Calculation of nonlinear magnetic susceptibility tensors for a uniaxial antiferromagnet
Lim, Siew-Choo; Osman, Junaidah; Tilley, D. R.
2000-11-01
In this paper, we present a derivation of the nonlinear susceptibility tensors for a two-sublattice uniaxial antiferromagnet up to the third-order effects within the standard definition by which the rf magnetization m is defined as a power series expansion in the rf fields h with the susceptibility tensors χ(q) as the coefficients. The starting point is the standard set of torque equations of motion for this problem. A complete set of tensor elements is derived for the case of a single-frequency input wave. Within a circular polarization frame (pnz) expressions are given for the first-order susceptibility, second-harmonic generation, optical rectification, third-harmonic generation and intensity-dependent susceptibility. Some of the coefficients with representative resonance features in the far infrared are illustrated graphically and we conclude with a brief discussion of the implications of the resonance features arising from the calculations and their potential applications.
A nonlinear theory of tensor distributions
Vickers, J A
1998-01-01
The coordinate invariant theory of generalised functions of Colombeau and Meril is reviewed and extended to enable the construction of multi-index generalised tensor functions whose transformation laws coincide with their counterparts in classical distribution theory.
Tensor methods for large sparse systems of nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
1996-12-31
This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.
Nonlinear susceptibility magnitude imaging of magnetic nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Ficko, Bradley W., E-mail: Bradley.W.Ficko@Dartmouth.edu; Giacometti, Paolo; Diamond, Solomon G.
2015-03-15
This study demonstrates a method for improving the resolution of susceptibility magnitude imaging (SMI) using spatial information that arises from the nonlinear magnetization characteristics of magnetic nanoparticles (mNPs). In this proof-of-concept study of nonlinear SMI, a pair of drive coils and several permanent magnets generate applied magnetic fields and a coil is used as a magnetic field sensor. Sinusoidal alternating current (AC) in the drive coils results in linear mNP magnetization responses at primary frequencies, and nonlinear responses at harmonic frequencies and intermodulation frequencies. The spatial information content of the nonlinear responses is evaluated by reconstructing tomographic images with sequentially increasing voxel counts using the combined linear and nonlinear data. Using the linear data alone it is not possible to accurately reconstruct more than 2 voxels with a pair of drive coils and a single sensor. However, nonlinear SMI is found to accurately reconstruct 12 voxels (R{sup 2}=0.99, CNR=84.9) using the same physical configuration. Several time-multiplexing methods are then explored to determine if additional spatial information can be obtained by varying the amplitude, phase and frequency of the applied magnetic fields from the two drive coils. Asynchronous phase modulation, amplitude modulation, intermodulation phase modulation, and frequency modulation all resulted in accurate reconstruction of 6 voxels (R{sup 2}>0.9) indicating that time multiplexing is a valid approach to further increase the resolution of nonlinear SMI. The spatial information content of nonlinear mNP responses and the potential for resolution enhancement with time multiplexing demonstrate the concept and advantages of nonlinear SMI. - Highlights: • Development of a nonlinear susceptibility magnitude imaging model • Demonstration of nonlinear SMI with primary and harmonic frequencies • Demonstration of nonlinear SMI with primary and intermodulation
Cascaded second-order contribution to the third-order nonlinear susceptibility
Kolleck, Christian
2004-05-01
Cascading of second-order nonlinear effects leads to an effective third-order nonlinearity. In addition to the macroscopic electric field at the intermediate frequencies another term has to be taken into account which is due to the locality of the intermediate polarization sources. Combining the correction terms at the three intermediate frequencies gives rise to a third-order susceptibility tensor, which exhibits the same symmetry properties as an intrinsic susceptibility. This particularly applies to the contributions from the rectified and the second-harmonic fields to the degenerate susceptibility.
Peterson, D.
1979-01-01
Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.
Nonlinear susceptibility magnitude imaging of magnetic nanoparticles
Ficko, Bradley W.; Giacometti, Paolo; Diamond, Solomon G.
2015-03-01
This study demonstrates a method for improving the resolution of susceptibility magnitude imaging (SMI) using spatial information that arises from the nonlinear magnetization characteristics of magnetic nanoparticles (mNPs). In this proof-of-concept study of nonlinear SMI, a pair of drive coils and several permanent magnets generate applied magnetic fields and a coil is used as a magnetic field sensor. Sinusoidal alternating current (AC) in the drive coils results in linear mNP magnetization responses at primary frequencies, and nonlinear responses at harmonic frequencies and intermodulation frequencies. The spatial information content of the nonlinear responses is evaluated by reconstructing tomographic images with sequentially increasing voxel counts using the combined linear and nonlinear data. Using the linear data alone it is not possible to accurately reconstruct more than 2 voxels with a pair of drive coils and a single sensor. However, nonlinear SMI is found to accurately reconstruct 12 voxels (R2=0.99, CNR=84.9) using the same physical configuration. Several time-multiplexing methods are then explored to determine if additional spatial information can be obtained by varying the amplitude, phase and frequency of the applied magnetic fields from the two drive coils. Asynchronous phase modulation, amplitude modulation, intermodulation phase modulation, and frequency modulation all resulted in accurate reconstruction of 6 voxels (R2>0.9) indicating that time multiplexing is a valid approach to further increase the resolution of nonlinear SMI. The spatial information content of nonlinear mNP responses and the potential for resolution enhancement with time multiplexing demonstrate the concept and advantages of nonlinear SMI.
Extended arrays for nonlinear susceptibility magnitude imaging
Ficko, Bradley W.; Giacometti, Paolo; Diamond, Solomon G.
2016-01-01
This study implements nonlinear susceptibility magnitude imaging (SMI) with multifrequency intermodulation and phase encoding. An imaging grid was constructed of cylindrical wells of 3.5-mm diameter and 4.2-mm height on a hexagonal two-dimensional 61-voxel pattern with 5-mm spacing. Patterns of sample wells were filled with 40-μl volumes of Fe3O4 starch-coated magnetic nanoparticles (mNPs) with a hydrodynamic diameter of 100 nm and a concentration of 25 mg/ml. The imaging hardware was configured with three excitation coils and three detection coils in anticipation that a larger imaging system will have arrays of excitation and detection coils. Hexagonal and bar patterns of mNP were successfully imaged (R2 > 0.9) at several orientations. This SMI demonstration extends our prior work to feature a larger coil array, enlarged field-of-view, effective phase encoding scheme, reduced mNP sample size, and more complex imaging patterns to test the feasibility of extending the method beyond the pilot scale. The results presented in this study show that nonlinear SMI holds promise for further development into a practical imaging system for medical applications. PMID:26124044
Transistor-based metamaterials with dynamically tunable nonlinear susceptibility
Barrett, John P.; Katko, Alexander R.; Cummer, Steven A.
2016-08-01
We present the design, analysis, and experimental demonstration of an electromagnetic metamaterial with a dynamically tunable effective nonlinear susceptibility. Split-ring resonators loaded with transistors are shown theoretically and experimentally to act as metamaterials with a second-order nonlinear susceptibility that can be adjusted through the use of a bias voltage. Measurements confirm that this allows for the design of a nonlinear metamaterial with adjustable mixing efficiency.
Third-Order Nonlinear Optical Susceptibility of Indium Phosphide Nanocrystals
Institute of Scientific and Technical Information of China (English)
WANG Hong-Li; WANG Dong; CHEN Guang-De; LIU Hui
2007-01-01
InP nanocrystals synthesized by refluxing and annealing of organic solvent are determined from XRD measurements to have an average granularity of 25 nm. The nonlinear optical properties of the InP nanocrystals studied by using laser Z-scan technique with 50ps pulses at 532nm are found to reveal strong nonlinear optical properties and two-photon absorption phenomenon. Also, the nonlinear absorption coefficient, the nonlinear refractive index and the third-order nonlinear optical susceptibility are determined by experiments, in which the nonlinear refractive index is three orders of magnitude larger than that of bulk InP.
Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
The non-existence of asymptotically flat, neutral black holes and asymptotically flat, charged black holes in the Maxwell electrodynamics, with non-trivial scalar field has been proved for a large class of scalar-tensor theories. The no-scalar-hair theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Born-Infeld type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. The causal structure and properties of the solutions are studied, and a comparison between these solutions and the corresponding solutions in the General Relativity is made. The presence of the scalar field leads to a much more simple causal structure. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.
Investigation of odd-order nonlinear susceptibilities in atomic vapors
Energy Technology Data Exchange (ETDEWEB)
Yan, Yaqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Teaching and Research Section of Maths and Physics, Guangzhou Commanding Academy of Chinese People’s Armed Police Force, Guangzhou, 510440 (China); Wu, Zhenkun; Si, Jinhai; Yan, Lihe; Zhang, Yiqi; Yuan, Chenzhi; Sun, Jia [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
2013-06-15
We theoretically deduce the macroscopic symmetry constraints for arbitrary odd-order nonlinear susceptibilities in homogeneous media including atomic vapors for the first time. After theoretically calculating the expressions using a semiclassical method, we demonstrate that the expressions for third- and fifth-order nonlinear susceptibilities for undressed and dressed four- and six-wave mixing (FWM and SWM) in atomic vapors satisfy the macroscopic symmetry constraints. We experimentally demonstrate consistence between the macroscopic symmetry constraints and the semiclassical expressions for atomic vapors by observing polarization control of FWM and SWM processes. The experimental results are in reasonable agreement with our theoretical calculations. -- Highlights: •The macroscopic symmetry constraints are deduced for homogeneous media including atomic vapors. •We demonstrate that odd-order nonlinear susceptibilities satisfy the constraints. •We experimentally demonstrate the deduction in part.
Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
Recent results show that when non-linear electrodynamics is considered the no-scalar-hair theorems in the scalar-tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented. What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to non-linear electrodynamics in a special class of scalar-tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other four phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar-tensor theories considered, the black holes have a single, non-degenerate horizon, i.e., their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicate...
Enhanced nonlinear susceptibility via double-double electromagnetically induced transparency
Alotaibi, Hessa M. M.; Sanders, Barry C.
2016-11-01
We investigate the nonlinear optical susceptibility of an alkali-metal atom with tripod electronic configuration responsible for generating cross-phase modulation and self-phase modulation under the condition of double-double electromagnetically induced transparency. Our investigation demonstrates an enhancement in the nonlinear optical susceptibility of an alkali-metal atom by a factor of 1000 in the region of the second transparency window. This enhancement is in comparison with the atom's susceptibility in the first transparency window for the same parameters under the same conditions. Nonlinear-absorption enhancement arises by canceling Raman-gain generation, which arises when the probe and signal fields have equal intensities. At the center of the second transparency window, we obtain the condition required to attain a nonvanishing nonlinear optical susceptibility. In the bare-state picture, the coupling field must be off resonant from a bare-to-bare-state transition, while working in the semiclassical dressed picture required the signal field to be tuned off resonantly with a bare-to-dressed-state transition. The relation that governs the values of coupling- and signal-field detuning are also obtained. Our scheme exhibits the fact that the second transparency window has advantages over the first transparency window with respect to obtaining an enhanced Kerr effect, and our calculation includes simulation of both low-temperature and Doppler-broadened regimes.
Ageing of the nonlinear optical susceptibility in soft matter
Energy Technology Data Exchange (ETDEWEB)
Ghofraniha, N [SMC-INFM-CNR, c/o Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185, Rome (Italy); Conti, C [Research Centre ' Enrico Fermi' , Via Panisperna 89/A, 00184 Rome (Italy); Leonardo, R Di [SOFT-INFM-CNR, c/o Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185, Rome (Italy); Ruzicka, B [SOFT-INFM-CNR, c/o Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185, Rome (Italy); Ruocco, G [SOFT-INFM-CNR, c/o Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185, Rome (Italy)
2007-05-23
We investigate the nonlinear optics response of a colloidal dispersion undergoing dynamics slowing down with age, by using Z-scan and dynamic light scattering measurements. We study the high optical nonlinearity of an organic dye (rhodamine B) dispersed in a water-clay (laponite) suspension. We consider different clay concentrations (2.0-2.6 wt%) experiencing dynamics arrest. We find that (i) the concentration dependent exponential growth of both mean relaxation time and nonlinear absorption coefficient can be individually scaled to a master curve and (ii) the scaling times are the same for the two physical quantities. These findings indicate that the optical nonlinear susceptibility exhibits the same ageing universal scaling behaviour, typical of disordered out of equilibrium systems.
Dynamic magnetic hysteresis and nonlinear susceptibility of antiferromagnetic nanoparticles
Kalmykov, Yuri P.; Ouari, Bachir; Titov, Serguey V.
2016-08-01
The nonlinear ac stationary response of antiferromagnetic nanoparticles subjected to both external ac and dc fields of arbitrary strength and orientation is investigated using Brown's continuous diffusion model. The nonlinear complex susceptibility and dynamic magnetic hysteresis (DMH) loops of an individual antiferromagnetic nanoparticle are evaluated and compared with the linear regime for extensive ranges of the anisotropy, the ac and dc magnetic fields, damping, and the specific antiferromagnetic parameter. It is shown that the shape and area of the DMH loops of antiferromagnetic particles are substantially altered by applying a dc field that permits tuning of the specific magnetic power loss in the nanoparticles.
Hybrid quantum systems for enhanced nonlinear optical susceptibilities
Sullivan, Dennis; Kuzyk, Mark G
2016-01-01
Significant effort has been expended in the search for materials with ultra-fast nonlinear-optical susceptibilities, but most fall far below the fundamental limits. This work applies a theoretical materials development program that has identified a promising new hybrid made of a nanorod and a molecule. This system uses the electrostatic dipole moment of the molecule to break the symmetry of the metallic nanostructure that shifts the energy spectrum to make it optimal for a nonlinear-optical response near the fundamental limit. The structural parameters are varied to determine the ideal configuration, providing guidelines for making the best structures.
Scalar-tensor black holes coupled to Euler-Heisenberg nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
The no-scalar-hair conjecture rules out the existence of asymptotically flat black holes with a scalar dressing for a large class of theories. No-scalar-hair theorems have been proved for the cases of neutral black holes and for charged black holes in the Maxwell electrodynamics. These theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Euler-Heisenberg type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. In comparison to the corresponding solution in General Relativity the presented solution has a simpler causal structure the reason for which is the presence of the scalar field. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.
Nonlinear dynamic susceptibilities of interacting and noninteracting magnetic nanoparticles
Joensson, P; García-Palacios, J L; Svedlindh, P
2000-01-01
The linear and cubic dynamic susceptibilities of solid dispersions of nanosized maghemite gamma-Fe sub 2 O sub 3 particles have been measured for three samples with a volume concentration of magnetic particles ranging from 0.3% to 17%, in order to study the effect of dipole-dipole interactions. Significant differences between the dynamic response of the samples are observed. While the linear and cubic dynamic susceptibilities of the most dilute sample compare reasonably well with the corresponding expressions proposed by Raikher and Stepanov for noninteracting particles, the nonlinear dynamic response of the most concentrated sample exhibits at low temperatures similar features as observed in a Ag(11 at% Mn) spin glass.
Nonlinear wave mixing and susceptibility properties of negative refractive index materials.
Chowdhury, Aref; Tataronis, John A
2007-01-01
We present an analysis of second-order and third-order nonlinear susceptibilities and wave-mixing properties of negative refractive index materials. We show that the nonlinear susceptibilities for noncentrosymmetric and centrosymmetric media may be positive or negative and away from resonance depending on the frequency of interest relative to the resonant frequencies of the material. Manipulation of the signs of the nonlinear susceptibilities is important in the field of optics, particularly for solitons and compensation of nonlinear effects. We also show that three- and four-wave mixing can be naturally phase matched in the material.
Nonlinear optical susceptibility of multicomponent tellurite thin film glasses
Munoz-Martin, D.; Fernandez, H.; Fernandez-Navarro, J. M.; Gonzalo, J.; Solis, J.; Fierro, J. L. G.; Domingo, C.; Garcia-Ramos, J. V.
2008-12-01
Tellurite (TeO2-TiO2-Nb2O5) thin film glasses have been produced by pulsed laser deposition. The dispersion of the real and imaginary parts of the linear refractive index has been measured in the range from 300 to 1700 nm. Films present high refractive index (n =2.01) and reduced absorption (k nm. The nonlinear third order optical susceptibility (|χ(3)|) has been determined at four different wavelengths (600, 800, 1200, and 1500 nm). The out-of-resonance |χ(3)| values (˜10-12 esu) are found to be ten times higher than those of the bulk glass and 102 times higher than that of silica. Compositional and structural analysis reveals an increase of both the Ti atomic content and the fraction of nonbridging oxygen bonds in the deposited films. Both factors lead to a higher hyperpolarizability of the film constituents that is proposed to be responsible for the high |χ(3)| value of the films.
Madsen, Niels K; Godtliebsen, Ian H; Christiansen, Ove
2017-04-07
Vibrational coupled-cluster (VCC) theory provides an accurate method for calculating vibrational spectra and properties of small to medium-sized molecules. Obtaining these properties requires the solution of the non-linear VCC equations which can in some cases be hard to converge depending on the molecule, the basis set, and the vibrational state in question. We present and compare a range of different algorithms for solving the VCC equations ranging from a full Newton-Raphson method to approximate quasi-Newton models using an array of different convergence-acceleration schemes. The convergence properties and computational cost of the algorithms are compared for the optimization of VCC states. This includes both simple ground-state problems and difficult excited states with strong non-linearities. Furthermore, the effects of using tensor-decomposed solution vectors and residuals are investigated and discussed. The results show that for standard ground-state calculations, the conjugate residual with optimal trial vectors algorithm has the shortest time-to-solution although the full Newton-Raphson method converges in fewer macro-iterations. Using decomposed tensors does not affect the observed convergence rates in our test calculations as long as the tensors are decomposed to sufficient accuracy.
Solookinejad, G.
2016-09-01
In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.
Energy Technology Data Exchange (ETDEWEB)
Solookinejad, G., E-mail: ghsolooki@gmail.com
2016-09-15
In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.
Scaling of ac susceptibility and the nonlinear response function of high-temperature superconductors
Institute of Scientific and Technical Information of China (English)
CHEN; Kaixuan; NING; Zhenhua; XU; Hengyi; QI; Zhi; LU; Guo
2005-01-01
The amplitude-dependent ac susceptibility of high-temperature superconductors is shown to obey some empirical scaling relations. We try to analyze this behavior by extending a dc nonlinear response function of mixed state to the ac cases. The derived equations for critical current and ac susceptibility x(T) agree with the scaling relations of experimental data.
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system
Energy Technology Data Exchange (ETDEWEB)
Zeng, Zaiping; Garoufalis, Christos S.; Baskoutas, Sotirios, E-mail: bask@upatras.gr
2014-07-18
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system have been theoretically studied. In general, we find that the structure parameters of the coupled system significantly affect the optical susceptibilities. The enhancement of the coupling effects between the dot and ring is found to increase considerably the optical susceptibilities and redshift drastically the transition energies. Comparing to the linear susceptibility, the nonlinear optical susceptibility is found to be more sensitive to the variation of the structure parameters. A comprehensive analysis of the electron probability density movement with respect to the modification of the structure parameters is provided, which offers a unique perspective of the ground-state localization. - Highlights: • Optical susceptibilities in a quantum-dot–quantum-ring system are studied. • The structure parameters significantly affect the optical susceptibilities. • The enhancement of the coupling effects increases the optical susceptibilities. • The nonlinear susceptibility is more sensitive to the change in structure parameters. • A comprehensive analysis of the electron probability density movement is provided.
TensorLy: Tensor Learning in Python
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. Writte
TensorLy: Tensor learning in Python
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. Writt
TensorLy: Tensor Learning in Python
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.
Quantum Size- Dependent Third- Order Nonlinear Optical Susceptibility in Semiconductor Quantum Dots
Institute of Scientific and Technical Information of China (English)
SUN Ting; XIONG Gui-guang
2005-01-01
The density matrix approach has been employed to investigate the optical nonlinear polarization in a single semiconductor quantum dot(QD). Electron states are considered to be confined within a quantum dot with infinite potential barriers. It is shown, by numerical calculation, that the third-order nonlinear optical susceptibilities for a typical Si quantum dot is dependent on the quantum size of the quantum dot and the frequency of incident light.
TensorLy: Tensor Learning in Python
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. Written in Python, it aims at following the same standard adopted by the main projects of the Python scientific community and fully integrating with these. It allows for fast and straightforward tensor d...
Knoester, Jasper; Mukamel, Shaul
1989-01-01
Reduced equations of motion for material and radiation field variables in a molecular crystal are presented that allow us to calculate linear- and nonlinear-optical susceptibilities, accounting in a systematic way for intermolecular interactions. These equations are derived starting from the multipo
Study of third-order nonlinear susceptibility of polySchiff base containing triphenylamine
Institute of Scientific and Technical Information of China (English)
NIU HaiJun; WANG Wen; HUANG YuDong; ZHANG YunDong; ZHANG YunJun; BAI XuDuo; LIU Yuan
2007-01-01
PolySchiff base containing triphenylamine has been synthesized by polycondensation and characterized by FT-IR, NMR, UV-visible spectrometer. Measurements of the third-order optical nonlinear susceptibility x(3)by Z-scan technique have shown that the large nonlinearity is dominated by the two-photon absorption in PSB. The sign and size of real part Rex(3), nonlinear refractive index n2 have been measured with the condition of 532 nm, 8 ns-duration pulses to be -1.23x10-10esu, -3.06x10-12esu;nonlinear absorption index β and size of image part Imx(3) to be 3.63x10-10 m/W, 1.15x10-11 esu, respectively, so the third-order nonlinear susceptibility x(3) is 1.19x10-11 esu. The value is larger than other polymers reported. PSB is self-focusing material and has potential application in nonlinear optic field.
Study of third-order nonlinear susceptibility of polySchiff base containing triphenylamine
Institute of Scientific and Technical Information of China (English)
2007-01-01
PolySchiff base containing triphenylamine has been synthesized by polycondensation and character-ized by FT-IR,NMR,UV-visible spectrometer. Measurements of the third-order optical nonlinear sus-ceptibility χ(3) by Z-scan technique have shown that the large nonlinearity is dominated by the two-photon absorption in PSB. The sign and size of real part Reχ(3) ,nonlinear refractive index n2 have been measured with the condition of 532 nm,8 ns-duration pulses to be -1.23×10-10 esu,-3.06×10-12 esu;nonlinear absorption index β and size of image part Imχ(3) to be 3.63×10-10 m/W,1.15×10-11 esu,respec-tively,so the third-order nonlinear susceptibility χ(3) is 1.19×10-11 esu. The value is larger than other polymers reported. PSB is self-focusing material and has potential application in nonlinear optic field.
Tuer, Adam E; Akens, Margarete K; Krouglov, Serguei; Sandkuijl, Daaf; Wilson, Brian C; Whyne, Cari M; Barzda, Virginijus
2012-11-21
The second-order nonlinear polarization properties of fibrillar collagen in various rat tissues (vertebrae, tibia, tail tendon, dermis, and cornea) are investigated with polarization-dependent second-harmonic generation (P-SHG) microscopy. Three parameters are extracted: the second-order susceptibility ratio, R = [Formula: see text] ; a measure of the fibril distribution asymmetry, |A|; and the weighted-average fibril orientation, . A hierarchical organizational model of fibrillar collagen is developed to interpret the second-harmonic generation polarization properties. Highlights of the model include: collagen type (e.g., type-I, type-II), fibril internal structure (e.g., straight, constant-tilt), and fibril architecture (e.g., parallel fibers, intertwined, lamellae). Quantifiable differences in internal structure and architecture of the fibrils are observed. Occurrence histograms of R and |A| distinguished parallel from nonparallel fibril distributions. Parallel distributions possessed low parameter values and variability, whereas nonparallel distributions displayed an increase in values and variability. From the P-SHG parameters of vertebrae tissue, a three-dimensional reconstruction of lamellae of intervertebral disk is presented.
Time-Dependent Nonlinear Optical Susceptibility of an Out-of-Equilibrium Soft Material
Ghofraniha, Neda; Conti, Claudio; Ruocco, Giancarlo; Zamponi, Francesco
2009-01-01
We investigate the time-dependent nonlinear optical absorption of a clay dispersion (Laponite) in an organic dye (rhodamine B) water solution displaying liquid-arrested state transition. Specifically, we determine the characteristic time τD of the nonlinear susceptibility buildup due to the Soret effect. By comparing τD with the relaxation time provided by standard dynamic light scattering measurements we report on the decoupling of the two collective diffusion times at the two very different length scales during the aging of the out-of-equilibrium system. With this demonstration experiment we also show the potentiality of nonlinear optics measurements in the study of the late stage of arrest in soft materials.
Second-order nonlinear susceptibility in quantum dot structure under applied electric field
Abdullah, M.; Noori, Farah T. Mohammed; Al-Khursan, Amin H.
2015-06-01
A model for quantum dot (QD) subbands, when the dots are in the form of quantum disks, under applied electric field was stated. Then, subbands of dots with different disk radii and heights were calculated under applied field. The competition between the shift due to confinement by field and the size was shown for subbands. Second-order nonlinear susceptibility in quantum dots (QDs) was derived using density matrix theory which is, then, simulated using the calculated subbands. Both interband (IB) and intersubband (ISB) transitions were discussed. High second-order susceptibility in QDs was predicted. The results show a reduction in the susceptibility with the applied field while the peak wavelength was mainly relates to energy difference between subbands. A good match between theory and laboratory experiments was observed. Laboratory experiments at terahertz region might be possible using valence intersubband which is important in many device applications.
Chiarucci, Riccardo; Madeo, Dario; Loffredo, Maria I.; Castellani, Eleonora; Santarcangelo, Enrica L.; Mocenni, Chiara
2014-07-01
Assessment of hypnotic susceptibility is usually obtained through the application of psychological instruments. A satisfying classification obtained through quantitative measures is still missing, although it would be very useful for both diagnostic and clinical purposes. Aiming at investigating the relationship between the cortical brain activity and the hypnotic susceptibility level, we propose the combined use of two methodologies - Recurrence Quantification Analysis and Detrended Fluctuation Analysis - both inherited from nonlinear dynamics. Indicators obtained through the application of these techniques to EEG signals of individuals in their ordinary state of consciousness allowed us to obtain a clear discrimination between subjects with high and low susceptibility to hypnosis. Finally a neural network approach was used to perform classification analysis.
Energy Technology Data Exchange (ETDEWEB)
Reshak, A. H., E-mail: maalidph@yahoo.com [New Technologies - Research Centre, University of West Bohemia, Univerzitni 8, 306 14 Pilsen (Czech Republic); Center of Excellence Geopolymer and Green Technology, School of Material Engineering, University Malaysia Perlis, 01007 Kangar, Perlis (Malaysia); Brik, M. G. [College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Institute of Physics, University of Tartu, Ravila 14C, Tartu 50411 (Estonia); Auluck, S. [Council of Scientific and Industrial Research—National Physical Laboratory Dr. K S Krishnan Marg, New Delhi 110012 (India)
2014-09-14
Based on the electronic band structure, we have calculated the dispersion of the linear and nonlinear optical susceptibilities for the mixed CuAl(S{sub 1–x}Se{sub x})₂ chaclcopyrite compounds with x=0.0, 0.25, 0.5, 0.75, and 1.0. Calculations are performed within the Perdew-Becke-Ernzerhof general gradient approximation. The investigated compounds possess a direct band gap of about 2.2 eV (CuAlS₂), 1.9 eV (CuAl(S₀.₇₅Se₀.₂₅)₂), 1.7 eV (CuAl(S₀.₅Se₀.₅)₂), 1.5 eV (CuAl(S₀.₂₅Se₀.₇₅)₂), and 1.4 eV (CuAlSe₂) which tuned to make them optically active for the optoelectronics and photovoltaic applications. These results confirm that substituting S by Se causes significant band gaps' reduction. The optical function's dispersion ε₂{sup xx}(ω) and ε₂{sup zz}(ω)/ε₂{sup xx}(ω), ε₂{sup yy}(ω), and ε₂{sup zz}(ω) was calculated and discussed in detail. To demonstrate the effect of substituting S by Se on the complex second-order nonlinear optical susceptibility tensors, we performed detailed calculations for the complex second-order nonlinear optical susceptibility tensors, which show that the neat parents compounds CuAlS₂ and CuAlSe₂ exhibit | χ₁₂₂²}(-2ω;ω;ω) | as the dominant component, while the mixed alloys exhibit | χ₁₁₁²(-2ω;ω;ω) | as the dominant component. The features of | χ₁₂₃²}(-2ω;ω;ω) | and | χ{sub 111}²}(-2ω;ω;ω) | spectra were analyzed on the basis of the absorptive part of the corresponding dielectric function ε₂(ω) as a function of both ω/2 and ω.
Derkowska-Zielinska, Beata
2017-02-01
The influence of solvent polarity on nonlinear optical properties of tris-(8-hydroxyquinoline)-aluminum (Alqsub>3sub>) was investigated by the degenerate four-wave mixing method at the 532 nm. It was obtained that the effective values of the third-order nonlinear optical susceptibility (χeff⟨3⟩) and the second-order hyperpolarizability (γsub>effsub>) of Alqsub>3sub> depend on the solvent polarity. Additionally, it was found that Alqsub>3sub> dissolved in dimethyl sulfoxide has the highest values of χeff⟨3⟩ and γsub>effsub>. Furthermore, two Stegeman's figures of merit were also calculated. The obtained results suggest that Alqsub>3sub> is also promising material for application in all-optical signal processing devices.
Yan, Xiao-Qing; Liu, Zhi-Bo; Zhang, Xiao-Liang; Zang, Wei-Ping; Tian, Jian-Guo
2010-05-10
The normal elliptically polarized light Z-scan method is modified by adding a quarter-wave plate and an analyzer before the detector. The normalized transmittance formulas of modified elliptically polarized light Z-scan are obtained for media with negligible nonlinear absorption. Compared with normal linearly and elliptically polarized light Z-scan methods, an increase of sensitivity by a factor of larger than 4 is achieved for the real part of third-order susceptibility component's measurements using this modified elliptically polarized light Z-scan method. The analytical results are verified by studying the real part of independent susceptibility components of CS(2) liquid. Moreover, the potential application for cross-polarized wave generation is discussed. (c) 2010 Optical Society of America.
Institute of Scientific and Technical Information of China (English)
M. Singh; P. Aghamkar; S. Duhan
2008-01-01
Using electromagnetic treatment, an expression of effective nonlinear optical susceptibility Xe[= Xe(2) + Xe(3) E] is obtained for Ⅲ-Ⅴ semiconducting crystals in an applied transverse dc magnetic field under off-resonant transition regime. The origin of nonlinear interaction lies in nonlinear polarization arising from the crystal properties such as piezoelectricity and electrostriction. Numerical estimates have been made by a representative n-InSb crystal at 77K duly irradiated by a pulsed lO.6-μm CO2 laser under off-resonant transition regime. Efforts are dedicated to optimizing doping level and externally applied dc magnetic field to achieve maximum Xe(2) and Xe(3). The results are found to be in good agreement with the available literature. The analysis shows that Xe(2) and Xe(3)can be significantly enhanced in doped Ⅲ-Ⅴ semiconductors by the proper selection of doping concentration and dc magnetic field, which confirms its potential as a candidate material for the fabrication of nonlinear optical devices.
Second-order nonlinear optical susceptibilities of AIIBVI and AIIIBV semiconductors
Kumar, V.; Sinha, Anita; Singh, B. P.; Chandra, S.
2016-10-01
The second-order nonlinear optical (NLO) susceptibilities χ123(2) of AIIBVI and AIIIBV groups of semiconductors with zincblende (ZB) structure have been studied. Two relations have been proposed for the calculation of χ123(2) (0) at zero frequency. One is based on bond charge model of Levine and the other is based on plasma oscillations theory of solids. Calculated values of χ123(2) (0) for all compounds are in fair agreement with the available experimental and reported values.
Kuzyk, Mark G
2014-01-01
The Thomas Kuhn Reich sum rules and the sum-over-states (SOS) expression for the hyperpolarizabilities are truncated when calculating the fundamental limits of nonlinear susceptibilities. Truncation of the SOS expression can lead to an accurate approximation of the first and second hyperpolarizabilities due to energy denominators, which can make the truncated series converge to within 10% of the full series after only a few excited states are included in the sum. The terms in the sum rule series, however, are weighted by the state energies, so convergence of the series requires that the position matrix elements scale at most in inverse proportion to the square root of the energy. Even if the convergence condition is met, serious pathologies arise, including self inconsistent sum rules and equations that contradict reality. As a result, using the truncated sum rules alone leads to pathologies that make any rigorous calculations impossible, let alone yielding even good approximations. This paper discusses condi...
Woodward, R. I.; Murray, R. T.; Phelan, C. F.; de Oliveira, R. E. P.; Runcorn, T. H.; Kelleher, E. J. R.; Li, S.; de Oliveira, E. C.; Fechine, G. J. M.; Eda, G.; de Matos, C. J. S.
2017-03-01
We report second- and third-harmonic generation in monolayer MoS2 as a tool for imaging and accurately characterizing the material’s nonlinear optical properties under 1560 nm excitation. Using a surface nonlinear optics treatment, we derive expressions relating experimental measurements to second- and third-order nonlinear sheet susceptibility magnitudes, obtaining values of | {χ }{{s}}(2)| =2.0× {10}-20 m2 V-1 and, for the first time for monolayer MoS2, | {χ }{{s}}(3)| =1.7× {10}-28 m3 V-2. These sheet susceptibilities correspond to effective bulk nonlinear susceptibility values of | {χ }{{b}}(2)| =2.9 × {10}-11 m V-1 and | {χ }{{b}}(3)| =2.4× {10}-19 m2 V-2, accounting for the sheet thickness. Experimental comparisons between MoS2 and graphene are also performed, demonstrating ˜3.4 times stronger third-order sheet nonlinearity in monolayer MoS2, highlighting the material’s potential for nonlinear photonics in the telecommunications C band.
Directory of Open Access Journals (Sweden)
Qiaomei Su
2017-07-01
Full Text Available Landslide susceptibility mapping is the first and most important step involved in landslide hazard assessment. The purpose of the present study is to compare three nonlinear approaches for landslide susceptibility mapping and test whether coal mining has a significant impact on landslide occurrence in coal mine areas. Landslide data collected by the Bureau of Land and Resources are represented by the X, Y coordinates of its central point; causative factors were calculated from topographic and geologic maps, as well as satellite imagery. The five-fold cross-validation method was adopted and the landslide/non-landslide datasets were randomly split into a ratio of 80:20. From this, five subsets for 20 times were acquired for training and validating models by GIS Geostatistical analysis methods, and all of the subsets were employed in a spatially balanced sample design. Three landslide models were built using support vector machine (SVM, logistic regression (LR, and artificial neural network (ANN models by selecting the median of the performance measures. Then, the three fitted models were compared using the area under the receiver operating characteristics (ROC curves (AUC and the performance measures. The results show that the prediction accuracies are between 73.43% and 87.45% in the training stage, and 67.16% to 73.13% in the validating stage for the three models. AUCs vary from 0.807 to 0.906 and 0.753 to 0.944 in the two stages, respectively. Additionally, three landslide susceptibility maps were obtained by classifying the range of landslide probabilities into four classes representing low (0–0.02, medium (0.02–0.1, high (0.1–0.85, and very high (0.85–1 probabilities of landslides. For the distributions of landslide and area percentages under different susceptibility standards, the SVM model has more relative balance in the four classes compared to the LR and the ANN models. The result reveals that the SVM model possesses better
Woodward, R I; Phelan, C F; de Oliveira, R E P; Runcorn, T H; Kelleher, E J R; Li, S; de Oliveira, E C; Fechine, G J M; Eda, G; de Matos, C J S
2016-01-01
We report second- and third-harmonic generation in monolayer MoS$_2$ as a tool for imaging and accurately characterizing the material's nonlinear optical properties under 1560 nm excitation. Using a surface nonlinear optics treatment, we derive expressions relating experimental measurements to second- and third-order nonlinear sheet susceptibility magnitudes, obtaining values of $|\\chi_s^{(2)}|=2\\times10^{-20}$ m$^2$ V$^{-1}$ and for the first time for monolayer MoS$_2$, $|\\chi_s^{(3)}|=2\\times10^{-28}$ m$^3$ V$^{-2}$. Experimental comparisons between MoS$_2$ and graphene are also performed, demonstrating $\\sim$4 times stronger third-order nonlinearity in monolayer MoS$_2$, highlighting the material's potential for nonlinear photonics in the telecommunications C band.
