eldridge, Alison L; Harkness, Laura; Green, Hilary; Slavin, Joanne L

2011-01-01

Conventional wisdom suggests that fiber consumption leads to lower postprandial glucose and insulin response. We hypothesized that increasing doses of mixed, viscous fiber would lower glucose and insulin levels in a dose-dependent manner. Healthy men (n = 10) and women (n = 10) with a body mass index of 24 ± 2 (mean ± SEM) participated in this double-blind, crossover study. On 4 separate visits, fasting subjects consumed an approximately 2093 kJ (500 calorie) muffin with 0, 4, 8, or 12 g of mixed fibers. Blood was drawn to measure glucose and insulin at regular intervals throughout a 3-hour test period. Area under the curve (AUC) glucose was significantly lower after 0 g of fiber than after 4, 8, or 12 g of fiber (arbitrary AUC units ± SEM: 25.3 ± 5.2 vs 44.6 ± 7.7, 49.7 ± 7.9, 51.5 ± 6.6, respectively; P < .006). Area under the curve glucose increased with increasing fiber doses (P for trend = .0003). Area under the curve insulin was higher after the 4-g dose than after the 0-, 8-, and 12-g doses (arbitrary AUC units ± SEM: 84.4 ± 8.0 vs 60.1 ± 6.5, 69.4 ± 8.7, 69.7 ± 8.5, respectively; P < .05); it did not change in a dose-dependent manner. Area under the curve glucose and AUC insulin did not correlate with each other. Glucose and insulin did not decrease in a dose-dependent manner after 0, 4, 8, and 12 g of mixed fibers were consumed in muffins for breakfast. The lack of differences was largely based on the individual variation in glucose response. Caution should be used when making general claims about the expected impact of fiber on glucose and insulin levels. Copyright © 2011 Elsevier Inc. All rights reserved.

Nanoscale Strontium Titanate Sheets and Crystals

NASA Astrophysics Data System (ADS)

Tilka, Jack Andrew

The physical properties of materials are dominated by their structure and composition. Insight into the structure of complex oxide materials has the potential to improve our understanding and eventually control of their physical properties. This PhD thesis reports the development of characterization and fabrication techniques relevant to improving the scientific understanding of complex oxide materials. The work presented here has two components. I report a way to use ideas that were originally developed in semiconductor processing to control the elastic strain state and crystallization process of the model complex oxide SrTiO3. An additional component is an important series of advances in the analysis of diffraction patterns acquired with focused x-ray nanobeams. The fabrication and characterization of nanoscale SrTiO3 has been experimentally shown to allow the introduction of elastic strain into SrTiO3. The creation of thin SrTiO3 crystals from (001)-oriented SrTiO3 bulk single crystals using focused ion beam milling techniques yields sheets with submicron thickness and arbitrary orientation within the (001) plane. Synchrotron x-ray nanodiffraction experiments show that the SrTiO 3 sheets have rocking curves with angular widths less than 0.02°. These widths are less than a factor of two larger than bulk SrTiO3, which shows that the sheets are suitable substrates for epitaxial thin film growth. A precisely selected elastic strain can be introduced into the SrTiO 3 sheets using a silicon nitride stressor layer. Synchrotron x-ray nanodiffraction studies show that the strain introduced in the SrTiO3 sheets is on the order of 10-4, matching the predictions of an elastic model. This approach to elastic strain sharing in complex oxides allows the strain to be selected within a wide and continuous range of values, an effect not achievable in heteroepitaxy on rigid substrates. An additional fabrication technique is also evaluated here based on the crystallization of SrTiO3 from initially amorphous thin films. This process is known as solid-phase epitaxy in two-dimensional samples but is just beginning to be explored in more complex geometries. I report experiments in both homoepitaxy and heteroepitaxy including measurements of crystal growth rates and the crystallographic orientations of crystals formed in this way. The lateral growth rates are consistent with previously measured vertical growth. This result indicated that previous work on vertical solid-phase epitaxy could be extended into lateral solid-phase epitaxy, which has the power to be applied to complicated non-planar geometries. The highly coherent and tightly focused x-ray beams produced by hard x-ray light sources enable the nanoscale structural characterization of materials but are accompanied by significant challenges in the interpretation of diffraction and scattering patterns. I report here a series of methods that expand the range of physical problems that can be accurately captured by coherent x-ray optical simulations. My approach has been to expand simulations methods to include arbitrary x-ray incident angles and arbitrary epitaxial heterostructures. I first applied these methods to extract the misorientation of lattice planes and the strain of individual layers of Si/SiGe heterostructures relevant to applications in quantum electronics. Further applications reported in this thesis are in probing defects created in the processing of SrTiO3 and in measuring the change in lattice parameter introduced into strained SrTiO3 sheets. The systematic interpretation of nanobeam diffraction patterns aids in the fabrication of SrTiO3 nanostructures.

Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling

NASA Astrophysics Data System (ADS)

Gao, Hongwei; Zhang, Jianfeng

2008-09-01

The perfectly matched layer (PML) absorbing boundary condition is incorporated into an irregular-grid elastic-wave modelling scheme, thus resulting in an irregular-grid PML method. We develop the irregular-grid PML method using the local coordinate system based PML splitting equations and integral formulation of the PML equations. The irregular-grid PML method is implemented under a discretization of triangular grid cells, which has the ability to absorb incident waves in arbitrary directions. This allows the PML absorbing layer to be imposed along arbitrary geometrical boundaries. As a result, the computational domain can be constructed with smaller nodes, for instance, to represent the 2-D half-space by a semi-circle rather than a rectangle. By using a smooth artificial boundary, the irregular-grid PML method can also avoid the special treatments to the corners, which lead to complex computer implementations in the conventional PML method. We implement the irregular-grid PML method in both 2-D elastic isotropic and anisotropic media. The numerical simulations of a VTI lamb's problem, wave propagation in an isotropic elastic medium with curved surface and in a TTI medium demonstrate the good behaviour of the irregular-grid PML method.

Novel Perceptually Uniform Chromatic Space.

PubMed

da Fonseca, María; Samengo, Inés

2018-06-01

Chromatically perceptive observers are endowed with a sense of similarity between colors. For example, two shades of green that are only slightly discriminable are perceived as similar, whereas other pairs of colors, for example, blue and yellow, typically elicit markedly different sensations. The notion of similarity need not be shared by different observers. Dichromat and trichromat subjects perceive colors differently, and two dichromats (or two trichromats, for that matter) may judge chromatic differences inconsistently. Moreover, there is ample evidence that different animal species sense colors diversely. To capture the subjective metric of color perception, here we construct a notion of distance in color space based on the physiology of the retina, and is thereby individually tailored for different observers. By applying the Fisher metric to an analytical model of color representation, we construct a notion of distance that reproduces behavioral experiments of classical discrimination tasks. We then derive a coordinate transformation that defines a new chromatic space in which the Euclidean distance between any two colors is equal to the perceptual distance, as seen by one individual subject, endowed with an arbitrary number of color-sensitive photoreceptors, each with arbitrary absorption probability curves and appearing in arbitrary proportions.

General relativity exactly described in terms of Newton's laws within curved geometries

NASA Astrophysics Data System (ADS)

Savickas, D.

2014-07-01

Many years ago Milne and McCrea showed in their well-known paper that the Hubble expansion occurring in general relativity could be exactly described by the use of Newtonian mechanics. It will be shown that a similar method can be extended to, and used within, curved geometries when Newton's second law is expressed within a four-dimensional curved spacetime. The second law will be shown to yield an equation that is exactly identical to the geodesic equation of motion of general relativity. This in itself yields no new information concerning relativity since the equation is mathematically identical to the relativistic equation. However, when the time in the second law is defined to have a constant direction as effectively occurs in Newtonian mechanics, and no longer acts as a fourth dimension as exists in relativity theory, it separates into a vector equation in a curved three-dimensional space and an additional second scalar equation that describes conservation of energy. It is shown that the curved Newtonian equations of motion define the metric coefficients which occur in the Schwarzschild solution and that they also define its equations of motion. Also, because the curved Newtonian equations developed here use masses as gravitational sources, as occurs in Newtonian mechanics, they make it possible to derive the solution for other kinds of mass distributions and are used here to find the metric equation for a thin mass-rod and the equation of motion for a mass particle orbiting it in its relativistic gravitational field.

Constraining physical parameters of ultra-fast outflows in PDS 456 with Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Hagino, K.; Odaka, H.; Done, C.; Gandhi, P.; Takahashi, T.

2014-07-01

Deep absorption lines with extremely high velocity of ˜0.3c observed in PDS 456 spectra strongly indicate the existence of ultra-fast outflows (UFOs). However, the launching and acceleration mechanisms of UFOs are still uncertain. One possible way to solve this is to constrain physical parameters as a function of distance from the source. In order to study the spatial dependence of parameters, it is essential to adopt 3-dimensional Monte Carlo simulations that treat radiation transfer in arbitrary geometry. We have developed a new simulation code of X-ray radiation reprocessed in AGN outflow. Our code implements radiative transfer in 3-dimensional biconical disk wind geometry, based on Monte Carlo simulation framework called MONACO (Watanabe et al. 2006, Odaka et al. 2011). Our simulations reproduce FeXXV and FeXXVI absorption features seen in the spectra. Also, broad Fe emission lines, which reflects the geometry and viewing angle, is successfully reproduced. By comparing the simulated spectra with Suzaku data, we obtained constraints on physical parameters. We discuss launching and acceleration mechanisms of UFOs in PDS 456 based on our analysis.

Progress report on PIXIE3D, a fully implicit 3D extended MHD solver

NASA Astrophysics Data System (ADS)

Chacon, Luis

2008-11-01

Recently, invited talk at DPP07 an optimal, massively parallel implicit algorithm for 3D resistive magnetohydrodynamics (PIXIE3D) was demonstrated. Excellent algorithmic and parallel results were obtained with up to 4096 processors and 138 million unknowns. While this is a remarkable result, further developments are still needed for PIXIE3D to become a 3D extended MHD production code in general geometries. In this poster, we present an update on the status of PIXIE3D on several fronts. On the physics side, we will describe our progress towards the full Braginskii model, including: electron Hall terms, anisotropic heat conduction, and gyroviscous corrections. Algorithmically, we will discuss progress towards a robust, optimal, nonlinear solver for arbitrary geometries, including preconditioning for the new physical effects described, the implementation of a coarse processor-grid solver (to maintain optimal algorithmic performance for an arbitrarily large number of processors in massively parallel computations), and of a multiblock capability to deal with complicated geometries. L. Chac'on, Phys. Plasmas 15, 056103 (2008);

Thermal homogeneity of plastication processes in single-screw extruders

NASA Astrophysics Data System (ADS)

Bu, L. X.; Agbessi, Y.; Béreaux, Y.; Charmeau, J.-Y.

2018-05-01

Single-screw plastication, used in extrusion and in injection moulding, is a major way of processing commodity thermoplastics. During the plastication phase, the polymeric material is melted by the combined effects of shear-induced self-heating (viscous dissipation) and heat conduction coming from the barrel. In injection moulding, a high level of reliability is usually achieved that makes this process ideally suited to mass market production. Nonetheless, process fluctuations still appear that make moulded part quality control an everyday issue. In this work, we used a combined modelling of plastication, throughput calculation and laminar dispersion, to investigate if, and how, thermal fluctuations could propagate along the screw length and affect the melt homogeneity at the end of the metering section. To do this, we used plastication models to relate changes in processing parameters to changes in the plastication length. Moreover, a simple model of throughput calculation is used to relate the screw geometry, the polymer rheology and the processing parameters to get a good estimate of the mass flow rate. Hence, we found that the typical residence time in a single screw is around one tenth of the thermal diffusion time scale. This residence time is too short for the dispersion coefficient to reach a steady state, but too long to be able to neglect radial thermal diffusion and resort to a purely convective solution. Therefore, a full diffusion/convection problem has to be solved with a base flow described by the classic pressure and drag velocity field. Preliminary results already show the major importance of the processing parameters in the breakthrough curve of an arbitrary temperature fluctuation at the end of the metering section of injection moulding screw. When the flow back-pressure is high, the temperature fluctuation is spread more evenly with time, whereas a pressure drop in the flow will results in a breakthrough curve which presents a larger peak of fluctuation.

A Modal Approach to Compact MIMO Antenna Design

NASA Astrophysics Data System (ADS)

Yang, Binbin

MIMO (Multiple-Input Multiple-Output) technology offers new possibilities for wireless communication through transmission over multiple spatial channels, and enables linear increases in spectral efficiency as the number of the transmitting and receiving antennas increases. However, the physical implementation of such systems in compact devices encounters many physical constraints mainly from the design of multi-antennas. First, an antenna's bandwidth decreases dramatically as its electrical size reduces, a fact known as antenna Q limit; secondly, multiple antennas closely spaced tend to couple with each other, undermining MIMO performance. Though different MIMO antenna designs have been proposed in the literature, there is still a lack of a systematic design methodology and knowledge of performance limits. In this dissertation, we employ characteristic mode theory (CMT) as a powerful tool for MIMO antenna analysis and design. CMT allows us to examine each physical mode of the antenna aperture, and to access its many physical parameters without even exciting the antenna. For the first time, we propose efficient circuit models for MIMO antennas of arbitrary geometry using this modal decomposition technique. Those circuit models demonstrate the powerful physical insight of CMT for MIMO antenna modeling, and simplify MIMO antenna design problem to just the design of specific antenna structural modes and a modal feed network, making possible the separate design of antenna aperture and feeds. We therefore develop a feed-independent shape synthesis technique for optimization of broadband multi-mode apertures. Combining the shape synthesis and circuit modeling techniques for MIMO antennas, we propose a shape-first feed-next design methodology for MIMO antennas, and designed and fabricated two planar MIMO antennas, each occupying an aperture much smaller than the regular size of lambda/2 x lambda/2. Facilitated by the newly developed source formulation for antenna stored energy and recently reported work on antenna Q factor minimization, we extend the minimum Q limit to antennas of arbitrary geometry, and show that given an antenna aperture, any antenna design based on its substructure will result into minimum Q factors larger than or equal to that of the complete structure. This limit is much tighter than Chu's limit based on spherical modes, and applies to antennas of arbitrary geometry. Finally, considering the almost inevitable presence of mutual coupling effects within compact multiport antennas, we develop new decoupling networks (DN) and decoupling network synthesis techniques. An information-theoretic metric, information mismatch loss (Gammainfo), is defined for DN characterization. Based on this metric, the optimization of decoupling networks for broadband system performance is conducted, which demonstrates the limitation of the single-frequency decoupling techniques and room for improvement.

A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2014-10-01

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with stiff relaxation source terms.

