Baby Skyrmion chains

International Nuclear Information System (INIS)

Foster, David

2010-01-01

The Baby Skyrmion model is a two-dimensional analogue of the full three-dimensional Skyrme model. It is not just useful for guiding investigations in the Skyrme model, it also has applications in condensed matter physics. Previous results on multi-charged Baby Skyrmion solutions have pointed to a modular structure, comprised of charge two rings and single charge one Skyrmions, which combine to form higher charged structures. In this paper we present alternative numerical solutions that correspond to new finite Baby Skyrmion chains, which have lower energy than those found previously, and are also good candidates for the global minimum energy solutions. We then proceed from the infinite plane, to Baby Skyrmions on a cylinder and then a torus, to obtain the solutions of periodic Baby Skyrmions, of which periodic segments will correspond to sections of large charge Baby Skyrmions in the plane

Relativistic interpretation of the nature of the nuclear tensor force

Science.gov (United States)

Zong, Yao-Yao; Sun, Bao-Yuan

2018-02-01

The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force. Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)

Magnetic skyrmions

Science.gov (United States)

2018-06-01

Welcome to the special issue of Journal of Magnetism and Magnetic Materials on magnetic skyrmions. We are proud to present, with great pleasure, a timely collection of 9 original research articles on the recent hot topic "magnetic skyrmions" which studies the static and dynamic properties of skyrmions and the methods to control them in a variety of ways, including magnetic field, electric current and applied strain.

Topological dynamics and current-induced motion in a skyrmion lattice

Science.gov (United States)

Martinez, J. C.; Jalil, M. B. A.

2016-03-01

We study the Thiele equation for current-induced motion in a skyrmion lattice through two soluble models of the pinning potential. Comprised by a Magnus term, a dissipative term and a pinning force, Thiele’s equation resembles Newton’s law but in virtue of the topological character to the first, it differs significantly from Newtonian mechanics and because the Magnus force is dominant, unlike its mechanical counterpart—the Coriolis force—skyrmion trajectories do not necessarily have mechanical counterparts. This is important if we are to understand skyrmion dynamics and tap into its potential for data-storage technology. We identify a pinning threshold velocity for the one-dimensional pinning potential and for a two-dimensional attractive potential we find a pinning point and the skyrmion trajectories toward that point are spirals whose frequency (compare Kepler’s second law) and amplitude-decay depend only on the Gilbert constant and potential at the pinning point. Other scenarios, e.g. other choices of initial spin velocity, a repulsive potential, etc are also investigated.

Topological dynamics and current-induced motion in a skyrmion lattice

International Nuclear Information System (INIS)

Martinez, J C; Jalil, M B A

2016-01-01

We study the Thiele equation for current-induced motion in a skyrmion lattice through two soluble models of the pinning potential. Comprised by a Magnus term, a dissipative term and a pinning force, Thiele’s equation resembles Newton’s law but in virtue of the topological character to the first, it differs significantly from Newtonian mechanics and because the Magnus force is dominant, unlike its mechanical counterpart—the Coriolis force—skyrmion trajectories do not necessarily have mechanical counterparts. This is important if we are to understand skyrmion dynamics and tap into its potential for data-storage technology. We identify a pinning threshold velocity for the one-dimensional pinning potential and for a two-dimensional attractive potential we find a pinning point and the skyrmion trajectories toward that point are spirals whose frequency (compare Kepler’s second law) and amplitude-decay depend only on the Gilbert constant and potential at the pinning point. Other scenarios, e.g. other choices of initial spin velocity, a repulsive potential, etc are also investigated. (paper)

Magnus-induced ratchet effects for skyrmions interacting with asymmetric substrates

Science.gov (United States)

Reichhardt, C.; Ray, D.; Olson Reichhardt, C. J.

2015-07-01

We show using numerical simulations that pronounced ratchet effects can occur for ac driven skyrmions moving over asymmetric quasi-one-dimensional substrates. We find a new type of ratchet effect called a Magnus-induced transverse ratchet that arises when the ac driving force is applied perpendicular rather than parallel to the asymmetry direction of the substrate. This transverse ratchet effect only occurs when the Magnus term is finite, and the threshold ac amplitude needed to induce it decreases as the Magnus term becomes more prominent. Ratcheting skyrmions follow ordered orbits in which the net displacement parallel to the substrate asymmetry direction is quantized. Skyrmion ratchets represent a new ac current-based method for controlling skyrmion positions and motion for spintronic applications.

Pion correlation from Skyrmion--anti-Skyrmion annihilation

International Nuclear Information System (INIS)

Lu, Y.; Amado, R.D.

1995-01-01

We study two pion correlations from Skyrmion and anti-Skyrmion collision, using the product ansatz and an approximate random grooming method for nucleon projection. The spatial-isospin coupling inherent in the Skyrme model, along with empirical averages, leads to correlations not only among pions of like charges but also among unlike charge types

Skyrmions in condensed matter

CERN Document Server

Han, Jung Hoon

2017-01-01

This book summarizes some of the most exciting theoretical developments in the topological phenomena of skyrmions in noncentrosymmetric magnetic systems over recent decades. After presenting pedagogical backgrounds to the Berry phase and homotopy theory, the author systematically discusses skyrmions in the order of their development, from the Ginzburg-Landau theory, CP1 theory, Landau-Lifshitz-Gilbert theory, and Monte Carlo numerical approaches. Modern topics, such as the skyrmion-electron interaction, skyrmion-magnon interaction, and various generation mechanisms of the skyrmion are examined with a focus on their general theoretical aspects. The book concludes with a chapter on the skyrmion phenomena in the cold atom context. The topics are presented at a level accessible to beginning graduate students without a substantial background in field theory. The book can also be used as a text for those who wish to engage in the physics of skyrmions in magnetic systems, or as an introduction to the various theoret...

Creation of skyrmion through resonance excitation

Energy Technology Data Exchange (ETDEWEB)

Li, Zhi-xiong; Chen, Yi-fu; Zhou, Zhen-wei; Nie, Yao-zhuang; Xia, Qing-lin; Wang, Dao-wei; Guo, Guang-hua, E-mail: guogh@mail.csu.edu.cn

2017-07-01

Highlights: • Intrinsic oscillation modes of skyrmion are studied by using micromagnetic simulation. • Creation of skyrmion through resonant excitation is proposed. • The number of generated skyrmions can be effectively controlled by manipulating the driving field. • Skyrmion lattice in extended film is generated via resonant excitation. - Abstract: Controllable creation of magnetic skyrmions in nanostructures is a prerequisite for the application of skyrmions in spintronics. Here, we propose a new method for the creation of skyrmions. We show by using micromagnetic simulations that the skyrmions can be nucleated by resonantly exciting one of the skyrmion intrinsic oscillation modes. We first studied the dynamics of skyrmion in a ferromagnetic nanodisk with perpendicular anisotropy. One breathing mode and two non-degenerate gyrotropic modes are identified. Then we applied a circular-polarized microwave field to excite the uniformly magnetized nanodisk. When the frequency of the driving field is equal to the eigenfrequency of the skyrmion gyrotropic mode, stable skyrmions can be created from the initial uniform state. The number of skyrmions can be effectively controlled by appropriately choosing the duration of the driving field or tuning the field amplitude.

Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques

Science.gov (United States)

Kovalev, Alexey A.

2014-06-01

We derive thermomagnonic torque and its "β-type" dissipative correction from the stochastic Landau-Lifshitz-Gilbert equation. The β-type dissipative correction describes viscous coupling between magnetic dynamics and magnonic current and it stems from spin mistracking of the magnetic order. We show that thermomagnonic torque is important for describing temperature gradient induced motion of skyrmions in helical magnets while dissipative correction plays an essential role in generating transverse Magnus force. We propose to detect such skyrmionic motion by employing the transverse spin Seebeck effect geometry.

Interplay between tensor force and deformation in even–even nuclei

Energy Technology Data Exchange (ETDEWEB)

Bernard, Rémi N., E-mail: rbernard@ugr.es; Anguiano, Marta

2016-09-15

In this work we study the effect of the nuclear tensor force on properties related with deformation. We focus on isotopes in the Mg, Si, S, Ar, Sr and Zr chains within the Hartree–Fock–Bogoliubov theory using the D1ST2a Gogny interaction. Contributions to the tensor energy in terms of saturated and unsaturated subshells are analyzed. Like–particle and proton–neutron parts of the tensor term are independently examinated. We found that the tensor term may considerably modify the potential energy landscapes and change the ground state shape. We analyze too how the pairing characteristics of the ground state change when the tensor force is included.

Skyrmion-based multi-channel racetrack

Science.gov (United States)

Song, Chengkun; Jin, Chendong; Wang, Jinshuai; Xia, Haiyan; Wang, Jianbo; Liu, Qingfang

2017-11-01

Magnetic skyrmions are promising for the application of racetrack memories, logic gates, and other nano-devices, owing to their topologically protected stability, small size, and low driving current. In this work, we propose a skyrmion-based multi-channel racetrack memory where the skyrmion moves in the selected channel by applying voltage-controlled magnetic anisotropy gates. It is demonstrated numerically that a current-dependent skyrmion Hall effect can be restrained by the additional potential of the voltage-controlled region, and the skyrmion velocity and moving channel in the racetrack can be operated by tuning the voltage-controlled magnetic anisotropy, gate position, and current density. Our results offer a potential application of racetrack memory based on skyrmions.

Nonlinear Magnus-induced dynamics and Shapiro spikes for ac and dc driven skyrmions on periodic quasi-one-dimensional substrates

Science.gov (United States)

Reichhardt, Charles; Reichhardt, Cynthia J. Olson

We numerically examine skyrmions interacting with a periodic quasi-one-dimensional substrate. When we drive the skyrmions perpendicular to the substrate periodicity direction, a rich variety of nonlinear Magnus-induced effects arise, in contrast to an overdamped system that shows only a linear velocity-force curve for this geometry. The skyrmion velocity-force curve is strongly nonlinear and we observe a Magnus-induced speed-up effect when the pinning causes the Magnus velocity response to align with the dissipative response. At higher applied drives these components decouple, resulting in strong negative differential conductivity. For skyrmions under combined ac and dc driving, we find a new class of phase locking phenomena in which the velocity-force curves contain a series of what we call Shapiro spikes, distinct from the Shapiro steps observed in overdamped systems. There are also regimes in which the skyrmion moves in the direction opposite to the applied dc drive to give negative mobility.

Cooperative Charge Pumping and Enhanced Skyrmion Mobility

KAUST Repository

Abbout, Adel; Weston, Joseph; Waintal, Xavier; Manchon, Aurelien

2018-01-01

. It is shown that the ability of steadily moving skyrmions to pump large charge currents arises from their non-trivial magnetic topology, i.e. the coexistence between spin-motive force and topological Hall effect. Based on an adiabatic scattering theory, we

Topics in Skyrmion physics

International Nuclear Information System (INIS)

1986-01-01

The first part of the thesis is concerned with the spectrum of fermions interacting with a topological Skyrmion background field. It is shown that, in contradiction to the usual interpretation of a result obtained with the adiabatic approximation, no fermion charge is localized on the Skyrmion through the mechanism of vacuum polarization. This result is obtained by explicitly solving for the continuum spectrum with a simplified Skyrmion profile. However, the Skyrmion can acquire charge if there is spectral flow across zero energy, and an argument is given for why the adiabatic method gives the correct charge under certain conditions. The implications of this understanding of Skyrmion charge for Skyrmion bags are discussed. The second part of the thesis is an investigation into the phenomenology of Skyrmion-like solitons in the standard electroweak model with a large Higgs mass. Estimates of the masses, couplings, and widths of such solitons are derived. The possibility of a resonance analogous to the rho meson in hadron physics is entertained, and the assumption that this resonance is a soliton-antisoliton bound state is used to estimate that its mass is on the order of a TeV. Unitarity arguments are used to get an estimate for the width of this resonance

Direct writing of room temperature and zero field skyrmion lattices by a scanning local magnetic field

KAUST Repository

Zhang, Senfu; Zhang, Junwei; Zhang, Qiang; Barton, Craig; Neu, Volker; Zhao, Yuelei; Hou, Zhipeng; Wen, Yan; Gong, Chen; Kazakova, Olga; Wang, Wenhong; Peng, Yong; Garanin, Dmitry A.; Chudnovsky, Eugene M.; Zhang, Xixiang

2018-01-01

Magnetic skyrmions are topologically protected nanoscale spin textures exhibiting fascinating physical behaviors. Recent observations of room temperature skyrmions in sputtered multilayer films are an important step towards their use in ultra-low power devices. Such practical applications prefer skyrmions to be stable at zero magnetic fields and room temperature. Here, we report the creation of skyrmion lattices in Pt/Co/Ta multilayers by a scanning local field using magnetic force microscopy tips. We also show that those newly created skyrmion lattices are stable at both room temperature and zero fields. Lorentz transmission electron microscopy measurements reveal that the skyrmions in our films are of Néel-type. To gain a deeper understanding of the mechanism behind the creation of a skyrmion lattice by the scanning of local fields, we perform micromagnetic simulations and find the experimental results to be in agreement with our simulation data. This study opens another avenue for the creation of skyrmion lattices in thin films.

Direct writing of room temperature and zero field skyrmion lattices by a scanning local magnetic field

KAUST Repository

Zhang, Senfu

2018-03-29

Magnetic skyrmions are topologically protected nanoscale spin textures exhibiting fascinating physical behaviors. Recent observations of room temperature skyrmions in sputtered multilayer films are an important step towards their use in ultra-low power devices. Such practical applications prefer skyrmions to be stable at zero magnetic fields and room temperature. Here, we report the creation of skyrmion lattices in Pt/Co/Ta multilayers by a scanning local field using magnetic force microscopy tips. We also show that those newly created skyrmion lattices are stable at both room temperature and zero fields. Lorentz transmission electron microscopy measurements reveal that the skyrmions in our films are of Néel-type. To gain a deeper understanding of the mechanism behind the creation of a skyrmion lattice by the scanning of local fields, we perform micromagnetic simulations and find the experimental results to be in agreement with our simulation data. This study opens another avenue for the creation of skyrmion lattices in thin films.

Direct writing of room temperature and zero field skyrmion lattices by a scanning local magnetic field

Science.gov (United States)

Zhang, Senfu; Zhang, Junwei; Zhang, Qiang; Barton, Craig; Neu, Volker; Zhao, Yuelei; Hou, Zhipeng; Wen, Yan; Gong, Chen; Kazakova, Olga; Wang, Wenhong; Peng, Yong; Garanin, Dmitry A.; Chudnovsky, Eugene M.; Zhang, Xixiang

2018-03-01

Magnetic skyrmions are topologically protected nanoscale spin textures exhibiting fascinating physical behaviors. Recent observations of room temperature skyrmions in sputtered multilayer films are an important step towards their use in ultra-low power devices. Such practical applications prefer skyrmions to be stable at zero magnetic fields and room temperature. Here, we report the creation of skyrmion lattices in Pt/Co/Ta multilayers by a scanning local field using magnetic force microscopy tips. We also show that those newly created skyrmion lattices are stable at both room temperature and zero fields. Lorentz transmission electron microscopy measurements reveal that the skyrmions in our films are of Néel-type. To gain a deeper understanding of the mechanism behind the creation of a skyrmion lattice by the scanning of local fields, we perform micromagnetic simulations and find the experimental results to be in agreement with our simulation data. This study opens another avenue for the creation of skyrmion lattices in thin films.

Dynamics of current induced nano-skyrmions

Energy Technology Data Exchange (ETDEWEB)

Natarajan, Kanimozhi; Rajamani, Amuda, E-mail: amuacademics@gmail.com; Arumugam, Brinda

2017-08-01

Highlights: • We have revised and organised section II. • The expression for H{sub eff} is now expressed clearly. • We have added Appendix which explains the derivation of the solution and the occurrence of the oscillatory factor. - Abstract: The dynamics of magnetic skyrmions is investigated in a composite free layer spin valve nano pillar for different coupling mechanisms in the absence of Dzyaloshinski-Moriya Interaction (DMI). Nano meter sized skyrmions and anti skyrmions are trapped with different helices in the free layer. The spin polarised current under specific choice of system parameters changes the droplet solitons into skyrmions and anti skyrmions. The current driven dynamics is studied and the condition at which an isolated skyrmion exists, is reported. We have optimised the current density (J) and spin wave vector (k) for which Skyrmion Hall Effect (SHE) completely vanishes and as a result the velocity, size and shape of skyrmions are preserved. When the coupling between the composite free layers is changed, skyrmion-anti skyrmion pair and radial skyrmion-chiral skyrmion pair emerge. For the specific values of ‘J’ and ‘k’ these pairs show coupled motion along the layer and hence these pairs could also be used as a bit in the data processing and storage devices. Our investigation ascertains that a single material can host all the localised magnetic structures if the current density, spin wave vector and coupling constant are suitably chosen and tuned. This study would really be of fundamental importance owing to the possible applications in information processing and data storage in skyrmion based logic circuits and magnetic sensors.