Nickl-Jockschat, Thomas; Stöcker, Tony; Markov, Valentin; Krug, Axel; Huang, Ruihuang; Schneider, Frank; Habel, Ute; Zerres, Klaus; Nöthen, Markus M; Treutlein, Jens; Rietschel, Marcella; Shah, N Jon; Kircher, Tilo
2012-04-02
Schizophrenia is a severe neuropsychiatric disorder with high heritability, though its exact etiopathogenesis is yet unknown. An increasing number of studies point to the importance of white matter anomalies in the pathophysiology of schizophrenia. While several studies have identified the impact of schizophrenia susceptibility gene variants on gray matter anatomy in both schizophrenia patients and healthy risk variant carriers, studies dealing with the impact of these gene variants on white matter integrity are still scarce. We here present a study on the effects of a Dysbindin schizophrenia susceptibility gene variant on fiber tract integrity in healthy young subjects. 101 subjects genotyped for Dysbindin-gene variant rs1018381, though without personal or first degree relative history of psychiatric disorders underwent diffusion tensor imaging (DTI), 83 of them were included in the final analysis. We used Tract-Based Spatial Statistics (TBSS) analysis to delineate the major fiber tracts. Carriers of the minor allele T of the rs1018381 in the Dysbindin gene showed two clusters of reduced fractional anisotropy (FA) values in the perihippocampal region of the right temporal lobe compared to homozygote carriers of the major allele C. Clusters of increased FA values in T-allele carriers were found in the left prefrontal white matter, the right fornix, the right midbrain area, the left callosal body, the left cerebellum and in proximity of the right superior medial gyrus. Dysbindin has been implicated in neurite outgrowth and morphology. Impairments in anatomic connectivity as found associated with the minor Dysbindin allele in our study may result in increased risk for schizophrenia due to altered fiber tracts. Copyright Â© 2011. Published by Elsevier Inc.
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Xia Zhicheng; Nguyen, Bao D.; La Mar, Gerd N. [University of California, Department of Chemistry (United States)
2000-06-15
The use of dipolar shifts as important constraints in refining molecular structure of paramagnetic metalloproteins by solution NMR is now well established. A crucial initial step in this procedure is the determination of the orientation of the anisotropic paramagnetic susceptibility tensor in the molecular frame which is generated interactively with the structure refinement. The use of dipolar shifts as constraints demands knowledge of the diamagnetic shift, which, however, is very often not directly and easily accessible. We demonstrate that temperature gradients of dipolar shifts can serve as alternative constraints for determining the orientation of the magnetic axes, thereby eliminating the need to estimate the diamagnetic shifts. This approach is tested on low-spin, ferric sperm whale cyanometmyoglobin by determining the orientation, anisotropies and anisotropy temperature gradients by the alternate routes of using dipolar shifts and dipolar shift gradients as constraints. The alternate routes ultimately lead to very similar orientation of the magnetic axes, magnetic anisotropies and magnetic anisotropy temperature gradients which, by inference, would lead to an equally valid description of the molecular structure. It is expected that the use of the dipolar shift temperature gradients, rather than the dipolar shifts directly, as constraints will provide an accurate shortcut in a solution structure determination of a paramagnetic metalloprotein.
Carlberg, Kevin
2010-10-28
A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.
Energy Technology Data Exchange (ETDEWEB)
Cristea, M.; Radu, A., E-mail: radu@physics.pub.ro; Niculescu, E.C.
2013-11-15
Third-order nonlinear optical processes associated with the interlevel transitions in ZnS/CdSe core–shell quantum dots under electric fields are theoretically investigated. Taking into account the dielectric mismatch with the surrounding matrix, the electronic structure of the dots is obtained within the effective mass and parabolic band approximations. It is shown that large applied electric fields break the symmetry of the confinement potential and lead to a significant blue-shift of the peak positions in the nonlinear optical spectrum. The size effect is also discussed and it is proved that large nonlinear susceptibility can be obtained by increasing the thickness of the nanocrystal shell. Our results suggest that external factors such as the applied electric field and orientation of the incident light polarization can be used – in addition to spatial confinement – to improve the performances of the optical devices. -- Highlights: • Nonlinear optical processes in ZnS/CdSe QDs under electric field were studied. • The effective mass and parabolic band approximations were used. • The dielectric mismatch of the QDs with the surrounding matrix was considered. • Increasing the thickness of the shell could lead to large nonlinear susceptibility. • Incident light polarization with respect to the electric field was discussed.
Lacivita, Valentina; Rérat, Michel; Kirtman, Bernard; Ferrero, Mauro; Orlando, Roberto; Dovesi, Roberto
2009-11-01
The high-frequency dielectric ɛ and the first nonlinear electric susceptibility χ(2) tensors of crystalline potassium dihydrogen phosphate (KH2PO4) are calculated by using the coupled perturbed Hartree-Fock and Kohn-Sham methods as implemented in the CRYSTAL code. The effect of basis sets of increasing size on ɛ and χ(2) is explored. Five different levels of theory, namely, local-density approximation, generalized gradient approximation (PBE), hybrids (B3LYP and PBE0), and HF are compared using the experimental and theoretical structures corresponding not only to the tetragonal geometry I4d2 at room temperature but also to the orthorhombic phase Fdd2 at low temperature. Comparison between the two phases and their optical behavior is made. The calculated results for the tetragonal phase are in good agreement with the experimental data.
Stoller, Patrick C.; Kim, Beop-Min; Rubenchik, Alexander M.; Reiser, Karen M.; Da Silva, Luiz B.
2001-05-01
The measurement of the second order nonlinear susceptibility of collagen in various biological tissues has potential applications in the detection of structural changes which are related to different pathological conditions. We investigate second harmonic generation in a rat-tail tendon, a highly organized collagen structure consisting of parallel fibers. Using an electro-optic modulator and a quarter-wave plate, we modulate the linear polarization of an ultra-short pulse laser beam that is used to measure second harmonic generation in a confocal microscopy setup. Phase-sensitive detection of the generated signal, coupled with a simple model of the collagen protein structures, allows us to measure a parameter (gamma) related to nonlinear susceptibility and to determine the relative orientation of the structures. Our preliminary results indicate that it may be possible to use this parameter to characterize the structure.
Energy Technology Data Exchange (ETDEWEB)
Stoller, P; Kim, B-M; Rubenchik, A M; Reiser, K M; Da Silva, L B
2001-03-03
The measurement of the second order nonlinear susceptibility of collagen in various biological tissues has potential applications in the detection of structural changes which are related to different pathological conditions. We investigate second harmonic generation in rat-tail tendon, a highly organized collagen structure consisting of parallel fibers. Using an electro-optic modulator and a quarter-wave plate, we modulate the linear polarization of an ultra-short pulse laser beam that is used to measure second harmonic generation (SHG) in a confocal microscopy setup. Phase-sensitive detection of the generated signal, coupled with a simple model of the collagen protein structures, allows us to measure a parameter {gamma} related to nonlinear susceptibility and to determine the relative orientation of the structures. Our preliminary results indicate that it may be possible to use this parameter to characterize the structure.
1994-06-15
with the second order nonlinear susceptibility measured by ON SHG. The temperature dependance of the decay time constant of the SHG signal is found to...increasing with increasing chromophore :oncentration. This concentraton dependance is interpreted as due to orientational pair I:orrelation between...Pockels coefficient is compared with the second order nonlinear susceptibility measured by SHG. The temperature dependance of the decay time constant of
Avramopoulos, A; Papadopoulos, M G; Reis, H
2007-03-15
A discrete model based on the multipolar expansion including terms up to hexadecapoles was employed to describe the electrostatic interactions in liquid acetonitrile. Liquid structures obtained form molecular dynamics simulations with different classical, nonpolarizable potentials were used to analyze the electrostatic interactions. The computed average local field was employed for the determination of the environmental effects on the linear and nonlinear electrical molecular properties. Dipole-dipole interactions yield the dominant contribution to the local field, whereas higher multipolar contributions are small but not negligible. Using the effective in-phase properties, macroscopic linear and nonlinear susceptibilities of the liquid were computed. Depending on the partial charges describing the Coulomb interactions of the force field employed, either the linear properties (refractive index and dielectric constant) were reproduced in good agreement with experiment or the nonlinear properties [third-harmonic generation (THG) and electric field induced second-harmonic (EFISH) generation] and the bulk density but never both sets of properties together. It is concluded that the partial charges of the force fields investigated are not suitable for reliable dielectric properties. New methods are probably necessary for the determination of partial charges, which should take into account the collective and long-range nature of electrostatic interactions more precisely.
Zhou, Juefei
This dissertation combines theoretical and experimental studies of organic molecules to understand light-matter interactions with the goal of making more efficient nonlinear-optical molecules. We use a finite element method to numerically calculate and optimize the nonlinear-optical susceptibilities of 1-dimensional molecules, which resulted in a new paradigm for fabricating molecules with better nonlinear properties. This approach was used as a guide by researchers to identify and characterize a record-high intrinsic hyperpolarizability. Using the results of a sum rule analysis, we propose a new method for modeling the nonlinear-optical spectra of molecules. We apply our theory to the two-photon absorption cross section of the Air Force dye called AF455, and find that it is consistent with our measurements. The properties of the first two excited states of AF455 determined with a combination of linear absorption spectroscopy and hyper-Rayleigh scattering measurements are sufficient to predict, within experimental uncertainty, the full two-photon absorption spectrum.
Tensor-tensor theory of gravitation
Gogberashvili, Merab
1996-01-01
We consider the standard gauge theory of Poincar\\'{e} group, realizing as a subgroup of GL(5. R). The main problem of this theory was appearing of the fields connected with non-Lorentz symmetries, whose physical sense was unclear. In this paper we treat the gravitation as a Higgs-Goldstone field, and the translation gauge field as a new tensor field. The effective metric tensor in this case is hybrid of two tensor fields. In the linear approximation the massive translation gauge field can give the Yukava type correction to the Newtons potential. Also outer potentials of a sphere and ball of the same mass are different in this case. Corrections to the standard Einshtein post Newtonian formulas of the light deflection and radar echo delay is obtained. The string like solution of the nonlinear equations of the translation gauge fields is found. This objects can results a Aharonov-Bohm type effect even for the spinless particles. They can provide density fluctuations in the early universe, necessary for galaxy fo...
Nonlinear optical and magneto-optical effects in non-spherical magnetic granular composite
Institute of Scientific and Technical Information of China (English)
Ping Xu(须萍); Zhenya Li(李振亚)
2004-01-01
The magnetization-induced nonlinear optical and nonlinear magneto-optical properties in a magnetic metal-insulator composite are studied based on a tensor effective medium approximation with shape factor and Taylcr-expansion method. There is a weakly nonlinear relation between electric displacement D and elcctric field E in the composite. The results of our studies on the effective dielectric tensor and the nonlinear susceptibility tensor in a magnetic nanocomposite are surveyed. It is shown that such a metal-insulator composite exhibits the enhancements of optical and magneto-optical nonlinearity. The frequencies at which the enhancements occur, and the amplitude of the enhancement factors depend on the concentration and shape of the magnetic grains.
Zhao, Xiaohui; Zheng, Yuanlin; Ren, Huaijin; An, Ning; Deng, Xuewei; Chen, Xianfeng
2017-04-01
In this article, we demonstrate that the angles at which second-harmonic (SH) waves are generated at ferroelectric domain walls satisfy the Snell law for nonlinear media. Nonlinear reflection and refraction are observed experimentally and the relation is found to be in good agreement with theoretical predictions. The ratio of the intensities of refracted and reflected waves has been measured. Under an anomalous-dispersion-like condition, the forbidden nonlinear reflection and refraction is analyzed and found to have a behavior similar to that of the total internal reflection in linear optics. In the periodic domain structure, the coherent superposition of SH waves has been observed, on the basis of which we have proposed a comprehensive theory to explain nonlinear effects in multilayered structures.
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Victor
2015-01-01
Is there a vector space whose dimension is the golden ratio? Of course not-the golden ratio is not an integer! But this can happen for generalizations of vector spaces-objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This bo
Directory of Open Access Journals (Sweden)
Julie A Simpson
Full Text Available The analysis of in vitro anti-malarial drug susceptibility testing is vulnerable to the effects of different statistical approaches and selection biases. These confounding factors were assessed with respect to pfmdr1 gene mutation and amplification in 490 clinical isolates. Two statistical approaches for estimating the drug concentration associated with 50% effect (EC50 were compared: the commonly used standard two-stage (STS method, and nonlinear mixed-effects modelling. The in vitro concentration-effect relationships for, chloroquine, mefloquine, lumefantrine and artesunate, were derived from clinical isolates obtained from patients on the western border of Thailand. All isolates were genotyped for polymorphisms in the pfmdr1 gene. The EC50 estimates were similar for the two statistical approaches but 15-28% of isolates in the STS method had a high coefficient of variation (>15% for individual estimates of EC50 and these isolates had EC50 values that were 32 to 66% higher than isolates derived with more precision. In total 41% (202/490 of isolates had amplification of pfmdr1 and single nucleotide polymorphisms were found in 50 (10%. Pfmdr1 amplification was associated with an increase in EC50 for mefloquine (139% relative increase in EC50 for 2 copies, 188% for 3+ copies, lumefantrine (82% and 75% for 2 and 3+ copies respectively and artesunate (63% and 127% for 2 and 3+ copies respectively. In contrast pfmdr1 mutation at codons 86 or 1042 were associated with an increase in chloroquine EC50 (44-48%. Sample size calculations showed that to demonstrate an EC50 shift of 50% or more with 80% power if the prevalence was 10% would require 430 isolates and 245 isolates if the prevalence was 20%. In conclusion, although nonlinear mixed-effects modelling did not demonstrate any major advantage for determining estimates of anti-malarial drug susceptibility, the method includes all isolates, thereby, potentially improving confirmation of candidate
Wang, Sijia; Peterson, Daniel J.; Gatenby, J. C.; Li, Wenbin; Grabowski, Thomas J.; Madhyastha, Tara M.
2017-01-01
Correction of echo planar imaging (EPI)-induced distortions (called “unwarping”) improves anatomical fidelity for diffusion magnetic resonance imaging (MRI) and functional imaging investigations. Commonly used unwarping methods require the acquisition of supplementary images during the scanning session. Alternatively, distortions can be corrected by nonlinear registration to a non-EPI acquired structural image. In this study, we compared reliability using two methods of unwarping: (1) nonlinear registration to a structural image using symmetric normalization (SyN) implemented in Advanced Normalization Tools (ANTs); and (2) unwarping using an acquired field map. We performed this comparison in two different test-retest data sets acquired at differing sites (N = 39 and N = 32). In both data sets, nonlinear registration provided higher test-retest reliability of the output fractional anisotropy (FA) maps than field map-based unwarping, even when accounting for the effect of interpolation on the smoothness of the images. In general, field map-based unwarping was preferable if and only if the field maps were acquired optimally.
Near-resonant second-order nonlinear susceptibility in c-axis oriented ZnO nanorods
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Liu, Weiwei; Wang, Kai; Long, Hua; Wang, Bing, E-mail: wangbing@hust.edu.cn; Lu, Peixiang, E-mail: lupeixiang@hust.edu.cn [Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074 (China); Chu, Sheng [School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275 (China)
2014-08-18
Near-resonant second-harmonic generation (SHG) in c-axis oriented ZnO nanorods is studied under the femtosecond laser with wavelength from 780 nm to 810 nm. A highly efficient SHG is obtained, which is attributed to the d{sub 131} component of the second-order nonlinear susceptibility. The largest d{sub 131} value is estimated to be 10.2 pm/V at the pumping wavelength of 800 nm, which indicates a large SHG response of the c-axis oriented ZnO nanorods in the near-resonant region. Theoretical calculation based on finite-difference time-domain simulation suggests a four-fold local-field enhancement of the SHG.
Pereira Silva, Pedro S.; Pereira Gonçalves, M. A.; Ramos Silva, Manuela; Paixão, José A.
2017-02-01
A new organic compound, guanidinium cyclopropanecarboxylate, has been synthesized and characterized by single crystal X-ray diffraction, infrared spectroscopy and nonlinear optical measurements. The infrared spectrum was calculated with density functional theory (DFT). The second-order NLO response was evaluated with the Kurtz and Perry powder method. From the molecular structure, the molecular hyperpolarizability tensor was determined with Hartree-Fock and DFT methods. The second-order susceptibility tensor of the crystal was evaluated by the summation of the effective hyperpolarizability tensors calculated for the asymmetric unit surrounded by ESP-derived charges.
Jensen, L; van Duijnen, PT
2005-01-01
We have calculated the frequency-dependent refractive index and the third-order nonlinear susceptibility for C-60 in the condensed phase, which is related to third-harmonic generation (THG) and degenerate four-wave mixing (DFWM) experiments. This was done using the recently developed discrete solven
Bornacelli, Jhovani; Torres-Torres, Carlos; Silva-Pereyra, Héctor Gabriel; Rodríguez-Fernández, Luis; Avalos-Borja, Miguel; Cheang-Wong, Juan Carlos; Oliver, Alicia
2017-05-09
-diffraction decay time is less than 25 ps, regardless of the average size of the nanoparticles studied. The evolution of the self-diffracted intensities derived from temperature was also linked to the mean size of the nanoparticles in the samples. Comparative two-wave mixing evaluations also validated a modification in third order nonlinear susceptibility exhibited by annealed samples. An important role of the localized surface plasmon resonance phenomena associated with the platinum nanoparticles for photoluminescence and optical nonlinearities was identified. A proposed hypothetical electronic mechanism that may explain the exceptional optical transitions related to low-dimensional platinum systems is discussed.
Bornacelli, Jhovani; Torres-Torres, Carlos; Silva-Pereyra, Héctor Gabriel; Rodríguez-Fernández, Luis; Avalos-Borja, Miguel; Cheang-Wong, Juan Carlos; Oliver, Alicia
2017-06-01
-diffraction decay time is less than 25 ps, regardless of the average size of the nanoparticles studied. The evolution of the self-diffracted intensities derived from temperature was also linked to the mean size of the nanoparticles in the samples. Comparative two-wave mixing evaluations also validated a modification in third order nonlinear susceptibility exhibited by annealed samples. An important role of the localized surface plasmon resonance phenomena associated with the platinum nanoparticles for photoluminescence and optical nonlinearities was identified. A proposed hypothetical electronic mechanism that may explain the exceptional optical transitions related to low-dimensional platinum systems is discussed.
Morais, C. V.; Zimmer, F. M.; Lazo, M. J.; Magalhães, S. G.; Nobre, F. D.
2016-06-01
The behavior of the nonlinear susceptibility χ3 and its relation to the spin-glass transition temperature Tf in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue λAT (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature Tf can be traced by a divergence in the spin-glass susceptibility χSG, which presents a term inversely proportional to the replicon λAT. As a result of a relation between χSG and χ3, the latter also presents a divergence at Tf, which comes as a direct consequence of λAT=0 at Tf. However, our results show that, in the presence of random fields, χ3 presents a rounded maximum at a temperature T* which does not coincide with the spin-glass transition temperature Tf (i.e., T*>Tf for a given applied random field). Thus, the maximum value of χ3 at T* reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that χ3 still maintains a dependence on the replicon λAT, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the LiHoxY1 -xF4 compound.
Ganguly, Jayanta; Saha, Surajit; Pal, Suvajit; Ghosh, Manas
2016-03-01
We perform a meticulous analysis of profiles of third-order nonlinear optical susceptibility (TONOS) of impurity doped quantum dots (QDs) in the presence and absence of noise. We have invoked Gaussian white noise in the present study and noise has been introduced to the system additively and multiplicatively. The QD is doped with a Gaussian impurity. A magnetic field applied perpendicularly serves as a confinement source and the doped system has been exposed to a static external electric field. The TONOS profiles have been monitored against a continuous variation of incident photon energy when several important parameters such as electric field strength, magnetic field strength, confinement energy, dopant location, Al concentration, dopant potential, relaxation time, anisotropy, and noise strength assume different values. Moreover, the influence of mode of introduction of noise (additive/multiplicative) on the TONOS profiles has also been addressed. The said profiles are found to be consisting of interesting observations such as shift of TONOS peak position and maximization/minimization of TONOS peak intensity. The presence of noise alters the features of TONOS profiles and sometimes enhances the TONOS peak intensity from that of noise-free state. Furthermore, the mode of application of noise also often tailors the TONOS profiles in diverse fashions. The observations accentuate the possibility of tuning the TONOS of doped QD systems in the presence of noise.
Strictly nonnegative tensors and nonnegative tensor partition
Institute of Scientific and Technical Information of China (English)
HU ShengLong; HUANG ZhengHai; QI LiQun
2014-01-01
We introduce a new class of nonnegative tensors—strictly nonnegative tensors.A weakly irreducible nonnegative tensor is a strictly nonnegative tensor but not vice versa.We show that the spectral radius of a strictly nonnegative tensor is always positive.We give some necessary and su？cient conditions for the six wellconditional classes of nonnegative tensors,introduced in the literature,and a full relationship picture about strictly nonnegative tensors with these six classes of nonnegative tensors.We then establish global R-linear convergence of a power method for finding the spectral radius of a nonnegative tensor under the condition of weak irreducibility.We show that for a nonnegative tensor T,there always exists a partition of the index set such that every tensor induced by the partition is weakly irreducible;and the spectral radius of T can be obtained from those spectral radii of the induced tensors.In this way,we develop a convergent algorithm for finding the spectral radius of a general nonnegative tensor without any additional assumption.Some preliminary numerical results show the feasibility and effectiveness of the algorithm.
Das, T.; Panda, M.; Panda, S.; Panda, B. K.
2017-05-01
In this work, the variation of optical properties in the AlGaN/GaN quantum well after thermal annealing is studied. The potential profile change of the quantum well resulting from the interdiffusion of Ga and Al atoms across the interface of the well and the barrier during the thermal treatments is assumed to follow Fick's law. The results show that the thermal annealing can induce an increase of the optical susceptibilities in the AlGaN/GaN quantum well. However the third-order nonlinear optical susceptibilities are red shifted with increasing in diffusion lengths.
An Algorithm to Simplify Tensor Expressions
Portugal, R
1998-01-01
The problem of simplifying tensor expressions is addressed in two parts. The first part presents an algorithm designed to put tensor expressions into a canonical form, taking into account the symmetries with respect to index permutations and the renaming of dummy indices. The tensor indices are split into classes and a natural place for them is defined. The canonical form is the closest configuration to the natural configuration. In the second part, the Groebner basis method is used to simplify tensor expressions which obey the linear identities that come from cyclic symmetries (or more general tensor identities, including non-linear identities). The algorithm is suitable for implementation in general purpose computer algebra systems. Some timings of an experimental implementation over the Riemann package are shown.
Energy Technology Data Exchange (ETDEWEB)
Bahedi, K., E-mail: bahedikhadija@yahoo.fr [Laboratoire Optoelectronique et Physico-chimie des Materiaux, associe au CNRST, Universite Ibn Tofail, Faculte des Sciences BP 133, Kenitra 14000 (Morocco); Addou, M.; El Jouad, M.; Bayoud, S.; Sofiani, Z. [Laboratoire Optoelectronique et Physico-chimie des Materiaux, associe au CNRST, Universite Ibn Tofail, Faculte des Sciences BP 133, Kenitra 14000 (Morocco)
2009-08-30
Zirconium doped zinc oxide thin films were deposited by reactive chemical pulverization spray pyrolysis technique on heated glass substrates at 400 deg. C, 450 deg. C and 500 deg. C using zinc and zirconium chlorides as precursors. The effect of zirconium dopant and surface roughness on the nonlinear optical properties was investigated using atomic force microscopy (AFM) and third harmonic generation (THG). The best value of susceptibility {chi}{sup (3)} was obtained from the doped films with less roughness. A strong third order nonlinear optical susceptibility {chi}{sup (3)} = 20.49 x 10{sup -12} (esu) of the studied films was found for the 5% doped sample at 450 deg. C.
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
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-...
Karakas, A.; Karakaya, M.; Ceylan, Y.; El Kouari, Y.; Taboukhat, S.; Boughaleb, Y.; Sofiani, Z.
2016-06-01
In this talk, after a short introduction on the methodologies used for computing dipole polarizability (α), second and third-order hyperpolarizability and susceptibility; the results of theoretical studies performed on density functional theory (DFT) and ab-initio quantum mechanical calculations of nonlinear optical (NLO) properties for a few selected organic compounds and polymers will be explained. The electric dipole moments (μ) and dispersion-free first hyperpolarizabilities (β) for a family of azo-azulenes and a styrylquinolinium dye have been determined by DFT at B3LYP level. To reveal the frequency-dependent NLO behavior, the dynamic α, second hyperpolarizabilities (γ), second (χ(2)) and third-order (χ(3)) susceptibilites have been evaluated using time-dependent HartreeFock (TDHF) procedure. To provide an insight into the third-order NLO phenomena of a series of pyrrolo-tetrathiafulvalene-based molecules and pushpull azobenzene polymers, two-photon absorption (TPA) characterizations have been also investigated by means of TDHF. All computed results of the examined compounds are compared with their previous experimental findings and the measured data for similar structures in the literature. The one-photon absorption (OPA) characterizations of the title molecules have been theoretically obtained by configuration interaction (CI) method. The highest occupied molecular orbitals (HOMO), the lowest unoccupied molecular orbitals (LUMO) and the HOMO-LUMO band gaps have been revealed by DFT at B3LYP level for azo-azulenes, styrylquinolinium dye, push-pull azobenzene polymers and by parametrization method 6 (PM6) for pyrrolo-tetrathiafulvalene-based molecules.
3D reconstruction of tensors and vectors
Energy Technology Data Exchange (ETDEWEB)
Defrise, Michel; Gullberg, Grant T.
2005-02-17
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.
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.
Gurau, Razvan
2016-09-01
This article is preface to the SIGMA special issue ''Tensor Models, Formalism and Applications'', http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field. This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.
Applications of tensor analysis
McConnell, A J
2011-01-01
Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers.
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.
Renormalizable Tensor Field Theories
Geloun, Joseph Ben
2016-01-01
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in any dimension and therefore form an interesting class of models for studying quantum gravity. We review the class of perturbatively renormalizable tensor field theories and some of their features.
Li, Chao; Yin, Wenlong; Gong, Pifu; Li, Xiaoshuang; Zhou, Molin; Mar, Arthur; Lin, Zheshuai; Yao, Jiyong; Wu, Yicheng; Chen, Chuangtian
2016-05-18
A new mercury selenide BaHgSe2 was synthesized. This air-stable compound displays a large nonlinear optical (NLO) response and melts congruently. The structure contains chains of corner-sharing [HgSe3](4-) anions in the form of trigonal planar units, which may serve as a new kind of basic functional group in IR NLO materials to confer large NLO susceptibilities and physicochemical stability. Such trigonal planar units may inspire a path to finding new classes of IR NLO materials of practical utility that are totally different from traditional chalcopyrite materials.
Pereira Gonçalves, Mauro A.; Silva, Pedro S. Pereira; Silva, Manuela Ramos; Paixão, José A.
2017-02-01
A new organic compound, L-histidinium thiocyanurate thiocyanuric acid dihydrate, has been synthesized and characterized by single crystal X-ray diffraction, infrared spectroscopy and nonlinear optical measurements. The efficiency of the second-harmonic generation was evaluated with the Kurtz and Perry powder method at a fundamental wavelength of 1064 nm. By using the experimental structure, the molecular first hyperpolarizability tensor was determined with Hartree-Fock and density functional theory methods. The second-order susceptibility tensor of the crystal was evaluated using the oriented gas model with the Lorenz-Lorentz and the Wortmann-Bishop local-field corrections.
Irreducible Killing Tensors from Third Rank Killing-Yano Tensors
Popa, Florian Catalin; Tintareanu-Mircea, Ovidiu
2006-01-01
We investigate higher rank Killing-Yano tensors showing that third rank Killing-Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric were from two rank Killing-Yano tensors we obtain a reducible Killing tensor and from third rank Killing-Yano tensors we obtain three Killing tensors, one reducible and two irreducible.
InfTucker: t-Process based Infinite Tensor Decomposition
Xu, Zenglin; Yuan,; Qi,
2011-01-01
Tensor decomposition is a powerful tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---conduct multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g. missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose a tensor-variate latent $t$ process model, InfTucker, for robust multiway data analysis: it conducts robust Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, it handles both continuous and binary data in a probabilistic framework. Unlike previous nonparametric Bayesian models on matrices and tensors, our latent $t$-process model focuses on multiway analysis and uses nonlinear covariance functions. To efficiently learn InfTucker from data, we develop a novel variational inference technique on tensors. Compared with classical implementation,...
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.
Metzler, S; Miettinen, P
2015-01-01
Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required to be binary and we use Boolean algebra -- much of that hardness comes from the possibility of overlapping components. Yet, in many applications we are perfectly happy to partition at least one of the modes. In this paper we investigate what consequences doe...
Gurau, Razvan
2016-01-01
Preface to the SIGMA special issue "Tensor Models, Formalism and Applications." The SIGMA special issue "Tensor Models, Formalism and Applications" is a collection of eight excellent, up to date reviews \\cite{Ryan:2016sundry,Bonzom:2016dwy,Rivasseau:2016zco,Carrozza:2016vsq,Krajewski:2016svb,Rivasseau:2016rgt,Tanasa:2015uhr,Gielen:2016dss} on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field. This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.
Cartesian tensors an introduction
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
Gómez-Sosa, Gustavo; Ogawa, Takeshi; Isoshima, Takashi; Hara, Masahiko
The second-order nonlinear optical susceptibilities χ(2) of two isomeric polymers containing an azo dye, Disperse Red 19, were determined by the first-order electroabsorption spectroscopy (EAS), and compared with values previously obtained by SHG measurements. The para-polymer was found to have higher susceptibility than the corresponding meta-polymer. χ(2) were found to be 5-6 × 10-8 esu, which are comparable to those obtained by the Maker Fringe method.
On the tensor Permutation Matrices
Rakotonirina, Christian
2011-01-01
A property that tensor permutation matrices permutate tensor product of rectangle matrices is shown. Some examples, in the particular case of tensor commutation matrices, for studying some linear matricial equations are given.
Syvorotka, Ihor I.; Pavlyk, Lyubomyr P.; Ubizskii, Sergii B.; Buryy, Oleg A.; Savytskyy, Hrygoriy V.; Mitina, Nataliya Y.; Zaichenko, Oleksandr S.
2017-04-01
Method of determining of magnetic moment and size from measurements of dependence of the nonlinear magnetic susceptibility upon magnetic field is proposed, substantiated and tested for superparamagnetic nanoparticles (SPNP) of the "magnetic core-polymer shell" type which are widely used in biomedical technologies. The model of the induction response of the SPNP ensemble on the combined action of the magnetic harmonic excitation field and permanent bias field is built, and the analysis of possible ways to determine the magnetic moment and size of the nanoparticles as well as the parameters of the distribution of these variables is performed. Experimental verification of the proposed method was implemented on samples of SPNP with maghemite core in dry form as well as in colloidal systems. The results have been compared with the data obtained by other methods. Advantages of the proposed method are analyzed and discussed, particularly in terms of its suitability for routine express testing of SPNP for biomedical technology.
Mantica, Carlo A
2012-01-01
The algebraic condition of Riemann compatibility for symmetric tensors generalizes the differential Codazzi condition, but preserves much of the geometric content. The compatibility condition can be extended to other curvature tensors. This paper is about Weyl compatible tensors and vectors. In particular it is shown that the existence of a Weyl compatible vector implies the Weyl tensor to be algebraically special, and it is a necessary and sufficient condition for the magnetic part to vanish. Some theorems (Derdzinski and Shen, Hall) are extended to the broader hypothesis of Weyl or Riemann compatibility. Weyl compatibility includes conditions that were investigated in the literature of general relativity (as McIntosh et al.). Hypersurfaces of pseudo Euclidean spaces provide a simple example of Weyl compatible Ricci tensor.
Ganguly, Jayanta; Saha, Surajit; Bera, Aindrila; Ghosh, Manas
2017-03-01
We study the profiles of electro-optic effect (EOE) and third-order nonlinear optical susceptibility (TONOS) of impurity doped GaAs quantum dots (QDs) under the combined influence of hydrostatic pressure (HP) and temperature (T) taking into account the presence of Gaussian white noise. Noise has been introduced to the system additively and multiplicatively. The doped dot has been subjected to a polarized monochromatic electromagnetic field. Effect of application of noise is elegantly reflected through prominent change of peak shift (blue/red) and variation of peak height (increase/ıdecrease) of above nonlinear optical (NLO) properties as temperature and pressure are varied over a range. Interestingly, all such changes subtly depend on mode of application (additive/multiplicative) of noise. The noteworthy influence of the interplay between noise strength and its mode of application on the said NLO properties has also been critically scrutinized. The findings highlight remarkable role played by noise in tuning above NLO properties of doped QD system under the prominent presence of both hydrostatic pressure and temperature.
Reshak, Ali H; Auluck, S; Kityk, I V
2009-02-26
We have performed ab inito theoretical calculations of the electronic structure and the linear and nonlinear optical susceptibilities for calcium neodymium oxyborate Ca4NdO(BO3)3 using two approximations for the exchange correlation (XC) potentials, the local density approximation (LDA) and the generalized gradient approximation (GGA). Our calculations show that this compound is metallic-like, with density of states at the Fermi energy E(F), N(E(F)), of 5.95 and 10.33 states/Ry-cell or bare electronic specific heat coefficients of 1.03 and 1.79 mJ/mol-K2 for LDA and GGA, respectively. The overlap between the valence and conduction bands is strong, resulting in metallic behavior. We found that Nd-s/p/d, Ca-s/p, B-p, and O-s/p states controlled the overlapping around E(F). The effect of LDA and GGA on the band structure, density of states, and linear optical properties is very small, while for the nonlinear optical properties, it is very pronounced. Our calculations show that χ(111)(2)(ω) is the dominant component for both LDA and GGA. We find opposite signs of the contributions of the 2ω and 1ω inter/intraband to the real and imaginary parts for the dominant component throughout the wide optical frequency range.
Obtaining the Weyl tensor from the Bel-Robinson tensor
Ferrando, Joan J; 10.1007/s10714-009-0921-8
2010-01-01
The algebraic study of the Bel-Robinson tensor proposed and initiated in a previous work (Gen. Relativ. Gravit. {\\bf 41}, see ref [11]) is achieved. The canonical form of the different algebraic types is obtained in terms of Bel-Robinson eigen-tensors. An algorithmic determination of the Weyl tensor from the Bel-Robinson tensor is presented.
Tensor Network Skeletonization
Ying, Lexing
2016-01-01
We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations effectively at every scale. This approach is first presented in the setting of 2D statistical Ising model and is then extended to higher dimensional tensor networks and disordered systems. When applied to the Euclidean path integral formulation, this approach also gives rise to new efficient representations of the ground states for 1D and 2D quantum Ising models.
Sugimoto, Noriaki; Koiwai, Akihiko; Hyodo, Shi-aki; Hioki, Tatsumi; Noda, Shoji
1995-02-01
Nonresonant third-order harmonic generation from CdS clusters encapsulated in zeolite A and X was observed at a fundamental wavelength of 1900 nm. To avoid scattering from the surfaces of the small zeolite crystals, the powder samples were dispersed in a liquid with nearly the same refractive index as that of the samples. The third-order optical susceptibilities of CdS-encapsulated zeolite A and X estimated from the intensity of their Maker fringe patterns were 4.1×10-12 and 1.1×10-11 esu, respectively. These values were slightly smaller than those reported for the 1.5 nm surface-capped CdS cluster. The hyperpolarizabilities of CdS clusters encapsulated in zeolite A and X were estimated by assuming the Lorentz local field to be in the range of 380-480×10-36 and 270-390×10-36 esu, respectively.
Westerhof, E.
1996-01-01
The hot plasma dielectric tensor is discussed in its various approximations. Collisionless cyclotron resonant damping and ion/electron Bernstein waves are discussed to exemplify the significance of a kinetic description of plasma waves.
Chung, Daniel J H
2016-01-01
We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.
Tensors and their applications
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 Network Renormalization.
Evenbly, G; Vidal, G
2015-10-30
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.
Energy Technology Data Exchange (ETDEWEB)
Zhang, L. [State Key Laboratory for Mesoscopic Physics, and School of Physics, Peking University, Beijing 100871 (China) and Department of Mechanism and Electron, Panyu Polytechnic, Panyu 511483 (China)]. E-mail: zhangli-gz@263.net; Chi Yuemeng [State Key Laboratory for Mesoscopic Physics, and School of Physics, Peking University, Beijing 100871 (China); Shi, J.-J. [State Key Laboratory for Mesoscopic Physics, and School of Physics, Peking University, Beijing 100871 (China)
2007-06-25
Based on the density matrix method and the iterative treatment, the second-harmonic generation (SHG) susceptibility of a wurtzite nitride coupling quantum well (CQW) with strong built-in electric fields have been theoretically investigated. The effect of the band non-parabolicity effect has been taken into account. A typical wurtzite GaN/In{sub x}Ga{sub 1-x}N CQW are chosen to perform numerical calculations. The localized properties of the electronic ground state and the low-excited states in the system are analyzed in detail. The calculated SHG coefficients reach the order of magnitude of 10{sup -7}m/V, which is two-order larger than the corresponding values in wurtzite single quantum wells. Moreover, it is confirmed that the SHG coefficients are not monotonic functions of the well width, barrier width and the doped concentration of the CQW systems, but have complicated dependent relations on them. The reasons resulting in these characteristics can be attributed to the intense competition between the strong built-in electric field effect and the quantum size effect for the electronic confined situation in the wurtzite CQWs. The calculated results also show that a strong SHG effect can be realized in the nitride CQW by choosing a group of optimized structural parameters and doped fraction.
A Review of Tensors and Tensor Signal Processing
Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.
Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.
Physical states in the canonical tensor model from the perspective of random tensor networks
Narain, Gaurav; Sato, Yuki
2014-01-01
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 physical wave-functions, which do not seem straightforward to solve 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 con...
Monte Carlo Volcano Seismic Moment Tensors
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.
