Detection of ferromagnetic target based on mobile magnetic gradient tensor system

Energy Technology Data Exchange (ETDEWEB)

Gang, Y.I.N., E-mail: gang.gang88@163.com; Yingtang, Zhang; Zhining, Li; Hongbo, Fan; Guoquan, Ren

2016-03-15

Attitude change of mobile magnetic gradient tensor system critically affects the precision of gradient measurements, thereby increasing ambiguity in target detection. This paper presents a rotational invariant-based method for locating and identifying ferromagnetic targets. Firstly, unit magnetic moment vector was derived based on the geometrical invariant, such that the intermediate eigenvector of the magnetic gradient tensor is perpendicular to the magnetic moment vector and the source–sensor displacement vector. Secondly, unit source–sensor displacement vector was derived based on the characteristic that the angle between magnetic moment vector and source–sensor displacement is a rotational invariant. By introducing a displacement vector between two measurement points, the magnetic moment vector and the source–sensor displacement vector were theoretically derived. To resolve the problem of measurement noises existing in the realistic detection applications, linear equations were formulated using invariants corresponding to several distinct measurement points and least square solution of magnetic moment vector and source–sensor displacement vector were obtained. Results of simulation and principal verification experiment showed the correctness of the analytical method, along with the practicability of the least square method. - Highlights: • Ferromagnetic target detection method is proposed based on rotational invariants • Intermediate eigenvector is perpendicular to magnetic moment and displacement vector • Angle between magnetic moment and displacement vector is a rotational invariant • Magnetic moment and displacement vector are derived based on invariants of two points.

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

Science.gov (United States)

Song, Chenchen; Martínez, Todd J.

2017-10-01

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. The resulting energy conservation in micro-canonical AIMD demonstrates that the implementation provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.

Simultaneous inversion of seismic velocity and moment tensor using elastic-waveform inversion of microseismic data: Application to the Aneth CO2-EOR field

Science.gov (United States)

Chen, Y.; Huang, L.

2017-12-01

Moment tensors are key parameters for characterizing CO2-injection-induced microseismic events. Elastic-waveform inversion has the potential to providing accurate results of moment tensors. Microseismic waveforms contains information of source moment tensors and the wave propagation velocity along the wavepaths. We develop an elastic-waveform inversion method to jointly invert the seismic velocity model and moment tensor. We first use our adaptive moment-tensor joint inversion method to estimate moment tensors of microseismic events. Our adaptive moment-tensor inversion method jointly inverts multiple microseismic events with similar waveforms within a cluster to reduce inversion uncertainty for microseismic data recorded using a single borehole geophone array. We use this inversion result as the initial model for our elastic-waveform inversion to minimize the cross-correlated-based data misfit between observed data and synthetic data. We verify our method using synthetic microseismic data and obtain improved results of both moment tensors and seismic velocity model. We apply our new inversion method to microseismic data acquired at a CO2-enhanced oil recovery field in Aneth, Utah, using a single borehole geophone array. The results demonstrate that our new inversion method significantly reduces the data misfit compared to the conventional ray-theory-based moment-tensor inversion.

Application of velocity imaging and gradient-recalled echo in neuroimaging

International Nuclear Information System (INIS)

Boyko, O.B.; Pelc, N.J.; Shimakawa, A.

1990-01-01

This paper describes the initial clinical experience with imaging blood flow at 1.5 T by means of a phase-sensitive gradient refocused pulse sequence. A spin-echo flow-encoding technique was modified to a gradient recalled acquisition in a steady state sequence, producing a velocity imaging and gradient recalled echo (VIGRE) sequence (TR = 24 msec, TE = 13 msec, flip angle = 45 degrees, 24-cm field of view, 7 mm contiguous sections). Two views per phase-encoding step are acquired; one using the first-moment flow-compensation gradient waveform and the second having a (selectable) nonzero first moment. A phase subtraction image is obtained where the signal is dependent on the direction and velocity of flow. The sequence was done following routine spin-echo imaging in 35 patients

Full Tensor Gradient of Simulated Gravity Data for Prospect Scale Delineation

Directory of Open Access Journals (Sweden)

Hendra Grandis

2014-07-01

Full Text Available Gravity gradiometry measurement allows imaging of anomalous sources in more detail than conventional gravity data. The availability of this new technique is limited to airborne gravity surveys using very specific instrumentation. In principle, the gravity gradients can be calculated from the vertical component of the gravity commonly measured in a ground-based gravity survey. We present a calculation of the full tensor gradient (FTG of the gravity employing the Fourier transformation. The calculation was applied to synthetic data associated with a simple block model and also with a more realistic model. The latter corresponds to a 3D model in which a thin coal layer is embedded in a sedimentary environment. Our results show the utility of the FTG of the gravity for prospect scale delineation.

Inversion of gravity gradient tensor data: does it provide better resolution?

Science.gov (United States)

Paoletti, V.; Fedi, M.; Italiano, F.; Florio, G.; Ialongo, S.

2016-04-01

The gravity gradient tensor (GGT) has been increasingly used in practical applications, but the advantages and the disadvantages of the analysis of GGT components versus the analysis of the vertical component of the gravity field are still debated. We analyse the performance of joint inversion of GGT components versus separate inversion of the gravity field alone, or of one tensor component. We perform our analysis by inspection of the Picard Plot, a Singular Value Decomposition tool, and analyse both synthetic data and gradiometer measurements carried out at the Vredefort structure, South Africa. We show that the main factors controlling the reliability of the inversion are algebraic ambiguity (the difference between the number of unknowns and the number of available data points) and signal-to-noise ratio. Provided that algebraic ambiguity is kept low and the noise level is small enough so that a sufficient number of SVD components can be included in the regularized solution, we find that: (i) the choice of tensor components involved in the inversion is not crucial to the overall reliability of the reconstructions; (ii) GGT inversion can yield the same resolution as inversion with a denser distribution of gravity data points, but with the advantage of using fewer measurement stations.

Impact of Gradient Number and Voxel Size on Diffusion Tensor Imaging Tractography for Resective Brain Surgery

NARCIS (Netherlands)

Hoefnagels, Friso W. A.; de Witt Hamer, Philip C.; Pouwels, Petra J. W.; Barkhof, Frederik; Vandertop, W. Peter

2017-01-01

To explore quantitatively and qualitatively how the number of gradient directions (NGD) and spatial resolution (SR) affect diffusion tensor imaging (DTI) tractography in patients planned for brain tumor surgery, using routine clinical magnetic resonance imaging protocols. Of 67 patients with

Relationship between velocity gradients and magnetic turbulence in the solar wind

International Nuclear Information System (INIS)

Garrett, H.B.

1974-01-01

The correlations among the time derivative of the solar-wind velocity, the magnitude of the interplanetary magnetic field (IMF), and the IMF turbulence level are examined to test the idea that interaction between two colliding solar-wind streams can generate turbulence in the solar wind and the IMF. Data obtained by Explorer 33 on the solar wind and IMF are described, and the analysis techniques are outlined. The results indicate that the IMF turbulence level, as measured by the variance, is correlated with the existence of positive velocity gradients in the solar wind. It is noted that while the variance is an increasing function of the field magnitude, it is also independently correlated with the solar-wind velocity gradient

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

Science.gov (United States)

Leone, Frank A., Jr.

2015-01-01

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Diffusive Promotion by Velocity Gradient of Cytoplasmic Streaming (CPS in Nitella Internodal Cells.

Directory of Open Access Journals (Sweden)

Kenji Kikuchi

Full Text Available Cytoplasmic streaming (CPS is well known to assist the movement of nutrients, organelles and genetic material by transporting all of the cytoplasmic contents of a cell. CPS is generated by motility organelles that are driven by motor proteins near a membrane surface, where the CPS has been found to have a flat velocity profile in the flow field according to the sliding theory. There is a consistent mixing of contents inside the cell by CPS if the velocity gradient profile is flattened, which is not assisted by advection diffusion but is only supported by Brownian diffusion. Although the precise flow structure of the cytoplasm has an important role for cellular metabolism, the hydrodynamic mechanism of its convection has not been clarified. We conducted an experiment to visualise the flow of cytoplasm in Nitella cells by injecting tracer fluorescent nanoparticles and using a flow visualisation system in order to understand how the flow profile affects their metabolic system. We determined that the velocity field in the cytosol has an obvious velocity gradient, not a flattened gradient, which suggests that the gradient assists cytosolic mixing by Taylor-Aris dispersion more than by Brownian diffusion.

The local quantum-mechanical stress tensor in Thomas-Fermi approximation and gradient expansion method

International Nuclear Information System (INIS)

Kaschner, R.; Graefenstein, J.; Ziesche, P.

1988-12-01

From the local momentum balance using density functional theory an expression for the local quantum-mechanical stress tensor (or stress field) σ(r) of non-relativistic Coulomb systems is found out within the Thomas-Fermi approximation and its generalizations including gradient expansion method. As an illustration the stress field σ(r) is calculated for the jellium model of the interface K-Cs, containing especially the adhesive force between the two half-space jellia. (author). 23 refs, 1 fig

Calculation of pressure gradients from MR velocity data in a laminar flow model

International Nuclear Information System (INIS)

Adler, R.S.; Chenevert, T.L.; Fowlkes, J.B.; Pipe, J.G.; Rubin, J.M.

1990-01-01

This paper reports on the ability of current imaging modalities to provide velocity-distribution data that offers the possibility of noninvasive pressure-gradient determination from an appropriate rheologic model of flow. A simple laminar flow model is considered at low Reynolds number, RE calc = 0.59 + (1.13 x (dp/dz) meas ), R 2 = .994, in units of dyne/cm 2 /cm for the range of flows considered. The authors' results indicate the potential usefulness of noninvasive pressure-gradient determinations from quantitative analysis of imaging-derived velocity data

Acoustic beam control in biomimetic projector via velocity gradient

Energy Technology Data Exchange (ETDEWEB)

Gao, Xiaowei; Dong, Erqian; Song, Zhongchang [Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education, Xiamen University, Xiamen 361005 (China); Zhang, Yu, E-mail: yuzhang@xmu.edu.cn, E-mail: dzk@psu.edu; Tang, Liguo [Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education, Xiamen University, Xiamen 361005 (China); State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen 361005 (China); Cao, Wenwu, E-mail: yuzhang@xmu.edu.cn, E-mail: dzk@psu.edu [Department of Mathematics and Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802 (United States); Li, Songhai [Sanya Key Laboratory of Marin Mammal and Marine Bioacoustics, Sanya Institute of Deep-Sea Science and Engineering, Chinese Academy of Science, Sanya 57200 (China); Zhang, Sai [Faculty of Science, Jiangsu University, Zhenjiang 212013 (China)

2016-07-04

A biomimetic projector (BioP) based on computerized tomography of pygmy sperm whale's biosonar system has been designed using gradient-index (GRIN) material. The directivity of this BioP device was investigated as function of frequency and the velocity gradient of the GRIN material. A strong beam control over a broad bandwidth at the subwavelength scale has been achieved. Compared with a bare subwavelength source, the main lobe pressure of the BioP is about five times as high and the angular resolution is one order of magnitude better. Our results indicate that this BioP has excellent application potential in miniaturized underwater sonars.

Instability of shallow open channel flow with lateral velocity gradients

Energy Technology Data Exchange (ETDEWEB)

Lima, A C; Izumi, N, E-mail: adriano@eng.hokudai.ac.jp, E-mail: nizumi@eng.hokudai.ac.jp [River and Watershed Engineering Laboratory, Hokkaido University, Sapporo, 060-8628 (Japan)

2011-12-22

The turbulent flow in a wide rectangular open channel partially covered with vegetation is studied using linear stability analysis. In the base state normal flow condition, the water depth is constant and the transverse velocity vanishes, while there is a lateral gradient in the streamwise velocity with an inflexion point at the boundary between the vegetated zone and the main channel. The Reynolds stress is expressed by introducing the eddy viscosity, which is obtained from assuming a logarithmic distribution of the velocity near the bed. Perturbation expansions are introduced to the streamwise and transverse velocities, as well as to the water depth. The system of governing equations was solved in order to determine the maximum growth rate of the perturbations as a function of parameters which describe physical characteristics of the channel and the flow.

The Study of Geological Structures in Suli and Tulehu Geothermal Regions (Ambon, Indonesia Based on Gravity Gradient Tensor Data Simulation and Analytic Signal

Directory of Open Access Journals (Sweden)

Richard Lewerissa

2017-12-01

Full Text Available In early 2017, the geothermal system in the Suli and Tulehu areas of Ambon (Indonesia was investigated using a gravity gradient tensor and analytic signal. The gravity gradient tensor and analytic signal were obtained through forward modeling based on a rectangular prism. It was applied to complete Bouguer anomaly data over the study area by using Fast Fourier Transform (FFT. The analysis was conducted to enhance the geological structure like faults as a pathway of geothermal fluid circulation that is not visible on the surface because it is covered by sediment. The complete Bouguer anomaly ranges of 93 mGal up to 105 mGal decrease from the southwest in Suli to the northeast in Tulehu. A high gravity anomaly indicates a strong magmatic intrusion below the Suli region. The gravity anomalies decrease occurs in the Eriwakang mountain and most of Tulehu, and it is associated with a coral limestone. The lower gravity anomalies are located in the north to the northeast part of Tulehu are associated with alluvium. The residual anomaly shows that the drill well TLU-01 and geothermal manifestations along with the Banda, and Banda-Hatuasa faults are associated with lowest gravity anomaly (negative zone. The gravity gradient tensor simulation and an analytic signal of Suli and Tulehu give more detailed information about the geological features. The gzz component allows accurate description of the shape structures, especially the Banda fault associated with a zero value. This result will be useful as a geophysical constraint to subsurface modeling according to gravity gradient inversion over the area.

Symmetric Tensor Decomposition

DEFF Research Database (Denmark)

Brachat, Jerome; Comon, Pierre; Mourrain, Bernard

2010-01-01

We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....

Tensor voting for robust color edge detection

OpenAIRE

Moreno, Rodrigo; García, Miguel Ángel; Puig, Domenec

2014-01-01

The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-007-7584-8_9 This chapter proposes two robust color edge detection methods based on tensor voting. The first method is a direct adaptation of the classical tensor voting to color images where tensors are initialized with either the gradient or the local color structure tensor. The second method is based on an extension of tensor voting in which the encoding and voting processes are specifically tailored to ...

Hydrogen bond interactions in sulfamerazine: DFT study of the O-17, N-14, and H-2 electric field gradient tensors

International Nuclear Information System (INIS)

Aghazadeh, Mustafa; Mirzaei, Mahmoud

2008-01-01

Hydrogen bond (HB) interactions are studied in the real crystalline structure of sulfamerazine by density functional theory (DFT) calculations of the electric field gradient (EFG) tensors at the sites of O-17, N-14, and H-2 nuclei. One-molecule (single) and four-molecule (cluster) models of sulfamerazine are created by available crystal coordinates and the EFG tensors are calculated in both models to indicate the influence of HB interactions on the tensors. Directly relate to the experiments, the calculated EFG tensors are converted to the experimentally measurable nuclear quadrupole resonance (NQR) parameters, quadrupole coupling constant (qcc) and asymmetry parameter (η Q ). The evaluated NQR parameters reveal that due to contribution of the target molecule to N-H...N and N-H...O types of HB interactions, the EFG tensors at the sites of various nuclei are influenced from single model to the target molecule in cluster. Additionally, O2, N4, and H2 nuclei of the target molecule are significantly influenced by HB interactions, consequently, they have the major contributions to HB interactions in cluster model of sulfamerazine. The calculations are performed employing B3LYP method and 6-311++G** basis set using GAUSSIAN 98 suite of program

A Gradient Based Iterative Solutions for Sylvester Tensor Equations

Directory of Open Access Journals (Sweden)

Zhen Chen

2013-01-01

proposed by Ding and Chen, 2005, and by using tensor arithmetic concepts, an iterative algorithm and its modification are established to solve the Sylvester tensor equation. Convergence analysis indicates that the iterative solutions always converge to the exact solution for arbitrary initial value. Finally, some examples are provided to show that the proposed algorithms are effective.

Diffusion tensor MR microscopy of tissues with low diffusional anisotropy.

Science.gov (United States)

Bajd, Franci; Mattea, Carlos; Stapf, Siegfried; Sersa, Igor

2016-06-01

Diffusion tensor imaging exploits preferential diffusional motion of water molecules residing within tissue compartments for assessment of tissue structural anisotropy. However, instrumentation and post-processing errors play an important role in determination of diffusion tensor elements. In the study, several experimental factors affecting accuracy of diffusion tensor determination were analyzed. Effects of signal-to-noise ratio and configuration of the applied diffusion-sensitizing gradients on fractional anisotropy bias were analyzed by means of numerical simulations. In addition, diffusion tensor magnetic resonance microscopy experiments were performed on a tap water phantom and bovine articular cartilage-on-bone samples to verify the simulation results. In both, the simulations and the experiments, the multivariate linear regression of the diffusion-tensor analysis yielded overestimated fractional anisotropy with low SNRs and with low numbers of applied diffusion-sensitizing gradients. An increase of the apparent fractional anisotropy due to unfavorable experimental conditions can be overcome by applying a larger number of diffusion sensitizing gradients with small values of the condition number of the transformation matrix. This is in particular relevant in magnetic resonance microscopy, where imaging gradients are high and the signal-to-noise ratio is low.

On the effect of velocity gradients on the depth of correlation in μPIV

International Nuclear Information System (INIS)

Mustin, B; Stoeber, B

2016-01-01

The present work revisits the effect of velocity gradients on the depth of the measurement volume (depth of correlation) in microscopic particle image velocimetry (μPIV). General relations between the μPIV weighting functions and the local correlation function are derived from the original definition of the weighting functions. These relations are used to investigate under which circumstances the weighting functions are related to the curvature of the local correlation function. Furthermore, this work proposes a modified definition of the depth of correlation that leads to more realistic results than previous definitions for the case when flow gradients are taken into account. Dimensionless parameters suitable to describe the effect of velocity gradients on μPIV cross correlation are derived and visual interpretations of these parameters are proposed. We then investigate the effect of the dimensionless parameters on the weighting functions and the depth of correlation for different flow fields with spatially constant flow gradients and with spatially varying gradients. Finally this work demonstrates that the results and dimensionless parameters are not strictly bound to a certain model for particle image intensity distributions but are also meaningful when other models for particle images are used. (paper)

On the effect of velocity gradients on the depth of correlation in μPIV

Science.gov (United States)

Mustin, B.; Stoeber, B.

2016-03-01

The present work revisits the effect of velocity gradients on the depth of the measurement volume (depth of correlation) in microscopic particle image velocimetry (μPIV). General relations between the μPIV weighting functions and the local correlation function are derived from the original definition of the weighting functions. These relations are used to investigate under which circumstances the weighting functions are related to the curvature of the local correlation function. Furthermore, this work proposes a modified definition of the depth of correlation that leads to more realistic results than previous definitions for the case when flow gradients are taken into account. Dimensionless parameters suitable to describe the effect of velocity gradients on μPIV cross correlation are derived and visual interpretations of these parameters are proposed. We then investigate the effect of the dimensionless parameters on the weighting functions and the depth of correlation for different flow fields with spatially constant flow gradients and with spatially varying gradients. Finally this work demonstrates that the results and dimensionless parameters are not strictly bound to a certain model for particle image intensity distributions but are also meaningful when other models for particle images are used.

New Models for Velocity/Pressure-Gradient Correlations in Turbulent Boundary Layers

Science.gov (United States)

Poroseva, Svetlana; Murman, Scott

2014-11-01

To improve the performance of Reynolds-Averaged Navier-Stokes (RANS) turbulence models, one has to improve the accuracy of models for three physical processes: turbulent diffusion, interaction of turbulent pressure and velocity fluctuation fields, and dissipative processes. The accuracy of modeling the turbulent diffusion depends on the order of a statistical closure chosen as a basis for a RANS model. When the Gram-Charlier series expansions for the velocity correlations are used to close the set of RANS equations, no assumption on Gaussian turbulence is invoked and no unknown model coefficients are introduced into the modeled equations. In such a way, this closure procedure reduces the modeling uncertainty of fourth-order RANS (FORANS) closures. Experimental and direct numerical simulation data confirmed the validity of using the Gram-Charlier series expansions in various flows including boundary layers. We will address modeling the velocity/pressure-gradient correlations. New linear models will be introduced for the second- and higher-order correlations applicable to two-dimensional incompressible wall-bounded flows. Results of models' validation with DNS data in a channel flow and in a zero-pressure gradient boundary layer over a flat plate will be demonstrated. A part of the material is based upon work supported by NASA under award NNX12AJ61A.

Real-time positioning technology in horizontal directional drilling based on magnetic gradient tensor measurement

Science.gov (United States)

Deng, Guoqing; Yao, Aiguo

2017-04-01

Horizontal directional drilling (HDD) technology has been widely used in Civil Engineering. The dynamic position of the drill bit during construction is one of significant facts determining the accuracy of the trajectory of HDD. A new method now has been proposed to detecting the position of drill bit by measuring the magnetic gradient tensor of the ground solenoid magnetic beacon. Compared with traditional HDD positioning technologies, this new model is much easier to apply with lower request for construction sites and higher positioning efficiency. A direct current (DC) solenoid as a magnetic dipole is placed on ground near the drill bit, and related sensors array which contains four Micro-electromechanical Systems (MEMS ) tri-axial magnetometers, one MEMS tri-axial accelerometer and one MEMS tri-axial gyroscope is set up for measuring the magnetic gradient tensor of the magnetic dipole. The related HDD positioning model has been established and simulation experiments have been carried out to verify the feasibility and reliability of the proposed method. The experiments show that this method has good positioning accuracy in horizontal and vertical direction, and totally avoid the impact of the environmental magnetic field. It can be found that the posture of the magnetic beacon will impact the remote positioning precision within valid positioning range, and the positioning accuracy is higher with longer baseline for limited space in drilling tools. The results prove that the relative error can be limited in 2% by adjusting position of the magnetic beacon, the layers of the enameled coil, the sensitive of magnetometers and the baseline distance. Conclusion can be made that this new method can be applied in HDD positioning with better effect and wider application range than traditional method.

Homogenization and implementation of a 3D regional velocity model in Mexico for its application in moment tensor inversion of intermediate-magnitude earthquakes

Science.gov (United States)

Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala; Caló, Marco

2017-04-01

Moment tensor inversions for intermediate and small earthquakes (M. < 4.5) are challenging as they principally excite relatively short period seismic waves that interact strongly with local heterogeneities. Incorporating detailed regional 3D velocity models permits obtaining realistic synthetic seismograms and recover the seismic source parameters these smaller events. Two 3D regional velocity models have recently been developed for Mexico, using surface waves and seismic noise tomography (Spica et al., 2016; Gaite et al., 2015), which could be used to model the waveforms of intermediate magnitud earthquakes in this region. Such models are parameterized as layered velocity profiles and for some of the profiles, the velocity difference between two layers are considerable. The "jump" in velocities between two layers is inconvenient for some methods and algorithms that calculate synthetic waveforms, in particular for the method that we are using, the spectral element method (SPECFEM3D GLOBE, Komatitsch y Tromp, 2000), when the mesh does not follow the layer boundaries. In order to make the velocity models more easily implementec in SPECFEM3D GLOBE it is neccesary to apply a homogenization algorithm (Capdeville et al., 2015) such that the (now anisotropic) layer velocities are smoothly varying with depth. In this work, we apply a homogenization algorithm to the regional velocity models in México for implementing them in SPECFEM3D GLOBE, calculate synthetic waveforms for intermediate-magnitude earthquakes in México and invert them for the seismic moment tensor.

Measurement of rotation and strain-rate tensors by using stereoscopic PIV

DEFF Research Database (Denmark)

Özcan, O.; Meyer, Knud Erik; Larsen, Poul Scheel

2004-01-01

A simple technique is described for measuring the mean rate-of-displacement (velocity gradient) tensor in a plane by using a conventional stereoscopic PIV system. The technique involves taking PIV data in two or three closely-spaced parallel planes at different times. All components of the mean...... are presented to show the applicability of the proposed technique. The PIV cameras and light sheet optics shown in Fig. 1a are mounted on the same traverse mechanism in order to displace the measurement plane accurately. Data obtained in constant-y and -z planes are presented. Fig. 1b shows a contour plot...

Numerical simulation of bubble behavior in subcooled flow boiling under velocity and temperature gradient

International Nuclear Information System (INIS)

Bahreini, Mohammad; Ramiar, Abas; Ranjbar, Ali Akbar

2015-01-01

Highlights: • Condensing bubble is numerically investigated using VOF model in OpenFOAM package. • Bubble mass reduces as it goes through condensation and achieves higher velocities. • At a certain time the slope of changing bubble diameter with time, varies suddenly. • Larger bubbles experience more lateral migration to higher velocity regions. • Bubbles migrate back to a lower velocity region for higher liquid subcooling rates. - Abstract: In this paper, numerical simulation of the bubble condensation in the subcooled boiling flow is performed. The interface between two-phase is tracked via the volume of fluid (VOF) method with continuous surface force (CSF) model, implemented in the open source OpenFOAM CFD package. In order to simulate the condensing bubble with the OpenFOAM code, the original energy equation and mass transfer model for phase change have been modified and a new solver is developed. The Newtonian flow is solved using the finite volume scheme based on the pressure implicit with splitting of operators (PISO) algorithm. Comparison of the simulation results with previous experimental data revealed that the model predicted well the behavior of the actual condensing bubble. The bubble lifetime is almost proportional to bubble initial size and is prolonged by increasing the system pressure. In addition, the initial bubble size, subcooling of liquid and velocity gradient play an important role in the bubble deformation behavior. Velocity gradient makes the bubble move to the higher velocity region and the subcooling rate makes it to move back to the lower velocity region.

Numerical simulation of bubble behavior in subcooled flow boiling under velocity and temperature gradient

Energy Technology Data Exchange (ETDEWEB)

Bahreini, Mohammad, E-mail: m.bahreini1990@gmail.com; Ramiar, Abas, E-mail: aramiar@nit.ac.ir; Ranjbar, Ali Akbar, E-mail: ranjbar@nit.ac.ir

2015-11-15

Highlights: • Condensing bubble is numerically investigated using VOF model in OpenFOAM package. • Bubble mass reduces as it goes through condensation and achieves higher velocities. • At a certain time the slope of changing bubble diameter with time, varies suddenly. • Larger bubbles experience more lateral migration to higher velocity regions. • Bubbles migrate back to a lower velocity region for higher liquid subcooling rates. - Abstract: In this paper, numerical simulation of the bubble condensation in the subcooled boiling flow is performed. The interface between two-phase is tracked via the volume of fluid (VOF) method with continuous surface force (CSF) model, implemented in the open source OpenFOAM CFD package. In order to simulate the condensing bubble with the OpenFOAM code, the original energy equation and mass transfer model for phase change have been modified and a new solver is developed. The Newtonian flow is solved using the finite volume scheme based on the pressure implicit with splitting of operators (PISO) algorithm. Comparison of the simulation results with previous experimental data revealed that the model predicted well the behavior of the actual condensing bubble. The bubble lifetime is almost proportional to bubble initial size and is prolonged by increasing the system pressure. In addition, the initial bubble size, subcooling of liquid and velocity gradient play an important role in the bubble deformation behavior. Velocity gradient makes the bubble move to the higher velocity region and the subcooling rate makes it to move back to the lower velocity region.

Field estimates of floc dynamics and settling velocities in a tidal creek with significant along-channel gradients in velocity and SPM

Science.gov (United States)

Schwarz, C.; Cox, T.; van Engeland, T.; van Oevelen, D.; van Belzen, J.; van de Koppel, J.; Soetaert, K.; Bouma, T. J.; Meire, P.; Temmerman, S.

2017-10-01

A short-term intensive measurement campaign focused on flow, turbulence, suspended particle concentration, floc dynamics and settling velocities were carried out in a brackish intertidal creek draining into the main channel of the Scheldt estuary. We compare in situ estimates of settling velocities between a laser diffraction (LISST) and an acoustic Doppler technique (ADV) at 20 and 40 cm above bottom (cmab). The temporal variation in settling velocity estimated were compared over one tidal cycle, with a maximum flood velocity of 0.46 m s-1, a maximum horizontal ebb velocity of 0.35 m s-1 and a maximum water depth at high water slack of 2.41 m. Results suggest that flocculation processes play an important role in controlling sediment transport processes in the measured intertidal creek. During high-water slack, particles flocculated to sizes up to 190 μm, whereas at maximum flood and maximum ebb tidal stage floc sizes only reached up to 55 μm and 71 μm respectively. These large differences indicate that flocculation processes are mainly governed by turbulence-induced shear rate. In this study, we specifically recognize the importance of along-channel gradients that places constraints on the application of the acoustic Doppler technique due to conflicts with the underlying assumptions. Along-channel gradients were assessed by additional measurements at a second location and scaling arguments which could be used as an indication whether the Reynolds-flux method is applicable. We further show the potential impact of along-channel advection of flocs out of equilibrium with local hydrodynamics influencing overall floc sizes.

The tensor distribution function.

Science.gov (United States)

Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M

2009-01-01

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Gravitational Metric Tensor Exterior to Rotating Homogeneous ...

African Journals Online (AJOL)

The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...

TensorLy: Tensor Learning in Python

NARCIS (Netherlands)

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.

An optimization approach for fitting canonical tensor decompositions.

Energy Technology Data Exchange (ETDEWEB)

Dunlavy, Daniel M. (Sandia National Laboratories, Albuquerque, NM); Acar, Evrim; Kolda, Tamara Gibson

2009-02-01

Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methods have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.

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

Science.gov (United States)

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

2018-04-01

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

Airborne full tensor magnetic gradiometry surveys in the Thuringian basin, Germany

Science.gov (United States)

Queitsch, M.; Schiffler, M.; Goepel, A.; Stolz, R.; Meyer, M.; Meyer, H.; Kukowski, N.

2013-12-01

In this contribution we introduce a newly developed fully operational full tensor magnetic gradiometer (FTMG) instrument based on Superconducting Quantum Interference Devices (SQUIDs) and show example data acquired in 2012 within the framework of the INFLUINS (Integrated Fluid Dynamics in Sedimentary basins) project. This multidisciplinary project aims for a better understanding of movements and interaction between shallow and deep fluids in the Thuringian Basin in the center of Germany. In contrast to mapping total magnetic field intensity (TMI) in conventional airborne magnetic surveys for industrial exploration of mineral deposits and sedimentary basins, our instrument measures all components of the magnetic field gradient tensor using highly sensitive SQUID gradiometers. This significantly constrains the solutions of the inverse problem. Furthermore, information on the ratio between induced and remanent magnetization is obtained. Special care has been taken to reduce motion noise while acquiring data in airborne operation. Therefore, the sensors are mounted in a nonmagnetic and aerodynamically shaped bird made of fiberglas with a high drag tail which stabilizes the bird even at low velocities. The system is towed by a helicopter and kept at 30m above ground during data acquisition. Additionally, the system in the bird incorporates an inertial unit for geo-referencing and enhanced motion noise compensation, a radar altimeter for topographic correction and a GPS system for high precision positioning. Advanced data processing techniques using reference magnetometer and inertial unit data result in a very low system noise of less than 60 pT/m peak to peak in airborne operation. To show the performance of the system we present example results from survey areas within the Thuringian basin and along its bordering highlands. The mapped gradient tensor components show a high correlation to existing geologic maps. Furthermore, the measured gradient components indicate

TensorLy: Tensor Learning in Python

OpenAIRE

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...

A new phase coding method using a slice selection gradient for high speed flow velocity meaurements in NMR tomography

International Nuclear Information System (INIS)

Oh, C.H.; Cho, Z.H.; California Univ., Irvine

1986-01-01

A new phase coding method using a selection gradient for high speed NMR flow velocity measurements is introduced and discussed. To establish a phase-velocity relationship of flow under the slice selection gradient and spin-echo RF pulse, the Bloch equation was numerically solved under the assumption that only one directional flow exists, i.e. in the direction of slice selection. Details of the numerical solution of the Bloch equation and techniques related to the numerical computations are also given. Finally, using the numerical calculation, high speed flow velocity measurement was attempted and found to be in good agreement with other complementary controlled measurements. (author)

Experimental estimation of fluctuating velocity and scalar gradients in turbulence

Energy Technology Data Exchange (ETDEWEB)

Hearst, R.J.; Lavoie, P. [University of Toronto, Institute for Aerospace Studies, Toronto, ON (Canada); Buxton, O.R.H. [The University of Texas at Austin, Center for Aeromechanics Research, Austin, TX (United States); Ganapathisubramani, B. [University of Southampton, Aerodynamics and Flight Mechanics Research Group, Southampton (United Kingdom)

2012-10-15

The effect of numerical differentiation is investigated in the context of evaluating fluctuating velocity and scalar quantities in turbulent flows. In particular, 2-point forward-difference and 3-, 5-, 7-, and 9-point centred-difference schemes are investigated. The spectral technique introduced by Wyngaard (in J Sci Instr 1(2):1105-1108, 1968) for homogeneous turbulence is used to quantify the effects of the schemes. Numerical differentiation is shown to attenuate gradient spectra over a range of wavenumbers. The spectral attenuation, which varies with the order of the scheme, results in a reduction in the measured mean-squared gradients. High-order schemes (e.g. 7- or 9-point) are shown to significantly decrease the attenuation at all wavenumbers and as a result produce more accurate gradients. Hot-wire measurements and direct numerical simulations of decaying homogeneous, isotropic turbulence are found to be in good agreement with the predictions of the analysis, which suggests that high-order schemes can be used to improve empirical gradient estimates. The shape of the probability density functions is also found to be sensitive to the choice of numerical differentiation scheme. The effect of numerical differentiation is also discussed with respect to particle image velocimetry (PIV) measurements of a nominally two-dimensional planar mixing layer. It is found that the relatively low signal-to-noise ratio inherent in typical PIV measurements necessitates the use of low-order schemes to prevent excessive noise amplification, which increases with the order of the scheme. The results of the present work demonstrate that high-order numerical differentiation schemes can be employed to more accurately resolve gradients measured at a given resolution provided the measurements have an adequate signal-to-noise ratio. (orig.)