Tensor force and debye screening in quarkonium-type mesons

International Nuclear Information System (INIS)

Kovacs, L.B.; Kovacs, T.G.; Lovas, I.

1990-01-01

We use a non-relativistic quantum-mechanical model to investigate the effect of a screening plasma on two quarkonium-type mesons: the charmonium and bottonium. The stability of these mesons in the plasma is estimated in two cases: including the tensor and spin-orbit term in the potential and without these terms. It turns out that while the bottonium is somewhat stabilized by the tensor force, the charmonium becomes less stabil due to this modification of the potential. Thus the charmonium seems to be a more sensitive probe of the quark-gluon plasma formation than it was thought to be without including the tensor force. (Authors)

Universal current-velocity relation of skyrmion motion in chiral magnets

Science.gov (United States)

Iwasaki, Junichi; Mochizuki, Masahito; Nagaosa, Naoto

2013-03-01

Current-driven motion of the magnetic domain wall requires large critical current density jc ~109 -1012 A/m2, at which the joule heating is a serious problem. The skyrmions recently discovered in chiral magnets, on the other hand, have much smaller critical current of jc ~105 -106 A/m2. We present a numerical simulation of the Landau-Lifshitz-Gilbert equation, which reveals a remarkably robust and universal current-velocity relation of the slyrmion motion driven by the spin transfer torque unaffected by either impurities or nonadiabatic effect in sharp contrast to the case of domain wall or spin helix (HL). Simulation results are analyzed using a theory based on Thiele's equation, and it is concluded that this surprising behavior is due to the Magnus force and flexible shape-deformation of individual skyrmions and skyrmion crystal (SkX), which enable them to avoid pinning centers and then weaken the net pinning force. Dynamical deformation of SkX leads to the fluctuation of Bragg peak with large amplitude, which can be detected by the recent neutron-scattering experiment.

The multifaceted skyrmion

CERN Document Server

Rho, Mannque

2010-01-01

This is a sequel to the World Scientific volume edited by Gerald E Brown in 1994 entitled ""Selected Papers"", with Commentary, of 'Tony Hilton Royle Skyrme'. There has been a series of impressive developments in the application of the skyrmion structure to wide-ranging physical phenomena. The first volume was mainly focused on the rediscovery of the skyrmion in 1983 in the context of Quantum Chromodynamics (QCD) and on its striking role in nuclear physics. Since 1994, skyrmions have been found to play an even greater role not only in various aspects of particle physics and astrophysics but al

Tuning the stability and the skyrmion Hall effect in magnetic skyrmions by adjusting their exchange strengths with magnetic disks

Science.gov (United States)

Sun, L.; Wu, H. Z.; Miao, B. F.; Wu, D.; Ding, H. F.

2018-06-01

Magnetic skyrmion is a promising candidate for the future information technology due to its small size, topological protection and the ultralow current density needed to displace it. The applications, however, are currently limited by its narrow phase diagram and the skyrmion Hall effect which prevents the skyrmion motion at high speed. In this work, we study the Dzyaloshinskii-Moriya interaction induced magnetic skyrmion that exchange coupled with magnetic nano-disks utilizing the micromagnetic simulation. We find that the stability and the skyrmion Hall effect of the created skyrmion can be tuned effectively with the coupling strength, thus opens the space to optimize the performance of the skyrmion based devices.

The half-skyrmion phase in a chiral-quark model

International Nuclear Information System (INIS)

Mantovani Sarti, Valentina; Vento, Vicente

2014-01-01

The Chiral Dilaton Model, where baryons arise as non-topological solitons built from the interaction of quarks and chiral mesons, shows in the high density low temperature regime a two phase scenario in the nuclear matter phase diagram. Dense soliton matter described by the Wigner–Seitz approximation generates a periodic potential in terms of the sigma and pion fields that leads to the formation of a band structure. The analysis up to three times nuclear matter density shows that soliton matter undergoes two separate phase transitions: a delocalization of the baryon number density leading to B=1/2 structures, as in skyrmion matter, at moderate densities, and quark deconfinement at larger densities. This description fits well into the so-called quarkyonic phase where, before deconfinement, nuclear matter should undergo structural changes involving the restoration of fundamental symmetries of QCD

Skyrmion creation and annihilation by spin waves

International Nuclear Information System (INIS)

Liu, Yizhou; Yin, Gen; Lake, Roger K.; Zang, Jiadong; Shi, Jing

2015-01-01

Single skyrmion creation and annihilation by spin waves in a crossbar geometry are theoretically analyzed. A critical spin-wave frequency is required both for the creation and the annihilation of a skyrmion. The minimum frequencies for creation and annihilation are similar, but the optimum frequency for creation is below the critical frequency for skyrmion annihilation. If a skyrmion already exists in the cross bar region, a spin wave below the critical frequency causes the skyrmion to circulate within the central region. A heat assisted creation process reduces the spin-wave frequency and amplitude required for creating a skyrmion. The effective field resulting from the Dzyaloshinskii-Moriya interaction and the emergent field of the skyrmion acting on the spin wave drive the creation and annihilation processes

Stray field signatures of Néel textured skyrmions in Ir/Fe/Co/Pt multilayer films

Science.gov (United States)

Yagil, A.; Almoalem, A.; Soumyanarayanan, Anjan; Tan, Anthony K. C.; Raju, M.; Panagopoulos, C.; Auslaender, O. M.

2018-05-01

Skyrmions are nanoscale spin configurations with topological properties that hold great promise for spintronic devices. Here, we establish their Néel texture, helicity, and size in Ir/Fe/Co/Pt multilayer films by constructing a multipole expansion to model their stray field signatures and applying it to magnetic force microscopy images. Furthermore, the demonstrated sensitivity to inhomogeneity in skyrmion properties, coupled with a unique capability to estimate the pinning force governing dynamics, portend broad applicability in the burgeoning field of topological spin textures.

Magnetic skyrmions: from fundamental to applications

International Nuclear Information System (INIS)

Finocchio, Giovanni; Büttner, Felix; Tomasello, Riccardo; Carpentieri, Mario; Kläui, Mathias

2016-01-01

In this topical review, we will discuss recent advances in the field of skyrmionics (fundamental and applied aspects) mainly focusing on skyrmions that can be realized in thin film structures where an ultrathin ferromagnetic layer (<1 nm) is coupled to materials with large spin–orbit coupling. We review the basic topological nature of the skyrmion spin structure that can entail a stabilization due to the chiral exchange interaction present in many multilayer systems with structural inversion asymmetry. The static spin structures and the dynamics of the skyrmions are also discussed. In particular, we show that skyrmions can be displaced with high reliability and efficiency as needed for the use in devices. We discuss major possible applications, such as memory, microwave oscillators and logic, and combinations of these, making skyrmions very promising candidates for future low power IT devices. (topical review)

Skyrmions and Hall viscosity

Science.gov (United States)

Kim, Bom Soo

2018-05-01

We discuss the contribution of magnetic Skyrmions to the Hall viscosity and propose a simple way to identify it in experiments. The topological Skyrmion charge density has a distinct signature in the electric Hall conductivity that is identified in existing experimental data. In an electrically neutral system, the Skyrmion charge density is directly related to the thermal Hall conductivity. These results are direct consequences of the field theory Ward identities, which relate various physical quantities based on symmetries and have been previously applied to quantum Hall systems.

Spin eigenmodes of magnetic skyrmions and the problem of the effective skyrmion mass

Science.gov (United States)

Kravchuk, Volodymyr P.; Sheka, Denis D.; Rößler, Ulrich K.; van den Brink, Jeroen; Gaididei, Yuri

2018-02-01

The properties of magnon modes localized on a ferromagnetic skyrmion are studied. Mode eigenfrequencies display three types of asymptotic behavior for large skyrmion radius Rs, namely, ω0∝Rs-2 for the breathing mode and ω-|μ |∝Rs-1 and ω|μ |∝Rs-3 for modes with negative and positive azimuthal quantum numbers, respectively. A number of properties of the magnon eigenfunctions are determined. This enables us to demonstrate that the skyrmion dynamics for a traveling-wave ansatz obeys the massless Thiele equation.

Spin motive force driven by the magnetization dynamics in chiral magnets

International Nuclear Information System (INIS)

Ohe, Jun-ichiro; Shimada, Yuhki

2015-01-01

The magnetization dynamics induces the spin-dependent force on the conduction electrons via the s-d coupling. We have investigated numerically this force, so called 'spin-motive force', generated in chiral magnets forming the Skyrmion structure. We solve the Landau-Lifshitz-Gilbert equation and obtain the Skyrmion lattice structure (SkX) by introducing the Dzyaloshinskii-Moriya (DM) interaction. The corrective mode of the Skyrmion core is obtained by applying the in-plane AC magnetic field. The spin-motive force is generated perpendicular to the velocity of the Skyrmion core. The total voltage due to the spin-motive force is enhanced by the cascade effect of the voltage for each Skyrmion core. For the isolated magnetic disc system, the corrective mode of the Skyrmion lattice is modulated from that of the bulk system by the influence of the edge structure. The phase-locking motion of each Skyrmion core is obtained only in the lowest frequency mode in which the cascade effect of the spin-motive force still remain. (author)

Strength of tensor force and s-d-shell effective interactions

International Nuclear Information System (INIS)

Jiang, M.; Machleidt, R.; Stout, D.B.; Kuo, T.T.S.

1989-01-01

The s-d-shell effective interaction is derived from the Bonn NN potential, using a G-matrix folded-diagram method. It is found that due to the relatively weak-tensor-force characteristic for the Bonn potential, the effective interaction matrix elements, particularly those with isospin T=0, come out generally more attractive than in previous derivations which were based on conventional local strong-tensor-force NN potentials. This renders the results obtained with the Bonn potential in considerably better agreement with the recent s-d-shell matrix elements of Wildenthal

Reversible Vector Ratchet Effect in Skyrmion Systems

Science.gov (United States)

Ma, Xiaoyu; Reichhardt, Charles; Reichhardt, Cynthia

Magnetic skyrmions are topological non-trivial spin textures found in several magnetic materials. Since their motion can be controlled using ultralow current densities, skyrmions are appealing for potential applications in spintronics as information carriers and processing devices. In this work, we studied the collective transport properties of driven skyrmions based on a particle-like model with molecular dynamics (MD) simulation. Our results show that ac driven skyrmions interacting with an asymmetric substrate provide a realization of a new class of ratchet system, which we call a vector ratchet, that arises due to the effect of the Magnus term on the skyrmion dynamics. In a vector ratchet, the dc motion induced by the ac drive can be described as a vector that can be rotated up to 360 degrees relative to the substrate asymmetry direction. This could represent a new method for controlling skyrmion motion for spintronic applications.

Creation and Annihilation of Skyrmions in the Frustrated Magnets with Competing Exchange Interactions.

Science.gov (United States)

Hu, Yong; Chi, Xiaodan; Li, Xuesi; Liu, Yan; Du, An

2017-11-22

In triangular-lattice magnets, the coexistence of third-neighbor antiferromagnetic and nearest-neighbor ferromagnetic exchange interactions can induce rich magnetic phases including noncoplanar skyrmion crystals. Based on Monte Carlo simulation, we studied the dependence of magnetic phase transition on exchange interaction strength. Under the consideration of uniaxial anisotropy and magnetic field both perpendicular to the film plane, a large antiferromagnetic exchange interaction induces a high frustration. When the value of antiferromagnetic exchange interaction is one and a half times larger than the ferromagnetic one, a magnetic phase composed of canting spin stripes, never observed in the chiral magnets, forms. Interestingly, different canting spin stripes along three 120 degree propagation directions may coexist randomly in a magnetic phase, attesting that the canting spin stripes are three-fold degenerate states akin to helices and the multiple state of canting spin stripes is a circular configuration with zero skyrmion charge number. Moreover, skyrmions and antiskyrmions can be observed simultaneously in the configuration at the low temperature nearly close to 0 K, and their configuration and diameter properties are discussed. Finally, the mechanisms of skyrmion creation and annihilation are properly interpreted by comparing exchange and Zeeman energy terms.

Investigation of the nucleon-nucleon tensor force in three-nucleon system

Energy Technology Data Exchange (ETDEWEB)

Clajus, M.; Egun, P.M.; Gruebler, W.; Hautle, P. (Eidgenoessische Technische Hochschule, Zurich (Switzerland). Inst. fuer Mittelenergiephysik); Slaus, I. (Institut Rudjer Boskovic, Zagreb (Yugoslavia)); Vuaridel, B. (Michigan Univ., Ann Arbor (USA) Brookhaven National Lab., Upton, NY (USA)); Sperisen, F. (Indiana Univ., Bloomington (USA). Cyclotron Facility); Kretschmer, W.; Rauscher, A.; Schuster, W.; Weidmann, R.; Haller, M. (Erlangen-Nuernberg Univ., Erlangen (Germany, F.R.)); Bruno, M.; Cannata, F.; D' Agostino, M. (Istituto Nazionale di Fisica Nucleare, Bologna (Italy)); Witala, H.; Cornelius, T.; Gloeckle, W. (Bochum Univ. (Germany, F.R.)); Schmelzbach, P.A. (Paul Scherrer Inst., Villigen (Switzerland))

1990-08-16

Proton-deuteron elastic scattering has been investigated at E{sub p}=22.7 MeV by comparison of rigorous Faddeev calculations with experimental results. The observable most sensitive to the tensor force is the nucleon-nucleon polarization transfer coefficient K{sub y}sup(y'). The new angular distribution of K{sub y}sup(y') clearly favours the tensor force of the Bonn A potential, which is weaker than the one of the Paris potential. (orig.).

Noncommutative baby Skyrmions

International Nuclear Information System (INIS)

Ioannidou, Theodora; Lechtenfeld, Olaf

2009-01-01

We subject the baby Skyrme model to a Moyal deformation, for unitary or Grassmannian target spaces and without a potential term. In the Abelian case, the radial BPS configurations of the ordinary noncommutative sigma model also solve the baby Skyrme equation of motion. This gives a class of exact analytic noncommutative baby Skyrmions, which have a singular commutative limit but are stable against scaling due to the noncommutativity. We compute their energies, investigate their stability and determine the asymptotic two-Skyrmion interaction.

Squirming motion of baby skyrmions in nematic fluids.

Science.gov (United States)

Ackerman, Paul J; Boyle, Timothy; Smalyukh, Ivan I

2017-09-22

Skyrmions are topologically protected continuous field configurations that cannot be smoothly transformed to a uniform state. They behave like particles and give origins to the field of skyrmionics that promises racetrack memory and other technological applications. Unraveling the non-equilibrium behavior of such topological solitons is a challenge. We realize skyrmions in a chiral liquid crystal and, using numerical modeling and polarized video microscopy, demonstrate electrically driven squirming motion. We reveal the intricate details of non-equilibrium topology-preserving textural changes driving this behavior. Direction of the skyrmion's motion is robustly controlled in a plane orthogonal to the applied field and can be reversed by varying frequency. Our findings may spur a paradigm of soliton dynamics in soft matter, with a rich interplay between topology, chirality, and orientational viscoelasticity.A skyrmion is a topological object originally introduced to model elementary particles and a baby skyrmion is its two-dimensional counterpart which can be realized as a defect in liquid crystals. Here the authors show that an electric field can drive uniform motion of baby skyrmions in liquid crystals.

Interaction of Individual Skyrmions in a Nanostructured Cubic Chiral Magnet

Science.gov (United States)

Du, Haifeng; Zhao, Xuebing; Rybakov, Filipp N.; Borisov, Aleksandr B.; Wang, Shasha; Tang, Jin; Jin, Chiming; Wang, Chao; Wei, Wensheng; Kiselev, Nikolai S.; Zhang, Yuheng; Che, Renchao; Blügel, Stefan; Tian, Mingliang

2018-05-01

We report direct evidence of the field-dependent character of the interaction between individual magnetic skyrmions as well as between skyrmions and edges in B 20 -type FeGe nanostripes observed by means of high-resolution Lorentz transmission electron microscopy. It is shown that above certain critical values of an external magnetic field the character of such long-range skyrmion interactions changes from attraction to repulsion. Experimentally measured equilibrium inter-skyrmion and skyrmion-edge distances as a function of the applied magnetic field shows quantitative agreement with the results of micromagnetic simulations. The important role of demagnetizing fields and the internal symmetry of three-dimensional magnetic skyrmions are discussed in detail.