Ringin' the water bell: dynamic modes of curved fluid sheets

NASA Astrophysics Data System (ADS)

Kolinski, John; Aharoni, Hillel; Fineberg, Jay; Sharon, Eran

2015-11-01

A water bell is formed by fluid flowing in a thin, coherent sheet in the shape of a bell. Experimentally, a water bell is created via the impact of a cylindrical jet on a flat surface. Its shape is set by the splash angle (the separation angle) of the resulting cylindrically symmetric water sheet. The separation angle is altered by adjusting the height of a lip surrounding the impact point, as in a water sprinkler. We drive the lip's height sinusoidally, altering the separation angle, and ringin' the water bell. This forcing generates disturbances on the steady-state water bell that propagate forward and backward in the fluid's reference frame at well-defined velocities, and interact, resulting in the emergence of an interference pattern unique to each steady-state geometry. We analytically model these dynamics by linearizing the amplitude of the bell's response about the underlying curved geometry. This simple model predicts the nodal structure over a wide range of steady-state water bell configurations and driving frequencies. Due to the curved water bell geometry, the nodal structure is quite complex; nevertheless, the predicted nodal structure agrees extremely well with the experimental data. When we drive the bell beyond perturbative separation angles, the nodal locations surprisingly persist, despite the strikingly altered underlying water bell shape. At extreme driving amplitudes the water sheet assumes a rich variety of tortuous, non-convex shapes; nevertheless, the fluid sheet remains intact.

RefleX: X-ray absorption and reflection in active galactic nuclei for arbitrary geometries

NASA Astrophysics Data System (ADS)

Paltani, S.; Ricci, C.

2017-11-01

Reprocessed X-ray radiation carries important information about the structure and physical characteristics of the material surrounding the supermassive black hole (SMBH) in active galactic nuclei (AGN). We report here on a newly developed simulation platform, RefleX, which allows to reproduce absorption and reflection by quasi-arbitrary geometries. We show here the reliability of our approach by comparing the results of our simulations with existing spectral models such as pexrav, MYTorus and BNTorus. RefleX implements both Compton scattering on free electrons and Rayleigh scattering and Compton scattering on bound electrons. We show the effect of bound-electron corrections on a torus geometry simulated like in MYTorus. We release with this paper the RefleX executable, as well as RXTorus, a model that assumes absorption and reflection from a torus with a varying ratio of the minor to major axis of the torus. To allow major flexibility RXTorus is also distributed in three components: absorbed primary emission, scattered radiation and fluorescent lines. RXTorus is provided for different values of the abundance, and with (atomic configuration) or without (free-electron configuration) taking into account Rayleigh scattering and bound electrons. We apply the RXTorus model in both configurations on the XMM-Newton and NuSTAR spectrum of the Compton-thick AGN NGC 424 and find that the models are able to reproduce very well the observations, but that the assumption on the bound or free state of the electrons has significant consequences on the fit parameters. RefleX executable, user manual and example models are available at http://www.astro.unige.ch/reflex. A copy of the RefleX executable is also available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/607/A31

Three-dimensional rearrangement of single atoms using actively controlled optical microtraps.

PubMed

Lee, Woojun; Kim, Hyosub; Ahn, Jaewook

2016-05-02

We propose and demonstrate three-dimensional rearrangements of single atoms. In experiments performed with single ⁸⁷Rb atoms in optical microtraps actively controlled by a spatial light modulator, we demonstrate various dynamic rearrangements of up to N = 9 atoms including rotation, 2D vacancy filling, guiding, compactification, and 3D shuffling. With the capability of a phase-only Fourier mask to generate arbitrary shapes of the holographic microtraps, it was possible to place single atoms at arbitrary geometries of a few μm size and even continuously reconfigure them by conveying each atom. For this purpose, we loaded a series of computer-generated phase masks in the full frame rate of 60 Hz of the spatial light modulator, so the animation of phase mask transformed the holographic microtraps in real time, driving each atom along the assigned trajectory. Possible applications of this method of transformation of single atoms include preparation of scalable quantum platforms for quantum computation, quantum simulation, and quantum many-body physics.

Flexible approach to vibrational sum-frequency generation using shaped near-infrared light

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

Chowdhury, Azhad U.; Liu, Fangjie; Watson, Brianna R.

We describe a new approach that expands the utility of vibrational sum-frequency generation (vSFG) spectroscopy using shaped near-infrared (NIR) laser pulses. Here, we demonstrate that arbitrary pulse shapes can be specified to match experimental requirements without the need for changes to the optical alignment. In this way, narrowband NIR pulses as long as 5.75 ps are readily generated, with a spectral resolution of about 2.5 cm -1, an improvement of approximately a factor of 3 compared to a typical vSFG system. Moreover, the utility of having complete control over the NIR pulse characteristics is demonstrated through nonresonant background suppression frommore » a metallic substrate by generating an etalon waveform in the pulse shaper. The flexibility afforded by switching between arbitrary NIR waveforms at the sample position with the same instrument geometry expands the type of samples that can be studied without extensive modifications to existing apparatuses or large investments in specialty optics.« less

Eddies in a bottleneck: an arbitrary Debye length theory for capillary electroosmosis.

PubMed

Park, Stella Y; Russo, Christopher J; Branton, Daniel; Stone, Howard A

2006-05-15

Using an applied electrical field to drive fluid flows becomes desirable as channels become smaller. Although most discussions of electroosmosis treat the case of thin Debye layers, here electroosmotic flow (EOF) through a constricted cylinder is presented for arbitrary Debye lengths (kappa(-1)) using a long wavelength perturbation of the cylinder radius. The analysis uses the approximation of small potentials. The varying diameter of the cylinder produces radially and axially varying effective electric fields, as well as an induced pressure gradient. We predict the existence of eddies for certain constricted geometries and propose the possibility of electrokinetic trapping in these regions. We also present a leading-order criterion which predicts central eddies in very narrow constrictions at the scale of the Debye length. Eddies can be found both in the center of the channel and along the perimeter, and the presence of the eddies is a consequence of the induced pressure gradient that accompanies electrically driven flow into a narrow constriction.

Eddies in a Bottleneck: An Arbitrary Debye Length Theory for Capillary Electroosmosis

PubMed Central

Park, Stella Y.; Russo, Christopher J.; Branton, Daniel; Stone, Howard A.

2011-01-01

Using an applied electrical field to drive fluid flows becomes desirable as channels become smaller. Although most discussions of electroosmosis treat the case of thin Debye layers, here electroosmotic flow (EOF) through a constricted cylinder is presented for arbitrary Debye lengths (κ−1) using a long wavelength perturbation of the cylinder radius. The analysis uses the approximation of small potentials. The varying diameter of the cylinder produces radially and axially varying effective electric fields, as well as an induced pressure gradient. We predict the existence of eddies for certain constricted geometries and propose the possibility of electrokinetic trapping in these regions. We also present a leading-order criterion which predicts central eddies in very narrow constrictions at the scale of the Debye length. Eddies can be found both in the center of the channel and along the perimeter, and the presence of the eddies is a consequence of the induced pressure gradient that accompanies electrically driven flow into a narrow constriction. PMID:16376361

Radial fingering under arbitrary viscosity and density ratios

NASA Astrophysics Data System (ADS)

Anjos, Pedro H. A.; Dias, Eduardo O.; Miranda, José A.

2017-08-01

We study viscous fingering formation in radial Hele-Shaw cell geometry considering the combined action of capillary and inertial effects for arbitrary values of viscosity and density ratios. We tackle the problem by employing a perturbative mode-coupling approach and focus our attention on weakly nonlinear stages of the dynamics. If inertial effects are neglected, our theoretical results indicate that the shape of the resulting interfacial patterns is significantly affected by changes in the viscosity ratio. Under such conditions, the growing fingers tend to proliferate through a repeated ramification process (e.g., by finger bifurcation, quadrifurcation, etc.) as the capillary number is increased. Nevertheless, we find that this scenario is dramatically altered when inertia is taken into account. When inertia is relevant, the conventional finger splitting morphologies are replaced by three-lobed structures, characterized by the occurrence of sidebranching phenomena. We verify that slightly different types of sidebranched patterns arise, presenting either wide or sharp fingertips, for a range of capillary numbers and density ratios.

Efficient propagation-inside-layer expansion algorithm for solving the scattering from three-dimensional nested homogeneous dielectric bodies with arbitrary shape.

PubMed

Bellez, Sami; Bourlier, Christophe; Kubické, Gildas

2015-03-01

This paper deals with the evaluation of electromagnetic scattering from a three-dimensional structure consisting of two nested homogeneous dielectric bodies with arbitrary shape. The scattering problem is formulated in terms of a set of Poggio-Miller-Chang-Harrington-Wu integral equations that are afterwards converted into a system of linear equations (impedance matrix equation) by applying the Galerkin method of moments (MoM) with Rao-Wilton-Glisson basis functions. The MoM matrix equation is then solved by deploying the iterative propagation-inside-layer expansion (PILE) method in order to obtain the unknown surface current densities, which are thereafter used to handle the radar cross-section (RCS) patterns. Some numerical results for various structures including canonical geometries are presented and compared with those of the FEKO software in order to validate the PILE-based approach as well as to show its efficiency to analyze the full-polarized RCS patterns.

Noise characteristics of nanoscaled redox-cycling sensors: investigations based on random walks.

PubMed

Kätelhön, Enno; Krause, Kay J; Singh, Pradyumna S; Lemay, Serge G; Wolfrum, Bernhard

2013-06-19

We investigate noise effects in nanoscaled electrochemical sensors using a three-dimensional simulation based on random walks. The presented approach allows the prediction of time-dependent signals and noise characteristics for redox cycling devices of arbitrary geometry. We demonstrate that the simulation results closely match experimental data as well as theoretical expectations with regard to measured currents and noise power spectra. We further analyze the impact of the sensor design on characteristics of the noise power spectrum. Specific transitions between independent noise sources in the frequency domain are indicative of the sensor-reservoir coupling and can be used to identify stationary design features or time-dependent blocking mechanisms. We disclose the source code of our simulation. Since our approach is highly flexible with regard to the implemented boundary conditions, it opens up the possibility for integrating a variety of surface-specific molecular reactions in arbitrary electrochemical systems. Thus, it may become a useful tool for the investigation of a wide range of noise effects in nanoelectrochemical sensors.

Tomographic active optical trapping of arbitrarily shaped objects by exploiting 3D refractive index maps

NASA Astrophysics Data System (ADS)

Kim, Kyoohyun; Park, Yongkeun

2017-05-01

Optical trapping can manipulate the three-dimensional (3D) motion of spherical particles based on the simple prediction of optical forces and the responding motion of samples. However, controlling the 3D behaviour of non-spherical particles with arbitrary orientations is extremely challenging, due to experimental difficulties and extensive computations. Here, we achieve the real-time optical control of arbitrarily shaped particles by combining the wavefront shaping of a trapping beam and measurements of the 3D refractive index distribution of samples. Engineering the 3D light field distribution of a trapping beam based on the measured 3D refractive index map of samples generates a light mould, which can manipulate colloidal and biological samples with arbitrary orientations and/or shapes. The present method provides stable control of the orientation and assembly of arbitrarily shaped particles without knowing a priori information about the sample geometry. The proposed method can be directly applied in biophotonics and soft matter physics.

Overview of the ArbiTER edge plasma eigenvalue code

NASA Astrophysics Data System (ADS)

Baver, Derek; Myra, James; Umansky, Maxim

2011-10-01

The Arbitrary Topology Equation Reader, or ArbiTER, is a flexible eigenvalue solver that is currently under development for plasma physics applications. The ArbiTER code builds on the equation parser framework of the existing 2DX code, extending it to include a topology parser. This will give the code the capability to model problems with complicated geometries (such as multiple X-points and scrape-off layers) or model equations with arbitrary numbers of dimensions (e.g. for kinetic analysis). In the equation parser framework, model equations are not included in the program's source code. Instead, an input file contains instructions for building a matrix from profile functions and elementary differential operators. The program then executes these instructions in a sequential manner. These instructions may also be translated into analytic form, thus giving the code transparency as well as flexibility. We will present an overview of how the ArbiTER code is to work, as well as preliminary results from early versions of this code. Work supported by the U.S. DOE.

Flexible approach to vibrational sum-frequency generation using shaped near-infrared light

DOE PAGES

Chowdhury, Azhad U.; Liu, Fangjie; Watson, Brianna R.; ...

2018-04-23

We describe a new approach that expands the utility of vibrational sum-frequency generation (vSFG) spectroscopy using shaped near-infrared (NIR) laser pulses. Here, we demonstrate that arbitrary pulse shapes can be specified to match experimental requirements without the need for changes to the optical alignment. In this way, narrowband NIR pulses as long as 5.75 ps are readily generated, with a spectral resolution of about 2.5 cm -1, an improvement of approximately a factor of 3 compared to a typical vSFG system. Moreover, the utility of having complete control over the NIR pulse characteristics is demonstrated through nonresonant background suppression frommore » a metallic substrate by generating an etalon waveform in the pulse shaper. The flexibility afforded by switching between arbitrary NIR waveforms at the sample position with the same instrument geometry expands the type of samples that can be studied without extensive modifications to existing apparatuses or large investments in specialty optics.« less

Superconducting fluctuations at arbitrary disorder strength

NASA Astrophysics Data System (ADS)

Stepanov, Nikolai A.; Skvortsov, Mikhail A.

2018-04-01

We study the effect of superconducting fluctuations on the conductivity of metals at arbitrary temperatures T and impurity scattering rates τ-1. Using the standard diagrammatic technique but in the Keldysh representation, we derive the general expression for the fluctuation correction to the dc conductivity applicable for any space dimensionality and analyze it in the case of the film geometry. We observe that the usual classification in terms of the Aslamazov-Larkin, Maki-Thompson, and density-of-states diagrams is to some extent artificial since these contributions produce similar terms, which partially cancel each other. In the diffusive limit, our results fully coincide with recent calculations in the Keldysh technique. In the ballistic limit near the transition, we demonstrate the absence of a divergent term (Tτ ) 2 attributed previously to the density-of-states contribution. In the ballistic limit far above the transition, the temperature-dependent part of the conductivity correction is shown to grow as T τ /ln(T /Tc) , where Tc is the critical temperature.

A new method to include the gravitational forces in a finite element model of the scoliotic spine.

PubMed

Clin, Julien; Aubin, Carl-Éric; Lalonde, Nadine; Parent, Stefan; Labelle, Hubert

2011-08-01

The distribution of stresses in the scoliotic spine is still not well known despite its biomechanical importance in the pathomechanisms and treatment of scoliosis. Gravitational forces are one of the sources of these stresses. Existing finite element models (FEMs), when considering gravity, applied these forces on a geometry acquired from radiographs while the patient was already subjected to gravity, which resulted in a deformed spine different from the actual one. A new method to include gravitational forces on a scoliotic trunk FEM and compute the stresses in the spine was consequently developed. The 3D geometry of three scoliotic patients was acquired using a multi-view X-ray 3D reconstruction technique and surface topography. The FEM of the patients' trunk was created using this geometry. A simulation process was developed to apply the gravitational forces at the centers of gravity of each vertebra level. First the "zero-gravity" geometry was determined by applying adequate upwards forces on the initial geometry. The stresses were reset to zero and then the gravity forces were applied to compute the geometry of the spine subjected to gravity. An optimization process was necessary to find the appropriate zero-gravity and gravity geometries. The design variables were the forces applied on the model to find the zero-gravity geometry. After optimization the difference between the vertebral positions acquired from radiographs and the vertebral positions simulated with the model was inferior to 3 mm. The forces and compressive stresses in the scoliotic spine were then computed. There was an asymmetrical load in the coronal plane, particularly, at the apices of the scoliotic curves. Difference of mean compressive stresses between concavity and convexity of the scoliotic curves ranged between 0.1 and 0.2 MPa. In conclusion, a realistic way of integrating gravity in a scoliotic trunk FEM was developed and stresses due to gravity were explicitly computed. This is a valuable improvement for further biomechanical modeling studies of scoliosis.