The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity

Directory of Open Access Journals (Sweden)

František FOJTÍK

2014-06-01

Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.

Tensor-based morphometry with stationary velocity field diffeomorphic registration: application to ADNI.

Science.gov (United States)

Bossa, Matias; Zacur, Ernesto; Olmos, Salvador

2010-07-01

Tensor-based morphometry (TBM) is an analysis technique where anatomical information is characterized by means of the spatial transformations mapping a customized template with the observed images. Therefore, accurate inter-subject non-rigid registration is an essential prerequisite for both template estimation and image warping. Subsequent statistical analysis on the spatial transformations is performed to highlight voxel-wise differences. Most of previous TBM studies did not explore the influence of the registration parameters, such as the parameters defining the deformation and the regularization models. In this work performance evaluation of TBM using stationary velocity field (SVF) diffeomorphic registration was performed in a subset of subjects from Alzheimer's Disease Neuroimaging Initiative (ADNI) study. A wide range of values of the registration parameters that define the transformation smoothness and the balance between image matching and regularization were explored in the evaluation. The proposed methodology provided brain atrophy maps with very detailed anatomical resolution and with a high significance level compared with results recently published on the same data set using a non-linear elastic registration method. Copyright (c) 2010 Elsevier Inc. All rights reserved.

Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow

Science.gov (United States)

Alam, Meheboob; Saha, Saikat

2014-11-01

The non-Newtonian stress tensor and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal stress difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment tensor] and (v) the angle (ϕ) between the principal directions of the shear tensor and the second moment tensor. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank tensor for which explicit expressions are derived.

Local Tensor Radiation Conditions For Elastic Waves

DEFF Research Database (Denmark)

Krenk, S.; Kirkegaard, Poul Henning

2001-01-01

A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...

Mean template for tensor-based morphometry using deformation tensors.

Science.gov (United States)

Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

2007-01-01

Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

Tensor-based morphometry with mappings parameterized by stationary velocity fields in Alzheimer's disease neuroimaging initiative.

Science.gov (United States)

Bossa, Matías Nicolás; Zacur, Ernesto; Olmos, Salvador

2009-01-01

Tensor-based morphometry (TBM) is an analysis technique where anatomical information is characterized by means of the spatial transformations between a customized template and observed images. Therefore, accurate inter-subject non-rigid registration is an essential prerrequisite. Further statistical analysis of the spatial transformations is used to highlight some useful information, such as local statistical differences among populations. With the new advent of recent and powerful non-rigid registration algorithms based on the large deformation paradigm, TBM is being increasingly used. In this work we evaluate the statistical power of TBM using stationary velocity field diffeomorphic registration in a large population of subjects from Alzheimer's Disease Neuroimaging Initiative project. The proposed methodology provided atrophy maps with very detailed anatomical resolution and with a high significance compared with results published recently on the same data set.

Velocity gradient induced line splitting in x-ray emission accompanying plasma-wall interaction

Czech Academy of Sciences Publication Activity Database

Šmíd, Michal; Renner, Oldřich; Liska, R.

2013-01-01

Roč. 125, Aug (2013), s. 38-44 ISSN 0022-4073 R&D Projects: GA ČR GAP205/10/0814; GA ČR GAP205/11/0571 Institutional support: RVO:68378271 Keywords : laser-produced plasmas * x-ray spectroscopy * plasma-wall interaction * spectral line profiles * Doppler shift * ion velocity gradients Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.288, year: 2013

Pressure gradients fail to predict diffusio-osmosis

Science.gov (United States)

Liu, Yawei; Ganti, Raman; Frenkel, Daan

2018-05-01

We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been proposed for computing such flows and compare them with a reference calculation based on direct, non-equilibrium molecular dynamics simulations. As alternatives, we consider schemes that compute diffusio-osmotic flow from the gradient of the chemical potentials of the constituent species and from the gradient of the component of the pressure tensor parallel to the interface. We find that the approach based on treating chemical potential gradients as external forces acting on various species agrees with the direct simulations, thereby supporting the approach of Marbach et al (2017 J. Chem. Phys. 146 194701). In contrast, an approach based on computing the gradients of the microscopic pressure tensor does not reproduce the direct non-equilibrium results.

Non-Conventional Thermodynamics and Models of Gradient Elasticity

Directory of Open Access Journals (Sweden)

Hans-Dieter Alber

2018-03-01

Full Text Available We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrange derivative of the free energy with respect to the strain. The present paper aims at developing a first version of gradient elasticity of non-Toupin–Mindlin’s type, i.e., a theory employing Cauchy stress tensors, which are not necessarily expressed as Euler–Lagrange derivatives. This is accomplished in the framework of non-conventional thermodynamics. A one-dimensional boundary value problem is solved in detail in order to illustrate the differences of the present theory with Toupin–Mindlin’s gradient elasticity theory.

Applications of seismic spatial wavefield gradient and rotation data in exploration seismology

Science.gov (United States)

Schmelzbach, C.; Van Renterghem, C.; Sollberger, D.; Häusler, M.; Robertsson, J. O. A.

2017-12-01

Seismic spatial wavefield gradient and rotation data have the potential to open up new ways to address long-standing problems in land-seismic exploration such as identifying and separating P-, S-, and surface waves. Gradient-based acquisition and processing techniques could enable replacing large arrays of densely spaced receivers by sparse spatially-compact receiver layouts or even one single multicomponent station with dedicated instruments (e.g., rotational seismometers). Such approaches to maximize the information content of single-station recordings are also of significant interest for seismic measurements at sites with limited access such as boreholes, the sea bottom, and extraterrestrial seismology. Arrays of conventional three-component (3C) geophones enable measuring not only the particle velocity in three dimensions but also estimating their spatial gradients. Because the free-surface condition allows to express vertical derivatives in terms of horizontal derivatives, the full gradient tensor and, hence, curl and divergence of the wavefield can be computed. In total, three particle velocity components, three rotational components, and divergence, result seven-component (7C) seismic data. Combined particle velocity and gradient data can be used to isolate the incident P- or S-waves at the land surface or the sea bottom using filtering techniques based on the elastodynamic representation theorem. Alternatively, as only S-waves exhibit rotational motion, rotational measurements can directly be used to identify S-waves. We discuss the derivations of the gradient-based filters as well as their application to synthetic and field data, demonstrating that rotational data can be of particular interest to S-wave reflection and P-to-S-wave conversion imaging. The concept of array-derived gradient estimation can be extended to source arrays as well. Therefore, source arrays allow us to emulate rotational (curl) and dilatational (divergence) sources. Combined with 7C

Massless and massive quanta resulting from a mediumlike metric tensor

International Nuclear Information System (INIS)

Soln, J.

1985-01-01

A simple model of the ''primordial'' scalar field theory is presented in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less than c. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the ''spontaneous'' splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle. (author)

Least squares inversion of Stokes profiles in the presence of velocity gradients

International Nuclear Information System (INIS)

Skumanich, A.; Rees, D.E.; Lites, B.W.; Sacramento Peak Observatory, Sunspot, NM)

1985-01-01

The Auer, Heasley and House Stokes inversion procedure in use at High Altitude Observatory is based on the analytic solution of the equation of transfer for polarized light where the representation of the thermodynamic and magnetic structure of the atmosphere is assumed to have a high degree of invariance, namely, a Milne-Eddington (ME) structure with a constant magnetic field. In the presence of invariance breaking gradients the resultant Stokes profiles are represented only approximately, if at all, by analytic forms. The accuracy of the inversion parameters and their significance as measures of actual structure are explored for the ME and the Landman-Finn sunspot models under the effects of velocity gradients. The resulting field parameters are good to a few percent and prove to be insensitive to the errors committed by the use of a ME-representation, but the resulting ME parameters yield a less precise measure of thermal structure

Primordial vorticity and gradient expansion

CERN Document Server

Giovannini, Massimo

2012-01-01

The evolution equations of the vorticities of the electrons, ions and photons in a pre-decoupling plasma are derived, in a fully inhomogeneous geometry, by combining the general relativistic gradient expansion and the drift approximation within the Adler-Misner-Deser decomposition. The vorticity transfer between the different species is discussed in this novel framework and a set of general conservation laws, connecting the vorticities of the three-component plasma with the magnetic field intensity, is derived. After demonstrating that a source of large-scale vorticity resides in the spatial gradients of the geometry and of the electromagnetic sources, the total vorticity is estimated to lowest order in the spatial gradients and by enforcing the validity of the momentum constraint. By acknowledging the current bounds on the tensor to scalar ratio in the (minimal) tensor extension of the $\\Lambda$CDM paradigm the maximal comoving magnetic field induced by the total vorticity turns out to be, at most, of the or...

Structure of the Einstein tensor for class-1 embedded space time

Energy Technology Data Exchange (ETDEWEB)

Krause, J [Universidad Central de Venezuela, Caracas

1976-04-11

Continuing previous work, some features of the flat embedding theory of class-1 curved space-time are further discussed. In the two-metric formalism provided by the embedding approach the Gauss tensor obtains as the flat-covariant gradient of a fundamental vector potential. The Einstein tensor is then examined in terms of the Gauss tensor. It is proved that the Einstein tensor is divergence free in flat space-time, i.e. a true Lorentz-covariant conservation law for the Einstein tensor is shown to hold. The form of the Einstein tensor in flat space-time also appears as a canonical energy-momentum tensor of the vector potential. The corresponding Lagrangian density, however, does not provide us with a set of field equations for the fundamental vector potential; indeed, the Euler-Lagrange ''equations'' collapse to a useless identity, while the Lagrangian density has the form of a flat divergence.

Joint eigenvector estimation from mutually anisotropic tensors improves susceptibility tensor imaging of the brain, kidney, and heart.

Science.gov (United States)

Dibb, Russell; Liu, Chunlei

2017-06-01

To develop a susceptibility-based MRI technique for probing microstructure and fiber architecture of magnetically anisotropic tissues-such as central nervous system white matter, renal tubules, and myocardial fibers-in three dimensions using susceptibility tensor imaging (STI) tools. STI can probe tissue microstructure, but is limited by reconstruction artifacts because of absent phase information outside the tissue and noise. STI accuracy may be improved by estimating a joint eigenvector from mutually anisotropic susceptibility and relaxation tensors. Gradient-recalled echo image data were simulated using a numerical phantom and acquired from the ex vivo mouse brain, kidney, and heart. Susceptibility tensor data were reconstructed using STI, regularized STI, and the proposed algorithm of mutually anisotropic and joint eigenvector STI (MAJESTI). Fiber map and tractography results from each technique were compared with diffusion tensor data. MAJESTI reduced the estimated susceptibility tensor orientation error by 30% in the phantom, 36% in brain white matter, 40% in the inner medulla of the kidney, and 45% in myocardium. This improved the continuity and consistency of susceptibility-based fiber tractography in each tissue. MAJESTI estimation of the susceptibility tensors yields lower orientation errors for susceptibility-based fiber mapping and tractography in the intact brain, kidney, and heart. Magn Reson Med 77:2331-2346, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Tensor calculus and analytical dynamics a classical introduction to holonomic and nonholonomic tensor calculus ; and its principal applications to the Lagrangean dynamics of constrained mechanical systems : for engineers, physicists, and mathematicians

CERN Document Server

Papastavridis, John G

1999-01-01

Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints.

Comparative study of the temperature and velocity gradients for the interphases obtained during directional solidification of Al-Cu alloys

International Nuclear Information System (INIS)

Ares, Alicia Esther; Gueijman, Sergio Fabian; Schvezov, Carlos E

2004-01-01

Previous studies determined that in directionally solidified lead-tin alloys, the position in which the transition occurs from columnar to equiaxial structure depending on the distribution of temperatures in the system, occurs when a minimum and critical thermal gradient value is attained in the liquid before the interphase that separates the (liquid) phase from the (solid + liquid) phase and this critical gradient value is independent from the solute concentration, natural convection, degree of overheating, the mold geometry and the number of columnar and equiaxial grains that form. The study now includes aluminum-copper alloys, for which the temperature gradient test values in the liquid before the (liquid)/(solid + liquid) interphase and the speeds of the (liquid)/(solid+liquid)/(solid) interphases are determined. The values of interphase gradients and velocities contrast with the values predicted by the Hunt model for the same alloy system. The velocities of the interphases are also compared with those calculated with the Lipton equation and used in the Wang and Beckermann model for dendritic equiaxial growth. The results are compared with those obtained previously in the lead-tin system (CW)

All-at-once Optimization for Coupled Matrix and Tensor Factorizations

DEFF Research Database (Denmark)

Evrim, Acar Ataman; Kolda, Tamara G.; Dunlavy, Daniel M.

2011-01-01

.g., the person by person social network matrix or the restaurant by category matrix, and higher-order tensors, e.g., the "ratings" tensor of the form restaurant by meal by person. In this paper, we are particularly interested in fusing data sets with the goal of capturing their underlying latent structures. We...... formulate this problem as a coupled matrix and tensor factorization (CMTF) problem where heterogeneous data sets are modeled by fitting outer-product models to higher-order tensors and matrices in a coupled manner. Unlike traditional approaches solving this problem using alternating algorithms, we propose...... an all-at-once optimization approach called CMTF-OPT (CMTF-OPTimization), which is a gradient-based optimization approach for joint analysis of matrices and higher-order tensors. We also extend the algorithm to handle coupled incomplete data sets. Using numerical experiments, we demonstrate...

The effects of noise over the complete space of diffusion tensor shape.

Science.gov (United States)

Gahm, Jin Kyu; Kindlmann, Gordon; Ennis, Daniel B

2014-01-01

Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants. Copyright © 2013 Elsevier B.V. All rights reserved.

The influence of velocity gradient on properties and filterability of suspension formed during water treatment

Czech Academy of Sciences Publication Activity Database

Bubáková, Petra; Pivokonský, Martin

2012-01-01

Roč. 92, May (2012), s. 161-167 ISSN 1383-5866. [European Conference on Fluid-Particle Separation (FPS 2010). Lyon, 05.10.2010-07.10.2010] R&D Projects: GA ČR GAP105/11/0247 Institutional research plan: CEZ:AV0Z20600510 Keywords : aggregation * fractal dimension * filtration * particle size distribution * velocity gradient Subject RIV: BK - Fluid Dynamics Impact factor: 2.894, year: 2012

Monte Carlo Volcano Seismic Moment Tensors

Science.gov (United States)

Waite, G. P.; Brill, K. A.; Lanza, F.

2015-12-01

Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.

Velocity ratio predicts outcomes in patients with low gradient severe aortic stenosis and preserved EF

DEFF Research Database (Denmark)

Jander, Nikolaus; Hochholzer, Willibald; Kaufmann, Beat A

2014-01-01

OBJECTIVE: To evaluate the usefulness of velocity ratio (VR) in patients with low gradient severe aortic stenosis (LGSAS) and preserved EF. BACKGROUND: LGSAS despite preserved EF represents a clinically challenging entity. Reliance on mean pressure gradient (MPG) may underestimate stenosis severity...... for severe stenosis. We hypothesised that VR may have conceptual advantages over MPG and AVA, predict clinical outcomes and thereby be useful in the management of patients with LGSAS. METHODS: Patients from the prospective Simvastatin and Ezetimibe in Aortic Stenosis (SEAS) study with an AVA...≤40 mm Hg and EF≥55% and asymptomatic at baseline were stratified according to VR with a cut-off value of 0.25. Outcomes were evaluated according to aortic valve-related events and cardiovascular death. RESULTS: Of 435 patients with LGSAS, 197 (45%) had VRVR≥0...

Velocity Gradient Across the San Andreas Fault and Changes in Slip Behavior as Outlined by Full non Linear Tomography

Science.gov (United States)

Chiarabba, C.; Giacomuzzi, G.; Piana Agostinetti, N.

2017-12-01

The San Andreas Fault (SAF) near Parkfield is the best known fault section which exhibit a clear transition in slip behavior from stable to unstable. Intensive monitoring and decades of studies permit to identify details of these processes with a good definition of fault structure and subsurface models. Tomographic models computed so far revealed the existence of large velocity contrasts, yielding physical insight on fault rheology. In this study, we applied a recently developed full non-linear tomography method to compute Vp and Vs models which focus on the section of the fault that exhibit fault slip transition. The new tomographic code allows not to impose a vertical seismic discontinuity at the fault position, as routinely done in linearized codes. Any lateral velocity contrast found is directly dictated by the data themselves and not imposed by subjective choices. The use of the same dataset of previous tomographic studies allows a proper comparison of results. We use a total of 861 earthquakes, 72 blasts and 82 shots and the overall arrival time dataset consists of 43948 P- and 29158 S-wave arrival times, accurately selected to take care of seismic anisotropy. Computed Vp and Vp/Vs models, which by-pass the main problems related to linarized LET algorithms, excellently match independent available constraints and show crustal heterogeneities with a high resolution. The high resolution obtained in the fault surroundings permits to infer lateral changes of Vp and Vp/Vs across the fault (velocity gradient). We observe that stable and unstable sliding sections of the SAF have different velocity gradients, small and negligible in the stable slip segment, but larger than 15 % in the unstable slip segment. Our results suggest that Vp and Vp/Vs gradients across the fault control fault rheology and the attitude of fault slip behavior.

Susceptibility Tensor Imaging (STI) of the Brain

Science.gov (United States)

Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu

2016-01-01

Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169

STRUCTURE TENSOR IMAGE FILTERING USING RIEMANNIAN L1 AND L∞ CENTER-OF-MASS

Directory of Open Access Journals (Sweden)

Jesus Angulo

2014-06-01

Full Text Available Structure tensor images are obtained by a Gaussian smoothing of the dyadic product of gradient image. These images give at each pixel a n×n symmetric positive definite matrix SPD(n, representing the local orientation and the edge information. Processing such images requires appropriate algorithms working on the Riemannian manifold on the SPD(n matrices. This contribution deals with structure tensor image filtering based on Lp geometric averaging. In particular, L1 center-of-mass (Riemannian median or Fermat-Weber point and L∞ center-of-mass (Riemannian circumcenter can be obtained for structure tensors using recently proposed algorithms. Our contribution in this paper is to study the interest of L1 and L∞ Riemannian estimators for structure tensor image processing. In particular, we compare both for two image analysis tasks: (i structure tensor image denoising; (ii anomaly detection in structure tensor images.

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2018-01-01

textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2017-01-01

textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in

Tensor rank is not multiplicative under the tensor product

OpenAIRE

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2017-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2018-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2016-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new

Tensor rank is not multiplicative under the tensor product

DEFF Research Database (Denmark)

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2018-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...

An introduction to tensor calculus, relativity and cosmology /3rd edition/

Science.gov (United States)

Lawden, D. F.

This textbook introduction to the principles of special relativity proceeds within the context of cartesian tensors. Newton's laws of motion are reviewed, as are the Lorentz transformations, Minkowski space-time, and the Fitzgerald contraction. Orthogonal transformations are described, and invariants, gradients, tensor derivatives, contraction, scalar products, divergence, pseudotensors, vector products, and curl are defined. Special relativity mechanics are explored in terms of mass, momentum, the force vector, the Lorentz transformation equations for force, calculations for photons and neutrinos, the development of the Lagrange and Hamilton equations, and the energy-momentum tensor. Electrodynamics is investigated, together with general tensor calculus and Riemmanian space. The General Theory of Relativity is presented, along with applications to astrophysical phenomena such as black holes and gravitational waves. Finally, analytical discussions of cosmological problems are reviewed, particularly Einstein, de Sitter, and Friedmann universes, redshifts, event horizons, and the redshift.

Motion Detection in Ultrasound Image-Sequences Using Tensor Voting

Science.gov (United States)

Inba, Masafumi; Yanagida, Hirotaka; Tamura, Yasutaka

2008-05-01

Motion detection in ultrasound image sequences using tensor voting is described. We have been developing an ultrasound imaging system adopting a combination of coded excitation and synthetic aperture focusing techniques. In our method, frame rate of the system at distance of 150 mm reaches 5000 frame/s. Sparse array and short duration coded ultrasound signals are used for high-speed data acquisition. However, many artifacts appear in the reconstructed image sequences because of the incompleteness of the transmitted code. To reduce the artifacts, we have examined the application of tensor voting to the imaging method which adopts both coded excitation and synthetic aperture techniques. In this study, the basis of applying tensor voting and the motion detection method to ultrasound images is derived. It was confirmed that velocity detection and feature enhancement are possible using tensor voting in the time and space of simulated ultrasound three-dimensional image sequences.

Peak negative myocardial velocity gradient in early diastole as a noninvasive indicator of left ventricular diastolic function: comparison with transmitral flow velocity indices.

Science.gov (United States)

Shimizu, Y; Uematsu, M; Shimizu, H; Nakamura, K; Yamagishi, M; Miyatake, K

1998-11-01

We sought to assess the clinical significance of peak negative myocardial velocity gradient (MVG) in early diastole as a noninvasive indicator of left ventricular (LV) diastolic function. Peak systolic MVG has been shown useful for the quantitative assessment of regional wall motion abnormalities, but limited data exist regarding the diastolic MVG as an indicator of LV diastolic function. Peak negative MVG was obtained from M-mode tissue Doppler imaging (TDI) in 43 subjects with or without impairment of systolic and diastolic performance: 12 normal subjects, 12 patients with hypertensive heart disease (HHD) with normal systolic performance and 19 patients with dilated cardiomyopathy (DCM), and was compared with standard Doppler transmitral flow velocity indices. In a subgroup of 30 patients, effects of preload increase on these indices were assessed by performing passive leg lifting. In an additional 11 patients with congestive heart failure at the initial examination, the measurements were repeated after 26+/-16 days of volume-reducing therapy. Peak negative MVG was significantly depressed both in HHD (-3.9+/-1.3/s, p indices failed to distinguish DCM from normal due to the pseudonormalization. Transmitral flow velocity indices were significantly altered (peak early/late diastolic filling velocity [E/A]=1.1+/-0.5 to 1.5+/-0.7, p indicator of LV diastolic function that is less affected by preload alterations than the transmitral flow velocity indices, and thereby could be used for the follow-up of patients with nonischemic LV dysfunction presenting congestive heart failure.

Tensor Factorization for Low-Rank Tensor Completion.

Science.gov (United States)

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

Impact of Gradient Number and Voxel Size on Diffusion Tensor Imaging Tractography for Resective Brain Surgery.

Science.gov (United States)

Hoefnagels, Friso W A; de Witt Hamer, Philip C; Pouwels, Petra J W; Barkhof, Frederik; Vandertop, W Peter

2017-09-01

To explore quantitatively and qualitatively how the number of gradient directions (NGD) and spatial resolution (SR) affect diffusion tensor imaging (DTI) tractography in patients planned for brain tumor surgery, using routine clinical magnetic resonance imaging protocols. Of 67 patients with intracerebral lesions who had 2 different DTI scans, 3 DTI series were reconstructed to compare the effects of NGD and SR. Tractographies for 4 clinically relevant tracts (corticospinal tract, superior longitudinal fasciculus, optic radiation, and inferior fronto-occipital fasciculus) were constructed with a probabilistic tracking algorithm and automated region of interest placement and compared for 3 quantitative measurements: tract volume, median fiber density, and mean fractional anisotropy, using linear mixed-effects models. The mean tractography volume and intersubject reliability were visually compared across scanning protocols, to assess the clinical relevance of the quantitative differences. Both NGD and SR significantly influenced tract volume, median fiber density, and mean fractional anisotropy, but not to the same extent. In particular, higher NGD increased tract volume and median fiber density. More importantly, these effects further increased when tracts were affected by disease. The effects were tract specific, but not dependent on threshold. The superior longitudinal fasciculus and inferior fronto-occipital fasciculus showed the most significant differences. Qualitative assessment showed larger tract volumes given a fixed confidence level, and better intersubject reliability for the higher NGD protocol. SR in the range we considered seemed less relevant than NGD. This study indicates that, under time constraints of clinical imaging, a higher number of diffusion gradients is more important than spatial resolution for superior DTI probabilistic tractography in patients undergoing brain tumor surgery. Copyright © 2017 Elsevier Inc. All rights reserved.

Effect of increasing diffusion gradient direction number on diffusion tensor imaging fiber tracking in the human brain

International Nuclear Information System (INIS)

Yao, Xu Fang; Liang, Bie Bei; Xia, Tian; Huang, Qin Ming; Zhuang, Song Lin; Yu, Tong Gang

2015-01-01

To assess the effects of varying the number of diffusion gradient directions (NDGDs) on diffusion tensor fiber tracking (FT) in human brain white matter using tract characteristics. Twelve normal volunteers underwent diffusion tensor imaging (DTI) scanning with NDGDs of 6, 11, 15, 21, and 31 orientations. Three fiber tract groups, including the splenium of the corpus callosum (CC), the entire CC, and the full brain tract, were reconstructed by deterministic DTI-FT. Tract architecture was first qualitatively evaluated by visual observation. Six quantitative tract characteristics, including the number of fibers (NF), average length (AL), fractional anisotropy (FA), relative anisotropy (RA), mean diffusivity (MD), and volume ratio (VR) were measured for the splenium of the CC at the tract branch level, for the entire CC at tract level, and for the full brain tract at the whole brain level. Visual results and those of NF, AL, FA, RA, MD, and VR were compared among the five different NDGDs. The DTI-FT with NDGD of 11, 15, 21, and 31 orientations gave better tracking results compared with NDGD of 6 after the visual evaluation. NF, FA, RA, MD, and VR values with NDGD of six were significantly greater (smallest p = 0.001 to largest p = 0.042) than those with four other NDGDs (11, 15, 21, or 31 orientations), whereas AL measured with NDGD of six was significantly smaller (smallest p = 0.001 to largest p = 0.041) than with four other NDGDs (11, 15, 21, or 31 orientations). No significant differences were observed in the results among the four NDGD groups of 11, 15, 21, and 31 directions (smallest p = 0.059 to largest p = 1.000). The main fiber tracts were detected with NDGD of six orientations; however, the use of larger NDGD (> or = 11 orientations) could provide improved tract characteristics at the expense of longer scanning time.

Effect of increasing diffusion gradient direction number on diffusion tensor imaging fiber tracking in the human brain

Energy Technology Data Exchange (ETDEWEB)

Yao, Xu Fang; Liang, Bie Bei; Xia, Tian; Huang, Qin Ming; Zhuang, Song Lin [School of Optical-Electrical and Computer Engineering, Shanghai Medical Instrument College, University of Shanghai for Science and Technology, Shanghai (China); Yu, Tong Gang [Dept. of Radiology, Huashan Hospital, Fudan University, Shanghai (China)

2015-04-15

To assess the effects of varying the number of diffusion gradient directions (NDGDs) on diffusion tensor fiber tracking (FT) in human brain white matter using tract characteristics. Twelve normal volunteers underwent diffusion tensor imaging (DTI) scanning with NDGDs of 6, 11, 15, 21, and 31 orientations. Three fiber tract groups, including the splenium of the corpus callosum (CC), the entire CC, and the full brain tract, were reconstructed by deterministic DTI-FT. Tract architecture was first qualitatively evaluated by visual observation. Six quantitative tract characteristics, including the number of fibers (NF), average length (AL), fractional anisotropy (FA), relative anisotropy (RA), mean diffusivity (MD), and volume ratio (VR) were measured for the splenium of the CC at the tract branch level, for the entire CC at tract level, and for the full brain tract at the whole brain level. Visual results and those of NF, AL, FA, RA, MD, and VR were compared among the five different NDGDs. The DTI-FT with NDGD of 11, 15, 21, and 31 orientations gave better tracking results compared with NDGD of 6 after the visual evaluation. NF, FA, RA, MD, and VR values with NDGD of six were significantly greater (smallest p = 0.001 to largest p = 0.042) than those with four other NDGDs (11, 15, 21, or 31 orientations), whereas AL measured with NDGD of six was significantly smaller (smallest p = 0.001 to largest p = 0.041) than with four other NDGDs (11, 15, 21, or 31 orientations). No significant differences were observed in the results among the four NDGD groups of 11, 15, 21, and 31 directions (smallest p = 0.059 to largest p = 1.000). The main fiber tracts were detected with NDGD of six orientations; however, the use of larger NDGD (> or = 11 orientations) could provide improved tract characteristics at the expense of longer scanning time.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

Science.gov (United States)

Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L

2014-03-01

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.

Low Multilinear Rank Approximation of Tensors and Application in Missing Traffic Data

Directory of Open Access Journals (Sweden)

Huachun Tan

2014-02-01

Full Text Available The problem of missing data in multiway arrays (i.e., tensors is common in many fields such as bibliographic data analysis, image processing, and computer vision. We consider the problems of approximating a tensor by another tensor with low multilinear rank in the presence of missing data and possibly reconstructing it (i.e., tensor completion. In this paper, we propose a weighted Tucker model which models only the known elements for capturing the latent structure of the data and reconstructing the missing elements. To treat the nonuniqueness of the proposed weighted Tucker model, a novel gradient descent algorithm based on a Grassmann manifold, which is termed Tucker weighted optimization (Tucker-Wopt, is proposed for guaranteeing the global convergence to a local minimum of the problem. Based on extensive experiments, Tucker-Wopt is shown to successfully reconstruct tensors with noise and up to 95% missing data. Furthermore, the experiments on traffic flow volume data demonstrate the usefulness of our algorithm on real-world application.

Susceptibility tensor imaging (STI) of the brain.

Science.gov (United States)

Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu

2017-04-01

Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Stress tensor of a quark moving through N=4 thermal plasma

International Nuclear Information System (INIS)

Friess, Joshua J.; Gubser, Steven S.; Michalogiorgakis, Georgios; Pufu, Silviu S.

2007-01-01

We develop the linear equations that describe graviton perturbations of AdS 5 -Schwarzschild generated by a string trailing behind an external quark moving with constant velocity. Solving these equations allows us to evaluate the stress tensor in the boundary gauge theory. Components of the stress tensor exhibit directional structures in Fourier space at both large and small momenta. We comment on the possible relevance of our results to relativistic heavy-ion collisions

Simplification and Validation of a Spectral-Tensor Model for Turbulence Including Atmospheric Stability

Science.gov (United States)

Chougule, Abhijit; Mann, Jakob; Kelly, Mark; Larsen, Gunner C.

2018-02-01

A spectral-tensor model of non-neutral, atmospheric-boundary-layer turbulence is evaluated using Eulerian statistics from single-point measurements of the wind speed and temperature at heights up to 100 m, assuming constant vertical gradients of mean wind speed and temperature. The model has been previously described in terms of the dissipation rate ɛ , the length scale of energy-containing eddies L , a turbulence anisotropy parameter Γ, the Richardson number Ri, and the normalized rate of destruction of temperature variance η _θ ≡ ɛ _θ /ɛ . Here, the latter two parameters are collapsed into a single atmospheric stability parameter z / L using Monin-Obukhov similarity theory, where z is the height above the Earth's surface, and L is the Obukhov length corresponding to Ri,η _θ. Model outputs of the one-dimensional velocity spectra, as well as cospectra of the streamwise and/or vertical velocity components, and/or temperature, and cross-spectra for the spatial separation of all three velocity components and temperature, are compared with measurements. As a function of the four model parameters, spectra and cospectra are reproduced quite well, but horizontal temperature fluxes are slightly underestimated in stable conditions. In moderately unstable stratification, our model reproduces spectra only up to a scale ˜ 1 km. The model also overestimates coherences for vertical separations, but is less severe in unstable than in stable cases.

The 2011 Tohoku-oki Earthquake related to a large velocity gradient within the Pacific plate

Science.gov (United States)

Matsubara, Makoto; Obara, Kazushige

2015-04-01

We conduct seismic tomography using arrival time data picked by the high sensitivity seismograph network (Hi-net) operated by National Research Institute for Earth Science and Disaster Prevention (NIED). We used earthquakes off the coast outside the seismic network around the source region of the 2011 Tohoku-oki Earthquake with the centroid depth estimated from moment tensor inversion by NIED F-net (broadband seismograph network) as well as earthquakes within the seismic network determined by Hi-net. The target region, 20-48N and 120-148E, covers the Japanese Islands from Hokkaido to Okinawa. A total of manually picked 4,622,346 P-wave and 3,062,846 S-wave arrival times for 100,733 earthquakes recorded at 1,212 stations from October 2000 to August 2009 is available for use in the tomographic method. In the final iteration, we estimate the P-wave slowness at 458,234 nodes and the S-wave slowness at 347,037 nodes. The inversion reduces the root mean square of the P-wave traveltime residual from 0.455 s to 0.187 s and that of the S-wave data from 0.692 s to 0.228 s after eight iterations (Matsubara and Obara, 2011). Centroid depths are determined using a Green's function approach (Okada et al., 2004) such as in NIED F-net. For the events distant from the seismic network, the centroid depth is more reliable than that determined by NIED Hi-net, since there are no stations above the hypocenter. We determine the upper boundary of the Pacific plate based on the velocity structure and earthquake hypocentral distribution. The upper boundary of the low-velocity (low-V) oceanic crust corresponds to the plate boundary where thrust earthquakes are expected to occur. Where we do not observe low-V oceanic crust, we determine the upper boundary of the upper layer of the double seismic zone within high-V Pacific plate. We assume the depth at the Japan Trench as 7 km. We can investigate the velocity structure within the Pacific plate such as 10 km beneath the plate boundary since the

Magnetic resonance temporal diffusion tensor spectroscopy of disordered anisotropic tissue

DEFF Research Database (Denmark)

Nielsen, Jonathan Scharff; Dyrby, Tim Bjørn; Lundell, Henrik

2018-01-01

of the oscillating gradient spin echo (OGSE) experiment, giving a basic contrast mechanism closely linked to both the temporal diffusion spectrum and the compartment anisotropy. We demonstrate our new method on post mortem brain tissue and show that we retrieve the correct temporal diffusion tensor spectrum...