Skyrmion physics in Bose-Einstein ferromagnets

NARCIS (Netherlands)

Al Khawaja, U.; Stoof, H.T.C.

2001-01-01

We show that a ferromagnetic Bose-Einstein condensate has not only line-like vortex excitations, but in general, also allows for pointlike topological excitations, i.e., skyrmions. We discuss the thermodynamic stability and the dynamic properties of these skyrmions for both spin-1/2 and

Rational maps, monopoles and skyrmions

International Nuclear Information System (INIS)

Houghton, C.J.; Manton, N.S.

1998-01-01

We discuss the similarities between BPS monopoles and skyrmions, and point to an underlying connection in terms of rational maps between Riemann spheres. This involves the introduction of a new ansatz for Skyrme fields. We use this to construct good approximations to several known skyrmions, including all the minimal energy configurations up to baryon number nine, and some new solutions such as a baryon number seventeen Skyrme field with the truncated icosahedron structure of a buckyball. The new approach is also used to understand the low-lying vibrational modes of skyrmions, which are required for quantization. Along the way we discover an interesting Morse function on the space of rational maps which may be of use in understanding the Sen forms on the monopole moduli spaces. (orig.)

Very heavy dark Skyrmions

International Nuclear Information System (INIS)

Dick, Rainer

2017-01-01

A dark sector with a solitonic component provides a means to circumvent the problem of generically low annihilation cross sections of very heavy dark matter particles. At the same time, enhanced annihilation cross sections are necessary for indirect detection of very heavy dark matter components beyond 100 TeV. Non-thermally produced dark matter in this mass range could therefore contribute to the cosmic γ-ray and neutrino flux above 100 TeV, and massive Skyrmions provide an interesting framework for the discussion of these scenarios. Therefore a Higgs portal and a neutrino portal for very heavy Skyrmion dark matter are discussed. The Higgs portal model demonstrates a dark mediator bottleneck, where limitations on particle annihilation cross sections will prevent a signal from the potentially large soliton annihilation cross sections. This problem can be avoided in models where the dark mediator decays. This is illustrated by the neutrino portal for Skyrmion dark matter. (orig.)

Very heavy dark Skyrmions

Energy Technology Data Exchange (ETDEWEB)

Dick, Rainer [University of Saskatchewan, Department of Physics and Engineering Physics, Saskatoon, SK (Canada)

2017-12-15

A dark sector with a solitonic component provides a means to circumvent the problem of generically low annihilation cross sections of very heavy dark matter particles. At the same time, enhanced annihilation cross sections are necessary for indirect detection of very heavy dark matter components beyond 100 TeV. Non-thermally produced dark matter in this mass range could therefore contribute to the cosmic γ-ray and neutrino flux above 100 TeV, and massive Skyrmions provide an interesting framework for the discussion of these scenarios. Therefore a Higgs portal and a neutrino portal for very heavy Skyrmion dark matter are discussed. The Higgs portal model demonstrates a dark mediator bottleneck, where limitations on particle annihilation cross sections will prevent a signal from the potentially large soliton annihilation cross sections. This problem can be avoided in models where the dark mediator decays. This is illustrated by the neutrino portal for Skyrmion dark matter. (orig.)

Tunable surface configuration of skyrmion lattices in cubic helimagnets

Science.gov (United States)

Wan, Xuejin; Hu, Yangfan; Wang, Biao

2018-06-01

In bulk helimagnets, the presence of magnetic skyrmion lattices is always accompanied by a periodic stress field due to the intrinsic magnetoelastic coupling. The release of this nontrivial stress field at the surface causes a periodic displacement field, which characterizes a novel particle-like property of skyrmion: its surface configuration. Here, we derive the analytical solution of this displacement field for semi-infinite cubic helimagnet with the skyrmion magnetization approximated by the triple-Q representation. For MnSi, we show that the skyrmion lattices have a bumpy surface configuration characterized by periodically arranged peaks with a characteristic height of about 10‑13 m. The pattern of the peaks can be controlled by varying the strength of the applied magnetic field. Moreover, we prove that the surface configuration varies together with the motion and deformation of the skyrmion lattices. As a result, the surface configuration can be tuned by application of electric current, mechanical loads, as well as any other effective external fields for skyrmion lattices.

Face Centered Cubic and Hexagonal Close Packed Skyrmion Crystals in Centrosymmetric Magnets

Science.gov (United States)

Lin, Shi-Zeng; Batista, Cristian D.

2018-02-01

Skyrmions are disklike objects that typically form triangular crystals in two-dimensional systems. This situation is analogous to the so-called pancake vortices of quasi-two-dimensional superconductors. The way in which Skyrmion disks or "pancake Skyrmions" pile up in layered centrosymmetric materials is dictated by the interlayer exchange. Unbiased Monte Carlo simulations and simple stabilization arguments reveal face centered cubic and hexagonal close packed Skyrmion crystals for different choices of the interlayer exchange, in addition to the conventional triangular crystal of Skyrmion lines. Moreover, an inhomogeneous current induces a sliding motion of pancake Skyrmions, indicating that they behave as effective mesoscale particles.

Stability of skyrmions on curved surfaces in the presence of a magnetic field

Energy Technology Data Exchange (ETDEWEB)

Carvalho-Santos, V.L., E-mail: vagson.carvalho@usach.cl [Instituto Federal de Educação, Ciência e Tecnologia Baiano - Campus Senhor do Bonfim, Km 04 Estrada da Igara, 48970-000 Senhor do Bonfim, Bahia (Brazil); Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Avda. Ecuador 3493, Santiago (Chile); Elias, R.G.; Altbir, D. [Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Avda. Ecuador 3493, Santiago (Chile); Fonseca, J.M. [Universidade Federal de Viçosa, Departamento de Física, Avenida Peter Henry Rolfs s/n, 36570-000 Viçosa, MG (Brazil)

2015-10-01

We study the stability and energetics associated to skyrmions appearing as excitations on curved surfaces. Using a continuum model we show that the presence of cylindrically radial and azimuthal fields destabilize the skyrmions that appear in the absence of an external field. Weak fields generate fractional skyrmions while strong magnetic fields yield stable 2π-skyrmions, which have their widths diminished by the magnetic field strength. Under azimuthal fields vortex appears as stable state on the curved surface. - Highlights: • Stability of skyrmions on curved surfaces in the presence of a magnetic field. • Weak fields can destabilize skyrmions. • Strong magnetic fields yield the appearing of 2π-skyrmions. • The width of skyrmions is determined by the curvature and magnetic field strength. • Under azimuthal fields vortex appears as stable states.

BPS Skyrmions as neutron stars

Energy Technology Data Exchange (ETDEWEB)

Adam, C., E-mail: adam@fpaxp1.usc.es [Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela (Spain); Naya, C.; Sanchez-Guillen, J.; Vazquez, R. [Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela (Spain); Wereszczynski, A. [Institute of Physics, Jagiellonian University, Reymonta 4, Kraków (Poland)

2015-03-06

The BPS Skyrme model has been demonstrated already to provide a physically intriguing and quantitatively reliable description of nuclear matter. Indeed, the model has both the symmetries and the energy–momentum tensor of a perfect fluid, and thus represents a field theoretic realization of the “liquid droplet” model of nuclear matter. In addition, the classical soliton solutions together with some obvious corrections (spin–isospin quantization, Coulomb energy, proton-neutron mass difference) provide an accurate modeling of nuclear binding energies for heavier nuclei. These results lead to the rather natural proposal to try to describe also neutron stars by the BPS Skyrme model coupled to gravity. We find that the resulting self-gravitating BPS Skyrmions provide excellent results as well as some new perspectives for the description of bulk properties of neutron stars when the parameter values of the model are extracted from nuclear physics. Specifically, the maximum possible mass of a neutron star before black-hole formation sets in is a few solar masses, the precise value of which depends on the precise values of the model parameters, and the resulting neutron star radius is of the order of 10 km.

Skyrmion based microwave detectors and harvesting

International Nuclear Information System (INIS)

Finocchio, G.; Giordano, A.; Ricci, M.; Burrascano, P.; Tomasello, R.; Lanuzza, M.; Puliafito, V.; Azzerboni, B.; Carpentieri, M.

2015-01-01

Magnetic skyrmions are topologically protected states that are very promising for the design of the next generation of ultra-low-power electronic devices. In this letter, we propose a magnetic tunnel junction based spin-transfer torque diode with a magnetic skyrmion as ground state and a perpendicular polarizer patterned as nano-contact for a local injection of the current. The key result is the possibility to achieve sensitivities (i.e., detection voltage over input microwave power) larger than 2000 V/W for optimized contact diameters. We also pointed out that large enough voltage controlled magnetocrystalline anisotropy could significantly improve the sensitivity. Our results can be very useful for the identification of a class of spin-torque diodes with a non-uniform ground state and to understand the fundamental physics of the skyrmion dynamical properties

Skyrmion based microwave detectors and harvesting

Energy Technology Data Exchange (ETDEWEB)

Finocchio, G.; Giordano, A. [Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d' Alcontres 31, 98166 Messina (Italy); Ricci, M.; Burrascano, P. [Department of Engineering, Polo Scientifico Didattico di Terni, University of Perugia, Terni, TR I-50100 (Italy); Tomasello, R.; Lanuzza, M. [Department of Computer Science, Modelling, Electronics and System Science, University of Calabria, via P. Bucci 41C, I-87036 Rende (CS) (Italy); Puliafito, V.; Azzerboni, B. [Department of Engineering, University of Messina, c.da di Dio, I-98166 Messina (Italy); Carpentieri, M. [Department of Electrical and Information Engineering, Politecnico di Bari, via E. Orabona 4, I-70125 Bari (Italy)

2015-12-28

Magnetic skyrmions are topologically protected states that are very promising for the design of the next generation of ultra-low-power electronic devices. In this letter, we propose a magnetic tunnel junction based spin-transfer torque diode with a magnetic skyrmion as ground state and a perpendicular polarizer patterned as nano-contact for a local injection of the current. The key result is the possibility to achieve sensitivities (i.e., detection voltage over input microwave power) larger than 2000 V/W for optimized contact diameters. We also pointed out that large enough voltage controlled magnetocrystalline anisotropy could significantly improve the sensitivity. Our results can be very useful for the identification of a class of spin-torque diodes with a non-uniform ground state and to understand the fundamental physics of the skyrmion dynamical properties.

Control and manipulation of antiferromagnetic skyrmions in racetrack

Science.gov (United States)

Xia, Haiyan; Jin, Chendong; Song, Chengkun; Wang, Jinshuai; Wang, Jianbo; Liu, Qingfang

2017-12-01

Controllable manipulations of magnetic skyrmions are essential for next-generation spintronic devices. Here, the duplication and merging of skyrmions, as well as logical AND and OR functions, are designed in antiferromagnetic (AFM) materials with a cusp or smooth Y-junction structures. The operational time are in the dozens of picoseconds, enabling ultrafast information processing. A key factor for the successful operation is the relatively complex Y-junction structures, where domain walls propagate through in a controlled manner, without significant risks of pinning, vanishing or unwanted depinning of existing domain walls, as well as the nucleation of new domain walls. The motions of a multi-bit, namely the motion of an AFM skyrmion-chain in racetrack, are also investigated. Those micromagnetic simulations may contribute to future AFM skyrmion-based spintronic devices, such as nanotrack memory, logic gates and other information processes.

B =5 Skyrmion as a two-cluster system

Science.gov (United States)

Gudnason, Sven Bjarke; Halcrow, Chris

2018-06-01

The classical B =5 Skyrmion can be approximated by a two-cluster system in which a B =1 Skyrmion is attached to a core B =4 Skyrmion. We quantize this system, allowing the B =1 to freely orbit the core. The configuration space is 11 dimensional but simplifies significantly after factoring out the overall spin and isospin degrees of freedom. We exactly solve the free quantum problem and then include an interaction potential between the Skyrmions numerically. The resulting energy spectrum is compared to the corresponding nuclei—the helium-5/lithium-5 isodoublet. We find approximate parity doubling not seen in the experimental data. In addition, we fail to obtain the correct ground-state spin. The framework laid out for this two-cluster system can readily be modified for other clusters and in particular for other B =4 n +1 nuclei, of which B =5 is the simplest example.

Nucleon-deuteron breakup quantities calculated with separable interactions including tensor forces and P-wave interactions

International Nuclear Information System (INIS)

Bruinsma, J.; Wageningen, R. van

1977-01-01

Nucleon-deuteron breakup calculations at a nucleon bombarding energy of 22.7 MeV have been performed with separable interactions including a tensor force and P-wave interactions. Differential cross sections and a selection of polarization quantities have been computed for special regions of the phase space. The influence of a tensor force and P-wave interactions on the differential cross section is of the order of 20%. Large discrepancies between theory and experiment occur for the vector analyzing powers, both for the kinematically complete and for the incomplete situation. The calculations show that there are kinematical situations in which the differential cross sections and the tensor analyzing powers are sufficiently large to make measurements feasible. (Auth.)

Short-distance expansion for the electromagnetic half-space Green's tensor: general results and an application to radiative lifetime computations

International Nuclear Information System (INIS)

Panasyuk, George Y; Schotland, John C; Markel, Vadim A

2009-01-01

We obtain a short-distance expansion for the half-space, frequency domain electromagnetic Green's tensor. The small parameter of the theory is ωε 1 L/c, where ω is the frequency, ε 1 is the permittivity of the upper half-space, in which both the source and the point of observation are located, and which is assumed to be transparent, c is the speed of light in vacuum and L is a characteristic length, defined as the distance from the point of observation to the reflected (with respect to the planar interface) position of the source. In the case when the lower half-space (the substrate) is characterized by a complex permittivity ε 2 , we compute the expansion to third order. For the case when the substrate is a transparent dielectric, we compute the imaginary part of the Green's tensor to seventh order. The analytical calculations are verified numerically. The practical utility of the obtained expansion is demonstrated by computing the radiative lifetime of two electromagnetically interacting molecules in the vicinity of a transparent dielectric substrate. The computation is performed in the strong interaction regime when the quasi-particle pole approximation is inapplicable. In this regime, the integral representation for the half-space Green's tensor is difficult to use while its electrostatic limiting expression is grossly inadequate. However, the analytical expansion derived in this paper can be used directly and efficiently. The results of this study are also relevant to nano-optics and near-field imaging, especially when tomographic image reconstruction is involved

Skyrmions and anomalies

International Nuclear Information System (INIS)

Rho, M.

1987-02-01

The author summarizes the works presented at the meeting on skyrmions and anomalies. He divides the principal issues of this workshop into five categories: QCD effective lagrangians, chiral bags and the Cheshire cat principle, strangeness problem, phenomenology, mathematical structure

The effect of including tensor forces in nucleon-nucleon interaction on three-nucleon binding energy

International Nuclear Information System (INIS)

Osman, A.; Ramadan, S.

1986-01-01

Separable two-body interactions are used in considering the three-nucleon problem. The nucleon-nucleon potentials are taken to include attraction and repulsion as well as tensor forces. The separable approximation is used in order to investigate the effect of the tensor forces. The separable expansion is introduced in the three-nucleon problem, by which the Faddeev equations are reduced to a well-behaved set of coupled integral equations. Numerical calculations are carried out for the obtained integral equations using potential functions of the Yamaguchi, Gaussian, Takabin, Mongan and Reid forms. The present calculated values of the binding energies of the 3 H and 3 He nuclei are in good agreement with the experimental values. The effect of including the tensor forces in the nucleon-nucleon interactions is found to improve the three-nucleon binding energy by about 4.490% to 8.324%. 37 refs., 2 tabs. (author)

Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application

Energy Technology Data Exchange (ETDEWEB)

Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2016-08-15

Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-)equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion, Skyrmion crystal and lattice with asymmetry, likely to be detected in precision experiments.