Freeform manufacturing of a microoptical lens array on a steep curved substrate by use of a voice coil fast tool servo.

PubMed

Scheiding, Sebastian; Yi, Allen Y; Gebhardt, Andreas; Li, Lei; Risse, Stefan; Eberhardt, Ramona; Tünnermann, Andreas

2011-11-21

We report what is to our knowledge the first approach to diamond turn microoptical lens array on a steep curved substrate by use of a voice coil fast tool servo. In recent years ultraprecision machining has been employed to manufacture accurate optical components with 3D structure for beam shaping, imaging and nonimaging applications. As a result, geometries that are difficult or impossible to manufacture using lithographic techniques might be fabricated using small diamond tools with well defined cutting edges. These 3D structures show no rotational symmetry, but rather high frequency asymmetric features thus can be treated as freeform geometries. To transfer the 3D surface data with the high frequency freeform features into a numerical control code for machining, the commonly piecewise differentiable surfaces are represented as a cloud of individual points. Based on this numeric data, the tool radius correction is calculated to account for the cutting-edge geometry. Discontinuities of the cutting tool locations due to abrupt slope changes on the substrate surface are bridged using cubic spline interpolation.When superimposed with the trajectory of the rotationally symmetric substrate the complete microoptical geometry in 3D space is established. Details of the fabrication process and performance evaluation are described. © 2011 Optical Society of America

Interpreting Gas Production Decline Curves By Combining Geometry and Topology

NASA Astrophysics Data System (ADS)

Ewing, R. P.; Hu, Q.

2014-12-01

Shale gas production forms an increasing fraction of domestic US energy supplies, but individual gas production wells show steep production declines. Better understanding of this production decline would allow better economic forecasting; better understanding of the reasons behind the decline would allow better production management. Yet despite these incentives, production declines curves remain poorly understood, and current analyses range from Arps' purely empirical equation to new sophisticated approaches requiring multiple unavailable parameters. Models often fail to capture salient features: for example, in log-log space many wells decline with an exponent markedly different from the -0.5 expected from diffusion, and often show a transition from one decline mode to another. We propose a new approach based on the assumption that the rate-limiting step is gas movement from the matrix to the induced fracture network. The matrix is represented as an assemblage of equivalent spheres (geometry), with low matrix pore connectivity (topology) that results in a distance-dependent accessible porosity profile given by percolation theory. The basic theory has just 2 parameters: the sphere size distribution (geometry), and the crossover distance (topology) that characterizes the porosity distribution. The theory is readily extended to include e.g. alternative geometries and bi-modal size distributions. Comparisons with historical data are promising.

Theoretical background of retrieving Green's function by cross-correlation: one-dimensional case

NASA Astrophysics Data System (ADS)

Nakahara, Hisashi

2006-06-01

Recently, an assertion has been verified experimentally and theoretically that Green's function between two receivers can be reproduced by cross-correlating the records at the receivers. In this paper, we have theoretically proved the assertion for 1-D media with the free surface by using the Thomson-Haskell matrix method. Strictly speaking, one side of the cross-correlation between records at two receivers is the convolution between Green's function and the autocorrelation function of the source wavelet. This study extends the geometry considered by Claerbout to two receivers vertically apart, and is a special case of the proof by Wapenaar et al. which dealt with 3-D arbitrary inhomogeneous media. However, a simple geometry in 1-D problems enables us to make the proof without any approximations and to better understand the physical background with more ease. That is the main advantage of this study. Though a 1-D geometry seems far from reality, it may be sufficient if an appropriate combination of receivers and earthquakes is selected. In fact, such a geometry is often seen in seismological observations by a vertical array of seismographs in the shallow subsurface. Therefore, we refer to a possibility that the proof in this paper is applied to the estimation of site amplification factors by using records of a vertical seismographic array.

DIATOM (Data Initialization and Modification) Library Version 7.0

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

Crawford, David A.; Schmitt, Robert G.; Hensinger, David M.

DIATOM is a library that provides numerical simulation software with a computational geometry front end that can be used to build up complex problem geometries from collections of simpler shapes. The library provides a parser which allows for application-independent geometry descriptions to be embedded in simulation software input decks. Descriptions take the form of collections of primitive shapes and/or CAD input files and material properties that can be used to describe complex spatial and temporal distributions of numerical quantities (often called “database variables” or “fields”) to help define starting conditions for numerical simulations. The capability is designed to be generalmore » purpose, robust and computationally efficient. By using a combination of computational geometry and recursive divide-and-conquer approximation techniques, a wide range of primitive shapes are supported to arbitrary degrees of fidelity, controllable through user input and limited only by machine resources. Through the use of call-back functions, numerical simulation software can request the value of a field at any time or location in the problem domain. Typically, this is used only for defining initial conditions, but the capability is not limited to just that use. The most recent version of DIATOM provides the ability to import the solution field from one numerical solution as input for another.« less

A design tool for direct and non-stochastic calculations of near-field radiative transfer in complex structures: The NF-RT-FDTD algorithm

NASA Astrophysics Data System (ADS)

Didari, Azadeh; Pinar Mengüç, M.

2017-08-01

Advances in nanotechnology and nanophotonics are inextricably linked with the need for reliable computational algorithms to be adapted as design tools for the development of new concepts in energy harvesting, radiative cooling, nanolithography and nano-scale manufacturing, among others. In this paper, we provide an outline for such a computational tool, named NF-RT-FDTD, to determine the near-field radiative transfer between structured surfaces using Finite Difference Time Domain method. NF-RT-FDTD is a direct and non-stochastic algorithm, which accounts for the statistical nature of the thermal radiation and is easily applicable to any arbitrary geometry at thermal equilibrium. We present a review of the fundamental relations for far- and near-field radiative transfer between different geometries with nano-scale surface and volumetric features and gaps, and then we discuss the details of the NF-RT-FDTD formulation, its application to sample geometries and outline its future expansion to more complex geometries. In addition, we briefly discuss some of the recent numerical works for direct and indirect calculations of near-field thermal radiation transfer, including Scattering Matrix method, Finite Difference Time Domain method (FDTD), Wiener Chaos Expansion, Fluctuating Surface Current (FSC), Fluctuating Volume Current (FVC) and Thermal Discrete Dipole Approximations (TDDA).

Helical Peierls distortion: Formation of helices of polyketone and polyisocyanide

NASA Astrophysics Data System (ADS)

Cui, Chang-Xing; Kertesz, Miklos

1990-06-01

A new type of Peierls-like distortion, the formation of a helix due to the existence of partially filled crossing bands, is reported for polyketone and polyisocyanide. The torsional potential curves, optimized geometries, band structures and phonon dispersion curves are derived. A comparison with the well-known Peierls-distorted all-trans polyacetylene indicates close similarity between the two types of Peierls distortions.

Fabrication and convergent X-ray nanobeam diffraction characterization of submicron-thickness SrTiO 3 crystalline sheets

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

Tilka, J. A.; Park, J.; Sampson, K. C.

The creation of thin SrTiO3 crystals from (001)-oriented SrTiO3 bulk single crystals using focused ion beam milling techniques yields sheets with submicron thickness and arbitrary orientation within the (001) plane. Synchrotron x-ray nanodiffraction rocking curve widths of these SrTiO3 sheets are less than 0.02 degrees, less than a factor of two larger than bulk SrTiO3, making these crystals suitable substrates for epitaxial thin film growth. The change in the rocking curve width is sufficiently small that we deduce that dislocations are not introduced into the SrTiO3 sheets. Observed lattice distortions are consistent with a low concentration of point defects.

Assessment of cortical bone fracture resistance curves by fusing artificial neural networks and linear regression.

PubMed

Vukicevic, Arso M; Jovicic, Gordana R; Jovicic, Milos N; Milicevic, Vladimir L; Filipovic, Nenad D

2018-02-01

Bone injures (BI) represents one of the major health problems, together with cancer and cardiovascular diseases. Assessment of the risks associated with BI is nontrivial since fragility of human cortical bone is varying with age. Due to restrictions for performing experiments on humans, only a limited number of fracture resistance curves (R-curves) for particular ages have been reported in the literature. This study proposes a novel decision support system for the assessment of bone fracture resistance by fusing various artificial intelligence algorithms. The aim was to estimate the R-curve slope, toughness threshold and stress intensity factor using the two input parameters commonly available during a routine clinical examination: patients age and crack length. Using the data from the literature, the evolutionary assembled Artificial Neural Network was developed and used for the derivation of Linear regression (LR) models of R-curves for arbitrary age. Finally, by using the patient (age)-specific LR models and diagnosed crack size one could estimate the risk of bone fracture under given physiological conditions. Compared to the literature, we demonstrated improved performances for estimating nonlinear changes of R-curve slope (R 2 = 0.82 vs. R 2 = 0.76) and Toughness threshold with ageing (R 2 = 0.73 vs. R 2 = 0.66).

Unsteady Newton-Busemann flow theory. Part 2: Bodies of revolution

NASA Technical Reports Server (NTRS)

Hui, W. H.; Tobak, M.

1981-01-01

Newtonian flow theory for unsteady flow past oscillating bodies of revolution at very high Mach numbers is completed by adding a centrifugal force correction to the impact pressures. Exact formulas for the unsteady pressure and the stability derivatives are obtained in closed form and are applicable to bodies of revolution that have arbitrary shapes, arbitrary thicknesses, and either sharp or blunt noses. The centrifugal force correction arising from the curved trajectories followed by the fluid particles in unsteady flow cannot be neglected even for the case of a circular cone. With this correction, the present theory is in excellent agreement with experimental results for sharp cones and for cones with small nose bluntness; gives poor agreement with the results of experiments in air for bodies with moderate or large nose bluntness. The pitching motions of slender power-law bodies of revulution are shown to be always dynamically stable according to Newton-Busemann theory.

Automated computation of autonomous spectral submanifolds for nonlinear modal analysis

NASA Astrophysics Data System (ADS)

Ponsioen, Sten; Pedergnana, Tiemo; Haller, George

2018-04-01

We discuss an automated computational methodology for computing two-dimensional spectral submanifolds (SSMs) in autonomous nonlinear mechanical systems of arbitrary degrees of freedom. In our algorithm, SSMs, the smoothest nonlinear continuations of modal subspaces of the linearized system, are constructed up to arbitrary orders of accuracy, using the parameterization method. An advantage of this approach is that the construction of the SSMs does not break down when the SSM folds over its underlying spectral subspace. A further advantage is an automated a posteriori error estimation feature that enables a systematic increase in the orders of the SSM computation until the required accuracy is reached. We find that the present algorithm provides a major speed-up, relative to numerical continuation methods, in the computation of backbone curves, especially in higher-dimensional problems. We illustrate the accuracy and speed of the automated SSM algorithm on lower- and higher-dimensional mechanical systems.

Metal Catalyst for Low-Temperature Growth of Controlled Zinc Oxide Nanowires on Arbitrary Substrates

PubMed Central

Kim, Baek Hyun; Kwon, Jae W.

2014-01-01

Zinc oxide nanowires generated by hydrothermal method present superior physical and chemical characteristics. Quality control of the growth has been very challenging and controlled growth is only achievable under very limited conditions using homogeneous seed layers with high temperature processes. Here we show the controlled ZnO nanowire growth on various organic and inorganic materials without the requirement of a homogeneous seed layer and a high temperature process. We also report the discovery of an important role of the electronegativity in the nanowire growth on arbitrary substrates. Using heterogeneous metal oxide interlayers with low-temperature hydrothermal methods, we demonstrate well-controlled ZnO nanowire arrays and single nanowires on flat or curved surfaces. A metal catalyst and heterogeneous metal oxide interlayers are found to determine lattice-match with ZnO and to largely influence the controlled alignment. These findings will contribute to the development of novel nanodevices using controlled nanowires. PMID:24625584

Preliminary results with microchannel array plates employing curved microchannels to inhibit ion feedback. [for photon counters

NASA Technical Reports Server (NTRS)

Timothy, J. G.; Bybee, R. L.

1977-01-01

Up to now, microchannel array plates (MCPs) have been constructed with microchannels having a straight geometry and hence have been prone to ion-feedback instabilities at high operating potentials and high ambient pressures. This paper describes the performances of MCPs with curved (J and C configuration) microchannels to inhibit ion feedback. Plates with curved microchannels have demonstrated performances comparable to those of conventional channel electron multipliers with saturated output pulse-height distributions and modal gain values in excess of 10 to the 6th electrons/pulse.

Experimental study on incident wave speed and the mechanisms of deflagration-to-detonation transition in a bent geometry

NASA Astrophysics Data System (ADS)

Li, L.; Li, J.; Teo, C. J.; Chang, P. H.; Khoo, B. C.

2018-03-01

The study of deflagration-to-detonation transition (DDT) in bent tubes is important with many potential applications including fuel pipeline and mine tunnel designs for explosion prevention and detonation engines for propulsion. The aim of this study is to exploit low-speed incident shock waves for DDT using an S-shaped geometry and investigate its effectiveness as a DDT enhancement device. Experiments were conducted in a valveless detonation chamber using ethylene-air mixture at room temperature and pressure (303 K, 1 bar). High-speed Schlieren photography was employed to keep track of the wave dynamic evolution. Results showed that waves with velocity as low as 500 m/s can experience a successful DDT process through this S-shaped geometry. To better understand the mechanism, clear images of local explosion processes were captured in either the first curved section or the second curved section depending on the inlet wave velocity, thus proving that this S-shaped tube can act as a two-stage device for DDT. Owing to the curved wall structure, the passing wave was observed to undergo a continuous compression phase which could ignite the local unburnt mixture and finally lead to a local explosion and a detonation transition. Additionally, the phenomenon of shock-vortex interaction near the wave diffraction region was also found to play an important role in the whole process. It was recorded that this interaction could not only result in local head-on reflection of the reflected wave on the wall that could ignite the local mixture, and it could also contribute to the recoupling of the shock-flame complex when a detonation wave is successfully formed in the first curved section.

Probing Millisecond Pulsar Emission Geometry Using Light Curves From the Fermi Large Area Telescope

NASA Technical Reports Server (NTRS)

Venter, Christo; Harding, Alice; Guillemot, L.

2009-01-01

An interesting new high-energy pulsar sub-population is emerging following early discoveries of gamma-ray millisecond pulsars (MSPs) by the Fermi Large Area Telescope (LAT). We present results from 3D emission modeling, including the Special Relativistic effects of aberration and time-of-flight delays and also rotational sweepback of 13-field lines, in the geometric context of polar cap (PC), slot gap (SG), outer gap (OG), and two-pole caustic (TPC) pulsar models. In contrast to the general belief that these very old, rapidly-rotating neutron stars (NSs) should have largely pair-starved magnetospheres due to the absence of significant pair production, we find that most of the light curves are best fit by SG and OG models, which indicates the presence of narrow accelerating gaps limited by robust pair production -- even in these pulsars with very low spin-down luminosities. The gamma-ray pulse shapes and relative phase lags with respect to the radio pulses point to high-altitude emission being dominant for all geometries. We also find exclusive differentiation of the current gamma-ray MSP population into two MSP sub-classes: light curve shapes and lags across wavebands impose either pair-starved PC (PSPC) or SG / OG-type geometries. In the first case, the radio pulse has a small lag with respect to the single gamma-ray pulse, while the (first) gamma-ray peak usually trails the radio by a large phase offset in the latter case. Finally, we find that the flux correction factor as a function of magnetic inclination and observer angles is typically of order unity for all models. Our calculation of light curves and flux correction factor f(_, _, P) for the case of MSPs is therefore complementary to the "ATLAS paper" of Watters et al. for younger pulsars.