A moment-tensor catalog for intermediate magnitude earthquakes in Mexico

Science.gov (United States)

Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala; Martínez-Peláez, Liliana; Franco, Sara; Iglesias Mendoza, Arturo

2016-04-01

Located among five tectonic plates, Mexico is one of the world's most seismically active regions. The earthquake focal mechanisms provide important information on the active tectonics. A widespread technique for estimating the earthquake magnitud and focal mechanism is the inversion for the moment tensor, obtained by minimizing a misfit function that estimates the difference between synthetic and observed seismograms. An important element in the estimation of the moment tensor is an appropriate velocity model, which allows for the calculation of accurate Green's Functions so that the differences between observed and synthetics seismograms are due to the source of the earthquake rather than the velocity model. However, calculating accurate synthetic seismograms gets progressively more difficult as the magnitude of the earthquakes decreases. Large earthquakes (M>5.0) excite waves of longer periods that interact weakly with lateral heterogeneities in the crust. For these events, using 1D velocity models to compute Greens functions works well and they are well characterized by seismic moment tensors reported in global catalogs (eg. USGS fast moment tensor solutions and GCMT). The opposite occurs for small and intermediate sized events, where the relatively shorter periods excited interact strongly with lateral heterogeneities in the crust and upper mantle. To accurately model the Green's functions for the smaller events in a large heterogeneous area, requires 3D or regionalized 1D models. To obtain a rapid estimate of earthquake magnitude, the National Seismological Survey in Mexico (Servicio Sismológico Nacional, SSN) automatically calculates seismic moment tensors for events in the Mexican Territory (Franco et al., 2002; Nolasco-Carteño, 2006). However, for intermediate-magnitude and small earthquakes the signal-to-noise ratio could is low for many of the seismic stations, and without careful selection and filtering of the data, obtaining a stable focal mechanism

Concepts and procedures required for successful reduction of tensor magnetic gradiometer data obtained from an unexploded ordnance detection demonstration at Yuma Proving Grounds, Arizona

Science.gov (United States)

Bracken, Robert E.; Brown, Philip J.

2006-01-01

On March 12, 2003, data were gathered at Yuma Proving Grounds, in Arizona, using a Tensor Magnetic Gradiometer System (TMGS). This report shows how these data were processed and explains concepts required for successful TMGS data reduction. Important concepts discussed include extreme attitudinal sensitivity of vector measurements, low attitudinal sensitivity of gradient measurements, leakage of the common-mode field into gradient measurements, consequences of thermal drift, and effects of field curvature. Spatial-data collection procedures and a spin-calibration method are addressed. Discussions of data-reduction procedures include tracking of axial data by mathematically matching transfer functions among the axes, derivation and application of calibration coefficients, calculation of sensor-pair gradients, thermal-drift corrections, and gradient collocation. For presentation, the magnetic tensor at each data station is converted to a scalar quantity, the I2 tensor invariant, which is easily found by calculating the determinant of the tensor. At important processing junctures, the determinants for all stations in the mapped area are shown in shaded relief map-view. Final processed results are compared to a mathematical model to show the validity of the assumptions made during processing and the reasonableness of the ultimate answer obtained.

Tensor gauge condition and tensor field decomposition

Science.gov (United States)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

Tensor spherical harmonics and tensor multipoles. II. Minkowski space

International Nuclear Information System (INIS)

Daumens, M.; Minnaert, P.

1976-01-01

The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation

Spectral edge: gradient-preserving spectral mapping for image fusion.

Science.gov (United States)

Connah, David; Drew, Mark S; Finlayson, Graham D

2015-12-01

This paper describes a novel approach to image fusion for color display. Our goal is to generate an output image whose gradient matches that of the input as closely as possible. We achieve this using a constrained contrast mapping paradigm in the gradient domain, where the structure tensor of a high-dimensional gradient representation is mapped exactly to that of a low-dimensional gradient field which is then reintegrated to form an output. Constraints on output colors are provided by an initial RGB rendering. Initially, we motivate our solution with a simple "ansatz" (educated guess) for projecting higher-D contrast onto color gradients, which we expand to a more rigorous theorem to incorporate color constraints. The solution to these constrained optimizations is closed-form, allowing for simple and hence fast and efficient algorithms. The approach can map any N-D image data to any M-D output and can be used in a variety of applications using the same basic algorithm. In this paper, we focus on the problem of mapping N-D inputs to 3D color outputs. We present results in five applications: hyperspectral remote sensing, fusion of color and near-infrared or clear-filter images, multilighting imaging, dark flash, and color visualization of magnetic resonance imaging diffusion-tensor imaging.

Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

Science.gov (United States)

Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.

2015-01-01

Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085

Visual Tracking via Feature Tensor Multimanifold Discriminate Analysis

Directory of Open Access Journals (Sweden)

Ting-quan Deng

2014-01-01

Full Text Available In the visual tracking scenarios, if there are multiple objects, due to the interference of similar objects, tracking may fail in the progress of occlusion to separation. To address this problem, this paper proposed a visual tracking algorithm with discrimination through multimanifold learning. Color-gradient-based feature tensor was used to describe object appearance for accommodation of partial occlusion. A prior multimanifold tensor dataset is established through the template matching tracking algorithm. For the purpose of discrimination, tensor distance was defined to determine the intramanifold and intermanifold neighborhood relationship in multimanifold space. Then multimanifold discriminate analysis was employed to construct multilinear projection matrices of submanifolds. Finally, object states were obtained by combining with sequence inference. Meanwhile, the multimanifold dataset and manifold learning embedded projection should be updated online. Experiments were conducted on two real visual surveillance sequences to evaluate the proposed algorithm with three state-of-the-art tracking methods qualitatively and quantitatively. Experimental results show that the proposed algorithm can achieve effective and robust effect in multi-similar-object mutual occlusion scenarios.

Alignment of stress, mean wind, and vertical gradient of the velocity vector

DEFF Research Database (Denmark)

Berg, Jacob; Mann, Jakob; Patton, E.G.

2012-01-01

In many applications in the atmospheric surface layer the turbulent-viscosity hypothesis is applied, i.e. the stress vector can be described through the vertical gradient of velocity. In the atmospheric surface layer, where the Coriolis force and baroclinic effects are considered negligible......, this is supposedly a good approximation. High resolution large-eddy simulation (LES) data show that it is indeed the case. Through analysis of WindCube lidar measurements accompanied by sonic measurements we show that this is, on the other hand, rarely the case in the real atmosphere. This might indicate that large...... of atmospheric boundary layer modeling. The measurements are from the Danish wind turbine test sites at Høvsøre. With theWindCube lidar we are able to reach heights of 250 meters and hence capture the entire atmospheric surface layer both in terms of wind speed and the direction of the mean stress vector....

The Role of the Velocity Gradient in Laminar Convective Heat Transfer through a Tube with a Uniform Wall Heat Flux

Science.gov (United States)

Wang, Liang-Bi; Zhang, Qiang; Li, Xiao-Xia

2009-01-01

This paper aims to contribute to a better understanding of convective heat transfer. For this purpose, the reason why thermal diffusivity should be placed before the Laplacian operator of the heat flux, and the role of the velocity gradient in convective heat transfer are analysed. The background to these analyses is that, when the energy…

Thermodynamical inequivalence of quantum stress-energy and spin tensors

International Nuclear Information System (INIS)

Becattini, F.; Tinti, L.

2011-01-01

It is shown that different couples of stress-energy and spin tensors of quantum-relativistic fields, which would be otherwise equivalent, are in fact inequivalent if the second law of thermodynamics is taken into account. The proof of the inequivalence is based on the analysis of a macroscopic system at full thermodynamical equilibrium with a macroscopic total angular momentum and a specific instance is given for the free Dirac field, for which we show that the canonical and Belinfante stress-energy tensors are not equivalent. For this particular case, we show that the difference between the predicted angular momentum densities for a rotating system at full thermodynamical equilibrium is a quantum effect, persisting in the nonrelativistic limit, corresponding to a polarization of particles of the order of (ℎ/2π)ω/KT (ω being the angular velocity) and could in principle be measured experimentally. This result implies that specific stress-energy and spin tensors are physically meaningful even in the absence of gravitational coupling and raises the issue of finding the thermodynamically right (or the right class of) tensors. We argue that the maximization of the thermodynamic potential theoretically allows us to discriminate between two different couples, yet for the present we are unable to provide a theoretical method to single out the best couple of tensors in a given quantum field theory. The existence of a nonvanishing spin tensor would have major consequences in hydrodynamics, gravity and cosmology.

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

Science.gov (United States)

Abdoli-Arani, A.; Ramezani-Arani, R.

2012-11-01

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.

Diffusion tensor image registration using hybrid connectivity and tensor features.

Science.gov (United States)

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-07-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.

Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.

Science.gov (United States)

Li, Wei; Liu, Chunlei

2013-10-01

Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.

Killing tensors and conformal Killing tensors from conformal Killing vectors

International Nuclear Information System (INIS)

Rani, Raffaele; Edgar, S Brian; Barnes, Alan

2003-01-01

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors

Tensors for physics

CERN Document Server

Hess, Siegfried

2015-01-01

This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics,  at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to  tensors of any rank, at graduate level.  Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...

Large-N limit of the gradient flow in the 2D O(N) nonlinear sigma model

International Nuclear Information System (INIS)

Makino, Hiroki; Sugino, Fumihiko; Suzuki, Hiroshi

2015-01-01

The gradient flow equation in the 2D O(N) nonlinear sigma model with lattice regularization is solved in the leading order of the 1/N expansion. By using this solution, we analytically compute the thermal expectation value of a lattice energy–momentum tensor defined through the gradient flow. The expectation value reproduces thermodynamic quantities obtained by the standard large-N method. This analysis confirms that the above lattice energy–momentum tensor restores the correct normalization automatically in the continuum limit, in a system with a non-perturbative mass gap

Histogram analysis of noise performance on fractional anisotropy brain MR image with different diffusion gradient numbers

International Nuclear Information System (INIS)

Chang, Yong Min; Kim, Yong Sun; Kang, Duk Sik; Lee, Young Joo; Sohn, Chul Ho; Woo, Seung Koo; Suh, Kyung Jin

2005-01-01

We wished to analyze, qualitatively and quantitatively, the noise performance of fractional anisotropy brain images along with the different diffusion gradient numbers by using the histogram method. Diffusion tensor images were acquired using a 3.0 T MR scanner from ten normal volunteers who had no neurological symptoms. The single-shot spin-echo EPI with a Stejskal-Tanner type diffusion gradient scheme was employed for the diffusion tensor measurement. With a b-valuee of 1000 s/mm 2 , the diffusion tensor images were obtained for 6, 11, 23, 35 and 47 diffusion gradient directions. FA images were generated for each DTI scheme. The histograms were then obtained at selected ROIs for the anatomical structures on the FA image. At the same ROI location, the mean FA value and the standard deviation of the mean FA value were calculated. The quality of the FA image was improved as the number of diffusion gradient directions increased by showing better contrast between the WM and GM. The histogram showed that the variance of FA values was reduced as the number of diffusion gradient directions increased. This histogram analysis was in good agreement with the result obtained using quantitative analysis. The image quality of the FA map was significantly improved as the number of diffusion gradient directions increased. The histogram analysis well demonstrated that the improvement in the FA images resulted from the reduction in the variance of the FA values included in the ROI

An exploration into diffusion tensor imaging in the bovine ocular lens

Directory of Open Access Journals (Sweden)

Ehsan eVaghefi

2013-03-01

Full Text Available We describe our development of the diffusion tensor imaging modality for the bovine ocular lens. Diffusion gradients were added to a spin-echo pulse sequence and the relevant parameters of the sequence were refined to achieve good diffusion weighting in the lens tissue, which demonstrated heterogeneous regions of diffusive signal attenuation. Decay curves for b-value (loosely summarizes the strength of diffusion weighting and TE (determines the amount of MRI-obtained signal were used to estimate apparent diffusion coefficients (ADC and T2 in different lens regions. The ADCs varied by over an order of magnitude and revealed diffusive anisotropy in the lens. Up to 30 diffusion gradient directions, and 8 signal acquisition averages, were applied to lenses in culture in order to improve maps of diffusion tensor eigenvalues, equivalent to ADC, across the lens. From these maps, fractional anisotropy maps were calculated and compared to known spatial distributions of anisotropic molecular fluxes in the lens. This comparison suggested new hypotheses and experiments to quantitatively assess models of circulation in the avascular lens.

The 1/ N Expansion of Tensor Models with Two Symmetric Tensors

Science.gov (United States)

Gurau, Razvan

2018-06-01

It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.

Monitoring of the spatio-temporal change in the interplate coupling at northeastern Japan subduction zone based on the spatial gradients of surface velocity field

Science.gov (United States)

Iinuma, Takeshi

2018-04-01

A monitoring method to grasp the spatio-temporal change in the interplate coupling in a subduction zone based on the spatial gradients of surface displacement rate fields is proposed. I estimated the spatio-temporal change in the interplate coupling along the plate boundary in northeastern (NE) Japan by applying the proposed method to the surface displacement rates based on global positioning system observations. The gradient of the surface velocities is calculated in each swath configured along the direction normal to the Japan Trench for time windows such as 0.5, 1, 2, 3 and 5 yr being shifted by one week during the period of 1997-2016. The gradient of the horizontal velocities is negative and has a large magnitude when the interplate coupling at the shallow part (less than approximately 50 km in depth) beneath the profile is strong, and the sign of the gradient of the vertical velocity is sensitive to the existence of the coupling at the deep part (greater than approximately 50 km in depth). The trench-parallel variation of the spatial gradients of a displacement rate field clearly corresponds to the trench-parallel variation of the amplitude of the interplate coupling on the plate interface, as well as the rupture areas of previous interplate earthquakes. Temporal changes in the trench-parallel variation of the spatial gradient of the displacement rate correspond to the strengthening or weakening of the interplate coupling. We can monitor the temporal change in the interplate coupling state by calculating the spatial gradients of the surface displacement rate field to some extent without performing inversion analyses with applying certain constraint conditions that sometimes cause over- and/or underestimation at areas of limited spatial resolution far from the observation network. The results of the calculation confirm known interplate events in the NE Japan subduction zone, such as the post-seismic slip of the 2003 M8.0 Tokachi-oki and 2005 M7.2 Miyagi

Characteristics of the Residual Stress tensor when filter width is larger than the Ozmidov scale

Science.gov (United States)

de Bragança Alves, Felipe Augusto; de Bruyn Kops, Stephen

2017-11-01

In stratified turbulence, the residual stress tensor is statistically anisotropic unless the smallest resolved length scale is smaller than the Ozmidov scale and the buoyancy Reynolds number is sufficiently high for there to exist a range of scales that is statistically isotropic. We present approximations to the residual stress tensor that are derived analytically. These approximations are evaluated by filtering data from direct numerical simulations of homogeneous stratified turbulence, with unity Prandtl number, resolved on up to 8192 × 8192 × 4096 grid points along with an isotropic homogeneous case resolved on 81923 grid points. It is found that the best possible scaling of the strain rate tensor yields a residual stress tensor (RST) that is less well statistically aligned with the exact RST than a randomly generated tensor. It is also found that, while a scaling of the strain rate tensor can dissipate the right amount of energy, it produces incorrect anisotropic dissipation, removing energy from the wrong components of the velocity vector. We find that a combination of the strain rate tensor and a tensor related to energy redistribution caused by a Newtonian fluid viscous stress yields an excellent tensorial basis for modelling the RST.

Effects of finite electron temperature on gradient drift instabilities in partially magnetized plasmas

Science.gov (United States)

Lakhin, V. P.; Ilgisonis, V. I.; Smolyakov, A. I.; Sorokina, E. A.; Marusov, N. A.

2018-01-01

The gradient-drift instabilities of partially magnetized plasmas in plasma devices with crossed electric and magnetic fields are investigated in the framework of the two-fluid model with finite electron temperature in an inhomogeneous magnetic field. The finite electron Larmor radius (FLR) effects are also included via the gyroviscosity tensor taking into account the magnetic field gradient. This model correctly describes the electron dynamics for k⊥ρe>1 in the sense of Padé approximants (here, k⊥ and ρe are the wavenumber perpendicular to the magnetic field and the electron Larmor radius, respectively). The local dispersion relation for electrostatic plasma perturbations with the frequency in the range between the ion and electron cyclotron frequencies and propagating strictly perpendicular to the magnetic field is derived. The dispersion relation includes the effects of the equilibrium E ×B electron current, finite ion velocity, electron inertia, electron FLR, magnetic field gradients, and Debye length effects. The necessary and sufficient condition of stability is derived, and the stability boundary is found. It is shown that, in general, the electron inertia and FLR effects stabilize the short-wavelength perturbations. In some cases, such effects completely suppress the high-frequency short-wavelength modes so that only the long-wavelength low-frequency (with respect to the lower-hybrid frequency) modes remain unstable.

Investigation of the aerodynamics of an innovative vertical-axis wind turbine

International Nuclear Information System (INIS)

Kludzinska, K; Tesch, K; Doerffer, P

2014-01-01

This paper presents a preliminary three dimensional analysis of the transient aerodynamic phenomena occurring in the innovative modification of classic Savonius wind turbine. An attempt to explain the increased efficiency of the innovative design in comparison with the traditional solution is undertaken. Several vorticity measures such as enstrophy, absolute helicity and the integral of the velocity gradient tensor second invariant are proposed in order to evaluate and compare designs. Discussed criteria are related to the vortex structures and energy dissipation. These structures are generated by the rotor and may affect the efficiency. There are also different vorticity measure taking advantage of eigenvalues of the velocity gradient tensor.

Usefulness of Diffusion Tensor Imaging of White Matter in Alzheimer Disease and Vascular Dementia

International Nuclear Information System (INIS)

Sugihara, S.; Kinoshita, T.; Matsusue, E.; Fujii, S.; Ogawa, T.

2004-01-01

Purpose: To evaluate the usefulness of diffusion tensor imaging in detecting the water diffusivity caused by neuro pathological change in Alzheimer disease and vascular dementia. Material and Methods: Twenty patients with Alzheimer disease, 20 with vascular dementia, and 10 control subjects were examined. Diffusion tensor imaging applied diffusion gradient encoding in six non-collinear directions. Fractional anisotropy values were compared in the genu and splenium of the corpus callosum, and anterior and posterior white matter among the three groups. Results: In the patients with Alzheimer disease, fractional anisotropy values of the posterior white matter were significantly lower than those of controls. In patients with vascular dementia, fractional anisotropy values of the anterior white matter tended to be lower than those of the posterior white matter (P=0.07). Conclusion: Diffusion tensor imaging reflects the neuro pathological changes in the white matter, and may be useful in the diagnosis of Alzheimer disease and vascular dementia. Keywords: Alzheimer disease, .; diffusion tensor imaging, .; vascular dementia

Scalewise invariant analysis of the anisotropic Reynolds stress tensor for atmospheric surface layer and canopy sublayer turbulent flows

Science.gov (United States)

Brugger, Peter; Katul, Gabriel G.; De Roo, Frederik; Kröniger, Konstantin; Rotenberg, Eyal; Rohatyn, Shani; Mauder, Matthias

2018-05-01

Anisotropy in the turbulent stress tensor, which forms the basis of invariant analysis, is conducted using velocity time series measurements collected in the canopy sublayer (CSL) and the atmospheric surface layer (ASL). The goal is to assess how thermal stratification and surface roughness conditions simultaneously distort the scalewise relaxation towards isotropic state from large to small scales when referenced to homogeneous turbulence. To achieve this goal, conventional invariant analysis is extended to allow scalewise information about relaxation to isotropy in physical (instead of Fourier) space to be incorporated. The proposed analysis shows that the CSL is more isotropic than its ASL counterpart at large, intermediate, and small (or inertial) scales irrespective of the thermal stratification. Moreover, the small (or inertial) scale anisotropy is more prevalent in the ASL when compared to the CSL, a finding that cannot be fully explained by the intensity of the mean velocity gradient acting on all scales. Implications to the validity of scalewise Rotta and Lumley models for return to isotropy as well as advantages to using barycentric instead of anisotropy invariant maps for such scalewise analysis are discussed.

Cosmological simulations using a static scalar-tensor theory

Energy Technology Data Exchange (ETDEWEB)

RodrIguez-Meza, M A [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico); Gonzalez-Morales, A X [Departamento Ingenierias, Universidad Iberoamericana, Prol. Paseo de la Reforma 880 Lomas de Santa Fe, Mexico D.F. Mexico (Mexico); Gabbasov, R F [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico); Cervantes-Cota, Jorge L [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico)

2007-11-15

We present {lambda}CDM N-body cosmological simulations in the framework of of a static general scalar-tensor theory of gravity. Due to the influence of the non-minimally coupled scalar field, the gravitational potential is modified by a Yukawa type term, yielding a new structure formation dynamics. We present some preliminary results and, in particular, we compute the density and velocity profiles of the most massive group.

Analysis of magnetic gradients to study gravitropism.

Science.gov (United States)

Hasenstein, Karl H; John, Susan; Scherp, Peter; Povinelli, Daniel; Mopper, Susan

2013-01-01

Gravitropism typically is generated by dense particles that respond to gravity. Experimental stimulation by high-gradient magnetic fields provides a new approach to selectively manipulate the gravisensing system. The movement of corn, wheat, and potato starch grains in suspension was examined with videomicroscopy during parabolic flights that generated 20 to 25 s of weightlessness. During weightlessness, a magnetic gradient was generated by inserting a wedge into a uniform, external magnetic field that caused repulsion of starch grains. The resultant velocity of movement was compared with the velocity of sedimentation under 1 g conditions. The high-gradient magnetic fields repelled the starch grains and generated a force of at least 0.6 g. Different wedge shapes significantly affected starch velocity and directionality of movement. Magnetic gradients are able to move diamagnetic compounds under weightless or microgravity conditions and serve as directional stimulus during seed germination in low-gravity environments. Further work can determine whether gravity sensing is based on force or contact between amyloplasts and statocyte membrane system.

Seismic velocity structure and microearthquake source properties at The Geysers, California, geothermal area

Energy Technology Data Exchange (ETDEWEB)

O' Connell, D.R.

1986-12-01

The method of progressive hypocenter-velocity inversion has been extended to incorporate S-wave arrival time data and to estimate S-wave velocities in addition to P-wave velocities. S-wave data to progressive inversion does not completely eliminate hypocenter-velocity tradeoffs, but they are substantially reduced. Results of a P and S-wave progressive hypocenter-velocity inversion at The Geysers show that the top of the steam reservoir is clearly defined by a large decrease of V/sub p//V/sub s/ at the condensation zone-production zone contact. The depth interval of maximum steam production coincides with minimum observed V/sub p//V/sub s/, and V/sub p//V/sub s/ increses below the shallow primary production zone suggesting that reservoir rock becomes more fluid saturated. The moment tensor inversion method was applied to three microearthquakes at The Geysers. Estimated principal stress orientations were comparable to those estimated using P-wave firstmotions as constraints. Well constrained principal stress orientations were obtained for one event for which the 17 P-first motions could not distinguish between normal-slip and strike-slip mechanisms. The moment tensor estimates of principal stress orientations were obtained using far fewer stations than required for first-motion focal mechanism solutions. The three focal mechanisms obtained here support the hypothesis that focal mechanisms are a function of depth at The Geysers. Progressive inversion as developed here and the moment tensor inversion method provide a complete approach for determining earthquake locations, P and S-wave velocity structure, and earthquake source mechanisms.

The energy–momentum tensor(s in classical gauge theories

Directory of Open Access Journals (Sweden)

Daniel N. Blaschke

2016-11-01

Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.

A software to measure phase-velocity dispersion from ambient-noise correlations and its application to the SNSN data

Science.gov (United States)

Sadeghisorkhani, Hamzeh; Gudmundsson, Ólafur

2017-04-01

Graphical software for phase-velocity dispersion measurements of surface waves in noise-correlation traces, called GSpecDisp, is presented. It is an interactive environment for the measurements and presentation of the results. It measures phase-velocity dispersion curves in the frequency domain based on matching of the real part of the cross-correlation spectrum with the appropriate Bessel function. The inputs are time-domain cross-correlations in SAC format. It can measure two types of phase-velocity dispersion curves; 1- average phase-velocity of a region, and 2- single-pair phase velocity. The average phase-velocity dispersion curve of a region can be used as a reference curve to automatically select the dispersion curves from each single-pair cross-correlation in that region. It also allows the users to manually refine the selections. Therefore, no prior knowledge is needed for an unknown region. GSpecDisp can measure the phase velocity of Rayleigh and Love waves from all possible components of the noise correlation tensor, including diagonal and off-diagonal components of the tensor. First, we explain how GSpecDisp is applied to measure phase-velocity dispersion curves. Then, we demonstrate measurement results on synthetic and real data from the Swedish National Seismic Network (SNSN). We compare the results with two other methods of phase-velocity dispersion measurements. Finally, we compare phase-velocity dispersion curves of Rayleigh waves obtained from different components of the correlation tensor.

Efficient tensor completion for color image and video recovery: Low-rank tensor train

OpenAIRE

Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.

2016-01-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...

Accurate thermoelastic tensor and acoustic velocities of NaCl

Energy Technology Data Exchange (ETDEWEB)

Marcondes, Michel L., E-mail: michel@if.usp.br [Physics Institute, University of Sao Paulo, Sao Paulo, 05508-090 (Brazil); Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455 (United States); Shukla, Gaurav, E-mail: shukla@physics.umn.edu [School of Physics and Astronomy, University of Minnesota, Minneapolis, 55455 (United States); Minnesota supercomputer Institute, University of Minnesota, Minneapolis, 55455 (United States); Silveira, Pedro da [Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455 (United States); Wentzcovitch, Renata M., E-mail: wentz002@umn.edu [Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455 (United States); Minnesota supercomputer Institute, University of Minnesota, Minneapolis, 55455 (United States)

2015-12-15

Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor by using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.

Tensor completion and low-n-rank tensor recovery via convex optimization

International Nuclear Information System (INIS)

Gandy, Silvia; Yamada, Isao; Recht, Benjamin

2011-01-01

In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers

Calibrating a tensor magnetic gradiometer using spin data

Science.gov (United States)

Bracken, Robert E.; Smith, David V.; Brown, Philip J.

2005-01-01

Scalar magnetic data are often acquired to discern characteristics of geologic source materials and buried objects. It is evident that a great deal can be done with scalar data, but there are significant advantages to direct measurement of the magnetic gradient tensor in applications with nearby sources, such as unexploded ordnance (UXO). To explore these advantages, we adapted a prototype tensor magnetic gradiometer system (TMGS) and successfully implemented a data-reduction procedure. One of several critical reduction issues is the precise determination of a large group of calibration coefficients for the sensors and sensor array. To resolve these coefficients, we devised a spin calibration method, after similar methods of calibrating space-based magnetometers (Snare, 2001). The spin calibration procedure consists of three parts: (1) collecting data by slowly revolving the sensor array in the Earth?s magnetic field, (2) deriving a comprehensive set of coefficients from the spin data, and (3) applying the coefficients to the survey data. To show that the TMGS functions as a tensor gradiometer, we conducted an experimental survey that verified that the reduction procedure was effective (Bracken and Brown, in press). Therefore, because it was an integral part of the reduction, it can be concluded that the spin calibration was correctly formulated with acceptably small errors.

Tensor eigenvalues and their applications

CERN Document Server

Qi, Liqun; Chen, Yannan

2018-01-01

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Hydraulic gradients in rock aquifers

International Nuclear Information System (INIS)

Dahlblom, P.

1992-05-01

This report deals with fractured rock as a host for deposits of hazardous waste. In this context the rock, with its fractures containing moving groundwater, is called the geological barrier. The desired properties of the geological barrier are low permeability to water, low hydraulic gradients and ability to retain matter dissolved in the water. The hydraulic gradient together with the permeability and the porosity determines the migration velocity. Mathematical modelling of the migration involves calculation of the water flow and the hydrodynamic dispersion of the contaminant. The porous medium approach can be used to calculate mean flow velocities and hydrodynamic dispersion of a large number of fractures are connected, which means that a large volume have to be considered. It is assumed that the porous medium approach can be applied, and a number of idealized examples are shown. It is assumed that the groundwater table is replenished by percolation at a constant rate. One-dimensional analytical calculations show that zero hydraulic gradients may exist at relatively large distance from the coast. Two-dimensional numerical calculations show that it may be possible to find areas with low hydraulic gradients and flow velocities within blocks surrounded by areas with high hydraulic conductivity. (au)

Seismic moment tensor inversion using 3D velocity model and its application to the 2013 Lushan earthquake sequence

Science.gov (United States)

Zhu, Lupei; Zhou, Xiaofeng

2016-10-01

Source inversion of small-magnitude events such as aftershocks or mine collapses requires use of relatively high frequency seismic waveforms which are strongly affected by small-scale heterogeneities in the crust. In this study, we developed a new inversion method called gCAP3D for determining general moment tensor of a seismic source using Green's functions of 3D models. It inherits the advantageous features of the ;Cut-and-Paste; (CAP) method to break a full seismogram into the Pnl and surface-wave segments and to allow time shift between observed and predicted waveforms. It uses grid search for 5 source parameters (relative strengths of the isotropic and compensated-linear-vector-dipole components and the strike, dip, and rake of the double-couple component) that minimize the waveform misfit. The scalar moment is estimated using the ratio of L2 norms of the data and synthetics. Focal depth can also be determined by repeating the inversion at different depths. We applied gCAP3D to the 2013 Ms 7.0 Lushan earthquake and its aftershocks using a 3D crustal-upper mantle velocity model derived from ambient noise tomography in the region. We first relocated the events using the double-difference method. We then used the finite-differences method and reciprocity principle to calculate Green's functions of the 3D model for 20 permanent broadband seismic stations within 200 km from the source region. We obtained moment tensors of the mainshock and 74 aftershocks ranging from Mw 5.2 to 3.4. The results show that the Lushan earthquake is a reverse faulting at a depth of 13-15 km on a plane dipping 40-47° to N46° W. Most of the aftershocks occurred off the main rupture plane and have similar focal mechanisms to the mainshock's, except in the proximity of the mainshock where the aftershocks' focal mechanisms display some variations.

Second rank direction cosine spherical tensor operators and the nuclear electric quadrupole hyperfine structure Hamiltonian of rotating molecules

Science.gov (United States)

di Lauro, C.

2018-03-01

Transformations of vector or tensor properties from a space-fixed to a molecule-fixed axis system are often required in the study of rotating molecules. Spherical components λμ,ν of a first rank irreducible tensor can be obtained from the direction cosines between the two axis systems, and a second rank tensor with spherical components λμ,ν(2) can be built from the direct product λ × λ. It is shown that the treatment of the interaction between molecular rotation and the electric quadrupole of a nucleus is greatly simplified, if the coefficients in the axis-system transformation of the gradient of the electric field of the outer charges at the coupled nucleus are arranged as spherical components λμ,ν(2). Then the reduced matrix elements of the field gradient operators in a symmetric top eigenfunction basis, including their dependence on the molecule-fixed z-angular momentum component k, can be determined from the knowledge of those of λ(2) . The hyperfine structure Hamiltonian Hq is expressed as the sum of terms characterized each by a value of the molecule-fixed index ν, whose matrix elements obey the rule Δk = ν. Some of these terms may vanish because of molecular symmetry, and the specific cases of linear and symmetric top molecules, orthorhombic molecules, and molecules with symmetry lower than orthorhombic are considered. Each ν-term consists of a contraction of the rotational tensor λ(2) and the nuclear quadrupole tensor in the space-fixed frame, and its matrix elements in the rotation-nuclear spin coupled representation can be determined by the standard spherical tensor methods.

Tensor Transpose and Its Properties

OpenAIRE

Pan, Ran

2014-01-01

Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.

LES of the adverse-pressure gradient turbulent boundary layer

International Nuclear Information System (INIS)

Inoue, M.; Pullin, D.I.; Harun, Z.; Marusic, I.