Aharonov–Bohm protection of black hole's baryon/skyrmion hair

Directory of Open Access Journals (Sweden)

Gia Dvali

2017-05-01

Full Text Available The baryon/skyrmion correspondence implies that the baryon number is encoded into a topological surface integral. Under certain conditions that we clarify, this surface integral can be measured by an asymptotic observer in form of an Aharonov–Bohm phase-shift in an experiment in which the skyrmion passes through a loop of a probe string. In such a setup the baryon/skyrmion number must be respected by black holes, despite the fact that it produces no long-range classical field. If initially swallowed by a black hole, the baryon number must resurface in form of a classical skyrmion hair, after the black hole evaporates below a certain critical size. Needless to say, the respect of the baryon number by black holes is expected to have potentially-interesting astrophysical consequences.

Skyrmions with holography and hidden local symmetry

International Nuclear Information System (INIS)

Nawa, Kanabu; Hosaka, Atsushi; Suganuma, Hideo

2009-01-01

We study baryons as Skyrmions in holographic QCD with D4/D8/D8 multi-D brane system in type IIA superstring theory, and also in the nonlinear sigma model with hidden local symmetry. Comparing these two models, we find that the extra dimension and its nontrivial curvature can largely change the role of (axial) vector mesons for baryons in four-dimensional space-time. In the hidden local symmetry approach, the ρ-meson field as a massive Yang-Mills field has a singular configuration in Skyrmion, which gives a strong repulsion for the baryon as a stabilizer. When the a 1 meson is added in this approach, the stability of Skyrmion is lost by the cancellation of ρ and a 1 contributions. On the contrary, in holographic QCD, the ρ-meson field does not appear as a massive Yang-Mills field due to the extra dimension and its nontrivial curvature. We show that the ρ-meson field has a regular configuration in Skyrmion, which gives a weak attraction for the baryon in holographic QCD. We argue that Skyrmion with π, ρ, and a 1 mesons become stable due to the curved extra dimension and also the presence of the Skyrme term in holographic QCD. From this result, we also discuss the features of our truncated-resonance analysis on baryon properties with π and ρ mesons below the cutoff scale M KK ∼1 GeV in holographic QCD, which is compared with other 5D instanton analysis.

Controllable transport of a skyrmion in a ferromagnetic narrow channel with voltage-controlled magnetic anisotropy

Science.gov (United States)

Wang, Junlin; Xia, Jing; Zhang, Xichao; Zhao, G. P.; Ye, Lei; Wu, Jing; Xu, Yongbing; Zhao, Weisheng; Zou, Zhigang; Zhou, Yan

2018-05-01

Magnetic skyrmions have potential applications in next-generation spintronic devices with ultralow energy consumption. In this work, the current-driven skyrmion motion in a narrow ferromagnetic nanotrack with voltage-controlled magnetic anisotropy (VCMA) is studied numerically. By utilizing the VCMA effect, the transport of skyrmion can be unidirectional in the nanotrack, leading to a one-way information channel. The trajectory of the skyrmion can also be modulated by periodically located VCMA gates, which protects the skyrmion from destruction by touching the track edge. In addition, the location of the skyrmion can be controlled by adjusting the driving pulse length in the presence of the VCMA effect. Our results provide guidelines for practical realization of the skyrmion-based information channel, diode, and skyrmion-based electronic devices such as racetrack memory.

Tensor force and delta excitation for the structure of light nuclei

International Nuclear Information System (INIS)

Horii, K; Myo, T; Toki, H

2014-01-01

We treat explicitly Δ(1232) isobar degrees of freedom using a bare nucleon-nucleon interaction for few-body systems, where Δ excitations can be the origin of the three-body force via the pion exchange. We adopt the Argonne two-body potential including Δ, named as AV28 potential, and study the role of Δ explicitly in two-body and three-body systems. It was found that the additional Δ states generate strong tensor correlations caused by the transitions between N and Δ states, and change tensor matrix elements largely from the results with only nucleons. We studied the effects of three-body force in the triton and obtained 0.8 MeV attraction due to the intermediate Δ excitation. Due to the lack of the total binding energy for the triton in the delta model, we further studied carefully the effects of the delta excitation in various two body channels and compared with the nucleon only model in the AV14 potential. We modified slightly the AV28 potential in the singlet S channel so that we could reproduce the triton binding energy due to the appropriate amount of the three-body force effects

Skyrmion burst and multiple quantum walk in thin ferromagnetic films

International Nuclear Information System (INIS)

Ezawa, Motohiko

2011-01-01

We propose a new type of quantum walk in thin ferromagnetic films. A giant Skyrmion collapses to a singular point in a thin ferromagnetic film, emitting spin waves, when external magnetic field is increased beyond the critical one. After the collapse the remnant is a quantum walker carrying spin S. We determine its time evolution and show the diffusion process is a continuous-time quantum walk. We also analyze an interference of two quantum walkers after two Skyrmion bursts. The system presents a new type of quantum walk for S>1/2, where a quantum walker breaks into 2S quantum walkers. -- Highlights: → A giant Skyrmion collapses to a singular point by applying strong magnetic field. → Quantum walk is realized in thin ferromagnetic films by Skyrmion collapsing. → Quantum walks for S=1/2 and 1 are exact solvable, where S represents the spin. → Quantum walks for >1/2 presents a new type of quantum walks, i.e., 'multiple quantum walks'. → Skyrmion bursts which occur simultaneously exhibit an interference as a manifestation of quantum walk.

Micromagnetic study of skyrmion stability in confined magnetic structures with perpendicular anisotropy

Science.gov (United States)

Novak, R. L.; Garcia, F.; Novais, E. R. P.; Sinnecker, J. P.; Guimarães, A. P.

2018-04-01

Skyrmions are emerging topological spin structures that are potentially revolutionary for future data storage and spintronics applications. The existence and stability of skyrmions in magnetic materials is usually associated to the presence of the Dzyaloshinskii-Moriya interaction (DMI) in bulk magnets or in magnetic thin films lacking inversion symmetry. While some methods have already been proposed to generate isolated skyrmions in thin films with DMI, a thorough study of the conditions under which the skyrmions will remain stable in order to be manipulated in an integrated spintronic device are still an open problem. The stability of such structures is believed to be a result of ideal combinations of perpendicular magnetic anisotropy (PMA), DMI and the interplay between geometry and magnetostatics. In the present work we show some micromagnetic results supporting previous experimental observations of magnetic skyrmions in spin-valve stacks with a wide range of DMI values. Using micromagnetic simulations of cobalt-based disks, we obtain the magnetic ground state configuration for several values of PMA, DMI and geometric parameters. Skyrmion numbers, corresponding to the topological charge, are calculated in all cases and confirm the occurrence of isolated, stable, axially symmetric skyrmions for several combinations of DMI and anisotropy constant. The stability of the skyrmions in disks is then investigated under magnetic field and spin-polarized current, in finite temperature, highlighting the limits of applicability of these spin textures in spintronic devices.

The influence of the edge effect on the skyrmion generation in a magnetic nanotrack

Directory of Open Access Journals (Sweden)

N. Ran

2017-02-01

Full Text Available Magnetic skyrmions might be used for building next-generation nanomagnetic and spintronic devices, as they have several perspective properties, such as topologically protected stability, nanoscale size, and ultra-low depinning current density. Here we study the influence of the edge effect on the current-induced generation of a magnetic skyrmion in a finite-length thin-film ferromagnetic nanotrack with interface-induced Dzyaloshinskii-Moriya interaction. It shows that a stable skyrmion or a bunch of skyrmions can be successfully generated as long as the distance between the current injection region and the nanotrack terminal is larger than a certain threshold. We investigate the failed skyrmion generation caused by the edge effect, which will lead to an error writing event. We also present the phase diagrams of the skyrmion generation obtained for different material and geometric parameters. Our results could be useful for designing skyrmion-based information storage devices.

Monopole Black Hole Skyrmions

OpenAIRE

Moss, Ian G; Shiiki, N; Winstanley, E

2000-01-01

Charged black hole solutions with pion hair are discussed. These can be\\ud used to study monopole black hole catalysis of proton decay.\\ud There also exist\\ud multi-black hole skyrmion solutions with BPS monopole behaviour.

Possible signature of thee-nucleon tensor forces

International Nuclear Information System (INIS)

Sagara, Kenshi

2004-01-01

After a review of history of three-nucleon forces (3NF), a possible signature of new 3NF, which has been found in recent pd capture experiments by Kyushu group, is described. In pd capture at E d = 200 MeV, a large discrepancy in A xx between experiment and calculations and a curious relation of A xx approx. = A yy were found. The discrepancy and the relation were also found in a recent pd capture experiment at 140 MeV. To our knowledge, relation of A xx approx. = -(0.5 - 0.2)A yy holds in most other reactions induced by polarized deuterons. The relation A xx approx. = A yy in pd capture means the axial symmetry with respect to z-axis, and indicates that the reaction occurs at the central part of a deuteron. We, therefore, consider that the relation A xx approx. = A yy in pd capture is a possible signature of short-range three-nucleon tensor forces. (author)

Origin of temperature and field dependence of magnetic skyrmion size in ultrathin nanodots

Science.gov (United States)

Tomasello, R.; Guslienko, K. Y.; Ricci, M.; Giordano, A.; Barker, J.; Carpentieri, M.; Chubykalo-Fesenko, O.; Finocchio, G.

2018-02-01

Understanding the physical properties of magnetic skyrmions is important for fundamental research with the aim to develop new spintronic device paradigms where both logic and memory can be integrated at the same level. Here, we show a universal model based on the micromagnetic formalism that can be used to study skyrmion stability as a function of magnetic field and temperature. We consider ultrathin, circular ferromagnetic magnetic dots. Our results show that magnetic skyrmions with a small radius—compared to the dot radius—are always metastable, while large radius skyrmions form a stable ground state. The change of energy profile determines the weak (strong) size dependence of the metastable (stable) skyrmion as a function of temperature and/or field.

Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree-Fock approximation

Science.gov (United States)

López-Quelle, M.; Marcos, S.; Niembro, R.; Savushkin, L. N.

2018-03-01

Within a nonlinear relativistic Hartree-Fock approximation combined with the BCS method, we study the effect of the nucleon-nucleon tensor force of the π-exchange potential on the spin- and pseudospin-orbit doublets along the Ca and Sn isotopic chains. We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect. Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon-nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.

Electrical detection of single magnetic skyrmion at room temperature

Directory of Open Access Journals (Sweden)

Riccardo Tomasello

2017-05-01

Full Text Available This paper proposes a protocol for the electrical detection of a magnetic skyrmion via the change of the tunneling magnetoresistive (TMR signal in a three-terminal device. This approach combines alternating spin-transfer torque from both spin-filtering (due to a perpendicular polarizer and spin-Hall effect with the TMR signal. Micromagnetic simulations, used to test and verify such working principle, show that there exists a frequency region particularly suitable for this achievement. This result can be at the basis of the design of a TMR based read-out for skyrmion detection, overcoming the difficulties introduced by the thermal drift of the skyrmion once nucleated.

Topological mass of magnetic Skyrmions probed by ultrafast dynamic imaging

International Nuclear Information System (INIS)

Buettner, Felix

2013-01-01

In this thesis, we investigate the GHz dynamics of skyrmionic spin structures by means of pump-probe dynamic imaging to determine the equation of motion that governs the behavior of these technologically relevant spin structures. To achieve this goal, we first designed and optimized a perpendicular magnetic anisotropy CoB/Pt multilayer material for low magnetic pinning, as required for ultrafast pump-probe imaging experiments. Second, we developed an integrated sample design for X-ray holography capable of tracking relative magnetic positional changes down to 3 nm spatial resolution. These advances enabled us to image the trajectory of a single magnetic Skyrmion. We find that the motion is comprised of two gyrotropic modes, one clockwise and one counterclockwise. The existence of two modes shows that Skyrmions are massive quasiparticles. From their derived frequencies we find an inertial mass for the Skyrmion which is a factor of five larger than expected based on existing models for inertia in magnetism. Our results demonstrate that the mass of Skyrmions is based on a novel mechanism emerging from their confined nature, which is a direct consequence of their topology.

Writing and deleting single magnetic skyrmions.

Science.gov (United States)

Romming, Niklas; Hanneken, Christian; Menzel, Matthias; Bickel, Jessica E; Wolter, Boris; von Bergmann, Kirsten; Kubetzka, André; Wiesendanger, Roland

2013-08-09

Topologically nontrivial spin textures have recently been investigated for spintronic applications. Here, we report on an ultrathin magnetic film in which individual skyrmions can be written and deleted in a controlled fashion with local spin-polarized currents from a scanning tunneling microscope. An external magnetic field is used to tune the energy landscape, and the temperature is adjusted to prevent thermally activated switching between topologically distinct states. Switching rate and direction can then be controlled by the parameters used for current injection. The creation and annihilation of individual magnetic skyrmions demonstrates the potential for topological charge in future information-storage concepts.

Skyrmion states in thin confined polygonal nanostructures

Science.gov (United States)

Pepper, Ryan Alexander; Beg, Marijan; Cortés-Ortuño, David; Kluyver, Thomas; Bisotti, Marc-Antonio; Carey, Rebecca; Vousden, Mark; Albert, Maximilian; Wang, Weiwei; Hovorka, Ondrej; Fangohr, Hans

2018-03-01

Recent studies have demonstrated that skyrmionic states can be the ground state in thin-film FeGe disk nanostructures in the absence of a stabilising applied magnetic field. In this work, we advance this understanding by investigating to what extent this stabilisation of skyrmionic structures through confinement exists in geometries that do not match the cylindrical symmetry of the skyrmion—such as squares and triangles. Using simulation, we show that skyrmionic states can form the ground state for a range of system sizes in both triangular and square-shaped FeGe nanostructures of 10 nm thickness in the absence of an applied field. We further provide data to assist in the experimental verification of our prediction; to imitate an experiment where the system is saturated with a strong applied field before the field is removed, we compute the time evolution and show the final equilibrium configuration of magnetization fields, starting from a uniform alignment.

Aharonov–Bohm protection of black hole's baryon/skyrmion hair

Energy Technology Data Exchange (ETDEWEB)

Dvali, Gia [Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003 (United States); Gußmann, Alexander, E-mail: alexander.gussmann@physik.uni-muenchen.de [Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität, 80333 München (Germany)

2017-05-10

The baryon/skyrmion correspondence implies that the baryon number is encoded into a topological surface integral. Under certain conditions that we clarify, this surface integral can be measured by an asymptotic observer in form of an Aharonov–Bohm phase-shift in an experiment in which the skyrmion passes through a loop of a probe string. In such a setup the baryon/skyrmion number must be respected by black holes, despite the fact that it produces no long-range classical field. If initially swallowed by a black hole, the baryon number must resurface in form of a classical skyrmion hair, after the black hole evaporates below a certain critical size. Needless to say, the respect of the baryon number by black holes is expected to have potentially-interesting astrophysical consequences.

Performance of synthetic antiferromagnetic racetrack memory: domain wall versus skyrmion

International Nuclear Information System (INIS)

Tomasello, R; Puliafito, V; Martinez, E; Manchon, A; Ricci, M; Carpentieri, M; Finocchio, G

2017-01-01

A storage scheme based on racetrack memory, where the information can be coded in a domain or a skyrmion, seems to be an alternative to conventional hard disk drive for high density storage. Here, we perform a full micromagnetic study of the performance of synthetic antiferromagnetic (SAF) racetrack memory in terms of velocity and sensitivity to defects by using experimental parameters. We find that, to stabilize a SAF skyrmion, the Dzyaloshinskii–Moriya interaction in the top and the bottom ferromagnet should have an opposite sign. The velocity of SAF skyrmions and SAF Néel domain walls are of the same order and can reach values larger than 1200 m s −1 if a spin–orbit torque from the spin-Hall effect with opposite sign is applied to both ferromagnets. The presence of disordered anisotropy in the form of randomly distributed grains introduces a threshold current for both SAF skyrmions and SAF domain walls motions. (paper)

Performance of synthetic antiferromagnetic racetrack memory: domain wall versus skyrmion

KAUST Repository

Tomasello, R

2017-06-20

A storage scheme based on racetrack memory, where the information can be coded in a domain or a skyrmion, seems to be an alternative to conventional hard disk drive for high density storage. Here, we perform a full micromagnetic study of the performance of synthetic antiferromagnetic (SAF) racetrack memory in terms of velocity and sensitivity to defects by using experimental parameters. We find that, to stabilize a SAF skyrmion, the Dzyaloshinskii–Moriya interaction in the top and the bottom ferromagnet should have an opposite sign. The velocity of SAF skyrmions and SAF Néel domain walls are of the same order and can reach values larger than 1200 m s−1 if a spin–orbit torque from the spin-Hall effect with opposite sign is applied to both ferromagnets. The presence of disordered anisotropy in the form of randomly distributed grains introduces a threshold current for both SAF skyrmions and SAF domain walls motions.