Light deflection and Gauss-Bonnet theorem: definition of total deflection angle and its applications

NASA Astrophysics Data System (ADS)

Arakida, Hideyoshi

2018-05-01

In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild-de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle α of the light ray by constructing a quadrilateral Σ^4 on the optical reference geometry M^opt determined by the optical metric \\bar{g}_{ij}. On the basis of the definition of the total deflection angle α and the Gauss-Bonnet theorem, we derive two formulas to calculate the total deflection angle α ; (1) the angular formula that uses four angles determined on the optical reference geometry M^opt or the curved (r, φ ) subspace M^sub being a slice of constant time t and (2) the integral formula on the optical reference geometry M^opt which is the areal integral of the Gaussian curvature K in the area of a quadrilateral Σ ^4 and the line integral of the geodesic curvature κ _g along the curve C_{Γ}. As the curve C_{Γ}, we introduce the unperturbed reference line that is the null geodesic Γ on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting Γ vertically onto the curved (r, φ ) subspace M^sub. We demonstrate that the two formulas give the same total deflection angle α for the Schwarzschild and the Schwarzschild-de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein-Shapiro's formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild-de Sitter case, there appear order O(Lambda;m) terms in addition to the Schwarzschild-like part, while order O(Λ) terms disappear.

Benefits of curved serrations on broadband trailing-edge noise reduction

NASA Astrophysics Data System (ADS)

Avallone, F.; van der Velden, W. C. P.; Ragni, D.

2017-07-01

Far-field noise and flow field over a novel curved trailing-edge serration (named as iron-shaped serration) are investigated. Spectra of the far-field broadband noise, directivity plots and the flow-field over the iron-shaped serration are obtained from numerical computations performed using a compressible Lattice-Boltzmann solver. The new design is compared to a conventional trailing-edge serration with a triangular geometry. Both serration geometries were retrofitted to a NACA 0018 airfoil at zero degree angle of attack. The iron-shaped geometry is found to reduce far-field broadband noise of approximately 2 dB more than the conventional sawtooth serration for chord-based Strouhal numbers Stc<15. At higher frequencies, the far-field broadband noise for the two serration geometries has comparable intensity. Near-wall velocity distribution and surface pressure fluctuations show that their intensity and spectra are independent on the serration geometry, but a function of the streamwise location. It is found that the larger noise reduction achieved by the iron-shaped trailing-edge serration is due to the mitigation of the scattered noise at the root. This effect is obtained by mitigating the interaction between the two sides of the serration, by delaying toward the tip both the outward (i.e., the tendency of the flow to deviate from the centerline to the edge of the serration) and the downward (i.e., the tendency of the flow to merge between the upper and bottom side of the serration) flow motions present at the root of the sawtooth.

Development of regional curves relating bankfull-channel geometry and discharge to drainage area for streams in Pennsylvania and selected areas of Maryland

USGS Publications Warehouse

Chaplin, Jeffrey J.

2005-01-01

Natural-stream designs are commonly based on the dimensions of the bankfull channel, which is capable of conveying discharges that transport sediment without excessive erosion or deposition. Regional curves relate bankfull-channel geometry and discharge to drainage area in watersheds with similar runoff characteristics and commonly are utilized by practitioners of natural-stream design to confirm or refute selection of the field-identified bankfull channel. Data collected from 66 streamflow-gaging stations and associated stream reaches between December 1999 and December 2003 were used in one-variable ordinary least-squares regression analyses to develop regional curves relating drainage area to cross-sectional area, discharge, width, and mean depth of the bankfull channel. Watersheds draining to these stations are predominantly within the Piedmont, Ridge and Valley, and Appalachian Plateaus Physiographic Provinces of Pennsylvania and northern Maryland. Statistical analyses of physiography, percentage of watershed area underlain by carbonate bedrock, and percentage of watershed area that is glaciated indicate that carbonate bedrock, not physiography or glaciation, has a controlling influence on the slope of regional curves. Regional curves developed from stations in watersheds underlain by 30 percent or less carbonate bedrock generally had steeper slopes than the corresponding relations developed from watersheds underlain by greater than 30 percent carbonate bedrock. In contrast, there is little evidence to suggest that regional curves developed from stations in the Piedmont or Ridge and Valley Physiographic Province are different from the corresponding relations developed from stations in the Appalachian Plateaus Physiographic Province. On the basis of these findings, regional curves are presented to represent two settings that are independent of physiography: (1) noncarbonate settings characterized by watersheds with carbonate bedrock underlying 30 percent or less of watershed area, and (2) carbonate settings characterized by watersheds with carbonate bedrock underlying greater than 30 percent of watershed area. All regional curves presented in this report have slopes that are significantly different from zero and normally distributed residuals that vary randomly with drainage area. Drainage area explains the most variability in bankfull cross-sectional area and bankfull discharge in the noncarbonate setting (R2 = 0.92 for both). Less variability is explained in bankfull width and depth (R2 = 0.81 and 0.72, respectively). Regional curves representing the carbonate setting are generally not as statistically robust as the corresponding noncarbonate relations because there were only 11 stations available to develop these curves and drainage area cannot explain variance resulting from karst features. The carbonate regional curves generally are characterized by less confidence, lower R2 values, and higher residual standard errors. Poor representation by watersheds less than 40 mi2 causes the carbonate regional curves for bankfull discharge, cross-sectional area, and mean depth to be disproportionately influenced by the smallest watershed (values of Cook's Distance range from 3.6 to 8.4). Additional bankfull discharge and channel-geometry data from small watersheds might reduce this influence, increase confidence, and generally improve regional curves representing the carbonate setting. Limitations associated with streamflow-gaging station selection and development of the curves result in some constraints for the application of regional curves presented in this report. These curves apply only to streams within the study area in watersheds having land use, streamflow regulation, and drainage areas that are consistent with the criteria used for station selection. Regardless of the setting, the regional curves presented here are not intended for use as the sole method for estimation of bankfull characteristics; however, th

Additive manufacturing method for SRF components of various geometries

DOEpatents

Rimmer, Robert; Frigola, Pedro E; Murokh, Alex Y

2015-05-05

An additive manufacturing method for forming nearly monolithic SRF niobium cavities and end group components of arbitrary shape with features such as optimized wall thickness and integral stiffeners, greatly reducing the cost and technical variability of conventional cavity construction. The additive manufacturing method for forming an SRF cavity, includes atomizing niobium to form a niobium powder, feeding the niobium powder into an electron beam melter under a vacuum, melting the niobium powder under a vacuum in the electron beam melter to form an SRF cavity; and polishing the inside surface of the SRF cavity.

Active and Passive 3D Vector Radiative Transfer with Preferentially-Aligned Ice Particles

NASA Technical Reports Server (NTRS)

Adams, Ian S.; Munchak, Stephen J.; Pelissier, Craig S.; Kuo, Kwo-Sen; Heymsfield, Gerald M.

2017-01-01

For the purposes of interpreting active (radar) and passive (radiometer) microwave and millimeter wave remote sensing data, we have constructed a consistent radiative transfer modeling framework to simulate the responses for arbitrary sensors with differing sensing geometries and hardware configurations. As part of this work, we have implemented a recent method for calculating the electromagnetic properties of individual ice crystals and snow flakes. These calculations will allow us to exploit polarized remote sensing observations to discriminate different particles types and elucidate dynamics of cloud and precipitating systems.

A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel.

PubMed Central

Kurnikova, M G; Coalson, R D; Graf, P; Nitzan, A

1999-01-01

A lattice relaxation algorithm is developed to solve the Poisson-Nernst-Planck (PNP) equations for ion transport through arbitrary three-dimensional volumes. Calculations of systems characterized by simple parallel plate and cylindrical pore geometries are presented in order to calibrate the accuracy of the method. A study of ion transport through gramicidin A dimer is carried out within this PNP framework. Good agreement with experimental measurements is obtained. Strengths and weaknesses of the PNP approach are discussed. PMID:9929470

Spur-Gear-System Efficiency at Part and Full Load

NASA Technical Reports Server (NTRS)

Anderson, N. E.; Loewenthal, S. H.

1980-01-01

A simple method for predicting the part- and full-load power loss of a steel spur gearset of arbitrary geometry supported by ball bearings is described. The analysis algebraically accounts for losses due to gear sliding, rolling traction, and windage in addition to support-ball-bearing losses. The analysis compares favorably with test data. A theoretical comparison of the component losses indicates that losses due to gear rolling traction, windage, and support bearings are significant and should be included along with gear sliding loss in a calculation of gear-system power loss.

Consistency Conditions and Constraints on Generalized f(R) Gravity with Arbitrary Geometry-Matter Coupling

NASA Astrophysics Data System (ADS)

Si-Yu, Wu; Ya-Bo, Wu; Yue-Yue, Zhao; Xue, Zhang; Cheng-Yuan, Zhang; Bo-Hai, Chen

2016-03-01

Not Available Supported by the National Natural Science Foundation of China under Grant Nos 11175077, 11575075 and 11547156, the Joint Specialized Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China under Grant No 20122136110002, the Open Project Program of State Key Laboratory of Theoretical Physics of Institute of Theoretical Physics under Grant No Y4KF101CJ1, and the Project of Key Discipline of Theoretical Physics of Department of Education in Liaoning Province under Grant Nos 905035 and 905061.

Renormalization group contraction of tensor networks in three dimensions

NASA Astrophysics Data System (ADS)

García-Sáez, Artur; Latorre, José I.

2013-02-01

We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three-dimensional quantum system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.

Stresslets Induced by Active Swimmers.

PubMed

Lauga, Eric; Michelin, Sébastien

2016-09-30

Active particles disturb the fluid around them as force dipoles, or stresslets, which govern their collective dynamics. Unlike swimming speeds, the stresslets of active particles are rarely determined due to the lack of a suitable theoretical framework for arbitrary geometry. We propose a general method, based on the reciprocal theorem of Stokes flows, to compute stresslets as integrals of the velocities on the particle's surface, which we illustrate for spheroidal chemically active particles. Our method will allow tuning the stresslet of artificial swimmers and tailoring their collective motion in complex environments.

A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Perez, Alejandro

2017-05-01

We show that the non-Abelian nature of geometric fluxes—the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG)—follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus identifies more clearly the root of the discreteness of geometric operators in LQG. Our statement generalizes to arbitrary gauge theories and relies only on the validity of the Gauss law.

A multistage time-stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, E.

1985-01-01

A class of explicit multistage time-stepping schemes is used to construct an algorithm for solving the compressible Navier-Stokes equations. Flexibility in treating arbitrary geometries is obtained with a finite-volume formulation. Numerical efficiency is achieved by employing techniques for accelerating convergence to steady state. Computer processing is enhanced through vectorization of the algorithm. The scheme is evaluated by solving laminar and turbulent flows over a flat plate and an NACA 0012 airfoil. Numerical results are compared with theoretical solutions or other numerical solutions and/or experimental data.

Proportional-scanning-phase method to suppress the vibrational noise in nonisotope dual-atom-interferometer-based weak-equivalence-principle-test experiments

NASA Astrophysics Data System (ADS)

Chen, Xi; Zhong, Jiaqi; Song, Hongwei; Zhu, Lei; Wang, Jin; Zhan, Mingsheng

2014-08-01

Vibrational noise is one of the most important noises that limits the performance of the nonisotopes atom-interferometers (AIs) -based weak-equivalence-principle (WEP) -test experiment. By analyzing the vibration-induced phases, we find that, although the induced phases are not completely common, their ratio is always a constant at every experimental data point, which is not fully utilized in the traditional elliptic curve-fitting method. From this point, we propose a strategy that can greatly suppress the vibration-induced phase noise by stabilizing the Raman laser frequencies at high precision and controlling the scanning-phase ratio. The noise rejection ratio can be as high as 1015 with arbitrary dual-species AIs. Our method provides a Lissajous curve, and the shape of the curve indicates the breakdown of the weak-equivalence-principle signal. Then we manage to derive an estimator for the differential phase of the Lissajous curve. This strategy could be helpful in extending the candidates of atomic species for high-precision AIs-based WEP-test experiments.

An experimental investigation of turbulent boundary layers along curved surfaces

NASA Technical Reports Server (NTRS)

So, R. M. C.; Mellor, G. L.

1972-01-01

A curved wall tunnel was designed, and an equilibrium turbulent boundary layer was set up on the straight section preceding the curved test section. Turbulent boundary layer flows with uniform and adverse pressure distributions along convex and concave walls were investigated. Hot-wire measurements along the convex surface indicated that turbulent mixing between fluid layers was very much reduced. However, the law of the wall held and the skin friction, thus determined, correlated well with other measurements. Hot-wire measurements along the concave test wall revealed a system of longitudinal vortices inside the boundary layer and confirmed that concave curvature enhances mixing. A self-consistent set of turbulent boundary layer equations for flows along curved surfaces was derived together with a modified eddy viscosity. Solution of these equations together with the modified eddy viscosity gave results that correlated well with the present data on flows along the convex surface with arbitrary pressure distribution. However, it could only be used to predict the mean characteristics of the flow along concave walls because of the existence of the system of longitudinal vortices inside the boundary layer.

Testing Modified Newtonian Dynamics with Low Surface Brightness Galaxies: Rotation Curve FITS

NASA Astrophysics Data System (ADS)

de Blok, W. J. G.; McGaugh, S. S.

1998-11-01

We present modified Newtonian dynamics (MOND) fits to 15 rotation curves of low surface brightness (LSB) galaxies. Good fits are readily found, although for a few galaxies minor adjustments to the inclination are needed. Reasonable values for the stellar mass-to-light ratios are found, as well as an approximately constant value for the total (gas and stars) mass-to-light ratio. We show that the LSB galaxies investigated here lie on the one, unique Tully-Fisher relation, as predicted by MOND. The scatter on the Tully-Fisher relation can be completely explained by the observed scatter in the total mass-to-light ratio. We address the question of whether MOND can fit any arbitrary rotation curve by constructing a plausible fake model galaxy. While MOND is unable to fit this hypothetical galaxy, a normal dark-halo fit is readily found, showing that dark matter fits are much less selective in producing fits. The good fits to rotation curves of LSB galaxies support MOND, especially because these are galaxies with large mass discrepancies deep in the MOND regime.

Influence of tooth profile on the noncircular gear tooth contact

NASA Astrophysics Data System (ADS)

Cristescu, A.; Andrei, L.; Cristescu, B.