Tensor analysis for physicists
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...
Tensors, relativity, and cosmology
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...
Symmetric tensor decomposition
Brachat, Jerome; Mourrain, Bernard; Tsigaridas, Elias
2009-01-01
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 total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. Exploiting this duality, we propose necessary and sufficient conditions for the existence of such a decomposition of a given rank, using the properties of Hankel (and quasi-Hankel) matrices, derived from multivariate polynomials and normal form computations. This leads to the resolution of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on th...
Physical components of tensors
Altman, Wolf
2014-01-01
""This book provides a clear explanation of the mathematical properties of tensors, from a physical perspective. The book is rigorous and concise, yet easy to read and very accessible. The reader will enjoy the wide variety of examples and exercises with solution, which make the book very pedagogical. I believe this can be a very useful book for anyone interested in learning about the mathematics of tensors, no matter the field of study or research. I would definitely like to have this book on my shelf, and use it as a reference in my own lectures."" -Román Orús, Institut für Physik, Jo
Clemmen, StÉphane; Solano, Eduardo; Dendooven, Jolien; Koskinen, Kalle; Kauranen, Martti; Brainis, Edouard; Detavernier, Christophe; Baets, Roel
2015-01-01
We report the fabrication of artificial unidimensional crystals exhibiting an effective bulk second-order nonlinearity. The crystals are created by cycling atomic layer deposition of three dielectric materials such that the resulting metamaterial is non-centrosymmetric in the direction of the deposition. Characterization of the structures by second-harmonic generation Maker-fringe measurements shows that the main component of their nonlinear susceptibility tensor is about 5 pm/V which is comparable to well-established materials and more than an order of magnitude greater than reported for a similar crystal [1-Alloatti et al, arXiv:1504.00101[cond-mat.mtrl- sci
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle s...
Heil, Konstantin; Moroianu, Andrei; Semmelmann, Uwe
2017-07-01
We show that Killing tensors on conformally flat n-dimensional tori whose conformal factor only depends on one variable, are polynomials in the metric and in the Killing vector fields. In other words, every first integral of the geodesic flow polynomial in the momenta on the sphere bundle of such a torus is linear in the momenta.
Energy Technology Data Exchange (ETDEWEB)
Palmkvist, Jakob, E-mail: palmkvist@ihes.fr [Institut des Hautes Etudes Scientifiques, 35 Route de Chartres, FR-91440 Bures-sur-Yvette (France)
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
Gravity in warped compactications and the holographic stress tensor
Haro, S. de; Skenderis, K.; Solodukhin, S.N.
2001-01-01
We study gravitational aspects of Brane-World scenarios. We show that the bulk Einstein equations together with the junction condition imply that the induced metric on the brane satisfies the full non-linear Einstein equations with a specific effective stress energy tensor. This result holds for any
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.)
2010-11-30
ELECTROMAGNEETIC SURFACE IMPEDANCE PROPERTIES FA9550-09-C-0198 DR. ADOUR KABAKIAN HUGHES RESEARCH LABS AFOSR / RSE 875 North Randolph Street, Suit...325 Room 3112 Arlington, Virginia 22203-1768 AFOSR / RSE AFRL-OSR-VA-TR-2012-0770 Distribution A We have investigated and determined how the tensor...the case of a TM wave, which favors propagation along the shorter principal axis. Standard terms apply U U U UU Arje Nachman RSE (Program Manager
Trirefringence in nonlinear metamaterials
De Lorenci, Vitorio A
2012-01-01
We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their permeability are assumed positive and dependent on the electric field. We show that light waves experience triple refraction -- trirefringence. Additionally to the ordinary wave, two extraordinary waves propagate in such media.
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Physical states in the canonical tensor model from the perspective of random tensor networks
Narain, Gaurav; Sasakura, Naoki; Sato, Yuki
2015-01-01
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.
E6Tensors: A Mathematica Package for E6 Tensors
Deppisch, Thomas
2016-01-01
We present the Mathematica package E6Tensors, a tool for explicit tensor calculations in E6 gauge theories. In addition to matrix expressions for the group generators of E6, it provides structure constants, various higher rank tensors and expressions for the representations 27, 78, 351 and 351'. This paper comes along with a short manual including physically relevant examples. I further give a complete list of gauge invariant, renormalisable terms for superpotentials and Lagrangians.
Matsueda, Hiroaki; Hashizume, Yoichiro
2012-01-01
A tensor network formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, multiscale entanglement renormalization anzats (MERA) reproduces an AdS black hole at finite temperature. Our finding shows rich functionalities of MERA as efficient graphical representation of AdS/CFT correspondence.
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
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 total degree d as a sum of powers of linear forms (Waring’s problem), incidence properties on secant varieties of the Veronese variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester’s approach from the dual point of view...
Hu, Yonggang; Wu, Yi; 10.3150/10-BEJ317
2012-01-01
The conventional definition of a depth function is vector-based. In this paper, a novel projection depth (PD) technique directly based on tensors, such as matrices, is instead proposed. Tensor projection depth (TPD) is still an ideal depth function and its computation can be achieved through the iteration of PD. Furthermore, we also discuss the cases for sparse samples and higher order tensors. Experimental results in data classification with the two projection depths show that TPD performs much better than PD for data with a natural tensor form, and even when the data have a natural vector form, TPD appears to perform no worse than PD.
Tensor norms and operator ideals
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
Spatial solitons in nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independe...... of the small-scale structure of the Earth’s lithospheric field....
Group-theoretical method for physical property tensors of quasicrystals
Institute of Scientific and Technical Information of China (English)
Gong Ping; Hu Cheng-Zheng; Zhou Xiang; Wang Ai-Jun; Miao Ling
2006-01-01
In addition to the phonon variable there is the phason variable in hydrodynamics for quasicrystals. These two kinds of hydrodynamic variables have different transformation properties. The phonon variable transforms under the vector representation, whereas the phason variable transforms under another related representation. Thus, a basis (or a set of basis functions) in the representation space should include such two kinds of variables. This makes it more difficult to determine the physical property tensors of quasicrystals. In this paper the group-theoretical method is given to determine the physical property tensors of quasicrystals. As an illustration of this method we calculate the third-order elasticity tensors of quasicrystals with five-fold symmetry by means of basis functions. It follows that the linear phonon elasticity is isotropic, but the nonlinear phonon elasticity is anisotropic for pentagonal quasicrystals. Meanwhile, the basis functions are constructed for all noncrystallographic point groups of quasicrystals.
Susceptibilities of QCD Vacuum from Renormalized Dyson-Schwinger Equations
Institute of Scientific and Technical Information of China (English)
CHEN Wei; QI Shi; SUN Wei-Min; ZONG Hong-Shi
2004-01-01
The pion and tensor vacuum susceptibilities are calculated in the framework of the renormalizable DysonSchwinger equations. A comparison with the results of other nonperturbative QCD approaches is given.
Tensor Network Contractions for #SAT
Biamonte, Jacob D.; Morton, Jason; Turner, Jacob
2015-09-01
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g. 2-SAT, which is in ), determining the number of solutions can be #-hard. Recently, computational methods simulating quantum systems experienced advancements due to the development of tensor network algorithms and associated quantum physics-inspired techniques. By these methods, we give an algorithm using an axiomatic tensor contraction language for n-variable #SAT instances with complexity where c is the number of COPY-tensors, g is the number of gates, and d is the maximal degree of any COPY-tensor. Thus, n-variable counting problems can be solved efficiently when their tensor network expression has at most COPY-tensors and polynomial fan-out. This framework also admits an intuitive proof of a variant of the Tovey conjecture (the r,1-SAT instance of the Dubois-Tovey theorem). This study increases the theory, expressiveness and application of tensor based algorithmic tools and provides an alternative insight on these problems which have a long history in statistical physics and computer science.
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.
Yamada, Hirofumi
2012-01-01
Based on the strong coupling expansion, we reinvestigate the scaling behavior of the susceptibility chi of two-dimensional O(N) sigma model on the square lattice by the use of Pade-Borel approximants. To exploit the Borel transform, we express the bare coupling g in series expansion in chi. At large N, Pade-Borel approximants exhibit the scaling behavior at the four-loop level. Then, the estimation of the non-perturbative constant associated with the susceptibility is performed for N>=3 and the results are compared with the available theoretical results and Monte Carlo data.
Solving Tensor Structured Problems with Computational Tensor Algebra
Morozov, Oleksii
2010-01-01
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often originate from multidimensional data, might profit from even higher levels of abstraction. We developed a framework for solving tensor structured problems with tensor algebra that unifies concepts from tensor analysis, multilinear algebra and multidimensional signal processing. In contrast to the conventional matrix approach, it allows the formulation of multidimensional problems, in a multidimensional way, preserving structure and data coherence; and the implementation of automated optimizations of solving algorithms, based on the commutativity of all tensor operations. Its ability to handle large scientific tasks is showcased by a real-world, 4D medical imaging problem, with more than 30 million unknown parameters solved on a current, inexpensive hardware. This significantly...
Nonlocal homogenization for nonlinear metamaterials
Gorlach, Maxim A; Lapine, Mikhail; Kivshar, Yuri S; Belov, Pavel A
2016-01-01
We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects of spatial dispersion become especially pronounced in the vicinity of effective permittivity resonance where nonlinear susceptibilities reach their maxima. In that case spatial dispersion may enable simultaneous generation of two harmonic signals with the same frequency and polarization but different wave vectors. We also prove that the derived expressions for nonlinear susceptibilities transform into the known form when spatial dispersion effects are negligible. In addition to revealing new physical phenomena, our results provide useful theoretical tools for analysing resonant nonlinear metamaterials.
Black holes in vector-tensor theories
Heisenberg, Lavinia; Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji
2017-08-01
We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.
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.
Invariant tensors for simple groups
Energy Technology Data Exchange (ETDEWEB)
De Azcarraga, J.A.; Macfarlane, A.J.; Mountain, A.J.; Perez Bueno, J.C. [Cambridge Univ. (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics (DAMTP)
1998-01-26
The forms of the invariant primitive tensors for the simple Lie algebras A{sub l}, B{sub l}, C{sub l} and D{sub l} are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A{sub l} algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) and su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given. (orig.). 34 refs.
MACH: Fast Randomized Tensor Decompositions
Tsourakakis, Charalampos E
2009-01-01
Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor decompositions such as the Tucker decomposition are used to analyze multi-aspect data and extract latent factors, which capture the multilinear data structure. Such decompositions are powerful mining tools, for extracting patterns from large data volumes. However, most frequently used algorithms for such decompositions involve the computationally expensive Singular Value Decomposition. In this paper we propose MACH, a new sampling algorithm to compute such decompositions. Our method is of significant practical value for tensor streams, such as environmental monitoring systems, IP traffic matrices over time, where large amounts of data are accumulated and the analysis is computationally intensive but also in "post-mortem" data analysis cases where the tensor does not fit in the availa...
Tensor computations in computer algebra systems
Korolkova, A V; Sevastyanov, L A
2014-01-01
This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. We briefly overview the current state of tensor computations in different computer algebra systems. The tensor computations are illustrated with appropriate examples implemented in specific systems: Cadabra and Maxima.
Clemmen, Stéphane; Hermans, Artur; Solano, Eduardo; Dendooven, Jolien; Koskinen, Kalle; Kauranen, Martti; Brainis, Edouard; Detavernier, Christophe; Baets, Roel
2015-11-15
We report the fabrication of artificial unidimensional crystals exhibiting an effective bulk second-order nonlinearity. The crystals are created by cycling atomic layer deposition of three dielectric materials such that the resulting metamaterial is noncentrosymmetric in the direction of the deposition. Characterization of the structures by second-harmonic generation Maker-fringe measurements shows that the main component of their nonlinear susceptibility tensor is about 5 pm/V, which is comparable to well-established materials and more than an order of magnitude greater than reported for a similar crystal [Appl. Phys. Lett.107, 121903 (2015)APPLAB0003-695110.1063/1.4931492]. Our demonstration opens new possibilities for second-order nonlinear effects on CMOS-compatible nanophotonic platforms.
Tensor Product of Massey Products
Institute of Scientific and Technical Information of China (English)
Qi Bing ZHENG
2006-01-01
In this paper, we interpret Massey products in terms of realizations (twitsting cochains)of certain differential graded coalgebras with values in differential graded algebras. In the case where the target algebra is the cobar construction of a differential graded commutative Hopf algebra, we construct the tensor product of realizations and show that the tensor product is strictly associative,and commutative up to homotopy.
Tensor 2-sums and entanglement
Klavzar, Sandi
2009-01-01
To define a minimal mathematical framework for isolating some of the characteristic properties of quantum entanglement, we introduce a generalization of the tensor product of graphs. Inspired by the notion of a density matrix, the generalization is a simple one: every graph can be obtained by addiction modulo two, possibly with many summands, of tensor products of adjacency matrices. In this picture, we are still able to prove a combinatorial analogue of the Peres-Horodecki criterion for testing separability.
Intrinsic nonlinear response of surface plasmon polaritons
Im, Song-Jin; Kim, Gum-Hyok
2015-01-01
We offer a model to describe the intrinsic nonlinear response of surface plasmon polaritons (SPPs). Relation of the complex nonlinear coefficient of SPPs to the third-order nonlinear susceptibility of the metal is provided. As reported in a recent study, gold is highly lossy and simultaneously highly nonlinear due to interband absorption and interband thermo-modulation at a wavelength shorter than 700 nm. The effect of the high loss of the metal on the SPP nonlinear propagation is taken into account in our model. With the model we show difference in sign of real and imaginary parts between the nonlinear propagation coefficient and the nonlinear susceptibility of component material for the first time to our knowledge. Our model could have practical importance in studying plasmonic devices utilizing the nonlinear phase modulation and the nonlinear absorption of SPPs. For example, it allows one to extract the complex nonlinear susceptibility of gold through a measurement of SPP nonlinear propagation at the visib...
Hasan, Khader M; Sankar, Ambika; Halphen, Christopher; Kramer, Larry A; Brandt, Michael E; Juranek, Jenifer; Cirino, Paul T; Fletcher, Jack M; Papanicolaou, Andrew C; Ewing-Cobbs, Linda
2007-10-29
We used a diffusion tensor imaging-based whole-brain tissue segmentation to characterize age-related changes in (a) whole-brain grey matter, white matter, and cerebrospinal fluid relative to intracranial volume and (b) the corresponding brain tissue microstructure using measures of diffusion tensor anisotropy and mean diffusivity. The sample, a healthy cohort of 119 right-handed males and females aged 7-68 years. Our results demonstrate that white matter and grey matter volumes and their corresponding diffusion tensor anisotropy and mean diffusivity follow nonlinear trajectories with advancing age. In contrast, cerebrospinal fluid volume increases linearly with age.
Positivity and conservation of superenergy tensors
Pozo, J M
2002-01-01
Two essential properties of energy-momentum tensors T submu subnu are their positivity and conservation. This is mathematically formalized by, respectively, an energy condition, as the dominant energy condition, and the vanishing of their divergence nabla supmu T submu subnu = 0. The classical Bel and Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors, respectively, are rank-4 tensors. But they share these two properties with energy-momentum tensors: the dominant property (DP) and the divergence-free property in the absence of sources (vacuum). Senovilla defined a universal algebraic construction which generates a basic superenergy tensor T left brace A right brace from any arbitrary tensor A. In this construction, the seed tensor A is structured as an r-fold multivector, which can always be done. The most important feature of the basic superenergy tensors is that they satisfy automatically the DP, independently of the generating tensor A. We presented a more compact definition of T...
Hilbert complexes of nonlinear elasticity
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
Institute of Scientific and Technical Information of China (English)
Yaochen Bai(白瑶晨); Jingliang Liu(刘景良); Duanzheng Yao(姚端正)
2004-01-01
The third-order susceptibility of InxGa1-xN/GaN quantum well (QW) has been investigated by taking into account the strain-induced piezoelectric (PZ) field, and the effective-mass SchrSdinger equation is solved numerically. It is shovn that the third-order susceptibility for third harmonic generation (THG)of InxGa1-x,N/GaN QW is related to indium content in QW and the intensity of the PZ field. The characteristics ofX(3)THG(-3ω,(3) ω, ω,ω) as the function of the wavelength of incident beam, well width and indium content, have been analyzed.
On the performance of tensor methods for solving ill-conditioned problems.
Energy Technology Data Exchange (ETDEWEB)
Schnabel, Robert B. (University of Colorado at Boulder, Boulder, CO); Bader, Brett William
2004-09-01
This paper investigates the performance of tensor methods for solving small- and large-scale systems of nonlinear equations where the Jacobian matrix at the root is ill-conditioned or singular. This condition occurs on many classes of problems, such as identifying or approaching turning points in path following problems. The singular case has been studied more than the highly ill-conditioned case, for both Newton and tensor methods. It is known that Newton-based methods do not work well with singular problems because they converge linearly to the solution and, in some cases, with poor accuracy. On the other hand, direct tensor methods have performed well on singular problems and have superlinear convergence on such problems under certain conditions. This behavior originates from the use of a special, restricted form of the second-order term included in the local tensor model that provides information lacking in a (nearly) singular Jacobian. With several implementations available for large-scale problems, tensor methods now are capable of solving larger problems. We compare the performance of tensor methods and Newton-based methods for both small- and large-scale problems over a range of conditionings, from well-conditioned to ill-conditioned to singular. Previous studies with tensor methods only concerned the ends of this spectrum. Our results show that tensor methods are increasingly superior to Newton-based methods as the problem grows more ill-conditioned.
On the Nonlinear Evolution of Cosmic Web: Lagrangian Dynamics Revisited
Wang, Xin
2014-01-01
We investigate the nonlinear evolution of cosmic morphologies of the large-scale structure by examining the Lagrangian dynamics of various tensors of a cosmic fluid element, including the velocity gradient tensor, the Hessian matrix of the gravitational potential as well as the deformation tensor. Instead of the eigenvalue representation, the first two tensors, which associate with the "kinematic" and "dynamical" cosmic web classification algorithm respectively, are studied in a more convenient parameter space. These parameters are defined as the rotational invariant coefficients of the characteristic equation of the tensor. In the nonlinear local model (NLM) where the magnetic part of Weyl tensor vanishes, these invariants are fully capable of characterizing the dynamics. Unlike the Zeldovich approximation (ZA), where various morphologies do not change before approaching a one-dimensional singularity, the sheets in NLM are unstable for both overdense and underdense perturbations. While it has long been known...
Microwave emission by nonlinear crystals irradiated with a high-intensity, mode-locked laser
Borghesani, A F; Guarise, M
2016-01-01
We report on the experimental investigation of the efficiency of some nonlinear crystals to generate microwave (RF) radiation as a result of optical rectification (OR) when irradiated with intense pulse trains delivered by a mode-locked laser at $1064\\,$nm. We have investigated lithium triborate (LBO), lithium niobate (LiNbO$_3$), zinc selenide (ZnSe), and also potassium titanyl orthophosphate (KTP) for comparison with previous measurements. The results are in good agreement with the theoretical predictions based on the form of the second-order nonlinear susceptibility tensor. For some crystals we investigated also the second harmonic generation (SHG) to cross check the theoretical model. We confirm the theoretical prediction that OR leads to the production of higher order RF harmonics that are overtones of the laser repetition rate.
Hypersurfaces with Isotropic Para-Blaschke Tensor
Institute of Scientific and Technical Information of China (English)
Jian Bo FANG; Kun ZHANG
2014-01-01
Let Mn be an n-dimensional submanifold without umbilical points in the (n+1)-dimen-sional unit sphere Sn+1. Four basic invariants of Mn under the Moebius transformation group of Sn+1 are a1-form Φ called moebius form, a symmetric (0, 2) tensor A called Blaschke tensor, a symmetric (0, 2) tensor B called Moebius second fundamental form and a positive definite (0, 2) tensor g called Moebius metric. A symmetric (0, 2) tensor D = A+μB called para-Blaschke tensor, where μ is constant, is also an Moebius invariant. We call the para-Blaschke tensor is isotropic if there exists a function λ such that D = λg. One of the basic questions in Moebius geometry is to classify the hypersurfaces with isotropic para-Blaschke tensor. When λ is not constant, all hypersurfaces with isotropic para-Blaschke tensor are explicitly expressed in this paper.
Compressive sensing of sparse tensors.
Friedland, Shmuel; Li, Qun; Schonfeld, Dan
2014-10-01
Compressive sensing (CS) has triggered an enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact reconstruction through relatively few nonadaptive linear measurements. While conventional CS theory relies on data representation in the form of vectors, many data types in various applications, such as color imaging, video sequences, and multisensor networks, are intrinsically represented by higher order tensors. Application of CS to higher order data representation is typically performed by conversion of the data to very long vectors that must be measured using very large sampling matrices, thus imposing a huge computational and memory burden. In this paper, we propose generalized tensor compressive sensing (GTCS)-a unified framework for CS of higher order tensors, which preserves the intrinsic structure of tensor data with reduced computational complexity at reconstruction. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we propound two reconstruction procedures, a serial method and a parallelizable method. We then compare the performance of the proposed method with Kronecker compressive sensing (KCS) and multiway compressive sensing (MWCS). We demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both reconstruction accuracy (within a range of compression ratios) and processing speed. The major disadvantage of our methods (and of MWCS as well) is that the compression ratios may be worse than that offered by KCS.
Understanding the Magnetic Polarizability Tensor
Ledger, P D
2015-01-01
The aim of this paper is provide new insights into the properties of the rank 2 polarizability tensor $\\check{\\check{\\mathcal M}}$ proposed in (P.D. Ledger and W.R.B. Lionheart Characterising the shape and material properties of hidden targets from magnetic induction data, IMA Journal of Applied Mathematics, doi: 10.1093/imamat/hxv015) for describing the perturbation in the magnetic field caused by the presence of a conducting object in the eddy current regime. In particular, we explore its connection with the magnetic polarizability tensor and the P\\'olya-Szeg\\"o tensor and how, by introducing new splittings of $\\check{\\check{\\mathcal M}}$, they form a family of rank 2 tensors for describing the response from different categories of conducting (permeable) objects. We include new bounds on the invariants of the P\\'olya-Szeg\\"o tensor and expressions for the low frequency and high conductivity limiting coefficients of $\\check{\\check{\\mathcal M}}$. We show, for the high conductivity case (and for frequencies at...
Semi-tensor product of matrices and its application to Morgen's problem
Institute of Scientific and Technical Information of China (English)
程代展
2001-01-01
This paper proposes a new matrix product, namely, semi-tensor product. It is a generalization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The purpose of introducing this product is twofold: (i) treat multi-dimensional data; (ii) treat nonlinear problems in a linear way. Then the computer and numerical methods can be easily used for solving nonlinear problems. Properties and formulas are deduced. As an application, the Morgen's problem for control systems is formulated as a numerically solvable problem.
Nonlinear Effects in the Cosmic Microwave Background
Maartens, R
2000-01-01
Major advances in the observation and theory of cosmic microwave background anisotropies have opened up a new era in cosmology. This has encouraged the hope that the fundamental parameters of cosmology will be determined to high accuracy in the near future. However, this optimism should not obscure the ongoing need for theoretical developments that go beyond the highly successful but simplified standard model. Such developments include improvements in observational modelling (e.g. foregrounds, non-Gaussian features), extensions and alternatives to the simplest inflationary paradigm (e.g. non-adiabatic effects, defects), and investigation of nonlinear effects. In addition to well known nonlinear effects such as the Rees-Sciama and Ostriker-Vishniac effects, further nonlinear effects have recently been identified. These include a Rees-Sciama-type tensor effect, time-delay effects of scalar and tensor lensing, nonlinear Thomson scattering effects and a nonlinear shear effect. Some of the nonlinear effects and th...
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....
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.
Theoretical study of the relativistic molecular rotational g-tensor
Energy Technology Data Exchange (ETDEWEB)
Aucar, I. Agustín, E-mail: agustin.aucar@conicet.gov.ar; Gomez, Sergio S., E-mail: ssgomez@exa.unne.edu.ar [Institute for Modeling and Technological Innovation, IMIT (CONICET-UNNE) and Faculty of Exact and Natural Sciences, Northeastern University of Argentina, Avenida Libertad 5400, W3404AAS Corrientes (Argentina); Giribet, Claudia G.; Ruiz de Azúa, Martín C. [Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina)
2014-11-21
An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH{sup +} (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH{sup +} systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.
Carrozza, Sylvain; Tanasa, Adrian
2016-11-01
We define in this paper a class of three-index tensor models, endowed with {O(N)^{⊗ 3}} invariance ( N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U( N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
Tensor interactions and {tau} decays
Energy Technology Data Exchange (ETDEWEB)
Godina Nava, J.J.; Lopez Castro, G. [Departamento de Fisica, Cinvestav del IPN, Apartado Postal 14-740, 07000 Mexico, D.F. (Mexico)
1995-09-01
We study the effects of charged tensor weak currents on the strangeness-changing decays of the {tau} lepton. First, we use the available information on the {ital K}{sub {ital e}3}{sup +} form factors to obtain {ital B}({tau}{sup {minus}}{r_arrow}{ital K}{sup {minus}}{pi}{sup 0}{nu}{sub {tau}}){similar_to}10{sup {minus}4} when the {ital K}{pi} system is produced in an antisymmetric tensor configuration. Then we propose a mechanism for the direct production of the {ital K}{sub 2}{sup *}(1430) in {tau} decays. Using the current upper limit on this decay we set a bound on the symmetric tensor interactions.
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.......e., the “cores”) comprising the functional TT decomposition. This result motivates an approximation scheme employing polynomial approximations of the cores. For functions with appropriate regularity, the resulting spectral tensor-train decomposition combines the favorable dimension-scaling of the TT...... decomposition with the spectral convergence rate of polynomial approximations, yielding efficient and accurate surrogates for high-dimensional functions. To construct these decompositions, we use the sampling algorithm \\tt TT-DMRG-cross to obtain the TT decomposition of tensors resulting from suitable...
Minutia Tensor Matrix: A New Strategy for Fingerprint Matching
Fu, Xiang; Feng, Jufu
2015-01-01
Establishing correspondences between two minutia sets is a fundamental issue in fingerprint recognition. This paper proposes a new tensor matching strategy. First, the concept of minutia tensor matrix (simplified as MTM) is proposed. It describes the first-order features and second-order features of a matching pair. In the MTM, the diagonal elements indicate similarities of minutia pairs and non-diagonal elements indicate pairwise compatibilities between minutia pairs. Correct minutia pairs are likely to establish both large similarities and large compatibilities, so they form a dense sub-block. Minutia matching is then formulated as recovering the dense sub-block in the MTM. This is a new tensor matching strategy for fingerprint recognition. Second, as fingerprint images show both local rigidity and global nonlinearity, we design two different kinds of MTMs: local MTM and global MTM. Meanwhile, a two-level matching algorithm is proposed. For local matching level, the local MTM is constructed and a novel local similarity calculation strategy is proposed. It makes full use of local rigidity in fingerprints. For global matching level, the global MTM is constructed to calculate similarities of entire minutia sets. It makes full use of global compatibility in fingerprints. Proposed method has stronger description ability and better robustness to noise and nonlinearity. Experiments conducted on Fingerprint Verification Competition databases (FVC2002 and FVC2004) demonstrate the effectiveness and the efficiency. PMID:25822489
Minutia tensor matrix: a new strategy for fingerprint matching.
Fu, Xiang; Feng, Jufu
2015-01-01
Establishing correspondences between two minutia sets is a fundamental issue in fingerprint recognition. This paper proposes a new tensor matching strategy. First, the concept of minutia tensor matrix (simplified as MTM) is proposed. It describes the first-order features and second-order features of a matching pair. In the MTM, the diagonal elements indicate similarities of minutia pairs and non-diagonal elements indicate pairwise compatibilities between minutia pairs. Correct minutia pairs are likely to establish both large similarities and large compatibilities, so they form a dense sub-block. Minutia matching is then formulated as recovering the dense sub-block in the MTM. This is a new tensor matching strategy for fingerprint recognition. Second, as fingerprint images show both local rigidity and global nonlinearity, we design two different kinds of MTMs: local MTM and global MTM. Meanwhile, a two-level matching algorithm is proposed. For local matching level, the local MTM is constructed and a novel local similarity calculation strategy is proposed. It makes full use of local rigidity in fingerprints. For global matching level, the global MTM is constructed to calculate similarities of entire minutia sets. It makes full use of global compatibility in fingerprints. Proposed method has stronger description ability and better robustness to noise and nonlinearity. Experiments conducted on Fingerprint Verification Competition databases (FVC2002 and FVC2004) demonstrate the effectiveness and the efficiency.
Phase Transition in Tensor Models
Delepouve, Thibault
2015-01-01
Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a $1/N$ expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a fluctuation field around a vacuum state corresponding to the resummation of the entire leading order in $1/N$ (a resummation of the melonic family). We then prove that the critical regime in which the continuum limit in the sense of dynamical triangulations is reached is precisely a phase transition in the field theory sense for the fluctuation field.
Tensor networks for dynamic spacetimes
May, Alex
2016-01-01
Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it is necessary to give a new definition of length in the network, and propose a definition based on the mutual information. We show that by associating a set of networks with a single quantum state and making use of the mutual information based definition of length, a network analogue of the maximin formula can be used to calculate the entropy of boundary regions.
Tensor calculus for physics a concise guide
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...
A Model for Lightcone Fluctuations due to Stress Tensor Fluctuations
Bessa, C H G; Ford, L H; Ribeiro, C C H
2016-01-01
We study a model for quantum lightcone fluctuations in which vacuum fluctuations of the electric field and of the squared electric field in a nonlinear dielectric material produce variations in the flight times of probe pulses. When this material has a non-zero third order polarizability, the flight time variations arise from squared electric field fluctuations, and are analogous to effects expected when the stress tensor of a quantized field drives passive spacetime geometry fluctuations. We also discuss the dependence of the squared electric field fluctuations upon the geometry of the material, which in turn determines a sampling function for averaging the squared electric field along the path of the pulse. This allows us to estimate the probability of especially large fluctuations, which is a measure of the probability distribution for quantum stress tensor fluctuations.
Catino, Giovanni; Mazzieri, Lorenzo
2012-01-01
We discuss a gap in Besse's book, recently pointed out by Merton, which concerns the classification of Riemannian manifolds admitting a Codazzi tensors with exactly two distinct eigenvalues. For such manifolds, we prove a structure theorem, without adding extra hypotheses and then we conclude with some application of this theory to the classification of three-dimensional gradient Ricci solitons.
Suneetha, T; Kundu, S; Kashyap, Subhash C; Gupta, H C; Nath, T K
2013-01-01
The Mn0.5Zn0.5Fe2O4 nanoparticles has been synthesized using citrate-gel-precursor method. The direct mixing of nitrates and acetates yields homogeneous nanoparticles. Phase formation and crystal structure of the synthesized powder were examined through the X-ray diffraction (XRD). Fourier transform infrared (FTIR) spectra of the sample confirm the spinel structure. The average particle size was determined by transmission electron microscopy (TEM) and field emission scanning electron microscopy (FESEM). The average particle size is found to be about 13 nm. Superparamagnetic-like nature of the nanoparticles of Mn0.5Zn0.5Fe2O4 has been revealed through various dc and linear and non-linear ac magnetization measurements. However, the nanoparticles do not behave like ideal non-interacting superparamagnets. The magnetic particle size is found to be about 8 nm with saturation magnetization about 18.1 emu/g. The blocking temperature (T(B)) of the nanoparticle assembly is found to be about 150 K as observed from dc and ac magnetization measurements. The frequency dependence of the blocking temperature (T(B)) is found to follow Vogel-Fulcher law. The associated characteristic time tau0 is found to be 10(-5) s. This value is different from that generally found for non-interacting superparamagnetic (SPM) systems (tau0 = 10(-9)-10(-10) s).
Hrouda, Frantisek; Chadima, Martin; Jezek, Josef
2017-04-01
Pyrrhotite shows strong and non-linear variations of both the in-phase and out-of-phase magnetic susceptibilities with magnetizing field unlike to magnetite and paramagnetic minerals whose susceptibility is field independent if measured in low fields. Consequently, the magnetic sub-fabric of pyrrhotite unaffected by magnetite/paramagnetics can be directly investigated either through the anisotropy of field-dependent in-phase susceptibility (hdAMS) or through the anisotropy of out-of-phase susceptibility (opAMS). If the driving fields used for the susceptibility measurement are really low, within the range of validity of the Rayleigh Law, both the field-dependent component of the hdAMS and the opAMS are represented by the field-independent second rank Rayleigh Tensor. The determination of the Rayleigh Tensor via hdAMS requires the AMS measurements in several fields within the Rayleigh Law range, while in the determination of the Rayleigh Tensor via opAMS the measurement in one field is sufficient. It should be noted that if the AMS is measured by the KLY5 Kappabridge, the opAMS is measured simultaneously with standard in-phase AMS (ipAMS) during one measuring process. The Rayleigh Tensors determined by the above two methods should be more or less identical provided that the opAMS of pyrrhotite is dominantly due to weak field hysteresis, virtually unaffected by electrical eddy currents or viscous relaxation. In a collection of various pyrrhotite-bearing rocks, both the hdAMS and opAMS were investigated using the KLY5 Kappabridge and the correlations between the Rayleigh Tensors determined by the above two methods were made in terms of the anisotropy degree, shape parameter, and the orientations of principal directions. Reasonable correlations were found indicating that the pyrrhotite opAMS is dominantly due to weak field hysteresis. As the opAMS is measured automatically and simultaneously with standard ipAMS, the advantage of the opAMS in the determination of the
Vector and tensor analysis with applications
Borisenko, A I; Silverman, Richard A
1979-01-01
Concise and readable, this text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. It also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Worked-out problems and solutions. 1968 edition.
Nonlinear optical spectroscopy of isotropic and anisotropic metallic nanocomposites
Energy Technology Data Exchange (ETDEWEB)
Fernandez-Hernandez, R C; Gleason-Villagran, R; Cheang-Wong, J C; Crespo-Sosa, A; Rodriguez-Fernandez, L; Lopez-Suarez, A; Oliver, A; Reyes-Esqueda, J A [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico, D. F. 04510 (Mexico); Torres-Torres, C [Seccion de Estudios de Posgrado e Investigacion, ESIME-Zacatenco, Instituto Politecnico Nacional, Mexico, D. F. 07338 (Mexico); Rangel-Rojo, R, E-mail: reyes@fisica.unam.mx [CICESE/Depto. de Optica, A.P. 360, Ensenada, B. C. 22860 (Mexico)
2011-01-01
In this work, we studied the nonlinear absorption and refraction of isotropic and anisotropic metallic nanocomposites, which consist of Au and Ag nanoparticles (NPs) embedded in matrices of SiO{sub 2}. We performed this study at different wavelengths using the Z-scan technique in the picosecond regime. The wavelengths were selected accordingly to the absorption spectra of the nanocomposites, choosing wavelengths into the inter- and intra-band transitions regions, including the surface plasmon (SP) resonance, as well as in the transparent region. For the anisotropic nanocomposites, the polarization and the incident angle were varied in order to evaluate the different components of the third order susceptibility tensor, {chi}{sup (3)}. We observed dramatic changes of sign for both, nonlinear refraction and absorption, when passing from Au to Ag and/or varying the wave length. The results accentuate the importance of the hot-electrons contribution to the nonlinear optical response at this temporal regime, when compared to inter-band and intra-band transitions contributions.
Bilayer linearized tensor renormalization group approach for thermal tensor networks
Dong, Yong-Liang; Chen, Lei; Liu, Yun-Jing; Li, Wei
2017-04-01
Thermal tensor networks constitute an efficient and versatile representation for quantum lattice models at finite temperatures. By Trotter-Suzuki decomposition, one obtains a D +1 dimensional TTN for the D -dimensional quantum system and then employs efficient renormalizaton group (RG) contractions to obtain the thermodynamic properties with high precision. The linearized tensor renormalization group (LTRG) method, which can be used to contract TTN efficiently and calculate the thermodynamics, is briefly reviewed and then generalized to a bilayer form. We dub this bilayer algorithm as LTRG++ and explore its performance in both finite- and infinite-size systems, finding the numerical accuracy significantly improved compared to single-layer algorithm. Moreover, we show that the LTRG++ algorithm in an infinite-size system is in essence equivalent to transfer-matrix renormalization group method, while reformulated in a tensor network language. As an application of LTRG++, we simulate an extended fermionic Hubbard model numerically, where the phase separation phenomenon, ground-state phase diagram, as well as quantum criticality-enhanced magnetocaloric effects, are investigated.
Killing(-Yano) Tensors in String Theory
Chervonyi, Yuri
2015-01-01
We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.
Senthil, K.; Kalainathan, S.; Kondo, Y.; Hamada, F.; Yamada, M.
2017-05-01
-order nonlinear optical susceptibility χ(3) =4.229×10-6 esu and second-order hyperpolarizability (γ) =1.468×10-33 esu. It is found to be larger than that of some organic NLO materials. All the obtained results are making it a potential candidate as useful non-linear optical (NLO) applications.