Evolution of topological skyrmions across the spin reorientation transition in Pt/Co/Ta multilayers

Science.gov (United States)

He, Min; Li, Gang; Zhu, Zhaozhao; Zhang, Ying; Peng, Licong; Li, Rui; Li, Jianqi; Wei, Hongxiang; Zhao, Tongyun; Zhang, X.-G.; Wang, Shouguo; Lin, Shi-Zeng; Gu, Lin; Yu, Guoqiang; Cai, J. W.; Shen, Bao-gen

2018-05-01

Magnetic skyrmions in multilayers are particularly appealing as next generation memory devices due to their topological compact size, the robustness against external perturbations, the capability of electrical driving and detection, and the compatibility with the existing spintronic technologies. To date, Néel-type skyrmions at room temperature (RT) have been studied mostly in multilayers with easy-axis magnetic anisotropy. Here, we systematically broadened the evolution of magnetic skyrmions with sub-50-nm size in a series of Pt/Co/Ta multilayers where the magnetic anisotropy is tuned continuously from easy axis to easy plane by increasing the ferromagnetic Co layer thickness. The existence of nontrivial skyrmions is identified via the combination of in situ Lorentz transmission electron microscopy (L-TEM) and Hall transport measurements. A high density of magnetic skyrmions over a wide temperature range is observed in the multilayers with easy-plane anisotropy, which will stimulate further exploration for new materials and accelerate the development of skyrmion-based spintronic devices.

Skyrmions in magnetic multilayers

Energy Technology Data Exchange (ETDEWEB)

Jiang, Wanjun; Chen, Gong; Liu, Kai; Zang, Jiadong; te Velthuis, Suzanne G. E.; Hoffmann, Axel

2017-08-01

Symmetry breaking together with strong spin orbit interaction gives rise to many exciting phenomena within condensed matter physics. A recent example is the existence of chiral spin textures, which are observed in magnetic systems lacking inversion symmetry. These chiral spin textures, including domain walls and magnetic skyrmions, are both fundamentally interesting and technologically promising. For example, they can be driven very efficiently by electrical currents, and exhibit many new physical properties determined by their real-space topological characteristics. Depending on the details of the competing interactions, these spin textures exist in different parameter spaces. However, the governing mechanism underlying their physical behaviors remains essentially the same. In this review article, the fundamental topological physics underlying these chiral spin textures, the key factors for materials optimization, and current developments and future challenges will be discussed. In the end, a few promising directions that will advance the development of skyrmion based spintronics will be highlighted.

Pinning of magnetic skyrmions in a monolayer Co film on Pt(111): Theoretical characterization and exemplified utilization

Science.gov (United States)

Stosic, Dusan; Ludermir, Teresa B.; Milošević, Milorad V.

2017-12-01

Magnetic skyrmions are nanoscale windings of the spin structure that can be observed in chiral magnets and hold promise for potential applications in storing or processing information. Pinning due to ever-present material imperfections crucially affects the mobility of skyrmions. Therefore, a proper understanding of how magnetic skyrmions pin to defects is necessary for the development and performance of spintronic devices. Here we present a fundamental analysis on the interactions of single skyrmions with atomic defects of distinctly different origins, in a Co monolayer on Pt, based on minimum-energy paths considerations and atomic-spin simulations. We first report the preferred pinning loci of the skyrmion as a function of its nominal size and the type of defect being considered, to further reveal the manipulation and "breathing" of skyrmion core in the vicinity of a defect. We also show the behavior of skyrmions in the presence of an extended defect of particular geometry, that can lead to ratcheted skyrmion motion or a facilitated guidance on a defect "trail." We close the study with reflections on the expected thermal stability of the skyrmion against collapse on itself for a given nature of the defect, and discuss the applications where control of skyrmions by defects is of particular interest.

The skyrmion-bubble transition in a ferromagnetic thin film

Directory of Open Access Journals (Sweden)

Anne Bernand-Mantel, Lorenzo Camosi, Alexis Wartelle, Nicolas Rougemaille, Michaël Darques, Laurent Ranno

2018-05-01

Full Text Available Magnetic skyrmions and bubbles, observed in ferromagnetic thin films with perpendicular magnetic anisotropy, are topological solitons which differ by their characteristic size and the balance in the energies at the origin of their stabilisation. However, these two spin textures have the same topology and a continuous transformation between them is allowed. In the present work, we derive an analytical model to explore the skyrmion-bubble transition. We evidence a region in the parameter space where both topological soliton solutions coexist and close to which transformations between skyrmion and bubbles are observed as a function of the magnetic field. Above a critical point, at which the energy barrier separating both solutions vanishes, only one topological soliton solution remains, which size can be continuously tuned from micrometer to nanometer with applied magnetic field.

Low-Field Bi-Skyrmion Formation in a Noncentrosymmetric Chimney Ladder Ferromagnet

Science.gov (United States)

Takagi, R.; Yu, X. Z.; White, J. S.; Shibata, K.; Kaneko, Y.; Tatara, G.; Rønnow, H. M.; Tokura, Y.; Seki, S.

2018-01-01

The real-space spin texture and the relevant magnetic parameters were investigated for an easy-axis noncentrosymmetric ferromagnet Cr11 Ge19 with Nowotny chimney ladder structure. Using Lorentz transmission electron microscopy, we report the formation of bi-Skyrmions, i.e., pairs of spin vortices with opposite magnetic helicities. The quantitative evaluation of the magnetocrystalline anisotropy and Dzyaloshinskii-Moriya interaction (DMI) proves that the magnetic dipolar interaction plays a more important role than the DMI on the observed bi-Skyrmion formation. Notably, the critical magnetic field value required for the formation of bi-Skyrmions turned out to be extremely small in this system, which is ascribed to strong easy-axis anisotropy associated with the characteristic helix crystal structure. The family of Nowotny chimney ladder compounds may offer a unique material platform where two distinctive Skyrmion formation mechanisms favoring different topological spin textures can become simultaneously active.

Instanton and tensor-force effects in the strong decays of mesons

International Nuclear Information System (INIS)

Bonnaz, R.; Silvestre-Brac, B.

2001-01-01

The strong decays of mesons are studied in the framework of the 3 P 0 model with a momentum-dependent vertex. The mesons wave functions are obtained from quark-antiquark potentials including a finite quark size, instanton effects, spin-orbit and tensor-force effects. Several prescriptions for treating the decays into three mesons are proposed and analyzed. Comparison to experimental data is presented in detail. (author)

Topological Hall and spin Hall effects in disordered skyrmionic textures

KAUST Repository

Ndiaye, Papa Birame; Akosa, Collins Ashu; Manchon, Aurelien

2017-01-01

We carry out a thorough study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy-band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real-space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and find that the adiabatic approximation still holds for large skyrmions as well as for nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that the topological Hall effect is highly sensitive to momentum scattering.

Topological Hall and spin Hall effects in disordered skyrmionic textures

KAUST Repository

Ndiaye, Papa Birame

2017-02-24

We carry out a thorough study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy-band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real-space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and find that the adiabatic approximation still holds for large skyrmions as well as for nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that the topological Hall effect is highly sensitive to momentum scattering.

Manipulation of magnetic Skyrmions with a Scanning Tunneling Microscope

OpenAIRE

Wieser, R.

2016-01-01

The dynamics of a single magnetic Skyrmion in an atomic spin system under the influence of Scanning Tunneling Microscope is investigated by computer simulations solving the Landau-Lifshitz-Gilbert equation. Two possible scenarios are described: manipulation with aid of a spin-polarized tunneling current and by an electric field created by the scanning tunneling microscope. The dynamics during the creation and annihilation process is studied and the possibility to move single Skyrmions is showed.

Coordinate invariance, the differential force law, and the divergence of the stress-energy tensor

International Nuclear Information System (INIS)

Epstein, S.T.

1975-01-01

Hermitian operators linear in momenta generate coordinate transformations. The associated hypervirial theorems are written in the form of moments of a differential force law, and a connection is made with the stress-energy tensor of the Schrodinger field in configuration space

4He binding energy calculation including full tensor-force effects

Science.gov (United States)

Fonseca, A. C.

1989-09-01

The four-body equations of Alt, Grassberger, and Sandhas are solved in the version where the (2)+(2) subamplitudes are treated exactly by convolution, using one-term separable Yamaguchy nucleon-nucleon potentials in the 1S0 and 3S1-3D1 channels. The resulting jp=1/2+ and (3/2+ three-body subamplitudes are represented in a separable form using the energy-dependent pole expansion. Converged bound-state results are calculated for the first time using the full interaction, and are compared with those obtained from a simplified treatment of the tensor force. The Tjon line that correlates three-nucleon and four-nucleon binding energies is shown using different nucleon-nucleon potentials. In all calculations the Coulomb force has been neglected.

Skyrmion black hole hair: Conservation of baryon number by black holes and observable manifestations

Energy Technology Data Exchange (ETDEWEB)

Dvali, Gia [Arnold Sommerfeld Center, Ludwig-Maximilians-Universität, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003 (United States); Gußmann, Alexander, E-mail: alexander.gussmann@physik.uni-muenchen.de [Arnold Sommerfeld Center, Ludwig-Maximilians-Universität, 80333 München (Germany)

2016-12-15

We show that the existence of black holes with classical skyrmion hair invalidates standard proofs that global charges, such as the baryon number, cannot be conserved by a black hole. By carefully analyzing the standard arguments based on a Gedankenexperiment in which a black hole is seemingly-unable to return the baryon number that it swallowed, we identify inconsistencies in this reasoning, which does not take into the account neither the existence of skyrmion black holes nor the baryon/skyrmion correspondence. We then perform a refined Gedankenexperiment by incorporating the new knowledge and show that no contradiction with conservation of baryon number takes place at any stage of black hole evolution. Our analysis also indicates no conflict between semi-classical black holes and the existence of baryonic gauge interaction arbitrarily-weaker than gravity. Next, we study classical cross sections of a minimally-coupled massless probe scalar field scattered by a skyrmion black hole. We investigate how the skyrmion hair manifests itself by comparing this cross section with the analogous cross section caused by a Schwarzschild black hole which has the same ADM mass as the skyrmion black hole. Here we find an order-one difference in the positions of the characteristic peaks in the cross sections. The peaks are shifted to smaller scattering angles when the skyrmion hair is present. This comes from the fact that the skyrmion hair changes the near horizon geometry of the black hole when compared to a Schwarzschild black hole with same ADM mass. We keep the study of this second aspect general so that the qualitative results which we obtain can also be applied to black holes with classical hair of different kind.

Field-free deterministic ultrafast creation of magnetic skyrmions by spin-orbit torques

Science.gov (United States)

Büttner, Felix; Lemesh, Ivan; Schneider, Michael; Pfau, Bastian; Günther, Christian M.; Hessing, Piet; Geilhufe, Jan; Caretta, Lucas; Engel, Dieter; Krüger, Benjamin; Viefhaus, Jens; Eisebitt, Stefan; Beach, Geoffrey S. D.

2017-11-01

Magnetic skyrmions are stabilized by a combination of external magnetic fields, stray field energies, higher-order exchange interactions and the Dzyaloshinskii-Moriya interaction (DMI). The last favours homochiral skyrmions, whose motion is driven by spin-orbit torques and is deterministic, which makes systems with a large DMI relevant for applications. Asymmetric multilayers of non-magnetic heavy metals with strong spin-orbit interactions and transition-metal ferromagnetic layers provide a large and tunable DMI. Also, the non-magnetic heavy metal layer can inject a vertical spin current with transverse spin polarization into the ferromagnetic layer via the spin Hall effect. This leads to torques that can be used to switch the magnetization completely in out-of-plane magnetized ferromagnetic elements, but the switching is deterministic only in the presence of a symmetry-breaking in-plane field. Although spin-orbit torques led to domain nucleation in continuous films and to stochastic nucleation of skyrmions in magnetic tracks, no practical means to create individual skyrmions controllably in an integrated device design at a selected position has been reported yet. Here we demonstrate that sub-nanosecond spin-orbit torque pulses can generate single skyrmions at custom-defined positions in a magnetic racetrack deterministically using the same current path as used for the shifting operation. The effect of the DMI implies that no external in-plane magnetic fields are needed for this aim. This implementation exploits a defect, such as a constriction in the magnetic track, that can serve as a skyrmion generator. The concept is applicable to any track geometry, including three-dimensional designs.

Avalanches and Criticality in Driven Magnetic Skyrmions

Science.gov (United States)

Díaz, S. A.; Reichhardt, C.; Arovas, D. P.; Saxena, A.; Reichhardt, C. J. O.

2018-03-01

We show using numerical simulations that slowly driven Skyrmions interacting with random pinning move via correlated jumps or avalanches. The avalanches exhibit power-law distributions in their duration and size, and the average avalanche shape for different avalanche durations can be scaled to a universal function, in agreement with theoretical predictions for systems in a nonequilibrium critical state. A distinctive feature of Skyrmions is the influence of the nondissipative Magnus term. When we increase the ratio of the Magnus term to the damping term, a change in the universality class of the behavior occurs, the average avalanche shape becomes increasingly asymmetric, and individual avalanches exhibit motion in the direction perpendicular to their own density gradient.

Tensor Force and D-state Effects Upon (d,x) Cross Sections

Science.gov (United States)

Hawk, Eric; McNeil, James; Cecil, F. Edward; Hofstee, Mariet; Greife, Uwe; Pallone, Arthur

2000-09-01

The effects of the inclusion of the tensor force and the internal deuteron D-state upon low-energy deuteron-stripping reactions (d,x) are examined within the context of the distorted-wave Born approximation (DWBA). Inclusion of these effects requires a relaxation of the commonly employed zero-range approximation. This relaxation is treated via a derivative expansion. Comparisons with the differential cross sections found using zero-range, S-state calculations are made for several low-Z nuclei.

Skyrmion dynamics in single-hole Neel ordered doped two-dimensional antiferromagnets with arbitrary spin

International Nuclear Information System (INIS)

Moura, A.R.; Pereira, A.R.; Moura-Melo, W.A.; Pires, A.S.T.

2008-01-01

We develop an effective theory to study the skyrmion dynamics in the presence of a hole (removed spins from the lattice) in Neel ordered two-dimensional antiferromagnets with arbitrary spin value S. The general equation of motion for the 'mass center' of this structure is obtained. The frequency of small amplitude oscillations of pinned skyrmions around the defect center is calculated. It is proportional to the hole size and inversely proportional to the square of the skyrmion size

Intrinsic nonadiabatic topological torque in magnetic skyrmions and vortices

KAUST Repository

Akosa, Collins Ashu; Ndiaye, Papa Birame; Manchon, Aurelien

2017-01-01

We propose that topological spin currents flowing in topologically nontrivial magnetic textures, such as magnetic skyrmions and vortices, produce an intrinsic nonadiabatic torque of the form Tt∼[(∂xm×∂ym)·m]∂ym. We show that this torque, which is absent in one-dimensional domain walls and/or nontopological textures, is responsible for the enhanced nonadiabaticity parameter observed in magnetic vortices compared to one-dimensional textures. The impact of this torque on the motion of magnetic skyrmions is expected to be crucial, especially to determine their robustness against defects and pinning centers.

Intrinsic nonadiabatic topological torque in magnetic skyrmions and vortices

KAUST Repository

Akosa, Collins Ashu

2017-03-01

We propose that topological spin currents flowing in topologically nontrivial magnetic textures, such as magnetic skyrmions and vortices, produce an intrinsic nonadiabatic torque of the form Tt∼[(∂xm×∂ym)·m]∂ym. We show that this torque, which is absent in one-dimensional domain walls and/or nontopological textures, is responsible for the enhanced nonadiabaticity parameter observed in magnetic vortices compared to one-dimensional textures. The impact of this torque on the motion of magnetic skyrmions is expected to be crucial, especially to determine their robustness against defects and pinning centers.