2017-02-01

With noncircular gears, the continuous modification of the tooth meshing, in terms of variation of the tooth profiles and the line of action position and inclination, makes difficult the implementation of a general standard procedure for the analysis of the noncircular gears tooth contact. In this paper, the authors present a graphical approach that enables the tooth contact static pattern to be produced and evaluated in case of a noncircular gear with complex geometry of the pitch curve. The study is virtually developed, in AutoCAD environment, by animating and investigating the gear solid models in mesh. The tooth static contact analysis enables the path of contact area and distribution to be evaluated in correlation with the following variable initial data: gear pitch curve geometry, tooth profile geometry, as a consequence of different generating procedures, and the gear pressure angle. It was found out that the noncircular gear tooth contact could be improved by choosing different procedures for the tooth flank generation in concave and convex zones and by increasing the gear pressure angle.

On the universality of Marangoni-driven spreading

NASA Astrophysics Data System (ADS)

Visser, Claas; van Capelleveen, Bram; Koldeweij, Robin; Lohse, Detlef

2017-11-01

When two liquids of different surface tensions come into contact, the liquid with lower surface tension spreads over the other. Here we measure the dynamics of this Marangoni-driven spreading in the drop-drop geometry, revealing universal behavior with respect to the control parameters as well as other geometries (such as spreading over a flat interface). The distance L over which the low-surface-tension liquid has covered the high-surface-tension droplet is measured as a function of time t, surface tension difference between the liquids Δσ , and viscosity η, revealing power-law behavior L(t) tα . The exponent α is discussed for the early and late spreading regimes. Spreading inhibition is observed at high viscosity, for which the threshold is discussed. Finally, we show that our results collapse onto a single curve of dimensionless L(t) as a function of dimensionless time, which also captures previous results for different geometries, surface tension modifiers, and miscibility. As this curve spans 7 orders of magnitude, Marangoni-induced spreading can be considered a universal phenomenon for many practically encountered liquid-liquid systems.

Measurement of drill grinding parameters using laser sensor

NASA Astrophysics Data System (ADS)

Yanping, Peng; Kumehara, Hiroyuki; Wei, Zhang; Nomura, Takashi

2005-12-01

To measure the grinding parameters and geometry parameters accurately for a drill point is essential to its design and reconditioning. In recent years, a number of non-contact coordinate measuring apparatuses, using CCD camera or laser sensors, are developed. But, a lot work is to be done for further improvement. This paper reports another kind of laser coordinate meter. As an example of its application, the method for geometry inspection of the drill flank surface is detailed. Measured data from laser scanning on the flank surface around some points with several 2-dimensional curves are analyzed with mathematical procedure. If one of these curves turns to be a straight line, it must be the generatrix of the grinding cone. Thus, the grinding parameters are determined by a set of three generatrices. Then, the measurement method and data processing procedure are proposed. Its validity is assessed by measuring a sample with given parameters. The point geometry measured agrees well with the known values. In comparison with other methods in the published literature, it is simpler in computation and more accurate in results.

Realistic simulations of a cyclotron spiral inflector within a particle-in-cell framework

NASA Astrophysics Data System (ADS)

Winklehner, Daniel; Adelmann, Andreas; Gsell, Achim; Kaman, Tulin; Campo, Daniela

2017-12-01

We present an upgrade to the particle-in-cell ion beam simulation code opal that enables us to run highly realistic simulations of the spiral inflector system of a compact cyclotron. This upgrade includes a new geometry class and field solver that can handle the complicated boundary conditions posed by the electrode system in the central region of the cyclotron both in terms of particle termination, and calculation of self-fields. Results are benchmarked against the analytical solution of a coasting beam. As a practical example, the spiral inflector and the first revolution in a 1 MeV /amu test cyclotron, located at Best Cyclotron Systems, Inc., are modeled and compared to the simulation results. We find that opal can now handle arbitrary boundary geometries with relative ease. Simulated injection efficiencies and beam shape compare well with measured efficiencies and a preliminary measurement of the beam distribution after injection.

Tuning and Freezing Disorder in Photonic Crystals using Percolation Lithography.

PubMed

Burgess, Ian B; Abedzadeh, Navid; Kay, Theresa M; Shneidman, Anna V; Cranshaw, Derek J; Lončar, Marko; Aizenberg, Joanna

2016-01-21

Although common in biological systems, synthetic self-assembly routes to complex 3D photonic structures with tailored degrees of disorder remain elusive. Here we show how liquids can be used to finely control disorder in porous 3D photonic crystals, leading to complex and hierarchical geometries. In these optofluidic crystals, dynamically tunable disorder is superimposed onto the periodic optical structure through partial wetting or evaporation. In both cases, macroscopic symmetry breaking is driven by subtle sub-wavelength variations in the pore geometry. These variations direct site-selective infiltration of liquids through capillary interactions. Incorporating cross-linkable resins into our liquids, we developed methods to freeze in place the filling patterns at arbitrary degrees of partial wetting and intermediate stages of drying. These percolation lithography techniques produced permanent photonic structures with adjustable disorder. By coupling strong changes in optical properties to subtle differences in fluid behavior, optofluidic crystals may also prove useful in rapid analysis of liquids.

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

Martin, Shawn

This code consists of Matlab routines which enable the user to perform non-manifold surface reconstruction via triangulation from high dimensional point cloud data. The code was based on an algorithm originally developed in [Freedman (2007), An Incremental Algorithm for Reconstruction of Surfaces of Arbitrary Codimension Computational Geometry: Theory and Applications, 36(2):106-116]. This algorithm has been modified to accommodate non-manifold surface according to the work described in [S. Martin and J.-P. Watson (2009), Non-Manifold Surface Reconstruction from High Dimensional Point Cloud DataSAND #5272610].The motivation for developing the code was a point cloud describing the molecular conformation space of cyclooctane (C8H16). Cyclooctanemore » conformation space was represented using points in 72 dimensions (3 coordinates for each molecule). The code was used to triangulate the point cloud and thereby study the geometry and topology of cyclooctane. Futures applications are envisioned for peptides and proteins.« less

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Thermodynamics of dyonic black holes with Thurston horizon geometries

NASA Astrophysics Data System (ADS)

Bravo-Gaete, Moisés; Hassaïne, Mokhtar

2018-01-01

In five dimensions, we consider a model described by the Einstein gravity with a source given by a scalar field and various Abelian gauge fields with dilatoniclike couplings. For this model, we are able to construct two dyonic black holes whose three-dimensional horizons are modeled by two nontrivial homogeneous Thurston's geometries. The dyonic solutions are of Lifshitz type with an arbitrary value of the dynamical exponent. In fact, the first gauge field ensures the anisotropy asymptotic while the remaining Abelian fields sustain the electric and magnetic charges. Using the Hamiltonian formalism, the mass, the electric, and magnetic charges are explicitly computed. Interestingly enough, the dyonic solutions behave like Chern-Simons vortices in the sense that their electric and magnetic charges turn to be proportional. The extension with an hyperscaling violating factor is also scrutinized where we notice that for specific values of the violating factor, purely magnetic solutions are possible.

Complex Geometric Models of Diffusion and Relaxation in Healthy and Damaged White Matter

PubMed Central

Farrell, Jonathan A.D.; Smith, Seth A.; Reich, Daniel S.; Calabresi, Peter A.; van Zijl, Peter C.M.

2010-01-01

Which aspects of tissue microstructure affect diffusion weighted MRI signals? Prior models, many of which use Monte-Carlo simulations, have focused on relatively simple models of the cellular microenvironment and have not considered important anatomic details. With the advent of higher-order analysis models for diffusion imaging, such as high-angular-resolution diffusion imaging (HARDI), more realistic models are necessary. This paper presents and evaluates the reproducibility of simulations of diffusion in complex geometries. Our framework is quantitative, does not require specialized hardware, is easily implemented with little programming experience, and is freely available as open-source software. Models may include compartments with different diffusivities, permeabilities, and T2 time constants using both parametric (e.g., spheres and cylinders) and arbitrary (e.g., mesh-based) geometries. Three-dimensional diffusion displacement-probability functions are mapped with high reproducibility, and thus can be readily used to assess reproducibility of diffusion-derived contrasts. PMID:19739233

Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum

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

Dotti, Gustavo; Instituto de Fisica Enrique Gaviola, CONICET, Cordoba; Oliva, Julio

2010-07-15

The classification of a certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in d{>=}5 dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of the real line and an arbitrary base manifold. It is shown that for a generic value of the Gauss-Bonnet coupling, the base manifold must be necessarily Einstein, with an additional restriction on its Weyl tensor for d>5. The boundary admits a wider class of geometries only in the special case when the Gauss-Bonnet coupling is such that the theory admits a unique maximallymore » symmetric solution. The additional freedom in the boundary metric enlarges the class of allowed geometries in the bulk, which are classified within three main branches, containing new black holes and wormholes in vacuum.« less

Mobile robot motion estimation using Hough transform

NASA Astrophysics Data System (ADS)

Aldoshkin, D. N.; Yamskikh, T. N.; Tsarev, R. Yu

2018-05-01

This paper proposes an algorithm for estimation of mobile robot motion. The geometry of surrounding space is described with range scans (samples of distance measurements) taken by the mobile robot’s range sensors. A similar sample of space geometry in any arbitrary preceding moment of time or the environment map can be used as a reference. The suggested algorithm is invariant to isotropic scaling of samples or map that allows using samples measured in different units and maps made at different scales. The algorithm is based on Hough transform: it maps from measurement space to a straight-line parameters space. In the straight-line parameters, space the problems of estimating rotation, scaling and translation are solved separately breaking down a problem of estimating mobile robot localization into three smaller independent problems. The specific feature of the algorithm presented is its robustness to noise and outliers inherited from Hough transform. The prototype of the system of mobile robot orientation is described.

A Cartesian grid approach with hierarchical refinement for compressible flows

NASA Technical Reports Server (NTRS)

Quirk, James J.

1994-01-01

Many numerical studies of flows that involve complex geometries are limited by the difficulties in generating suitable grids. We present a Cartesian boundary scheme for two-dimensional, compressible flows that is unfettered by the need to generate a computational grid and so it may be used, routinely, even for the most awkward of geometries. In essence, an arbitrary-shaped body is allowed to blank out some region of a background Cartesian mesh and the resultant cut-cells are singled out for special treatment. This is done within a finite-volume framework and so, in principle, any explicit flux-based integration scheme can take advantage of this method for enforcing solid boundary conditions. For best effect, the present Cartesian boundary scheme has been combined with a sophisticated, local mesh refinement scheme, and a number of examples are shown in order to demonstrate the efficacy of the combined algorithm for simulations of shock interaction phenomena.

Design of various fixed-geometry water-lubricated hydrodynamic journal bearings for maximum stability

NASA Technical Reports Server (NTRS)

Schuller, F. T.

1973-01-01

This publication is the result of over 260 fractional-frequency-whirl stability tests on a variety of fixed-geometry journal bearings. It is intended principally as a guide in the selection and design of antiwhirl bearings that must operate at high speeds and low loads in low-viscosity fluids such as water or liquid metals. However, the various fixed-geometry configurations can be employed as well in applications where other lubricants, such as oil, are used and fractional-frequency whirl is a problem. The important parameters that effect stability are discussed for each bearing type, and design curves to facilitate the design of optimum-geometry bearings are included. A comparison of the stability of the different bearing configurations tested is also given.

Crashes and near-crashes on horizontal curves along rural two-lane highways: Analysis of naturalistic driving data.

PubMed

Wang, Bo; Hallmark, Shauna; Savolainen, Peter; Dong, Jing

2017-12-01

Prior research has shown the probability of a crash occurring on horizontal curves to be significantly higher than on similar tangent segments, and a disproportionally higher number of curve-related crashes occurred in rural areas. Challenges arise when analyzing the safety of horizontal curves due to imprecision in integrating information as to the temporal and spatial characteristics of each crash with specific curves. The second Strategic Highway Research Program(SHRP 2) conducted a large-scale naturalistic driving study (NDS),which provides a unique opportunity to better understand the contributing factors leading to crash or near-crash events. This study utilizes high-resolution behavioral data from the NDS to identify factors associated with 108 safety critical events (i.e., crashes or near-crashes) on rural two-lane curves. A case-control approach is utilized wherein these events are compared to 216 normal, baseline-driving events. The variables examined in this study include driver demographic characteristics, details of the traffic environment and roadway geometry, as well as driver behaviors such as in-vehicle distractions. Logistic regression models are estimated to discern those factors affecting the likelihood of a driver being crash-involved. These factors include high-risk behaviors, such as speeding and visual distractions, as well as curve design elements and other roadway characteristics such as pavement surface conditions. This paper successfully integrated driver behavior, vehicle characteristics, and roadway environments into the same model. Logistic regression model was found to be an effective way to investigate crash risks using naturalistic driving data. This paper revealed a number of contributing factors to crashes on rural two-lane curves, which has important implications in traffic safety policy and curve geometry design. This paper also discussed limitations and lessons learned from working with the SHRP 2 NDS data. It will benefit future researchers who work with similar type of data. Copyright © 2017 National Safety Council and Elsevier Ltd. All rights reserved.

Guiding curve based on the normal breathing as monitored by thermocouple for regular breathing.

PubMed

Lim, Sangwook; Park, Sung Ho; Ahn, Seung Do; Suh, Yelin; Shin, Seong Soo; Lee, Sang-wook; Kim, Jong Hoon; Choi, Eun Kyoung; Yi, Byong Yong; Kwon, Soo Il; Kim, Sookil; Jeung, Tae Sig

2007-11-01

Adapting radiation fields to a moving target requires information continuously on the location of internal target by detecting it directly or indirectly. The aim of this study is to make the breathing regular effectively with minimizing stress to the patient. A system for regulating patient's breath consists of a respiratory monitoring mask (ReMM), a thermocouple module, a screen, inner earphones, and a personal computer. A ReMM with thermocouple was developed previously to measure the patient's respiration. A software was written in LabView 7.0 (National Instruments, TX), which acquires respiration signal and displays its pattern. Two curves are displayed on the screen: One is a curve indicating the patient's current breathing pattern; the other is a guiding curve, which is iterated with one period of the patient's normal breathing curve. The guiding curves were acquired for each volunteer before they breathed with guidance. Ten volunteers participated in this study to evaluate this system. A cycle of the representative guiding curve was acquired by monitoring each volunteer's free breathing with ReMM and was then generated iteratively. The regularity was compared between a free breath curve and a guided breath curve by measuring standard deviations of amplitudes and periods of two groups of breathing. When the breathing was guided, the standard deviation of amplitudes and periods on average were reduced from 0.0029 to 0.00139 (arbitrary units) and from 0.359 s to 0.202 s, respectively. And the correlation coefficients between breathing curves and guiding curves were greater than 0.99 for all volunteers. The regularity was improved statistically when the guiding curve was used.

DUO: Spectra of diatomic molecules

NASA Astrophysics Data System (ADS)

Yurchenko, Sergei N.; Lodi, Lorenzo; Tennyson, Jonathan; Stolyarov, Andrey V.

2016-05-01

Duo computes rotational, rovibrational and rovibronic spectra of diatomic molecules. The software, written in Fortran 2003, solves the Schrödinger equation for the motion of the nuclei for the simple case of uncoupled, isolated electronic states and also for the general case of an arbitrary number and type of couplings between electronic states. Possible couplings include spin-orbit, angular momenta, spin-rotational and spin-spin. Introducing the relevant couplings using so-called Born-Oppenheimer breakdown curves can correct non-adiabatic effects.

Non-linear behavior of fiber composite laminates

NASA Technical Reports Server (NTRS)

Hashin, Z.; Bagchi, D.; Rosen, B. W.