2013-01-01

Highlights: • The adverse-pressure gradient turbulent boundary layer at high Re is studied. • Wall-model LES works well for nonequilibrium turbulent boundary layer. • Relationship of skin-friction to Re and Clauser pressure parameter is explored. • Self-similarity is observed in the velocity statistics over a wide range of Re. -- Abstract: We describe large-eddy simulations (LES) of the flat-plate turbulent boundary layer in the presence of an adverse pressure gradient. The stretched-vortex subgrid-scale model is used in the domain of the flow coupled to a wall model that explicitly accounts for the presence of a finite pressure gradient. The LES are designed to match recent experiments conducted at the University of Melbourne wind tunnel where a plate section with zero pressure gradient is followed by section with constant adverse pressure gradient. First, LES are described at Reynolds numbers based on the local free-stream velocity and the local momentum thickness in the range 6560–13,900 chosen to match the experimental conditions. This is followed by a discussion of further LES at Reynolds numbers at approximately 10 times and 100 times these values, which are well out of range of present day direct numerical simulation and wall-resolved LES. For the lower Reynolds number runs, mean velocity profiles, one-point turbulent statistics of the velocity fluctuations, skin friction and the Clauser and acceleration parameters along the streamwise, adverse pressure-gradient domain are compared to the experimental measurements. For the full range of LES, the relationship of the skin-friction coefficient, in the form of the ratio of the local free-stream velocity to the local friction velocity, to both Reynolds number and the Clauser parameter is explored. At large Reynolds numbers, a region of collapse is found that is well described by a simple log-like empirical relationship over two orders of magnitude. This is expected to be useful for constant adverse

Universal formula for the energy–momentum tensor via a flow equation in the Gross–Neveu model

International Nuclear Information System (INIS)

Suzuki, Hiroshi

2015-01-01

For the fermion field in the two-dimensional Gross–Neveu model, we introduce a flow equation that allows a simple 1/N expansion. By employing the 1/N expansion, we examine the validity of a universal formula for the energy–momentum tensor which is based on the small flow-time expansion. We confirm that the formula reproduces a correct normalization and the conservation law of the energy–momentum tensor by computing the translation Ward–Takahashi relation in the leading non-trivial order in the 1/N expansion. Also, we confirm that the expectation value at finite temperature correctly reproduces thermodynamic quantities. These observations support the validity of a similar construction of the energy–momentum tensor via the gradient/Wilson flow in lattice gauge theory

A new validation technique for estimations of body segment inertia tensors: Principal axes of inertia do matter.

Science.gov (United States)

Rossi, Marcel M; Alderson, Jacqueline; El-Sallam, Amar; Dowling, James; Reinbolt, Jeffrey; Donnelly, Cyril J

2016-12-08

The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

The tensor rank of tensor product of two three-qubit W states is eight

OpenAIRE

Chen, Lin; Friedland, Shmuel

2017-01-01

We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.

Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

Science.gov (United States)

Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N

2017-05-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Bowen-York tensors

International Nuclear Information System (INIS)

Beig, Robert; Krammer, Werner

2004-01-01

For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York

Harmonic d-tensors

Energy Technology Data Exchange (ETDEWEB)

Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)

2016-07-01

Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.

Moment tensor inversions using strong motion waveforms of Taiwan TSMIP data, 1993–2009

Science.gov (United States)

Chang, Kaiwen; Chi, Wu-Cheng; Gung, Yuancheng; Dreger, Douglas; Lee, William H K.; Chiu, Hung-Chie

2011-01-01

Earthquake source parameters are important for earthquake studies and seismic hazard assessment. Moment tensors are among the most important earthquake source parameters, and are now routinely derived using modern broadband seismic networks around the world. Similar waveform inversion techniques can also apply to other available data, including strong-motion seismograms. Strong-motion waveforms are also broadband, and recorded in many regions since the 1980s. Thus, strong-motion data can be used to augment moment tensor catalogs with a much larger dataset than that available from the high-gain, broadband seismic networks. However, a systematic comparison between the moment tensors derived from strong motion waveforms and high-gain broadband waveforms has not been available. In this study, we inverted the source mechanisms of Taiwan earthquakes between 1993 and 2009 by using the regional moment tensor inversion method using digital data from several hundred stations in the Taiwan Strong Motion Instrumentation Program (TSMIP). By testing different velocity models and filter passbands, we were able to successfully derive moment tensor solutions for 107 earthquakes of Mw >= 4.8. The solutions for large events agree well with other available moment tensor catalogs derived from local and global broadband networks. However, for Mw = 5.0 or smaller events, we consistently over estimated the moment magnitudes by 0.5 to 1.0. We have tested accelerograms, and velocity waveforms integrated from accelerograms for the inversions, and found the results are similar. In addition, we used part of the catalogs to study important seismogenic structures in the area near Meishan Taiwan which was the site of a very damaging earthquake a century ago, and found that the structures were dominated by events with complex right-lateral strike-slip faulting during the recent decade. The procedures developed from this study may be applied to other strong-motion datasets to compliment or fill

Current density tensors

Science.gov (United States)

Lazzeretti, Paolo

2018-04-01

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

Uncertainty assessment of 3D instantaneous velocity model from stack velocities

Science.gov (United States)

Emanuele Maesano, Francesco; D'Ambrogi, Chiara

2015-04-01

3D modelling is a powerful tool that is experiencing increasing applications in data analysis and dissemination. At the same time the need of quantitative uncertainty evaluation is strongly requested in many aspects of the geological sciences and by the stakeholders. In many cases the starting point for 3D model building is the interpretation of seismic profiles that provide indirect information about the geology of the subsurface in the domain of time. The most problematic step in the 3D modelling construction is the conversion of the horizons and faults interpreted in time domain to the depth domain. In this step the dominant variable that could lead to significantly different results is the velocity. The knowledge of the subsurface velocities is related mainly to punctual data (sonic logs) that are often sparsely distributed in the areas covered by the seismic interpretation. The extrapolation of velocity information to wide extended horizons is thus a critical step to obtain a 3D model in depth that can be used for predictive purpose. In the EU-funded GeoMol Project, the availability of a dense network of seismic lines (confidentially provided by ENI S.p.A.) in the Central Po Plain, is paired with the presence of 136 well logs, but few of them have sonic logs and in some portion of the area the wells are very widely spaced. The depth conversion of the 3D model in time domain has been performed testing different strategies for the use and the interpolation of velocity data. The final model has been obtained using a 4 layer cake 3D instantaneous velocity model that considers both the initial velocity (v0) in every reference horizon and the gradient of velocity variation with depth (k). Using this method it is possible to consider the geological constraint given by the geometries of the horizons and the geo-statistical approach to the interpolation of velocities and gradient. Here we present an experiment based on the use of set of pseudo-wells obtained from the

Flat rotation curves using scalar-tensor theories

Energy Technology Data Exchange (ETDEWEB)

Cervantes-Cota, Jorge L [Depto de Fisica, Instituto Nacional de Investigaciones Nucleares, A.P. 18-1027, 11801 D.F. (Mexico); RodrIguez-Meza, M A [Depto de Fisica, Instituto Nacional de Investigaciones Nucleares, A.P. 18-1027, 11801 D.F. (Mexico); Nunez, Dario [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 D.F. (Mexico)

2007-11-15

We computed flat rotation curves from scalar-tensor theories in their weak field limit. Our model, by construction, fits a flat rotation profile for velocities of stars. As a result, the form of the scalar field potential and DM distribution in a galaxy are determined. By taking into account the constraints for the fundamental parameters of the theory ({lambda}, {alpha}), it is possible to obtain analytical results for the density profiles. For positive and negative values of {alpha}, the DM matter profile is as cuspy as NFW's.

Gradient computation for VTI acoustic wavefield tomography

KAUST Repository

Li, Vladimir; Wang, Hui; Tsvankin, Ilya; Diaz, Esteban; Alkhalifah, Tariq Ali

2016-01-01

-power objective functions. We also obtain the gradient expressions for the data-domain objective function, which can incorporate borehole information necessary for stable VTI velocity analysis. These gradients are compared to the ones obtained with a space

A parametric study of adverse pressure gradient turbulent boundary layers

International Nuclear Information System (INIS)

Monty, J.P.; Harun, Z.; Marusic, I.

2011-01-01

There are many open questions regarding the behaviour of turbulent boundary layers subjected to pressure gradients and this is confounded by the large parameter space that may affect these flows. While there have been many valuable investigations conducted within this parameter space, there are still insufficient data to attempt to reduce this parameter space. Here, we consider a parametric study of adverse pressure gradient turbulent boundary layers where we restrict our attention to the pressure gradient parameter, β, the Reynolds number and the acceleration parameter, K. The statistics analyzed are limited to the streamwise fluctuating velocity. The data show that the mean velocity profile in strong pressure gradient boundary layers does not conform to the classical logarithmic law. Moreover, there appears to be no measurable logarithmic region in these cases. It is also found that the large-scale motions scaling with outer variables are energised by the pressure gradient. These increasingly strong large-scale motions are found to be the dominant contributor to the increase in turbulence intensity (scaled with friction velocity) with increasing pressure gradient across the boundary layer.

Vorticity and helicity decompositions and dynamics with real Schur form of the velocity gradient

Science.gov (United States)

Zhu, Jian-Zhou

2018-03-01

The real Schur form (RSF) of a generic velocity gradient field ∇u is exploited to expose the structures of flows, in particular, our field decomposition resulting in two vorticities with only mutual linkage as the topological content of the global helicity (accordingly decomposed into two equal parts). The local transformation to the RSF may indicate alternative (co)rotating frame(s) for specifying the objective argument(s) of the constitutive equation. When ∇u is uniformly of RSF in a fixed Cartesian coordinate frame, i.e., ux = ux(x, y) and uy = uy(x, y), but uz = uz(x, y, z), the model, with the decomposed vorticities both frozen-in to u, is for two-component-two-dimensional-coupled-with-one-component-three-dimensional flows in between two-dimensional-three-component (2D3C) and fully three-dimensional-three-component ones and may help curing the pathology in the helical 2D3C absolute equilibrium, making the latter effectively work in more realistic situations.

The role of the velocity gradient in laminar convective heat transfer through a tube with a uniform wall heat flux

International Nuclear Information System (INIS)

Wang Liangbi; Zhang Qiang; Li Xiaoxia

2009-01-01

This paper aims to contribute to a better understanding of convective heat transfer. For this purpose, the reason why thermal diffusivity should be placed before the Laplacian operator of the heat flux, and the role of the velocity gradient in convective heat transfer are analysed. The background to these analyses is that, when the energy conservation equation of convective heat transfer is used to explain convective heat transfer there are two points that are difficult for teachers to explain and for undergraduates to understand: thermal diffusivity is placed before the Laplacian operator of temperature; on the wall surface (the fluid side) the velocity is zero, a diffusion equation of temperature is gained from energy conservation equation, however, temperature cannot be transported. Consequently, the real physical meaning of thermal diffusivity is not clearly reflected in the energy conservation equation, and whether heat transfer occurs through a diffusion process or a convection process on the wall surface is not clear. Through a simple convective heat transfer case: laminar convective heat transfer in a tube with a uniform wall heat flux on the tube wall, this paper explains these points more clearly. The results declare that it is easier for teachers to explain and for undergraduates to understand these points when a description of heat transfer in terms of the heat flux is used. In this description, thermal diffusivity is placed before the Laplacian operator of the heat flux; the role of the velocity gradient in convective heat transfer appears, on the wall surface, the fact whether heat transfer occurs through a diffusion process or a convection process can be explained and understood easily. The results are not only essential for teachers to improve the efficiency of university-level physics education regarding heat transfer, but they also enrich the theories for understanding heat transfer

Piezo-optic tensor of crystals from quantum-mechanical calculations.

Science.gov (United States)

Erba, A; Ruggiero, M T; Korter, T M; Dovesi, R

2015-10-14

An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic tensor of crystals belonging to any space group of symmetry. Elastic stiffness and compliance constants are obtained as numerical first derivatives of analytical energy gradients with respect to the strain and photo-elastic constants as numerical derivatives of analytical dielectric tensor components, which are in turn computed through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach, with respect to the strain. Both point and translation symmetries are exploited at all steps of the calculation, within the framework of periodic boundary conditions. The scheme is applied to the determination of the full set of ten symmetry-independent piezo-optic constants of calcium tungstate CaWO4, which have recently been experimentally reconstructed. Present calculations unambiguously determine the absolute sign (positive) of the π61 constant, confirm the reliability of 6 out of 10 experimentally determined constants and provide new, more accurate values for the remaining 4 constants.

Superconducting RF for Low-Velocity and Intermediate-Velocity Beams

CERN Document Server

Grimm, Terry L

2005-01-01

Existing superconducting radio frequency (SRF) linacs are used to accelerate ions (protons through uranium) with velocities less than about 15% the speed of light, or electrons with velocities approximately equal to the speed of light. In the last ten years, prototype SRF cavities have completely covered the remaining range of velocities. They have demonstrated that SRF linacs will be capable of accelerating electrons from rest up to the speed of light, and ions from less than 1% up to the speed of light. When the Spallation Neutron Source is operational, SRF ion linacs will have covered the full range of velocities except for v/c ~ 0.15 to v/c ~ 0.5. A number of proposed projects (RIA, EURISOL) would span the latter range of velocities. Future SRF developments will have to address the trade-offs associated with a number of issues, including high gradient operation, longitudinal and transverse acceptance, microphonics, Lorentz detuning, operating temperature, cryogenic load, number of gaps or cells per cavity...

Migration of inclusions in solids in stress gradients

International Nuclear Information System (INIS)

Olander, D.R.

1980-01-01

A theoretical method of assessing the influence of stress and temperature gradients on the motion of inclusions in solids is developed. In nonuniform stress fields, the stress distribution on the surface of the cavity must be calculated and transformed to a potential gradient for driving a surface atom flux. The bubble migration velocity is the first Legendre coefficient of the surface flux. Higher order components represent distortion. The stress gradient effect appears only in small-magnitude terms in the surface chemical potential, specifically in the stress effect on the solid atomic volume and in the elastic energy density. The migration velocities of spherical and faceted bubbles in solids are computed and the extent of distortion of a spherical bubble is estimated. The role of vacancy exchange with the bulk solid on the migration velocity is assessed. (author)

Segmentation of DTI based on tensorial morphological gradient

Science.gov (United States)

Rittner, Leticia; de Alencar Lotufo, Roberto

2009-02-01

This paper presents a segmentation technique for diffusion tensor imaging (DTI). This technique is based on a tensorial morphological gradient (TMG), defined as the maximum dissimilarity over the neighborhood. Once this gradient is computed, the tensorial segmentation problem becomes an scalar one, which can be solved by conventional techniques, such as watershed transform and thresholding. Similarity functions, namely the dot product, the tensorial dot product, the J-divergence and the Frobenius norm, were compared, in order to understand their differences regarding the measurement of tensor dissimilarities. The study showed that the dot product and the tensorial dot product turned out to be inappropriate for computation of the TMG, while the Frobenius norm and the J-divergence were both capable of measuring tensor dissimilarities, despite the distortion of Frobenius norm, since it is not an affine invariant measure. In order to validate the TMG as a solution for DTI segmentation, its computation was performed using distinct similarity measures and structuring elements. TMG results were also compared to fractional anisotropy. Finally, synthetic and real DTI were used in the method validation. Experiments showed that the TMG enables the segmentation of DTI by watershed transform or by a simple choice of a threshold. The strength of the proposed segmentation method is its simplicity and robustness, consequences of TMG computation. It enables the use, not only of well-known algorithms and tools from the mathematical morphology, but also of any other segmentation method to segment DTI, since TMG computation transforms tensorial images in scalar ones.

Space-time symmetries and the Yang-Mills gradient flow

CERN Document Server

Del Debbio, Luigi; Rago, Antonio

2013-01-01

The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In this paper we introduce infinitesimal translations along the gradient flow for gauge theories, and study the corresponding Ward identities. This approach is readily generalized to the case of gauge theories defined on a lattice, where the regulator breaks translation invariance. The Ward identities in this case lead to a nonperturbative renormalization of the energy-momentum tensor. We discuss an application of this method to the study of dilatations and scale invariance on the lattice.

TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow

OpenAIRE

Hafner, Danijar; Davidson, James; Vanhoucke, Vincent

2017-01-01

We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...

A one-dimensional seismic model for Uturuncu volcano, Bolivia, and its impact on full moment tensor inversions

KAUST Repository

Shen, Weisen; Alvizuri, Celso; Lin, Fan-Chi; Tape, Carl

2016-01-01

Using receiver functions, Rayleigh wave phase velocity dispersion determined from ambient noise and teleseismic earthquakes, and Rayleigh wave horizontal to vertical ground motion amplitude ratios from earthquakes observed across the PLUTONS seismic array, we construct a one-dimensional (1-D) S-wave velocity (Vs) seismic model with uncertainties for Uturuncu volcano, Bolivia, located in the central Andes and overlying the eastward-subducting Nazca plate. We find a fast upper crustal lid placed upon a low-velocity zone (LVZ) in the mid-crust. By incorporating all three types of measurements with complimentary sensitivity, we also explore the average density and Vp/Vs (ratio of P-wave to S-wave velocity) structures beneath the young silicic volcanic field. We observe slightly higher Vp/Vs and a decrease in density near the LVZ, which implies a dacitic source of the partially molten magma body. We exploit the impact of the 1-D model on full moment tensor inversion for the two largest local earthquakes recorded (both magnitude ∼3), demonstrating that the 1-D model influences the waveform fits and the estimated source type for the full moment tensor. Our 1-D model can serve as a robust starting point for future efforts to determine a three-dimensional velocity model for Uturuncu volcano.

A one-dimensional seismic model for Uturuncu volcano, Bolivia, and its impact on full moment tensor inversions

KAUST Repository

Shen, Weisen

2016-11-24

Using receiver functions, Rayleigh wave phase velocity dispersion determined from ambient noise and teleseismic earthquakes, and Rayleigh wave horizontal to vertical ground motion amplitude ratios from earthquakes observed across the PLUTONS seismic array, we construct a one-dimensional (1-D) S-wave velocity (Vs) seismic model with uncertainties for Uturuncu volcano, Bolivia, located in the central Andes and overlying the eastward-subducting Nazca plate. We find a fast upper crustal lid placed upon a low-velocity zone (LVZ) in the mid-crust. By incorporating all three types of measurements with complimentary sensitivity, we also explore the average density and Vp/Vs (ratio of P-wave to S-wave velocity) structures beneath the young silicic volcanic field. We observe slightly higher Vp/Vs and a decrease in density near the LVZ, which implies a dacitic source of the partially molten magma body. We exploit the impact of the 1-D model on full moment tensor inversion for the two largest local earthquakes recorded (both magnitude ∼3), demonstrating that the 1-D model influences the waveform fits and the estimated source type for the full moment tensor. Our 1-D model can serve as a robust starting point for future efforts to determine a three-dimensional velocity model for Uturuncu volcano.

A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

OpenAIRE

SASAKURA, NAOKI

2010-01-01

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue.

Science.gov (United States)

Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J

2002-01-01

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.

Velocity and concentration fields in turbulent buoyant mixing in tilted tubes

Science.gov (United States)

Znaien, J.; Moisy, F.; Hulin, J. P.; Salin, D.; Hinch, E. J.

2008-11-01

2D PIV and LIF measurements have been performed on buoyancy driven flows of two miscible fluids of the same viscosity in a tube tilted at different angles θ from vertical and at different density contrasts (characterized by the Atwood number At). As θ increases and At decreases, the flow regime evolves, behind the front, from a turbulent shear flow towards a laminar counter flow with 3 layers of different concentrations. Time variations of the structure function show that both intermittent and developed turbulence occur in intermediate conditions. In the turbulent regime (Reλ˜60) the magnitudes of the longitudinal u'^2 and transverse v'^2 velocity fluctuations and of the component u'v' of the Reynolds stress tensor are shown to be largest on the tube axis while viscous stresses is only important close to the walls. The analyzis of the momentum transfer in the flow with buoyancy forces estimated from the concentration gradients demonstrates that 3D effects are required to achieve the momentum balance. These results are discussed in the framework of classical turbulence models.

Non-gyrotropic pressure anisotropy induced by velocity shear.

Science.gov (United States)

Tenerani, A.; Del Sarto, D.; Pegoraro, F.; Califano, F.

2015-12-01

We discuss how, in a collisionless magnetized plasma, a sheared velocity field may lead to the anisotropization of an initial Maxwellian state. By including the full pressure tensor dynamics in a fluid plasma model, we show, analytically and numerically, that a sheared velocity field makes an initial isotropic state anisotropic and non-gyrotropic [1], i.e., makes the plasma pressure tensor anisotropic also in the plane perpendicular to the magnetic field. The propagation of transverse magneto-elastic waves in the anisotropic plasma affects the process of formation of a non-gyrotropic pressure and can lead to its spatial filamentation. This plasma dynamics implies in particular that isotropic MHD equilibria cease to be equilibria in presence of a stationary sheared flow. Similarly, in the case of turbulence, where small-scale spatial inhomogeneities are naturally developed during the direct cascade, we may expect that isotropic turbulent states are not likely to exist whenever a full pressure tensor evolution is accounted for. These results may be relevant to understanding the agyrotropic pressure configurations which are well documented in solar wind measurements and possibly correlated to plasma flows (see e.g. Refs.[2,3]), and which have also been measured in Vlasov simulations of Alfvenic turbulence [4]. [1] D. Del Sarto, F. Pegoraro, F. Califano, "Pressure anisotropy and small spatial scales induced by a velocity shear", http://arxiv.org/abs/1507.04895 [2] H.F. Astudillo, E. Marsch, S. Livi, H. Rosenbauer, "TAUS measurements of non-gyrotropic distribution functions of solar wind alpha particles", AIP Conf. Proc. 328, 289 (1996). [3] A. Posner, M.W. Liemhon, T.H. Zurbuchen, "Upstream magnetospheric ion flux tube within a magnetic cloud: Wind/STICS", Geophys. Res. Lett. 30, (2003). [4] S. Servidio, F. Valentini, F. Califano, P. Veltri, "Local kinetic effects in Two-Dimensional Plasma Turbulence", Phys. Rev. Lett. 108, 045001 (2012).

Time integration of tensor trains

OpenAIRE

Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart

2014-01-01

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...

Tensor spaces and exterior algebra

CERN Document Server

Yokonuma, Takeo

1992-01-01

This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

Gravitation is a Gradient in the Velocity of Light

Science.gov (United States)

Froedge, Dt

2017-01-01

It is well known that a photon moving in a gravitational field has a trajectory that can be defined by Fermat's principle with a variable speed of light and no other gravitational influence. If it can be shown that a particle composed of speed of light sub-particles has the same acceleration in a variable index of refraction as a particle in a gravitational field, then there is no need to ascribe any other mechanism to gravitation than a gradient in c. This makes gravitation an electromagnetic phenomenon, and if QFT can illustrate a gradient in c can be produced by the internal motion of lightspeed sub-particles then the unification of QM and gravitation becomes more straightforward. http://www.arxdtf.org/css/GravAPS.pdf.

The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging

NARCIS (Netherlands)

Akkerman, Erik M.

2010-01-01

Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional

Aortic-Brachial Pulse Wave Velocity Ratio: A Measure of Arterial Stiffness Gradient Not Affected by Mean Arterial Pressure.

Science.gov (United States)

Fortier, Catherine; Desjardins, Marie-Pier; Agharazii, Mohsen

2018-03-01

Aortic stiffness, measured by carotid-femoral pulse wave velocity (cf-PWV), is used for the prediction of cardiovascular risk. This mini-review describes the nonlinear relationship between cf-PWV and operational blood pressure, presents the proposed methods to adjust for this relationship, and discusses a potential place for aortic-brachial PWV ratio (a measure of arterial stiffness gradient) as a blood pressure-independent measure of vascular aging. PWV is inherently dependent on the operational blood pressure. In cross-sectional studies, PWV adjustment for mean arterial pressure (MAP) is preferred, but still remains a nonoptimal approach, as the relationship between PWV and blood pressure is nonlinear and varies considerably among individuals due to heterogeneity in genetic background, vascular tone, and vascular remodeling. Extrapolations from the blood pressure-independent stiffness parameter β (β 0 ) have led to the creation of stiffness index β, which can be used for local stiffness. A similar approach has been used for cardio-ankle PWV to generate a blood pressure-independent cardio-ankle vascular index (CAVI). It was recently demonstrated that stiffness index β and CAVI remain slightly blood pressure-dependent, and a more appropriate formula has been proposed to make the proper adjustments. On the other hand, the negative impact of aortic stiffness on clinical outcomes is thought to be mediated through attenuation or reversal of the arterial stiffness gradient, which can also be influenced by a reduction in peripheral medium-sized muscular arteries in conditions that predispose to accelerate vascular aging. Arterial stiffness gradient, assessed by aortic-brachial PWV ratio, is emerging to be at least as good as cf-PWV for risk prediction, but has the advantage of not being affected by operating MAP. The negative impacts of aortic stiffness on clinical outcomes are proposed to be mediated through attenuation or reversal of arterial stiffness gradient

Direct diffusion tensor estimation using a model-based method with spatial and parametric constraints.

Science.gov (United States)

Zhu, Yanjie; Peng, Xi; Wu, Yin; Wu, Ed X; Ying, Leslie; Liu, Xin; Zheng, Hairong; Liang, Dong

2017-02-01

To develop a new model-based method with spatial and parametric constraints (MB-SPC) aimed at accelerating diffusion tensor imaging (DTI) by directly estimating the diffusion tensor from highly undersampled k-space data. The MB-SPC method effectively incorporates the prior information on the joint sparsity of different diffusion-weighted images using an L1-L2 norm and the smoothness of the diffusion tensor using a total variation seminorm. The undersampled k-space datasets were obtained from fully sampled DTI datasets of a simulated phantom and an ex-vivo experimental rat heart with acceleration factors ranging from 2 to 4. The diffusion tensor was directly reconstructed by solving a minimization problem with a nonlinear conjugate gradient descent algorithm. The reconstruction performance was quantitatively assessed using the normalized root mean square error (nRMSE) of the DTI indices. The MB-SPC method achieves acceptable DTI measures at an acceleration factor up to 4. Experimental results demonstrate that the proposed method can estimate the diffusion tensor more accurately than most existing methods operating at higher net acceleration factors. The proposed method can significantly reduce artifact, particularly at higher acceleration factors or lower SNRs. This method can easily be adapted to MR relaxometry parameter mapping and is thus useful in the characterization of biological tissue such as nerves, muscle, and heart tissue. © 2016 American Association of Physicists in Medicine.

Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation

Energy Technology Data Exchange (ETDEWEB)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)

2015-06-24

Relativistic hydrodynamics dual to Einstein-Gauss-Bonnet gravity in asymptotic AdS{sub 5} space is under study. To linear order in the amplitude of the fluid velocity and temperature, we derive the fluid’s stress-energy tensor via an all-order resummation of the derivative terms. Each order is accompanied by new transport coefficients, which all together could be compactly absorbed into two functions of momenta, referred to as viscosity functions. Via inverse Fourier transform, these viscosities appear as memory functions in the constitutive relation between components of the stress-energy tensor.

Color gradients in elliptical galaxies

International Nuclear Information System (INIS)

Franx, M.; Illingworth, G.

1990-01-01

The relationship of the color gradients within ellipticals and the color differences between them are studied. It is found that the local color appears to be strongly related to the escape velocity. This suggests that the local escape velocity is the primary factor that determines the metallicity of the stellar population. Models with and without dark halos give comparable results. 27 refs

Gogny interactions with tensor terms

Energy Technology Data Exchange (ETDEWEB)

Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)

2016-07-15

We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)

Tensor structure for Nori motives

OpenAIRE

Barbieri-Viale, Luca; Huber, Annette; Prest, Mike

2018-01-01

We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.

Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.

Science.gov (United States)

Iwasaki, Tohru; Furukawa, Tetsuo

2016-05-01

In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.

On Inverse Coefficient Heat-Conduction Problems on Reconstruction of Nonlinear Components of the Thermal-Conductivity Tensor of Anisotropic Bodies

Science.gov (United States)

Formalev, V. F.; Kolesnik, S. A.

2017-11-01

The authors are the first to present a closed procedure for numerical solution of inverse coefficient problems of heat conduction in anisotropic materials used as heat-shielding ones in rocket and space equipment. The reconstructed components of the thermal-conductivity tensor depend on temperature (are nonlinear). The procedure includes the formation of experimental data, the implicit gradient-descent method, the economical absolutely stable method of numerical solution of parabolic problems containing mixed derivatives, the parametric identification, construction, and numerical solution of the problem for elements of sensitivity matrices, the development of a quadratic residual functional and regularizing functionals, and also the development of algorithms and software systems. The implicit gradient-descent method permits expanding the quadratic functional in a Taylor series with retention of the linear terms for the increments of the sought functions. This substantially improves the exactness and stability of solution of the inverse problems. Software systems are developed with account taken of the errors in experimental data and disregarding them. On the basis of a priori assumptions of the qualitative behavior of the functional dependences of the components of the thermal-conductivity tensor on temperature, regularizing functionals are constructed by means of which one can reconstruct the components of the thermal-conductivity tensor with an error no higher than the error of the experimental data. Results of the numerical solution of the inverse coefficient problems on reconstruction of nonlinear components of the thermal-conductivity tensor have been obtained and are discussed.

Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

OpenAIRE

Loveridge, Lee C.

2004-01-01

Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors.

Science.gov (United States)

Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M

2008-01-01

This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.

Thermal-gradient migration of brine inclusions in salt crystals

International Nuclear Information System (INIS)

Yagnik, S.K.

1982-09-01

It has been proposed that high-level nuclear waste be disposed in a geologic repository. Natural-salt deposits, which are being considered for this purpose, contain a small volume fraction of water in the form of brine inclusions distributed throughout the salt. Radioactive-decay heating of the nuclear wastes will impose a temperature gradient on the surrounding salt which mobilizes the brine inclusions. Inclusions filled completely with brine migrate up the temperature gradient and eventually accumulate brine near the buried waste forms. The brine may slowly corrode or degrade the waste forms which is undesirable. In this work, thermal gradient migration of both all-liquid and gas-liquid inclusions was experimentally studied in synthetic single crystals of NaCl and KCl using a hot-stage attachment to an optical microscope which was capable of imposing temperature gradients and axial compressive loads on the crystals. The migration velocities of the inclusions were found to be dependent on temperature, temperature gradient, and inclusion shape and size. The velocities were also dictated by the interfacial mass transfer resistance at brine/solid interface. This interfacial resistance depends on the dislocation density in the crystal, which in turn, depends on the axial compressive loading of the crystal. At low axial loads, the dependence between the velocity and temperature gradient is non-linear.At high axial loads, however, the interfacial resistance is reduced and the migration velocity depends linearly on the temperature gradient. All-liquid inclusions filled with mixed brines were also studied. For gas-liquid inclusions, three different gas phases (helium, air and argon) were compared. Migration studies were also conducted on single crystallites of natural salt as well as in polycrystalline natural salt samples. The behavior of the inclusions at large angle grain boundaries was observed. 35 figures, 3 tables

Thermal gradient migration of brine inclusions in salt crystals

International Nuclear Information System (INIS)

Yagnik, S.K.

1982-01-01

Natural salt deposits, which are being considered for high-level nuclear wastes repositories, contain a small volume fraction of water in the form of brine inclusions distributed throughout the salt. Radioactive decay heating of the nuclear wastes will impose a temperature gradient on the surrounding salt which mobilizes the brine inclusions. Inclusions filled completely with brine (the all-liquid inclusions) migrate up the temperature gradient and eventually accumulate brine near the buried waste forms. The brine may slowly corrode or degrade the waste forms which is undesirable. In the present work, thermal gradient migration of both all-liquid and gas-liquid inclusions was experimentally studied in synthetic single crystals of NaCl and KCl using a hot-stage attachment to an optical microscope which was capable of imposing temperature gradients and axial compressive loads on the crystals. The migration velocities of the inclusions were found to be dependent on temperature, temperature gradient, and inclusion shape and size. The velocities were also dictated by the interfacial mass transfer resistance at brine/solid interface. This interfacial resistance depends on the dislocation density in the crystal, which in turn, depends on the axial compressive loading of the crystal. At low axial loads, the dependence between the velocity and temperature gradient is nonlinear. At high axial loads, however, the interfacial resistance is reduced and the migration velocity depends linearly on the temperature gradient. All-liquid inclusions filled with mixed brines were also studied. For gas-liquid inclusions, three different gas phases (helium, air and argon) were compared. Migration studies were also conducted on single crystallites of natural salt as well as in polycrystalline natural salt samples. The behavior of the inclusions at large angle grain boudaries was observed

Development of the Tensoral Computer Language

Science.gov (United States)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

Science.gov (United States)

Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

2017-08-02

It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

Killing-Yano tensors and Nambu mechanics

International Nuclear Information System (INIS)

Baleanu, D.

1998-01-01

Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3

Detection of antisymmetric tensor contribution to the magnetic screening of 13C nuclei

International Nuclear Information System (INIS)

Kuhn, W.

1983-01-01

In the present thesis for the first time a practicable way for the detection of antisymmetric contributions to the tensor of the magnetic screening of atomic nuclei is indicated. The detection is based on the relaxation efficiency of the antisymmetric screening. The measurements were performed on the 13 C nuclei of phthalic acid anhydride. Measured were the spin-lattice relaxation times of all 13 C nuclei of the molecule at field strengths between 4.69 T and 11.74 T, this corresponds to 1 H resonance frequencies in the range from 200 MHz to 500 MHz. From this the interaction-specific relaxation rates could be determined without problems. The space-group of the crystal and the molecule geometry were determined by X-ray structure analysis. For the accurate determination of the hydrogen position on a deuterated monocrystal by means of deuterium nuclear resonance measurements the electric field gradient tensors were measured and from the orientation of the main axes of these tensors the bonding angles calculated. On a monocrystal enriched in the C(7) respectively C(8) position with 13 C the symmetric part of the tensor of the magnetic screening of these two nuclei was measured. With these values and the relaxation rates of the 13 C nuclei by an iterative procedure from the equations for the theoretical relaxation rates of all 13 C nuclei of the molecule the main values of the rotation-diffusion tensor could be determined. On the base of the plane molecule geometry from this the tensor element sigmasub(xz)sup(A) could be explicety detected according to an amount of 11.7 ppm. (orig.) [de

Categorical Tensor Network States

Directory of Open Access Journals (Sweden)

Jacob D. Biamonte

2011-12-01

Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.