Creation of Single Chain of Nanoscale Skyrmion Bubbles with Record-high Temperature Stability in a Geometrically Confined Nanostripe

KAUST Repository

Hou, Zhipeng; Zhang, Qiang; Xu, Guizhou; Gong, Chen; Ding, Bei; Wang, Yue; Li, Hang; Liu, Enke; Xu, Feng; Zhang, Hongwei; Yao, Yuan; Wu, Guangheng; Zhang, Xixiang; Wang, Wenhong

2018-01-01

Nanoscale topologically nontrivial spin textures, such as magnetic skyrmions, have been identified as promising candidates for the transport and storage of information for spintronic applications, notably magnetic racetrack memory devices. The design and realization of a single skyrmion chain at room temperature (RT) and above in the low-dimensional nanostructures are of great importance for future practical applications. Here, we report the creation of a single skyrmion bubble chain in a geometrically confined Fe3Sn2 nanostripe with a width comparable to the featured size of a skyrmion bubble. Systematic investigations on the thermal stability have revealed that the single chain of skyrmion bubbles can keep stable at temperatures varying from RT up to a record-high temperature of 630 K. This extreme stability can be ascribed to the weak temperature-dependent magnetic anisotropy and the formation of edge states at the boundaries of the nanostripes. The realization of the highly stable skyrmion bubble chain in a geometrically confined nanostructure is a very important step toward the application of skyrmion-based spintronic devices.

Creation of Single Chain of Nanoscale Skyrmion Bubbles with Record-high Temperature Stability in a Geometrically Confined Nanostripe

KAUST Repository

Hou, Zhipeng

2018-01-04

Nanoscale topologically nontrivial spin textures, such as magnetic skyrmions, have been identified as promising candidates for the transport and storage of information for spintronic applications, notably magnetic racetrack memory devices. The design and realization of a single skyrmion chain at room temperature (RT) and above in the low-dimensional nanostructures are of great importance for future practical applications. Here, we report the creation of a single skyrmion bubble chain in a geometrically confined Fe3Sn2 nanostripe with a width comparable to the featured size of a skyrmion bubble. Systematic investigations on the thermal stability have revealed that the single chain of skyrmion bubbles can keep stable at temperatures varying from RT up to a record-high temperature of 630 K. This extreme stability can be ascribed to the weak temperature-dependent magnetic anisotropy and the formation of edge states at the boundaries of the nanostripes. The realization of the highly stable skyrmion bubble chain in a geometrically confined nanostructure is a very important step toward the application of skyrmion-based spintronic devices.

Effects of tensor forces in nuclear spin–orbit splittings from ab initio calculations

Directory of Open Access Journals (Sweden)

Shihang Shen

2018-03-01

Full Text Available A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin–orbit splittings in neutron drops. This result is obtained from relativistic Brueckner–Hartree–Fock theory using the bare nucleon–nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.

Negative baryon density and the folding structure of the B = 3 skyrmion

International Nuclear Information System (INIS)

Foster, D; Krusch, S

2013-01-01

The Skyrme model is a nonlinear field theory whose solitonic solutions, once quantized, describe atomic nuclei. The classical static soliton solutions, so-called skyrmions, have interesting symmetries and can only be calculated numerically. Mathematically, these skyrmions can be viewed as maps between two three-manifolds and, as such, their stable singularities can only be folds, cusps and swallowtails. Physically, the occurrence of singularities is related to negative baryon density. In this paper, we calculate the charge three skyrmion to a high resolution in order to examine its singularity structure in detail. Thereby, we explore regions of negative baryon density. We also discuss how the negative baryon density depends on the pion mass. (paper)

Spontaneous nucleation and topological stabilization of skyrmions in magnetic nanodisks with the interfacial Dzyaloshinskii-Moriya interaction

Science.gov (United States)

Kolesnikov, A. G.; Samardak, A. S.; Stebliy, M. E.; Ognev, A. V.; Chebotkevich, L. A.; Sadovnikov, A. V.; Nikitov, S. A.; Kim, Yong Jin; Cha, In Ho; Kim, Young Keun

2017-05-01

One of the major societal challenges is reducing the power consumption of information technology (IT) devices and numerous data centers. Distinct from the current approaches based on switching of magnetic single-domain nanostructures or on movement of domain walls under high currents, an original magnetic skyrmion technology offers ultra-low power, fast, high-density, and scalable spintronic devices, including non-volatile random access memory. Using data-driven micromagnetic simulations, we demonstrate the possibility of spontaneous nucleation and stabilization of different skyrmionic states, such as skyrmions, merons, and meron-like configurations, in heavy metal/ferromagnetic nanodisks with the interfacial Dzyaloshinskii-Moriya interaction (iDMI) as a result of quasi-static magnetization reversal only. Since iDMI is not easily modulated in real systems, we show that skyrmion stabilization is easily achievable by manipulating magnetic anisotropy, saturation magnetization, and the diameters of nanodisks. The state diagrams, presented in terms of the topological charge, allow to explicitly distinguish the intermediate states between skyrmions and merons and can be used for developing a skyrmionic medium, which has been recently proposed to be a building block for future spin-orbitronic devices.

Spontaneous nucleation and topological stabilization of skyrmions in magnetic nanodisks with the interfacial Dzyaloshinskii–Moriya interaction

Energy Technology Data Exchange (ETDEWEB)

Kolesnikov, A.G. [Laboratory of Thin Film Technologies, School of Natural Sciences, Far Eastern Federal University, Vladivostok 690950 (Russian Federation); Samardak, A.S., E-mail: samardak.as@dvfu.ru [Laboratory of Thin Film Technologies, School of Natural Sciences, Far Eastern Federal University, Vladivostok 690950 (Russian Federation); Stebliy, M.E.; Ognev, A.V.; Chebotkevich, L.A. [Laboratory of Thin Film Technologies, School of Natural Sciences, Far Eastern Federal University, Vladivostok 690950 (Russian Federation); Sadovnikov, A.V.; Nikitov, S.A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Kim, Yong Jin; Cha, In Ho [Department of Materials Science and Engineering, Korea University, Seoul 02841 (Korea, Republic of); Kim, Young Keun, E-mail: ykim97@korea.ac.kr [Department of Materials Science and Engineering, Korea University, Seoul 02841 (Korea, Republic of)

2017-05-01

One of the major societal challenges is reducing the power consumption of information technology (IT) devices and numerous data centers. Distinct from the current approaches based on switching of magnetic single-domain nanostructures or on movement of domain walls under high currents, an original magnetic skyrmion technology offers ultra-low power, fast, high-density, and scalable spintronic devices, including non-volatile random access memory. Using data-driven micromagnetic simulations, we demonstrate the possibility of spontaneous nucleation and stabilization of different skyrmionic states, such as skyrmions, merons, and meron-like configurations, in heavy metal/ferromagnetic nanodisks with the interfacial Dzyaloshinskii–Moriya interaction (iDMI) as a result of quasi-static magnetization reversal only. Since iDMI is not easily modulated in real systems, we show that skyrmion stabilization is easily achievable by manipulating magnetic anisotropy, saturation magnetization, and the diameters of nanodisks. The state diagrams, presented in terms of the topological charge, allow to explicitly distinguish the intermediate states between skyrmions and merons and can be used for developing a skyrmionic medium, which has been recently proposed to be a building block for future spin-orbitronic devices.

Topological Hall and Spin Hall Effects in Disordered Skyrmionic Textures

OpenAIRE

N'diaye, P. B.; Akosa, C. A.; Manchon, A.

2016-01-01

We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-B\\"uttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic a...

Scattering of a two skyrmion configuration on potential holes or barriers in a model Landau-Lifshitz equation

International Nuclear Information System (INIS)

Collins, J C; Zakrzewski, W J

2009-01-01

The dynamics of a baby-skyrmion configuration, in a model Landau-Lifshitz equation, was studied in the presence of various potential obstructions. The baby-skyrmion configuration was constructed from two Q = 1 hedgehog solutions to the baby-skyrme model in (2+1) dimensions. The potential obstructions were created by introducing a new term into the Lagrangian which resulted in a localized inhomogeneity in the potential terms' coefficient. In the barrier system, the normal circular path was deformed as the skyrmions traversed the barrier. During the same period, it was seen that the skyrmions sped up as they went over the barrier. For critical values of the barrier height and width, the skyrmions were no longer bound and were free to separate. In the case of a potential hole, the baby skyrmions no longer formed a bound state and moved asymptotically along the axis of the hole. It is shown how to modify the definition of the angular momentum to include the effects of the obstructions, so that it is conserved

Skyrmion clusters from Bloch lines in ferromagnetic films

KAUST Repository

Garanin, Dmitry A.

2017-12-29

Conditions under which various skyrmion objects emerge in experiments on thin magnetic films remain largely unexplained. We investigate numerically centrosymmetric spin lattices in films of finite thickness with ferromagnetic exchange, magnetic anisotropy, and dipole-dipole interaction. Evolution of labyrinth domains into compact topological structures on application of the magnetic field is found to be governed by the configuration of Bloch lines inside domain walls. Depending on the combination of Bloch lines, the magnetic domains evolve into individual skyrmions, biskyrmions, or more complex topological objects. While the geometry of such objects is sensitive to the parameters, their topological charge is uniquely determined by the topological charge of Bloch lines inside the magnetic domain from which the object emerges.

Thermal effects on current-related skyrmion formation in a nanobelt

Science.gov (United States)

Zhao, Xuebing; Wang, Shasha; Wang, Chao; Che, Renchao

2018-05-01

We report an in-situ Lorentz transmission electron microscopy (LTEM) investigation to study the thermal effects on the generation of magnetic skyrmions within a nanobelt. Under an action of a moderate current pulse, magnetic skyrmions appear even in the temperature range far below the critical temperature and even at zero field. Finite element simulation reveals that the Joule heating plays an essential role in this behavior. Our results also uncover the importance of the cooling conditions in the current-related in situ LTEM research.

Self-consistent mean field theory studies of the thermodynamics and quantum spin dynamics of magnetic Skyrmions.

Science.gov (United States)

Wieser, R

2017-05-04

A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S  =  1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.

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.)

Enhanced interfacial Dzyaloshinskii-Moriya interaction and isolated skyrmions in the inversion-symmetry-broken Ru/Co/W/Ru films

Science.gov (United States)

Samardak, Alexander; Kolesnikov, Alexander; Stebliy, Maksim; Chebotkevich, Ludmila; Sadovnikov, Alexandr; Nikitov, Sergei; Talapatra, Abhishek; Mohanty, Jyoti; Ognev, Alexey

2018-05-01

An enhancement of the spin-orbit effects arising on an interface between a ferromagnet (FM) and a heavy metal (HM) is possible through the strong breaking of the structural inversion symmetry in the layered films. Here, we show that an introduction of an ultrathin W interlayer between Co and Ru in Ru/Co/Ru films enables to preserve perpendicular magnetic anisotropy (PMA) and simultaneously induce a large interfacial Dzyaloshinskii-Moriya interaction (iDMI). The study of the spin-wave propagation in the Damon-Eshbach geometry by Brillouin light scattering spectroscopy reveals the drastic increase in the iDMI value with the increase in W thickness (tW). The maximum iDMI of -3.1 erg/cm2 is observed for tW = 0.24 nm, which is 10 times larger than for the quasi-symmetrical Ru/Co/Ru films. We demonstrate the evidence of the spontaneous field-driven nucleation of isolated skyrmions supported by micromagnetic simulations. Magnetic force microscopy measurements reveal the existence of sub-100-nm skyrmions in the zero magnetic field. The ability to simultaneously control the strength of PMA and iDMI in quasi-symmetrical HM/FM/HM trilayer systems through the interface engineered inversion asymmetry at the nanoscale excites new fundamental and practical interest in ultrathin ferromagnets, which are a potential host for stable magnetic skyrmions.

Skyrmions and Novel Spin Textures in FeGe Thin Films and Artificial B20 Heterostructures

Science.gov (United States)

Ahmed, Adam Saied

Skyrmions are magnetic spin textures that have a non-zero topological winding number associated with them. They have attracted much interest recently since they can be as small as 1 nm and could be the next generation of magnetic memory and logic. First, we grow epitaxial films of FeGe by molecular beam epitaxy and characterized the skyrmion properties. This had led us to image skyrmions in real-space with Lorentz transmission electron microscopy for the first time in the United States. Next, from an extensive series of thin and thick films, we have experimentally shown the existence of a magnetic surface state in FeGe and, consequently, any skyrmion material for the first time. Complementary theoretical calculations supported the existence of chiral bobbers--a surface state only predicted in 2015. Next, we fabricated for the first time a new class of skyrmion materials: B20 superlattices. These novel heterostructures of [FeGe/MnGe/CrGe] have now opened the door for tunable skyrmion systems with both Dresselhaus and Rashba Dzyaloshinskii-Moriya interactions. Additionally, we perform resonant soft x-ray scattering to image magnetic spin textures in reciprocal space for FeGe thin films in transmission. We have accomplished the removal of substrate and left an isolated single-crystal FeGe film. Lastly, SrO is grown on graphene as a crystalline, atomically smooth, and pinhole free tunnel barrier for spin injection.

Azimuthal spin-wave excitations in magnetic nanodots over the soliton background: Vortex, Bloch, and Néel-like skyrmions

Science.gov (United States)

Mruczkiewicz, M.; Gruszecki, P.; Krawczyk, M.; Guslienko, K. Y.

2018-02-01

We study azimuthal spin-wave (SW) excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically nontrivial magnetization states, specifically, vortex, Bloch-type skyrmion, and Néel-type skyrmion states. A continuous transition between these states is realized by gradually changing the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction (DMI), and the corresponding SW spectra are calculated for each state. We observe the lifting of degeneracy of SW mode frequencies and a change in the systematics of frequency levels. The latter effect is induced by the geometric Berry phase, which occurs in SWs localized at the edge of the dot in the vortex state, and vanishes in the skyrmion states. Furthermore, channeling of edge-localized azimuthal SWs and a related large frequency splitting are observed in the skyrmion states. This is attributed to DMI-induced nonreciprocity, while the coupling of the breathing and gyrotropic modes is related to the skyrmion motion. Finally, we demonstrate efficient coupling of the dynamic magnetization to a uniform magnetic field in nanodots of noncircular symmetry in the skyrmion states.

Dynamics of skyrmions and edge states in the resistive regime of mesoscopic p-wave superconductors

Energy Technology Data Exchange (ETDEWEB)

Fernández Becerra, V., E-mail: VictorLeonardo.FernandezBecerra@uantwerpen.be; Milošević, M.V., E-mail: milorad.milosevic@uantwerpen.be

2017-02-15

Highlights: • Voltage–current characterization of a mesoscopic p-wave superconducting sample. • Skyrmions and edge states are stabilized with an out-of-plane applied magnetic field. • In the resistive regime, moving skyrmions and the edge state behave distinctly different from the conventional kinematic vortices. - Abstract: In a mesoscopic sample of a chiral p-wave superconductor, novel states comprising skyrmions and edge states have been stabilized in out-of-plane applied magnetic field. Using the time-dependent Ginzburg–Landau equations we shed light on the dynamic response of such states to an external applied current. Three different regimes are obtained, namely, the superconducting (stationary), resistive (non-stationary) and normal regime, similarly to conventional s-wave superconductors. However, in the resistive regime and depending on the external current, we found that moving skyrmions and the edge state behave distinctly different from the conventional kinematic vortex, thereby providing new fingerprints for identification of p-wave superconductivity.

TensorLy: Tensor Learning in Python

NARCIS (Netherlands)

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

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

A point particle model of lightly bound skyrmions

Directory of Open Access Journals (Sweden)

Mike Gillard

2017-04-01

Full Text Available A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number 1≤B≤8 obtained by numerical simulation of the full field theory. For 9≤B≤23, a large number of static solutions of the point particle model are found, all closely resembling size B subsets of a face centred cubic lattice, with the particle orientations dictated by a simple colouring rule. Rigid body quantization of these solutions is performed, and the spin and isospin of the corresponding ground states extracted. As part of the quantization scheme, an algorithm to compute the symmetry group of an oriented point cloud, and to determine its corresponding Finkelstein–Rubinstein constraints, is devised.

Theory of Topological Spin Hall Effect in Antiferromagnetic Skyrmion: Impact on Current-induced Motion

KAUST Repository

Akosa, Collins Ashu

2017-09-09

We demonstrate that the nontrivial magnetic texture of antiferromagnetic skyrmions (AFM-Sks) promotes a non-vanishing topological spin Hall effect (TSHE) on the flowing electrons. This results in a substantial enhancement of the non-adiabatic torque and hence improves the skyrmion mobility. This non-adiabatic torque increases when decreasing the skyrmion size, and therefore scaling down results in a much higher torque efficiency. In clean AFM-Sks, we find a significant boost of the TSHE close to van Hove singularity. Interestingly, this effect is enhanced away from the band gap in the presence of non-magnetic interstitial defects. Furthermore, unlike their ferromagnetic counterpart, TSHE in AFM-Sks increases with increase in disorder strength thus opening promising avenues for materials engineering of this effect.