1974-01-01

The non-linear behavior of fiber composite laminates which results from lamina non-linear characteristics was examined. The analysis uses a Ramberg-Osgood representation of the lamina transverse and shear stress strain curves in conjunction with deformation theory to describe the resultant laminate non-linear behavior. A laminate having an arbitrary number of oriented layers and subjected to a general state of membrane stress was treated. Parametric results and comparison with experimental data and prior theoretical results are presented.

Application of fracture toughness scaling models to the ductile-to- brittle transition

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

Link, R.E.; Joyce, J.A.

1996-01-01

An experimental investigation of fracture toughness in the ductile-brittle transition range was conducted. A large number of ASTM A533, Grade B steel, bend and tension specimens with varying crack lengths were tested throughout the transition region. Cleavage fracture toughness scaling models were utilized to correct the data for the loss of constraint in short crack specimens and tension geometries. The toughness scaling models were effective in reducing the scatter in the data, but tended to over-correct the results for the short crack bend specimens. A proposed ASTM Test Practice for Fracture Toughness in the Transition Range, which employs a mastermore » curve concept, was applied to the results. The proposed master curve over predicted the fracture toughness in the mid-transition and a modified master curve was developed that more accurately modeled the transition behavior of the material. Finally, the modified master curve and the fracture toughness scaling models were combined to predict the as-measured fracture toughness of the short crack bend and the tension specimens. It was shown that when the scaling models over correct the data for loss of constraint, they can also lead to non-conservative estimates of the increase in toughness for low constraint geometries.« less

Modeling for stress-strain curve of a porous NiTi under compressive loading

NASA Astrophysics Data System (ADS)

Zhao, Ying; Taya, Minoru

2005-05-01

Two models for predicting the stress-strain curve of porous NiTi under compressive loading are presented in this paper. Porous NiTi shape memory alloy is investigated as a composite composed of solid NiTi as matrix and pores as inclusions. Eshelby"s equivalent inclusion method and Mori-Tanaka"s mean-field theory are employed in both models. In the first model, the geometry of the pores is assumed as sphere. The composite is with close-cells. While in the second model, two geometries of the pores, sphere and ellipsoid, are investigated. The pores are interconnected to each other forming an open-cell microstructure. The two adjacent pores connected along equator ring are investigated as a unit. Two pores interact with each other as they are connected. The average eigenstrain of each unit is obtained by taking the average of each pore"s eigenstrain. The stress-strain curves of porous shape memory alloy with spherical pores and ellipsoidal pores are compared, it is found that the shape of the pores has a nonignorable influence on the mechanical property of the porous NiTi. Comparison of the stress-strain curves of the two models shows that introducing of the average eigenstrains in the second model makes the predictions more agreeable to the experimental results.

Research on the Integration of Bionic Geometry Modeling and Simulation of Robot Foot Based on Characteristic Curve

NASA Astrophysics Data System (ADS)

He, G.; Zhu, H.; Xu, J.; Gao, K.; Zhu, D.

2017-09-01

The bionic research of shape is an important aspect of the research on bionic robot, and its implementation cannot be separated from the shape modeling and numerical simulation of the bionic object, which is tedious and time-consuming. In order to improve the efficiency of shape bionic design, the feet of animals living in soft soil and swamp environment are taken as bionic objects, and characteristic skeleton curve, section curve, joint rotation variable, position and other parameters are used to describe the shape and position information of bionic object’s sole, toes and flipper. The geometry modeling of the bionic object is established by using the parameterization of characteristic curves and variables. Based on this, the integration framework of parametric modeling and finite element modeling, dynamic analysis and post-processing of sinking process in soil is proposed in this paper. The examples of bionic ostrich foot and bionic duck foot are also given. The parametric modeling and integration technique can achieve rapid improved design based on bionic object, and it can also greatly improve the efficiency and quality of robot foot bionic design, and has important practical significance to improve the level of bionic design of robot foot’s shape and structure.

Differentially photo-crosslinked polymers enable self-assembling microfluidics

PubMed Central

Jamal, Mustapha; Zarafshar, Aasiyeh M.; Gracias, David H.

2012-01-01

An important feature of naturally self-assembled systems such as leaves and tissues is that they are curved and have embedded fluidic channels that enable the transport of nutrients to, or removal of waste from, specific three-dimensional (3D) regions. Here, we report the self-assembly of photopatterned polymers, and consequently microfluidic devices, into curved geometries. We discovered that differentially photo-crosslinked SU-8 films spontaneously and reversibly curved upon film de-solvation and re-solvation. Photolithographic patterning of the SU-8 films enabled the self-assembly of cylinders, cubes, and bidirectionally folded sheets. We integrated polydimethylsiloxane (PDMS) microfluidic channels with these SU-8 films to self-assemble curved microfluidic networks. PMID:22068594

Kinematics, structural mechanics, and design of origami structures with smooth folds

NASA Astrophysics Data System (ADS)

Peraza Hernandez, Edwin Alexander

Origami provides novel approaches to the fabrication, assembly, and functionality of engineering structures in various fields such as aerospace, robotics, etc. With the increase in complexity of the geometry and materials for origami structures that provide engineering utility, computational models and design methods for such structures have become essential. Currently available models and design methods for origami structures are generally limited to the idealization of the folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures having non-negligible thickness or maximum curvature at the folds restricted by material limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate representations of structural response and a new approach is needed. The first contribution of this dissertation is a model for the kinematics of origami structures having realistic folds of non-zero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of the smooth folds and the constraints on their associated kinematic variables are presented. A numerical implementation of the model allowing for kinematic simulation of structures having arbitrary fold patterns is also described. Examples illustrating the capability of the model to capture realistic structural folding response are provided. Subsequently, a method for solving the origami design problem of determining the geometry of a single planar sheet and its pattern of smooth folds that morphs into a given three-dimensional goal shape, discretized as a polygonal mesh, is presented. The design parameterization of the planar sheet and the constraints that allow for a valid pattern of smooth folds and approximation of the goal shape in a known folded configuration are presented. Various testing examples considering goal shapes of diverse geometries are provided. Afterwards, a model for the structural mechanics of origami continuum bodies with smooth folds is presented. Such a model entails the integration of the presented kinematic model and existing plate theories in order to obtain a structural representation for folds having non-zero thickness and comprised of arbitrary materials. The model is validated against finite element analysis. The last contribution addresses the design and analysis of active material-based self-folding structures that morph via simultaneous folding towards a given three-dimensional goal shape starting from a planar configuration. Implementation examples including shape memory alloy (SMA)-based self-folding structures are provided.

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium.

PubMed

Yura, H T; Thrane, L; Andersen, P E

2000-12-01

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.

Quantum particles in general spacetimes: A tangent bundle formalism

NASA Astrophysics Data System (ADS)

Wohlfarth, Mattias N. R.

2018-06-01

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new type of nonminimal coupling of the fields and is shown to admit a canonical quantization procedure. For the resulting quantum theory we demonstrate the emergence of a particle interpretation, fully consistent with general relativistic geometry. The path dependency of parallel transport forces each observer to carry their own quantum state; we find that the communication of the corresponding quantum information may generate extra particles on curved spacetimes. A speculative link between quantum information and spacetime curvature is discussed which might lead to novel explanations for quantum decoherence and vanishing interference in double-slit or interaction-free measurement scenarios, in the mere presence of additional observers.

A method of plane geometry primitive presentation

NASA Astrophysics Data System (ADS)

Jiao, Anbo; Luo, Haibo; Chang, Zheng; Hui, Bin

2014-11-01

Point feature and line feature are basic elements in object feature sets, and they play an important role in object matching and recognition. On one hand, point feature is sensitive to noise; on the other hand, there are usually a huge number of point features in an image, which makes it complex for matching. Line feature includes straight line segment and curve. One difficulty in straight line segment matching is the uncertainty of endpoint location, the other is straight line segment fracture problem or short straight line segments joined to form long straight line segment. While for the curve, in addition to the above problems, there is another difficulty in how to quantitatively describe the shape difference between curves. Due to the problems of point feature and line feature, the robustness and accuracy of target description will be affected; in this case, a method of plane geometry primitive presentation is proposed to describe the significant structure of an object. Firstly, two types of primitives are constructed, they are intersecting line primitive and blob primitive. Secondly, a line segment detector (LSD) is applied to detect line segment, and then intersecting line primitive is extracted. Finally, robustness and accuracy of the plane geometry primitive presentation method is studied. This method has a good ability to obtain structural information of the object, even if there is rotation or scale change of the object in the image. Experimental results verify the robustness and accuracy of this method.

Grid Generation Techniques Utilizing the Volume Grid Manipulator

NASA Technical Reports Server (NTRS)

Alter, Stephen J.

1998-01-01

This paper presents grid generation techniques available in the Volume Grid Manipulation (VGM) code. The VGM code is designed to manipulate existing line, surface and volume grids to improve the quality of the data. It embodies an easy to read rich language of commands that enables such alterations as topology changes, grid adaption and smoothing. Additionally, the VGM code can be used to construct simplified straight lines, splines, and conic sections which are common curves used in the generation and manipulation of points, lines, surfaces and volumes (i.e., grid data). These simple geometric curves are essential in the construction of domain discretizations for computational fluid dynamic simulations. By comparison to previously established methods of generating these curves interactively, the VGM code provides control of slope continuity and grid point-to-point stretchings as well as quick changes in the controlling parameters. The VGM code offers the capability to couple the generation of these geometries with an extensive manipulation methodology in a scripting language. The scripting language allows parametric studies of a vehicle geometry to be efficiently performed to evaluate favorable trends in the design process. As examples of the powerful capabilities of the VGM code, a wake flow field domain will be appended to an existing X33 Venturestar volume grid; negative volumes resulting from grid expansions to enable flow field capture on a simple geometry, will be corrected; and geometrical changes to a vehicle component of the X33 Venturestar will be shown.

Extending laboratory automation to the wards: effect of an innovative pneumatic tube system on diagnostic samples and transport time.

PubMed

Suchsland, Juliane; Winter, Theresa; Greiser, Anne; Streichert, Thomas; Otto, Benjamin; Mayerle, Julia; Runge, Sören; Kallner, Anders; Nauck, Matthias; Petersmann, Astrid

2017-02-01

The innovative pneumatic tube system (iPTS) transports one sample at a time without the use of cartridges and allows rapid sending of samples directly into the bulk loader of a laboratory automation system (LAS). We investigated effects of the iPTS on samples and turn-around time (TAT). During transport, a mini data logger recorded the accelerations in three dimensions and reported them in arbitrary area under the curve (AUC) units. In addition representative quantities of clinical chemistry, hematology and coagulation were measured and compared in 20 blood sample pairs transported by iPTS and courier. Samples transported by iPTS were brought to the laboratory (300 m) within 30 s without adverse effects on the samples. The information retrieved from the data logger showed a median AUC of 7 and 310 arbitrary units for courier and iPTS transport, respectively. This is considerably below the reported limit for noticeable hemolysis of 500 arbitrary units. iPTS reduces TAT by reducing the hands-on time and a fast transport. No differences in the measurement results were found for any of the investigated 36 analytes between courier and iPTS transport. Based on these findings the iPTS was cleared for clinical use in our hospital.

Ten years in the library: new data confirm paleontological patterns

NASA Technical Reports Server (NTRS)

Sepkoski, J. J. Jr; Sepkoski JJ, J. r. (Principal Investigator)

1993-01-01

A comparison is made between compilations of times of origination and extinction of fossil marine animal families published in 1982 and 1992. As a result of ten years of library research, half of the information in the compendia has changed: families have been added and deleted, low-resolution stratigraphic data been improved, and intervals of origination and extinction have been altered. Despite these changes, apparent macroevolutionary patterns for the entire marine fauna have remained constant. Diversity curves compiled from the two data bases are very similar, with a goodness-of-fit of 99%; the principal difference is that the 1992 curve averages 13% higher than the older curve. Both numbers and percentages of origination and extinction also match well, with fits ranging from 83% to 95%. All major events of radiation and extinction are identical. Therefore, errors in large paleontological data bases and arbitrariness of included taxa are not necessarily impediments to the analysis of pattern in the fossil record, so long as the data are sufficiently numerous.

Structural efficiency studies of corrugated compression panels with curved caps and beaded webs

NASA Technical Reports Server (NTRS)

Davis, R. C.; Mills, C. T.; Prabhakaran, R.; Jackson, L. R.

1984-01-01

Curved cross-sectional elements are employed in structural concepts for minimum-mass compression panels. Corrugated panel concepts with curved caps and beaded webs are optimized by using a nonlinear mathematical programming procedure and a rigorous buckling analysis. These panel geometries are shown to have superior structural efficiencies compared with known concepts published in the literature. Fabrication of these efficient corrugation concepts became possible by advances made in the art of superplastically forming of metals. Results of the mass optimization studies of the concepts are presented as structural efficiency charts for axial compression.

Adiabatic quantum games and phase-transition-like behavior between optimal strategies

NASA Astrophysics Data System (ADS)

de Ponte, M. A.; Santos, Alan C.

2018-06-01

In this paper we propose a game of a single qubit whose strategies can be implemented adiabatically. In addition, we show how to implement the strategies of a quantum game through controlled adiabatic evolutions, where we analyze the payment of a quantum player for various situations of interest: (1) when the players receive distinct payments, (2) when the initial state is an arbitrary superposition, and (3) when the device that implements the strategy is inefficient. Through a graphical analysis, it is possible to notice that the curves that represent the gains of the players present a behavior similar to the curves that give rise to a phase transition in thermodynamics. These transitions are associated with optimal strategy changes and occur in the absence of entanglement and interaction between the players.

[Different sedimentation rates of X- and Y- sperm and the question of arbitrary sex determination].

PubMed

Bhattacharya, B C

1962-01-01

Separation of X and Y sperm using their sedimentation rates is repor ted. A colloidal medium (egg yolk and glycocoll solution) of a particular viscosity and density was developed for this purpose. Rabbit and bull sperm yeilded a 2-peaked curve when separated into sedimentatio n fractions, while rooster sperm gave a single-peak curve. Sedimentation rate of live and dead sperm were similar. 176 female rabbits were fertilized with various sedimentation fractions. 23.3% became pregnant, resulting in 122 young. The sex of the young was clearly related to the sedimentation rate of the sperm: the 2 uppermost fractions yielded 77.4% (P 0.01) male offspring, while the 2 lowest fractions gave 28.2% males (p 0.01) and the middle yielded 54.7% male young.

Differential Multiscale Modeling of Chemically Complex Materials under Heavy Deformation: Biological, Bioinspired and Synthetic Hierarchical Materials

DTIC Science & Technology

2010-06-01

Buehler, “Meso- Origami : Folding Multilayer Graphene Sheets”, Applied Physics Letters, Vol. 95, paper #: 123121, 2009 D. Sen and M.J. Buehler, “Size and... geometry effects on flow stress in bioinspired de novo metal-matrix nanocomposites”, Advanced Engineering Materials, Vol. 11(10), pp. 774-781, 2009...behavior is recovered. Second, a subset of all geometries shows the inverse banana curve behavior. Interestingly, only 2% of all structures give the

An interactive user-friendly approach to surface-fitting three-dimensional geometries

NASA Technical Reports Server (NTRS)

Cheatwood, F. Mcneil; Dejarnette, Fred R.