Tensor Permutation Matrices in Finite Dimensions

OpenAIRE

Christian, Rakotonirina

2005-01-01

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...

Thermal conduction down steep temperature gradients

International Nuclear Information System (INIS)

Bell, A.R.; Evans, R.G.; Nicholas, D.J.

1980-08-01

The Fokker-Planck equation has been solved numerically in one spatial and two velocity dimensions in order to study thermal conduction in large temperature gradients. An initially cold plasma is heated at one end of the spatial grid producing temperature gradients with scale lengths of a few times the electron mean free path. The heat flow is an order of magnitude smaller than that predicted by the classical theory which is valid in the limit of small temperature gradients. (author)

Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration

Science.gov (United States)

Becattini, F.; Grossi, E.

2015-08-01

We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with nonvanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are second order in the gradients of the thermodynamic fields. Their relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second-order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between ρ and p , that is, the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field—both massive and massless—and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and very low temperature. Finally, these nonideal terms depend on the explicit form of the stress-energy operator, implying that different stress-energy tensors of the scalar field—canonical or improved—are thermodynamically inequivalent.

Electron velocity distribution function in a plasma with temperature gradient and in the presence of suprathermal electrons: application to incoherent-scatter plasma lines

Directory of Open Access Journals (Sweden)

P. Guio

Full Text Available The plasma dispersion function and the reduced velocity distribution function are calculated numerically for any arbitrary velocity distribution function with cylindrical symmetry along the magnetic field. The electron velocity distribution is separated into two distributions representing the distribution of the ambient electrons and the suprathermal electrons. The velocity distribution function of the ambient electrons is modelled by a near-Maxwellian distribution function in presence of a temperature gradient and a potential electric field. The velocity distribution function of the suprathermal electrons is derived from a numerical model of the angular energy flux spectrum obtained by solving the transport equation of electrons. The numerical method used to calculate the plasma dispersion function and the reduced velocity distribution is described. The numerical code is used with simulated data to evaluate the Doppler frequency asymmetry between the up- and downshifted plasma lines of the incoherent-scatter plasma lines at different wave vectors. It is shown that the observed Doppler asymmetry is more dependent on deviation from the Maxwellian through the thermal part for high-frequency radars, while for low-frequency radars the Doppler asymmetry depends more on the presence of a suprathermal population. It is also seen that the full evaluation of the plasma dispersion function gives larger Doppler asymmetry than the heat flow approximation for Langmuir waves with phase velocity about three to six times the mean thermal velocity. For such waves the moment expansion of the dispersion function is not fully valid and the full calculation of the dispersion function is needed.

Key words. Non-Maxwellian electron velocity distribution · Incoherent scatter plasma lines · EISCAT · Dielectric response function

Electron velocity distribution function in a plasma with temperature gradient and in the presence of suprathermal electrons: application to incoherent-scatter plasma lines

Directory of Open Access Journals (Sweden)

P. Guio

1998-10-01

Full Text Available The plasma dispersion function and the reduced velocity distribution function are calculated numerically for any arbitrary velocity distribution function with cylindrical symmetry along the magnetic field. The electron velocity distribution is separated into two distributions representing the distribution of the ambient electrons and the suprathermal electrons. The velocity distribution function of the ambient electrons is modelled by a near-Maxwellian distribution function in presence of a temperature gradient and a potential electric field. The velocity distribution function of the suprathermal electrons is derived from a numerical model of the angular energy flux spectrum obtained by solving the transport equation of electrons. The numerical method used to calculate the plasma dispersion function and the reduced velocity distribution is described. The numerical code is used with simulated data to evaluate the Doppler frequency asymmetry between the up- and downshifted plasma lines of the incoherent-scatter plasma lines at different wave vectors. It is shown that the observed Doppler asymmetry is more dependent on deviation from the Maxwellian through the thermal part for high-frequency radars, while for low-frequency radars the Doppler asymmetry depends more on the presence of a suprathermal population. It is also seen that the full evaluation of the plasma dispersion function gives larger Doppler asymmetry than the heat flow approximation for Langmuir waves with phase velocity about three to six times the mean thermal velocity. For such waves the moment expansion of the dispersion function is not fully valid and the full calculation of the dispersion function is needed.Key words. Non-Maxwellian electron velocity distribution · Incoherent scatter plasma lines · EISCAT · Dielectric response function

Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

International Nuclear Information System (INIS)

Senovilla, Jose M M

2010-01-01

The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)

Measurement of carotid bifurcation pressure gradients using the Bernoulli principle.

Science.gov (United States)

Illig, K A; Ouriel, K; DeWeese, J A; Holen, J; Green, R M

1996-04-01

Current randomized prospective studies suggest that the degree of carotid stenosis is a critical element in deciding whether surgical or medical treatment is appropriate. Of potential interest is the actual pressure drop caused by the blockage, but no direct non-invasive means of quantifying the hemodynamic consequences of carotid artery stenoses currently exists. The present prospective study examined whether preoperative pulsed-Doppler duplex ultrasonographic velocity (v) measurements could be used to predict pressure gradients (delta P) caused by carotid artery stenoses, and whether such measurements could be used to predict angiographic percent diameter reduction. Preoperative Doppler velocity and intraoperative direct pressure measurements were obtained, and per cent diameter angiographic stenosis measured in 76 consecutive patients who underwent 77 elective carotid endarterectomies. Using the Bernoulli principle (delta P = 4v(2), pressure gradients across the stenoses were calculated. The predicted delta P, as well as absolute velocities and internal carotid artery/common carotid velocity ratios were compared with the actual delta P measured intraoperatively and with preoperative angiography and oculopneumoplethysmography (OPG) results. An end-diastolic velocity of > or = 1 m/s and an end-diastolic internal carotid artery/common carotid artery velocity ratio of > or = 10 predicted a 50% diameter angiographic stenosis with 100% specificity. Although statistical significance was reached, preoperative pressure gradients derived from the Bernoulli equation could not predict actual individual intraoperative pressure gradients with enough accuracy to allow decision making on an individual basis. Velocity measurements were as specific and more sensitive than OPG results. Delta P as predicted by the Bernoulli equation is not sufficiently accurate at the carotid bifurcation to be useful for clinical decision making on an individual basis. However, end

Diffusion tensor imaging using multiple coils for mouse brain connectomics.

Science.gov (United States)

Nouls, John C; Badea, Alexandra; Anderson, Robert B J; Cofer, Gary P; Allan Johnson, G

2018-04-19

The correlation between brain connectivity and psychiatric or neurological diseases has intensified efforts to develop brain connectivity mapping techniques on mouse models of human disease. The neural architecture of mouse brain specimens can be shown non-destructively and three-dimensionally by diffusion tensor imaging, which enables tractography, the establishment of a connectivity matrix and connectomics. However, experiments on cohorts of animals can be prohibitively long. To improve throughput in a 7-T preclinical scanner, we present a novel two-coil system in which each coil is shielded, placed off-isocenter along the axis of the magnet and connected to a receiver circuit of the scanner. Preservation of the quality factor of each coil is essential to signal-to-noise ratio (SNR) performance and throughput, because mouse brain specimen imaging at 7 T takes place in the coil-dominated noise regime. In that regime, we show a shielding configuration causing no SNR degradation in the two-coil system. To acquire data from several coils simultaneously, the coils are placed in the magnet bore, around the isocenter, in which gradient field distortions can bias diffusion tensor imaging metrics, affect tractography and contaminate measurements of the connectivity matrix. We quantified the experimental alterations in fractional anisotropy and eigenvector direction occurring in each coil. We showed that, when the coils were placed 12 mm away from the isocenter, measurements of the brain connectivity matrix appeared to be minimally altered by gradient field distortions. Simultaneous measurements on two mouse brain specimens demonstrated a full doubling of the diffusion tensor imaging throughput in practice. Each coil produced images devoid of shading or artifact. To further improve the throughput of mouse brain connectomics, we suggested a future expansion of the system to four coils. To better understand acceptable trade-offs between imaging throughput and connectivity

Influence of velocity gradient on optimisation of the aggregation process and physical properties of formed aggregates. Part 1. Inline high density suspension (IHDS) aggregation process

Czech Academy of Sciences Publication Activity Database

Polášek, Pavel

2011-01-01

Roč. 59, č. 2 (2011), s. 107-117 ISSN 0042-790X R&D Projects: GA ČR GA103/07/1016 Institutional research plan: CEZ:AV0Z20600510 Keywords : flocculation optimum * inline high density suspension (IHDS) formation process * properties of aggregates * intensity of agitation * velocity gradient G Subject RIV: BK - Fluid Dynamics Impact factor: 0.340, year: 2011

Statistical analysis of the velocity and scalar fields in reacting turbulent wall-jets

Science.gov (United States)

Pouransari, Z.; Biferale, L.; Johansson, A. V.

2015-02-01

The concept of local isotropy in a chemically reacting turbulent wall-jet flow is addressed using direct numerical simulation (DNS) data. Different DNS databases with isothermal and exothermic reactions are examined. The chemical reaction and heat release effects on the turbulent velocity, passive scalar, and reactive species fields are studied using their probability density functions (PDFs) and higher order moments for velocities and scalar fields, as well as their gradients. With the aid of the anisotropy invariant maps for the Reynolds stress tensor, the heat release effects on the anisotropy level at different wall-normal locations are evaluated and found to be most accentuated in the near-wall region. It is observed that the small-scale anisotropies are persistent both in the near-wall region and inside the jet flame. Two exothermic cases with different Damköhler numbers are examined and the comparison revealed that the Damköhler number effects are most dominant in the near-wall region, where the wall cooling effects are influential. In addition, with the aid of PDFs conditioned on the mixture fraction, the significance of the reactive scalar characteristics in the reaction zone is illustrated. We argue that the combined effects of strong intermittency and strong persistency of anisotropy at the small scales in the entire domain can affect mixing and ultimately the combustion characteristics of the reacting flow.

Hepatic venous pressure gradients measured by duplex ultrasound

International Nuclear Information System (INIS)

Tasu, J.-P.; Rocher, L.; Peletier, G.; Kuoch, V.; Kulh, E.; Miquel, A.; Buffet, C.; Biery, M.

2002-01-01

AIMS: The hepatic venous pressure gradient is a major prognostic factor in portal hypertension but its measurement is complex and requires invasive angiography. This study investigated the relationship between the hepatic venous pressure gradient and a number of Doppler measurements, including the arterial acceleration index. METHOD: We measured the hepatic venous pressure gradient in 50 fasting patients at hepatic venography. Immediately afterwards, a duplex sonographic examination of the liver was performed at which multiple measurements and indices of the venous and arterial hepatic vasculature were made. RESULTS: Hepatic arterial acceleration was correlated directly with the hepatic venous pressure gradient (r = 0.83, P -2 provided a positive predictive value of 95%, a sensitivity of 65% and a specificity of 95% for detecting patients with severe portal hypertension (hepatic venous pressure gradient > 12 mmHg). A correlation between the hepatic venous pressure gradient and the congestion index of the portal vein velocity (r = 0.45,P = 0.01) and portal vein velocity (r = 0.40,P = 0.044), was also noted. CONCLUSION: Measuring the hepatic arterial acceleration index may help in the non-invasive evaluation of portal hypertension. Tasu, J.-P. et al. (2002)

Monograph On Tensor Notations

Science.gov (United States)

Sirlin, Samuel W.

1993-01-01

Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.

Strain gradient effects on steady state crack growth in rate-sensitive materials

DEFF Research Database (Denmark)

Nielsen, Kim Lau; Niordson, Christian Frithiof; Hutchinson, John W.

2012-01-01

, a characteristic velocity, at which the toughness becomes independent of the rate-sensitivity, has been observed. It is the aim to bring forward a similar characteristic velocity for the current strain gradient visco-plastic model, as-well as to signify its use in future visco-plastic material modeling.......Steady state crack propagation produce substantial plastic strain gradients near the tip, which are accompanied by a high density of geometrically necessary dislocations and additional local strain hardening. Here, the objective is to study these gradient effects on Mode I toughness...... of a homogeneous rate-sensitive metal, using a higher order plasticity theory. Throughout, emphasis is on the toughness rate-sensitivity, as a recent numerical study of a conventional material (no gradient effects) has indicated a significant influence of both strain rate hardening and crack tip velocity. Moreover...

Source-Type Identification Analysis Using Regional Seismic Moment Tensors

Science.gov (United States)

Chiang, A.; Dreger, D. S.; Ford, S. R.; Walter, W. R.

2012-12-01

Waveform inversion to determine the seismic moment tensor is a standard approach in determining the source mechanism of natural and manmade seismicity, and may be used to identify, or discriminate different types of seismic sources. The successful applications of the regional moment tensor method at the Nevada Test Site (NTS) and the 2006 and 2009 North Korean nuclear tests (Ford et al., 2009a, 2009b, 2010) show that the method is robust and capable for source-type discrimination at regional distances. The well-separated populations of explosions, earthquakes and collapses on a Hudson et al., (1989) source-type diagram enables source-type discrimination; however the question remains whether or not the separation of events is universal in other regions, where we have limited station coverage and knowledge of Earth structure. Ford et al., (2012) have shown that combining regional waveform data and P-wave first motions removes the CLVD-isotropic tradeoff and uniquely discriminating the 2009 North Korean test as an explosion. Therefore, including additional constraints from regional and teleseismic P-wave first motions enables source-type discrimination at regions with limited station coverage. We present moment tensor analysis of earthquakes and explosions (M6) from Lop Nor and Semipalatinsk test sites for station paths crossing Kazakhstan and Western China. We also present analyses of smaller events from industrial sites. In these sparse coverage situations we combine regional long-period waveforms, and high-frequency P-wave polarity from the same stations, as well as from teleseismic arrays to constrain the source type. Discrimination capability with respect to velocity model and station coverage is examined, and additionally we investigate the velocity model dependence of vanishing free-surface traction effects on seismic moment tensor inversion of shallow sources and recovery of explosive scalar moment. Our synthetic data tests indicate that biases in scalar

Cartesian tensors an introduction

CERN Document Server

Temple, G

2004-01-01

This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t

MATLAB tensor classes for fast algorithm prototyping.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)

2004-10-01

Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.

Turbulent flow velocity distribution at rough walls

International Nuclear Information System (INIS)

Baumann, W.

1978-08-01

Following extensive measurements of the velocity profile in a plate channel with artificial roughness geometries specific investigations were carried out to verify the results obtained. The wall geometry used was formed by high transverse square ribs having a large pitch. The measuring position relative to the ribs was varied as a parameter thus providing a statement on the local influence of roughness ribs on the values measured. As a fundamental result it was found that the gradient of the logarithmic rough wall velocity profiles, which differs widely from the value 2.5, depends but slightly on the measuring position relative to the ribs. The gradients of the smooth wall velocity profiles deviate from 2.5 near the ribs, only. This fact can be explained by the smooth wall shear stress varying with the pitch of the ribs. (orig.) 891 GL [de

Tensor quasiparticle interaction and spin-isospin sound in nuclear matter

International Nuclear Information System (INIS)

Haensel, P.

1979-01-01

The effect of the tensor components of the quasiparticle interaction in nuclear matter on the spin-isospin sound type excitations is studied. Numerical results are obtained using a simplified model of the quasiparticle interaction in nuclear matter. The quasiparticle distribution matrix corresponding to the spin-isospin sound is found to be qualitatively different from that obtained for purely central quasiparticle interaction. The macroscopic effects, however, are restricted to a small change in the phase velocity of the spin-isospin sound. (Auth.)

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

Energy Technology Data Exchange (ETDEWEB)

Krtous, Pavel [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Kubiznak, David [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Page, Don N. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada); Frolov, Valeri P. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada)

2007-02-15

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 {<=} j {<=} k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

International Nuclear Information System (INIS)

Krtous, Pavel; Kubiznak, David; Page, Don N.; Frolov, Valeri P.

2007-01-01

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 ≤ j ≤ k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Grid-Based Moment Tensor Inversion Technique by Using 3-D Green's Functions Database: A Demonstration of the 23 October 2004 Taipei Earthquake

Directory of Open Access Journals (Sweden)

Shiann-Jong Lee

2010-01-01

Full Text Available Moment tensor inversion is a routine procedure to obtain information on an earthquake source for moment magnitude and focal mechanism. However, the inversion quality is usually controlled by factors such as knowledge of an earthquake location and the suitability of a 1-D velocity model used. Here we present an improved method to invert the moment tensor solution for local earthquakes. The proposed method differs from routine centroid-moment-tensor inversion of the Broadband Array in Taiwan for Seismology in three aspects. First, the inversion is repeated in the neighborhood of an earthquake_?s hypocenter on a grid basis. Second, it utilizes Green_?s functions based on a true three-dimensional velocity model. And third, it incorporates most of the input waveforms from strong-motion records. The proposed grid-based moment tensor inversion is applied to a local earthquake that occurred near the Taipei basin on 23 October 2004 to demonstrate its effectiveness and superiority over methods used in previous studies. By using the grid-based moment tensor inversion technique and 3-D Green_?s functions, the earthquake source parameters, including earthquake location, moment magnitude and focal mechanism, are accurately found that are sufficiently consistent with regional ground motion observations up to a frequency of 1.0 Hz. This approach can obtain more precise source parameters for other earthquakes in or near a well-modeled basin and crustal structure.

Tensor-based spatiotemporal saliency detection

Science.gov (United States)

Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen

2018-03-01

This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.

Diffusion tensor in electron swarm transport

International Nuclear Information System (INIS)

Makabe, T.; Mori, T.

1983-01-01

Expression for the diffusion tensor of the electron (or light ion) swarm is presented from the higher-order expansion of the velocity distribution in the Boltzmann equation in hydrodynamic stage. Derived diffusion coefficients for the transverse and longitudinal directions include the additional terms representative of the curvature effect under the action of an electric field with the usual-two-term expressions. Numerical analysis is given for the electron swarm in model gases having the momentum transfer cross section Qsub(m)(epsilon)=Q 0 epsilon sup(beta) (β=0, 1/2, 1) using the present theory. As the result, appreciable degree of discrepancy appears between the transverse diffusion coefficient defined here and the conventional expression with increasing of β in Qsub(m). (Author)

Generalized dielectric permittivity tensor

International Nuclear Information System (INIS)

Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.

1986-01-01

The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form

Tensor analysis for physicists

CERN Document Server

Schouten, J A

1989-01-01

This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...

Sparse alignment for robust tensor learning.

Science.gov (United States)

Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

2014-10-01

Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

TensorPack: a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity

International Nuclear Information System (INIS)

Huf, P A; Carminati, J

2015-01-01

In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)

Measurement bias of fluid velocity in molecular simulations

International Nuclear Information System (INIS)

Tysanner, Martin W.; Garcia, Alejandro L.

2004-01-01

In molecular simulations of fluid flow, the measurement of mean fluid velocity is considered to be a straightforward computation, yet there is some ambiguity in its definition. We show that in systems far from equilibrium, such as those with large temperature or velocity gradients, two commonly used definitions give slightly different results. Specifically, a bias can arise when computing the mean fluid velocity by measuring the mean particle velocity in a cell and averaging this mean over samples. We show that this bias comes from the correlation of momentum and density fluctuations in non-equilibrium fluids, obtain an analytical expression for predicting it, and discuss what system characteristics (e.g., number of particles per cell, temperature gradients) reduce or magnify the error. The bias has a physical origin so although we demonstrate it by direct simulation Monte Carlo (DSMC) computations, the same effect will be observed with other particle-based simulation methods, such as molecular dynamics and lattice gases

MR diffusion tensor analysis of schizophrenic brain using statistical parametric mapping

International Nuclear Information System (INIS)

Yamada, Haruyasu; Abe, Osamu; Kasai, Kiyoto

2005-01-01

The purpose of this study is to investigate diffusion anisotropy in the schizophrenic brain by voxel-based analysis of diffusion tensor imaging (DTI), using statistical parametric mapping (SPM). We studied 33 patients with schizophrenia diagnosed by diagnostic and statistical manual of mental disorders (DSM)-IV criteria and 42 matched controls. The data was obtained with a 1.5 T MRI system. We used single-shot spin-echo planar sequences (repetition time/echo time (TR/TE)=5000/102 ms, 5 mm slice thickness and 1.5 mm gap, field of view (FOV)=21 x 21 cm 2 , number of excitation (NEX)=4, 128 x 128 pixel matrix) for diffusion tensor acquisition. Diffusion gradients (b-value of 500 or 1000 s/mm 2 ) were applied on two axes simultaneously. Diffusion properties were measured along 6 non-linear directions. The structural distortion induced by the large diffusion gradients was corrected, based on each T 2 -weighted echo-planar image (b=0 s/mm 2 ). The fractional anisotropy (FA) maps were generated on a voxel-by-voxel basis. T 2 -weighted echo-planar images were then segmented into gray matter, white matter, and cerebrospinal fluid, using SPM (Wellcome Department of Imaging, University College London, UK). All apparent diffusion coefficient (ADC) and FA maps in native space were transformed to the stereotactic space by registering each of the images to the same template image. The normalized data was smoothed and analyzed using SPM. The significant FA decrease in the patient group was found in the uncinate fasciculus, parahippocampal white matter, anterior cingulum and other areas (corrected p<0.05). No significant increased region was noted. Our results may reflect reduced diffusion anisotropy of the white matter pathway of the limbic system as shown by the decreased FA. Manual region-of-interest analysis is usually more sensitive than voxel-based analysis, but it is subjective and difficult to set with anatomical reproducibility. Voxel-based analysis of the diffusion tensor

Unique characterization of the Bel-Robinson tensor

International Nuclear Information System (INIS)

Bergqvist, G; Lankinen, P

2004-01-01

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors

Susceptibility tensor imaging and tractography of collagen fibrils in the articular cartilage.

Science.gov (United States)

Wei, Hongjiang; Gibbs, Eric; Zhao, Peida; Wang, Nian; Cofer, Gary P; Zhang, Yuyao; Johnson, G Allan; Liu, Chunlei

2017-11-01

To investigate the B 0 orientation-dependent magnetic susceptibility of collagen fibrils within the articular cartilage and to determine whether susceptibility tensor imaging (STI) can detect the 3D collagen network within cartilage. Multiecho gradient echo datasets (100-μm isotropic resolution) were acquired from fixed porcine articular cartilage specimens at 9.4 T. The susceptibility tensor was calculated using phase images acquired at 12 or 15 different orientations relative to B 0 . The susceptibility anisotropy of the collagen fibril was quantified and diffusion tensor imaging (DTI) was compared against STI. 3D tractography was performed to visualize and track the collagen fibrils with DTI and STI. STI experiments showed the distinct and significant anisotropic magnetic susceptibility of collagen fibrils within the articular cartilage. STI can be used to measure and quantify susceptibility anisotropy maps. Furthermore, STI provides orientation information of the underlying collagen network via 3D tractography. The findings of this study demonstrate that STI can characterize the orientation variation of collagen fibrils where diffusion anisotropy fails. We believe that STI could serve as a sensitive and noninvasive marker to study the collagen fibrils microstructure. Magn Reson Med 78:1683-1690, 2017. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Alignments of the galaxies in and around the Virgo cluster with the local velocity shear

International Nuclear Information System (INIS)

Lee, Jounghun; Rey, Soo Chang; Kim, Suk

2014-01-01

Observational evidence is presented for the alignment between the cosmic sheet and the principal axis of the velocity shear field at the position of the Virgo cluster. The galaxies in and around the Virgo cluster from the Extended Virgo Cluster Catalog that was recently constructed by Kim et al. are used to determine the direction of the local sheet. The peculiar velocity field reconstructed from the Sloan Digital Sky Survey Data Release 7 is analyzed to estimate the local velocity shear tensor at the Virgo center. Showing first that the minor principal axis of the local velocity shear tensor is almost parallel to the direction of the line of sight, we detect a clear signal of alignment between the positions of the Virgo satellites and the intermediate principal axis of the local velocity shear projected onto the plane of the sky. Furthermore, the dwarf satellites are found to appear more strongly aligned than their normal counterparts, which is interpreted as an indication of the following. (1) The normal satellites and the dwarf satellites fall in the Virgo cluster preferentially along the local filament and the local sheet, respectively. (2) The local filament is aligned with the minor principal axis of the local velocity shear while the local sheet is parallel to the plane spanned by the minor and intermediate principal axes. Our result is consistent with the recent numerical claim that the velocity shear is a good tracer of the cosmic web.

Tensor Product of Polygonal Cell Complexes

OpenAIRE

Chien, Yu-Yen

2017-01-01

We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

Science.gov (United States)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

Notes on super Killing tensors

Energy Technology Data Exchange (ETDEWEB)

Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)

2016-03-14

The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.

Tensor Train Neighborhood Preserving Embedding

Science.gov (United States)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

The Topology of Symmetric Tensor Fields

Science.gov (United States)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Energy-momentum tensor correlation function in Nf = 2 + 1 full QCD at finite temperature

Science.gov (United States)

Taniguchi, Yusuke; Ejiri, Shinji; Kanaya, Kazuyuki; Kitazawa, Masakiyo; Suzuki, Asobu; Suzuki, Hiroshi; Umeda, Takashi

2018-03-01

We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in Nf = 2 + 1 full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturba-tively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing = 0:07 fm. In this paper the temperature is limited to a single value T ≃ 232 MeV. The u, d quark mass is rather heavy with mπ=mρ ≃ 0:63 while the s quark mass is set to approximately its physical value.

Random SU(2) invariant tensors

Science.gov (United States)

Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei

2018-04-01

SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n  =  4. In this paper, we show that for n  >  4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.

Magnetometer-inferred, Equatorial, Daytime Vertical ExB Drift Velocities Observed in the African Longitude Sector

Science.gov (United States)

Anderson, D. N.; Yizengaw, E.

2011-12-01

A recent paper has investigated the sharp longitude gradients in the dayside ExB drift velocities associated with the 4-cell, non-migrating structures thought to be connected with the eastward propagating, diurnal, non-migrating (DE3) tides. Observations of vertical ExB drift velocities obtained from the Ion Velocity Meter (IVM) on the Communication/Navigation Outage Forecast System (C/NOFS) satellite were obtained in the Western Pacific, Eastern Pacific, Peruvian and Atlantic sectors for a few days during the months of October, March and December, 2009. Respective ExB drift velocity gradients at the cell boundaries for these 4 longitude sectors were a.) -1.3m/sec/degree, b.) 3m/sec/degree, c.) -4m/sec/degree and d.) 1m/sec/degree and were observed on a day-to-day basis. In this talk, we estimate the longitude gradients in the dayside, vertical ExB drift velocities from magnetometer H-component observations in the African sector. We briefly describe the technique for obtaining realistic ExB drift velocities associated with the difference in the H-component values between a magnetometer on the magnetic equator and one off the magnetic equator at 6 to 9 degrees dip latitude (delta H). We present magnetometer-inferred, dayside ExB drift velocities obtained from the AMBER (African Meridian B-field Education and Research) magnetometer chain in the East Africa (Ethiopian) longitude sector and the West African (Nigerian) longitude sector. We compare the longitude gradients in ExB drift velocities in the African sector with the C/NOFS- observed longitude gradients mentioned above. We also discuss the advantages of using ground-based magnetometer observations to infer ExB drift velocities compared with the C/NOFS satellite observations.

Atmospheric kinematics of high velocity long period variables

International Nuclear Information System (INIS)

Willson, L.A.

1982-01-01

Radial velocities of atomic absorption lines of three long period variables, RT Cyg, Z Oph and S Car, have been analysed in order to understand velocity gradients and discontinuities in their atmospheres. Phase coverage is from five days before maximum to 73 days after maximum for RT Cyg, from 17 days before to 44 days after maximum for Z Oph, and at 9 days before maximum for S Car. On a few spectrograms double lines were seen. All spectrograms were analysed by a four-parameter regression programme to yield the dependence of the radial velocity on the excitation potential, first ionization potential, wavelength and line strength, as indicators of the depth of line formation. The data were analysed to yield the velocity discontinuity across shock waves and velocity gradients between shock waves. Near maximum light the radial velocities cannot be understood by the presence of one shock only but rather require two shocks. The lower shock becomes apparent at the longer wavelengths. Consistent parameters are obtained if these stars are fundamental mode pulsators with total masses in the range of 0.5 to 1.0 solar mass and effective radii in the range of 0.85 to 1.5 x 10 13 cm. (author)

Is the temperature gradient or the derivative of the density gradient responsible for drift solitons?

International Nuclear Information System (INIS)

Salat, A.

1990-01-01

In conventional drift wave theory the density gradient κ n =d lnn/dχ determines the linear phase velocity, and the (electron) temperature gradient κ T =d lnT/dχ gives rise to a nonlinear term which leads to the existence of soliton-type solutions and solitary waves. LAKHIN, MIKHAILOVSKI and ONISHCHENKO, Phys. Lett. A 119, 348 (1987) and Plasma Phys. and Contr. Fus. 30, 457 (1988), recently claimed that it is not κ T but essentially the derivative of the density gradient, dκ n /dχ, that is relevant. This claim is refuted by means of an expansion scheme in ε=eΦ/T≤1, where Φ is the drift wave potential. (orig.)

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Improved tensor multiplets

International Nuclear Information System (INIS)

Wit, B. de; Rocek, M.

1982-01-01

We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.)

The evolution of tensor polarization

International Nuclear Information System (INIS)

Huang, H.; Lee, S.Y.; Ratner, L.

1993-01-01

By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake

Tensor algebra and tensor analysis for engineers with applications to continuum mechanics

CERN Document Server

Itskov, Mikhail

2015-01-01

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

The Limit Deposit Velocity model, a new approach

Directory of Open Access Journals (Sweden)

Miedema Sape A.

2015-12-01

Full Text Available In slurry transport of settling slurries in Newtonian fluids, it is often stated that one should apply a line speed above a critical velocity, because blow this critical velocity there is the danger of plugging the line. There are many definitions and names for this critical velocity. It is referred to as the velocity where a bed starts sliding or the velocity above which there is no stationary bed or sliding bed. Others use the velocity where the hydraulic gradient is at a minimum, because of the minimum energy consumption. Most models from literature are one term one equation models, based on the idea that the critical velocity can be explained that way.

Bayesian inference and interpretation of centroid moment tensors of the 2016 Kumamoto earthquake sequence, Kyushu, Japan

Science.gov (United States)

Hallo, Miroslav; Asano, Kimiyuki; Gallovič, František

2017-09-01

On April 16, 2016, Kumamoto prefecture in Kyushu region, Japan, was devastated by a shallow M JMA7.3 earthquake. The series of foreshocks started by M JMA6.5 foreshock 28 h before the mainshock. They have originated in Hinagu fault zone intersecting the mainshock Futagawa fault zone; hence, the tectonic background for this earthquake sequence is rather complex. Here we infer centroid moment tensors (CMTs) for 11 events with M JMA between 4.8 and 6.5, using strong motion records of the K-NET, KiK-net and F-net networks. We use upgraded Bayesian full-waveform inversion code ISOLA-ObsPy, which takes into account uncertainty of the velocity model. Such an approach allows us to reliably assess uncertainty of the CMT parameters including the centroid position. The solutions show significant systematic spatial and temporal variations throughout the sequence. Foreshocks are right-lateral steeply dipping strike-slip events connected to the NE-SW shear zone. Those located close to the intersection of the Hinagu and Futagawa fault zones are dipping slightly to ESE, while those in the southern area are dipping to WNW. Contrarily, aftershocks are mostly normal dip-slip events, being related to the N-S extensional tectonic regime. Most of the deviatoric moment tensors contain only minor CLVD component, which can be attributed to the velocity model uncertainty. Nevertheless, two of the CMTs involve a significant CLVD component, which may reflect complex rupture process. Decomposition of those moment tensors into two pure shear moment tensors suggests combined right-lateral strike-slip and normal dip-slip mechanisms, consistent with the tectonic settings of the intersection of the Hinagu and Futagawa fault zones.[Figure not available: see fulltext.