TensorLy: Tensor Learning in Python

OpenAIRE

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

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

Effects of second neighbor interactions on skyrmion lattices in chiral magnets

International Nuclear Information System (INIS)

Oliveira, E A S; Silva, R L; Silva, R C; Pereira, A R

2017-01-01

In this paper we investigate the influences of the second neighbor interactions on a skyrmion lattice in two-dimensional chiral magnets. Such a system contains the exchange and the Dzyaloshinskii–Moriya for the spin interactions and therefore, we analyse three situations: firstly, the second neighbor interaction is present only in the exchange coupling; secondly, it is present only in the Dzyaloshinskii–Moriya coupling. Finally, the second neighbor interactions are present in both exchange and Dzyaloshinskii–Moriya couplings. We show that such effects cause important modifications to the helical and skyrmion phases when an external magnetic field is applied. (paper)

Multi-skyrmion solutions of a sixth order Skyrme model

International Nuclear Information System (INIS)

Floratos, I.

2001-08-01

In this thesis, we study some of the classical properties of an extension of the Skyrme model defined by adding a sixth order derivative term to the Lagrangian. In chapter 1, we review the physical as well as the mathematical motivation behind the study of the Skyrme model and in chapter 2, we give a brief summary of various extended Skyrme models that have been proposed over the last few years. We then define a new sixth order Skyrme model by introducing a dimensionless parameter λ that denotes the mixing between the two higher order terms, the Skyrme term and the sixth order term. In chapter 3 we compute numerically the multi-skyrmion solutions of this extended model and show that they have the same symmetries with the usual skyrmion solutions. In addition, we analyse the dependence of the energy and radius of these classical solutions with respect to the coupling constant λ. We compare our results with experimental data and determine whether this modified model can provide us with better theoretical predictions than the original one. In chapter 4, we use the rational map ansatz, introduced by Houghton, Manton and Sutcliffe, to approximate minimum energy multi-skyrmion solutions with B ≤ 9 of the SU(2) model and with B ≤ 6 of the SU(3) model. We compare our results with the ones obtained numerically and show that the rational map ansatz works just as well for the generalised model as for the pure Skyrme model, at least for B ≤ 5. In chapter 5, we use a generalisation of the rational map ansatz, introduced by loannidou, Piette and Zakrzewski, to construct analytically some topologically non-trivial solutions of the extended model in SU(3). These solutions are spherically symmetric and some of them can be interpreted as bound states of skyrmions. Finally, we use the same ansatz to construct low energy configurations of the SU(N) sixth order Skyrme model. (author)

Pinning mode of integer quantum Hall Wigner crystal of skyrmions

Science.gov (United States)

Zhu, Han; Sambandamurthy, G.; Chen, Y. P.; Jiang, P.-H.; Engel, L. W.; Tsui, D. C.; Pfeiffer, L. N.; West, K. W.

2009-03-01

Just away from integer Landau level (LL) filling factors ν, the dilute quasi-particles/holes at the partially filled LL form an integer-quantum-Hall Wigner crystal, which exhibits microwave pinning mode resonances [1]. Due to electron-electron interaction, it was predicted that the elementary excitation around ν= 1 is not a single spin flip, but a larger-scale spin texture, known as a skyrmion [2]. We have compared the pinning mode resonances [1] of integer quantum Hall Wigner crystals formed in the partly filled LL just away from ν= 1 and ν= 2, in the presence of an in-plane magnetic field. As an in-plane field is applied, the peak frequencies of the resonances near ν= 1 increase, while the peak frequencies below ν= 2 show neligible dependence on in-plane field. We interpret this observation as due to a skyrmion crystal phase around ν= 1 and a single-hole Wigner crystal phase below ν= 2. The in-plane field increases the Zeeman gap and causes shrinking of the skyrmion size toward single spin flips. [1] Yong P. Chen et al., Phys. Rev. Lett. 91, 016801 (2003). [2] S. L. Sondhi et al., Phys. Rev. B 47, 16 419 (1993); L. Brey et al., Phys. Rev. Lett. 75, 2562 (1995).

Degeneracies and fluctuations of Neel skyrmions in confined geometries

NARCIS (Netherlands)

Keesman, Rick; Leonov, A. O.; van Dieten, P.; Buhrandt, Stefan; Barkema, G. T.; Fritz, Lars; Duine, R. A.

2015-01-01

The recent discovery of tunable Dzyaloshinskii-Moriya interactions in layered magnetic materials with perpendicular magnetic anisotropy makes them promising candidates for stabilization and manipulation of skyrmions at elevated temperatures. In this article, we use Monte Carlo simulations to

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

International Nuclear Information System (INIS)

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

1988-12-01

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

Skyrmion robustness in noncentrosymmetric magnets with axial symmetry: The role of anisotropy and tilted magnetic fields

Science.gov (United States)

Leonov, A. O.; Kézsmárki, I.

2017-12-01

We investigate the stability of Néel skyrmions against tilted magnetic fields in polar magnets with uniaxial anisotropy ranging from easy-plane to easy-axis type. We construct the corresponding phase diagrams and investigate the internal structure of skewed skyrmions with displaced cores. We find that moderate easy-plane anisotropy increases the stability range of Néel skyrmions for fields along the symmetry axis, while moderate easy-axis anisotropy enhances their robustness against tilted magnetic fields. We stress that the direction along which the skyrmion cores are shifted depends on the symmetry of the underlying crystal lattice. The cores of Néel skyrmions, realized in polar magnets with Cn v symmetry, are displaced either along or opposite to the off-axis (in-plane) component of the magnetic field depending on the rotation sense of the magnetization, dictated by the sign of the Dzyaloshinskii constant. The core shift of antiskyrmions, present in noncentrosymmetric magnets with D2 d symmetry, depends on the in-plane orientation of the magnetic field and can be parallel, antiparallel, or perpendicular to it. We argue that the role of anisotropy in magnets with axially symmetric crystal structure is different from that in cubic helimagnets. Our results can be applied to address recent experiments on polar magnets with C3 v symmetry, GaV4S8 and GaV4Se8 , and Mn1.4Pt0.9Pd0.1Sn with D2 d symmetry.

Study of the tensor correlation in oxygen isotopes using mean-field-type and shell model methods

International Nuclear Information System (INIS)

Sugimoto, Satoru

2007-01-01

The tensor force plays important roles in nuclear structure. Recently, we have developed a mean-field-type model which can treat the two-particle-two-hole correlation induced by the tensor force. We applied the model to sub-closed-shell oxygen isotopes and found that an sizable attractive energy comes from the tensor force. We also studied the tensor correlation in 16O using a shell model including two-particle-two-hole configurations. In this case, quite a large attractive energy is obtained for the correlation energy from the tensor force

Systematics of meson-Skyrmion scattering

International Nuclear Information System (INIS)

Mattis, M.P.

1986-02-01

The S-matrix characterizing the scattering of pions from nucleons is calculated in the context of skyrmion models of the nucleon. These are models in which the nucleon is considered a soliton in the field of pions. The spectrum of nucleon and delta resonances in the Skyrme model is calculated and found to be in overall good agreement with Nature. Model-independent sum rules between amplitudes in the same partial wave are derived and examined. An extension of the formalism to the case of three light flavors is presented. 31 refs., 26 figs., 6 tabs

Systematics of meson-Skyrmion scattering

Energy Technology Data Exchange (ETDEWEB)

Mattis, M.P.

1986-02-01

The S-matrix characterizing the scattering of pions from nucleons is calculated in the context of skyrmion models of the nucleon. These are models in which the nucleon is considered a soliton in the field of pions. The spectrum of nucleon and delta resonances in the Skyrme model is calculated and found to be in overall good agreement with Nature. Model-independent sum rules between amplitudes in the same partial wave are derived and examined. An extension of the formalism to the case of three light flavors is presented. 31 refs., 26 figs., 6 tabs.

Collective quantization of three-flavored Skyrmions reexamined

International Nuclear Information System (INIS)

Cherman, Aleksey; Cohen, Thomas D.; Dulaney, Timothy R.; Lynch, Erin M.

2005-01-01

A self-consistent large N c approach is developed for the collective quantization of SU(3) flavor hedgehog solitons, such as the Skyrmion. The key to this analysis is the determination of all of the zero-modes associated with small fluctuations around the hedgehog. These are used in the conventional way to construct collective coordinates. This approach differs from previous work in that it does not implicitly assume that each static zero-mode is associated with a dynamical zero-mode. It is demonstrated explicitly in the context of the Skyrmion that there are fewer dynamical zero-modes than static ones due to the Witten-Wess-Zumino term in the action. Group-theoretic methods are employed to identify the physical states resulting from canonical quantization of the collectively rotating soliton. The collective states fall into representations of SU(3) flavor labeled by (p,q) and are given by (2J,(Nc/2)-J) where J=(1/2),(3/2),··· is the spin of the collective state. States with strangeness S>0 do not arise as collective states from this procedure; thus the θ + (pentaquark) resonance does not arise as a collective excitation in models of this type

Observation of Various and Spontaneous Magnetic Skyrmionic Bubbles at Room Temperature in a Frustrated Kagome Magnet with Uniaxial Magnetic Anisotropy

KAUST Repository

Hou, Zhipeng

2017-06-07

The quest for materials hosting topologically protected skyrmionic spin textures continues to be fueled by the promise of novel devices. Although many materials have demonstrated the existence of such spin textures, major challenges remain to be addressed before devices based on magnetic skyrmions can be realized. For example, being able to create and manipulate skyrmionic spin textures at room temperature is of great importance for further technological applications because they can adapt to various external stimuli acting as information carriers in spintronic devices. Here, the first observation of skyrmionic magnetic bubbles with variable topological spin textures formed at room temperature in a frustrated kagome Fe3 Sn2 magnet with uniaxial magnetic anisotropy is reported. The magnetization dynamics are investigated using in situ Lorentz transmission electron microscopy, revealing that the transformation between different magnetic bubbles and domains is via the motion of Bloch lines driven by an applied external magnetic field. These results demonstrate that Fe3 Sn2 facilitates a unique magnetic control of topological spin textures at room temperature, making it a promising candidate for further skyrmion-based spintronic devices.

Double polarized neutron-proton scattering and nucleon-nucleon tensor force: An alternative analysis

International Nuclear Information System (INIS)

Tornow, W.; Gould, C.R.; Haase, D.G.; Walston, J.R.; Raichle, B.W.

2002-01-01

Previous neutron-proton total cross-section difference measurements Δσ L and Δσ T between E n =7.43 and 17.1 MeV have been analyzed in a new way that reduces experimental systematic uncertainties. The results obtained for the 3 S 1 - 3 D 1 mixing parameter ε 1 are very similar to the published values, substantiating the previous conclusion that the nucleon-nucleon tensor force at low energies is stronger than predicted by the Nijmegen partial-wave analysis and, therefore, by all the recent high-precision nucleon-nucleon potential models as well

The Skyrmions and quarks in nuclei

International Nuclear Information System (INIS)

Rho, M.

1984-08-01

It is proposed that the quark-bag description and the Skyrmion description of baryons are related to each other by quantized parameters. Topology (through a chiral anomaly) plays an important role in bridging the fundamental theory of the strong interactions (QCD) to effective theories. Some consequences on the efforts to see quark degrees of freedom in nuclear matter are discussed. It is suggested that at low energies there will be no ''smoking gun'' evidences for quark presence in nuclei

The rotationally improved Skyrmion, or RISKY

International Nuclear Information System (INIS)

Dorey, N.

1995-01-01

The perceived inability of the Skyrme model to reproduce pseudovector pion-baryon coupling has come to be known as the ''Yukawa problem.'' In this talk, we review the complete solution to this problem. The solution involves a new configuration known as the rotationally improved Skyrmion, or ''RISKY,'' in which the hedgehog structure is modified by a small quadrupole distortion. We illustrate our ideas both in the Skyrme model and in a simpler model with a global U(l) symmetry

Tensor-optimized shell model for the Li isotopes with a bare nucleon-nucleon interaction

Science.gov (United States)

Myo, Takayuki; Umeya, Atsushi; Toki, Hiroshi; Ikeda, Kiyomi

2012-08-01

We study the Li isotopes systematically in terms of the tensor-optimized shell model (TOSM) by using a bare nucleon-nucleon interaction as the AV8' interaction. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM + UCOM approach, we investigate the role of the tensor force on each spectrum of the Li isotopes. It is found that the tensor force produces quite a characteristic effect on various states in each spectrum and those spectra are affected considerably by the tensor force. The energy difference between the spin-orbit partner, the p1/2 and p3/2 orbits of the last neutron, in 5Li is caused by opposite roles of the tensor correlation. In 6Li, the spin-triplet state in the LS coupling configuration is favored energetically by the tensor force in comparison with jj coupling shell-model states. In 7,8,9Li, the low-lying states containing extra neutrons in the p3/2 orbit are favored energetically due to the large tensor contribution to allow the excitation from the 0s, orbit to the p1/2 orbit by the tensor force. Those three nuclei show the jj coupling character in their ground states which is different from 6Li.

Energy efficient and fast reversal of a fixed skyrmion two-terminal memory with spin current assisted by voltage controlled magnetic anisotropy

Science.gov (United States)

Bhattacharya, Dhritiman; Mamun Al-Rashid, Md; Atulasimha, Jayasimha

2017-10-01

Recent work (P-H Jang et al 2015 Appl. Phys. Lett. 107 202401, J. Sampaio et al 2016 Appl. Phys. Lett. 108 112403) suggests that ferromagnetic reversal with spin transfer torque (STT) requires more current in a system in the presence of Dzyaloshinskii-Moriya interaction (DMI) than switching a typical ferromagnet of the same dimensions and perpendicular magnetic anisotropy (PMA). However, DMI promotes the stabilization of skyrmions and we report that when perpendicular anisotropy is modulated (reduced) for both the skyrmion and ferromagnet, it takes a much smaller current to reverse the fixed skyrmion than to reverse the ferromagnet in the same amount of time, or the skyrmion reverses much faster than the ferromagnet at similar levels of current. We show with rigorous micromagnetic simulations that skyrmion switching proceeds along a different path at very low PMA, which results in a significant reduction in the spin current or time required for reversal. This can offer potential for memory applications where a relatively simple modification of the standard STT-RAM (to include a heavy metal adjacent to the soft magnetic layer and with appropriate design of the tunnel barrier) can lead to an energy efficient and fast magnetic memory device based on the reversal of fixed skyrmions.

The deuteron bound state wave function with tensor forces

International Nuclear Information System (INIS)

Takemasa, Tadashi

1991-01-01

A FORTRAN program named DEUTERON is developed to calculate the binding energy and wave function of a deuteron, when the interaction between two nucleons is described in terms of central, tensor, spin-orbit, and quadratic LS potentials with or without a hard core. An important use of the program is to provide the deuteron wave function required in nuclear reaction calculations involving a deuteron. Also, this program may be employed in nuclear Hartree-Fock calculations using an effective nucleon-nucleon interaction with a tensor component. (author)

A two dimensional fibre reinforced micropolar thermoelastic problem for a half-space subjected to mechanical force

Directory of Open Access Journals (Sweden)

Ailawalia Praveen

2015-01-01

Full Text Available The purpose of this paper is to study the two dimensional deformation of fibre reinforced micropolar thermoelastic medium in the context of Green-Lindsay theory of thermoelasticity. A mechanical force is applied along the interface of fluid half space and fibre reinforced micropolar thermoelastic half space. The normal mode analysis has been applied to obtain the exact expressions for displacement component, force stress, temperature distribution and tangential couple stress. The effect of anisotropy and micropolarity on the displacement component, force stress, temperature distribution and tangential couple stress has been depicted graphically.