Causality and Primordial Tensor Modes
Baumann, Daniel
2009-01-01
We introduce the real space correlation function of $B$-mode polarization of the cosmic microwave background (CMB) as a probe of superhorizon tensor perturbations created by inflation. By causality, any non-inflationary mechanism for gravitational wave production after reheating, like global phase transitions or cosmic strings, must have vanishing correlations for angular separations greater than the angle subtended by the particle horizon at recombination, i.e. $\\theta \\gtrsim 2^\\circ$. Since ordinary $B$-modes are defined non-locally in terms of the Stokes parameters $Q$ and $U$ and therefore don't have to respect causality, special care is taken to define `causal $\\tilde B$-modes' for the analysis. We compute the real space $\\tilde B$-mode correlation function for inflation and discuss its detectability on superhorizon scales where it provides an unambiguous test of inflationary gravitational waves. The correct identification of inflationary tensor modes is crucial since it relates directly to the energy s...
Scalar-tensor linear inflation
Artymowski, Michal
2016-01-01
We investigate two approaches to non minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for any form of the non-minimal coupling to gravity of the form of $f(\\varphi)R/2$; b) the particle physics approach, where we motivate the form of the Jordan frame potential by the loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced inflation, but instead of the Starobinsky attractor they lead to the linear inflation in the strong coupling limit.
Scalar-tensor linear inflation
Artymowski, Michał; Racioppi, Antonio
2017-04-01
We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f(varphi)R/2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.
Extended vector-tensor theories
Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke
2017-01-01
Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem.
Causality and primordial tensor modes
Energy Technology Data Exchange (ETDEWEB)
Baumann, Daniel; Zaldarriaga, Matias, E-mail: dbaumann@physics.harvard.edu, E-mail: mzaldarriaga@cfa.harvard.edu [Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, U.S.A. and Center for Astrophysics, Harvard University, 60 Garden Street, Cambridge, MA 02138 (United States)
2009-06-01
We introduce the real space correlation function of B-mode polarization of the cosmic microwave background (CMB) as a probe of superhorizon tensor perturbations created by inflation. By causality, any non-inflationary mechanism for gravitational wave production after reheating, like global phase transitions or cosmic strings, must have vanishing correlations for angular separations greater than the angle subtended by the particle horizon at recombination, i.e. θ ∼> 2°. Since ordinary B-modes are defined non-locally in terms of the Stokes parameters Q and U and therefore don't have to respect causality, special care is taken to define 'causal B-tilde -modes' for the analysis. We compute the real space B-tilde -mode correlation function for inflation and discuss its detectability on superhorizon scales where it provides an unambiguous test of inflationary gravitational waves. The correct identification of inflationary tensor modes is crucial since it relates directly to the energy scale of inflation. Wrongly associating tensor modes from causal seeds with inflation would imply an incorrect inference of the energy scale of inflation. We find that the superhorizon B-tilde -mode signal is above cosmic variance for the angular range 2° < θ < 4° and is therefore in principle detectable. In practice, the signal will be challenging to measure since it requires accurately resolving the recombination peak of the B-mode power spectrum. However, a future CMB satellite (CMBPol), with noise level Δ{sub P} ≅ 1μK-arcmin and sufficient resolution to efficiently correct for lensing-induced B-modes, should be able to detect the signal at more than 3σ if the tensor-to-scalar ratio isn't smaller than r ≅ 0.01.
Tensor Interaction Effect in Dibaryon
Institute of Scientific and Technical Information of China (English)
CHEN Ling-Zhi; PANG Hou-Rong; PING Jia-Lun; WANG Fan
2005-01-01
The gluon and Goldstone boson induced tensor interaction effect on the dibaryon mass and the D-wave decay width has been studied in the quark delocalization, color screening model. The effective S-D wave transition interactions induced by gluon and Goldstone boson exchanges decrease quickly as the increasing of the channel strangeness. The K and η meson tensor contribution is negligible in this model. No six-quark state in the light flavor world can become a bound one by the help of these tensor interactions except the deuteron. The partial D-wave decay width of Ijp = 1/2 2+NΩ state to spin 0, 1 ∧([1]) final state is 20.7 keV and 63.1 keV respectively. It is a very narrow dibaryon resonance and might be detected in the relativistic heavy ion reaction by the existing RHIC detectors through the reconstruction of the ∧([1]) vertex mass and the future COMPAS detector at CERN and FAIR project in Germany.
Sparse alignment for robust tensor learning.
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.
TIMER: tensor image morphing for elastic registration.
Yap, Pew-Thian; Wu, Guorong; Zhu, Hongtu; Lin, Weili; Shen, Dinggang
2009-08-15
We propose a novel diffusion tensor imaging (DTI) registration algorithm, called Tensor Image Morphing for Elastic Registration (TIMER), which leverages the hierarchical guidance of regional distributions and local boundaries, both extracted directly from the tensors. Currently available DTI registration methods generally extract tensor scalar features from each tensor to construct scalar maps. Subsequently, regional integration and other operations such as edge detection are performed to extract more features to guide the registration. However, there are two major limitations with these approaches. First, the computed regional features might not reflect the actual regional tensor distributions. Second, by the same token, gradient maps calculated from the tensor-derived scalar feature maps might not represent the actual tissue tensor boundaries. To overcome these limitations, we propose a new approach which extracts regional and edge information directly from a tensor neighborhood. Regional tensor distribution information, such as mean and variance, is computed in a multiscale fashion directly from the tensors by taking into account the voxel neighborhood of different sizes, and hence capturing tensor information at different scales, which in turn can be employed to hierarchically guide the registration. Such multiscale scheme can help alleviate the problem of local minimum and is also more robust to noise since one can better determine the statistical properties of each voxel by taking into account the properties of its surrounding. Also incorporated in our method is edge information extracted directly from the tensors, which is crucial to facilitate registration of tissue boundaries. Experiments involving real subjects, simulated subjects, fiber tracking, and atrophy detection indicate that TIMER performs better than the other methods (Yang et al., 2008; Zhang et al., 2006).
Nonlinear electrodynamics with birefringence
Kruglov, S I
2015-01-01
A new model of nonlinear electrodynamics with three parameters is suggested. The phenomena of vacuum birefringence takes place when there is the external constant magnetic field. We calculate the indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field. From the Bir\\'{e}fringence Magn\\'{e}tique du Vide (BMV) experiment one of the coefficients, $\\gamma\\approx 10^{-20}$ T$^{-2}$, was estimated. The canonical, symmetrical Belinfante energy-momentum tensors and dilatation current were obtained. The dilatation symmetry and the dual symmetry are broken in the model considered.
Fluid Registration of Diffusion Tensor Images Using Information Theory
Chiang, Ming-Chang; Leow, Alex D.; Klunder, Andrea D.; Dutton, Rebecca A.; Barysheva, Marina; Rose, Stephen E.; McMahon, Katie L.; de Zubicaray, Greig I.; Toga, Arthur W.; Thompson, Paul M.
2008-01-01
We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or J-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the J-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data. PMID:18390342
Susceptibility-weighted imaging and quantitative susceptibility mapping in the brain.
Liu, Chunlei; Li, Wei; Tong, Karen A; Yeom, Kristen W; Kuzminski, Samuel
2015-07-01
Susceptibility-weighted imaging (SWI) is a magnetic resonance imaging (MRI) technique that enhances image contrast by using the susceptibility differences between tissues. It is created by combining both magnitude and phase in the gradient echo data. SWI is sensitive to both paramagnetic and diamagnetic substances which generate different phase shift in MRI data. SWI images can be displayed as a minimum intensity projection that provides high resolution delineation of the cerebral venous architecture, a feature that is not available in other MRI techniques. As such, SWI has been widely applied to diagnose various venous abnormalities. SWI is especially sensitive to deoxygenated blood and intracranial mineral deposition and, for that reason, has been applied to image various pathologies including intracranial hemorrhage, traumatic brain injury, stroke, neoplasm, and multiple sclerosis. SWI, however, does not provide quantitative measures of magnetic susceptibility. This limitation is currently being addressed with the development of quantitative susceptibility mapping (QSM) and susceptibility tensor imaging (STI). While QSM treats susceptibility as isotropic, STI treats susceptibility as generally anisotropic characterized by a tensor quantity. This article reviews the basic principles of SWI, its clinical and research applications, the mechanisms governing brain susceptibility properties, and its practical implementation, with a focus on brain imaging.
Nonlinear optical properties of ultrathin metal layers
DEFF Research Database (Denmark)
Lysenko, Oleg
2016-01-01
. The optical characterization of the plasmonic waveguides is performed using femtosecond and picosecond optical pulses. Two nonlinear optical effects in the strip plasmonic waveguides are experimentally observed and reported. The first effect is the nonlinear power transmission of the plasmonic mode......-order nonlinear susceptibility of the plasmonic mode in the gold strip waveguides significantly depends on the metal layer thickness and laser pulse duration. This dependence is explained in detail in terms of the free-electron temporal dynamics in gold. The third-order nonlinear susceptibility of the gold layer...... duration dependence of the third-order nonlinear susceptibility of gold is calculated in the broad range from tens of femtoseconds to tens of picoseconds using the two-temperature model of the free-electron temporal dynamics of gold, and shows the saturation of the thirdorder nonlinear susceptibility...
Real-time framework for tensor-based image enhancement for object classification
Cyganek, Bogusław; Smołka, Bogdan
2016-04-01
In many practical situations visual pattern recognition is vastly burdened by low quality of input images due to noise, geometrical distortions, as well as low quality of the acquisition hardware. However, although there are techniques of image quality improvements, such as nonlinear filtering, there are only few attempts reported in the literature that try to build these enhancement methods into a complete chain for multi-dimensional object recognition such as color video or hyperspectral images. In this work we propose a joint multilinear signal filtering and classification system built upon the multi-dimensional (tensor) approach. Tensor filtering is performed by the multi-dimensional input signal projection into the tensor subspace spanned by the best-rank tensor decomposition method. On the other hand, object classification is done by construction of the tensor sub-space constructed based on the Higher-Order Singular Value Decomposition method applied to the prototype patters. In the experiments we show that the proposed chain allows high object recognition accuracy in the real-time even from the poor quality prototypes. Even more importantly, the proposed framework allows unified classification of signals of any dimensions, such as color images or video sequences which are exemplars of 3D and 4D tensors, respectively. The paper discussed also some practical issues related to implementation of the key components of the proposed system.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
The set of all surface tensors of a convex body K (Minkowski tensors derived from the surface area measure of K) determine K up to translation, and hereby, the surface tensors of K contain all information on the shape of K. Here, shape means the equivalence class of all convex bodies...... 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....... 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...
Killing tensors in pp-wave spacetimes
Energy Technology Data Exchange (ETDEWEB)
Keane, Aidan J [87 Carlton Place, Glasgow G5 9TD, Scotland (United Kingdom); Tupper, Brian O J, E-mail: aidan@countingthoughts.co, E-mail: bt32@rogers.co [Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3 (Canada)
2010-12-21
The formal solution of the second-order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.
Derivatives on the isotropic tensor functions
Institute of Scientific and Technical Information of China (English)
DUI; Guansuo; WANG; Zhengdao; JIN; Ming
2006-01-01
The derivative of the isotropic tensor function plays an important part in continuum mechanics and computational mechanics, and also it is still an opening problem. By means of a scalar response function and solving a tensor equation, this problem is well studied. A compact explicit expression for the derivative of the isotropic tensor function is presented, which is valid for both distinct and repeated eigenvalue cases. Throughout the analysis, the formulation holds for general isotropic tensor functions without need to solve eigenvector problems or determine coefficients. On the theoretical side, a very simple solution of a tensor equation is obtained. As an application to continuum mechanics, a base-free expression for the Hill's strain rate is given, which is more compact than the existent results. Finally, with an example we compute the derivative of an exponent tensor function. And the efficiency of the present formulations is demonstrated.
Tensor eigenvalues and entanglement of symmetric states
Bohnet-Waldraff, F.; Braun, D.; Giraud, O.
2016-10-01
Tensor eigenvalues and eigenvectors have been introduced in the recent mathematical literature as a generalization of the usual matrix eigenvalues and eigenvectors. We apply this formalism to a tensor that describes a multipartite symmetric state or a spin state, and we investigate to what extent the corresponding tensor eigenvalues contain information about the multipartite entanglement (or, equivalently, the quantumness) of the state. This extends previous results connecting entanglement to spectral properties related to the state. We show that if the smallest tensor eigenvalue is negative, the state is detected as entangled. While for spin-1 states the positivity of the smallest tensor eigenvalue is equivalent to separability, we show that for higher values of the angular momentum there is a correlation between entanglement and the value of the smallest tensor eigenvalue.
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...
Tensor Effect on Bubble Nuclei
Institute of Scientific and Technical Information of China (English)
WANG Yan-Zhao; GU Jian-Zhong; ZHANG Xi-Zhen; DONG Jian-Min
2011-01-01
In the framework of the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme interactions SLy5+T, SLy5+Tw and several sets of TIJ parametrizations, I.e. The Skyrme interaction parametrizations including the tensor terms, the proton density distribution in 34Si and 46Ar nuclei is calculated with and without the tensor force. It is shown that the bubble effect in 34Si does not depend a great deal on the Skyrme parametrization and the proton density distribution in 34Si is hardly influenced by the tensor force. As to 46Ar, the SLy5+Tw parametrization favors the formation of the bubble structure due to the inversion between the 2s1/2 and 1d3/2 orbits (2s1/2-ld3/2 inversion). The inversion mechanism induced by the SLy5+Tw interaction is analyzed based on the proton single-particle spectra obtained from the SLy5 and SLy5+Tw interactions as well as the wave functions of the 2s1/2 and 1d3/2 states.%In the framework of the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme interactions SLy5+ T,SLy5+ Tω and several sets of TIJ parametrizations,i.e.the Skyrme interaction pararmetrizations including the tensor terms,the proton density distribution in 34Si and 46 Ar nuclei is calculated with and without the tensor force.It is shown that the bubble effect in 34Si does not depend a great deal on the Skyrme parametrization and the proton density distribution in 34Si is hardly influenced by the tensor force.As to 46Ar,the SLy5+ Tω parametrization favors the formation of the bubble structure due to the inversion between the 2s1/2 and 1d3/2 orbits (2s1/2-1d3/2 inversion).The inversion mechanism induced by the SLy5+ Tω interaction is analyzed based on the proton single-particle spectra obtained from the SLy5 and SLy5+ Tω interactions as well as the wave functions of the 2s1/2 and 1d3/2 states.The study of exotic nuclear structures has been a hot topic in nuclear physics.[1-4] Exotic nuclei are unstabile,superheavy nuclei,halo nuclei and so forth,whose structures are quite different
Hard Exclusive Production of Tensor Mesons
Braun, V M
2001-01-01
We point out that hard exclusive production of tensor mesons $f_2(1270)$ with helicity $\\lambda=\\pm 2$ is dominated by the gluon component in the meson wave function and can be used to determine gluon admixture in tensor mesons in a theoretically clean manner. We present a detailed analysis of the tensor meson distribution amplitudes and calculate the transition form factor $\\gamma+\\gamma^*\\to f_2(1270)$ for one real and one virtual photon.
The Topology of Symmetric Tensor Fields
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.
Dirac tensor with heavy photon
Energy Technology Data Exchange (ETDEWEB)
Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2012-01-15
For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)
The tensor network theory library
Al-Assam, S.; Clark, S. R.; Jaksch, D.
2017-09-01
In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.
Tensor power spectrum and disformal transformations
Fumagalli, Jacopo; Postma, Marieke
2016-01-01
In a general effective theory description of inflation a disformal transformation can be used to set the tensor sound speed to one. After the transformation, the tensor power spectrum then automatically only depends on the Hubble parameter. We show that this disformal transformation, however, is nothing else than a change of units. It is a very useful tool for simplifying and interpreting computations, but it cannot change any physics. While the apparent parametrical dependence of the tensor power spectrum does change under a disformal transformation, the physics described is frame invariant. We further illustrate the frame invariance of the tensor power spectrum by writing it exclusively in terms of separately invariant quantities.
Loop Optimization for Tensor Network Renormalization
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
2017-03-01
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the 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.
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...
Loop Optimization for Tensor Network Renormalization.
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
2017-03-17
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the 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.
A uniform parameterization of moment tensors
Tape, C.; Tape, W.
2015-12-01
A moment tensor is a 3 x 3 symmetric matrix that expresses an earthquake source. We construct a parameterization of the five-dimensional space of all moment tensors of unit norm. The coordinates associated with the parameterization are closely related to moment tensor orientations and source types. The parameterization is uniform, in the sense that equal volumes in the coordinate domain of the parameterization correspond to equal volumes of moment tensors. Uniformly distributed points in the coordinate domain therefore give uniformly distributed moment tensors. A cartesian grid in the coordinate domain can be used to search efficiently over moment tensors. We find that uniformly distributed moment tensors have uniformly distributed orientations (eigenframes), but that their source types (eigenvalue triples) are distributed so as to favor double couples. An appropriate choice of a priori moment tensor probability is a prerequisite for parameter estimation. As a seemingly sensible choice, we consider the homogeneous probability, in which equal volumes of moment tensors are equally likely. We believe that it will lead to improved characterization of source processes.
Towards a double-scaling limit for tensor models: probing sub-dominant orders
Kaminski, Wojciech; Ryan, James P
2013-01-01
The definition of a double-scaling limit represents an important goal in the development of tensor models. We take the first steps towards this goal by extracting and analysing the next-to-leading order contributions, in the 1/N expansion, for the IID tensor models. We show that the radius of convergence of the NLO series coincides with that of the leading order melonic sector. Meanwhile, the value of the susceptibility exponent at NLO is 3/2, signaling a departure from the leading order behaviour. Both pieces of information provide clues for a non-trivial double-scaling limit, for which we put forward some precise conjecture.
Uncertainty propagation in orbital mechanics via tensor decomposition
Sun, Yifei; Kumar, Mrinal
2016-03-01
Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker-Planck equation (FPE) is defined on a relatively high dimensional (6-D) state-space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the x-y-z subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors' knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral ("super-fast") convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families...
Groupoid normalizers of tensor products
Fang, Junsheng; White, Stuart A; Wiggins, Alan D
2008-01-01
We consider an inclusion $B\\subseteq M$ of finite von Neumann algebras satisfying $B'\\cap M\\subseteq B$. A partial isometry $v\\in M$ is called a groupoid normalizer if $vBv^*, v^*Bv\\subseteq B$. Given two such inclusions $B_i\\subseteq M_i$, $i=1,2$, we find approximations to the groupoid normalizers of $B_1 \\vnotimes B_2$ in $M_1\\vnotimes M_2$, from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis $B_i'\\cap M_i\\subseteq B_i$, $i=1,2$. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries $v\\in M$ satisfying $vBv^*\\subseteq B$ and $v^*v, vv^*\\in B$.
Nonlinear susceptibilities of finite conjugated organic polymers
Beratan, David N.; Onuchic, Jose Nelson; Perry, Joseph W.
1987-01-01
Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The pi-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. This is the first two-'band' calculation of third-order hyperpolarizabilities on finite pi-electron systems of varying length. In contrast to the results of the one-'band' models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.
Park, Q H
1999-01-01
Using the Painlevé analysis, we investigate the integrability properties of a system of two coupled nonlinear Schrödinger equations that describe the propagation of orthogonally polarized optical waves in an isotropic medium. Besides the well-known integrable vector nonlinear Schrödinger equation, we show that there exist a new set of equations passing the Painlevé test where the self and cross phase modulational terms are of different magnitude. We introduce the Hirota bilinearization and the Bãcklund transformation to obtain soliton solutions and prove integrability by making a change of variables. The conditions on the third-order susceptibility tensor $\\chi^{(3)} $ imposed by these new integrable equations are explained.
Energy Technology Data Exchange (ETDEWEB)
Gazhulina, A.P., E-mail: asyagazhulina@yandex.ru; Marychev, M.O.
2015-02-25
Highlights: • We consider 111 compounds of B3 and B20 types by FP-LAPW method using LDA, GGA, mBJ. • Structural, electronic and nonlinear optical properties were investigated. • Some data calculated for the first time for a large part of considered compounds. • NLO properties considered in relation with pseudoinversion for all 111 crystals. - Abstract: The structural, electronic, and nonlinear optical properties of 111 crystals belonging to structural types B3 (84 crystals) and B20 (27 crystals) have been investigated by first-principles calculations using the full-potential linearized augmented plane wave (FP-LAPW) method in the framework of density functional theory. Calculations of the electronic band structure and nonlinear optical properties were performed using local-density approximation (LDA), generalized gradient approximation (GGA), and a combination of modified Becke—Johnson exchange potential plus LDA (mBJ + LDA) for exchange–correlation potential. Equilibrium lattice constant a{sub 0}, bulk modulus B{sub 0}, first pressure derivative B′ of the bulk modulus, band gaps E{sub g}, and second-order nonlinear susceptibility tensor components |χ{sub 123}| at 0 eV and at 1.064 and 10.6 μm wavelengths are presented. The obtained results are compared to available experimental and theoretical (computational) data. A correlation between the |χ{sub 123}| tensor component data arrays and the distributions of crystal structures with respect to their degree of pseudoinversion is analyzed.
Analysis of Nonlinear Electromagnetic Metamaterials
Poutrina, Ekaterina; Smith, David R
2010-01-01
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated metamaterial sample composed of an array of split ring resonators (SRRs) with packaged varactors embedded in the capacitive gaps in a manner similar to that of Wang et al. [Opt. Express 16, 16058 (2008)]. Because the SRRs exhibit a predominant magnetic response to electromagnetic fields, the varactor-loaded SRR composite can be described as a magnetic material with nonlinear terms in its effective magnetic susceptibility...
Bayesian regularization of diffusion tensor images
DEFF Research Database (Denmark)
Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif;
2007-01-01
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...
Tensor Products of Random Unitary Matrices
Tkocz, Tomasz; Kus, Marek; Zeitouni, Ofer; Zyczkowski, Karol
2012-01-01
Tensor products of M random unitary matrices of size N from the circular unitary ensemble are investigated. We show that the spectral statistics of the tensor product of random matrices becomes Poissonian if M=2, N become large or M become large and N=2.
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.
Directory of Open Access Journals (Sweden)
Kuang-dai Leng
2012-01-01
Full Text Available Fabric tensor has proved to be an effective tool statistically characterizing directional data in a smooth and frame-indifferent form. Directional data arising from microscopic physics and mechanics can be summed up as tensor-valued orientation distribution functions (ODFs. Two characterizations of the tensor-valued ODFs are proposed, using the asymmetric and symmetric fabric tensors respectively. The later proves to be nonconvergent and less accurate but still an available solution for where fabric tensors are required in full symmetry. Analytic solutions of the two types of fabric tensors characterizing centrosymmetric and anticentrosymmetric tensor-valued ODFs are presented in terms of orthogonal irreducible decompositions in both two- and three-dimensional (2D and 3D spaces. Accuracy analysis is performed on normally distributed random ODFs to evaluate the approximation quality of the two characterizations, where fabric tensors of higher orders are employed. It is shown that the fitness is dominated by the dispersion degree of the original ODFs rather than the orders of fabric tensors. One application of tensor-valued ODF and fabric tensor in continuum damage mechanics is presented.
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
On Lovelock analogs of the Riemann tensor
Energy Technology Data Exchange (ETDEWEB)
Camanho, Xian O. [Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik, Golm (Germany); Dadhich, Naresh [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Inter-University Centre for Astronomy and Astrophysics, Pune (India)
2016-03-15
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. (orig.)
Algebraically contractible topological tensor network states
Denny, S J; Jaksch, D; Clark, S R
2011-01-01
We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules. The contraction property does not depend on specifics such as geometry, but rather originates from the non-trivial algebraic properties of the constituent tensors. We then generalise the resulting tensor network from a spin-half lattice to a class of exactly contractible states on spin-S degrees of freedom, yielding the most efficient tensor network description of finite Abelian lattice gauge theories. We gain a new perspective on these states as examples of two-dimensional quantum states with algebraically contractible tensor network representations. The introduction of local perturbations to the network is shown to reduce the von Neumann entropy of string-like regions, creating an unentangled sub-system within the bulk in a certain limit. We also show how perturbations l...
Interpretation of the Weyl Tensor
Hofmann, Stefan; Schneider, Robert
2013-01-01
According to folklore in general relativity, the Weyl tensor can be decomposed into parts corresponding to Newton-like, incoming- and outgoing wave-like field components. It is shown here that this interpretation cannot be applied to space-time geometries with cylindrical isometries. This is done by investigating some well-known exact solutions of Einstein's field equations with whole-cylindrical symmetry, for which the physical interpretation is very clear, but for which the standard Weyl interpretation would give contradictory results. For planar or spherical geometries, however, the standard interpretation works for both, static and dynamical space-times. It is argued that one reason for the failure in the cylindrical case is that for waves spreading in two spatial dimensions there is no local criterion to distinguish incoming and outgoing waves already at the linear level. It turns out that Thorne's local energy notion, subject to certain qualifications, provides an efficient diagnostic tool to extract th...
Nguyen, Khoi Tan; Le Clair, Stéphanie V; Ye, Shuji; Chen, Zhan
2009-09-10
In this paper, we systematically presented the orientation determination of protein helical secondary structures using vibrational spectroscopic methods, particularly, nonlinear sum frequency generation (SFG) vibrational spectroscopy, along with linear vibrational spectroscopic techniques such as infrared spectroscopy and Raman scattering. SFG amide I signals can be collected using different polarization combinations of the input laser beams and output signal beam to measure the second-order nonlinear optical susceptibility components of the helical amide I modes, which are related to their molecular hyperpolarizability elements through the orientation distribution of these helices. The molecular hyperpolarizability elements of amide I modes of a helix can be calculated based on the infrared transition dipole moment and Raman polarizability tensor of the helix; these quantities are determined by using the bond additivity model to sum over the individual infrared transition dipole moments and Raman polarizability tensors, respectively, of the peptide units (or the amino acid residues). The computed overall infrared transition dipole moment and Raman polarizability tensor of a helix can be validated by experimental data using polarized infrared and polarized Raman spectroscopy on samples with well-aligned helical structures. From the deduced SFG hyperpolarizability elements and measured SFG second-order nonlinear susceptibility components, orientation information regarding helical structures can be determined. Even though such orientation information can also be measured using polarized infrared or polarized Raman amide I signals, SFG has a much lower detection limit, which can be used to study the orientation of a helix when its surface coverage is much lower than a monolayer. In addition, the combination of different vibrational spectroscopic techniques, for example, SFG and attenuated total reflectance Fourier transform infrared spectroscopy, provides more
Institute of Scientific and Technical Information of China (English)
胡业民; 胡希伟
2001-01-01
Numerical analyses for the nonlinear evolutions of stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) processes are given. Various effects of the second- and third-order nonlinear susceptibilities on the SRS and SBS processes are studied. The nonlinear evolutions of SRS and SBS processes are atfected more efficiently than their linear growth rates by the nonlinear susceptibility.
Modulational stability and dark solitons in periodic quadratic nonlinear media
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....
First principles crystal engineering of nonlinear optical materials. I. Prototypical case of urea
Masunov, Artëm E.; Tannu, Arman; Dyakov, Alexander A.; Matveeva, Anastasia D.; Freidzon, Alexandra Ya.; Odinokov, Alexey V.; Bagaturyants, Alexander A.
2017-06-01
The crystalline materials with nonlinear optical (NLO) properties are critically important for several technological applications, including nanophotonic and second harmonic generation devices. Urea is often considered to be a standard NLO material, due to the combination of non-centrosymmetric crystal packing and capacity for intramolecular charge transfer. Various approaches to crystal engineering of non-centrosymmetric molecular materials were reported in the literature. Here we propose using global lattice energy minimization to predict the crystal packing from the first principles. We developed a methodology that includes the following: (1) parameter derivation for polarizable force field AMOEBA; (2) local minimizations of crystal structures with these parameters, combined with the evolutionary algorithm for a global minimum search, implemented in program USPEX; (3) filtering out duplicate polymorphs produced; (4) reoptimization and final ranking based on density functional theory (DFT) with many-body dispersion (MBD) correction; and (5) prediction of the second-order susceptibility tensor by finite field approach. This methodology was applied to predict virtual urea polymorphs. After filtering based on packing similarity, only two distinct packing modes were predicted: one experimental and one hypothetical. DFT + MBD ranking established non-centrosymmetric crystal packing as the global minimum, in agreement with the experiment. Finite field approach was used to predict nonlinear susceptibility, and H-bonding was found to account for a 2.5-fold increase in molecular hyperpolarizability to the bulk value.
Generalized Tensor Analysis Model for Multi-Subcarrier Analog Optical Systems
DEFF Research Database (Denmark)
Zhao, Ying; Yu, Xianbin; Zheng, Xiaoping
2011-01-01
We propose and develop a general tensor analysis framework for a subcarrier multiplex analog optical fiber link for applications in microwave photonics. The goal of this work is to construct an uniform method to address nonlinear distortions of a discrete frequency transmission system. We employ ...... a study of two multi-subcarrier systems with detailed performance discussions. We believe the tensor model provides us not only a consolidated notation, but also an alternative numerical approach to effectively analyze multi-subcarrier analog optical systems.......We propose and develop a general tensor analysis framework for a subcarrier multiplex analog optical fiber link for applications in microwave photonics. The goal of this work is to construct an uniform method to address nonlinear distortions of a discrete frequency transmission system. We employ...... details compared with series-based approaches by hiding the underlying multi-fold summation and index operation. The integrity of the proposed methodology is validated by investigating the classical intensity modulated system. Furthermore, to give an application model of the tensor formalism, we make...
About Advances in Tensor Data Denoising Methods
Directory of Open Access Journals (Sweden)
Salah Bourennane
2008-10-01
Full Text Available Tensor methods are of great interest since the development of multicomponent sensors. The acquired multicomponent data are represented by tensors, that is, multiway arrays. This paper presents advances on filtering methods to improve tensor data denoising. Channel-by-channel and multiway methods are presented. The first multiway method is based on the lower-rank (K1,Ã¢Â€Â¦,KN truncation of the HOSVD. The second one consists of an extension of Wiener filtering to data tensors. When multiway tensor filtering is performed, the processed tensor is flattened along each mode successively, and singular value decomposition of the flattened matrix is performed. Data projection on the singular vectors associated with dominant singular values results in noise reduction. We propose a synthesis of crucial issues which were recently solved, that is, the estimation of the number of dominant singular vectors, the optimal choice of flattening directions, and the reduction of the computational load of multiway tensor filtering methods. The presented methods are compared through an application to a color image and a seismic signal, multiway Wiener filtering providing the best denoising results. We apply multiway Wiener filtering and its fast version to a hyperspectral image. The fast multiway filtering method is 29 times faster and yields very close denoising results.
Predicting nonlinear properties of metamaterials from the linear response.
O'Brien, Kevin; Suchowski, Haim; Rho, Junsuk; Salandrino, Alessandro; Kante, Boubacar; Yin, Xiaobo; Zhang, Xiang
2015-04-01
The discovery of optical second harmonic generation in 1961 started modern nonlinear optics. Soon after, R. C. Miller found empirically that the nonlinear susceptibility could be predicted from the linear susceptibilities. This important relation, known as Miller's Rule, allows a rapid determination of nonlinear susceptibilities from linear properties. In recent years, metamaterials, artificial materials that exhibit intriguing linear optical properties not found in natural materials, have shown novel nonlinear properties such as phase-mismatch-free nonlinear generation, new quasi-phase matching capabilities and large nonlinear susceptibilities. However, the understanding of nonlinear metamaterials is still in its infancy, with no general conclusion on the relationship between linear and nonlinear properties. The key question is then whether one can determine the nonlinear behaviour of these artificial materials from their exotic linear behaviour. Here, we show that the nonlinear oscillator model does not apply in general to nonlinear metamaterials. We show, instead, that it is possible to predict the relative nonlinear susceptibility of large classes of metamaterials using a more comprehensive nonlinear scattering theory, which allows efficient design of metamaterials with strong nonlinearity for important applications such as coherent Raman sensing, entangled photon generation and frequency conversion.
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....
Incremental Discriminant Analysis in Tensor Space
Chang, Liu; Weidong, Zhao; Tao, Yan; Qiang, Pu; Xiaodan, Du
2015-01-01
To study incremental machine learning in tensor space, this paper proposes incremental tensor discriminant analysis. The algorithm employs tensor representation to carry on discriminant analysis and combine incremental learning to alleviate the computational cost. This paper proves that the algorithm can be unified into the graph framework theoretically and analyzes the time and space complexity in detail. The experiments on facial image detection have shown that the algorithm not only achieves sound performance compared with other algorithms, but also reduces the computational issues apparently. PMID:26339229
Global nuclear structure aspects of tensor interaction
Satula, W; Dobaczewski, J; Olbratowski, P; Rafalski, M; Werner, T R; Wyss, R A
2008-01-01
A direct fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants to the f5/2-f7/2 SO splittings in 40Ca, 56Ni, and 48Ca requires: (i) a significant reduction of the standard isoscalar spin-orbit strength and (ii) strong attractive tensor coupling constants. The aim of this paper is to address the consequences of these strong attractive tensor and weak spin-orbit fields on total binding energies, two-neutron separation energies and nuclear deformability.
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....
Tensor methods for large, sparse unconstrained optimization
Energy Technology Data Exchange (ETDEWEB)
Bouaricha, A.
1996-11-01
Tensor methods for unconstrained optimization were first introduced by Schnabel and Chow [SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate size problems. This paper extends these methods to large, sparse unconstrained optimization problems. This requires an entirely new way of solving the tensor model that makes the methods suitable for solving large, sparse optimization problems efficiently. We present test results for sets of problems where the Hessian at the minimizer is nonsingular and where it is singular. These results show that tensor methods are significantly more efficient and more reliable than standard methods based on Newton`s method.
Tensor network and a black hole
Matsueda, Hiroaki; Ishihara, Masafumi; Hashizume, Yoichiro
2013-03-01
A tensor-network variational formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, a multiscale entanglement renormalization ansatz reproduces an anti-de Sitter black hole at finite temperature. Our finding shows rich functionalities of multiscale entanglement renormalization ansatz as efficient graphical representation of AdS/CFT correspondence.
Electromagnetic Stress Tensor in Ponderable Media
Mansuripur, Masud
2014-01-01
We derive an expression for the Maxwell stress tensor in a magnetic dielectric medium specified by its permittivity "epsilon" and permeability "mu." The derivation proceeds from the generalized form of the Lorentz law, which specifies the force exerted by the electromagnetic E and H fields on the polarization P and magnetization M of ponderable media. Our stress tensor differs from the well-known tensors of Abraham and Minkowski, which have been at the center of a century-old controversy surrounding the momentum of the electromagnetic field in transparent materials.
Optical bistability in nonlinear composites with coated ellipsoidal nanoparticles
Pinchuk, A
2003-01-01
Nonlinear composite structures show great promise for use in optical switching, signal processing, etc. We derive an effective nonlinear dielectric permittivity of composite structures where coated ellipsoidal nonlinear particles are imbedded in a linear host medium. The derived expression for the effective dielectric permittivity tensor follows the Clasius-Mossotti approximation. We observe conditions for the existence of the optical bistability effect in a coated ellipsoidal particle with a nonlinear core and a metallic shell. Our numerical results show stronger bistability effects in more dense suspensions of nonlinear heterogeneous ellipsoids.
Reyes-Esqueda, Jorge Alejandro; Rodríguez-Iglesias, Vladimir; Silva-Pereyra, Héctor-Gabriel; Torres-Torres, Carlos; Santiago-Ramírez, Ana-Laura; Cheang-Wong, Juan Carlos; Crespo-Sosa, Alejandro; Rodríguez-Fernández, Luis; López-Suárez, Alejandra; Oliver, Alicia
2009-07-20
High-energy metallic ions were implanted in silica matrices, obtaining spherical-like metallic nanoparticles (NPs) after a proper thermal treatment. These NPs were then deformed by irradiation with Si ions, obtaining an anisotropic metallic nanocomposite. An average large birefringence of 0.06 was measured for these materials in the 300-800 nm region. Besides, their third order nonlinear optical response was measured using self-diffraction and P-scan techniques at 532 nm with 26 ps pulses. By adjusting the incident light's polarization and the angular position of the nanocomposite, the measurements could be directly related to, at least, two of the three linear independent components of its third order susceptibility tensor, finding a large, but anisotropic, response of around 10(-7) esu with respect to other isotropic metallic systems. For the nonlinear optical absorption, we were able to shift from saturable to reverse saturable absorption depending on probing the Au NP's major or minor axes, respectively. This fact could be related to local field calculations and NP's electronic properties. For the nonlinear optical refraction, we passed from self-focusing to self-defocusing, when changing from Ag to Au.
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
A Tofighi
2012-04-01
We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and when → ∞ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.
[Face rejuvenation with tensor threads].
Cornette de Saint Cyr, B; Benouaiche, L
2017-08-25
The last decades has seen new priorities in treatment of a flabby, ageing face towards minimally invasive aesthetic surgery, to be accompanied and followed by the requirements to perform such interventions with the maximally reduced health hazards, with inconsiderable injury, without cuts and, respectively, to be followed by no resulting scars, as well as a short postoperative period. We propose a new reviewing presentation of the tensor threads. After having explained the technology of the threads, we will discuss the good patient indication, the criteria which determine the choice of the threads and methods for each type of patient. There are many techniques, which we will present. Then, we will discuss the results, unsatisfactory outcomes obtained and complications encountered, as well as how to improve the cosmetic outcomes to be obtained. To conclude, we will propose a strategy for the long-term treatment of the neck and the face, preventing surgical management of the aging process. Copyright © 2017. Published by Elsevier Masson SAS.