Tensor Calculus: Unlearning Vector Calculus

Science.gov (United States)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Hepatic venous pressure gradients measured by duplex ultrasound

Energy Technology Data Exchange (ETDEWEB)

Tasu, J.-P.; Rocher, L.; Peletier, G.; Kuoch, V.; Kulh, E.; Miquel, A.; Buffet, C.; Biery, M

2002-08-01

AIMS: The hepatic venous pressure gradient is a major prognostic factor in portal hypertension but its measurement is complex and requires invasive angiography. This study investigated the relationship between the hepatic venous pressure gradient and a number of Doppler measurements, including the arterial acceleration index. METHOD: We measured the hepatic venous pressure gradient in 50 fasting patients at hepatic venography. Immediately afterwards, a duplex sonographic examination of the liver was performed at which multiple measurements and indices of the venous and arterial hepatic vasculature were made. RESULTS: Hepatic arterial acceleration was correlated directly with the hepatic venous pressure gradient (r = 0.83, P < 0.0001) and with the Child-Pugh score (r = 0.63, P < 0.0001). An acceleration index cut-off value of 1 m.s{sup -2} provided a positive predictive value of 95%, a sensitivity of 65% and a specificity of 95% for detecting patients with severe portal hypertension (hepatic venous pressure gradient > 12 mmHg). A correlation between the hepatic venous pressure gradient and the congestion index of the portal vein velocity (r = 0.45,P = 0.01) and portal vein velocity (r = 0.40,P = 0.044), was also noted. CONCLUSION: Measuring the hepatic arterial acceleration index may help in the non-invasive evaluation of portal hypertension. Tasu, J.-P. et al. (2002)

Simultaneous inversion of the background velocity and the perturbation in full-waveform inversion

KAUST Repository

Wu, Zedong

2015-09-02

The gradient of standard full-waveform inversion (FWI) attempts to map the residuals in the data to perturbations in the model. Such perturbations may include smooth background updates from the transmission components and high wavenumber updates from the reflection components. However, if we fix the reflection components using imaging, the gradient of what is referred to as reflected-waveform inversion (RWI) admits mainly transmission background-type updates. The drawback of existing RWI methods is that they lack an optimal image capable of producing reflections within the convex region of the optimization. Because the influence of velocity on the data was given mainly by its background (propagator) and perturbed (reflectivity) components, we have optimized both components simultaneously using a modified objective function. Specifically, we used an objective function that combined the data generated from a source using the background velocity, and that by the perturbed velocity through Born modeling, to fit the observed data. When the initial velocity was smooth, the data modeled from the source using the background velocity will mainly be reflection free, and most of the reflections were obtained from the image (perturbed velocity). As the background velocity becomes more accurate and can produce reflections, the role of the image will slowly diminish, and the update will be dominated by the standard FWI gradient to obtain high resolution. Because the objective function was quadratic with respect to the image, the inversion for the image was fast. To update the background velocity smoothly, we have combined different components of the gradient linearly through solving a small optimization problem. Application to the Marmousi model found that this method converged starting with a linearly increasing velocity, and with data free of frequencies below 4 Hz. Application to the 2014 Chevron Gulf of Mexico imaging challenge data set demonstrated the potential of the

Link prediction via generalized coupled tensor factorisation

DEFF Research Database (Denmark)

Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.

2012-01-01

and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....

Propagation of the Semidiurnal Internal Tide: Phase Velocity Versus Group Velocity

Science.gov (United States)

Zhao, Zhongxiang

2017-12-01

The superposition of two waves of slightly different wavelengths has long been used to illustrate the distinction between phase velocity and group velocity. The first-mode M2 and S2 internal tides exemplify such a two-wave model in the natural ocean. The M2 and S2 tidal frequencies are 1.932 and 2 cycles per day, respectively, and their superposition forms a spring-neap cycle in the semidiurnal band. The spring-neap cycle acts like a wave, with its frequency, wave number, and phase being the differences of the M2 and S2 internal tides. The spring-neap cycle and energy of the semidiurnal internal tide propagate at the group velocity. Long-range propagation of M2 and S2 internal tides in the North Pacific is observed by satellite altimetry. Along a 3,400 km beam spanning 24°-54°N, the M2 and S2 travel times are 10.9 and 11.2 days, respectively. For comparison, it takes the spring-neap cycle 21.1 days to travel over this distance. Spatial maps of the M2 phase velocity, the S2 phase velocity, and the group velocity are determined from phase gradients of the corresponding satellite observed internal tide fields. The observed phase and group velocities agree with theoretical values estimated using the World Ocean Atlas 2013 annual-mean ocean stratification.

Energy-momentum tensor of the electromagnetic field

International Nuclear Information System (INIS)

Horndeski, G.W.; Wainwright, J.

1977-01-01

In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources

Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions

International Nuclear Information System (INIS)

Lin, Hongxia; Du, Lili

2013-01-01

In this paper, we give some new global regularity criteria for three-dimensional incompressible magnetohydrodynamics (MHD) equations. More precisely, we provide some sufficient conditions in terms of the derivatives of the velocity or pressure, for the global regularity of strong solutions to 3D incompressible MHD equations in the whole space, as well as for periodic boundary conditions. Moreover, the regularity criterion involving three of the nine components of the velocity gradient tensor is also obtained. The main results generalize the recent work by Cao and Wu (2010 Two regularity criteria for the 3D MHD equations J. Diff. Eqns 248 2263–74) and the analysis in part is based on the works by Cao C and Titi E (2008 Regularity criteria for the three-dimensional Navier–Stokes equations Indiana Univ. Math. J. 57 2643–61; 2011 Gobal regularity criterion for the 3D Navier–Stokes equations involving one entry of the velocity gradient tensor Arch. Rational Mech. Anal. 202 919–32) for 3D incompressible Navier–Stokes equations. (paper)

Slope-velocity equilibrium and evolution of surface roughness on a stony hillslope

Science.gov (United States)

Nearing, Mark A.; Polyakov, Viktor O.; Nichols, Mary H.; Hernandez, Mariano; Li, Li; Zhao, Ying; Armendariz, Gerardo

2017-06-01

Slope-velocity equilibrium is hypothesized as a state that evolves naturally over time due to the interaction between overland flow and surface morphology, wherein steeper areas develop a relative increase in physical and hydraulic roughness such that flow velocity is a unique function of overland flow rate independent of slope gradient. This study tests this hypothesis under controlled conditions. Artificial rainfall was applied to 2 m by 6 m plots at 5, 12, and 20 % slope gradients. A series of simulations were made with two replications for each treatment with measurements of runoff rate, velocity, rock cover, and surface roughness. Velocities measured at the end of each experiment were a unique function of discharge rates, independent of slope gradient or rainfall intensity. Physical surface roughness was greater at steeper slopes. The data clearly showed that there was no unique hydraulic coefficient for a given slope, surface condition, or rainfall rate, with hydraulic roughness greater at steeper slopes and lower intensities. This study supports the hypothesis of slope-velocity equilibrium, implying that use of hydraulic equations, such as Chezy and Manning, in hillslope-scale runoff models is problematic because the coefficients vary with both slope and rainfall intensity.

Evaluation of Maryland abutment scour equation through selected threshold velocity methods

Science.gov (United States)

Benedict, S.T.

2010-01-01

The U.S. Geological Survey, in cooperation with the Maryland State Highway Administration, used field measurements of scour to evaluate the sensitivity of the Maryland abutment scour equation to the critical (or threshold) velocity variable. Four selected methods for estimating threshold velocity were applied to the Maryland abutment scour equation, and the predicted scour to the field measurements were compared. Results indicated that performance of the Maryland abutment scour equation was sensitive to the threshold velocity with some threshold velocity methods producing better estimates of predicted scour than did others. In addition, results indicated that regional stream characteristics can affect the performance of the Maryland abutment scour equation with moderate-gradient streams performing differently from low-gradient streams. On the basis of the findings of the investigation, guidance for selecting threshold velocity methods for application to the Maryland abutment scour equation are provided, and limitations are noted.

The three-dimensional distributions of tangential velocity and total- temperature in vortex tubes

DEFF Research Database (Denmark)

Linderstrøm-Lang, C.U.

1971-01-01

The axial and radial gradients of the tangential velocity distribution are calculated from prescribed secondary flow functions on the basis of a zero-order approximation to the momentum equations developed by Lewellen. It is shown that secondary flow functions may be devised which meet pertinent...... physical requirements and which at the same time lead to realistic tangential velocity gradients. The total-temperature distribution in both the axial and radial directions is calculated from such secondary flow functions and corresponding tangential velocity results on the basis of an approximate...

Role of the vertical pressure gradient in wave boundary layers

DEFF Research Database (Denmark)

Jensen, Karsten Lindegård; Sumer, B. Mutlu; Vittori, Giovanna

2014-01-01

By direct numerical simulation (DNS) of the flow in an oscillatory boundary layer, it is possible to obtain the pressure field. From the latter, the vertical pressure gradient is determined. Turbulent spots are detected by a criterion involving the vertical pressure gradient. The vertical pressure...... gradient is also treated as any other turbulence quantity like velocity fluctuations and statistical properties of the vertical pressure gradient are calculated from the DNS data. The presence of a vertical pressure gradient in the near bed region has significant implications for sediment transport....

A new Weyl-like tensor of geometric origin

Science.gov (United States)

Vishwakarma, Ram Gopal

2018-04-01

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.

Tensor calculus for physics a concise guide

CERN Document Server

Neuenschwander, Dwight E

2015-01-01

Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...

Seamless warping of diffusion tensor fields

DEFF Research Database (Denmark)

Xu, Dongrong; Hao, Xuejun; Bansal, Ravi

2008-01-01

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...

Eckart frame vibration-rotation Hamiltonians: Contravariant metric tensor

International Nuclear Information System (INIS)

Pesonen, Janne

2014-01-01

Eckart frame is a unique embedding in the theory of molecular vibrations and rotations. It is defined by the condition that the Coriolis coupling of the reference structure of the molecule is zero for every choice of the shape coordinates. It is far from trivial to set up Eckart kinetic energy operators (KEOs), when the shape of the molecule is described by curvilinear coordinates. In order to obtain the KEO, one needs to set up the corresponding contravariant metric tensor. Here, I derive explicitly the Eckart frame rotational measuring vectors. Their inner products with themselves give the rotational elements, and their inner products with the vibrational measuring vectors (which, in the absence of constraints, are the mass-weighted gradients of the shape coordinates) give the Coriolis elements of the contravariant metric tensor. The vibrational elements are given as the inner products of the vibrational measuring vectors with themselves, and these elements do not depend on the choice of the body-frame. The present approach has the advantage that it does not depend on any particular choice of the shape coordinates, but it can be used in conjunction with all shape coordinates. Furthermore, it does not involve evaluation of covariant metric tensors, chain rules of derivation, or numerical differentiation, and it can be easily modified if there are constraints on the shape of the molecule. Both the planar and non-planar reference structures are accounted for. The present method is particular suitable for numerical work. Its computational implementation is outlined in an example, where I discuss how to evaluate vibration-rotation energies and eigenfunctions of a general N-atomic molecule, the shape of which is described by a set of local polyspherical coordinates

Tensor norms and operator ideals

CERN Document Server

Defant, A; Floret, K

1992-01-01

The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer

Shape anisotropy: tensor distance to anisotropy measure

Science.gov (United States)

Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.

2011-03-01

Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.

Determination of wall shear stress from mean velocity and Reynolds shear stress profiles

Science.gov (United States)

Volino, Ralph J.; Schultz, Michael P.

2018-03-01

An analytical method is presented for determining the Reynolds shear stress profile in steady, two-dimensional wall-bounded flows using the mean streamwise velocity. The method is then utilized with experimental data to determine the local wall shear stress. The procedure is applicable to flows on smooth and rough surfaces with arbitrary pressure gradients. It is based on the streamwise component of the boundary layer momentum equation, which is transformed into inner coordinates. The method requires velocity profiles from at least two streamwise locations, but the formulation of the momentum equation reduces the dependence on streamwise gradients. The method is verified through application to laminar flow solutions and turbulent DNS results from both zero and nonzero pressure gradient boundary layers. With strong favorable pressure gradients, the method is shown to be accurate for finding the wall shear stress in cases where the Clauser fit technique loses accuracy. The method is then applied to experimental data from the literature from zero pressure gradient studies on smooth and rough walls, and favorable and adverse pressure gradient cases on smooth walls. Data from very near the wall are not required for determination of the wall shear stress. Wall friction velocities obtained using the present method agree with those determined in the original studies, typically to within 2%.

Energy-momentum tensor correlation function in Nf = 2 + 1 full QCD at finite temperature

Directory of Open Access Journals (Sweden)

Taniguchi Yusuke

2018-01-01

Full Text Available We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in Nf = 2 + 1 full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturba-tively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing = 0:07 fm. In this paper the temperature is limited to a single value T ≃ 232 MeV. The u, d quark mass is rather heavy with mπ=mρ ≃ 0:63 while the s quark mass is set to approximately its physical value.

Tensors and their applications

CERN Document Server

Islam, Nazrul

2006-01-01

About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces

Tensor Completion Algorithms in Big Data Analytics

OpenAIRE

Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia

2017-01-01

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...

Efficient MATLAB computations with sparse and factored tensors.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)

2006-12-01

In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.

Study of thermal-gradient-induced migration of brine inclusions in salt. Final report

International Nuclear Information System (INIS)

Olander, D.R.

1984-08-01

Natural salt deposits, which are being considered for high-level waste disposal, contain a small volume fraction of water in the form of brine inclusions distributed throughout the salt. Radioactive decay heating of the nuclear wastes will impose a temperature gradient on the surrounding salt which mobilizes the brine inclusions. Inclusions filled completely with brine (the all-liquid inclusions) migrate up the temperature gradient and eventually accumulate brine near the buried waste forms. The brine may slowly corrode or degrade the waste forms, which is undesirable. Therefore it is important to consider the migration of brine inclusions in salt under imposed temperature gradients to properly evaluate the performance of a future salt repository for nuclear wastes. The migration velocities of the inclusions were found to be dependent on temperature, temperature gradient, and inclusion shape and size. The velocities were also dictated by the interfacial mass transfer resistance at brine/solid interface. This interfacial resistance depends on the dislocation density in the crystal, which in turn, depends on the axial compressive loading of the crystal. At low axial loads, the dependence between the velocity and temperature gradient is nonlinear. At high axial loads, the interfacial resistance is reduced and the migration velocity depends linearly on the temperature gradient. All-liquid inclusions filled with mixed brines were also studied. For gas-liquid inclusions, helium, air and argon were compared. Migration studies were also conducted on single crystallites of natural salt as well as in polycrystalline natural salt samples. The behavior of the inclusions at large-ange grain boundaries was observed

Study of thermal-gradient-induced migration of brine inclusions in salt. Final report

Energy Technology Data Exchange (ETDEWEB)

Olander, D.R.

1984-08-01

Natural salt deposits, which are being considered for high-level waste disposal, contain a small volume fraction of water in the form of brine inclusions distributed throughout the salt. Radioactive decay heating of the nuclear wastes will impose a temperature gradient on the surrounding salt which mobilizes the brine inclusions. Inclusions filled completely with brine (the all-liquid inclusions) migrate up the temperature gradient and eventually accumulate brine near the buried waste forms. The brine may slowly corrode or degrade the waste forms, which is undesirable. Therefore it is important to consider the migration of brine inclusions in salt under imposed temperature gradients to properly evaluate the performance of a future salt repository for nuclear wastes. The migration velocities of the inclusions were found to be dependent on temperature, temperature gradient, and inclusion shape and size. The velocities were also dictated by the interfacial mass transfer resistance at brine/solid interface. This interfacial resistance depends on the dislocation density in the crystal, which in turn, depends on the axial compressive loading of the crystal. At low axial loads, the dependence between the velocity and temperature gradient is nonlinear. At high axial loads, the interfacial resistance is reduced and the migration velocity depends linearly on the temperature gradient. All-liquid inclusions filled with mixed brines were also studied. For gas-liquid inclusions, helium, air and argon were compared. Migration studies were also conducted on single crystallites of natural salt as well as in polycrystalline natural salt samples. The behavior of the inclusions at large-ange grain boundaries was observed.

Reciprocal mass tensor : a general form

International Nuclear Information System (INIS)

Roy, C.L.

1978-01-01

Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)

A new deteriorated energy-momentum tensor

International Nuclear Information System (INIS)

Duff, M.J.

1982-01-01

The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)

Antisymmetric tensor generalizations of affine vector fields.

Science.gov (United States)

Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

2016-02-01

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

A new method for measurement of granular velocities

International Nuclear Information System (INIS)

Nyborg Andersen, B.

1984-01-01

A new, supplementary method to measure granular velocities is presented. The method utilizes the Doppler shift caused by the line of sight component of the solar rotation to cause a wavelength shift through spectral lines as function of heliocentric angle. By measuring the center-to-limb variation of the granular intensity fluctations at different wavelength positions in the lines, the velocities are found. To do this, assumptions regarding the geometrical structure of the velocity and intensity fields have to be made. Preliminary application of the method results in a steep velocity gradient suggesting zero velocity at a hight of 200 km above tau 500 = 1. Possible causes are discussed

Reflection and absorption of ion-acoustic waves in a plasma density gradient

International Nuclear Information System (INIS)

Ishihara, O.

1977-01-01

Plasma is characterized by electrical quasineutrality and the collective behavior. There exists a longitudinal low-frequency wave called an ion-acoustic wave in a plasma. One problem in the experimental study of ion-acoustic waves has been that sometimes they are observed to be reflected from discharge tube walls, and sometimes to be absorbed. Theoretical computation reveals that a velocity gradient produced by a density gradient plays a significant role in the reflection. The velocity gradient produces the subsonic-supersonic transition and long wavelength waves are reflected before reaching the transition while short wavelength waves penetrate over the transition and are absorbed in the supersonic flow plasma

(Ln-bar, g)-spaces. Special tensor fields

International Nuclear Information System (INIS)

Manoff, S.; Dimitrov, B.

1998-01-01

The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces

The Riemann-Lovelock Curvature Tensor

OpenAIRE

Kastor, David

2012-01-01

In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D

The Physical Interpretation of the Lanczos Tensor

OpenAIRE

Roberts, Mark D.

1999-01-01

The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...

Real-time object recognition in multidimensional images based on joined extended structural tensor and higher-order tensor decomposition methods

Science.gov (United States)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.

Ab-initio study of the relation between electric polarization and electric field gradients in ferroelectrics

CERN Document Server

Gonçalves, J N; Correia, J G; Butz, T; Picozzi, S; Fenta, A S; Amaral, V S

2012-01-01

The hyperfine interaction between the quadrupole moment of atomic nuclei and the electric field gradient (EFG) provides information on the electronic charge distribution close to a given atomic site. In ferroelectric materials, the loss of inversion symmetry of the electronic charge distribution is necessary for the appearance of the electric polarization. We present first-principles density functional theory calculations of ferroelectrics such as BaTiO$_{3}$, KNbO$_{3}$, PbTiO$_{3}$ and other oxides with perovskite structures, by focusing on both EFG tensors and polarization. We analyze the EFG tensor properties such as orientation and correlation between components and their relation with electric polarization. This work supports previous studies of ferroelectric materials where a relation between EFG tensors and polarization was observed, which may be exploited to study the ferroelectric order when standard techniques to measure polarization are not easily applied.

3D reconstruction of tensors and vectors

International Nuclear Information System (INIS)

Defrise, Michel; Gullberg, Grant T.

2005-01-01

Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields

Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI

Science.gov (United States)

Liu, Chunlei; Murphy, Nicole E.; Li, Wei

2012-01-01

Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987

The Definition Method and Optimization of Atomic Strain Tensors for Nuclear Power Engineering Materials

Directory of Open Access Journals (Sweden)

Xiangguo Zeng

2016-01-01

Full Text Available A common measure of deformation between atomic scale simulations and the continuum framework is provided and the strain tensors for multiscale simulations are defined in this paper. In order to compute the deformation gradient of any atom m, the weight function is proposed to eliminate the different contributions within the neighbor atoms which have different distances to atom m, and the weighted least squares error optimization model is established to seek the optimal coefficients of the weight function and the optimal local deformation gradient of each atom. The optimization model involves more than 9 parameters. To guarantee the reliability of subsequent parameters identification result and lighten the calculation workload of parameters identification, an overall analysis method of parameter sensitivity and an advanced genetic algorithm are also developed.

Time-domain full waveform inversion using the gradient preconditioning based on transmitted waves energy

KAUST Repository

Zhang, Xiao-bo

2017-06-01

The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge storage consumption in the gradient preconditioning algorithms based on Hessian matrices in time-domain full waveform inversion (FWI), but the accuracy is affected by the energy of reflected waves when strong reflectors are present in velocity model. To address this problem, we propose a gradient preconditioning method, which scales the gradient based on the energy of the “approximated transmitted wavefield” simulated by the nonreflecting acoustic wave equation. The method does not require computing or storing the Hessian matrix or its inverse. Furthermore, it can effectively eliminate the effects caused by geometric diffusion and non-uniformity illumination on gradient. The results of model experiments confirm that the time-domain FWI using the gradient preconditioning based on transmitted waves energy can achieve higher inversion precision for high-velocity body and the deep strata below when compared with using the gradient preconditioning based on seismic waves energy.

Weyl tensors for asymmetric complex curvatures

International Nuclear Information System (INIS)

Oliveira, C.G.

Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt

Measurement of sound velocity profiles in fluids for process monitoring

International Nuclear Information System (INIS)

Wolf, M; Kühnicke, E; Lenz, M; Bock, M

2012-01-01

In ultrasonic measurements, the time of flight to the object interface is often the only information that is analysed. Conventionally it is only possible to determine distances or sound velocities if the other value is known. The current paper deals with a novel method to measure the sound propagation path length and the sound velocity in media with moving scattering particles simultaneously. Since the focal position also depends on sound velocity, it can be used as a second parameter. Via calibration curves it is possible to determine the focal position and sound velocity from the measured time of flight to the focus, which is correlated to the maximum of averaged echo signal amplitude. To move focal position along the acoustic axis, an annular array is used. This allows measuring sound velocity locally resolved without any previous knowledge of the acoustic media and without a reference reflector. In previous publications the functional efficiency of this method was shown for media with constant velocities. In this work the accuracy of these measurements is improved. Furthermore first measurements and simulations are introduced for non-homogeneous media. Therefore an experimental set-up was created to generate a linear temperature gradient, which also causes a gradient of sound velocity.

Measurements of Dissipation Rate and Velocity/Pressure Gradient Correlation for Improvements to Gas Turbine Turbulent Flow Models

National Research Council Canada - National Science Library

Simpson, Roger L; Lowe, K. T; Orsi, Edgar

2006-01-01

... Reynolds number turbulent flows. With at least 4 particles at a given instant this results in the fine-spatial-resolution instantaneous measurement of the complete rate-of-strain and vorticity tensors and the dissipative...

Thermal gradient migration of brine inclusions in synthetic alkali halide single crystals

International Nuclear Information System (INIS)

Olander, D.R.; Machiels, A.J.; Balooch, M.; Yagnik, S.K.

1982-01-01

An apparatus consisting of an optical microscope with a hot stage attachment capable of simultaneously nonuniformly heating and mechanically loading small single crystals of salt was used to measure the velocities of all-liquid inclusions NaC1 and KC1 specimens under various conditions of temperature, temperature gradient, and uniaxial stress. The rate-controlling elementary step in the migration of the inclusions was found to be associated with interfacial processes, probably dissolution of the hot face. Dislocations are required for this step to take place. The small number of dislocation intersections with small inclusions in nearly perfect crystals causes substantial variations in the velocity, a sensitivity of the velocity to mechanical loading of the crystal, and a velocity which varies approximately as the second power of the temperature gradient

Should I use TensorFlow

OpenAIRE

Schrimpf, Martin

2016-01-01

Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...

Dictionary-Based Tensor Canonical Polyadic Decomposition

Science.gov (United States)

Cohen, Jeremy Emile; Gillis, Nicolas

2018-04-01

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.

Bayesian regularization of diffusion tensor images

DEFF Research Database (Denmark)

Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif

2007-01-01

Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...

Energy-momentum tensor in the fermion-pairing model

International Nuclear Information System (INIS)

Kawati, S.; Miyata, H.

1980-01-01

The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory

Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.

Science.gov (United States)

Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M

2017-08-01

Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.

A comparison of density functional theory and coupled cluster methods for the calculation of electric dipole polarizability gradients of methane

DEFF Research Database (Denmark)

Paidarová, Ivana; Sauer, Stephan P. A.

2012-01-01

We have compared the performance of density functional theory (DFT) using five different exchange-correlation functionals with four coupled cluster theory based wave function methods in the calculation of geometrical derivatives of the polarizability tensor of methane. The polarizability gradient...

Moment Tensor Inversion with 3D sensor configuration of Mining Induced Seismicity (Kiruna mine, Sweden)

Science.gov (United States)

Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian

2018-03-01

Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). Stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double couple and full moment tensor with high frequency data is very challenging. Moreover, the application to underground mining system requires accounting for the 3D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to 8 events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip, rake configurations of the double couple term were obtained. The orientations

Moment tensor inversion with three-dimensional sensor configuration of mining induced seismicity (Kiruna mine, Sweden)

Science.gov (United States)

Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian

2018-06-01

Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). A stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double-couple and full moment tensor with high frequency data, is very challenging. Moreover, the application to underground mining system requires accounting for the 3-D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3-D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in the presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to eight events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double-couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip and rake configurations of the double-couple term were obtained

THE EFFECTS OF GRADIENT VELOCITY AND DETENTION TIME TO COAGULATION – FLOCCULATION OF DYES AND ORGANIC COMPOUND IN DEEP WELL WATER

Directory of Open Access Journals (Sweden)

Muhamad Lindu

2010-06-01

Full Text Available The treatment of deep well water of Trisakti University by coagulation and flocculation using baffle channel system has been conducted. The detention time of hydrolic were varied. The coagulant dose was varied as 50, 100, 150, 200, 300, 350, 400, 450 and 500 ppm. Water of well sampel was added by coagulant with rotation velocity 200 rpm for 1 minute. The optimal coagulant dose was determined by measuring turbidity, colour, total suspended solids and organic compound. The result showed that the organic compound and colour of deep well water of Trisakti University could be reduced by coagulation and flocculation process by hydrolyc system. The optimal dose of the coagulant was 250 ppm. The removal efficiency of colour and organic compound using optimal dose for continuous flow reactor reached after water flow passed the reactor for 3 - 5 times detention time in the reactor. The optimal gradient velocity (G was 30 - 35 sec-1 and collision energy (GT was 65.000 - 79.000 to get optimal flocculation. With this condition, the removal efficiency of turbidity, colour and organic was more than 90%.   Keywords: coagulation, flocculation, colour, organic compound, deep well

The Einstein tensor characterizing some Riemann spaces

International Nuclear Information System (INIS)

Rahman, M.S.

1993-07-01

A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs

Radiative corrections in a vector-tensor model

International Nuclear Information System (INIS)

Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C.

2006-01-01

In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field

Transposes, L-Eigenvalues and Invariants of Third Order Tensors

OpenAIRE

Qi, Liqun

2017-01-01

Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...

Spectral tensor parameters for wind turbine load modeling from forested and agricultural landscapes

DEFF Research Database (Denmark)

Chougule, Abhijit S.; Mann, Jakob; Segalini, A.

2015-01-01

A velocity spectral tensor model was evaluated from the single-point measurements of wind speed. The model contains three parameters representing the dissipation rate of specific turbulent kinetic energy, a turbulence length scale and the turbulence anisotropy. Sonic anemometer measurements taken...... was better than that of the cross-wind component. No significant difference was found between the performance of the model at the forested and the agricultural areas. © 2014 The Authors. Wind Energy published by John Wiley & Sons, Ltd....

Flow behavior at different shear rates for dry powders

NARCIS (Netherlands)

Singh, A.; Singh, A.; Luding, Stefan; Nürnberg Messe GmbH,

2010-01-01

Using Discrete Element Simulations (DEM), an effort is made to study the so called “Split bottom ring shear cell” where a slow, quasi-static deformation leads to wide shear bands. Density, velocity and deformation gradients as well as structure and stress tensors, can be computed by a single

Joint Tensor Feature Analysis For Visual Object Recognition.

Science.gov (United States)

Wong, Wai Keung; Lai, Zhihui; Xu, Yong; Wen, Jiajun; Ho, Chu Po

2015-11-01

Tensor-based object recognition has been widely studied in the past several years. This paper focuses on the issue of joint feature selection from the tensor data and proposes a novel method called joint tensor feature analysis (JTFA) for tensor feature extraction and recognition. In order to obtain a set of jointly sparse projections for tensor feature extraction, we define the modified within-class tensor scatter value and the modified between-class tensor scatter value for regression. The k-mode optimization technique and the L(2,1)-norm jointly sparse regression are combined together to compute the optimal solutions. The convergent analysis, computational complexity analysis and the essence of the proposed method/model are also presented. It is interesting to show that the proposed method is very similar to singular value decomposition on the scatter matrix but with sparsity constraint on the right singular value matrix or eigen-decomposition on the scatter matrix with sparse manner. Experimental results on some tensor datasets indicate that JTFA outperforms some well-known tensor feature extraction and selection algorithms.

Graded tensor calculus

International Nuclear Information System (INIS)

Scheunert, M.

1982-10-01

We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)

Time-Dependent Moment Tensors of the First Four Source Physics Experiments (SPE) Explosions

Science.gov (United States)

Yang, X.

2015-12-01

We use mainly vertical-component geophone data within 2 km from the epicenter to invert for time-dependent moment tensors of the first four SPE explosions: SPE-1, SPE-2, SPE-3 and SPE-4Prime. We employ a one-dimensional (1D) velocity model developed from P- and Rg-wave travel times for Green's function calculations. The attenuation structure of the model is developed from P- and Rg-wave amplitudes. We select data for the inversion based on the criterion that they show consistent travel times and amplitude behavior as those predicted by the 1D model. Due to limited azimuthal coverage of the sources and the mostly vertical-component-only nature of the dataset, only long-period, diagonal components of the moment tensors are well constrained. Nevertheless, the moment tensors, particularly their isotropic components, provide reasonable estimates of the long-period source amplitudes as well as estimates of corner frequencies, albeit with larger uncertainties. The estimated corner frequencies, however, are consistent with estimates from ratios of seismogram spectra from different explosions. These long-period source amplitudes and corner frequencies cannot be fit by classical P-wave explosion source models. The results motivate the development of new P-wave source models suitable for these chemical explosions. To that end, we fit inverted moment-tensor spectra by modifying the classical explosion model using regressions of estimated source parameters. Although the number of data points used in the regression is small, the approach suggests a way for the new-model development when more data are collected.

(Ln-bar, g)-spaces. Ordinary and tensor differentials

International Nuclear Information System (INIS)

Manoff, S.; Dimitrov, B.

1998-01-01

Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces

Tensor network method for reversible classical computation

Science.gov (United States)

Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.

2018-03-01

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

Robust estimation of adaptive tensors of curvature by tensor voting.

Science.gov (United States)

Tong, Wai-Shun; Tang, Chi-Keung

2005-03-01

Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.

On the concircular curvature tensor of Riemannian manifolds

International Nuclear Information System (INIS)

Rahman, M.S.; Lal, S.

1990-06-01

Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs

Fabrication of Ni-Al/diamond composite based on layered and gradient structures of SHS system

Directory of Open Access Journals (Sweden)

Lu Jiafeng

2017-01-01

Full Text Available In this paper layered and gradient structures of Ni-Al SHS system were adopted to manufacture Ni-Al/diamond composites. The effect of the layered and the diamond mesh gradient structures of Ni-Al/diamond on the SHS process and the microstructure of the composites were investigated. It is found that with the increasing of the number of layers, the combustion wave velocity is decreased. The combustion wave velocity for diamond mesh size gradient structure of Ni-Al SHS is faster than that for the layered structure. A well bonding can be formed between diamond and the matrix in layered and gradient structure Ni-Al/diamond composites due to the melt of Ni-Cr brazing alloy.

Glyph-Based Comparative Visualization for Diffusion Tensor Fields.

Science.gov (United States)

Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna

2016-01-01

Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.

Tensoral for post-processing users and simulation authors

Science.gov (United States)

Dresselhaus, Eliot

1993-01-01

The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.

The geostrophic velocity field in shallow water over topography

Science.gov (United States)

Charnock, Henry; Killworth, Peter D.

1998-01-01

A recent note (Hopkins, T.S., 1996. A note on the geostrophic velocity field referenced to a point. Continental Shelf Research 16, 1621-1630) suggests a method for evaluating absolute pressure gradients in stratified water over topography. We demonstrate that this method requires no along-slope bottom velocity, in contradiction to what is usually observed, and that mass is not conserved.

Effects of Spatial Gradients on Electron Runaway Acceleration

Science.gov (United States)

MacNeice, Peter; Ljepojevic, N. N.

1996-01-01

The runaway process is known to accelerate electrons in many laboratory plasmas and has been suggested as an acceleration mechanism in some astrophysical plasmas, including solar flares. Current calculations of the electron velocity distributions resulting from the runaway process are greatly restricted because they impose spatial homogeneity on the distribution. We have computed runaway distributions which include consistent development of spatial gradients in the energetic tail. Our solution for the electron velocity distribution is presented as a function of distance along a finite length acceleration region, and is compared with the equivalent distribution for the infinitely long homogenous system (i.e., no spatial gradients), as considered in the existing literature. All these results are for the weak field regime. We also discuss the severe restrictiveness of this weak field assumption.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

Science.gov (United States)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

2018-05-01

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

Applications of tensor functions in creep mechanics

International Nuclear Information System (INIS)

Betten, J.

1991-01-01

Within this contribution a short survey is given of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The mechanical behaviour of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour. This paper presents certain principles, methods, and recent successfull applications of tensor functions in solid mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. (orig./RHM)

Tensor interaction in heavy-ion scattering. Pt. 1

International Nuclear Information System (INIS)

Nishioka, H.; Johnson, R.C.

1985-01-01

The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power anti Tsub(2q) have certain relations with each other for each type of tensor interaction (Tsub(R), Tsub(P) and Tsub(L) types). The predicted relations between the anti Tsub(2q) are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for 7 Li and 23 Na elastic scattering from 58 Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a Tsub(P)- or Tsub(L)-type tensor interaction in polarized heavy-ion scattering. The presence of a Tsub(P)-type tensor interaction is suggested by measured anti T 20 /anti T 22 ratios for 7 Li + 58 Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail. (orig.)