1988-01-01

A surface-fitting technique has been developed which addresses two problems with existing geometry packages: computer storage requirements and the time required of the user for the initial setup of the geometry model. Coordinates of cross sections are fit using segments of general conic sections. The next step is to blend the cross-sectional curve-fits in the longitudinal direction using general conics to fit specific meridional half-planes. Provisions are made to allow the fitting of fuselages and wings so that entire wing-body combinations may be modeled. This report includes the development of the technique along with a User's Guide for the various menus within the program. Results for the modeling of the Space Shuttle and a proposed Aeroassist Flight Experiment geometry are presented.

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

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

Can, Tankut, E-mail: tcan@scgp.stonybrook.edu; Laskin, Michael; Wiegmann, Paul B.

2015-11-15

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iteratingmore » a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.« less

Theory of the development of curved barbs and their effects on feather morphology.

PubMed

Feo, Teresa J; Simon, Emma; Prum, Richard O

2016-08-01

Feathers exhibit an extraordinary diversity of shapes, which are used by birds to accomplish a diverse set of functions. Pennaceous feathers have a double branched morphology that develops from a tube of epidermis, and variation in branch geometry determines feather shape. Feather development is both complex (i.e., a simple developmental modification can have multiple effects on mature feather shape), and redundant (i.e., different developmental modifications can create the same shape). Due to this, it is not readily apparent how different feather shapes develop. In many feathers, barbs are not straight, but instead curve in toward, or away, from the feather tip. Barb curvature can affect the shape of mature feathers but the development of curved barbs is unknown. Previous research has hypothesized that barb curvature could develop either during the helical growth of barb ridges in the tubular feather germ, or during barb angle expansion as the feather unfurls from the sheath. To better understand the development of curved barbs and their effects on mature feathers we present a theoretical model of curved barb development and test the model with empirical investigations of feathers. We find that curved barbs affect many aspects of feather morphology including vane width, barb length, and barb spacing. In real feathers, curved barbs can develop both during helical barb ridge growth and during barb angle expansion, with most of the observed curvature due to barb angle expansion. Our results demonstrate that barb angle expansion as a feather unfurls from the sheath is a complex and dynamic process that plays an important role in determining the shape and structure of mature feathers. Curved barbs create heterogeneity in barb geometry within the feather vane, which could have important implications for aerodynamic function and the development of within feather pigmentation patterns. J. Morphol. 277:995-1013, 2016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Properties of Superconductor-Normal Metal-Superconductor Microbridges.

DTIC Science & Technology

1980-07-21

H . A . Notarys, M. L. Yu, and J . E. Mercereau, Phys. Rev. Lett. 30, 743 ( 1973 ). 42. H . A . Notarys and J . E. Mercereau, Physica 55, 424... the mask. A high pressure mercury lamp with an incident flux of about 250 foot-candles gave exposure times of about three minutes. After the exposure... the I = 0 point. Both curves have the same current (horizontal) scale; the vertical scale for dV/dI is in arbitrary units. 56 fj -S 04) -

Analytical Shear Buckling Investigation of Curved Composite Panels.

DTIC Science & Technology

1984-12-01

Principle iiateria1 Axis from Arbitrary x-y axes [lo1 that normals to the midsurface remain normal after deformation is enforced throughout the...laminate. These assumptions lead to the strain equations X% 0 + Z Ky ( 4 )Y Y :.: I K y 0(4 where the o superscripts represent midsurface values and the...K’s are midsurface curvatures. The distance from the midsurface perpendicular to the x-y plane is given by z as shown in Fig. 2. The above strains and

Enhancement of surface definition and gridding in the EAGLE code

NASA Technical Reports Server (NTRS)

Thompson, Joe F.

1991-01-01

Algorithms for smoothing of curves and surfaces for the EAGLE grid generation program are presented. The method uses an existing automated technique which detects undesirable geometric characteristics by using a local fairness criterion. The geometry entity is then smoothed by repeated removal and insertion of spline knots in the vicinity of the geometric irregularity. The smoothing algorithm is formulated for use with curves in Beta spline form and tensor product B-spline surfaces.

Curved and conformal high-pressure vessel

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

Croteau, Paul F.; Kuczek, Andrzej E.; Zhao, Wenping

A high-pressure vessel is provided. The high-pressure vessel may comprise a first chamber defined at least partially by a first wall, and a second chamber defined at least partially by the first wall. The first chamber and the second chamber may form a curved contour of the high-pressure vessel. A modular tank assembly is also provided, and may comprise a first mid tube having a convex geometry. The first mid tube may be defined by a first inner wall, a curved wall extending from the first inner wall, and a second inner wall extending from the curved wall. The firstmore » inner wall may be disposed at an angle relative to the second inner wall. The first mid tube may further be defined by a short curved wall opposite the curved wall and extending from the second inner wall to the first inner wall.« less

Design and simulation of origami structures with smooth folds

PubMed Central

Peraza Hernandez, E. A.; Lagoudas, D. C.

2017-01-01

Origami has enabled new approaches to the fabrication and functionality of multiple structures. Current methods for origami design are restricted to the idealization of folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures of non-negligible fold thickness or maximum curvature at the folds restricted by material limitations. For such structures, folds are not properly represented as creases but rather as bent regions of higher-order geometric continuity. Such fold regions of arbitrary order of continuity are termed as smooth folds. This paper presents a method for solving the following origami design problem: given a goal shape represented as a polygonal mesh (termed as the goal mesh), find the geometry of a single planar sheet, its pattern of smooth folds, and the history of folding motion allowing the sheet to approximate the goal mesh. The parametrization of the planar sheet and the constraints that allow for a valid pattern of smooth folds are presented. The method is tested against various goal meshes having diverse geometries. The results show that every determined sheet approximates its corresponding goal mesh in a known folded configuration having fold angles obtained from the geometry of the goal mesh. PMID:28484322

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

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

Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.

Here, we present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to themore » proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. Lastly, while these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.« less

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

DOE PAGES

Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.

2016-10-12

Here, we present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to themore » proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. Lastly, while these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.« less

Design and simulation of origami structures with smooth folds.

PubMed

Peraza Hernandez, E A; Hartl, D J; Lagoudas, D C

2017-04-01

Origami has enabled new approaches to the fabrication and functionality of multiple structures. Current methods for origami design are restricted to the idealization of folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures of non-negligible fold thickness or maximum curvature at the folds restricted by material limitations. For such structures, folds are not properly represented as creases but rather as bent regions of higher-order geometric continuity. Such fold regions of arbitrary order of continuity are termed as smooth folds . This paper presents a method for solving the following origami design problem: given a goal shape represented as a polygonal mesh (termed as the goal mesh ), find the geometry of a single planar sheet, its pattern of smooth folds, and the history of folding motion allowing the sheet to approximate the goal mesh. The parametrization of the planar sheet and the constraints that allow for a valid pattern of smooth folds are presented. The method is tested against various goal meshes having diverse geometries. The results show that every determined sheet approximates its corresponding goal mesh in a known folded configuration having fold angles obtained from the geometry of the goal mesh.

Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy

NASA Astrophysics Data System (ADS)

Hasebe, Kazuki

2017-07-01

We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S 2 k - 1 in the SO (2 k - 1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S 2 k - 1 to the one-dimension higher SO (2 k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah-Patodi-Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.

Conservative treatment in Scheuermann's kyphosis: comparison between lateral curve and variation of the vertebral geometry.

PubMed

Aulisa, Angelo G; Falciglia, Francesco; Giordano, Marco; Mastantuoni, Giuseppe; Poscia, Andrea; Guzzanti, Vincenzo

2016-01-01

Conservative treatment in the Scheuermann's kyphosis obtain, during skeletal growth, remodelling of the deformed vertebras. In a previous paper on Scheuermann's kyphosis, we have studied the geometry variations of all vertebrae included in the curve, before and after the treatment. The purpose of this study was to confirm the effectiveness of conservative treatment in Scheuermann's kyphosis and was to evaluate and compare the variation of the vertebral geometry with the curve trend in Cobb degrees, before and after conservative treatment. From a consecutive series of patients, we selected 90 patients with thoracic Scheuermann's kyphosis, treated using anti-gravity brace: 59 male, 31 female. The mean age at the beginning of the treatment was 14 years. Radiographical measurements were performed on radiographs from a lateral projection, at the beginning (t1) and at the end of the treatment (t5). Vertebral geometry modifications at t1 and t5 were analysed according to the following parameters and evaluated by three independent observers: Anterior wedging angle (ALFA) of the apex vertebra and Posterior wall inclination (APOS) of the limiting lower vertebra. The curve was measured in Cobb degrees. The results from our study showed that of the 90 patients with a thoracic curve mean value of Cobb degrees was 57.8 ± 6.0 SD at t1 and 41.3 ± 5.6 SD at t5. The differences between t1(angle at baseline) and t5 (end of treatment) were calculated for Cobb, ALFA and APOS angle and were respectively -16.4 ± 4.5, -6.4 ± 1.4 and -2.7 ± 1.2; tested with paired t -test were significative ( p  < 0.01). The results of the regression analysis to test the relationship between the three measures for the kyphosis (Cobb degree, ALFA and APOS) showed that the best association was between Cobb t5 and ALFA t5 ( p  < 0.01) and Cobb t1 and APOS t1 ( p  < 0.01). No significative association was found between the difference between ALFA and APOS. We sustain that using new parameters to study vertebral remodelling allows us to reach a better comprehension of Scheuermann spine response to anti-gravity brace treatment. Furthermore, the evaluation of the ALFA angle of the apex vertebra confirms to be more reliable than Cobb's angle because it cannot be affected by the radiological position.

[The Effect of Observation Geometry on Polarized Skylight Spectrum].

PubMed

Zhang, Ren-bin; Wang, Ling-mei; Gao, Jun; Wang, Chi

2015-03-01

Study on polarized skylight spectral characters while observation geometry changing in different solar zenith angles (SZA), viewing zenith angles (VZA) or relative azimuth angles (RAA). Simulation calculation of cloudless daylight polarimetric spectrum is realized based on the solver, vector discrete ordinate method, of radiative transfer equation. In the Sun's principal and perpendicular plane, the spectral irradiance data, varying at wavelengths in the range between 0.4 and 3 μm, are calculated to extend the atmospheric polarization spectral information under the conditions: the MODTRAN solar reference spectrur is the only illuminant source; the main influencing factors of polarized radiative transfer include underlying surface albedo, aerosol layers and components, and the absorption of trace gases. Simulation analysis results: (1) While the relative azimuth angle is zero, the magnitude of spectrum U/I is lower than 10(-7) and V/I is negligible, the degree of polarization and the spectrum Q/I are shaped like the letter V or mirror-writing U. (2) In twilight, when the Sun is not in FOV of the detector, the polarization of the daytime sky has two maximum near 0.51 and 2.75 μm, and a minimum near 1.5 μm. For arbitrary observation geometry, the spectral signal of V/I may be ignored. According to observation geometry, choosing different spectral bands or polarized signal will be propitious to targets detection.

Epipolar Consistency in Transmission Imaging.

PubMed

Aichert, André; Berger, Martin; Wang, Jian; Maass, Nicole; Doerfler, Arnd; Hornegger, Joachim; Maier, Andreas K

2015-11-01

This paper presents the derivation of the Epipolar Consistency Conditions (ECC) between two X-ray images from the Beer-Lambert law of X-ray attenuation and the Epipolar Geometry of two pinhole cameras, using Grangeat's theorem. We motivate the use of Oriented Projective Geometry to express redundant line integrals in projection images and define a consistency metric, which can be used, for instance, to estimate patient motion directly from a set of X-ray images. We describe in detail the mathematical tools to implement an algorithm to compute the Epipolar Consistency Metric and investigate its properties with detailed random studies on both artificial and real FD-CT data. A set of six reference projections of the CT scan of a fish were used to evaluate accuracy and precision of compensating for random disturbances of the ground truth projection matrix using an optimization of the consistency metric. In addition, we use three X-ray images of a pumpkin to prove applicability to real data. We conclude, that the metric might have potential in applications related to the estimation of projection geometry. By expression of redundancy between two arbitrary projection views, we in fact support any device or acquisition trajectory which uses a cone-beam geometry. We discuss certain geometric situations, where the ECC provide the ability to correct 3D motion, without the need for 3D reconstruction.

Mixed-mode stress intensity factors for kink cracks with finite kink length loaded in tension and bending: application to dentin and enamel.

PubMed

Bechtle, Sabine; Fett, Theo; Rizzi, Gabriele; Habelitz, Stefan; Schneider, Gerold A

2010-05-01

Fracture toughness resistance curves describe a material's resistance against crack propagation. These curves are often used to characterize biomaterials like bone, nacre or dentin as these materials commonly exhibit a pronounced increase in fracture toughness with crack extension due to co-acting mechanisms such as crack bridging, crack deflection and microcracking. The knowledge of appropriate stress intensity factors which depend on the sample and crack geometry is essential for determining these curves. For the dental biomaterials enamel and dentin it was observed that, under bending and tensile loading, crack propagation occurs under certain constant angles to the initial notch direction during testing procedures used for fracture resistance curve determination. For this special crack geometry (a kink crack of finite length in a finite body) appropriate geometric function solutions are missing. Hence, we present in this study new mixed-mode stress intensity factors for kink cracks with finite kink length within samples of finite dimensions for two loading cases (tension and bending) which were derived from a combination of mixed-mode stress intensity factors of kink cracks with infinitely small kinks and of slant cracks. These results were further applied to determine the fracture resistance curves of enamel and dentin by testing single edge notched bending (SENB) specimens. It was found that kink cracks with finite kink length exhibit identical stress fields to slant cracks as soon as the kink length exceeds 0.15 times the initial straight crack or notch length. The use of stress intensity factor solutions for infinitely small kink cracks for the determination of dentin fracture resistance curves (as was done by other researchers) leads to an overestimation of dentin's fracture resistance of up to 30%. Copyright 2010 Elsevier Ltd. All rights reserved.

Visible Wavelength Exoplanet Phase Curves from Global Albedo Maps

NASA Astrophysics Data System (ADS)

Webber, Matthew; Cahoy, Kerri Lynn

2015-01-01

To investigate the effect of three-dimensional global albedo maps we use an albedo model that: calculates albedo spectra for each points across grid in longitude and latitude on the planetary disk, uses the appropriate angles for the source-observer geometry for each location, and then weights and sums these spectra using the Tschebychev-Gauss integration method. This structure permits detailed 3D modeling of an illuminated planetary disk and computes disk-integrated phase curves. Different pressure-temperature profiles are used for each location based on geometry and dynamics. We directly couple high-density pressure maps from global dynamic radiative-transfer models to compute global cloud maps. Cloud formation is determined from the correlation of the species condensation curves with the temperature-pressure profiles. We use the detailed cloud patterns, of spatial-varying composition and temperature, to determine the observable albedo spectra and phase curves for exoplanets Kepler-7b and HD189733b. These albedo spectra are used to compute planet-star flux ratios using PHOENIX stellar models, exoplanet orbital parameters, and telescope transmission functions. Insight from the Earthshine spectrum and solid surface albedo functions (e.g. water, ice, snow, rocks) are used with our planetary grid to determine the phase curve and flux ratios of non-uniform Earth and Super Earth-like exoplanets with various rotation rates and stellar types. Predictions can be tailored to the visible and Near-InfraRed (NIR) spectral windows for the Kepler space telescope, Hubble space telescope, and future observatories (e.g. WFIRST, JWST, Exo-C, Exo-S). Additionally, we constrain the effect of exoplanet urban-light on the shape of the night-side phase curve for Earths and Super-Earths.