Diffusion Tensor Imaging of Pedophilia.
Cantor, James M; Lafaille, Sophie; Soh, Debra W; Moayedi, Massieh; Mikulis, David J; Girard, Todd A
2015-11-01
Pedophilia is a principal motivator of child molestation, incurring great emotional and financial burdens on victims and society. Even among pedophiles who never commit any offense,the condition requires lifelong suppression and control. Previous comparison using voxel-based morphometry (VBM)of MR images from a large sample of pedophiles and controls revealed group differences in white matter. The present study therefore sought to verify and characterize white matter involvement using diffusion tensor imaging (DTI), which better captures the microstructure of white matter than does VBM. Pedophilics ex offenders (n=24) were compared with healthy, age-matched controls with no criminal record and no indication of pedophilia (n=32). White matter microstructure was analyzed with Tract-Based Spatial Statistics, and the trajectories of implicated fiber bundles were identified by probabilistic tractography. Groups showed significant, highly focused differences in DTI parameters which related to participants’ genital responses to sexual depictions of children, but not to measures of psychopathy or to childhood histories of physical abuse, sexual abuse, or neglect. Some previously reported gray matter differences were suggested under highly liberal statistical conditions (p(uncorrected)<.005), but did not survive ordinary statistical correction (whole brain per voxel false discovery rate of 5%). These results confirm that pedophilia is characterized by neuroanatomical differences in white matter microstructure, over and above any neural characteristics attributable to psychopathy and childhood adversity, which show neuroanatomic footprints of their own. Although some gray matter structures were implicated previously, only few have emerged reliably.
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...... deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create "seams" or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template...... space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation...
Shifted power method for computing tensor eigenpairs.
Energy Technology Data Exchange (ETDEWEB)
Mayo, Jackson R.; Kolda, Tamara Gibson
2010-10-01
Recent work on eigenvalues and eigenvectors for tensors of order m {>=} 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Ax{sup m-1} = {lambda}x subject to {parallel}x{parallel} = 1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a novel shifted symmetric higher-order power method (SS-HOPM), which we showis guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to fnding complex eigenpairs.
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory.
The Weyl tensor correlator in cosmological spacetimes
Fröb, Markus B
2014-01-01
We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lema\\^itre-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters $\\epsilon$ and $\\delta$, and the result is shown to have the correct de Sitter limit as $\\epsilon, \\delta \\to 0$. Furthermore, it is seen that the Weyl tensor correlation function does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.
Symbolic Tensor Calculus -- Functional and Dynamic Approach
Woszczyna, A; Czaja, W; Golda, Z A
2016-01-01
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
Multipartite Entanglement in Stabilizer Tensor Networks
Nezami, Sepehr
2016-01-01
Tensor network models reproduce important structural features of holography, including the Ryu-Takayanagi formula for the entanglement entropy and quantum error correction in the entanglement wedge. In contrast, only little is known about their multipartite entanglement structure, which has been of considerable recent interest. In this work, we study random stabilizer tensor networks and show that here the tripartite entanglement question has a sharp answer: The average number of GHZ triples that can be extracted from a stabilizer tensor network is small, implying that the entanglement is predominantly bipartite. As a consequence, we obtain a new operational interpretation of the monogamy of the Ryu-Takayanagi mutual information and an entropic diagnostic for higher-partite entanglement. Our technical contributions include a spin model for evaluating the average GHZ content of stabilizer tensor networks and a novel formula for the third moment of random stabilizer states.
Primordial tensor modes of the early Universe
Martínez, Florencia Benítez
2016-01-01
We study cosmological tensor perturbations on a quantized background within the hybrid quantization approach. In particular, we consider a flat, homogeneous and isotropic spacetime and small tensor inhomogeneities on it. We truncate the action to second order in the perturbations. The dynamics is ruled by a homogeneous scalar constraint. We carry out a canonical transformation in the system where the Hamiltonian for the tensor perturbations takes a canonical form. The new tensor modes now admit a standard Fock quantization with a unitary dynamics. We then combine this representation with a generic quantum scheme for the homogeneous sector. We adopt a Born-Oppenheimer ansatz for the solutions to the constraint operator, previously employed to study the dynamics of scalar inhomogeneities. We analyze the approximations that allow us to recover, on the one hand, a Schr\\"odinger equation similar to the one emerging in the dressed metric approach, and, on the other hand, the ones necessary for the effective evoluti...
Entangled scalar and tensor fluctuations during inflation
Energy Technology Data Exchange (ETDEWEB)
Collins, Hael; Vardanyan, Tereza [Department of Physics, Carnegie Mellon University,5000 Forbes Avenue, Pittsburgh, Pennsylvania (United States)
2016-11-29
We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.
An introduction to linear algebra and tensors
Akivis, M A; Silverman, Richard A
1978-01-01
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Unsupervised Tensor Mining for Big Data Practitioners.
Papalexakis, Evangelos E; Faloutsos, Christos
2016-09-01
Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.
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.
The Energy-Momentum Tensor(s) in Classical Gauge Theories
Blaschke, Daniel N; Reboud, Meril; Schweda, Manfred
2016-01-01
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.
Analysis of the tensor-tensor type scalar tetraquark states with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we study the ground states and the first radial excited states of the tensor-tensor type scalar hidden-charm tetraquark states with the QCD sum rules. We separate the ground state contributions from the first radial excited state contributions unambiguously, and obtain the QCD sum rules for the ground states and the first radial excited states, respectively. Then we search for the Borel parameters and continuum threshold parameters according to four criteria and obtain the masses of the tensor-tensor type scalar hidden-charm tetraquark states, which can be confronted to the experimental data in the future.
Renormalization procedure for random tensor networks and the canonical tensor model
Sasakura, Naoki
2015-01-01
We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum gravity. The result is the generalization of the previous one concerning the relation between the Ising model on random networks and the canonical tensor model with N=2. We also prove a general theorem which relates discontinuity of the renormalization-group flow and the phase transitions of random tensor networks.
Novel Physics with Tensor Polarized Deuteron Targets
Energy Technology Data Exchange (ETDEWEB)
Slifer, Karl J. [UNH; Long, Elena A. [UNH
2013-09-01
Development of solid spin-1 polarized targets will open the study of tensor structure functions to precise measurement, and holds the promise to enable a new generation of polarized scattering experiments. In this talk we will discuss a measurement of the leading twist tensor structure function b1, along with prospects for future experiments with a solid tensor polarized target. The recently approved JLab experiment E12-13-011 will measure the lead- ing twist tensor structure function b1, which provides a unique tool to study partonic effects, while also being sensitive to coherent nuclear properties in the simplest nuclear system. At low x, shadowing effects are expected to dominate b1, while at larger values, b1 provides a clean probe of exotic QCD effects, such as hidden color due to 6-quark configuration. Since the deuteron wave function is relatively well known, any non-standard effects are expected to be readily observable. All available models predict a small or vanishing value of b1 at moderate x. However, the first pioneer measurement of b1 at HERMES revealed a crossover to an anomalously large negative value in the region 0.2 < x < 0.5, albeit with relatively large experimental uncertainty. E12-13-011 will perform an inclusive measurement of the deuteron tensor asymmetry in the region 0.16 < x < 0.49, for 0.8 < Q2 < 5.0 GeV2. The UVa solid polarized ND3 target will be used, along with the Hall C spectrometers, and an unpolarized 115 nA beam. This measurement will provide access to the tensor quark polarization, and allow a test of the Close-Kumano sum rule, which vanishes in the absence of tensor polarization in the quark sea. Until now, tensor structure has been largely unexplored, so the study of these quantities holds the potential of initiating a new field of spin physics at Jefferson Lab.
Phylogenetic estimation with partial likelihood tensors
Sumner, J G
2008-01-01
We present an alternative method for calculating likelihoods in molecular phylogenetics. Our method is based on partial likelihood tensors, which are generalizations of partial likelihood vectors, as used in Felsenstein's approach. Exploiting a lexicographic sorting and partial likelihood tensors, it is possible to obtain significant computational savings. We show this on a range of simulated data by enumerating all numerical calculations that are required by our method and the standard approach.
Effects of tensor interactions in {tau} decays
Energy Technology Data Exchange (ETDEWEB)
Lopez Castro, G.; Godina Nava, J.J. [Departamento de Fisica, Cinvestav del IPN, Mexico DF. (MEXICO)
1996-02-01
Recent claims for the observation of antisymmetric weak tensor currents in {pi} and {ital K} decays are considered for the case of {tau}{r_arrow}{ital K}{pi}{nu} transitions. Assuming the existence of symmetric tensor currents, a mechanism for the direct production of the {ital K}{sub 2}{sup {asterisk}}(1430) spin-2 meson in {tau} decays is proposed. {copyright} {ital 1996 American Institute of Physics.}
Spontaneous Breaking of Lorentz Symmetry with an antisymmetric tensor
Hernaski, Carlos A
2016-01-01
Spontaneous violation of Lorentz symmetry by the vacuum condensation of an antisymmetric $2$-tensor is considered. The coset construction for nonlinear realization of spacetime symmetries is employed to build the most general low-energy effective action for the Goldstone modes interacting with photons. We analyze the model within the context of the Standard-Model Extension and noncommutative QED. Experimental bounds for some parameters of the model are discussed, and we readdress the subtle issues of stability and causality in Lorentz non-invariant scenarios. Besides the two photon polarizations, just one Goldstone mode must be dynamical to set a sensible low-energy effective model, and the enhancement of the stability by accounting interaction terms points to a protection against observational Lorentz violation.
C%2B%2B tensor toolbox user manual.
Energy Technology Data Exchange (ETDEWEB)
Plantenga, Todd D.; Kolda, Tamara Gibson
2012-04-01
The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.
Algebraically contractible topological tensor network states
Energy Technology Data Exchange (ETDEWEB)
Denny, S J; Jaksch, D; Clark, S R [Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU (United Kingdom); Biamonte, J D, E-mail: s.denny1@physics.ox.ac.uk [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore)
2012-01-13
We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with Z{sub 2} topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules. The contraction property does not depend on specifics such as geometry, but rather originates from the non-trivial algebraic properties of the constituent tensors. We then generalise the resulting tensor network from a spin-1/2 lattice to a class of exactly contractible states on spin-S degrees of freedom, yielding the most efficient tensor network description of finite Abelian lattice gauge theories. We gain a new perspective on these states as examples of two-dimensional quantum states with algebraically contractible tensor network representations. The introduction of local perturbations to the network is shown to reduce the von Neumann entropy of string-like regions, creating an unentangled sub-system within the bulk in a certain limit. We also show how local perturbations induce finite-range correlations in this system. This class of tensor networks is readily translated onto any lattice, and we differentiate between the physical consequences of bipartite and non-bipartite lattices on the properties of the corresponding quantum states. We explicitly show this on the hexagonal, square, kagome and triangular lattices. (paper)
TWIN SUPPORT TENSOR MACHINES FOR MCS DETECTION
Institute of Scientific and Technical Information of China (English)
Zhang Xinsheng; Gao Xinbo; Wang Ying
2009-01-01
Tensor representation is useful to reduce the overfitting problem in vector-based learning algorithm in pattern recognition.This is mainly because the structure information of objects in pattern analysis is a reasonable constraint to reduce the number of unknown parameters used to model a classifier.In this paper,we generalize the vector-based learning algorithm TWin Support Vector Machine (TWSVM)to the tensor-based method TWin Support Tensor Machines(TWSTM),which accepts general tensors as input.To examine the effectiveness of TWSTM,we implement the TWSTM method for Microcalcification Clusters (MCs) detection.In the tensor subspace domain,the MCs detection procedure is formulated as a supervised learning and classification problem.and TWSTM is used as a classifier to make decision for the presence of MCs or not.A large number of experiments were carried out to evaluate and compare the performance of the proposed MCs detection algorithm.By comparison with TWSVM,the tensor version reduces the overfitting problem.
Topological Susceptibility from Slabs
Bietenholz, Wolfgang; Gerber, Urs
2015-01-01
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.
Moment tensors of a dislocation in a porous medium
Wang, Zhi; Hu, Hengshan
2016-06-01
A dislocation can be represented by a moment tensor for calculating seismic waves. However, the moment tensor expression was derived in an elastic medium and cannot completely describe a dislocation in a porous medium. In this paper, effective moment tensors of a dislocation in a porous medium are derived. It is found that the dislocation is equivalent to two independent moment tensors, i.e., the bulk moment tensor acting on the bulk of the porous medium and the isotropic fluid moment tensor acting on the pore fluid. Both of them are caused by the solid dislocation as well as the fluid-solid relative motion corresponding to fluid injection towards the surrounding rocks (or fluid outflow) through the fault plane. For a shear dislocation, the fluid moment tensor is zero, and the dislocation is equivalent to a double couple acting on the bulk; for an opening dislocation or fluid injection, the two moment tensors are needed to describe the source. The fluid moment tensor only affects the radiated compressional waves. By calculating the ratio of the radiation fields generated by unit fluid moment tensor and bulk moment tensor, it is found that the fast compressional wave radiated by the bulk moment tensor is much stronger than that radiated by the fluid moment tensor, while the slow compressional wave radiated by the fluid moment tensor is several times stronger than that radiated by the bulk moment tensor.
Foundations of the non-linear mechanics of continua
Sedov, L I
1966-01-01
International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable
Mode matching in second order susceptibility metamaterials
Héron, Sébastien; Haïdar, Riad
2016-01-01
We present an effective model for a subwavelength periodically patterned metallic layer, its cavities being filled with a nonlinear dielectric material, which accounts for both the linear and second order behavior. The effective non linear susceptibility for the homogenized layer is driven by the nonlinearity of the dielectric material and by the geometrical parameters, thus leading to much higher susceptibility than existing materials. This leads to a huge enhancement of non linear processes when used together with resonances. Furthermore, multiple resonances are taking place in the metallic cavities, and we investigate the mode matching situations for frequency conversion processes and show how it enhances further their efficiency.
[Tensor veli palatini and tensor tympani muscles: anatomical, functional and symptomatic links].
Ramirez Aristeguieta, Luis Miguel; Ballesteros Acuña, Luis Ernesto; Sandoval Ortiz, Germán Pablo
2010-01-01
Temporomandibular disorders are associated with symptoms such as tinnitus, vertigo, sensation of hearing loss, ear fullness and otalgia. The connection and dysfunction of the tensor tympani and tensor veli palatini muscles seems to be associated with the aforementioned symptoms. We seek to demonstrate and explain this connection through the morphometry of these structures. We studied 22 paired blocks and 1 left side of human temporal bone. Digital measurements were made of the tensor tympani muscles and stapes. The average length of the stapedial muscle was 5.8 mm SD 0.61, and that of the tensor tympani was 19.69 mm SD 1.07. Anatomical connections were found in all the samples between the tensor veli palatini muscles through a common tendon. There is a need for an interdisciplinary management between physician and specialized dentist in cases of craniofacial pain. 2009 Elsevier España, S.L. All rights reserved.
Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
Zhao, Hui-Hai; Xie, Zhi-Yuan; Xiang, Tao; Imada, Masatoshi
2016-03-01
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.
The Effective AC Response of Nonlinear Composites
Institute of Scientific and Technical Information of China (English)
WEI En-Bo; GU Guo-Qing
2001-01-01
A perturbative approach is used to study the AC response of nonlinear composite media, which obey a current-field relation of the form J = σ E + χ|E|2 E with components having nonlinear response at finite frequencies. For a sinusoidal applied field, we extend the local potential in terms of sinusoidal components at fundamental frequency and high-order harmonic frequencies to treat the nonlinear composites. For nonlinear composite media vith a low concentrations of spherical inclusions, we give the formulae of the nonlinear effective AC susceptibility χ*3ω at the third harmonic frequency.
DEFF Research Database (Denmark)
Bache, Morten; Guo, Hairun; Zhou, Binbin
2013-01-01
We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (β-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant χ(3) cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments in the literat...
Testing gravity theories using tensor perturbations
Lin, Weikang; Ishak-Boushaki, Mustapha B.
2017-01-01
Primordial gravitational waves constitute a promising probe of the very early universe physics and the laws of gravity. We study the changes to tensor-mode perturbations that can arise in various modified gravity theories. These include a modified friction and a nonstandard dispersion relation. We introduce a physically motivated parametrization of these effects and use current data to obtain excluded parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by future experiments COrE, Stage-IV and PIXIE. For the tensor-to-scalar ratio r=0.01, we find the minimum detectible modified-gravity effects. In particular, the minimum detectable graviton mass is about 7.8˜9.7×10-33 eV, which is of the same order of magnitude as the graviton mass that allows massive gravity to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation. We find that, the tensor spectral index would be additionally related to the friction parameter ν0 by nT=-3ν0-r/8. In some cases, the future experiments will be able to distinguish this relation from the standard one. In sum, primordial gravitational waves provide a complementary avenue to test gravity theories.
Estimates of the Nucleon Tensor Charge
Gamberg, L P; Gamberg, Leonard; Goldstein, Gary R.
2001-01-01
Like the axial vector charges, defined from the forward nucleon matrix element of the axial vector current on the light cone, the nucleon tensor charge, defined from the corresponding matrix element of the tensor current, is essential for characterizing the momentum and spin structure of the nucleon. Because there must be a helicity flip of the struck quark in order to probe the transverse spin polarization of the nucleon, the transversity distribution (and thus the tensor charge) decouples at leading twist in deep inelastic scattering, although no such suppression appears in Drell-Yan processes. This makes the tensor charge difficult to measure and its non-conservation makes its prediction model dependent. We present a different approach. Exploiting an approximate SU(6)xO(3) symmetric mass degeneracy of the light axial vector mesons (a1(1260), b1(1235) and h1(1170)) and using pole dominance, we calculate the tensor charge. The result is simple in form and depends on the decay constants of the axial vector me...
Global nuclear structure effects of tensor interaction
Zalewski, M; Rafalski, M; Satula, W; Werner, T R; Wyss, R A
2009-01-01
A direct fit of the isoscalar spin-orbit (SO) and both isoscalar and isovector tensor coupling constants to the f5/2-f7/2 SO splittings in 40Ca, 56Ni, and 48Ca nuclei requires a drastic reduction of the isoscalar SO strength and strong attractive tensor coupling constants. The aim of this work is to address further consequences of these strong attractive tensor and weak SO fields on binding energies, nuclear deformability, and high-spin states. In particular, we show that contribution to the nuclear binding energy due to the tensor field shows generic magic structure with tensorial magic numbers at N(Z)=14, 32, 56, or 90 corresponding to the maximum spin-asymmetries in 1d5/2, 1f7/2-2p3/2, 1g9/2-2d5/2 and 1h11/2-2f7/2 single-particle configurations and that these numbers are smeared out by pairing correlations and deformation effects. We also examine the consequences of strong attractive tensor fields and weak SO interaction on nuclear stability at the drip lines, in particular close to the tensorial doubly ma...
Tensor scale-based image registration
Saha, Punam K.; Zhang, Hui; Udupa, Jayaram K.; Gee, James C.
2003-05-01
Tangible solutions to image registration are paramount in longitudinal as well as multi-modal medical imaging studies. In this paper, we introduce tensor scale - a recently developed local morphometric parameter - in rigid image registration. A tensor scale-based registration method incorporates local structure size, orientation and anisotropy into the matching criterion, and therefore, allows efficient multi-modal image registration and holds potential to overcome the effects of intensity inhomogeneity in MRI. Two classes of two-dimensional image registration methods are proposed - (1) that computes angular shift between two images by correlating their tensor scale orientation histogram, and (2) that registers two images by maximizing the similarity of tensor scale features. Results of applications of the proposed methods on proton density and T2-weighted MR brain images of (1) the same slice of the same subject, and (2) different slices of the same subject are presented. The basic superiority of tensor scale-based registration over intensity-based registration is that it may allow the use of local Gestalts formed by the intensity patterns over the image instead of simply considering intensities as isolated events at the pixel level. This would be helpful in dealing with the effects of intensity inhomogeneity and noise in MRI.
Particle creation from the quantum stress tensor
Firouzjaee, Javad T
2015-01-01
Among the different methods to derive particle creation, finding the quantum stress tensor expectation value gives a covariant quantity which can be used for examining the back-reaction issue. However this tensor also includes vacuum polarization in a way that depends on the vacuum chosen. Here we review different aspects of particle creation by looking at energy conservation and at the quantum stress tensor. It will be shown that in the case of general spherically symmetric black holes that have a \\emph{dynamical horizon}, as occurs in a cosmological context, one cannot have pair creation on the horizon because this violates energy conservation. This confirms the results obtained in other ways in a previous paper [25]. Looking at the expectation value of the quantum stress tensor with three different definitions of the vacuum state, we study the nature of particle creation and vacuum polarization in black hole and cosmological models, and the associated stress energy tensors. We show that the thermal tempera...
Entanglement, tensor networks and black hole horizons
Molina-Vilaplana, J.; Prior, J.
2014-11-01
We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization flow given by the class of tensor networks known as the Multi Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an additional entanglement structure at the length scale fixed by the temperature. The network comprises two copies of a MERA circuit with a fixed number of layers and a pure matrix product state which joins both copies by entangling the infrared degrees of freedom of both MERA networks. The entanglement distribution within this bridge state defines reduced density operators on both sides which cause analogous effects to the presence of a black hole horizon when computing the entanglement entropy at finite temperature in the AdS/CFT correspondence. The entanglement and correlations during the thermalization process of a system after a quantum quench are also analyzed. To this end, a full tensor network representation of the action of local unitary operations on the bridge state is proposed. This amounts to a tensor network which grows in size by adding succesive layers of bridge states. Finally, we discuss on the holographic interpretation of the tensor network through a notion of distance within the network which emerges from its entanglement distribution.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Time-optimized high-resolution readout-segmented diffusion tensor imaging.
Directory of Open Access Journals (Sweden)
Gernot Reishofer
Full Text Available Readout-segmented echo planar imaging with 2D navigator-based reacquisition is an uprising technique enabling the sampling of high-resolution diffusion images with reduced susceptibility artifacts. However, low signal from the small voxels and long scan times hamper the clinical applicability. Therefore, we introduce a regularization algorithm based on total variation that is applied directly on the entire diffusion tensor. The spatially varying regularization parameter is determined automatically dependent on spatial variations in signal-to-noise ratio thus, avoiding over- or under-regularization. Information about the noise distribution in the diffusion tensor is extracted from the diffusion weighted images by means of complex independent component analysis. Moreover, the combination of those features enables processing of the diffusion data absolutely user independent. Tractography from in vivo data and from a software phantom demonstrate the advantage of the spatially varying regularization compared to un-regularized data with respect to parameters relevant for fiber-tracking such as Mean Fiber Length, Track Count, Volume and Voxel Count. Specifically, for in vivo data findings suggest that tractography results from the regularized diffusion tensor based on one measurement (16 min generates results comparable to the un-regularized data with three averages (48 min. This significant reduction in scan time renders high resolution (1 × 1 × 2.5 mm(3 diffusion tensor imaging of the entire brain applicable in a clinical context.
Nonlinear Optics of Hexaphenyl Nanofibers
DEFF Research Database (Denmark)
Balzer, Frank; Al-Shamery, Katharina; Neuendorf, Rolf
2003-01-01
measurements reveal that the nonlinear optical transition dipole moment is oriented with an angle of 75° with respect to the needles long axes. The absolute value of the macroscopic second-order susceptibility, averaged over a size distribution of p-6P nanoaggregates, is estimated to be of the order of 6...
The pressure tensor in tangential equilibria
Directory of Open Access Journals (Sweden)
F. Mottez
2004-09-01
Full Text Available The tangential equilibria are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. Such equilibria can be spatially periodic (like waves, or they can separate two regions with asymptotic uniform conditions (like MHD tangential discontinuities. It is possible to compute the velocity moments of the particle distribution function. Even in very simple cases, the pressure tensor is not isotropic and not gyrotropic. The differences between a scalar pressure and the pressure tensor derived in the frame of the Maxwell-Vlasov theory are significant when the gradient scales are of the order of the Larmor radius; they concern mainly the ion pressure tensor.
Tensor calculus for engineers and physicists
de Souza Sánchez Filho, Emil
2016-01-01
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...
Spectral analysis of the full gravity tensor
Rummel, R.; van Gelderen, M.
1992-10-01
It is shown that, when the five independent components of the gravity tensor are grouped into (Gamma-zz), (Gamma-xz, Gamma-yz), and (Gamma-xx - Gamma-yy, 2Gamma-xy) sets and expanded into an infinite series of pure-spin spherical harmonic tensors, it is possible to derive simple eigenvalue connections between these three sets and the spherical harmonic expansion of the gravity potential. The three eigenvalues are (n + 1)(n + 2), -(n + 2) sq rt of n(n + 1), and sq rt of (n - 1)n(n + 1)(n + 2). The joint ESA and NASA Aristoteles mission is designed to measure with high precision the tensor components Gamma-zz, Gamma-yz, and Gamma-yy, which will make it possible to determine the global gravity field in six months time with a high precision.
Carrozza, Sylvain
2015-01-01
We define in this paper a class of three indices tensor models, endowed with $O(N)^{\\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the $U(N)$ invariant models. We first exhibit the existence of a large $N$ expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large $N$ expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
Carrozza, Sylvain; Tanasa, Adrian
2016-08-01
We define in this paper a class of three-index tensor models, endowed with {O(N)^{⊗ 3}} invariance (N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U(N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
Inflatonic baryogenesis with large tensor mode
Directory of Open Access Journals (Sweden)
Naoyuki Takeda
2015-06-01
Full Text Available We consider a complex inflaton field with a CP asymmetric term for its potential. This CP asymmetric term produces the global charge of the inflaton after inflation. With the assignment of the baryon number to the inflaton, the baryon asymmetry of the universe is produced by inflaton's decay. In addition to this, the U(1 breaking term modulates the curvature of the inflaton radial direction depending on its phase, which affects the tensor-to-scalar ratio. In this paper, we have studied the relation between the baryon asymmetry and the tensor-to-scalar ratio, then verified that the future CMB observation could test this baryogenesis scenario with large tensor modes.
Quantum Fluctuations Of The Stress Tensor
Wu, C
2002-01-01
Quantum fluctuations of the stress tensor are important in many branches of physics, including the study of the validity of semiclassical gravity and the backreaction problem in stochastic semiclassical gravity. The geometry fluctuations induced by stress tensor fluctuations are important to understand quantum gravity and the problem of lightcone fluctuations. Stress tensor fluctuations also hold the key to understand fundamental physical effects like quantum fluctuations of radiation pressure, and that is crucial to the sensitivity of interferometers and the limitations on the detection of gravitational waves. Even the wave-particle duality of light can be better understood by the study of quantum fluctuations of thermal radiation. It is well known in quantum field theory that the expectation value of the energy density, which contains quadratic field operators (e.g. E2 and B2 in the electromagnatic field case), is divergent and can be renormalized simply by normal ordering, which is subtracting out the vac...
List Decoding Tensor Products and Interleaved Codes
Gopalan, Parikshit; Raghavendra, Prasad
2008-01-01
We design the first efficient algorithms and prove new combinatorial bounds for list decoding tensor products of codes and interleaved codes. We show that for {\\em every} code, the ratio of its list decoding radius to its minimum distance stays unchanged under the tensor product operation (rather than squaring, as one might expect). This gives the first efficient list decoders and new combinatorial bounds for some natural codes including multivariate polynomials where the degree in each variable is bounded. We show that for {\\em every} code, its list decoding radius remains unchanged under $m$-wise interleaving for an integer $m$. This generalizes a recent result of Dinur et al \\cite{DGKS}, who proved such a result for interleaved Hadamard codes (equivalently, linear transformations). Using the notion of generalized Hamming weights, we give better list size bounds for {\\em both} tensoring and interleaving of binary linear codes. By analyzing the weight distribution of these codes, we reduce the task of boundi...
Codazzi Tensors with Two Eigenvalue Functions
Merton, Gabe
2011-01-01
This paper addresses a gap in the classifcation of Codazzi tensors with exactly two eigenfunctions on a Riemannian manifold of dimension three or higher. Derdzinski proved that if the trace of such a tensor is constant and the dimension of one of the the eigenspaces is $n-1$, then the metric is a warped product where the base is an open interval- a conclusion we will show to be true under a milder trace condition. Furthermore, we construct examples of Codazzi tensors having two eigenvalue functions, one of which has eigenspace dimension $n-1$, where the metric is not a warped product with interval base, refuting a remark in \\cite{Besse} that the warped product conclusion holds without any restriction on the trace.
Permittivity and permeability tensors for cloaking applications
Choudhury, Balamati; Jha, Rakesh Mohan
2016-01-01
This book is focused on derivations of analytical expressions for stealth and cloaking applications. An optimal version of electromagnetic (EM) stealth is the design of invisibility cloak of arbitrary shapes in which the EM waves can be controlled within the cloaking shell by introducing a prescribed spatial variation in the constitutive parameters. The promising challenge in design of invisibility cloaks lies in the determination of permittivity and permeability tensors for all the layers. This book provides the detailed derivation of analytical expressions of the permittivity and permeability tensors for various quadric surfaces within the eleven Eisenhart co-ordinate systems. These include the cylinders and the surfaces of revolutions. The analytical modeling and spatial metric for each of these surfaces are provided along with their tensors. This mathematical formulation will help the EM designers to analyze and design of various quadratics and their hybrids, which can eventually lead to design of cloakin...
Friction tensor concept for textured surfaces
Indian Academy of Sciences (India)
K R Y Simha; Anirudhan Pottirayil; Pradeep L Menezes; Satish V Kailas
2008-06-01
Directionality of grinding marks inﬂuences the coefﬁcient of friction during sliding. Depending on the sliding direction the coefﬁcient of friction varies between maximum and minimum for textured surfaces. For random surfaces without any texture the friction coefﬁcient becomes independent of the sliding direction. This paper proposes the concept of a friction tensor analogous to the heat conduction tensor in anisotropic media. This implies that there exists two principal friction coefﬁcients $\\mu_{1,2}$ analogous to the principal conductivities $k_{1,2}$. For symmetrically textured surfaces the principal directions are orthogonal with atleast one plane of symmetry. However, in the case of polished single crystalline solids in relative sliding motion, crystallographic texture controls the friction tensor.
Holographic duality from random tensor networks
Hayden, Patrick; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao
2016-01-01
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit simple models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models obey the Ryu-Takayanagi entropy formula for all boundary regions, whether connected or not, a fact closely related to known properties of the multipartite entanglement of assistance. Moreover, we find that all boundary regions faithfully encode the physics of their entire bulk entanglement wedges, not just their smaller causal wedges. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bu...
Image denoising using modified nonlinear diffusion approach
Upadhyay, Akhilesh R.; Talbar, Sanjay N.; Sontakke, Trimbak R.
2006-01-01
Partial Differential Equation (PDE) based, non-linear diffusion approaches are an effective way to denoise the images. In this paper, the work is extended to include anisotropic diffusion, where the diffusivity is a tensor valued function, which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. The diffusion tensor is a function of differential structure of the evolving image itself. Such a feedback leads to nonlinear diffusion filters. It shows improved performance in the presence of noise. The original anisotropic diffusion algorithm updates each point based on four nearest-neighbor differences, the progress of diffusion results in improved edges. In the proposed method the edges are better preserved because diffusion is controlled by the gray level differences of diagonal neighbors in addition to 4 nearest neighbors using coupled PDF formulation. The proposed algorithm gives excellent results for MRI images, Biomedical images and Fingerprint images with noise.
Energy Technology Data Exchange (ETDEWEB)
Kumar, Punith V., E-mail: drvldayal@gmail.com; Manju, M. R., E-mail: drvldayal@gmail.com; Dayal, Vijaylakshmi, E-mail: drvldayal@gmail.com [Department of Physics, Maharaja Institute of Technology, Mysore-571438, Karnataka (India)
2014-04-24
We present a comprehensive study on origin of Spin Glass (SG) property in polycrystalline La{sub 0.5}Bi{sub 0.5}MnO{sub 3} perovskite oxide using linear and higher order ac susceptibility (χ) measurements. The third order harmonic susceptibility (χ{sub 3}) vs. temperature (K) with varying magnetic fields from 0.95 to 9.45 Oe and the divergence in their χ{sub 3} (max) allows us to infer the SG behavior occurring in the sample possibly due to co-operative freezing of the spins.
Levine, G C; Cerise, J E
2012-01-01
In the United States electoral system, a candidate is elected indirectly by winning a majority of electoral votes cast by individual states, the election usually being decided by the votes cast by a small number of "swing states" where the two candidates historically have roughly equal probabilities of winning. The effective value of a swing state in deciding the election is determined not only by the number of its electoral votes but by the frequency of its appearance in the set of winning partitions of the electoral college. Since the electoral vote values of swing states are not identical, the presence or absence of a state in a winning partition is generally correlated with the frequency of appearance of other states and, hence, their effective values. We quantify the effective value of states by an {\\sl electoral susceptibility}, $\\chi_j$, the variation of the winning probability with the "cost" of changing the probability of winning state $j$. We study $\\chi_j$ for realistic data accumulated for the 201...
Orthogonal tensor invariants and the analysis of diffusion tensor magnetic resonance images.
Ennis, Daniel B; Kindlmann, Gordon
2006-01-01
This paper outlines the mathematical development and application of two analytically orthogonal tensor invariants sets. Diffusion tensors can be mathematically decomposed into shape and orientation information, determined by the eigenvalues and eigenvectors, respectively. The developments herein orthogonally decompose the tensor shape using a set of three orthogonal invariants that characterize the magnitude of isotropy, the magnitude of anisotropy, and the mode of anisotropy. The mode of anisotropy is useful for resolving whether a region of anisotropy is linear anisotropic, orthotropic, or planar anisotropic. Both tensor trace and fractional anisotropy are members of an orthogonal invariant set, but they do not belong to the same set. It is proven that tensor trace and fractional anisotropy are not mutually orthogonal measures of the diffusive process. The results are applied to the analysis and visualization of diffusion tensor magnetic resonance images of the brain in a healthy volunteer. The theoretical developments provide a method for generating scalar maps of the diffusion tensor data, including novel fractional anisotropy maps that are color encoded for the mode of anisotropy and directionally encoded colormaps of only linearly anisotropic structures, rather than of high fractional anisotropy structures.
Role of the tensor interaction in He isotopes with a tensor-optimized shell model
Myo, Takayuki; Toki, Hiroshi; Ikeda, Kiyomi
2011-01-01
We study the role of the tensor interaction in He isotopes systematically on the basis of the tensor-optimized shell model (TOSM). We use a bare nucleon-nucleon interaction AV8 obtained from nucleon-nucleon scattering data. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM+UCOM approach, we investigate the role of tensor interaction on each spectrum in He isotopes. It is found that the tensor interaction enhances the LS splitting energy observed in 5He, in which the p1/2 and p3/2 orbits play different roles on the tensor correlation. In {6,7,8}He, the low-lying states containing extra neutrons in the p3/2 orbit gain the tensor contribution. On the other hand, the excited states containing extra neutrons in the p1/2 orbit lose the tensor contribution due to the Pauli-blocking effect with the 2p2h states in the 4He core configuration.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
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. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors 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...
Vacuum stress-tensor in SSB theories
Asorey, Manuel; Ribeiro, Baltazar J; Shapiro, Ilya L
2012-01-01
The renormalized energy-momentum tensor of vacuum has been deeply explored many years ago. The main result of these studies was that such a tensor should satisfy the conservation laws which reflects the covariance of the theory in the presence of loop corrections. In view of this general result we address two important questions, namely how to implement the momentum cut-off in a covariant way and whether this general result holds in the theory with Spontaneous Symmetry Breaking. In the last case some new interesting details arise and although the calculations are more involved we show that the final result satisfies the conservation laws.
Raman Tensor Formalism for Optically Anisotropic Crystals.
Kranert, Christian; Sturm, Chris; Schmidt-Grund, Rüdiger; Grundmann, Marius
2016-03-25
We present a formalism for calculating the Raman scattering intensity dependent on the polarization configuration for optically anisotropic crystals. It can be applied to crystals of arbitrary orientation and crystal symmetry measured in normal incidence backscattering geometry. The classical Raman tensor formalism cannot be used for optically anisotropic materials due to birefringence causing the polarization within the crystal to be depth dependent. We show that in the limit of averaging over a sufficiently large scattering depth, the observed Raman intensities converge and can be described by an effective Raman tensor given here. Full agreement with experimental results for uniaxial and biaxial crystals is demonstrated.
Improving Tensor Based Recommenders with Clustering
DEFF Research Database (Denmark)
Leginus, Martin; Dolog, Peter; Zemaitis, Valdas
2012-01-01
Social tagging systems (STS) model three types of entities (i.e. tag-user-item) and relationships between them are encoded into a 3-order tensor. Latent relationships and patterns can be discovered by applying tensor factorization techniques like Higher Order Singular Value Decomposition (HOSVD),...... of the recommendations and execution time are improved and memory requirements are decreased. The clustering is motivated by the fact that many tags in a tag space are semantically similar thus the tags can be grouped. Finally, promising experimental results are presented...