On Lovelock analogs of the Riemann tensor

Science.gov (United States)

Camanho, Xián O.; Dadhich, Naresh

2016-03-01

It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.

The simplicial Ricci tensor

International Nuclear Information System (INIS)

Alsing, Paul M; McDonald, Jonathan R; Miller, Warner A

2011-01-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

The simplicial Ricci tensor

Science.gov (United States)

Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.

2011-08-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

Beyond Low Rank: A Data-Adaptive Tensor Completion Method

OpenAIRE

Zhang, Lei; Wei, Wei; Shi, Qinfeng; Shen, Chunhua; Hengel, Anton van den; Zhang, Yanning

2017-01-01

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explicitly represents both the low-rank and non-low-rank structures in a latent tensor. Representing the no...

Exploring the tensor networks/AdS correspondence

Energy Technology Data Exchange (ETDEWEB)

Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Physics, Indian Institute of Science,560012 Bangalore (India); Gao, Zhe-Shen [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); State Key Laboratory of Surface Physics and Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing, 210093 (China); Liu, Si-Nong [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China)

2016-08-11

In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.

Analytical Energy Gradients for Excited-State Coupled-Cluster Methods

Science.gov (United States)

Wladyslawski, Mark; Nooijen, Marcel

The equation-of-motion coupled-cluster (EOM-CC) and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) methods have been firmly established as accurate and routinely applicable extensions of single-reference coupled-cluster theory to describe electronically excited states. An overview of these methods is provided, with emphasis on the many-body similarity transform concept that is the key to a rationalization of their accuracy. The main topic of the paper is the derivation of analytical energy gradients for such non-variational electronic structure approaches, with an ultimate focus on obtaining their detailed algebraic working equations. A general theoretical framework using Lagrange's method of undetermined multipliers is presented, and the method is applied to formulate the EOM-CC and STEOM-CC gradients in abstract operator terms, following the previous work in [P.G. Szalay, Int. J. Quantum Chem. 55 (1995) 151] and [S.R. Gwaltney, R.J. Bartlett, M. Nooijen, J. Chem. Phys. 111 (1999) 58]. Moreover, the systematics of the Lagrange multiplier approach is suitable for automation by computer, enabling the derivation of the detailed derivative equations through a standardized and direct procedure. To this end, we have developed the SMART (Symbolic Manipulation and Regrouping of Tensors) package of automated symbolic algebra routines, written in the Mathematica programming language. The SMART toolkit provides the means to expand, differentiate, and simplify equations by manipulation of the detailed algebraic tensor expressions directly. The Lagrangian multiplier formulation establishes a uniform strategy to perform the automated derivation in a standardized manner: A Lagrange multiplier functional is constructed from the explicit algebraic equations that define the energy in the electronic method; the energy functional is then made fully variational with respect to all of its parameters, and the symbolic differentiations directly yield the explicit

The drift force on an object in an inviscid weakly-varying rotational flow

Energy Technology Data Exchange (ETDEWEB)

Wallis, G.B. [Dartmouth College, Hanover, NH (United States)

1995-12-31

The force on any stationary object in an inviscid incompressible extensive steady flow is derived in terms of the added mass tensor and gradient of velocity of the undisturbed fluid. Taylor`s theorem is extended to flows with weak vorticity. There are possible applications to constitutive equations for two-phase flow.

Scattering angle base filtering of the inversion gradients

KAUST Repository

Alkhalifah, Tariq Ali

2014-01-01

Full waveform inversion (FWI) requires a hierarchical approach based on the availability of low frequencies to maneuver the complex nonlinearity associated with the problem of velocity inversion. I develop a model gradient filter to help us access the parts of the gradient more suitable to combat this potential nonlinearity. The filter is based on representing the gradient in the time-lag normalized domain, in which low scattering angles of the gradient update are initially muted. The result are long-wavelength updates controlled by the ray component of the wavefield. In this case, even 10 Hz data can produce near zero wavelength updates suitable for a background correction of the model. Allowing smaller scattering angle to contribute provides higher resolution information to the model.

Analytical approximations of diving-wave imaging in constant-gradient medium

KAUST Repository

Stovas, Alexey

2014-06-24

Full-waveform inversion (FWI) in practical applications is currently used to invert the direct arrivals (diving waves, no reflections) using relatively long offsets. This is driven mainly by the high nonlinearity introduced to the inversion problem when reflection data are included, which in some cases require extremely low frequency for convergence. However, analytical insights into diving waves have lagged behind this sudden interest. We use analytical formulas that describe the diving wave’s behavior and traveltime in a constant-gradient medium to develop insights into the traveltime moveout of diving waves and the image (model) point dispersal (residual) when the wrong velocity is used. The explicit formulations that describe these phenomena reveal the high dependence of diving-wave imaging on the gradient and the initial velocity. The analytical image point residual equation can be further used to scan for the best-fit linear velocity model, which is now becoming a common sight as an initial velocity model for FWI. We determined the accuracy and versatility of these analytical formulas through numerical tests.

p-Norm SDD tensors and eigenvalue localization

Directory of Open Access Journals (Sweden)

Qilong Liu

2016-07-01

Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.

Tripolar vortex formation in dense quantum plasma with ion-temperature-gradients

Science.gov (United States)

Qamar, Anisa; Ata-ur-Rahman, Mirza, Arshad M.

2012-05-01

We have derived system of nonlinear equations governing the dynamics of low-frequency electrostatic toroidal ion-temperature-gradient mode for dense quantum magnetoplasma. For some specific profiles of the equilibrium density, temperature, and ion velocity gradients, the nonlinear equations admit a stationary solution in the form of a tripolar vortex. These results are relevant to understand nonlinear structure formation in dense quantum plasmas in the presence of equilibrium ion-temperature and density gradients.

Tripolar vortex formation in dense quantum plasma with ion-temperature-gradients

Energy Technology Data Exchange (ETDEWEB)

Qamar, Anisa; Ata-ur-Rahman [Institute of Physics and Electronics, University of Peshawar, Khyber Pakhtoon Khwa 25000 (Pakistan); National Center for Physics Shahdrah Valley Road, Islamabad 44000 (Pakistan); Mirza, Arshad M. [Theoretical Plasma Physics Group, Physics Department, Quaid-i-Azam University, Islamabad 45320 (Pakistan)

2012-05-15

We have derived system of nonlinear equations governing the dynamics of low-frequency electrostatic toroidal ion-temperature-gradient mode for dense quantum magnetoplasma. For some specific profiles of the equilibrium density, temperature, and ion velocity gradients, the nonlinear equations admit a stationary solution in the form of a tripolar vortex. These results are relevant to understand nonlinear structure formation in dense quantum plasmas in the presence of equilibrium ion-temperature and density gradients.

Tripolar vortex formation in dense quantum plasma with ion-temperature-gradients

International Nuclear Information System (INIS)

Qamar, Anisa; Ata-ur-Rahman; Mirza, Arshad M.

2012-01-01

We have derived system of nonlinear equations governing the dynamics of low-frequency electrostatic toroidal ion-temperature-gradient mode for dense quantum magnetoplasma. For some specific profiles of the equilibrium density, temperature, and ion velocity gradients, the nonlinear equations admit a stationary solution in the form of a tripolar vortex. These results are relevant to understand nonlinear structure formation in dense quantum plasmas in the presence of equilibrium ion-temperature and density gradients.

Differential invariants for higher-rank tensors. A progress report

International Nuclear Information System (INIS)

Tapial, V.

2004-07-01

We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)

Energy-momentum tensor in scalar QED

International Nuclear Information System (INIS)

Joglekar, S.D.; Misra, A.

1988-01-01

We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE

Calculus of tensors and differential forms

CERN Document Server

Sinha, Rajnikant

2014-01-01

Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.

Tensor Galileons and gravity

Energy Technology Data Exchange (ETDEWEB)

Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)

2017-03-13

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

Algebraic and computational aspects of real tensor ranks

CERN Document Server

Sakata, Toshio; Miyazaki, Mitsuhiro

2016-01-01

This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...

Decomposition of a symmetric second-order tensor

Science.gov (United States)

Heras, José A.

2018-05-01

In the three-dimensional space there are different definitions for the dot and cross products of a vector with a second-order tensor. In this paper we show how these products can uniquely be defined for the case of symmetric tensors. We then decompose a symmetric second-order tensor into its ‘dot’ part, which involves the dot product, and the ‘cross’ part, which involves the cross product. For some physical applications, this decomposition can be interpreted as one in which the dot part identifies with the ‘parallel’ part of the tensor and the cross part identifies with the ‘perpendicular’ part. This decomposition of a symmetric second-order tensor may be suitable for undergraduate courses of vector calculus, mechanics and electrodynamics.

Efficient Low Rank Tensor Ring Completion

OpenAIRE

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2017-01-01

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and ana...

Colored Tensor Models - a Review

Directory of Open Access Journals (Sweden)

Razvan Gurau

2012-04-01

Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.

Efficient Tensor Strategy for Recommendation

Directory of Open Access Journals (Sweden)

Aboagye Emelia Opoku

2017-07-01

Full Text Available The era of big data has witnessed the explosion of tensor datasets, and large scale Probabilistic Tensor Factorization (PTF analysis is important to accommodate such increasing trend of data. Sparsity, and Cold-Start are some of the inherent problems of recommender systems in the era of big data. This paper proposes a novel Sentiment-Based Probabilistic Tensor Analysis technique senti-PTF to address the problems. The propose framework first applies a Natural Language Processing technique to perform sentiment analysis taking advantage of the huge sums of textual data generated available from the social media which are predominantly left untouched. Although some current studies do employ review texts, many of them do not consider how sentiments in reviews influence recommendation algorithm for prediction. There is therefore this big data text analytics gap whose modeling is computationally expensive. From our experiments, our novel machine learning sentiment-based tensor analysis is computationally less expensive, and addresses the cold-start problem, for optimal recommendation prediction.

A primal–dual hybrid gradient method for nonlinear operators with applications to MRI

KAUST Repository

Valkonen, Tuomo

2014-05-01

We study the solution of minimax problems min xmax yG(x) + K(x), y - F*(y) in finite-dimensional Hilbert spaces. The functionals G and F* we assume to be convex, but the operator K we allow to be nonlinear. We formulate a natural extension of the modified primal-dual hybrid gradient method, originally for linear K, due to Chambolle and Pock. We prove the local convergence of the method, provided various technical conditions are satisfied. These include in particular the Aubin property of the inverse of a monotone operator at the solution. Of particular interest to us is the case arising from Tikhonov type regularization of inverse problems with nonlinear forward operators. Mainly we are interested in total variation and second-order total generalized variation priors. For such problems, we show that our general local convergence result holds when the noise level of the data f is low, and the regularization parameter α is correspondingly small. We verify the numerical performance of the method by applying it to problems from magnetic resonance imaging (MRI) in chemical engineering and medicine. The specific applications are in diffusion tensor imaging and MR velocity imaging. These numerical studies show very promising performance. © 2014 IOP Publishing Ltd.

A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics.

Science.gov (United States)

Hageman, Nathan S; Toga, Arthur W; Narr, Katherine L; Shattuck, David W

2009-03-01

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.

The Disruption of Geniculocalcarine Tract in Occipital Neoplasm: A Diffusion Tensor Imaging Study

Directory of Open Access Journals (Sweden)

Yan Zhang

2016-01-01

Full Text Available Aim. Investigate the disruption of geniculocalcarine tract (GCT in different occipital neoplasm by diffusion tensor imaging (DTI. Methods. Thirty-two subjects (44.1 ± 3.6 years who had single occipital neoplasm (9 gliomas, 6 meningiomas, and 17 metastatic tumors with ipsilateral GCT involved and thirty healthy subjects (39.2 ± 3.3 years underwent conventional sequences scanning and diffusion tensor imaging by a 1.5T MR scanner. The diffusion-sensitive gradient direction is 13. Compare the fractional anisotropy (FA and mean diffusivity (MD values of healthy GCT with the corresponding values of GCT in peritumoral edema area. Perform diffusion tensor tractography (DTT on GCT by the line propagation technique in all subjects. Results. The FA values of GCT in peritumoral edema area decreased (P=0.001 while the MD values increased (P=0.002 when compared with healthy subjects. There was no difference in the FA values across tumor types (P=0.114 while the MD values of GCT in the metastatic tumor group were higher than the other groups (P=0.001. GCTs were infiltrated in all the 9 gliomas cases, with displacement in 2 cases and disruption in 7 cases. GCTs were displaced in 6 meningiomas cases. GCTs were displaced in all the 7 metastatic cases, with disruption in 7 cases. Conclusions. DTI represents valid markers for evaluating GCT’s disruption in occipital neoplasm. The disruption of GCT varies according to the properties of neoplasm.

Conformal field theories and tensor categories. Proceedings

Energy Technology Data Exchange (ETDEWEB)

Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics

2014-08-01

First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

On improving the efficiency of tensor voting.

Science.gov (United States)

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-11-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.

Reduction schemes for one-loop tensor integrals

International Nuclear Information System (INIS)

Denner, A.; Dittmaier, S.

2006-01-01

We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e - ->4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex

Conformal field theories and tensor categories. Proceedings

International Nuclear Information System (INIS)

Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph

2014-01-01

First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

Loop optimization for tensor network renormalization

Science.gov (United States)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

The influence of molecular order and microstructure on the R2* and the magnetic susceptibility tensor.

Science.gov (United States)

Wisnieff, Cynthia; Liu, Tian; Wang, Yi; Spincemaille, Pascal

2016-06-01

In this work, we demonstrate that in the presence of ordered sub-voxel structure such as tubular organization, biomaterials with molecular isotropy exhibits only apparent R2* anisotropy, while biomaterials with molecular anisotropy exhibit both apparent R2* and susceptibility anisotropy by means of susceptibility tensor imaging (STI). To this end, R2* and STI from gradient echo magnitude and phase data were examined in phantoms made from carbon fiber and Gadolinium (Gd) solutions with and without intrinsic molecular order and sub-voxel structure as well as in the in vivo brain. Confidence in the tensor reconstructions was evaluated with a wild bootstrap analysis. Carbon fiber showed both apparent anisotropy in R2* and anisotropy in STI, while the Gd filled capillary tubes only showed apparent anisotropy on R2*. Similarly, white matter showed anisotropic R2* and magnetic susceptibility with higher confidence, while the cerebral veins displayed only strong apparent R2* tensor anisotropy. Ordered sub-voxel tissue microstructure leads to apparent R2* anisotropy, which can be found in both white matter tracts and cerebral veins. However, additional molecular anisotropy is required for magnetic susceptibility anisotropy, which can be found in white matter tracts but not in cerebral veins. Copyright © 2016 Elsevier Inc. All rights reserved.

The Twist Tensor Nuclear Norm for Video Completion.

Science.gov (United States)

Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui

2017-12-01

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.

Assessment of the Log-Euclidean Metric Performance in Diffusion Tensor Image Segmentation

Directory of Open Access Journals (Sweden)

Mostafa Charmi

2010-06-01

Full Text Available Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this paper is to assess the possible substitution of the geodesic metric with the Log-Euclidean one to reduce the computational cost of a statistical surface evolution algorithm. Materials and Methods: We incorporated the Log-Euclidean metric in the statistical surface evolution algorithm framework. To achieve this goal, the statistics and gradients of diffusion tensor images were defined using the Log-Euclidean metric. Numerical implementation of the segmentation algorithm was performed in the MATLAB software using the finite difference techniques. Results: In the statistical surface evolution framework, the Log-Euclidean metric was able to discriminate the torus and helix patterns in synthesis datasets and rat spinal cords in biological phantom datasets from the background better than the Euclidean and J-divergence metrics. In addition, similar results were obtained with the geodesic metric. However, the main advantage of the Log-Euclidean metric over the geodesic metric was the dramatic reduction of computational cost of the segmentation algorithm, at least by 70 times. Discussion and Conclusion: The qualitative and quantitative results have shown that the Log-Euclidean metric is a good substitute for the geodesic metric when using a statistical surface evolution algorithm in DTIs segmentation.

Off-shell N = 2 tensor supermultiplets

International Nuclear Information System (INIS)

Wit, Bernard de; Saueressig, Frank

2006-01-01

A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given

Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors

OpenAIRE

Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.

2008-01-01

This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...

Tensors, relativity, and cosmology

CERN Document Server

Dalarsson, Mirjana

2015-01-01

Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach.

Science.gov (United States)

Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir

2016-08-01

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

Science.gov (United States)

Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

Evolution of a Planar Wake in Adverse Pressure Gradient

Science.gov (United States)

Driver, David M.; Mateer, George G.

2016-01-01

In the interest of improving the predictability of high-lift systems at maximum lift conditions, a series of fundamental experiments were conducted to study the effects of adverse pressure gradient on a wake flow. Mean and fluctuating velocities were measured with a two-component laser-Doppler velocimeter. Data were obtained for several cases of adverse pressure gradient, producing flows ranging from no reversed flow to massively reversed flow. While the turbulent Reynolds stresses increase with increasing size of the reversed flow region, the gradient of Reynolds stress does not. Computations using various turbulence models were unable to reproduce the reversed flow.

Numerical modeling of the destruction of steel plates with a gradient substrate

Science.gov (United States)

Orlov, M. Yu.; Glazyrin, V. P.; Orlov, Yu. N.

2017-10-01

The paper presents the results of numerical simulation of the shock loading process of steel barriers with a gradient substrate. In an elastic plastic axisymmetric statement, a shock is simulated along the normal in the range of initial velocities up to 300 m / s. A range of initial velocities was revealed, in which the presence of a substrate "saved" the obstacle from spallation. New tasks were announced to deepen scientific knowledge about the behavior of unidirectional gradient barriers at impact. The results of calculations are obtained in the form of graphs, calculated configurations of the "impact - barrier" and tables.

Tucker tensor analysis of Matern functions in spatial statistics

KAUST Repository

Litvinenko, Alexander

2018-04-20

Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

2015-01-01

From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].

Science.gov (United States)

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.

A recursive reduction of tensor Feynman integrals

International Nuclear Information System (INIS)

Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.

2009-07-01

We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)

Tensor-based Dictionary Learning for Spectral CT Reconstruction

Science.gov (United States)

Zhang, Yanbo; Wang, Ge

2016-01-01

Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628

Tensor-Based Dictionary Learning for Spectral CT Reconstruction.

Science.gov (United States)

Zhang, Yanbo; Mou, Xuanqin; Wang, Ge; Yu, Hengyong

2017-01-01

Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods.

Multi-scale properties of large eddy simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

Science.gov (United States)

Linkmann, Moritz; Buzzicotti, Michele; Biferale, Luca

2018-06-01

We provide analytical and numerical results concerning multi-scale correlations between the resolved velocity field and the subgrid-scale (SGS) stress-tensor in large eddy simulations (LES). Following previous studies for Navier-Stokes equations, we derive the exact hierarchy of LES equations governing the spatio-temporal evolution of velocity structure functions of any order. The aim is to assess the influence of the subgrid model on the inertial range intermittency. We provide a series of predictions, within the multifractal theory, for the scaling of correlation involving the SGS stress and we compare them against numerical results from high-resolution Smagorinsky LES and from a-priori filtered data generated from direct numerical simulations (DNS). We find that LES data generally agree very well with filtered DNS results and with the multifractal prediction for all leading terms in the balance equations. Discrepancies are measured for some of the sub-leading terms involving cross-correlation between resolved velocity increments and the SGS tensor or the SGS energy transfer, suggesting that there must be room to improve the SGS modelisation to further extend the inertial range properties for any fixed LES resolution.

New perspectives in the PAW/GIPAW approach: J(P-O-Si) coupling constants, antisymmetric parts of shift tensors and NQR predictions.

Science.gov (United States)

Bonhomme, Christian; Gervais, Christel; Coelho, Cristina; Pourpoint, Frédérique; Azaïs, Thierry; Bonhomme-Coury, Laure; Babonneau, Florence; Jacob, Guy; Ferrari, Maude; Canet, Daniel; Yates, Jonathan R; Pickard, Chris J; Joyce, Siân A; Mauri, Francesco; Massiot, Dominique

2010-12-01

In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first-principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid-state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of (14)N and (35)Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear (2)J(P-O-Si) coupling constants in the case of silicophosphates and calcium phosphates [Si(5)O(PO(4))(6), SiP(2)O(7) polymorphs and α-Ca(PO(3))(2)]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C(3)X(4) (X = H, Cl, F) and (iii) (14)N and (35)Cl NQR predictions in the case of RDX (C(3)H(6)N(6)O(6)), β-HMX (C(4)H(8)N(8)O(8)), α-NTO (C(2)H(2)N(4)O(3)) and AlOPCl(6). RDX, β-HMX and α-NTO are explosive compounds. Copyright © 2010 John Wiley & Sons, Ltd.

Study on of Seepage Flow Velocity in Sand Layer Profile as Affected by Water Depth and Slope Gradience

Science.gov (United States)

Han, Z.; Chen, X.

2017-12-01

BACKGROUND: The subsurface water flow velocity is of great significance in understanding the hydrodynamic characteristics of soil seepage and the influence of interaction between seepage flow and surface runoff on the soil erosion and sediment transport process. OBJECTIVE: To propose a visualized method and equipment for determining the seepage flow velocity and measuring the actual flow velocity and Darcy velocity as well as the relationship between them.METHOD: A transparent organic glass tank is used as the test soil tank, the white river sand is used as the seepage test material and the fluorescent dye is used as the indicator for tracing water flow, so as to determine the thickness and velocity of water flow in a visualized way. Water is supplied at the same flow rate (0.84 L h-1) to the three parts with an interval of 1m at the bottom of the soil tank and the pore water velocity and the thickness of each water layer are determined under four gradient conditions. The Darcy velocity of each layer is calculated according to the water supply flow and the discharge section area. The effective discharge flow pore is estimated according to the moisture content and porosity and then the relationship between Darcy velocity and the measured velocity is calculated based on the water supply flow and the water layer thickness, and finally the correctness of the calculation results is verified. RESULTS: According to the velocity calculation results, Darcy velocity increases significantly with the increase of gradient; in the sand layer profile, the flow velocity of pore water at different depths increases with the increase of gradient; under the condition of the same gradient, the lower sand layer has the maximum flow velocity of pore water. The air-filled porosity of sand layer determines the proportional relationship between Darcy velocity and pore flow velocity. CONCLUSIONS: The actual flow velocity and Darcy velocity can be measured by a visualized method and the

Typesafe Abstractions for Tensor Operations

OpenAIRE

Chen, Tongfei

2017-01-01

We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.

Tensor network state correspondence and holography

Science.gov (United States)

Singh, Sukhwinder

2018-01-01

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.

Analytical performance bounds for multi-tensor diffusion-MRI.

Science.gov (United States)

Ahmed Sid, Farid; Abed-Meraim, Karim; Harba, Rachid; Oulebsir-Boumghar, Fatima

2017-02-01

To examine the effects of MR acquisition parameters on brain white matter fiber orientation estimation and parameter of clinical interest in crossing fiber areas based on the Multi-Tensor Model (MTM). We compute the Cramér-Rao Bound (CRB) for the MTM and the parameter of clinical interest such as the Fractional Anisotropy (FA) and the dominant fiber orientations, assuming that the diffusion MRI data are recorded by a multi-coil, multi-shell acquisition system. Considering the sum-of-squares method for the reconstructed magnitude image, we introduce an approximate closed-form formula for Fisher Information Matrix that has the simplicity and easy interpretation advantages. In addition, we propose to generalize the FA and the mean diffusivity to the multi-tensor model. We show the application of the CRB to reduce the scan time while preserving a good estimation precision. We provide results showing how the increase of the number of acquisition coils compensates the decrease of the number of diffusion gradient directions. We analyze the impact of the b-value and the Signal-to-Noise Ratio (SNR). The analysis shows that the estimation error variance decreases with a quadratic rate with the SNR, and that the optimum b-values are not unique but depend on the target parameter, the context, and eventually the target cost function. In this study we highlight the importance of choosing the appropriate acquisition parameters especially when dealing with crossing fiber areas. We also provide a methodology for the optimal tuning of these parameters using the CRB. Copyright © 2016 Elsevier Inc. All rights reserved.

Weyl curvature tensor in static spherical sources

International Nuclear Information System (INIS)

Ponce de Leon, J.

1988-01-01

The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed

Concatenated image completion via tensor augmentation and completion

OpenAIRE

Bengua, Johann A.; Tuan, Hoang D.; Phien, Ho N.; Do, Minh N.

2016-01-01

This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor,...

General projective relativity and the vector-tensor gravitational field

International Nuclear Information System (INIS)

Arcidiacono, G.

1986-01-01

In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation

Tensor harmonic analysis on homogenous space

International Nuclear Information System (INIS)

Wrobel, G.

1997-01-01

The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

Energy Technology Data Exchange (ETDEWEB)

Ringholm, Magnus; Ruud, Kenneth [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø – The Arctic University of Norway, 9037 Tromsø (Norway); Bast, Radovan [Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, AlbaNova University Center, S-10691 Stockholm (Sweden); PDC Center for High Performance Computing, Royal Institute of Technology, S-10044 Stockholm (Sweden); Oggioni, Luca [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø – The Arctic University of Norway, 9037 Tromsø (Norway); Department of Physics G. Occhialini, University of Milano Bicocca, Piazza della scienza 3, 20126 Milan (Italy); Ekström, Ulf [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo (Norway)

2014-10-07

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.

Tensor estimation for double-pulsed diffusional kurtosis imaging.

Science.gov (United States)

Shaw, Calvin B; Hui, Edward S; Helpern, Joseph A; Jensen, Jens H

2017-07-01

Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented. Copyright © 2017 John Wiley & Sons, Ltd.

Tensor network decompositions in the presence of a global symmetry

International Nuclear Information System (INIS)

Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre

2010-01-01

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.

An Adaptive Spectrally Weighted Structure Tensor Applied to Tensor Anisotropic Nonlinear Diffusion for Hyperspectral Images

Science.gov (United States)

Marin Quintero, Maider J.

2013-01-01

The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…

On the kinetic collisional theory of beam-plasma system (relativistic dielectric tensor). Vol. 2.

Energy Technology Data Exchange (ETDEWEB)

Khalil, Sh M; Sayed, Y A; Zaki, N G [Plasma Physics and Nuclear Fusion Department, Nuclear Research Center, Atomic Energy Authority, Cairo, (Egypt)

1996-03-01

Calculation of the dielectric tensor is useful for calculating and oscillations the stability of an inhomogeneous plasma. If the dielectric tensor is known, the problem of oscillations is reduced the derivation of the Maxwellian equations. In this case, there is no need to derive the equations of the motion of charged particles every time. The properties of the plasma, especially those connected to its instability, may be equally well specified through permittivity as through conductivity. The features of plasma instabilities and the plasma dielectric tensor are essentially affected by the presence of collision. Coloumb collisions (C.C.) are very important in the process of no linear saturation of some plasma instabilities (e.g., ion cyclotron instability, electron-ion two stream instability). For C.C., two basic properties are considered; (i) the cross section decreases rapidly as the particle velocity increases, (ii) the dominate contribution arises from a commutative effect of small-angle scattering or small-momentum transfer processes. If allowance is made for C.C. to derive the kinetic wave equations in a homogeneous plasma, it will remove the divergance in the matrix elements describing nonlinear interactions. In this paper, the collisional kinetic wave equation in cylindrical hot plasma is studied. The dielectric and polarizing tensor elements which describes the kinetic relativistic electron beam (REB) interaction with magnetized plasma into consideration the effect of pair C.C. is derived. Most research carried out in this direction has neglected the effect of C.C. In the absence of collisions, a `plauste` is formed on the distribution function, and the adsorption of the energy by the plasma stops. 1 fig.

Gradient computation for VTI acoustic wavefield tomography

KAUST Repository

Li, Vladimir

2016-09-06

Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ultimately, provide a higher resolution. Here, we implement forward and adjoint wavefield extrapolation for VTI (transversely isotropic with a vertical symmetry axis) media using a pseudospectral operator that employes a separable approximation of the P-wave dispersion relation. This operator is employed to derive the gradients of the differential semblance optimization (DSO) and modified stack-power objective functions. We also obtain the gradient expressions for the data-domain objective function, which can incorporate borehole information necessary for stable VTI velocity analysis. These gradients are compared to the ones obtained with a space-time finite-difference (FD) scheme for a system of coupled wave equations. Whereas the kernels computed with the two wave-equation operators are similar, the pseudospectral method is not hampered by the imprint of the shear-wave artifact. Numerical examples also show that the modified stack-power objective function produces cleaner gradients than the more conventional DSO operator.

Indicial tensor manipulation on MACSYMA

International Nuclear Information System (INIS)

Bogen, R.A.; Pavelle, R.

1977-01-01

A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)

Tensor based structure estimation in multi-channel images

DEFF Research Database (Denmark)

Schou, Jesper; Dierking, Wolfgang; Skriver, Henning

2000-01-01

. In the second part tensors are used for representing the structure information. This approach has the advantage, that tensors can be averaged either spatially or by applying several images, and the resulting tensor provides information of the average strength as well as orientation of the structure...

On energy-momentum tensors of gravitational field

International Nuclear Information System (INIS)

Nikishov, A.I.

2001-01-01

The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru

Kinematic morphology of large-scale structure: evolution from potential to rotational flow

International Nuclear Information System (INIS)

Wang, Xin; Szalay, Alex; Aragón-Calvo, Miguel A.; Neyrinck, Mark C.; Eyink, Gregory L.

2014-01-01

As an alternative way to describe the cosmological velocity field, we discuss the evolution of rotational invariants constructed from the velocity gradient tensor. Compared with the traditional divergence-vorticity decomposition, these invariants, defined as coefficients of the characteristic equation of the velocity gradient tensor, enable a complete classification of all possible flow patterns in the dark-matter comoving frame, including both potential and vortical flows. We show that this tool, first introduced in turbulence two decades ago, is very useful for understanding the evolution of the cosmic web structure, and in classifying its morphology. Before shell crossing, different categories of potential flow are highly associated with the cosmic web structure because of the coherent evolution of density and velocity. This correspondence is even preserved at some level when vorticity is generated after shell crossing. The evolution from the potential to vortical flow can be traced continuously by these invariants. With the help of this tool, we show that the vorticity is generated in a particular way that is highly correlated with the large-scale structure. This includes a distinct spatial distribution and different types of alignment between the cosmic web and vorticity direction for various vortical flows. Incorporating shell crossing into closed dynamical systems is highly non-trivial, but we propose a possible statistical explanation for some of the phenomena relating to the internal structure of the three-dimensional invariant space.

Kinematic morphology of large-scale structure: evolution from potential to rotational flow

Energy Technology Data Exchange (ETDEWEB)

Wang, Xin; Szalay, Alex; Aragón-Calvo, Miguel A.; Neyrinck, Mark C.; Eyink, Gregory L. [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (United States)

2014-09-20

As an alternative way to describe the cosmological velocity field, we discuss the evolution of rotational invariants constructed from the velocity gradient tensor. Compared with the traditional divergence-vorticity decomposition, these invariants, defined as coefficients of the characteristic equation of the velocity gradient tensor, enable a complete classification of all possible flow patterns in the dark-matter comoving frame, including both potential and vortical flows. We show that this tool, first introduced in turbulence two decades ago, is very useful for understanding the evolution of the cosmic web structure, and in classifying its morphology. Before shell crossing, different categories of potential flow are highly associated with the cosmic web structure because of the coherent evolution of density and velocity. This correspondence is even preserved at some level when vorticity is generated after shell crossing. The evolution from the potential to vortical flow can be traced continuously by these invariants. With the help of this tool, we show that the vorticity is generated in a particular way that is highly correlated with the large-scale structure. This includes a distinct spatial distribution and different types of alignment between the cosmic web and vorticity direction for various vortical flows. Incorporating shell crossing into closed dynamical systems is highly non-trivial, but we propose a possible statistical explanation for some of the phenomena relating to the internal structure of the three-dimensional invariant space.

From Boltzmann equations to steady wall velocities

International Nuclear Information System (INIS)

Konstandin, Thomas; Rues, Ingo; Nardini, Germano; California Univ., Santa Barbara, CA

2014-07-01

By means of a relativistic microscopic approach we calculate the expansion velocity of bubbles generated during a first-order electroweak phase transition. In particular, we use the gradient expansion of the Kadanoff-Baym equations to set up the fluid system. This turns out to be equivalent to the one found in the semi-classical approach in the non-relativistic limit. Finally, by including hydrodynamic deflagration effects and solving the Higgs equations of motion in the fluid, we determine velocity and thickness of the bubble walls. Our findings are compared with phenomenological models of wall velocities. As illustrative examples, we apply these results to three theories providing first-order phase transitions with a particle content in the thermal plasma that resembles the Standard Model.