Fracture mechanics technology for optimum pressure vessel design.

NASA Technical Reports Server (NTRS)

Bjeletich, J. G.; Morton, T. M.

1973-01-01

A technique has been developed to design a maximum efficiency reliable pressure vessel of given geometry and service life. The technique for ensuring reliability of the minimum weight vessel relies on the application of linear elastic fracture mechanics and fracture mechanics concepts. The resultant design incorporates potential fatigue and stress corrosion crack extension during service of a worst case initial flaw. Maximum stress for safe life is specified by the design technique, thereby minimizing weight. Ratios of pressure and toughness parameters are employed to avoid arbitrary specification of design stress level which would lead to a suboptimum design.

Dressed Wilson loops as dual condensates in response to magnetic and electric fields

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

Bruckmann, Falk; Endroedi, Gergely

2011-10-01

We introduce dressed Wilson loops as a novel confinement observable. It consists of closed planar loops of arbitrary geometry but fixed area, and its expectation values decay with the latter. The construction of dressed Wilson loops is based on chiral condensates in response to magnetic and electric fields, thus linking different physical concepts. We present results for generalized condensates and dressed Wilson loops on dynamical lattice configurations and confirm the agreement with conventional Wilson loops in the limit of large probe mass. We comment on the renormalization of dressed Wilson loops.

Monitoring of fluid motion in a micromixer by dynamic NMR microscopy.

PubMed

Ahola, Susanna; Casanova, Federico; Perlo, Juan; Münnemann, Kerstin; Blümich, Bernhard; Stapf, Siegfried

2006-01-01

The velocity distribution of liquid flowing in a commercial micromixer has been determined directly by using pulsed-field gradient NMR. Velocity maps with a spatial resolution of 29 microm x 43 microm were obtained by combining standard imaging gradient units with a homebuilt rectangular surface coil matching the mixer geometry. The technique provides access to mixers and reactors of arbitrary shape regardless of optical transparency. Local heterogeneities in the signal intensity and the velocity pattern were found and serve to investigate the quality and functionality of a micromixer, revealing clogging and inhomogeneous flow distributions.

A finite element formulation for scattering from electrically large 2-dimensional structures

NASA Technical Reports Server (NTRS)

Ross, Daniel C.; Volakis, John L.

1992-01-01

A finite element formulation is given using the scattered field approach with a fictitious material absorber to truncate the mesh. The formulation includes the use of arbitrary approximation functions so that more accurate results can be achieved without any modification to the software. Additionally, non-polynomial approximation functions can be used, including complex approximation functions. The banded system that results is solved with an efficient sparse/banded iterative scheme and as a consequence, large structures can be analyzed. Results are given for simple cases to verify the formulation and also for large, complex geometries.

Stress intensity factors in a hollow cylinder containing a radial crack

NASA Technical Reports Server (NTRS)

Delale, F.

1980-01-01

An exact formulation of the plane elasticity problem for a hollow cylinder or a disk containing a radial crack is given. The crack may be an external edge crack, an internal edge crack, or an embedded crack. It is assumed that on the crack surfaces the shear traction is zero and the normal traction is an arbitrary function of r. For various crack geometries and radius ratios, the numerical results are obtained for a uniform crack surface pressure, for a uniform pressure acting on the inside wall of the cylinder, and for a rotating disk.

Microwave Magnetochiral Dichroism in the Chiral-Lattice Magnet Cu2OSeO3

NASA Astrophysics Data System (ADS)

Okamura, Y.; Kagawa, F.; Seki, S.; Kubota, M.; Kawasaki, M.; Tokura, Y.

2015-05-01

Through broadband microwave spectroscopy in Faraday geometry, we observe distinct absorption spectra accompanying magnetoelectric (ME) resonance for oppositely propagating microwaves, i.e., directional dichroism, in the multiferroic chiral-lattice magnet Cu2OSeO3. The magnitude of the directional dichroism critically depends on the magnetic-field direction. Such behavior is well accounted for by considering the relative direction of the oscillating electric polarizations induced via the ME effect with respect to microwave electric fields. Directional dichroism in a system with an arbitrary form of ME coupling can be also discussed in the same manner.

Stress intensity factors in a hollow cylinder containing a radial crack

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

In this paper, an exact formulation of the plane elasticity problem for a hollow cylinder or a disk containing a radial crack is given. The crack may be an external edge crack, an internal edge crack, or an embedded crack. It is assumed that on the crack surfaces the shear traction is zero, and the normal traction is an arbitrary function of radius. For various crack geometries and radius ratios, the numerical results are obtained for a uniform crack surface pressure, for a uniform pressure acting on the inside wall of the cylinder, and for a rotating disk.

GAPD: a GPU-accelerated atom-based polychromatic diffraction simulation code.

PubMed

E, J C; Wang, L; Chen, S; Zhang, Y Y; Luo, S N

2018-03-01

GAPD, a graphics-processing-unit (GPU)-accelerated atom-based polychromatic diffraction simulation code for direct, kinematics-based, simulations of X-ray/electron diffraction of large-scale atomic systems with mono-/polychromatic beams and arbitrary plane detector geometries, is presented. This code implements GPU parallel computation via both real- and reciprocal-space decompositions. With GAPD, direct simulations are performed of the reciprocal lattice node of ultralarge systems (∼5 billion atoms) and diffraction patterns of single-crystal and polycrystalline configurations with mono- and polychromatic X-ray beams (including synchrotron undulator sources), and validation, benchmark and application cases are presented.

Contact and crack problems for an elastic wedge. [stress concentration in elastic half spaces

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.

1974-01-01

The contact and the crack problems for an elastic wedge of arbitrary angle are considered. The problem is reduced to a singular integral equation which, in the general case, may have a generalized Cauchy kernel. The singularities under the stamp as well as at the wedge apex were studied, and the relevant stress intensity factors are defined. The problem was solved for various wedge geometries and loading conditions. The results may be applicable to certain foundation problems and to crack problems in symmetrically loaded wedges in which cracks initiate from the apex.

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The development, validation and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems are discussed. A solution method that combines a finite-volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries was previously developed for fixed-grids. In the present research effort, this solution method is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

The Scaling Group of the 1-D Invisicid Euler Equations

NASA Astrophysics Data System (ADS)

Schmidt, Emma; Ramsey, Scott; Boyd, Zachary; Baty, Roy

2017-11-01

The one dimensional (1-D) compressible Euler equations in non-ideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1-D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials.

Brane world in non-Riemannian geometry

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

Maier, R.; Falciano, F. T.

2011-03-15

We carefully investigate the modified Einstein's field equation in a 4-dimensional (3-brane) arbitrary manifold embedded in a 5-dimensional non-Riemannian bulk spacetime with a noncompact extra dimension. In this context the Israel-Darmois matching conditions are extended assuming that the torsion in the bulk is continuous. The discontinuity in the torsion first derivatives are related to the matter distribution through the field equation. In addition, we develop a model that describes a flat FLRW model embedded in a 5-dimensional de Sitter or anti-de Sitter, where a 5-dimensional cosmological constant emerges from the torsion.

Proteus-MOC: A 3D deterministic solver incorporating 2D method of characteristics

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

Marin-Lafleche, A.; Smith, M. A.; Lee, C.

2013-07-01

A new transport solution methodology was developed by combining the two-dimensional method of characteristics with the discontinuous Galerkin method for the treatment of the axial variable. The method, which can be applied to arbitrary extruded geometries, was implemented in PROTEUS-MOC and includes parallelization in group, angle, plane, and space using a top level GMRES linear algebra solver. Verification tests were performed to show accuracy and stability of the method with the increased number of angular directions and mesh elements. Good scalability with parallelism in angle and axial planes is displayed. (authors)

Morphometric Analysis of the Clavicles in Chinese Population

PubMed Central

Yang, Jesse Chieh-Szu; Lin, Kang-Ping

2017-01-01

The clavicle has a complex geometry that makes plate fixation technically difficult. The current study aims to measure the anatomical parameters of Chinese clavicles as reference for plate design. One hundred clavicles were analyzed. The clavicle bone model was reconstructed by using computed tomography images. The length, diameters, and curvatures of the clavicle were then measured. The female clavicle was shorter, more slender, and less curved in lateral part than the male clavicle. There was a positive relationship between height and clavicle parameters except lateral curve and depth. The measurements of Chinese clavicles were generally smaller than Caucasians. The clavicle curves were correlated with the bone length; thus consideration of the curve variations may be necessary as designing size distribution of clavicle plate. PMID:28497066

Three dimensional range geometry and texture data compression with space-filling curves.

PubMed

Chen, Xia; Zhang, Song

2017-10-16

This paper presents a novel method to effectively store three-dimensional (3D) data and 2D texture data into a regular 24-bit image. The proposed method uses the Hilbert space-filling curve to map the normalized unwrapped phase map to two 8-bit color channels, and saves the third color channel for 2D texture storage. By further leveraging existing 2D image and video compression techniques, the proposed method can achieve high compression ratios while effectively preserving data quality. Since the encoding and decoding processes can be applied to most of the current 2D media platforms, this proposed compression method can make 3D data storage and transmission available for many electrical devices without requiring special hardware changes. Experiments demonstrate that if a lossless 2D image/video format is used, both original 3D geometry and 2D color texture can be accurately recovered; if lossy image/video compression is used, only black-and-white or grayscale texture can be properly recovered, but much higher compression ratios (e.g., 1543:1 against the ASCII OBJ format) are achieved with slight loss of 3D geometry quality.

Pre-evaluation and interactive editing of B-spline and GERBS curves and surfaces

NASA Astrophysics Data System (ADS)

Laksâ, Arne

2017-12-01

Interactive computer based geometry editing is very useful for designers and artists. Our goal has been to develop useful tools for geometry editing in a way that increases the ability for creative design. When we interactively editing geometry, we want to see the change happening gradually and smoothly on the screen. Pre-evaluation is a tool for increasing the speed of the graphics when doing interactive affine operation on control points and control surfaces. It is then possible to add details on surfaces, and change shape in a smooth and continuous way. We use pre-evaluation on basis functions, on blending functions and on local surfaces. Pre-evaluation can be made hierarchi-cally and is thus useful for local refinements. Sampling and plotting of curves, surfaces and volumes can today be handled by the GPU and it is therefore important to have a structured organization and updating system to be able to make interactive editing as smooth and user friendly as possible. In the following, we will show a structure for pre-evaluation and an optimal organisation of the computation and we will show the effect of implementing both of these techniques.

Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

PubMed

Hagerhall, C M; Laike, T; Küller, M; Marcheschi, E; Boydston, C; Taylor, R P

2015-01-01

Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.

Pulsar Emission Geometry and Accelerating Field Strength

DTIC Science & Technology

2011-11-01

ar X iv :1 11 1. 03 25 v1 [ as tr o- ph .H E ] 1 N ov 2 01 1 2011 Fermi Symposium, Roma., May. 9-12 1 Pulsar Emission Geometry and Accelerating...observations of gamma-ray pulsars have opened a new window to understanding the generation mechanisms of high-energy emission from these systems. The high...the Vela and CTA 1 pulsars with simulated high-energy light curves generated from geometrical representations of the outer gap and slot gap emission

Gravitation: Foundations and Frontiers

NASA Astrophysics Data System (ADS)

Padmanabhan, T.

2010-01-01

1. Special relativity; 2. Scalar and electromagnetic fields in special relativity; 3. Gravity and spacetime geometry: the inescapable connection; 4. Metric tensor, geodesics and covariant derivative; 5. Curvature of spacetime; 6. Einstein's field equations and gravitational dynamics; 7. Spherically symmetric geometry; 8. Black holes; 9. Gravitational waves; 10. Relativistic cosmology; 11. Differential forms and exterior calculus; 12. Hamiltonian structure of general relativity; 13. Evolution of cosmological perturbations; 14. Quantum field theory in curved spacetime; 15. Gravity in higher and lower dimensions; 16. Gravity as an emergent phenomenon; Notes; Index.

Synthetic Landau Levels and Spinor Vortex Matter on a Haldane Spherical Surface with a Magnetic Monopole.

PubMed

Zhou, Xiang-Fa; Wu, Congjun; Guo, Guang-Can; Wang, Ruquan; Pu, Han; Zhou, Zheng-Wei

2018-03-30

We present a flexible scheme to realize exact flat Landau levels on curved spherical geometry in a system of spinful cold atoms. This is achieved by applying the Floquet engineering of a magnetic quadrupole field to create a synthetic monopole field in real space. The system can be exactly mapped to the electron-monopole system on a sphere, thus realizing Haldane's spherical geometry for fractional quantum Hall physics. This method works for either bosons or fermions. We investigate the ground-state vortex pattern for an s-wave interacting atomic condensate by mapping this system to the classical Thompson's problem. The distortion and stability of the vortex pattern are further studied in the presence of dipolar interaction. Our scheme is compatible with the current experimental setup, and may serve as a promising route of investigating quantum Hall physics and exotic spinor vortex matter on curved space.

Monte Carol-Based Dosimetry of Beta-Emitters for Intravascular Brachytherapy

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

Choi, C.K.

2002-06-25

Monte Carlo simulations for radiation dosimetry and the experimental verifications of the simulations have been developed for the treatment geometry of intravascular brachytherapy, a form of radionuclide therapy for occluded coronary disease (restenosis). Monte Carlo code, MCNP4C, has been used to calculate the radiation dose from the encapsulated array of B-emitting seeds (Sr/Y-source train). Solid water phantoms have been fabricated to measure the dose on the radiochromic films that were exposed to the beta source train for both linear and curved coronary vessel geometries. While the dose difference for the 5-degree curved vessel at the prescription point of f+2.0 mmmore » is within the 10% guideline set by the AAPM, however, the difference increased dramatically to 16.85% for the 10-degree case which requires additional adjustment for the acceptable dosimetry planning. The experimental dose measurements agree well with the simulation results« less

Synthetic Landau Levels and Spinor Vortex Matter on a Haldane Spherical Surface with a Magnetic Monopole

NASA Astrophysics Data System (ADS)

Zhou, Xiang-Fa; Wu, Congjun; Guo, Guang-Can; Wang, Ruquan; Pu, Han; Zhou, Zheng-Wei

2018-03-01

We present a flexible scheme to realize exact flat Landau levels on curved spherical geometry in a system of spinful cold atoms. This is achieved by applying the Floquet engineering of a magnetic quadrupole field to create a synthetic monopole field in real space. The system can be exactly mapped to the electron-monopole system on a sphere, thus realizing Haldane's spherical geometry for fractional quantum Hall physics. This method works for either bosons or fermions. We investigate the ground-state vortex pattern for an s -wave interacting atomic condensate by mapping this system to the classical Thompson's problem. The distortion and stability of the vortex pattern are further studied in the presence of dipolar interaction. Our scheme is compatible with the current experimental setup, and may serve as a promising route of investigating quantum Hall physics and exotic spinor vortex matter on curved space.