Institute of Scientific and Technical Information of China (English)
TIAN Dongyan; JIN Ming; DUI Guansuo
2006-01-01
A new approach for the derivation of the principal invariants of the stretch tensor with respect to the right Cauchy Green tensor is presented in this paper. According to the definition of the derivation of tensor function, the three first-order derivatives for the principal invariants of the stretch tensor are obtained through derivation directly to the right Cauchy-Green tensor by incremental method. Then the three second-order derivatives are yielded by the derivation to the right Cauchy-Green strain tensor directly. Furthermore, an explicit expression of the tangent modulus of the general Varga material is given as an example.
Finite temperature Casimir effect in the presence of nonlinear dielectrics
Kheirandish, Fardin; Soltani, Morteza
2010-01-01
Starting from a Lagrangian, electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained and their relation to coupling functions are determined. Finally, the Casimir energy and force in the presence of a nonlinear medium at finite temperature is calculated.
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Simultaneous analysis and quality assurance for diffusion tensor imaging.
Directory of Open Access Journals (Sweden)
Carolyn B Lauzon
Full Text Available Diffusion tensor imaging (DTI enables non-invasive, cyto-architectural mapping of in vivo tissue microarchitecture through voxel-wise mathematical modeling of multiple magnetic resonance imaging (MRI acquisitions, each differently sensitized to water diffusion. DTI computations are fundamentally estimation processes and are sensitive to noise and artifacts. Despite widespread adoption in the neuroimaging community, maintaining consistent DTI data quality remains challenging given the propensity for patient motion, artifacts associated with fast imaging techniques, and the possibility of hardware changes/failures. Furthermore, the quantity of data acquired per voxel, the non-linear estimation process, and numerous potential use cases complicate traditional visual data inspection approaches. Currently, quality inspection of DTI data has relied on visual inspection and individual processing in DTI analysis software programs (e.g. DTIPrep, DTI-studio. However, recent advances in applied statistical methods have yielded several different metrics to assess noise level, artifact propensity, quality of tensor fit, variance of estimated measures, and bias in estimated measures. To date, these metrics have been largely studied in isolation. Herein, we select complementary metrics for integration into an automatic DTI analysis and quality assurance pipeline. The pipeline completes in 24 hours, stores statistical outputs, and produces a graphical summary quality analysis (QA report. We assess the utility of this streamlined approach for empirical quality assessment on 608 DTI datasets from pediatric neuroimaging studies. The efficiency and accuracy of quality analysis using the proposed pipeline is compared with quality analysis based on visual inspection. The unified pipeline is found to save a statistically significant amount of time (over 70% while improving the consistency of QA between a DTI expert and a pool of research associates. Projection of QA
Simultaneous analysis and quality assurance for diffusion tensor imaging.
Lauzon, Carolyn B; Asman, Andrew J; Esparza, Michael L; Burns, Scott S; Fan, Qiuyun; Gao, Yurui; Anderson, Adam W; Davis, Nicole; Cutting, Laurie E; Landman, Bennett A
2013-01-01
Diffusion tensor imaging (DTI) enables non-invasive, cyto-architectural mapping of in vivo tissue microarchitecture through voxel-wise mathematical modeling of multiple magnetic resonance imaging (MRI) acquisitions, each differently sensitized to water diffusion. DTI computations are fundamentally estimation processes and are sensitive to noise and artifacts. Despite widespread adoption in the neuroimaging community, maintaining consistent DTI data quality remains challenging given the propensity for patient motion, artifacts associated with fast imaging techniques, and the possibility of hardware changes/failures. Furthermore, the quantity of data acquired per voxel, the non-linear estimation process, and numerous potential use cases complicate traditional visual data inspection approaches. Currently, quality inspection of DTI data has relied on visual inspection and individual processing in DTI analysis software programs (e.g. DTIPrep, DTI-studio). However, recent advances in applied statistical methods have yielded several different metrics to assess noise level, artifact propensity, quality of tensor fit, variance of estimated measures, and bias in estimated measures. To date, these metrics have been largely studied in isolation. Herein, we select complementary metrics for integration into an automatic DTI analysis and quality assurance pipeline. The pipeline completes in 24 hours, stores statistical outputs, and produces a graphical summary quality analysis (QA) report. We assess the utility of this streamlined approach for empirical quality assessment on 608 DTI datasets from pediatric neuroimaging studies. The efficiency and accuracy of quality analysis using the proposed pipeline is compared with quality analysis based on visual inspection. The unified pipeline is found to save a statistically significant amount of time (over 70%) while improving the consistency of QA between a DTI expert and a pool of research associates. Projection of QA metrics to a low
Six-dimensional superconformal couplings of non-abelian tensor and hypermultiplets
Samtleben, Henning; Wimmer, Robert
2012-01-01
We construct six-dimensional superconformal models with non-abelian tensor and hypermultiplets. They describe the field content of (2,0) theories, coupled to (1,0) vector multiplets. The latter are part of the non-abelian gauge structure that also includes non-dynamical three- and four-forms. The hypermultiplets are described by gauged nonlinear sigma models with a hyper-Kaehler cone target space. We also address the question of constraints in these models and show that their resolution requires the inclusion of abelian factors. These provide couplings that were previously considered for anomaly cancellations with abelian tensor multiplets and resulted in the selection of ADE gauge groups.
Voxel-wise comparisons of the morphology of diffusion tensors across groups of experimental subjects
DEFF Research Database (Denmark)
Bansal, Ravi; Staib, Lawrence H; Plessen, Kerstin J;
2007-01-01
and eigenvectors that create the 3D morphologies of DTs. We present a mathematical framework that permits the direct comparison across groups of mean eigenvalues and eigenvectors of individual DTs. We show that group-mean eigenvalues and eigenvectors are multivariate Gaussian distributed, and we use the Delta...... method to compute their approximate covariance matrices. Our results show that the theoretically computed mean tensor (MT) eigenvectors and eigenvalues match well with their respective true values. Furthermore, a comparison of synthetically generated groups of DTs highlights the limitations of using FA...... neuropsychiatric illnesses. Comparisons of tensor morphology across groups have typically been performed on scalar measures of diffusivity, such as Fractional Anisotropy (FA) rather than directly on the complex 3D morphologies of DTs. Scalar measures, however, are related in nonlinear ways to the eigenvalues...
Liu, Wenyuan; Wang, Chao; Li, Yanbin; Lao, Yuyang; Han, Yongjian; Guo, Guang-Can; Zhao, Yong-Hua; He, Lixin
2015-03-01
Tensor network states (TNS) methods combined with the Monte Carlo (MC) technique have been proven a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling technique, by mapping the energy function of the TNS to that of a classical mechanical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg J1-J2 model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.
Tensor Fields in Relativistic Quantum Mechanics
Dvoeglazov, Valeriy V
2015-01-01
We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.
Radiation Forces and Torques without Stress (Tensors)
Bohren, Craig F.
2011-01-01
To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…
Holographic coherent states from random tensor networks
Qi, Xiao-Liang; Yang, Zhao; You, Yi-Zhuang
2017-08-01
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we generalize the random tensor network approach to allow quantum superposition of different spatial geometries. We setup a framework in which all possible bulk spatial geometries, characterized by weighted adjacient matrices of all possible graphs, are mapped to the boundary Hilbert space and form an overcomplete basis of the boundary. We name such an overcomplete basis as holographic coherent states. A generic boundary state can be expanded in this basis, which describes the state as a superposition of different spatial geometries in the bulk. We discuss how to define distinct classical geometries and small fluctuations around them. We show that small fluctuations around classical geometries define "code subspaces" which are mapped to the boundary Hilbert space isometrically with quantum error correction properties. In addition, we also show that the overlap between different geometries is suppressed exponentially as a function of the geometrical difference between the two geometries. The geometrical difference is measured in an area law fashion, which is a manifestation of the holographic nature of the states considered.
Quantum tensor product structures are observable induced.
Zanardi, Paolo; Lidar, Daniel A; Lloyd, Seth
2004-02-13
It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are then relative and observable induced. We develop a general algebraic framework aimed to formalize this concept.
Introduction to vector and tensor analysis
Wrede, Robert C
1972-01-01
A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
Pomeron as a Reggeized Tensor Glueball
Institute of Scientific and Technical Information of China (English)
MA Wei-Xing; A.W.Thomas; SHEN Peng-Nian; ZHOU Li-Juan
2001-01-01
We study gluonic content of the pomeron and propose that the pomeron could be a reggeized tensor glueball ζ(2230) with quantum numbers IG JPc = 0+2++.This conjecture is examined in high energy proton-proton elastic scattering,and the calculations lend a favorable support to our physical idea.``
Dark energy in scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Moeller, J.
2007-12-15
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
The magnetic stress tensor in magnetized matter
Espinosa, Olivier R; Espinosa, Olivier; Reisenegger, Andreas
2003-01-01
We derive the form of the magnetic stress tensor in a completely general, stationary magnetic medium, with an arbitrary magnetization field $vec M(vec r)$ and free current density $vec j(vec r)$. We start with the magnetic force density $vec f$ acting on a matter element, modelled as a collection of microscopic magnetic dipoles in addition to the free currents. We show that there is a unique tensor ${bf T}$ quadratic in the magnetic flux density $vec B(vec r)$ and the magnetic field $vec H(vec r)=vec B-4pivec M$ whose divergence is $nablacdot{bf T}=vec f$. In the limit $vec M=0$, the well-known vacuum magnetic stress tensor is recovered. However, the general form of the tensor is asymmetric, leading to a divergent angular acceleration for matter elements of vanishing size. We argue that this is not inconsistent, because it occurs only if $vec M$ and $vec B$ are not parallel, in which case the macroscopic field does indeed exert a torque on each of the microscopic dipoles, so this state is only possible if the...
Visualization and processing of tensor fields
Weickert, Joachim
2007-01-01
Presents information on the visualization and processing of tensor fields. This book serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as a textbook for specialized classes and seminars for graduate and doctoral students.
Primordial tensor modes from quantum corrected inflation
DEFF Research Database (Denmark)
Joergensen, Jakob; Sannino, Francesco; Svendsen, Ole
2014-01-01
. Finally we confront these theories with the Planck and BICEP2 data. We demonstrate that the discovery of primordial tensor modes by BICEP2 require the presence of sizable quantum departures from the $\\phi^4$-Inflaton model for the non-minimally coupled scenario which we parametrize and quantify. We...
Tensors, differential forms, and variational principles
Lovelock, David
1989-01-01
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.
Weinberg's Approach and Antisymmetric Tensor Fields
Dvoeglazov, V V
2002-01-01
We extend the previous series of articles \\cite{HPA} devoted to finding mappings between the Weinberg-Tucker-Hammer formalism and antisymmetric tensor fields. Now we take into account solutions of different parities of the Weinberg-like equations. Thus, the Proca, Duffin-Kemmer and Bargmann-Wigner formalisms are generalized.
Radiation Forces and Torques without Stress (Tensors)
Bohren, Craig F.
2011-01-01
To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…
Positivity of linear maps under tensor powers
Energy Technology Data Exchange (ETDEWEB)
Müller-Hermes, Alexander, E-mail: muellerh@ma.tum.de; Wolf, Michael M., E-mail: m.wolf@tum.de [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Reeb, David, E-mail: reeb.qit@gmail.com [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Institute for Theoretical Physics, Leibniz Universität Hannover, 30167 Hannover (Germany)
2016-01-15
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task.
Tensors in image processing and computer vision
De Luis García, Rodrigo; Tao, Dacheng; Li, Xuelong
2009-01-01
Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the developments in this branch of signal processing, offering research and discussions by experts in the area. It is suitable for advanced students working in the area of computer vision and image processing.
Tensor Squeezed Limits and the Higuchi Bound
Bordin, Lorenzo; Mirbabayi, Mehrdad; Noreña, Jorge
2016-01-01
We point out that tensor consistency relations-i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum-are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: De Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor con- sistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) Graviton exchange contribution to the scalar four-point function; (b) Quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background...
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 correlations in nuclei and exlusive electron scattering
Ryckebusch, J; Van Nespen, W; Debruyne, D
2000-01-01
The effect of tensor nucleon-nucleon correlations upon exclusive and semi-exclusive electronuclear reactions is studied. Differential cross sections for the semi-exclusive ^{16}O(e,e'p) and exclusive ^{16}O(e,e'pn) processes are computed by explicitly evaluating the dynamical electromagnetic coupling to a tensor correlated nucleon pair. In both reaction channels the tensor correlations contribute in a very substantial way. Tensor correlations are found to generate more electronuclear strength than central Jastrow correlations do.
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-03-05
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Conductivity tensor mapping of the human brain using diffusion tensor MRI
Tuch, David S.; Wedeen, Van J.; Dale, Anders M.; George, John S.; Belliveau, John W.
2001-09-01
Knowledge of the electrical conductivity properties of excitable tissues is essential for relating the electromagnetic fields generated by the tissue to the underlying electrophysiological currents. Efforts to characterize these endogenous currents from measurements of the associated electromagnetic fields would significantly benefit from the ability to measure the electrical conductivity properties of the tissue noninvasively. Here, using an effective medium approach, we show how the electrical conductivity tensor of tissue can be quantitatively inferred from the water self-diffusion tensor as measured by diffusion tensor magnetic resonance imaging. The effective medium model indicates a strong linear relationship between the conductivity and diffusion tensor eigenvalues (respectively, σ and d) in agreement with theoretical bounds and experimental measurements presented here (σ/d ≈ 0.844 ± 0.0545 S·s/mm3, r2 = 0.945). The extension to other biological transport phenomena is also discussed.
Tensor algebra and tensor analysis for engineers with applications to continuum mechanics
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.
Gauge theories of gravity: the nonlinear framework
Tiemblo, A
2004-01-01
Nonlinear realizations of spacetime groups are presented as a versatile mathematical tool providing a common foundation for quite different formulations of gauge theories of gravity. We apply nonlinear realizations in particular to both the Poincar\\'e and the affine group in order to develop Poincar\\'e gauge theory (PGT) and metric-affine gravity (MAG) respectively. Regarding PGT, two alternative nonlinear treatments of the Poincar\\'e group are developed, one of them being suitable to deal with the Lagrangian and the other one with the Hamiltonian version of the same gauge theory. We argue that our Hamiltonian approach to PGT is closely related to Ashtekar's approach to gravity. On the other hand, a brief survey on MAG clarifies the role played by the metric--affine metric tensor as a Goldsone field. All gravitational quantities in fact --the metric as much as the coframes and connections-- are shown to acquire a simple gauge--theoretical interpretation in the nonlinear framework.
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.
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...
The operator tensor formulation of quantum theory.
Hardy, Lucien
2012-07-28
In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation (e.g. B(b(2)a(3))(a(1))) can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. The operation B(b(2)a(3))(a(1)) has one system of type a inputted, and one system of type b and one system of type a outputted. We can wire together operations to form circuits, for example, A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Each repeated integer label here denotes a wire connecting an output to an input of the same type. As each operation in a circuit has an outcome associated with it, a circuit represents a set of outcomes that can happen in a run of the experiment. In the operator tensor formulation of quantum theory, each operation corresponds to an operator tensor. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator tensor B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator tensors as in Prob(A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3))) = Â(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Repeated integer labels indicate that we multiply in the associated subspace and then take the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
Multidimensional seismic data reconstruction using tensor analysis
Kreimer, Nadia
Exploration seismology utilizes the seismic wavefield for prospecting oil and gas. The seismic reflection experiment consists on deploying sources and receivers in the surface of an area of interest. When the sources are activated, the receivers measure the wavefield that is reflected from different subsurface interfaces and store the information as time-series called traces or seismograms. The seismic data depend on two source coordinates, two receiver coordinates and time (a 5D volume). Obstacles in the field, logistical and economical factors constrain seismic data acquisition. Therefore, the wavefield sampling is incomplete in the four spatial dimensions. Seismic data undergoes different processes. In particular, the reconstruction process is responsible for correcting sampling irregularities of the seismic wavefield. This thesis focuses on the development of new methodologies for the reconstruction of multidimensional seismic data. This thesis examines techniques based on tensor algebra and proposes three methods that exploit the tensor nature of the seismic data. The fully sampled volume is low-rank in the frequency-space domain. The rank increases when we have missing traces and/or noise. The methods proposed perform rank reduction on frequency slices of the 4D spatial volume. The first method employs the Higher-Order Singular Value Decomposition (HOSVD) immersed in an iterative algorithm that reinserts weighted observations. The second method uses a sequential truncated SVD on the unfoldings of the tensor slices (SEQ-SVD). The third method formulates the rank reduction problem as a convex optimization problem. The measure of the rank is replaced by the nuclear norm of the tensor and the alternating direction method of multipliers (ADMM) minimizes the cost function. All three methods have the interesting property that they are robust to curvature of the reflections, unlike many reconstruction methods. Finally, we present a comparison between the methods
Studies of Second Order Optical Nonlinearities of 4-Aminobenzophenone (ABP) Single Crystal Films
Bhowmik, Achintya; Thakur, Mrinal
1998-03-01
Specific organic materials exhibit very high second order optical susceptibilities. Growth of single crystal films of these materials and characterization of nonlinear optical properties are necessary for implementation of device applications. We have grown large-area films ( 1 cm^2 area, 4 μm thick) of ABP by a modification of the shear method. Single crystal nature of the films was confirmed by polarized optical microscopy. X-ray diffraction analysis showed a [100] surface orientation. The absorption spectra revealed transparency from 390 nm to 1940 nm. Significant elements of the second order optical susceptibility tensor were measured by detailed SHG experiments using a Nd:YAG laser (1064 nm, 100 ps, 82 MHz). Second-harmonic power was measured using lock-in detection with carefully selected polarization conditions while the film was rotated about the propagation direction. Using LiNbØas the reference, d-coefficients of ABP were found to be d_23=7.2 pm/V and d_22=0.7 pm/V. Type-I and type-II phase-matching directions were identified on the film by analyzing the optical indicatrix surfaces at fundamental and second-harmonic frequencies.
A preliminary report on the development of MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-07-01
We describe three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or N-way array. We present a tensor class for manipulating tensors which allows for tensor multiplication and 'matricization.' We have further added two classes for representing tensors in decomposed format: cp{_}tensor and tucker{_}tensor. We demonstrate the use of these classes by implementing several algorithms that have appeared in the literature.
On the averaging of cardiac diffusion tensor MRI data: the effect of distance function selection
Giannakidis, Archontis; Melkus, Gerd; Yang, Guang; Gullberg, Grant T.
2016-11-01
Diffusion tensor magnetic resonance imaging (DT-MRI) allows a unique insight into the microstructure of highly-directional tissues. The selection of the most proper distance function for the space of diffusion tensors is crucial in enhancing the clinical application of this imaging modality. Both linear and nonlinear metrics have been proposed in the literature over the years. The debate on the most appropriate DT-MRI distance function is still ongoing. In this paper, we presented a framework to compare the Euclidean, affine-invariant Riemannian and log-Euclidean metrics using actual high-resolution DT-MRI rat heart data. We employed temporal averaging at the diffusion tensor level of three consecutive and identically-acquired DT-MRI datasets from each of five rat hearts as a means to rectify the background noise-induced loss of myocyte directional regularity. This procedure is applied here for the first time in the context of tensor distance function selection. When compared with previous studies that used a different concrete application to juxtapose the various DT-MRI distance functions, this work is unique in that it combined the following: (i) metrics were judged by quantitative—rather than qualitative—criteria, (ii) the comparison tools were non-biased, (iii) a longitudinal comparison operation was used on a same-voxel basis. The statistical analyses of the comparison showed that the three DT-MRI distance functions tend to provide equivalent results. Hence, we came to the conclusion that the tensor manifold for cardiac DT-MRI studies is a curved space of almost zero curvature. The signal to noise ratio dependence of the operations was investigated through simulations. Finally, the ‘swelling effect’ occurrence following Euclidean averaging was found to be too unimportant to be worth consideration.
Third-order susceptibility of gold for ultrathin layers
DEFF Research Database (Denmark)
Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei
2016-01-01
This Letter presents an experimental study of nonlinear plasmonic effects in gold-stripe waveguides. The optical characterization is performed by a picosecond laser and reveals two nonlinear effects related to propagation of long-range surface plasmon polaritons: nonlinear power transmission...... of plasmonic modes and spectral broadening of plasmonic modes. The experimental values of the third-order susceptibility of the gold layers are extracted. They exhibit a clear dependence on layer thickness. (C) 2016 Optical Society of America...
Extended intrinsic mean spin tensor for turbulence modelling in non-inertial frame of reference
Institute of Scientific and Technical Information of China (English)
HUANG Yu-ning; MA Hui-yang
2008-01-01
We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference.It is described by the Euclidean group of transformations and,in particular,its significance and importance in the approach of the algebraic Reynolds stress modelling,such as in a nonlinear K-εmodel.To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling,we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data.Our results and analysis indicate that,only if the deficiencies of these models and the like be well understood and properly corrected,may in the near future,more sophisticated nonlinear K-ε models be 0eveloped to better predict complex turbulent flows in a non-inertial frame of reference.
On some properties of nonnegative weakly irreducible tensors
Yang, Yuning
2011-01-01
In this paper, we mainly focus on how to generalize some conclusions from \\emph{nonnegative irreducible tensors} to \\emph{nonnegative weakly irreducible tensors}. To do so, a basic lemma as Lemma 3.1 of \\cite{s11} is proven using new tools. First, we define the stochastic tensor. Then we show that every nonnegative weakly irreducible tensor with spectral radius be 1 is diagonally similar to a unique weakly irreducible stochastic tensor. Based on it, we prove some important lemmas, which help us to generalize the results.
Testing gravity theories using tensor perturbations
Lin, Weikang; Ishak, Mustapha
2016-12-01
Primordial gravitational waves constitute a promising probe of the very early Universe and the laws of gravity. We study in this work changes to tensor-mode perturbations that can arise in various proposed modified gravity theories. These include additional friction effects, nonstandard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically motivated parametrization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r =0.01 , we find that an additional friction of 3.5-4.5% compared to GR will be detected at 3 -σ by these experiments, while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be by 5-15% different from the speed of light for detection. We find that the minimum detectable graviton mass is about 7.8 - 9.7 ×10-33 eV , which is of the same order of magnitude as the graviton mass that allows massive gravity theories to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation using our parametrization. We find that, in addition to being related to r , the tensor spectral index would be related to the friction parameter ν0 by nT=-3 ν0-r /8 . Assuming that the friction parameter is unchanged throughout the history of the Universe, and that ν0 is much larger than r , the future experiments considered here will be able to distinguish this modified-gravity consistency relation from the standard inflation consistency relation, and thus can be used as a further test of modified gravity. In summary, tensor-mode perturbations and cosmic-microwave-background B
Exploring the Tensor Networks/AdS Correspondence
Bhattacharyya, Arpan; Hung, Ling-Yan; Liu, Si-Nong
2016-01-01
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. Study- ing 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, the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admits 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 ...
Tensors the mathematics of relativity and continuum mechanics
Das, A J
2007-01-01
Tensors: The Mathematics of Relativity Theory and Continuum Mechanics, by Anadijiban Das, emerged from courses taught over the years at the University College of Dublin, Carnegie-Mellon University and Simon Fraser University. This book will serve readers well as a modern introduction to the theories of tensor algebra and tensor analysis. Throughout Tensors, examples and worked-out problems are furnished from the theory of relativity and continuum mechanics. Topics covered in this book include, but are not limited to: -tensor algebra -differential manifold -tensor analysis -differential forms -connection forms -curvature tensors -Riemannian and pseudo-Riemannian manifolds The extensive presentation of the mathematical tools, examples and problems make the book a unique text for the pursuit of both the mathematical relativity theory and continuum mechanics.
A gravito-electromagnetic analogy based on tidal tensors
Costa, L F; Herdeiro, Carlos A. R.
2006-01-01
We propose a new approach to a physical analogy between General Relativity and Electromagnetism, based on comparing tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, from which the regime of validity of the analogy becomes manifest. Two explicit realisations of the analogy are given. The first one matches linearised gravitational tidal tensors to exact electromagnetic tidal tensors in Minkwoski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultra-stationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. We then establish a new proof for a class of tensor identities that define invariants of the type $\\vec{E}^2-\\vec{B}^2$ and $\\vec{E}\\cdot\\vec{B}$, and we exhibit the invariants built from tidal tensors in both gravity and electromagnetism. We contrast our approach with the two gravito-electromagnetic analogies commonly found in the literature, which are reviewed...
Algebraic and computational aspects of real tensor ranks
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...
DEFF Research Database (Denmark)
Lundell, Hans Magnus Henrik; Barthelemy, Dorothy; Biering-Sørensen, Fin
2013-01-01
Diffusion tensor imaging has been used in a number of spinal cord studies, but severe distortions caused by susceptibility induced field inhomogeneities limit its applicability to investigate small volumes within acceptable acquisition times. A way to evaluate image distortions is to map the poin...... artifacts or in high-field imaging settings where off-resonance effects are pronounced. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc....
Model of anisotropic nonlinearity in self-defocusing photorefractive media.
Barsi, C; Fleischer, J W
2015-09-21
We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.
Extended Scalar-Tensor Theories of Gravity
Crisostomi, Marco; Tasinato, Gianmassimo
2016-01-01
We determine new consistent scalar-tensor theories of gravity, with potentially interesting cosmological applications. We develop a general method to find the conditions for the existence of a primary constraint, which is necessary to prevent the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators in the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.
Oscillating Chiral Tensor Spectrum from Axionic Inflation
Obata, Ippei
2016-01-01
We study the axionic inflation with a modulated potential and examine if the primordial tensor power spectrum exhibits oscillatory feature, which is testable with future space-based gravitational wave experiments such as DECIGO and BBO. In the case of the single-field axion monodromy inflation, it turns out that it is difficult to detect the oscillation in the spectrum due to suppression of the sub-Planckian decay constant of axion. On the other hand, in the case of aligned chromo-natural inflation where the axion is coupled to a SU(2) gauge field, it turns out that the sizable oscillation in the tensor spectrum can occur due to the enhancement of chiral gravitational waves sourced by the gauge field. We expect that this feature will be a new probe to axion phenomenologies in early universe through the chiral gravitational waves.
Tensor modes on the string theory landscape
Energy Technology Data Exchange (ETDEWEB)
Westphal, Alexander
2012-06-15
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Tensor modes on the string theory landscape
Westphal, Alexander
2012-01-01
We attempt an estimate for the distribution of the tensor mode fraction $r$ over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Scalable Tensor Factorizations with Missing Data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.
2010-01-01
The problem of missing data is ubiquitous in domains such as biomedical signal processing, network trac analysis, bibliometrics, social network analysis, chemometrics, computer vision, and communication networks|all domains in which data collection is subject to occasional errors. Moreover......, these data sets can be quite large and have more than two axes of variation, e.g., sender, receiver, time. Many applications in those domains aim to capture the underlying latent structure of the data; in other words, they need to factorize data sets with missing entries. If we cannot address the problem...... 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...
Damage Tensor Analysis on Regional Seismic Status
Institute of Scientific and Technical Information of China (English)
Zhong Jimao; Cheng Wanzheng
2006-01-01
In this paper, we researched the regional seismic status by using theories of the Damage Mechanics. The macroscopic damage status of the earth crust block, which is caused by earthquake fracture, is described with several concepts-the damage degree, the damage rate and the strain rate. In the earthquake process, the average strain rate of the studied block is equal to the sum of all seismic moment tensors of the earthquakes taking place in unit time and physical volume. To describe the anisotropy of microdamage of the crust block, we use the damage tensor that is expressed in the fissure density. By means of the transformation from the focal coordinate system to the observation system, we obtained the external normal vector of the focal fault plane expressed in its observation system and obtained the macrodamage degree of the researched block, which is calculated in dyadic. This provides a new analysis method for recognizing the underground damage status and the stress status.
Fermionic orbital optimisation in tensor network states
Krumnow, C; Eisert, J
2015-01-01
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems, specifically in the context of quantum chemistry. A new freedom arising in such non-local fermionic systems is the choice of orbitals, it being far from clear what choice of fermionic orbitals to make. In this work, we propose a way to overcome this challenge. We suggest a method intertwining the optimisation over matrix product states with suitable fermionic Gaussian mode transformations, hence bringing the advantages of both approaches together. The described algorithm generalises basis changes in the spirit of the Hartree-Fock methods to matrix-product states, and provides a black box tool for basis optimisations in tensor network methods.
Review of Scalars, Vectors, Tensors, and Dyads
Schnack, Dalton D.
In MHD, we will deal with relationships between quantities such as the magnetic field and the velocity that have both magnitude and direction. These quantities are examples of vectors (or, as we shall soon see, pseudovectors). The basic concepts of scalar and vector quantities are introduced early in any scientific education. However, to formulate the laws of MHD precisely, it will be necessary to generalize these ideas and to introduce the less familiar concepts of matrices, tensors, and dyads. The ability to understand and manipulate these abstract mathematical concepts is essential to learning MHD. Therefore, for the sake of both reference and completeness, this lecture is about the mathematical properties of scalars, vectors, matrices, tensors, and dyads. If you are already an expert, or think you are, please skip class and go on to Lecture 3. You can always refer back here if needed!
Scalable tensor factorizations for incomplete data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.
2011-01-01
The problem of incomplete data—i.e., data with missing or unknown values—in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how...... 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......-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process....
Scalable Tensor Factorizations with Missing Data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.
2010-01-01
The problem of missing data is ubiquitous in domains such as biomedical signal processing, network trac analysis, bibliometrics, social network analysis, chemometrics, computer vision, and communication networks|all domains in which data collection is subject to occasional errors. Moreover......, these data sets can be quite large and have more than two axes of variation, e.g., sender, receiver, time. Many applications in those domains aim to capture the underlying latent structure of the data; in other words, they need to factorize data sets with missing entries. If we cannot address the problem...... 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...
Derived Metric Tensors for Flow Surface Visualization.
Obermaier, H; Joy, K I
2012-12-01
Integral flow surfaces constitute a widely used flow visualization tool due to their capability to convey important flow information such as fluid transport, mixing, and domain segmentation. Current flow surface rendering techniques limit their expressiveness, however, by focusing virtually exclusively on displacement visualization, visually neglecting the more complex notion of deformation such as shearing and stretching that is central to the field of continuum mechanics. To incorporate this information into the flow surface visualization and analysis process, we derive a metric tensor field that encodes local surface deformations as induced by the velocity gradient of the underlying flow field. We demonstrate how properties of the resulting metric tensor field are capable of enhancing present surface visualization and generation methods and develop novel surface querying, sampling, and visualization techniques. The provided results show how this step towards unifying classic flow visualization and more advanced concepts from continuum mechanics enables more detailed and improved flow analysis.
Entanglement, Tensor Networks and Black Hole Horizons
Molina-Vilaplana, Javier
2014-01-01
We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization flow given by the class of tensor networks known as the Multi Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an additional entanglement structure at the length scale fixed by the temperature. The network comprises two copies of a MERA circuit with a fixed number of layers and a pure matrix product state which joins both copies by entangling the infrared degrees of freedom of both MERA networks. The entanglement distribution within this bridge state defines reduced density operators on both sides which cause analogous effects to the presence of a black hole horizon when computing the entanglement entropy at finite temperature in the AdS/CFT correspondence. The entanglement and correlations during the thermalization process of a system after a quantum q...
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Symmetry of the polarizability tensors for molecules with D 5h and I h symmetry
Ramaniah, Lavanya M.; Nair, Selvakumar V.; Rustagi, Kailash C.
1993-02-01
We present the spatial symmetry relations between the components of the linear and nonlinear electric dipolar polarizability tensors for the symmetry groups of C 60 and C 70 molecules viz., I h and D 5h. We show that the first hyperpolarizability β of C 7 0 vanishes although the molecule is not inversion symmetric. The second hyperpolarizability γ for C 60 has the same structure as that for an isotropic system. Based on these results, optical harmonic generation measurements to study the inter-molecular bonding in C 60 and C 70 crystals are suggested.
Directory of Open Access Journals (Sweden)
Guoliang Zhao
2013-01-01
Full Text Available This paper proposes new methodologies for the design of adaptive integral-sliding mode control. A tensor product model transformation based adaptive integral-sliding mode control law with respect to uncertainties and perturbations is studied, while upper bounds on the perturbations and uncertainties are assumed to be unknown. The advantage of proposed controllers consists in having a dynamical adaptive control gain to establish a sliding mode right at the beginning of the process. Gain dynamics ensure a reasonable adaptive gain with respect to the uncertainties. Finally, efficacy of the proposed controller is verified by simulations on an uncertain nonlinear system model.
Zhao, Guoliang; Sun, Kaibiao; Li, Hongxing
2013-01-01
This paper proposes new methodologies for the design of adaptive integral-sliding mode control. A tensor product model transformation based adaptive integral-sliding mode control law with respect to uncertainties and perturbations is studied, while upper bounds on the perturbations and uncertainties are assumed to be unknown. The advantage of proposed controllers consists in having a dynamical adaptive control gain to establish a sliding mode right at the beginning of the process. Gain dynamics ensure a reasonable adaptive gain with respect to the uncertainties. Finally, efficacy of the proposed controller is verified by simulations on an uncertain nonlinear system model.
Pressure Tensor of Nanoscopic Liquid Drops
Directory of Open Access Journals (Sweden)
José G. Segovia-López
2015-04-01
Full Text Available This study describes the structure of an inhomogeneous fluid of one or several components that forms a spherical interface. Using the stress tensor of Percus–Romero, which depends on the density of one particle and the intermolecular potential, it provides an analytical development leading to the microscopic expressions of the pressure differences and the interfacial properties of both systems. The results are compared with a previous study and agree with the description of the mean field.
Inflation in anisotropic scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Pimentel, L.O.; Stein-Schabes, J.
1989-01-05
The existence of an inflationary phase in anisotropic scalar-tensor theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a non-trivial potential. We then use the explicit form of the potential and the no hair theorem to conclude that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.
Inflation in anisotropic scalar-tensor theories
Pimentel, Luis O.; Stein-Schabes, Jaime
1988-01-01
The existence of an inflationary phase in anisotropic Scalar-Tensor Theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a nontrivial potential. The explicit form of the potential is then used and the No Hair Theorem concludes that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.
Institute of Scientific and Technical Information of China (English)
HUANG YuNing; MA HuiYang; XU JingLei
2008-01-01
Modelling the turbulent flows in non-inertial frames of reference has long been a challenging task. Recently we introduced the notion of the "extended intrinsic mean spin tensor" for turbulence modelling and pointed out that, when applying the Reynolds stress models developed in the inertial frame of reference to model-ling the turbulence in a non-inertial frame of reference, the mean spin tensor should be replaced by the extended intrinsic mean spin tensor to correctly account for the rotation effects induced by the non-inertial frame of reference, to conform in phys-ics with the Reynolds stress transport equation. To exemplify the approach, we conducted numerical simulations of the fully developed turbulent channel flow in a rotating frame of reference by employing four non-linear K-εmodels. Our numerical results based on this approach at a wide range of Reynolds and Rossby numbers evince that, among the models tested, the non-linear K-ε model of Huang and Ma and the non-linear K-ε model of Craft, Launder and Suga can better capture the rotation effects and the resulting influence on the structures of turbulence, and therefore are satisfactorily applied to dealing with the turbulent flows of practical interest in engineering. The general approach worked out in this paper is also ap-plied to the second-moment closure and the large-eddy simulation of turbulence.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Modelling the turbulent flows in non-inertial frames of reference has long been a challenging task. Recently we introduced the notion of the "extended intrinsic mean spin tensor" for turbulence modelling and pointed out that, when applying the Reynolds stress models developed in the inertial frame of reference to model-ling the turbulence in a non-inertial frame of reference, the mean spin tensor should be replaced by the extended intrinsic mean spin tensor to correctly account for the rotation effects induced by the non-inertial frame of reference, to conform in phys-ics with the Reynolds stress transport equation. To exemplify the approach, we conducted numerical simulations of the fully developed turbulent channel flow in a rotating frame of reference by employing four non-linear K-ε models. Our numerical results based on this approach at a wide range of Reynolds and Rossby numbers evince that, among the models tested, the non-linear K-ε model of Huang and Ma and the non-linear K-ε model of Craft, Launder and Suga can better capture the rotation effects and the resulting influence on the structures of turbulence, and therefore are satisfactorily applied to dealing with the turbulent flows of practical interest in engineering. The general approach worked out in this paper is also ap-plied to the second-moment closure and the large-eddy simulation of turbulence.
Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
Cui, Zhu-Fang; Shi, Yuan-Mei; Wang, Yong-Long; Zong, Hong-Shi
2015-01-01
The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial-vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson-Schwinger equations.
Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
Energy Technology Data Exchange (ETDEWEB)
Cui, Zhu-Fang, E-mail: phycui@nju.edu.cn [Department of Physics, Nanjing University, Nanjing 210093 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing, 100190 (China); Hou, Feng-Yao [Institute of Theoretical Physics, CAS, Beijing 100190 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing, 100190 (China); Shi, Yuan-Mei [Department of Physics, Nanjing University, Nanjing 210093 (China); Department of Physics and Electronic Engineering, Nanjing Xiaozhuang University, Nanjing 211171 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing, 100190 (China); Wang, Yong-Long [Department of Physics, Nanjing University, Nanjing 210093 (China); Department of Physics, School of Science, Linyi University, Linyi 276005 (China); Zong, Hong-Shi, E-mail: zonghs@nju.edu.cn [Department of Physics, Nanjing University, Nanjing 210093 (China); Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing 210093 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing, 100190 (China)
2015-07-15
The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial–vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson–Schwinger equations.