Identification of small-scale discontinuities based on dip-oriented gradient energy entropy coherence estimation

Science.gov (United States)

Peng, Da; Yin, Cheng

2017-09-01

Locating small-scale discontinuities is one of the most challenging geophysical tasks; these subtle geological features are significant since they are often associated with subsurface petroleum traps. Subtle faults, fractures, unconformities, reef textures, channel boundaries, thin-bed boundaries and other structural and stratigraphic discontinuities have subtle geological edges which may provide lateral variation in seismic expression. Among the different geophysical techniques available, 3D seismic discontinuity attributes are particularly useful for highlighting discontinuities in the seismic data. Traditional seismic discontinuity attributes are sensitive to noise and are not very appropriate for detecting small-scale discontinuities. Thus, we present a dip-oriented gradient energy entropy (DOGEE) coherence estimation method to detect subtle faults and structural features. The DOGEE coherence estimation method uses the gradient structure tensor (GST) algorithm to obtain local dip information and construct a gradient correlation matrix to calculate gradient energy entropy. The proposed DOGEE coherence estimation method is robust to noise, and also improves the clarity of fault edges. It is effective for small-scale discontinuity characterisation and interpretation.

Effects of tensor forces in nuclei

International Nuclear Information System (INIS)

Tanihata, Isao

2013-01-01

Recent studies of nuclei far from the stability line have revealed drastic changes in nuclear orbitals and reported the appearance of new magic numbers and the disappearance of magic numbers observed at the stability line. One of the important reasons for such changes is considered to be because of the effect of tensor forces on nuclear structure. Although the role of tensor forces in binding very light nuclei such as deuterons and 4 He has been known, direct experimental evidence for the effect on nuclear structure is scarce. In this paper, I review known effects of tensor forces in nuclei and then discuss the recently raised question of s–p wave mixing in a halo nucleus of 11 Li. Following these reviews, the development of a new experiment to see the high-momentum components due to the tensor forces is discussed and some of the new data are presented. (paper)

Spectral Tensor-Train Decomposition

DEFF Research Database (Denmark)

Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.

2016-01-01

The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....

On the formulation of higher gradient single and polycrystal plasticity

International Nuclear Information System (INIS)

Menzel, A.; Steinmann, P.

1998-01-01

This contribution aims in a geometrically linear formulation of higher gradient plasticity of single and polycrystalline material based on the continuum theory of dislocations and incompatibilities. Thereby, general continuum dislocation densities and incompatibilities are introduced from the viewpoint of continuum mechanics by considering the spatial closure failure of arbitrary line integrals of the displacement differential. Then these findings are translated to the plastic parts of the displacement gradient, the so called plastic distortion, and the plastic strain, respectively, within an elasto-plastic solid thus defining tensor fields of plastic dislocation densities and plastic incompatibilities. Next, in the case of single crystalline material the plastic dislocation density and in the case of polycrystalline material the plastic incompatibility are considered within the exploitation of the thermodynamical principle of positive dissipation. As a result, a phenomenological but physically motivated description of hardening is obtained, which incorporates for single crystals second spatial derivatives of the plastic deformation gradient and for polycrystals fourth spatial derivatives of the plastic strains into the yield condition. Moreover, these modifications mimic the characteristic structure of kinematic hardening, whereby the backstress obeys a nonlocal evolution law. (orig.)

Scalable Tensor Factorizations with Missing Data

DEFF Research Database (Denmark)

Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.

2010-01-01

of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP...... is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram...

Scalable tensor factorizations for incomplete data

DEFF Research Database (Denmark)

Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.

2011-01-01

to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP...... experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP...

On improving the efficiency of tensor voting

OpenAIRE

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-01-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor v...

Toroidal Dielectric Tensor-Operator for Arbitrary Aspect-Ratio and Wave Frequency an Anisotropic-Resistivity MHD Formulation

International Nuclear Information System (INIS)

Komoshvili, K.; Cuperman, S.

1998-01-01

Motivated by the recently increased interest in small aspect ratio tokamaks, we have derived a 2(1/2)D dielectric tensor-operator which can properly describe the plasma response to r.f. waves, under conditions prevailing in the pre-heated stages of arbitrary aspect ratio, axisymmetric toroidal fusion devices. The derived dielectric tensor elements are based on a two-fluid, weakly collisional plasma description, with the Hall term included. They are characterized by the following features: (i) They are cast in a form evidencing the dielectric (non-operator) and operator contributions - the latter being due to the toroidal structure of the V-operators present in Maxwell's equations, on the background of equilibrium currents and pressure gradients; (ii) They are not subject to any I imitation on the (relative) magnitude of the toroidal effects - no expansion in the inverse aspect ratio parameter is used for their derivation; (iii) They include anisotropic - parallel and perpendicular to the magnetic field - contributions to the plasma resistivity; (iv) They are not Iimited by any restriction on the (relative) value of the wave frequency. The explicit, physically transparent formulation of the dielectric tensor is intended for the numerical solution of the full (E ll ≠ 0) wave equation and subsequently, evaluation of the Alfven wave current drive in small aspect ratio tokamaks

3D Inversion of SQUID Magnetic Tensor Data

DEFF Research Database (Denmark)

Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn

2012-01-01

Developments in SQUID-based technology have enabled direct measurement of magnetic tensor data for geophysical exploration. For quantitative interpretation, we introduce 3D regularized inversion for magnetic tensor data. For mineral exploration-scale targets, our model studies show that magnetic...... tensor data have significantly improved resolution compared to magnetic vector data for the same model. We present a case study for the 3D regularized inversion of magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D regularized inversion agree...

Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian limit

International Nuclear Information System (INIS)

Capozziello, S.; Stabile, A.; Troisi, A.

2010-01-01

Recently, a strong debate has been pursued about the Newtonian limit (i.e. small velocity and weak field) of fourth order gravity models. According to some authors, the Newtonian limit of f(R)-gravity is equivalent to the one of Brans-Dicke gravity with ω BD =0, so that the PPN parameters of these models turn out to be ill-defined. In this Letter, we carefully discuss this point considering that fourth order gravity models are dynamically equivalent to the O'Hanlon Lagrangian. This is a special case of scalar-tensor gravity characterized only by self-interaction potential and that, in the Newtonian limit, this implies a non-standard behavior that cannot be compared with the usual PPN limit of General Relativity. The result turns out to be completely different from the one of Brans-Dicke theory and in particular suggests that it is misleading to consider the PPN parameters of this theory with ω BD =0 in order to characterize the homologous quantities of f(R)-gravity. Finally the solutions at Newtonian level, obtained in the Jordan frame for an f(R)-gravity, reinterpreted as a scalar-tensor theory, are linked to those in the Einstein frame.

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

Science.gov (United States)

Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo

2017-10-12

Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.

The tensor bi-spectrum in a matter bounce

Energy Technology Data Exchange (ETDEWEB)

Chowdhury, Debika; Sreenath, V.; Sriramkumar, L., E-mail: debika@physics.iitm.ac.in, E-mail: sreenath@lsu.edu, E-mail: sriram@physics.iitm.ac.in [Department of Physics, Indian Institute of Technology Madras, Chennai 600036 (India)

2015-11-01

Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of tensor perturbations, just as de Sitter inflation does. In this work, we examine if the tensor bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the tensor bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter h{sub NL} that characterizes the amplitude of the tensor bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the tensor perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the tensor bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the tensor perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce. We discuss the implications of the results.

Endoscopic Anatomy of the Tensor Fold and Anterior Attic.

Science.gov (United States)

Li, Bin; Doan, Phi; Gruhl, Robert R; Rubini, Alessia; Marchioni, Daniele; Fina, Manuela

2018-02-01

Objectives The objectives of the study were to (1) study the anatomical variations of the tensor fold and its anatomic relation with transverse crest, supratubal recess, and anterior epitympanic space and (2) explore the most appropriate endoscopic surgical approach to each type of the tensor fold variants. Study Design Cadaver dissection study. Setting Temporal bone dissection laboratory. Subjects and Methods Twenty-eight human temporal bones (26 preserved and 2 fresh) were dissected through an endoscopic transcanal approach between September 2016 and June 2017. The anatomical variations of the tensor fold, transverse crest, supratubal recess, and anterior epitympanic space were studied before and after removing ossicles. Results Three different tensor fold orientations were observed: vertical (type A, 11/28, 39.3%) with attachment to the transverse crest, oblique (type B, 13/28, 46.4%) with attachment to the anterior tegmen tympani, and horizontal (type C, 4/28, 14.3%) with attachment to the tensor tympani canal. The tensor fold was a complete membrane in 20 of 28 (71.4%) specimens, preventing direct ventilation between the supratubal recess and anterior epitympanic space. We identified 3 surgical endoscopic approaches, which allowed visualization of the tensor fold without removing the ossicles. Conclusions The orientation of the tensor fold is the determining structure that dictates the conformation and limits of the epitympanic space. We propose a classification of the tensor fold based on 3 anatomical variants. We also describe 3 different minimally invasive endoscopic approaches to identify the orientation of the tensor fold while maintaining ossicular chain continuity.

Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary

International Nuclear Information System (INIS)

Ezin, J.P.; Mouhamadou Hassirou; Tossa, J.

2005-08-01

We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. As a consequence we establish the complete divergence theorem on a semi-Riemannian manifold with any kinds of smooth boundaries. This result contains the previous attempts to write this theorem on a semi-Riemannian manifold as Unal results. A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained. As a tool, an induced volume form is defined for a degenerate boundary by using a star like operator that we define on degenerate submanifolds. (author)

Potentials for transverse trace-free tensors

International Nuclear Information System (INIS)

Conboye, Rory; Murchadha, Niall Ó

2014-01-01

In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)

Gauge theories, duality relations and the tensor hierarchy

International Nuclear Information System (INIS)

Bergshoeff, Eric A.; Hohm, Olaf; Hartong, Jelle; Huebscher, Mechthild; OrtIn, Tomas

2009-01-01

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.

Reconstruction of convex bodies from surface tensors

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus

. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....

Confinement dependent chemotaxis in two-photon polymerized linear migration constructs with highly definable concentration gradients

DEFF Research Database (Denmark)

Hjortø, Gertrud Malene; Olsen, Mark Holm; Svane, Inge Marie

2015-01-01

Dendritic cell chemotaxis is known to follow chemoattractant concentration gradients through tissue of heterogeneous pore sizes, but the dependence of migration velocity on pore size and gradient steepness is not fully understood. We enabled chemotaxis studies for at least 42 hours at confinement...

Relativistic particles with spin and antisymmetric tensor fields

International Nuclear Information System (INIS)

Sandoval Junior, L.

1990-09-01

A study is made on antisymmetric tensor fields particularly on second order tensor field as far as his equivalence to other fields and quantization through the path integral are concerned. Also, a particle model is studied which has been recently proposed and reveals to be equivalent to antisymmetric tensor fields of any order. (L.C.J.A.)

Computational Strain Gradient Crystal Plasticity

DEFF Research Database (Denmark)

Niordson, Christian Frithiof; Kysar, Jeffrey W.

2011-01-01

A model for strain gradient crystal visco-plasticity is formulated along the lines proposed by Fleck andWillis (2009) for isotropic plasticity. Size-effects are included in the model due to the addition of gradient terms in both the free energy as well as through a dissipation potential. A finite...... element solution method is presented, which delivers the slip-rate field and the velocity-field based on two minimum principles. Some plane deformation problems relevant for certain specific orientations of a face centered cubic crystal under plane loading conditions are studied, and effective in......-plane parameters are developed based on the crystallographic properties of the material. The problem of cyclic shear of a single crystal between rigid platens is studied as well as void growth of a cylindrical void....

FLAPW Study of the EFG Tensor at Cd Impurities in In2O3

International Nuclear Information System (INIS)

Errico, L. A.; Renteria, M.; Fabricius, G.; Darriba, G. N.

2004-01-01

We report an ab initio study of the electric-field gradient tensor (EFG) at Cd impurities located at both nonequivalent cationic sites in the semiconductor In 2 O 3 . Calculations were performed with the FLAPW method that allows us to treat the electronic structure of the doped system and the atomic relaxations introduced by the impurities in the host in a fully self-consistent way. From our results for the EFG (in excellent agreement with the experiments), it is clear that the problem of the EFG at Cd impurities in In 2 O 3 cannot be described by the point-charge model and antishielding factors.

Prescribed curvature tensor in locally conformally flat manifolds

Science.gov (United States)

Pina, Romildo; Pieterzack, Mauricio

2018-01-01

A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.

Algebraic Rainich conditions for the fourth rank tensor V

International Nuclear Information System (INIS)

So, Lau Loi

2011-01-01

Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor B αβμν , a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor B αβμν fulfill these conditions, but so also does our recently proposed tensor V αβμν , which has many of the desirable properties of B αβμν . For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors, B αβμν and V αβμν , which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions.

On the skew-symmetric character of the couple-stress tensor

OpenAIRE

Hadjesfandiari, Ali R.

2013-01-01

In this paper, the skew-symmetric character of the couple-stress tensor is established as the result of arguments from tensor analysis. Consequently, the couple-stress pseudo-tensor has a true vectorial character. The fundamental step in this development is that the isotropic couple-stress tensor cannot exist.

Tensor products of higher almost split sequences

OpenAIRE

Pasquali, Andrea

2015-01-01

We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama gave a precise criterion for when the tensor product of an $n$-representation finite algebra and an $m$-representation finite algebra is $(n+m)$-representation finite. In this case we give a complete description of the higher almost split sequences over the tensor product by expressing every higher almost split sequence as the mapping cone of a suit...

The suitability of using dissolved gases to determine groundwater discharge to high gradient streams

Science.gov (United States)

Gleeson, Tom; Manning, Andrew H.; Popp, Andrea; Zane, Matthew; Clark, Jordan F.

2018-02-01

Determining groundwater discharge to streams using dissolved gases is known to be useful over a wide range of streamflow rates but the suitability of dissolved gas methods to determine discharge rates in high gradient mountain streams has not been sufficiently tested, even though headwater streams are critical as ecological habitats and water resources. The aim of this study is to test the suitability of using dissolved gases to determine groundwater discharge rates to high gradient streams by field experiments in a well-characterized, high gradient mountain stream and a literature review. At a reach scale (550 m) we combined stream and groundwater radon activity measurements with an in-stream SF6 tracer test. By means of numerical modeling we determined gas exchange velocities and derived very low groundwater discharge rates (∼15% of streamflow). These groundwater discharge rates are below the uncertainty range of physical streamflow measurements and consistent with temperature, specific conductance and streamflow measured at multiple locations along the reach. At a watershed-scale (4 km), we measured CFC-12 and δ18O concentrations and determined gas exchange velocities and groundwater discharge rates with the same numerical model. The groundwater discharge rates along the 4 km stream reach were highly variable, but were consistent with the values derived in the detailed study reach. Additionally, we synthesized literature values of gas exchange velocities for different stream gradients which show an empirical relationship that will be valuable in planning future dissolved gas studies on streams with various gradients. In sum, we show that multiple dissolved gas tracers can be used to determine groundwater discharge to high gradient mountain streams from reach to watershed scales.

The suitability of using dissolved gases to determine groundwater discharge to high gradient streams

Science.gov (United States)

Gleeson, Tom; Manning, Andrew H.; Popp, Andrea; Zane, Mathew; Clark, Jordan F.

2018-01-01

Determining groundwater discharge to streams using dissolved gases is known to be useful over a wide range of streamflow rates but the suitability of dissolved gas methods to determine discharge rates in high gradient mountain streams has not been sufficiently tested, even though headwater streams are critical as ecological habitats and water resources. The aim of this study is to test the suitability of using dissolved gases to determine groundwater discharge rates to high gradient streams by field experiments in a well-characterized, high gradient mountain stream and a literature review. At a reach scale (550 m) we combined stream and groundwater radon activity measurements with an in-stream SF6 tracer test. By means of numerical modeling we determined gas exchange velocities and derived very low groundwater discharge rates (∼15% of streamflow). These groundwater discharge rates are below the uncertainty range of physical streamflow measurements and consistent with temperature, specific conductance and streamflow measured at multiple locations along the reach. At a watershed-scale (4 km), we measured CFC-12 and δ18O concentrations and determined gas exchange velocities and groundwater discharge rates with the same numerical model. The groundwater discharge rates along the 4 km stream reach were highly variable, but were consistent with the values derived in the detailed study reach. Additionally, we synthesized literature values of gas exchange velocities for different stream gradients which show an empirical relationship that will be valuable in planning future dissolved gas studies on streams with various gradients. In sum, we show that multiple dissolved gas tracers can be used to determine groundwater discharge to high gradient mountain streams from reach to watershed scales.

The 'gravitating' tensor in the dualistic theory

International Nuclear Information System (INIS)

Mahanta, M.N.

1989-01-01

The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented

Physical states in the canonical tensor model from the perspective of random tensor networks

Energy Technology Data Exchange (ETDEWEB)

Narain, Gaurav [The Institute for Fundamental Study “The Tah Poe Academia Institute”,Naresuan University, Phitsanulok 65000 (Thailand); Sasakura, Naoki [Yukawa Institute for Theoretical Physics,Kyoto University, Kyoto 606-8502 (Japan); Sato, Yuki [National Institute for Theoretical Physics,School of Physics and Centre for Theoretical Physics,University of the Witwartersrand, WITS 2050 (South Africa)

2015-01-07

Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N=2,3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N=3, and comment on an extension of Airy function related to the solutions.

Reconstruction of convex bodies from surface tensors

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus

2016-01-01

We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...

The Riemann-Lovelock curvature tensor

International Nuclear Information System (INIS)

Kastor, David

2012-01-01

In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)

A General Expression for the Quartic Lovelock Tensor

OpenAIRE

Briggs, C. C.

1997-01-01

A general expression is given for the quartic Lovelock tensor in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for n-dimensional differentiable manifolds having a general linear connection. In addition, expressions are given (in the appendix) for the coefficient of the quartic Lovelock Lagrangian as well as for lower-order Lovelock tensors and Lovelock Lagrangian coefficients.

Tensor-GMRES method for large sparse systems of nonlinear equations

Science.gov (United States)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Tensor Network Quantum Virtual Machine (TNQVM)

Energy Technology Data Exchange (ETDEWEB)

2016-11-18

There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.

A Tour of TensorFlow

OpenAIRE

Goldsborough, Peter

2016-01-01

Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In November 2015, Google released $\\textit{TensorFlow}$, an open source deep learning software library for defining, training and deploying machine learning models. In this paper, we review TensorFlow and put it in context of modern deep learning concepts and ...

Theory of ion-temperature-gradient-driven turbulence in tokamaks

International Nuclear Information System (INIS)

Lee, G.S.; Diamond, P.H.

1986-01-01

An analytic theory of ion-temperature-gradient-driven turbulence in tokamaks is presented. Energy-conserving, renormalized spectrum equations are derived and solved in order to obtain the spectra of stationary ion-temperature-gradient-driven turbulence. Corrections to mixing-length estimates are calculated explicitly. The resulting anomalous ion thermal diffusivity chi/sub i/ = 0.4[(π/2)ln(1 + eta/sub i/)] 2 [(1 + eta/sub i/)/tau] 2 rho/sub s/ 2 c/sub s//L/sub s/ is derived and is found to be consistent with experimentally-deduced thermal diffusivities. The associated electron thermal diffusivity and particle and heat-pinch velocities are also calculated. The effect of impurity gradients on saturated ion-temperature-gradient-driven turbulence is discussed and a related explanation of density profile steepening during Z-mode operation is proposed. 35 refs., 4 figs

Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.

Science.gov (United States)

Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene

2016-03-01

Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.

Abelian gauge theories with tensor gauge fields

International Nuclear Information System (INIS)

Kapuscik, E.

1984-01-01

Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)

Theoretical study of lithium clusters by electronic stress tensor

International Nuclear Information System (INIS)

Ichikawa, Kazuhide; Nozaki, Hiroo; Komazawa, Naoya; Tachibana, Akitomo

2012-01-01

We study the electronic structure of small lithium clusters Li_n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.

Aspects of the Antisymmetric Tensor Field

Science.gov (United States)

Lahiri, Amitabha

1991-02-01

With the possible exception of gravitation, fundamental interactions are generally described by theories of point particles interacting via massless gauge fields. Since the advent of string theories the picture of physical interaction has changed to accommodate one in which extended objects interact with each other. The generalization of the gauge theories to extended objects leads to theories of antisymmetric tensor fields. At scales corresponding to present-day laboratory experiments one expects to see only point particles, their interactions modified by the presence of antisymmetric tensor fields in the theory. Therefore, in order to establish the validity of any theory with antisymmetric tensor fields one needs to look for manifestations of these fields at low energies. The principal problem of gauge theories is the failure to provide a suitable explanation for the generation of masses for the fields in the theory. While there is a known mechanism (spontaneous symmetry breaking) for generating masses for both the matter fields and the gauge fields, the lack of experimental evidence in support of an elementary scalar field suggests that one look for alternative ways of generating masses for the fields. The interaction of gauge fields with an antisymmetric tensor field seems to be an attractive way of doing so, especially since all indications point to the possibility that there will be no remnant degrees of freedom. On the other hand the interaction of such a field with black holes suggest an independent way of verifying the existence of such fields. In this dissertation the origins of the antisymmetric tensor field are discussed in terms of string theory. The interaction of black holes with such a field is discussed next. The last chapter discusses the effects of an antisymmetric tensor field on quantum electrodynamics when the fields are minimally coupled.

Tensor hypercontraction. II. Least-squares renormalization

Science.gov (United States)

Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

2012-12-01

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Analytical approximations of diving-wave imaging in constant-gradient medium

KAUST Repository

Stovas, Alexey; Alkhalifah, Tariq Ali

2014-01-01

behavior and traveltime in a constant-gradient medium to develop insights into the traveltime moveout of diving waves and the image (model) point dispersal (residual) when the wrong velocity is used. The explicit formulations that describe these phenomena

Ryu-Takayanagi formula for symmetric random tensor networks

Science.gov (United States)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.

The Topology of Three-Dimensional Symmetric Tensor Fields

Science.gov (United States)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

Visualizing Tensor Normal Distributions at Multiple Levels of Detail.

Science.gov (United States)

Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas

2016-01-01

Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.

Waveform inversion of lateral velocity variation from wavefield source location perturbation

KAUST Repository

Choi, Yun Seok

2013-09-22

It is challenge in waveform inversion to precisely define the deep part of the velocity model compared to the shallow part. The lateral velocity variation, or what referred to as the derivative of velocity with respect to the horizontal distance, with well log data can be used to update the deep part of the velocity model more precisely. We develop a waveform inversion algorithm to obtain the lateral velocity variation by inverting the wavefield variation associated with the lateral shot location perturbation. The gradient of the new waveform inversion algorithm is obtained by the adjoint-state method. Our inversion algorithm focuses on resolving the lateral changes of the velocity model with respect to a fixed reference vertical velocity profile given by a well log. We apply the method on a simple-dome model to highlight the methods potential.

Energy-momentum tensor in quantum field theory

International Nuclear Information System (INIS)

Fujikawa, K.

1981-01-01

The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path-integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat--space-time limit, all the Ward-Takahashi identities associated with space-time transformations including the global dilatation become free from anomalies in terms of this energy-momentum tensor, reflecting the general covariance of the integral measure; the trace of this tensor is thus finite at zero momentum transfer for renormalizable theories. The Jacobian for the local conformal transformation, however, becomes nontrivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization-group b function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise

Tensor and non-tensor tractography for the assessment of the corticospinal tract of children with motor disorders: a comparative study.

Science.gov (United States)

Stefanou, Maria-Ioanna; Lumsden, Daniel E; Ashmore, Jonathan; Ashkan, Keyoumars; Lin, Jean-Pierre; Charles-Edwards, Geoffrey

2016-10-01

Non-invasive measures of corticospinal tract (CST) integrity may help to guide clinical interventions, particularly in children and young people (CAYP) with motor disorders. We compared diffusion tensor imaging (DTI) metrics extracted from the CST generated by tensor and non-tensor based tractography algorithms. For a group of 25 CAYP undergoing clinical evaluation, the CST was reconstructed using (1) deterministic tensor-based tractography algorithm, (2) probabilistic tensor-based, and (3) constrained spherical deconvolution (CSD)-derived tractography algorithms. Choice of tractography algorithm significantly altered the results of tracking. Larger tracts were consistently defined with CSD, with differences in FA but not MD values for tracts to the pre- or post-central gyrus. Differences between deterministic and probabilistic tensor-based algorithms were minimal. Non-tensor reconstructed tracts appeared to be more anatomically representative. Examining metrics along the tract, difference in FA values appeared to be greatest in voxels with predominantly single-fibre orientations. Less pronounced differences were seen outwith of these regions. With an increasing interest in the applications of tractography analysis at all stages of movement disorder surgery, it is important that clinicians remain alert to the consequences of choice of tractography algorithm on subsequently generated tracts, including differences in volumes, anatomical reconstruction, and DTI metrics, the latter of which will have global as well as more regional effects. Tract-wide analysis of DTI based metrics is of limited utility, and a more segmental approach to analysis may be appropriate, particularly if disruption to a focal region of a white matter pathway is anticipated.

The effect of non-uniform temperature and velocity fields on long range ultrasonic measurement systems in MYRRHA

Energy Technology Data Exchange (ETDEWEB)

Van de Wyer, Nicolas; Schram, Christophe [von Karman Institute For Fluids Dynamic (Belgium); Van Dyck, Dries; Dierckx, Marc [Belgian Nuclear Research Center (Belgium)

2015-07-01

SCK.CEN, the Belgian Nuclear Research Center, is developing MYRRHA, a generation IV liquid metal cooled nuclear research reactor. As the liquid metal coolant is opaque to light, normal visual feedback during fuel manipulations is not available and must therefore be replaced by a system that is not hindered by the opacity of the coolant. In this respect ultrasonic based instrumentation is under development at SCK.CEN to provide feedback during operations under liquid metal. One of the tasks that will be tackled using ultrasound is the detection and localization of a potentially lost fuel assembly. In this application, the distance between ultrasonic sensor and target may be as large as 2.5 m. At these distances, non uniform velocity and temperature fields in the liquid metal potentially influence the propagation of the ultrasonic signals, affecting the performance of the ultrasonic systems. In this paper, we investigate how relevant temperature and velocity gradients inside the liquid metal influence the propagation of ultrasonic waves. The effect of temperature and velocity gradients are simulated by means of a newly developed numerical ray-tracing model. The performance of the model is validated by dedicated water experiments. The setup is capable of creating velocity and temperature gradients representative for MYRRHA conditions. Once validated in water, the same model is used to make predictions for the effect of gradients in the MYRRHA liquid metal environment. (authors)

Coherence measures in automatic time-migration velocity analysis

International Nuclear Information System (INIS)

Maciel, Jonathas S; Costa, Jessé C; Schleicher, Jörg

2012-01-01

Time-migration velocity analysis can be carried out automatically by evaluating the coherence of migrated seismic events in common-image gathers (CIGs). The performance of gradient methods for automatic time-migration velocity analysis depends on the coherence measures used as the objective function. We compare the results of four different coherence measures, being conventional semblance, differential semblance, an extended differential semblance using differences of more distant image traces and the product of the latter with conventional semblance. In our numerical experiments, the objective functions based on conventional semblance and on the product of conventional semblance with extended differential semblance provided the best velocity models, as evaluated by the flatness of the resulting CIGs. The method can be easily extended to anisotropic media. (paper)

Spectrum of resistivity gradient driven turbulence

International Nuclear Information System (INIS)

Terry, P.W.; Diamond, P.H.; Shaing, K.C.; Garcia, L.; Carreras, B.A.

1986-01-01

The resistivity fluctuation correlation function and electrostatic potential spectrum of resistivity gradient driven turbulence are calculated analytically and compared to the results of three dimensional numerical calculations. Resistivity gradient driven turbulence is characterized by effective Reynolds' numbers of order unity. Steady-state solution of the renormalized spectrum equations yields an electrostatic potential spectrum (circumflex phi 2 )/sub ktheta/ approx. k/sub theta//sup -3.25/. Agreement of the analytically calculated potential spectrum and mean-square radial velocity with the results of multiple helicity numerical calculations is excellent. This comparison constitutes a quantitative test of the analytical turbulence theory used. The spectrum of magnetic fluctuations is also calculated, and agrees well with that obtained from the numerical computations. 13 refs., 8 figs

Exact tensor network ansatz for strongly interacting systems

Science.gov (United States)

Zaletel, Michael P.

It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.

The normal conformal Cartan connection and the Bach tensor

International Nuclear Information System (INIS)

Korzynski, Mikolaj; Lewandowski, Jerzy

2003-01-01

The goal of this paper is to express the Bach tensor of a four-dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang-Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach tensor. As an example we study the case of a CNC connection which admits a twisting covariantly constant twistor field. This class of conformal geometries of this property is known as given by the Fefferman metric tensors. We use our result to calculate the Bach tensor of an arbitrary Fefferman metric and show that it is proportional to the tensorial square of the four-fold eigenvector of the Weyl tensor. Finally, we solve the Yang-Mills equations imposed on the CNC connection for all the homogeneous Fefferman metrics. The only solution is the Nurowski-Plebanski metric

An introduction to tensors and group theory for physicists

CERN Document Server

Jeevanjee, Nadir

2011-01-01

An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for go...

Tensor Excitations in Nambu - Jona-Lasinio Model

CERN Document Server

Chizhov, M V

1996-01-01

It is shown that in the one-flavour NJL model the vector and axial-vector quasiparticles described by the antisymmetric tensor field are generated. These excitations have tensor interactions with quarks in contrast to usual vector ones. Phenomenological applications are discussed.

On the energy-momentum tensor in Moyal space

International Nuclear Information System (INIS)

Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois

2015-01-01

We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)

Coordinate independent expression for transverse trace-free tensors

International Nuclear Information System (INIS)

Conboye, Rory

2016-01-01

The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the 3 + 1 formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT tensors in three-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived, however, in coordinate form, for all TT tensors in flat space which are also translationally or axially symmetric (Conboye and Murchadha 2014 Class. Quantum Grav. 31 085019). Since TT tensors are conformally covariant, these also give TT tensors in conformally flat space. In this article, the work above has been extended by giving a coordinate-independent expression for these TT tensors. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector. (paper)

Quantification of diffusion and anisotropy in intracranial epidermoids using diffusion tensor metrics and p: q tensor decomposition.

Science.gov (United States)

Srinivasan, K; Thomas, B; Shah, D; Kannath, S K; Menon, G; Sandhyamani, S; Kesavadas, C; Kapilamoorthy, T R

2016-12-01

To quantitatively evaluate the diffusion tensor metrics p, q, L and fractional anisotropy in intracranial epidermoids in comparison with normal white matter in the splenium of the corpus callosum. This retrospective study included 20 consecutive patients referred to our institute. All patients had a magnetic resonance imaging (MRI) study on a 1.5-Tesla MR system. A spin-echo echo-planar DTI sequence with diffusion gradients along 30 non-collinear directions was performed. The eigen values (λ 1 , λ 2 , λ 3 ) were computed for each voxel and, using p: q tensor decomposition, the DTI metrics p, q and L-values and fractional anositropy (FA) were calculated. The region of interest (ROI) (6 pixels each) was placed within the lesion in all the cases and in the splenium of the corpus callosum. The mean FA in the lesion and splenium were 0.50 and 0.88 respectively, with a statistically significant difference between them (Ptensor decomposition, the mean p-value in the epidermoid was 1.55±0.24 and 1.35±0.20 in the splenium; the mean q-values in the epidermoid was 0.67±0.13 and 1.27±0.17 in the splenium; the differences were statistically significant (P=0.01 and <0.01 respectively). The significant difference between p- and q-values in epidermoids compared with the splenium of callosum was probably due to structural and orientation differences in the keratin flakes in epidermoids and white matter bundles in the callosum. However, no significant statistical difference in L-values was noted (P=0.44). DTI metrics p and q have the potential to quantify the diffusion and anisotropy in various tissues thereby gaining information about their internal architecture. The results also suggest that significant differences of DTI metrics p and q between epidermoid and the splenium of the corpus callosum are due to the difference in structural organization within them. Copyright © 2016. Published by Elsevier Masson SAS.

The tree technique and irreducible tensor operators for the quantum algebra suq (2). The algebra of irreducible tensor operators

International Nuclear Information System (INIS)

Smirnov, Yu.F.; Tolstoi, V.N.; Kharitonov, Yu.I.

1993-01-01

The tree technique for the quantum algebra su q (2) developed in an earlier study is used to construct the q analog of the algebra of irreducible tensor operators. The adjoint action of the algebra su q (2) on irreducible tensor operators is discussed, and the adjoint R matrix is introduced. A set of expressions is obtained for the matrix elements of various irreducible tensor operators and combinations of them. As an application, the recursion relations for the Clebsch-Gordan and Racah coefficients of the algebra su q (2) are derived. 16 refs

Quantum mechanics of Yano tensors: Dirac equation in curved spacetime

International Nuclear Information System (INIS)

Cariglia, Marco

2004-01-01

In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

Science.gov (United States)

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S

2017-05-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order- k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k }. We derive general inequalities between the l p -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ( p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.

Tensor meson dominance and e+e--physics

International Nuclear Information System (INIS)

Genz, H.; Karlsruhe Univ.; Mallik, S.

1983-01-01

The phenomenological status of tensor meson dominance is reported. Some new results concerning hadronic decays of the 2 ++ -meson chi 2 (3.55) and the heavy lepton tau are also included. Considering experimental errors, tensor meson dominance is in agreement with experiment. (author)

The nonabelian tensor square of a bieberbach group with ...

African Journals Online (AJOL)

The main objective of this paper is to compute the nonabelian tensor square of one Bieberbach group with elementary abelian 2-group point group of dimension three by using the computational method of the nonabelian tensor square for polycyclic groups. The finding of the computation showed that the nonabelian tensor ...

A Numerical Method for Predicting Rayleigh Surface Wave Velocity in Anisotropic Crystals (Postprint)