Tensor integrand reduction via Laurent expansion
Hirschi, Valentin
2016-01-01
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem. We find that Ninja outperforms traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem which is however more limited and slower than Ninja. We considered many benchmark multi-scale processes of increasing ...
Renormalization persistency of tensor force in nuclei
Tsunoda, Naofumi; Tsukiyama, Koshiroh; Hjorth-Jensen, Morten
2011-01-01
In this work we analyze the tensor-force component of effective interactions appropriate for nuclear shell-model studies, with particular emphasis on the monopole term of the interactions. Standard nucleon-nucleon ($NN$) interactions such as AV8' and $\\chi$N$^3$LO are tailored to shell-model studies by employing $V_{low k}$ techniques to handle the short-range repulsion of the $NN$ interactions and by applying many-body perturbation theory to incorporate in-medium effects. We show, via numerical studies of effective interactions for the $sd$ and $pf$ shells, that the tensor-force contribution to the monopole term of the effective interaction is barely changed by these renormalization procedures, resulting in almost the same monopole term as the one of the bare $NN$ interactions. We propose to call this feature {\\it Renormalization Persistency} of the tensor force, as it is a remarkable property of the renormalization and should have many interesting consequences in nuclear systems. For higher multipole terms,...
Tensors, BICEP2, prior dependence, and dust
Cortês, Marina; Parkinson, David
2014-01-01
We investigate the prior dependence on the inferred spectrum of primordial tensor perturbations, in light of recent results from BICEP2 and taking into account a possible dust contribution to polarized anisotropies. We highlight an optimized parameterization of the tensor power spectrum, and adoption of a logarithmic prior on its amplitude $A_T$, leading to results that transform more evenly under change of pivot scale. In the absence of foregrounds the tension between the results of BICEP2 and Planck drives the tensor spectral index $n_T$ to be blue-tilted in a joint analysis, which would be in contradiction to the standard inflation prediction ($n_T<0$). When foregrounds are accounted for, the BICEP2 results no longer require non-standard inflationary parameter regions. We present limits on primordial $A_T$ and $n_T$, adopting foreground scenarios put forward by Mortonson & Seljak and motivated by Planck 353 GHz observations, and assess what dust contribution leaves a detectable cosmological signal. ...
Myelin water weighted diffusion tensor imaging.
Avram, Alexandru V; Guidon, Arnaud; Song, Allen W
2010-10-15
In this study we describe our development and implementation of a magnetization transfer (MT) prepared stimulated-echo diffusion tensor imaging (DTI) technique that can be made sensitive to the microanatomy of myelin tissue. The short echo time (TE) enabled by the stimulated-echo acquisition preserves significant signal from the short T(2) component (myelin water), and the MT preparation further provides differentiating sensitization to this signal. It was found that this combined strategy could provide sufficient sensitivity in our first attempt to image myelin microstructure. Compared to the diffusion tensor derived from the conventional DTI technique, the myelin water weighted (MWW) tensor has the same principal diffusion direction but exhibits a significant increase in fractional anisotropy (FA), which is mainly due to a decrease in radial diffusivity. These findings are consistent with the microstructural organization of the myelin sheaths that wrap around the axons in the white matter and therefore hinder radial diffusion. Given that many white matter diseases (e.g. multiple sclerosis) begin with a degradation of myelin microanatomy but not a loss of myelin content (e.g. loosening of the myelin sheaths), our newly implemented MWW DTI has the potential to lead to improved assessment of myelin pathology and early detection of demyelination.
Testing gravity theories using tensor perturbations
Lin, Weikang
2016-01-01
Primordial gravitational waves constitute a promising probe of the very-early universe and the laws of gravity. We study changes to tensor mode perturbations that can arise in various proposed modified gravity (MG) theories. These include additional friction effects, non-standard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically-motivated parameterization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor mode MG parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r=0.01, we find that an additional friction of 3.5-4.5% compared to GR will be detected at $3\\sigma$ by these experiments while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be 5-15% differen...
Irreducible Virasoro modules from tensor products
Tan, Haijun; Zhao, Kaiming
2016-04-01
In this paper, we obtain a class of irreducible Virasoro modules by taking tensor products of the irreducible Virasoro modules Ω(λ,b) with irreducible highest weight modules V(θ ,h) or with irreducible Virasoro modules Ind_{θ}(N) defined in Mazorchuk and Zhao (Selecta Math. (N.S.) 20:839-854, 2014). We determine the necessary and sufficient conditions for two such irreducible tensor products to be isomorphic. Then we prove that the tensor product of Ω(λ,b) with a classical Whittaker module is isomorphic to the module Ind_{θ, λ}({C}_{{m}}) defined in Mazorchuk and Weisner (Proc. Amer. Math. Soc. 142:3695-3703, 2014). As a by-product we obtain the necessary and sufficient conditions for the module Ind_{θ, λ}({C}_{{m}}) to be irreducible. We also generalize the module Ind_{θ, λ}({C}_{{m}}) to Ind_{θ,λ}({B}^{(n)}_{{s}}) for any non-negative integer n and use the above results to completely determine when the modules Ind_{θ,λ}({B}^{(n)}_{{s}}) are irreducible. The submodules of Ind_{θ,λ}({B}^{(n)}_{{s}}) are studied and an open problem in Guo et al. (J. Algebra 387:68-86, 2013) is solved. Feigin-Fuchs' Theorem on singular vectors of Verma modules over the Virasoro algebra is crucial to our proofs in this paper.
Effective elasticity tensor of a periodic composite
Nunan, Kevin C.; Keller, Joseph B.
THE EFFECTIVE elasticity tensor of a composite is defined to be the four-tensor C which relates the average stress to the average strain. We determine it for an array of rigid spheres centered on the points of a periodic lattice in a homogeneous isotropic elastic medium. We first express C in terms of the traction exerted on a single sphere by the medium, and then derive an integral equation for this traction. We solve this equation numerically for simple, body-centered and face-centered cubic lattices with inclusion concentrations up to 90% of the close-packing concentration. For lattices with cubic symmetry the effective elasticity tensor involves just three parameters, which we compute from the solution for the traction. We obtain approximate asymptotic formulas for low concentrations which agree well with the numerical results. We also derive asymptotic results for C at high inclusion concentrations for arbitrary lattice geometries. We find them to be in good agreement with the numerical results for cubic lattices. For low and moderate concentrations the approximate results of NEMAT- NASSERet al., also agree well with the numerical results for cubic lattices.
On Tensors, Sparsity, and Nonnegative Factorizations
Chi, Eric C
2011-01-01
Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive tensor factorization model of such data, along with appropriate algorithms and theory. To do so, we propose that the random variation is best described via a Poisson distribution, which better describes the zeros observed in the data as compared to the typical assumption of a Gaussian distribution. Under a Poisson assumption, we fit a model to observed data using the negative log-likelihood score. We present a new algorithm for Poisson tensor factorization called CANDECOMP--PARAFAC Alternating Poisson Regression (CP-APR) that is based on a majorization-minimization approach. It can be shown that CP-APR is a generalization of the Lee-Seung multiplicative updates. We show how to prevent the algorithm from converging to non-KKT points and prove convergence of CP-APR under mild con...
Scalable tensor factorizations with incomplete data.
Energy Technology Data Exchange (ETDEWEB)
Morup, Morten (Technical University of Denmark); Dunlavy, Daniel M. (Sandia National Laboratories, Albuquerque, NM); Acar, Evrim (Information Technologies Institute, Turkey); Kolda, Tamara Gibson
2010-07-01
The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how 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). In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) that uses a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical 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 x 1000 x 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process.
An $OSp$ extension of Canonical Tensor Model
Narain, Gaurav
2015-01-01
Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally constrained system with a number of first-class constraints, which have a similar algebraic structure as the constraints of the ADM formalism of general relativity. In this paper, we formulate a super-extension of CTM as an attempt to incorporate fermionic degrees of freedom. The kinematical symmetry group is extended from $O(N)$ to $OSp(N,\\tilde N)$, and the constraints are constructed so that they form a first-class constraint super-Poisson algebra. This is a straightforward super-extension, and the constraints and their algebraic structure are formally unchanged from the purely bosonic case, except for the additional signs associated to the order of the fermionic indices and dynamical variables. However, this extension of CTM leads to the existence of negative norm state...
Murg, V; Verstraete, F; Schneider, R; Nagy, P R; Legeza, Ö
2015-03-10
We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement.
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
On SL(2,R) symmetry in nonlinear electrodynamics theories
Babaei Velni, Komeil; Babaei-Aghbolagh, H.
2016-12-01
Recently, it has been observed that the Noether-Gaillard-Zumino (NGZ) identity holds order by order in α‧ expansion in nonlinear electrodynamics theories as Born-Infeld (BI) and Bossard-Nicolai (BN). The nonlinear electrodynamics theory that couples to an axion field is invariant under the SL (2 , R) duality in all orders of α‧ expansion in the Einstein frame. In this paper we show that there are the SL (2 , R) invariant forms of the energy momentum tensors of axion-nonlinear electrodynamics theories in the Einstein frame. These SL (2 , R) invariant structures appear in the energy momentum tensors of BI and BN theories at all orders of α‧ expansion. The SL (2 , R) symmetry appears in the BI and BN Lagrangians as a multiplication of Maxwell Lagrangian and a series of SL (2 , R) invariant structures.
On SL(2;R) symmetry in nonlinear electrodynamics theories
Velni, Komeil Babaei
2016-01-01
Recently, it has been observed that the Noether-Gaillard-Zumino (NGZ) identity holds order by order in $\\alpha'$ expansion in nonlinear electrodynamics theories as Born-Infeld (BI) and Bossard-Nicolai (BN). The nonlinear electrodynamics theory that couples to an axion field is invariant under the $SL(2,R)$ duality in all orders of $\\alpha'$ expansion in the Einstein frame. In this paper we show that there are the $SL(2,R)$ invariant forms of the energy momentum tensors of axion-nonlinear electrodynamics theories in the Einstein frame. These $SL(2,R)$ invariant structures appear in the energy momentum tensors of BI and BN theories at all orders of $\\alpha'$ expansion. The $SL(2,R)$ symmetry appears in the BI and BN Lagrangians as a multiplication of Maxwell Lagrangian and a series of $SL(2,R)$ invariant structures.
No Bel-Robinson Tensor for Quadratic Curvature Theories
Deser, S
2011-01-01
We attempt to generalize the familiar covariantly conserved Bel-Robinson tensor B ~ RR of GR and its recent topologically massive counterpart B ~ RDR, to quadratic curvature actions. Two very different models of current interest are examined: fourth order D=3 "new massive", and second order D>4 Gauss-Bonnet-Lovelock (GBL), gravity. On dimensional grounds, the candidates here become B ~ DRDR+RRR. For the D=3 model, there indeed exist conserved B ~ dR dR in the linearized limit. However, unlike for GR and TMG, and despite a plethora of available cubic terms, B cannot be extended to the full theory. The D>4 models are not even linearizable about flat space, since their field equations are quadratic in curvature; they also have no viable B, a fact that persists even if one includes cosmological or Einstein terms to allow linearization about the resulting dS vacua. These results are an unexpected, if hardly unique, example of non-linearization instability.
The velocity shear tensor: tracer of halo alignment
Libeskind, Noam I; Forero-Romero, Jaime; Gottlöber, Stefan; Knebe, Alexander; Steinmetz, Matthias; Klypin, Anatoly
2012-01-01
The alignment of DM halos and the surrounding large scale structure (LSS) is examined in the context of the cosmic web. Halo spin, shape and the orbital angular momentum of subhaloes is investigated relative to the LSS using the eigenvectors of the velocity shear tensor evaluated on a grid with a scale of 1 Mpc/h, deep within the non-linear regime. Knots, filaments, sheets and voids are associated with regions that are collapsing along 3, 2, 1 or 0 principal directions simultaneously. Each halo is tagged with a web classification (i.e. knot halo, filament halo, etc) according to the nature of the collapse at the halo's position. The full distribution of shear eigenvalues is found to be substantially different from that tagged to haloes, indicating that the observed velocity shear is significantly biased. We find that larger mass haloes live in regions where the shear is more isotropic, namely the expansion or collapse is more spherical. A correlation is found between the halo's shape and the eigenvectors of t...
Using Perturbation theory to reduce noise in diffusion tensor fields.
Bansal, Ravi; Staib, Lawrence H; Xu, Dongrong; Laine, Andrew F; Liu, Jun; Peterson, Bradley S
2009-08-01
We propose the use of Perturbation theory to reduce noise in Diffusion Tensor (DT) fields. Diffusion Tensor Imaging (DTI) encodes the diffusion of water molecules along different spatial directions in a positive definite, 3 x 3 symmetric tensor. Eigenvectors and eigenvalues of DTs allow the in vivo visualization and quantitative analysis of white matter fiber bundles across the brain. The validity and reliability of these analyses are limited, however, by the low spatial resolution and low Signal-to-Noise Ratio (SNR) in DTI datasets. Our procedures can be applied to improve the validity and reliability of these quantitative analyses by reducing noise in the tensor fields. We model a tensor field as a three-dimensional Markov Random Field and then compute the likelihood and the prior terms of this model using Perturbation theory. The prior term constrains the tensor field to be smooth, whereas the likelihood term constrains the smoothed tensor field to be similar to the original field. Thus, the proposed method generates a smoothed field that is close in structure to the original tensor field. We evaluate the performance of our method both visually and quantitatively using synthetic and real-world datasets. We quantitatively assess the performance of our method by computing the SNR for eigenvalues and the coherence measures for eigenvectors of DTs across tensor fields. In addition, we quantitatively compare the performance of our procedures with the performance of one method that uses a Riemannian distance to compute the similarity between two tensors, and with another method that reduces noise in tensor fields by anisotropically filtering the diffusion weighted images that are used to estimate diffusion tensors. These experiments demonstrate that our method significantly increases the coherence of the eigenvectors and the SNR of the eigenvalues, while simultaneously preserving the fine structure and boundaries between homogeneous regions, in the smoothed tensor
Component reduction in N=2 supergravity: the vector, tensor, and vector-tensor multiplets
Butter, Daniel
2012-01-01
Recent advances in curved N=2 superspace methods have rendered the component reduction of superspace actions more feasible than in the past. In this paper, we consider models involving both vector and tensor multiplets coupled to supergravity and demonstrate explicitly how component actions may be efficiently obtained. In addition, tensor multiplets coupled to conformal supergravity are considered directly within projective superspace, where their formulation is most natural. We then demonstrate how the inverse procedure -- the lifting of component results to superspace -- can simplify the analysis of complicated multiplets. We address the off-shell N=2 vector-tensor multiplet coupled to conformal supergravity with a central charge and demonstrate explicitly how its constraints and Lagrangian can be written in a simpler way using superfields.
DEFF Research Database (Denmark)
Bache, Morten; Guo, Hairun; Zhou, Binbin;
2013-01-01
We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (β-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant χ(3) cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments...... a complete list that we propose as reference of the four major cubic tensor components in BBO. We finally discuss the impact of using the cubic anisotropic response in ultrafast cascading experiments in BBO....
Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.
2016-05-01
Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator e-β H for a two-dimensional (2D) lattice system with a Hamiltonian H can be represented by a three-dimensional tensor network, the third dimension being the imaginary time (inverse temperature) β . Coarse graining the network along β results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension D . The coarse graining is performed by a tree tensor network of isometries. The isometries are optimized variationally, taking into account full tensor environment, to maximize the accuracy of the PEPO. The algorithm is applied to the isotropic quantum compass model on an infinite square lattice near a symmetry-breaking phase transition at finite temperature. From the linear susceptibility in the symmetric phase and the order parameter in the symmetry-broken phase, the critical temperature is estimated at Tc=0.0606 (4 ) J , where J is the isotropic coupling constant between S =1/2 pseudospins.
Magnetic susceptibility of the QCD vacuum in a nonlocal SU(3) PNJL model
Pagura, V P; Noguera, S; Scoccola, N N
2016-01-01
The magnetic susceptibility of the QCD vacuum is analyzed in the framework of a nonlocal SU(3) Polyakov-Nambu-Jona-Lasinio model. Considering two different model parametrizations, we estimate the values of the $u$ and $s$-quark tensor coefficients and magnetic susceptibilities and then we extend the analysis to finite temperature systems. Our numerical results are compared to those obtained in other theoretical approaches and in lattice QCD calculations.
Whittam, A J
2001-01-01
susceptibility from 26 pm/V (same film without octadecanoic acid) to 40 pm/V. This increase in the second-order susceptibility occurred even though the amount of NLO-active dye was effectively diluted by the addition of the inactive octadecanoic acid. The wavelength of the absorption maximum ranged from 346-440 nm and there was direct correlation between the susceptibilities and the transparency of the films at the harmonic wavelength. Hemicyanine dyes were synthesised, with the general formulae: - (a) C sub 1 sub 8 H sub 3 sub 7 -A sup + -[CH=CH-C sub 6 H sub 4] sub x -N(CH sub 3) sub 2 I (b) C sub 1 sub 8 H sub 3 sub 7 -A sup + -[CH=CH] sub y -C sub 6 H sub 4 -N(CH sub 3) sub 2 I where A sup + is a pyridinium or isoquinolinium acceptor, and x = 1 or 2, and y = 1 or 2. The optically nonlinear dyes were investigated via the Langmuir-Blodgett (LB) technique. The dyes all produced isotherm data, with molecular areas of 22-60 A sup 2 per molecule, which are consistent with the cross-sectional areas of the chromo...
Energy Technology Data Exchange (ETDEWEB)
Zmija, J.; Kaddouri, H. [Perpignan Univ. (France). LP2A; Majchrowski, A.; Mierczyk, Z. [Inst. of Applied Physics, MUT, Warsaw (Poland); Kityk, I.V. [Inst. of Physics Czestochowa (Poland)
2001-07-01
Acoustically induced optical second harmonic generation (SHG) and two-photon absorption (TPA) in ferroelectric Pb{sub 4.7}Ba{sub 0.3}Ge{sub 3}O{sub 11} crystals have been found. We have found that with increasing acoustical power, the SHG for YAG:Nd laser light ({lambda}=1.06 {mu}m) increases and achieves its maximum value at acoustical power density about 1.75 W/cm{sup 2}. The evaluated SHG values were 23% less comparing with {chi}{sub 222} tensor of the KDP single crystals. With decreasing temperature, the acoustically induced SHG signal strongly increases below 29 K. The maximal acoustically induced SHG has been observed at acoustical frequencies lying within the ranges 12-17 kHz, 22-23 kHz and above 26 kHz. This behavior reflects nonlinear superposition of the nonlinear optical susceptibilities stimulated by externally-induced electron-phonon anharmonicity. We have observed substantial increase of the TPA (for the acoustical power W= 1.8 W/cm{sup 2}) at high hydrostatic pressures (about 16 GPa) and low temperatures (below 16 K). This one confirms complicated influence of the electron-phonon interactions in the ferroelectrics on the observed nonlinear optical dependences. (orig.)
An introduction to tensors and group theory for physicists
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...
Reduction of noise in diffusion tensor images using anisotropic smoothing.
Ding, Zhaohua; Gore, John C; Anderson, Adam W
2005-02-01
To improve the accuracy of tissue structural and architectural characterization with diffusion tensor imaging, a novel smoothing technique is developed for reducing noise in diffusion tensor images. The technique extends the traditional anisotropic diffusion filtering method by allowing isotropic smoothing within homogeneous regions and anisotropic smoothing along structure boundaries. This is particularly useful for smoothing diffusion tensor images in which direction information contained in the tensor needs to be restored following noise corruption and preserved around tissue boundaries. The effectiveness of this technique is quantitatively studied with experiments on simulated and human in vivo diffusion tensor data. Illustrative results demonstrate that the anisotropic smoothing technique developed can significantly reduce the impact of noise on the direction as well as anisotropy measures of the diffusion tensor images.
On the algebraic types of the Bel-Robinson tensor
Ferrando, Joan J
2008-01-01
The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov-Bel types and the additional ones are intrinsically characterized in terms of the sole Bel-Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel-Robinson tensor in regular cases.
Emergent classical geometries on boundaries of randomly connected tensor networks
Chen, Hua; Sasakura, Naoki; Sato, Yuki
2016-03-01
It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors the dimensions of the spaces can be freely chosen, and the geometries—which are curved in general—can be varied. We give the explicit solvable examples of emergent flat tori in arbitrary dimensions, and the correspondence from the tensors to the geometries for general curved cases. The perturbative dynamics in the emergent space is shown to be described by an effective action which is invariant under the spatial diffeomorphism due to the underlying orthogonal group symmetry of the randomly connected tensor network. It is also shown that there are various phase transitions among spaces, including extended and point-like ones, under continuous change of the tensors.
Emergent classical geometries on boundaries of randomly connected tensor networks
Chen, Hua; Sato, Yuki
2016-01-01
It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be freely chosen, and the geometries, which are curved in general, can be varied. We give the explicit solvable examples of emergent flat tori in arbitrary dimensions, and the correspondence from the tensors to the geometries for general curved cases. The perturbative dynamics in the emergent space is shown to be described by an effective action which is invariant under the spatial diffeomorphism due to the underlying orthogonal group symmetry of the randomly connected tensor network. It is also shown that there are various phase transitions among spaces, including extended and point-like ones, under continuous change of the tensors.
Nonlinear optical model for strip plasmonic waveguides
DEFF Research Database (Denmark)
Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei
2016-01-01
This paper presents a theoretical model of nonlinear optical properties for strip plasmonic waveguides. The particular waveguides geometry that we investigate contains a gold core, adhesion layers, and silicon dioxide cladding. It is shown that the third-order susceptibility of the gold core...... significantly depends on the layer thickness and has the dominant contribution to the effective third-order susceptibility of the long-range plasmon polariton mode. This results in two nonlinear optical effects in plasmonic waveguides, which we experimentally observed and reported in [Opt. Lett. 41, 317 (2016......)]. The first effect is the nonlinear power saturation of the plasmonic mode, and the second effect is the spectral broadening of the plasmonic mode. Both nonlinear plasmonic effects can be used for practical applications and their appropriate model will be important for further developments in communication...
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Irreducible Cartesian tensors of highest weight, for arbitrary order
Mane, S. R.
2016-03-01
A closed form expression is presented for the irreducible Cartesian tensor of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural tensors and their projection operators, the other one employing purely coordinate-free tensor manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n), for dimensions n ≥ 3.
Construction of energy-momentum tensor of gravitation
Bamba, Kazuharu; Shimizu, Katsutaro
2016-10-01
We construct the gravitational energy-momentum tensor in general relativity through the Noether theorem. In particular, we explicitly demonstrate that the constructed quantity can vary as a tensor under the general coordinate transformation. Furthermore, we verify that the energy-momentum conservation is satisfied because one of the two indices of the energy-momentum tensor should be in the local Lorentz frame. It is also shown that the gravitational energy and the matter one cancel out in certain space-times.
Deformaciones miniversales de parejas de tensores de segundo orden
Clotet Juan, Josep; Magret Planas, María Dolors; Peña Carrera, Marta
2007-01-01
Consideramos en el espacio de parejas de tensores tension y deformacion la relacion de equivalencia que se corresponde con cambios de base ortonormales. Identificandolas con parejas de matrices cuadradas, podemos utilizar la tecnica de las deformaciones miniversales para averiguar, dada una pareja de tensores cualquiera, cuales son las parejas de tensores que se pueden obtener al perturbar ligeramente la dada, puesto que las clases de equivalencia se pueden identificar con las ...
Direct solution of the Chemical Master Equation using quantized tensor trains.
Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph
2014-03-01
The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage
Direct solution of the Chemical Master Equation using quantized tensor trains.
Directory of Open Access Journals (Sweden)
Vladimir Kazeev
2014-03-01
Full Text Available The Chemical Master Equation (CME is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species and sub-linearly in the mode size (maximum copy number, and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of
Symmetric Topological Phases and Tensor Network States
Jiang, Shenghan
Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.
Scalable tensor factorizations with missing data.
Energy Technology Data Exchange (ETDEWEB)
Morup, Morten (Technical University of Denmark); Dunlavy, Daniel M.; Acar, Evrim (Turkish National Research Institute of Electronics and Cryptology); Kolda, Tamara Gibson
2010-04-01
The problem of missing data is ubiquitous in domains such as biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, and communication networks|all domains in which data collection is subject to occasional errors. Moreover, these data sets can be quite large and have more than two axes of variation, e.g., sender, receiver, time. Many applications in those domains aim to capture the underlying latent structure of the data; in other words, they need to factorize data sets with missing entries. If we cannot address the problem 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), and formulate the CP model as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) using a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm 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) application where missing data is frequently encountered due to disconnections of electrodes.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Tensor Decompositions for Learning Latent Variable Models
2012-12-08
Isotropic PCA and affine-invariant clustering. In FOCS, 2008. [Car91] J.-F. Cardoso . Super-symmetric decomposition of the fourth-order cumulant tensor...3109–3112. IEEE, 1991. [Car94] J.-F. Cardoso . Perturbation of joint diagonalizers. ref# 94d027. Technical report, Télécom Paris, 1994. [Cat44] R. B...CC96] J.-F. Cardoso and Pierre Comon. Independent component analysis, a survey of some algebraic methods. In IEEE International Symposium on Circuits
Beam-plasma dielectric tensor with Mathematica
Bret, A.
2007-03-01
We present a Mathematica notebook allowing for the symbolic calculation of the 3×3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Program summaryTitle of program: Tensor Catalog identifier: ADYT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, Spain Operating system under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of bytes in distributed program, including test data, etc.: 33 439 No. of lines in distributed program, including test data, etc.: 3169 Distribution format: tar.gz Nature of the physical problem: The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables. Method of solution: The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère-Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the
Hyperbolicity of Scalar Tensor Theories of Gravity
Salgado, Marcelo; Alcubierre, Miguel; Núñez, Dario
2008-01-01
Two first order strongly hyperbolic formulations of scalar tensor theories of gravity (STT) allowing non-minimal couplings (Jordan frame) are presented along the lines of the 3+1 decomposition of spacetime. One is based on the Bona-Masso formulation while the other one employs a conformal decomposition similar to that of Baumgarte-Shapiro-Shibata-Nakamura. A modified Bona-Masso slicing condition adapted to the STT is proposed for the analysis. This study confirms that STT posses a well posed Cauchy problem even when formulated in the Jordan frame.
A Rastall Scalar-Tensor theory
Caramês, T; Oliveira, A M; Piattella, O F; Strokov, V
2015-01-01
We formulate a theory combining the principles of a scalar-tensor gravity and the Rastall proposal of a violation of the usual conservation laws. In the resulting Brans-Dicke-Rastall (BDR) theory the only exact, static, spherically symmetric solution is a Robinson-Bertotti type solution besides the trivial Schwarzschild one. The PPN constraints can be completely satisfied for some values of the free parameters.The cosmological solutions display, among others, a decelerate-accelerate transition in the matter dominated phase.
Tensor networks for gauge field theories
Buyens, Boye; Verstraete, Frank; Van Acoleyen, Karel
2015-01-01
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of (1+1)-dimensional systems. In this proceeding we use MPS to determine the elementary excitations of the Schwinger model in the presence of an electric background field. We obtain an estimate for the value of the background field where the one-particle excitation with the largest energy becomes unstable and decays into two other elementary particles with smaller energy.
Holographic duality from random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-11-02
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main
Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as heterogeneous data, i.e., datasets in the form of matrices...... 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....
Full Elasticity Tensor from Thermal Diffuse Scattering
Wehinger, Björn; Mirone, Alessandro; Krisch, Michael; Bosak, Alexeï
2017-01-01
We present a method for the precise determination of the full elasticity tensor from a single crystal diffraction experiment using monochromatic x rays. For the two benchmark systems calcite and magnesium oxide, we show that the measurement of thermal diffuse scattering in the proximity of Bragg reflections provides accurate values of the complete set of elastic constants. This approach allows for a reliable and model-free determination of the elastic properties and can be performed together with crystal structure investigation in the same experiment.
Modelamento mecanico-quantico de tensores polares
Harley Paiva Martins Filho
1994-01-01
Resumo: Os tensores polares de onze moléculas de halometanos e haletos de carbonila e tiocarbonila ( CH2Cl2, CF2Cl2, CF3Cl, CFCl3, CH3F, CH3Cl, CH3I, Cl2CO, F2CO, Cl2CS e F2CS ) foram determinados com o objetivo de verificar a validade de modelos de eletronegatividade para previsão de invariantes tensoriais (momento dipolar médio e carga efetiva) e somas de intensidades previamente estabelecidos. O método de determinação foi desenvolvido recentemente, baseando-se essencialmente na comparação ...
Scalar-Tensor Bianchi VI Models
Directory of Open Access Journals (Sweden)
J. A. Belinchón
2013-01-01
Full Text Available We study how may vary the gravitational and the cosmological “constants,” ( and in several scalar-tensor theories with Bianchi III, , and symmetries. By working under the hypothesis of self-similarity we find exact solutions for two different theoretical models, which are the Jordan-Brans-Dicke (JBD with and the usual JBD model with potential (that mimics the behaviour of . We compare both theoretical models, and some physical and geometrical properties of the solutions are also discussed putting special emphasis on the study of the isotropization of the solutions.
On the dynamic viscous permeability tensor symmetry.
Perrot, Camille; Chevillotte, Fabien; Panneton, Raymond; Allard, Jean-François; Lafarge, Denis
2008-10-01
Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and/or convergence assessment.
Tensor Modeling Based for Airborne LiDAR Data Classification
Li, N.; Liu, C.; Pfeifer, N.; Yin, J. F.; Liao, Z. Y.; Zhou, Y.
2016-06-01
Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the "raw" data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.
Practical definition of averages of tensors in general relativity
Boero, Ezequiel F
2016-01-01
We present a definition of tensor fields which are average of tensors over a manifold, with a straightforward and natural definition of derivative for the averaged fields; which in turn makes a suitable and practical construction for the study of averages of tensor fields that satisfy differential equations. Although we have in mind applications to general relativity, our presentation is applicable to a general n-dimensional manifold. The definition is based on the integration of scalars constructed from a physically motivated basis, making use of the least amount of geometrical structure. We also present definitions of covariant derivative of the averaged tensors and Lie derivative.
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.
TENSOR MODELING BASED FOR AIRBORNE LiDAR DATA CLASSIFICATION
Directory of Open Access Journals (Sweden)
N. Li
2016-06-01
Full Text Available Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the “raw” data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.
Physical properties of crystals their representation by tensors and matrices
Nye, J F
1985-01-01
First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.
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...
Vertical variations of wave-induced radiation stress tensor
Institute of Scientific and Technical Information of China (English)
Zheng Jinhai; Yan Yixin
2001-01-01
The distributions of the wave-induced radiation stress tensor over depth are studied by using the linear wave theory, which are divided into three regions, i.e., above the mean water level, below the wave trough level, and between these two levels. The computational expressions of the wave-induced radiation stress tensor at the arbitrary wave angle are established by means of the Eulerian coordinate transformation, and the asymptotic forms for deep and shallow water are also presented. The vertical variations of a 30° incident wave-induced radiation stress tensor in deep water, intermediate water and shallow water are calculated respectively. The following conclusions are obtained from computations.The wave-induced radiation stress tensor below the wave trough level is induced by the water wave particle velocities only, whereas both the water wave particle velocities and the wave pressure contribute to the tensor above the wave trough level. The vertical variations of the wave-induced radiation stress tensor are influenced substantially by the velocity component in the direction of wave propagation. The distributions of the wave-induced radiation stress tensor over depth are nonuniform and the proportion of the tensor below the wave trough level becomes considerable in the shallow water. From the water surface to the seabed, the reversed variations occur for the predominant tensor components.
The Topology of Three-Dimensional Symmetric Tensor Fields
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.
Non-Renormalization and Naturalness in a Class of Scalar-Tensor Theories
de Rham, Claudia; Heisenberg, Lavinia; Pirtskhalava, David
2012-01-01
We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under: (a) linear diffeomorphisms which represent an exact symmetry of the full non-linear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of non-topological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop-corrections, and identify the regime in which they are sub-leading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the non-renormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum co...
Nonrenormalization and naturalness in a class of scalar-tensor theories
de Rham, Claudia; Gabadadze, Gregory; Heisenberg, Lavinia; Pirtskhalava, David
2013-04-01
We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under (a) linear diffeomorphisms which represent an exact symmetry of the full nonlinear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of nontopological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop corrections, and identify the regime in which they are subleading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the nonrenormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum corrections to the three free parameters of the model, one of them being the graviton mass, are strongly suppressed. In particular, we show that having an arbitrarily small graviton mass is technically natural.
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
Lagos, Macarena; Ferreira, Pedro G; Noller, Johannes
2016-01-01
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and "Beyond Horndeski" theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (\\`a la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic act...
Energy Technology Data Exchange (ETDEWEB)
Stahl, R. [Institut fuer Klinische Radiologie - Grosshadern, Klinikum der Universitaet Muenchen (Germany); Institut fuer Klinische Radiologie - Grosshadern, Klinikum der Universitaet Muenchen, Marchioninistr. 15, 81377, Muenchen (Germany); Dietrich, O.; Reiser, M.F.; Schoenberg, S.O. [Institut fuer Klinische Radiologie - Grosshadern, Klinikum der Universitaet Muenchen (Germany); Teipel, S.; Hampel, H. [Klinik fuer Psychiatrie und Psychotherapie, Klinikum der Universitaet Muenchen (Germany)
2003-07-01
Alzheimer disease (AD) causes cortical degeneration with subsequent degenerative changes of the white matter. The aim of this study was to investigate the extent of white matter tissue damage of patients with Alzheimer's disease in comparison with healthy subjects using diffusion tensor MRI (DTI). The value of integrated parallel imaging techniques (iPAT) for reduction of image distortion was assessed. We studied 9 patients with mild AD and 10 age and gender matched healthy controls. DTI brain scans were obtained on a 1.5 tesla system (Siemens Magnetom Sonata) using parallel imaging (iPAT) and an EPI diffusion sequence with TE/TR 71 ms/6000 ms. We used an 8-element head coil and a GRAPPA reconstruction algorithm with an acceleration factor of 2. From the tensor, the mean diffusivity (D), the fractional anisotropy (FA), and the relative anisotropy (RA) of several white matter regions were determined. FA was significantly lower (p <0,05) in the white matter of the genu of corpus callosum from patients with AD than in the corresponding regions from healthy controls. There was a trend observed for slightly higher ADC values in the AD group (p=0,06). No significant changes were observed in the regions of the splenium, internal capsule, pericallosal areas, frontal, temporal, parietal, and occipital lobe. The images obtained with iPAT contained substantially less susceptibility artefacts and were less distorted than images acquired with non-parallel imaging technique. DTI is a method with potential to assess early stages of white matter damage in vivo. The altered FA and ADC values in the genu of corpus callosum of patients with AD presumably reflect the microscopic white matter degeneration. Acquisition time can be reduced by iPAT methods with less image distortion from susceptibility artefacts resulting in a more accurate calculation of the diffusion tensor. (orig.) [German] Bei der Alzheimer-Erkrankung (AD) kommt es zur kortikalen Degeneration und sekundaer zu
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Saliency Mapping Enhanced by Structure Tensor
Directory of Open Access Journals (Sweden)
Zhiyong He
2015-01-01
Full Text Available We propose a novel efficient algorithm for computing visual saliency, which is based on the computation architecture of Itti model. As one of well-known bottom-up visual saliency models, Itti method evaluates three low-level features, color, intensity, and orientation, and then generates multiscale activation maps. Finally, a saliency map is aggregated with multiscale fusion. In our method, the orientation feature is replaced by edge and corner features extracted by a linear structure tensor. Following it, these features are used to generate contour activation map, and then all activation maps are directly combined into a saliency map. Compared to Itti method, our method is more computationally efficient because structure tensor is more computationally efficient than Gabor filter that is used to compute the orientation feature and our aggregation is a direct method instead of the multiscale operator. Experiments on Bruce’s dataset show that our method is a strong contender for the state of the art.
Stability of Horndeski vector-tensor interactions
Energy Technology Data Exchange (ETDEWEB)
Jiménez, Jose Beltrán [Centre for Cosmology, Particle Physics and Phenomenology, Institute of Mathematics and Physics, Louvain University, 2 Chemin du Cyclotron, Louvain-la-Neuve, 1348 (Belgium); Durrer, Ruth; Heisenberg, Lavinia [Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève, 24 quai Ansermet, Genève 4, CH-1211 (Switzerland); Thorsrud, Mikjel, E-mail: jose.beltran@uclouvain.be, E-mail: ruth.durrer@unige.ch, E-mail: lavinia.heisenberg@unige.ch, E-mail: mikjel.thorsrud@astro.uio.no [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, Oslo, N-0315 (Norway)
2013-10-01
We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M{sup 2}, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M{sup 2} > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.
Stability of Horndeski vector-tensor interactions
Jiménez, Jose Beltrán; Heisenberg, Lavinia; Thorsrud, Mikjel
2013-01-01
We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M^2, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M^2>0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherica...
Stability of Horndeski vector-tensor interactions
Beltrán Jiménez, Jose; Durrer, Ruth; Heisenberg, Lavinia; Thorsrud, Mikjel
2013-10-01
We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M2, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M2 > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.
A Renormalizable 4-Dimensional Tensor Field Theory
Geloun, Joseph Ben
2011-01-01
We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on $U(1)^4$ is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the $\\phi^6$ rather than of the $\\phi^4$ type, since two different $\\phi^6$-type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new localit...
Phases of antisymmetric tensor field theories
Quevedo, Fernando; Quevedo, Fernando; Trugenberger, Carlo
1997-01-01
We study the different phases of field theories of compact antisymmetric tensors of rank h-1 in arbitrary space-time dimensions D=d+1. Starting in a `Coulomb' phase, topological defects of dimension d-h-1 ((d-h-1)-branes) may condense leading to a generalized `confinement' phase. If the dual theory is also compact the model may also have a third, generalized `Higgs' phase, driven by the condensation of the dual (h-2)-branes. Developing on the work of Julia and Toulouse for ordered solid-state media, we obtain the low energy effective action for these phases. Each phase has two dual descriptions in terms of antisymmetric tensors of different ranks, which are massless for the Coulomb phase but massive for the Higgs and confinement phases. We illustrate our prescription in detail for compact QED in 4D. Compact QED and O(2) models in 3D, as well as a periodic scalar field in 2D (strings on a circle), are also discussed. In this last case we show how T-duality is maintained if one considers both worldsheet instant...
Quantum chaos and holographic tensor models
Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P. N. Bala
2017-03-01
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large- N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
Interactive Volume Rendering of Diffusion Tensor Data
Energy Technology Data Exchange (ETDEWEB)
Hlawitschka, Mario; Weber, Gunther; Anwander, Alfred; Carmichael, Owen; Hamann, Bernd; Scheuermann, Gerik
2007-03-30
As 3D volumetric images of the human body become an increasingly crucial source of information for the diagnosis and treatment of a broad variety of medical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of depth. Furthermore, fading out clinically irrelevant aspects of the image while preserving contextual anatomical landmarks helps medical doctors to focus on important parts of the images without becoming disoriented. Our goal was to develop a tool that unifies interactive manipulation and context preserving visualization of medical images with a special focus on diffusion tensor imaging (DTI) data. At each image voxel, DTI provides a 3 x 3 tensor whose entries represent the 3D statistical properties of water diffusion locally. Water motion that is preferential to specific spatial directions suggests structural organization of the underlying biological tissue; in particular, in the human brain, the naturally occuring diffusion of water in the axon portion of neurons is predominantly anisotropic along the longitudinal direction of the elongated, fiber-like axons [MMM+02]. This property has made DTI an emerging source of information about the structural integrity of axons and axonal connectivity between brain regions, both of which are thought to be disrupted in a broad range of medical disorders including multiple sclerosis, cerebrovascular disease, and autism [Mos02, FCI+01, JLH+99, BGKM+04, BJB+03].
Nucleon tensor charges and electric dipole moments
Pitschmann, Mario; Seng, Chien-Yeah; Roberts, Craig D.; Schmidt, Sebastian M.
2015-04-01
A symmetry-preserving Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to compute dressed-quark-core contributions to the nucleon σ -term and tensor charges. The latter enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs. The presence of strong scalar and axial-vector diquark correlations within ground-state baryons is a prediction of this approach. These correlations are active participants in all scattering events and thereby modify the contribution of the singly represented valence quark relative to that of the doubly represented quark. Regarding the proton σ -term and that part of the proton mass which owes to explicit chiral symmetry breaking, with a realistic d -u mass splitting, the singly represented d quark contributes 37% more than the doubly represented u quark; and in connection with the proton's tensor charges, δTu , δTd , the ratio δTd /δTu is 18% larger than anticipated from simple quark models. Of particular note, the size of δTu is a sensitive measure of the strength of dynamical chiral symmetry breaking; and δTd measures the amount of axial-vector diquark correlation within the proton, vanishing if such correlations are absent.
Z-scan: A simple technique for determination of third-order optical nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Singh, Vijender, E-mail: chahal-gju@rediffmail.com [Department of Applied Science, N.C. College of Engineering, Israna, Panipat-132107, Haryana (India); Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.co.in [Department of Physics, Chaudhary Devi Lal University, Sirsa-125055, Haryana (India)
2015-08-28
Z-scan is a simple experimental technique to measure intensity dependent nonlinear susceptibilities of third-order nonlinear optical materials. This technique is used to measure the sign and magnitude of both real and imaginary part of the third order nonlinear susceptibility (χ{sup (3)}) of nonlinear optical materials. In this paper, we investigate third-order nonlinear optical properties of Ag-polymer composite film by using single beam z-scan technique with Q-switched, frequency doubled Nd: YAG laser (λ=532 nm) at 5 ns pulse. The values of nonlinear absorption coefficient (β), nonlinear refractive index (n{sub 2}) and third-order nonlinear optical susceptibility (χ{sup (3)}) of permethylazine were found to be 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.
Optical nonlinearities in semiconductor-doped glasses near and below the band edge
Bindra, K. S.; Oak, S. M.; Rustagi, K. C.
1998-03-01
We present a brief review of our recent experimental results on optical nonlinearities in semiconductor-doped glasses. It is shown that even below the absorption edge the nonlinearities are determined by nonlinear absorption. The optical Kerr effect is found to have a susceptibility which is comparable to that for nonlinear refraction. We also find that in degenerate four-wave mixing the observed intensity dependence can be strongly influenced by nonlinear absorption.
The Kummer tensor density in electrodynamics and in gravity
Energy Technology Data Exchange (ETDEWEB)
Baekler, Peter [University of Appl. Sciences, 40474 Düsseldorf (Germany); Favaro, Alberto [Inst. Physics, Carl-von-Ossietzky-Univ., 26111 Oldenburg (Germany); Itin, Yakov [Inst. Mathematics, Hebrew University of Jerusalem (Israel); Jerusalem College of Technology (Israel); Hehl, Friedrich W., E-mail: hehl@thp.uni-koeln.de [Inst. Theor. Physics, University of Cologne, 50923 Köln (Germany); Department of Physics and Astron., University of Missouri, Columbia, MO 65211 (United States)
2014-10-15
Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K{sup ijkl}. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T{sup ijkl}, which is antisymmetric in its first two and its last two indices: T{sup ijkl}=−T{sup jikl}=−T{sup ijlk}. Thus, K∼T{sup 3}, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R{sup ijkl} of a Riemann–Cartan spacetime, then K∼R{sup 3} and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3)
One-loop tensor Feynman integral reduction with signed minors
DEFF Research Database (Denmark)
Fleischer, Jochem; Riemann, Tord; Yundin, Valery
2012-01-01
We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in ter...
Black holes with surrounding matter in scalar-tensor theories.
Cardoso, Vitor; Carucci, Isabella P; Pani, Paolo; Sotiriou, Thomas P
2013-09-13
We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.
OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.
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 DoA estimation with directional elements
Raimondi, Francesca; DELEVOYE, Elisabeth; Comon, Pierre
2016-01-01
This paper introduces directivity gain pattern as a physical diversity for tensor array processing, in addition to time and space shift diversities. We show that tensor formulation allows to estimate Directions of Arrival (DoAs) under the assumption of unknown gain pattern, improving the performance of the omnidirectional case. The proposed approach is then applied to biologically inspired acoustic elements.
Electromagnetic Energy Momentum Tensor in a Spatially Dispersive Medium
Fietz, Chris
2016-01-01
We derive a generalized Minkowski Energy Momentum Tensor for a monochromatic wave in a lossless medium exhibiting temporal and spatial dispersion. The Energy Momentum Tensor is then related to familiar expressions for energy density and energy flux, as well as new expressions for momentum density and momentum flux.
Dynamic rotation and stretch tensors from a dynamic polar decomposition
Haller, George
2016-01-01
The local rigid-body component of continuum deformation is typically characterized by the rotation tensor, obtained from the polar decomposition of the deformation gradient. Beyond its well-known merits, the polar rotation tensor also has a lesser known dynamical inconsistency: it does not satisfy the fundamental superposition principle of rigid-body rotations over adjacent time intervals. As a consequence, the polar rotation diverts from the observed mean material rotation of fibers in fluids, and introduces a purely kinematic memory effect into computed material rotation. Here we derive a generalized polar decomposition for linear processes that yields a unique, dynamically consistent rotation component, the dynamic rotation tensor, for the deformation gradient. The left dynamic stretch tensor is objective, and shares the principal strain values and axes with its classic polar counterpart. Unlike its classic polar counterpart, however, the dynamic stretch tensor evolves in time without spin. The dynamic rotation tensor further decomposes into a spatially constant mean rotation tensor and a dynamically consistent relative rotation tensor that is objective for planar deformations. We also obtain simple expressions for dynamic analogues of Cauchy's mean rotation angle that characterize a deforming body objectively.
3D inversion of full tensor magnetic gradiometry (FTMG) data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2011-01-01
Following recent advances in SQUID technology, full tensor magnetic gradiometry (FTMG) is emerging as a practical exploration method. We introduce 3D regularized focusing inversion for FTMG data. Our model studies show that inversion of magnetic tensor data can significantly improve resolution...
A characterization of the Einstein tensor in terms of spinors
Energy Technology Data Exchange (ETDEWEB)
Anderson, I.M.; Lovelock, D.
1976-06-01
All tensors of contravariant rank two which are divergence-free on one index, concomitants of a spinor field sigma/sub iAX'/ together with its first two partial derivatives, and scalars under spin transformations are constructed. The Einstein and metric tensors are the only candidates. (AIP)
U-dual branes and mixed symmetry tensor fields
Energy Technology Data Exchange (ETDEWEB)
Chatzistavrakidis, A. [Institut fuer Theoretische Physik, Appelstrasse 2, 30167 Hannover (Germany); Gautason, F.F. [Institut fuer Theoretische Physik, Appelstrasse 2, 30167 Hannover (Germany); Center for Quantum Engineering and Spacetime Research, Appelstrasse 2, 30167 Hannover (Germany)
2014-09-11
We review and explain the relation between U-dual branes in string theory and mixed symmetry tensors of various degrees. In certain cases these mixed symmetry tensors can be related to diverse types of fluxes that play an important role in compactifications of string theory. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Chow groups and intersection products for tensor triangulated categories
Klein, S.A.
2014-01-01
This thesis deals with a generalization of an important family of invariants from algebraic geometry (the Chow groups of an algebraic variety) to the setting of tensor triangulated categories. It is shown that these tensor triangular Chow groups recover the usual notion of Chow groups of an
Special properties of Eshelby tensor for a regular polygonal inclusion
Institute of Scientific and Technical Information of China (English)
Baixiang Xu; Minzhong Wang
2005-01-01
When studying the regular polygonal inclusion in 1997, Nozaki and Taya discovered numerically some remarkable properties of Eshelby tensor: Eshelby tensor at the center and the averaged Eshelby tensor over the inclusion domain are equal to that of a circular inclusion and independent of the orientation of the inclusion. Then Kawashita and Nozaki justified the properties mathematically. In the present paper, some other properties of a regular polygonal inclusion are discovered. We find that for an N-fold regular polygonal inclusion except for a square, the arithmetic mean of Eshelby tensors at N rotational symmetrical points in the inclusion is also equal to the Eshelby tensor for a circular inclusion and independent of the orientation of the inclusion. Furthermore,in two corollaries, we point out that Eshelby tensor at the center, the averaged Eshelby tensor over the inclusion domain,and the line integral average of Eshelby tensors along any concentric circle of the inclusion are all identical with the arithmetic mean.
Transversely isotropic higher-order averaged structure tensors
Hashlamoun, Kotaybah; Federico, Salvatore
2017-08-01
For composites or biological tissues reinforced by statistically oriented fibres, a probability distribution function is often used to describe the orientation of the fibres. The overall effect of the fibres on the material response is accounted for by evaluating averaging integrals over all possible directions in space. The directional average of the structure tensor (tensor product of the unit vector describing the fibre direction by itself) is of high significance. Higher-order averaged structure tensors feature in several models and carry similarly important information. However, their evaluation has a quite high computational cost. This work proposes to introduce mathematical techniques to minimise the computational cost associated with the evaluation of higher-order averaged structure tensors, for the case of a transversely isotropic probability distribution of orientation. A component expression is first introduced, using which a general tensor expression is obtained, in terms of an orthonormal basis in which one of the vectors coincides with the axis of symmetry of transverse isotropy. Then, a higher-order transversely isotropic averaged structure tensor is written in an appropriate basis, constructed starting from the basis of the space of second-order transversely isotropic tensors, which is constituted by the structure tensor and its complement to the identity.
Chern-Simons Couplings and Inequivalent Vector-Tensor Multiplets
Claus, P.; Wit, B. de; Faux, M.; Termonia, P.
1996-01-01
The off-shell vector-tensor multiplet is considered in an arbitrary background of N=2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the vector field of the vector-tensor multiplet is contained
Exploring the tensor networks/AdS correspondence
Bhattacharyya, Arpan; Gao, Zhe-Shen; Hung, Ling-Yan; Liu, Si-Nong
2016-08-01
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.
Coordinate independent expression for transverse trace-free tensors
Conboye, Rory
2015-01-01
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 3-space possess only two degrees of freedom, they cannot ordinarily be given solely by two differential functions. However, coordinate expressions depending on two scalar potentials alone have been derived for all TT tensors in flat space (Conboye and \\'O Murchadha 2014 Class. Quantum Grav. 31, 085019), with either a linear or axial symmetry. Since TT tensors are conformally covariant, these also give TT tensors in conformally-flat space. Here, this work has been extended to give a coordinate-independent expression for these TT tensors, also generalizing the symmetry conditions to invariance along any hypersurface orthogonal Killing vector.
On the energy-momentum tensor in Moyal space
Energy Technology Data Exchange (ETDEWEB)
Balasin, Herbert; Schweda, Manfred [Vienna University of Technology, Institute for Theoretical Physics, Vienna (Austria); Blaschke, Daniel N. [Los Alamos National Laboratory, Theory Division, Los Alamos, NM (United States); Gieres, Francois [Universite de Lyon, Universite Claude Bernard Lyon 1 et CNRS/IN2P3, Institut de Physique Nucleaire de Lyon, Villeurbanne (France)
2015-06-15
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.)
Tensor classification of structure in smoothed particle hydrodynamics density fields
Forgan, Duncan; Lucas, William; Rice, Ken
2016-01-01
As hydrodynamic simulations increase in scale and resolution, identifying structures with non-trivial geometries or regions of general interest becomes increasingly challenging. There is a growing need for algorithms that identify a variety of different features in a simulation without requiring a "by-eye" search. We present tensor classification as such a technique for smoothed particle hydrodynamics (SPH). These methods have already been used to great effect in N-Body cosmological simulations, which require smoothing defined as an input free parameter. We show that tensor classification successfully identifies a wide range of structures in SPH density fields using its native smoothing, removing a free parameter from the analysis and preventing the need for tesselation of the density field, as required by some classification algorithms. As examples, we show that tensor classification using the tidal tensor and the velocity shear tensor successfully identifies filaments, shells and sheet structures in giant m...
Lagrange Multipliers and Third Order Scalar-Tensor Field Theories
Horndeski, Gregory W
2016-01-01
In a space of 4-dimensions, I will examine constrained variational problems in which the Lagrangian, and constraint scalar density, are concomitants of a (pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange multiplier for these constrained extremal problems will be a scalar field. For suitable choices of the Lagrangian, and constraint, we can obtain Euler-Lagrange equations which are second order in the scalar field and third order in the metric tensor. The effect of disformal transformations on the constraint Lagrangians, and their generalizations, is examined. This will yield other second order scalar-tensor Lagrangians which yield field equations which are at most of third order. No attempt is made to construct all possible third order scalar-tensor Euler-Lagrange equations in a 4-space, although nine classes of such field equations are presented. Two of these classes admit subclasses which yield conformally invariant field equations. A few remarks on scalar-tensor-connection theor...
Inflationary tensor fossils in large-scale structure
Dimastrogiovanni, Emanuela; Jeong, Donghui; Kamionkowski, Marc
2014-01-01
Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as non-attractor and solid inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attrac...
Tensor-optimized antisymmetrized molecular dynamics in nuclear physics
Myo, Takayuki; Ikeda, Kiyomi; Horiuchi, Hisashi; Suhara, Tadahiro
2015-01-01
We develop a new formalism to treat nuclear many-body systems using bare nucleon-nucleon interaction. It has become evident that the tensor interaction plays important role in nuclear many-body systems due to the role of the pion in strongly interacting system. We take the antisymmetrized molecular dynamics (AMD) as a basic framework and add a tensor correlation operator acting on the AMD wave function using the concept of the tensor-optimized shell model (TOSM). We demonstrate a systematical and straightforward formulation utilizing the Gaussian integration and differentiation method and the antisymmetrization technique to calculate all the matrix elements of the many-body Hamiltonian. We can include the three-body interaction naturally and calculate the matrix elements systematically in the progressive order of the tensor correlation operator. We call the new formalism "tensor-optimized antisymmetrized molecular dynamics".
A recursive approach to the reduction of tensor Feynman integrals
Diakonidis, Theodoros; Riemann, Tord; Tausk, Bas
2010-01-01
We describe a new, convenient, recursive tensor integral reduction scheme for one-loop $n$-point Feynman integrals. The reduction is based on the algebraic Davydychev-Tarasov formalism where the tensors are represented by scalars with shifted dimensions and indices, and then expressed by conventional scalars with generalized recurrence relations. The scheme is worked out explicitly for up to $n=6$ external legs and for tensor ranks $R\\leq n$. The tensors are represented by scalar one- to four-point functions in $d$ dimensions. For the evaluation of them, the Fortran code for the tensor reductions has to be linked with a package like QCDloop or LoopTools/FF. Typical numerical results are presented.
Xiao, Yunlong; Liu, Wenjian
2013-07-21
The relativistic molecular Hamiltonian written in the body-fixed frame of reference is the basis for high-precision calculations of spectroscopic parameters involving nuclear vibrations and/or rotations. Such a Hamiltonian that describes electrons fully relativistically and nuclei quasi-relativistically is just developed for semi-rigid nonlinear molecules [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)]. Yet, the formulation should somewhat be revised for linear molecules thanks to some unusual features arising from the redundancy of the rotation around the molecular axis. Nonetheless, the resulting isomorphic Hamiltonian is rather similar to that for nonlinear molecules. Consequently, the relativistic formulation of nuclear spin-rotation (NSR) tensor for linear molecules is very much the same as that for nonlinear molecules. So is the relativistic mapping between experimental NSR and NMR.
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
The atomistic representation of first strain-gradient elastic tensors
Admal, Nikhil Chandra; Marian, Jaime; Po, Giacomo
2017-02-01
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy-Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.
Neuroanatomic Differences Associated With Stress Susceptibility and Resilience.
Anacker, Christoph; Scholz, Jan; O'Donnell, Kieran J; Allemang-Grand, Rylan; Diorio, Josie; Bagot, Rosemary C; Nestler, Eric J; Hen, René; Lerch, Jason P; Meaney, Michael J
2016-05-15
We examined the neurobiological mechanisms underlying stress susceptibility using structural magnetic resonance imaging and diffusion tensor imaging to determine neuroanatomic differences between stress-susceptible and resilient mice. We also examined synchronized anatomic differences between brain regions to gain insight into the plasticity of neural networks underlying stress susceptibility. C57BL/6 mice underwent 10 days of social defeat stress and were subsequently tested for social avoidance. For magnetic resonance imaging, brains of stressed (susceptible, n = 11; resilient, n = 8) and control (n = 12) mice were imaged ex vivo at 56 µm resolution using a T2-weighted sequence. We tested for behavior-structure correlations by regressing social avoidance z-scores against local brain volume. For diffusion tensor imaging, brains were scanned with a diffusion-weighted fast spin echo sequence at 78 μm isotropic voxels. Structural covariance was assessed by correlating local volume between brain regions. Social avoidance correlated negatively with local volume of the cingulate cortex, nucleus accumbens, thalamus, raphe nuclei, and bed nucleus of the stria terminals. Social avoidance correlated positively with volume of the ventral tegmental area (VTA), habenula, periaqueductal gray, cerebellum, hypothalamus, and hippocampal CA3. Fractional anisotropy was increased in the hypothalamus and hippocampal CA3. We observed synchronized anatomic differences between the VTA and cingulate cortex, hippocampus and VTA, hippocampus and cingulate cortex, and hippocampus and hypothalamus. These correlations revealed different structural covariance between brain regions in susceptible and resilient mice. Stress-integrative brain regions shape the neural architecture underlying individual differences in susceptibility and resilience to chronic stress. Copyright © 2016. Published by Elsevier Inc.
The formalism of invariants in scalar-tensor and multiscalar-tensor theories of gravitation
Jarv, Laur; Saal, Margus; Vilson, Ott
2016-01-01
We give a brief summary of the formalism of invariants in general scalar-tensor and multiscalar-tensor gravities without derivative couplings. By rescaling of the metric and reparametrization of the scalar fields, the theory can be presented in different conformal frames and parametrizations. Due to this freedom in transformations, the scalar fields themselves do not carry independent physical meaning (in a generic parametrization). However, there are functions of the scalar fields and their derivatives which remain invariant under the transformations, providing a set of physical variables for the theory. We indicate how to construct such invariants and show how the observables like parametrized post-Newtonian parameters and characteristics of Friedmann-Lemaitre-Robertson-Walker cosmology can be neatly expressed in terms of the invariants.
Tensor Algebra and Tensor Analysis for Engineers With Applications to Continuum Mechanics
Itskov, Mikhail
2013-01-01
There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area. This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.
Gravity Gradient Tensor Eigendecomposition for Spacecraft Positioning
Chen, Pei; Han, Chao
2016-01-01
In this Note, a new approach to spacecraft positioning based on GGT inversion is presented. The gravity gradient tensor is initially measured in the gradiometer reference frame (GRF) and then transformed to the Earth-Centered Earth-Fixed (ECEF) frame via attitude information as well as Earth rotation parameters. Matrix Eigen-Decomposition is introduced to directly translate GGT into position based on the fact that the eigenvalues and eigenvectors of GGT are simplespecific functions of spherical coordinates of the observation position. without the need of an initial position. Unlike the strategy of inertial navigation aiding, no prediction or first guess of the spacecraft position is needed. The method makes use of the J2 gravity model, and is suitable for space navigation where higher frequency terrain contributions to the GGT signals can be neglected.
Chiral perturbation theory with tensor sources
Energy Technology Data Exchange (ETDEWEB)
Cata, Oscar; Cata, Oscar; Mateu, Vicent
2007-05-21
We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \\bar psi sigma_mu nu psi. In order to have only even terms in the chiral expansion, we consider the new source of O(p2). With this choice, we build the even-parity effective Lagrangian up to the p6-order (NLO). While there are only 4 new terms at the p4-order, at p6-order we find 78 terms for n_f=2 and 113 terms for n_f=3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p8-order (NNLO).
Electroproduction of tensor mesons in QCD
Braun, V M; Strohmaier, M; Vladimirov, A A
2016-01-01
Due to multiple possible polarizations hard exclusive production of tensor mesons by virtual photons or in heavy meson decays offers interesting possibilities to study the helicity structure of the underlying short-distance process. Motivated by the first measurement of the transition form factor $\\gamma^*\\gamma \\to f_2(1270)$ at large momentum transfers by the BELLE collaboration we present an improved QCD analysis of this reaction in the framework of collinear factorization including contributions of twist-three quark-antiquark-gluon operators and an estimate of soft end-point corrections using light-cone sum rules. The results appear to be in a very good agreement with the data, in particular the predicted scaling behavior is reproduced in all cases.
f(R)-gravity from Killing tensors
Paliathanasis, Andronikos
2016-04-01
We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.
Tensor products of commutative Banach algebras
Directory of Open Access Journals (Sweden)
U. B. Tewari
1982-01-01
Full Text Available Let A1, A2 be commutative semisimple Banach algebras and A1⊗∂A2 be their projective tensor product. We prove that, if A1⊗∂A2 is a group algebra (measure algebra of a locally compact abelian group, then so are A1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutative semi-simple Banach algebra, then the Banach algebra L1(G,A of A-valued Bochner integrable functions on G is a group algebra if and only if A is a group algebra. Furthermore, if A has the Radon-Nikodym property, then the Banach algebra M(G,A of A-valued regular Borel measures of bounded variation on G is a measure algebra only if A is a measure algebra.
Diffusion tensor imaging of peripheral nerves.
Jambawalikar, Sachin; Baum, Jeremy; Button, Terry; Li, Haifang; Geronimo, Veronica; Gould, Elaine S
2010-11-01
Magnetic resonance diffusion tensor imaging (DTI) allows the directional dependence of water diffusion to be studied. Analysis of the resulting image data allows for the determination of fractional anisotropy (FA), apparent diffusion coefficient (ADC), as well as allowing three-dimensional visualization of the fiber tract (tractography). We visualized the ulnar nerve of ten healthy volunteers with DTI. We found FA to be 0.752 ± 0.067 and the ADC to be 0.96 ± 0.13 × 10(-3) mm(2)/s. A nuts-and-bolts description of the physical aspects of DTI is provided as an educational process for readers.
Theory and design of nonlinear metamaterials
Rose, Alec Daniel
If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers
Purely nonlinear disorder-induced localizations and their parametric amplification
Folli, Viola; Conti, Claudio
2013-01-01
We investigate spatial localization in a quadratic nonlinear medium in the presence of randomness. By means of numerical simulations and theoretical analyses we show that, in the down conversion regime, the transverse random modulation of the nonlinear susceptibility generates localizations of the fundamental wave that grow exponentially in propagation. The localization length is optically controlled by the pump intensity which determines the amplification rate. The results also apply to cubic nonlinearities.
Estimation of tensors and tensor-derived measures in diffusional kurtosis imaging.
Tabesh, Ali; Jensen, Jens H; Ardekani, Babak A; Helpern, Joseph A
2011-03-01
This article presents two related advancements to the diffusional kurtosis imaging estimation framework to increase its robustness to noise, motion, and imaging artifacts. The first advancement substantially improves the estimation of diffusion and kurtosis tensors parameterizing the diffusional kurtosis imaging model. Rather than utilizing conventional unconstrained least squares methods, the tensor estimation problem is formulated as linearly constrained linear least squares, where the constraints ensure physically and/or biologically plausible tensor estimates. The exact solution to the constrained problem is found via convex quadratic programming methods or, alternatively, an approximate solution is determined through a fast heuristic algorithm. The computationally more demanding quadratic programming-based method is more flexible, allowing for an arbitrary number of diffusion weightings and different gradient sets for each diffusion weighting. The heuristic algorithm is suitable for real-time settings such as on clinical scanners, where run time is crucial. The advantage offered by the proposed constrained algorithms is demonstrated using in vivo human brain images. The proposed constrained methods allow for shorter scan times and/or higher spatial resolution for a given fidelity of the diffusional kurtosis imaging parametric maps. The second advancement increases the efficiency and accuracy of the estimation of mean and radial kurtoses by applying exact closed-form formulae.
Estimation of Tensors and Tensor-Derived Measures in Diffusional Kurtosis Imaging1
Tabesh, Ali; Jensen, Jens H.; Ardekani, Babak A.; Helpern, Joseph A.
2010-01-01
This paper presents two related advancements to the diffusional kurtosis imaging (DKI) estimation framework to increase its robustness to noise, motion, and imaging artifacts. The first advancement substantially improves the estimation of diffusion and kurtosis tensors parameterizing the DKI model. Rather than utilizing conventional unconstrained least squares (LS) methods, the tensor estimation problem is formulated as linearly constrained linear LS, where the constraints ensure physically and/or biologically plausible tensor estimates. The exact solution to the constrained problem is found via convex quadratic programming methods or, alternatively, an approximate solution is determined through a fast heuristic algorithm. The computationally more demanding quadratic programming-based method is more flexible, allowing for an arbitrary number of diffusion weightings and different gradient sets for each diffusion weighting. The heuristic algorithm is suitable for real-time settings such as on clinical scanners, where run time is crucial. The advantage offered by the proposed constrained algorithms is demonstrated using in vivo human brain images. The proposed constrained methods allow for shorter scan times and/or higher spatial resolution for a given fidelity of the DKI parametric maps. The second advancement increases the efficiency and accuracy of the estimation of mean and radial kurtoses by applying exact closed-form formulae. PMID:21337412
On the Decomposition of the Spacetime Metric Tensor and of Tensor Fields in Strained Spacetime
Directory of Open Access Journals (Sweden)
Millette P. A.
2012-10-01
Full Text Available We propose a natural decomposition of the spacetime metric tensor of General Relativ- ity into a background and a dynamical part based on an analysis from first principles of the effect of a test mass on the background metric. We find that the presence of mass results in strains in the spacetime continuum. Those strains correspond to the dy- namical part of the spacetime metric tensor. We then apply the stress-strain relation of Continuum Mechanics to the spacetime continuum to show that rest-mass energy den- sity arises from the volume dilatation of the spacetime continuum. Finally we propose a natural decomposition of tensor fields in strained spacetime, in terms of dilatations and distortions. We show that dilatations correspond to rest-mass energy density, while distortions correspond to massless shear transverse waves. We note that this decom- position in a massive dilatation and a massless transverse wave distortion, where both are present in spacetime continuum deformations, is somewhat reminiscent of wave- particle duality. We note that these results are considered to be local effects in the particular reference frame of the observer. In addition, the applicability of the proposed metric to the Einstein field equations remains open.
Reyna, Albert S
2014-01-01
We present a procedure for nonlinearity management of metal-dielectric composites. Varying the volume fraction occupied by silver nanoparticles suspended in acetone we could cancel the refractive index related to the third-order susceptibility, $\\chi_{eff}^{(3)}$, and the nonlinear refraction behavior was due to the fifth-order susceptibility, $\\chi_{eff}^{(5)}$. Hence, in a cross-phase modulation experiment, we demonstrated for the first time the effect of spatial-modulation- instability due to $\\chi_{eff}^{(5)}$. The results are corroborated with numerical calculations based on a generalized Maxwell-Garnet model.
Transmission Measurement of the Third-Order Susceptibility of Gold
Smith, David D.; Yoon, Youngkwon; Boyd, Robert W.; Crooks, Richard M.; George, Michael
1999-01-01
Gold nanoparticle composites are known to display large optical nonlinearities. In order to assess the validity of generalized effective medium theories (EMT's) for describing the linear and nonlinear optical properties of metal nanoparticle composites, knowledge of the linear and nonlinear susceptibilities of the constituent materials is a prerequisite. In this study the inherent nonlinearity of the metal is measured directly (rather than deduced from a suitable EMT) using a very thin gold film. Specifically, we have used the z-scan technique at a wavelength near the transmission window of bulk gold to measure the third-order susceptibility of a continuous thin gold film deposited on a quartz substrate surface-modified with a self-assembled monolayer to promote adhesion and uniformity without affecting the optical properties. We compare our results with predictions which ascribe the nonlinear response to a Fermi-smearing mechanism. Further, we note that the sign of the nonlinear susceptibility is reversed from that of gold nanoparticle composites.
Tensor classification of structure in smoothed particle hydrodynamics density fields
Forgan, Duncan; Bonnell, Ian; Lucas, William; Rice, Ken
2016-04-01
As hydrodynamic simulations increase in scale and resolution, identifying structures with non-trivial geometries or regions of general interest becomes increasingly challenging. There is a growing need for algorithms that identify a variety of different features in a simulation without requiring a `by eye' search. We present tensor classification as such a technique for smoothed particle hydrodynamics (SPH). These methods have already been used to great effect in N-Body cosmological simulations, which require smoothing defined as an input free parameter. We show that tensor classification successfully identifies a wide range of structures in SPH density fields using its native smoothing, removing a free parameter from the analysis and preventing the need for tessellation of the density field, as required by some classification algorithms. As examples, we show that tensor classification using the tidal tensor and the velocity shear tensor successfully identifies filaments, shells and sheet structures in giant molecular cloud simulations, as well as spiral arms in discs. The relationship between structures identified using different tensors illustrates how different forces compete and co-operate to produce the observed density field. We therefore advocate the use of multiple tensors to classify structure in SPH simulations, to shed light on the interplay of multiple physical processes.
Seismic moment tensors and estimated uncertainties in southern Alaska
Silwal, Vipul; Tape, Carl
2016-04-01
We present a moment tensor catalog of 106 earthquakes in southern Alaska, and we perform a conceptually based uncertainty analysis for 21 of them. For each earthquake, we use both body waves and surface waves to do a grid search over double couple moment tensors and source depths in order to find the minimum of the misfit function. Our uncertainty parameter or, rather, our confidence parameter is the average value of the curve 𝒫 (V), where 𝒫 (V) is the posterior probability as a function of the fractional volume V of moment tensor space surrounding the minimum misfit moment tensor. As a supplemental means for characterizing and visualizing uncertainties, we generate moment tensor samples of the posterior probability. We perform a series of inversion tests to quantify the impact of certain decisions made within moment tensor inversions and to make comparisons with existing catalogs. For example, using an L1 norm in the misfit function provides more reliable solutions than an L2 norm, especially in cases when all available waveforms are used. Using body waves in addition to surface waves, as well as using more stations, leads to the most accurate moment tensor solutions.
Generalized Einstein Tensor for a Weyl Manifold and Its Applications
Institute of Scientific and Technical Information of China (English)
Abdülkadir （O）ZDE（G）ER
2013-01-01
It is well known that the Einstein tensor G for a Piemannian manifold defined by Gβα =Rβα-1/2Rδα,Rβα =gβγRγα where Rγα and R are respectively the Ricci tensor and the scalar curvature of the manifold,plays an important part in Einstein's theory of gravitation as well as in proving some theorems in Riemannian geometry.In this work,we first obtain the generalized Einstein tensor for a Weyl manifold.Then,after studying some properties of generalized Einstein tensor,we prove that the conformed invariance of the generalized Einstein tensor implies the conformed invariance of the curvature tensor of the Weyl manifold and conversely.Moreover,we show that such Weyl manifolds admit a one-parameter family of hypersurfaces the orthogoned trajectories of which are geodesics.Finally,a necessary and sufficient condition in order that the generalized circles of a Weyl manifold be preserved by a conformal mapping is stated in terms of generalized Einstein tensors at corresponding points.
On the energy-momentum tensor in Moyal space
Balasin, Herbert; Gieres, Francois; Schweda, Manfred
2015-01-01
After reviewing the known results for the definition and properties of the energy-momentum tensor(s) in Minkowski space, 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 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 gauge invariant Wilson line. We show that the latter 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 prod...
The tensor bi-spectrum in a matter bounce
Sreenath, V.; Chowdhury, Debika; Sriramkumar, L.
2016-03-01
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 hNL 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.
Tensor-based dynamic reconstruction method for electrical capacitance tomography
Lei, J.; Mu, H. P.; Liu, Q. B.; Li, Z. H.; Liu, S.; Wang, X. Y.
2017-03-01
Electrical capacitance tomography (ECT) is an attractive visualization measurement method, in which the acquisition of high-quality images is beneficial for the understanding of the underlying physical or chemical mechanisms of the dynamic behaviors of the measurement objects. In real-world measurement environments, imaging objects are often in a dynamic process, and the exploitation of the spatial-temporal correlations related to the dynamic nature will contribute to improving the imaging quality. Different from existing imaging methods that are often used in ECT measurements, in this paper a dynamic image sequence is stacked into a third-order tensor that consists of a low rank tensor and a sparse tensor within the framework of the multiple measurement vectors model and the multi-way data analysis method. The low rank tensor models the similar spatial distribution information among frames, which is slowly changing over time, and the sparse tensor captures the perturbations or differences introduced in each frame, which is rapidly changing over time. With the assistance of the Tikhonov regularization theory and the tensor-based multi-way data analysis method, a new cost function, with the considerations of the multi-frames measurement data, the dynamic evolution information of a time-varying imaging object and the characteristics of the low rank tensor and the sparse tensor, is proposed to convert the imaging task in the ECT measurement into a reconstruction problem of a third-order image tensor. An effective algorithm is developed to search for the optimal solution of the proposed cost function, and the images are reconstructed via a batching pattern. The feasibility and effectiveness of the developed reconstruction method are numerically validated.
Modified Nonlinear Model of Arcsin-Electrodynamics
Kruglov, S. I.
2016-07-01
A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter γ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested. We have investigated the gauge covariant quantization of the nonlinear electrodynamics fields as well as the gauge fixing approach based on Dirac's brackets.
A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations
Shay, R. M., Jr.; Caruthers, J. M.
1987-01-01
Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.
The general dielectric tensor for bi-kappa magnetized plasmas
Gaelzer, Rudi; Meneses, Anelise Ramires
2016-01-01
In this paper we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.
Standard cosmological model with non vanishing Weyl tensor
Bittencourt, E
2013-01-01
We have solved Einstein's equations of general relativity for a homogeneous and isotropic metric with constant spatial curvature and found a non vanishing Weyl tensor in the presence of an anisotropic pressure component of the energy-momentum tensor. The time evolution of the space-time is guided by the usual Friedman equations and the properties of the spatial components comprise a separated system of equations that can be independently solved. The physical features of this solution are elucidated by using the Quasi-Maxwellian equations of general relativity which directly connect the anisotropic pressure to the electric part of the Weyl tensor for the cosmological fluid.