Performance of synthetic antiferromagnetic racetrack memory: domain wall versus skyrmion

KAUST Repository

Tomasello, R; Puliafito, V; Martinez, E; Manchon, Aurelien; Ricci, M; Carpentieri, M; Finocchio, G

2017-01-01

A storage scheme based on racetrack memory, where the information can be coded in a domain or a skyrmion, seems to be an alternative to conventional hard disk drive for high density storage. Here, we perform a full micromagnetic study

Electrical-field-induced magnetic Skyrmion ground state in a two-dimensional chromium tri-iodide ferromagnetic monolayer

Science.gov (United States)

Liu, Jie; Shi, Mengchao; Mo, Pinghui; Lu, Jiwu

2018-05-01

Using fully first-principles non-collinear self-consistent field density functional theory (DFT) calculations with relativistic spin-orbital coupling effects, we show that, by applying an out-of-plane electrical field on a free-standing two-dimensional chromium tri-iodide (CrI3) ferromagnetic monolayer, the Néel-type magnetic Skyrmion spin configurations become more energetically-favorable than the ferromagnetic spin configurations. It is revealed that the topologically-protected Skyrmion ground state is caused by the breaking of inversion symmetry, which induces the non-trivial Dzyaloshinskii-Moriya interaction (DMI) and the energetically-favorable spin-canting configuration. Combining the ferromagnetic and the magnetic Skyrmion ground states, it is shown that 4-level data can be stored in a single monolayer-based spintronic device, which is of practical interests to realize the next-generation energy-efficient quaternary logic devices and multilevel memory devices.

Exact BPS bound for noncommutative baby Skyrmions

International Nuclear Information System (INIS)

Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco

2013-01-01

The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory

Real-space Berry phases: Skyrmion soccer (invited)

Science.gov (United States)

Everschor-Sitte, Karin; Sitte, Matthias

2014-05-01

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.

Real-space Berry phases: Skyrmion soccer (invited)

Energy Technology Data Exchange (ETDEWEB)

Everschor-Sitte, Karin, E-mail: karin@physics.utexas.edu; Sitte, Matthias [The University of Texas at Austin, Department of Physics, 2515 Speedway, Austin, Texas 78712 (United States)

2014-05-07

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.

Real-space Berry phases: Skyrmion soccer (invited)

International Nuclear Information System (INIS)

Everschor-Sitte, Karin; Sitte, Matthias

2014-01-01

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects

The total energy-momentum tensor for electromagnetic fields in a dielectric

Science.gov (United States)

Crenshaw, Michael E.

2017-08-01

Radiation pressure is an observable consequence of optically induced forces on materials. On cosmic scales, radiation pressure is responsible for the bending of the tails of comets as they pass near the sun. At a much smaller scale, optically induced forces are being investigated as part of a toolkit for micromanipulation and nanofabrication technology [1]. A number of practical applications of the mechanical effects of light-matter interaction are discussed by Qiu, et al. [2]. The promise of the nascent nanophotonic technology for manufacturing small, low-power, high-sensitivity sensors and other devices has likely motivated the substantial current interest in optical manipulation of materials at the nanoscale, see, for example, Ref. [2] and the references therein. While substantial progress toward optical micromanipulation has been achieved, e.g. optical tweezers [1], in this report we limit our consideration to the particular issue of optically induced forces on a transparent dielectric material. As a matter of electromagnetic theory, these forces remain indeterminate and controversial. Due to the potential applications in nanotechnology, the century-old debate regarding these forces, and the associated momentums, has ramped up considerably in the physics community. The energy-momentum tensor is the centerpiece of conservation laws for the unimpeded, inviscid, incompressible flow of non-interacting particles in the continuum limit in an otherwise empty volume. The foundations of the energy-momentum tensor and the associated tensor conservation theory come to electrodynamics from classical continuum dynamics by applying the divergence theorem to a Taylor series expansion of a property density field of a continuous flow in an otherwise empty volume. The dust tensor is a particularly simple example of an energy-momentum tensor that deals with particles of matter in the continuum limit in terms of the mass density ρm, energy density ρmc 2 , and momentum density �

Skyrmion based universal memory operated by electric current

Energy Technology Data Exchange (ETDEWEB)

Zang, Jiadong; Chien, Chia-Ling; Li, Yufan; Lake, Roger K.; Yin, Gen

2017-09-26

A method for generating a skyrmion, comprising: depositing a vertical metallic nanopillar electrode on a first side of a helimagnetic thin film, the helimagnetic thin film having a contact on a second side to provide a current drain; injecting a current through the vertical metallic nanopillar electrode to generate a rotating field; and applying a static upward magnetic field perpendicular to the helimagnetic thin film to maintain an FM phase background.

Chiral bags, skyrmions and quarks in nuclei

International Nuclear Information System (INIS)

Rho, M.

1984-09-01

Recent developments on an intriguing connection between the quark-bag description of the baryons (nucleons in particular) and the Skyrmion model are discussed in terms of the constraints coming from chiral anomalies. Topics treated are the leaking baryon charge, axial charge and energy density; the role of chiral anomalies; the role of Skyrme's quartic term and the connection to the meson degrees of freedom; and finally some qualitative implications in nuclei. The presentation is purposely descriptive and intuitive instead of mathematically precise

Coordinate independent expression for transverse trace-free tensors

International Nuclear Information System (INIS)

Conboye, Rory

2016-01-01

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

The Topology of Three-Dimensional Symmetric Tensor Fields

Science.gov (United States)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

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

Weyl curvature tensor in static spherical sources

International Nuclear Information System (INIS)

Ponce de Leon, J.

1988-01-01

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

Hybridizing the Skyrmion with an Anti-de-Sitter bag

International Nuclear Information System (INIS)

Rosu, H.

1992-02-01

We discuss a phenomenological model of the nucleon in which a small Anti-de-Sitter bag is placed into the Skyrmion configuration. Such a bag has a timelike boundary and allows naturally the Cheshire Cat Principle. Very important in this model is the membrane of the bag, the 3-dimensional manifold S 1 xS 2 , in which topological techniques will come into play. (author). 63 refs

Steady motion of skyrmions and domains walls under diffusive spin torques

KAUST Repository

Elías, Ricardo Gabriel

2017-03-09

We explore the role of the spin diffusion of conducting electrons in two-dimensional magnetic textures (domain walls and skyrmions) with spatial variation of the order of the spin precession length λex. The effect of diffusion reflects in four additional torques that are third order in spatial derivatives of magnetization and bilinear in λex and in the nonadiabatic parameter β′. In order to study the dynamics of the solitons when these diffusive torques are present, we derive the Thiele equation in the limit of steady motion and we compare the results with the nondiffusive limit. When considering a homogenous current these torques increase the longitudinal velocity of transverse domain walls of width Δ by a factor (λex/Δ)2(α/3), α being the magnetic damping constant. In the case of single skyrmions with core radius r0 these new contributions tend to increase the Magnus effect in an amount proportional to (λex/r0)2(1+2αβ′).

Steady motion of skyrmions and domains walls under diffusive spin torques

KAUST Repository

Elí as, Ricardo Gabriel; Vidal-Silva, Nicolas; Manchon, Aurelien

2017-01-01

We explore the role of the spin diffusion of conducting electrons in two-dimensional magnetic textures (domain walls and skyrmions) with spatial variation of the order of the spin precession length λex. The effect of diffusion reflects in four additional torques that are third order in spatial derivatives of magnetization and bilinear in λex and in the nonadiabatic parameter β′. In order to study the dynamics of the solitons when these diffusive torques are present, we derive the Thiele equation in the limit of steady motion and we compare the results with the nondiffusive limit. When considering a homogenous current these torques increase the longitudinal velocity of transverse domain walls of width Δ by a factor (λex/Δ)2(α/3), α being the magnetic damping constant. In the case of single skyrmions with core radius r0 these new contributions tend to increase the Magnus effect in an amount proportional to (λex/r0)2(1+2αβ′).

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

Science.gov (United States)

Lawden, D. F.

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

Erratum to Surface‐wave green’s tensors in the near field

Science.gov (United States)

Haney, Matthew M.; Hisashi Nakahara,

2016-01-01

Haney and Nakahara (2014) derived expressions for surface‐wave Green’s tensors that included near‐field behavior. Building on the result for a force source, Haney and Nakahara (2014) further derived expressions for a general point moment tensor source using the exact Green’s tensors. However, it has come to our attention that, although the Green’s tensors were correct, the resulting expressions for a general point moment tensor source were missing some terms. In this erratum, we provide updated expressions with these missing terms. The inclusion of the missing terms changes the example given in Haney and Nakahara (2014).

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

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

2018-01-01

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

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

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

2017-01-01

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

Ultrafast generation of skyrmionic defects with vortex beams: Printing laser profiles on magnets

Science.gov (United States)

Fujita, Hiroyuki; Sato, Masahiro

2017-02-01

Controlling electric and magnetic properties of matter by laser beams is actively explored in the broad region of condensed matter physics, including spintronics and magneto-optics. Here we theoretically propose an application of optical and electron vortex beams carrying intrinsic orbital angular momentum to chiral ferro- and antiferromagnets. We analyze the time evolution of spins in chiral magnets under irradiation of vortex beams by using the stochastic Landau-Lifshitz-Gilbert equation. We show that beam-driven nonuniform temperature leads to a class of ring-shaped magnetic defects, what we call skyrmion multiplex, as well as conventional skyrmions. We discuss the proper beam parameters and the optimal way of applying the beams for the creation of these topological defects. Our findings provide an ultrafast scheme of generating topological magnetic defects in a way applicable to both metallic and insulating chiral (anti-) ferromagnets.

Tensor rank is not multiplicative under the tensor product

OpenAIRE

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

2017-01-01

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

Tensor surgery and tensor rank

NARCIS (Netherlands)

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

2018-01-01

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

Tensor surgery and tensor rank

NARCIS (Netherlands)

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

2016-01-01

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

Tensor rank is not multiplicative under the tensor product

DEFF Research Database (Denmark)

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

2018-01-01

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

Streamlined approach to mapping the magnetic induction of skyrmionic materials

International Nuclear Information System (INIS)

Chess, Jordan J.; Montoya, Sergio A.; Harvey, Tyler R.; Ophus, Colin; Couture, Simon; Lomakin, Vitaliy; Fullerton, Eric E.; McMorran, Benjamin J.

2017-01-01

Highlights: • A method to reconstruction the phase of electrons after pasting though a sample that requires a single defocused image is presented. • Restrictions as to when it is appropriate to apply this method are described. • The relative error associated with this method is compared to conventional transport of intensity equation analysis. - Abstract: Recently, Lorentz transmission electron microscopy (LTEM) has helped researchers advance the emerging field of magnetic skyrmions. These magnetic quasi-particles, composed of topologically non-trivial magnetization textures, have a large potential for application as information carriers in low-power memory and logic devices. LTEM is one of a very few techniques for direct, real-space imaging of magnetic features at the nanoscale. For Fresnel-contrast LTEM, the transport of intensity equation (TIE) is the tool of choice for quantitative reconstruction of the local magnetic induction through the sample thickness. Typically, this analysis requires collection of at least three images. Here, we show that for uniform, thin, magnetic films, which includes many skyrmionic samples, the magnetic induction can be quantitatively determined from a single defocused image using a simplified TIE approach.

Streamlined approach to mapping the magnetic induction of skyrmionic materials

Energy Technology Data Exchange (ETDEWEB)

Chess, Jordan J., E-mail: jchess@uoregon.edu [Department of Physics, University of Oregon, Eugene, OR 97403 (United States); Montoya, Sergio A. [Center for Memory and Recording Research, University of California, San Diego, CA 92093 (United States); Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA 92093 (United States); Harvey, Tyler R. [Department of Physics, University of Oregon, Eugene, OR 97403 (United States); Ophus, Colin [National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720 (United States); Couture, Simon; Lomakin, Vitaliy; Fullerton, Eric E. [Center for Memory and Recording Research, University of California, San Diego, CA 92093 (United States); Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA 92093 (United States); McMorran, Benjamin J. [Department of Physics, University of Oregon, Eugene, OR 97403 (United States)

2017-06-15

Highlights: • A method to reconstruction the phase of electrons after pasting though a sample that requires a single defocused image is presented. • Restrictions as to when it is appropriate to apply this method are described. • The relative error associated with this method is compared to conventional transport of intensity equation analysis. - Abstract: Recently, Lorentz transmission electron microscopy (LTEM) has helped researchers advance the emerging field of magnetic skyrmions. These magnetic quasi-particles, composed of topologically non-trivial magnetization textures, have a large potential for application as information carriers in low-power memory and logic devices. LTEM is one of a very few techniques for direct, real-space imaging of magnetic features at the nanoscale. For Fresnel-contrast LTEM, the transport of intensity equation (TIE) is the tool of choice for quantitative reconstruction of the local magnetic induction through the sample thickness. Typically, this analysis requires collection of at least three images. Here, we show that for uniform, thin, magnetic films, which includes many skyrmionic samples, the magnetic induction can be quantitatively determined from a single defocused image using a simplified TIE approach.

Current-induced rotational torques in the skyrmion lattice phase of chiral magnets

NARCIS (Netherlands)

Everschor, K.; Garst, M.; Duine, R.A.|info:eu-repo/dai/nl/304830127; Rosch, A.

2011-01-01

In chiral magnets without inversion symmetry, the magnetic structure can form a lattice of magnetic whirl lines, a two-dimensional skyrmion lattice, stabilized by spin-orbit interactions in a small range of temperatures and magnetic fields. The twist of the magnetization within this phase gives rise

Tensor Fermi liquid parameters in nuclear matter from chiral effective field theory

Science.gov (United States)

Holt, J. W.; Kaiser, N.; Whitehead, T. R.

2018-05-01

We compute from chiral two- and three-body forces the complete quasiparticle interaction in symmetric nuclear matter up to twice nuclear matter saturation density. Second-order perturbative contributions that account for Pauli blocking and medium polarization are included, allowing for an exploration of the full set of central and noncentral operator structures permitted by symmetries and the long-wavelength limit. At the Hartree-Fock level, the next-to-next-to-leading order three-nucleon force contributes to all noncentral interactions, and their strengths grow approximately linearly with the nucleon density up to that of saturated nuclear matter. Three-body forces are shown to enhance the already strong proton-neutron effective tensor interaction, while the corresponding like-particle tensor force remains small. We also find a large isovector cross-vector interaction but small center-of-mass tensor interactions in the isoscalar and isovector channels. The convergence of the expansion of the noncentral quasiparticle interaction in Landau parameters and Legendre polynomials is studied in detail.

Emergent Momentum-Space Skyrmion Texture on the Surface of Topological Insulators

Science.gov (United States)

Mohanta, Narayan; Kampf, Arno P.; Kopp, Thilo

The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like ``spin'' texture in momentum space. Here, we apply the previously formulated low-energy model for Bi2Se3, a parent compound for magnetic topological insulators, to a slab geometry in which an exchange field acts only within one of the surface layers. In this sample set up, the hedgehog transforms into a skyrmion texture beyond a critical exchange field. This critical field marks a transition between two topologically distinct phases. The topological phase transition takes place without energy gap closing at the Fermi level and leaves the transverse Hall conductance unchanged and quantized to e2 / 2 h . The momentum-space skyrmion texture persists in a finite field range. It may find its realization in hybrid heterostructures with an interface between a three-dimensional topological insulator and a ferromagnetic insulator. The work was supported by the Deutsche Forschungsgemeinschaft through TRR 80.

Study of the tensor correlation in a neutron-rich sd-shell region with the charge- and parity-projected Hartree-Fock method

International Nuclear Information System (INIS)

Sugimoto, Satoru; Toki, Hiroshi; Ikeda, Kiyomi

2008-01-01

We study the effect of the tensor force on nuclear structure with mean-field and beyond-mean-field methods. An important correlation induced by the tensor force is two-particle-two-hole (2p2h) correlation, which cannot be treated with a usual mean-filed method. To treat the 2p2h tensor correlation, we develop a new framework (charge- and parity-projected Hartree-Fock (CPPHF) method), which is a beyond-mean-field method. In the CPPHF method, we introduce single-particle states with parity and charge mixing. The parity and charge projections are performed on a total wave function before variation. We apply the CPPHF method to oxygen isotopes including neutron-rich ones. The potential energy from the tensor force has the same order of magnitude with that from the LS force and becomes smaller with neutron number, which indicates that excess neutrons do not contribute to the 2p2h tensor correlation significantly. We also study the effect of the tensor force on spin-orbit-splitting (ls-splitting) in a neutron-rich fluorine isotope 23 F. The tensor force reduces the ls-splitting for the proton d-orbits by about 3 MeV. This effect is important to reproduce the experimental value. We also find that the 2p2h tensor correlation does not affect the ls-splitting in 23 F

Tensor Factorization for Low-Rank Tensor Completion.

Science.gov (United States)

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

2018-03-01

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

Pseudo-particles picture in single-hole-doped two-dimensional Neel ordered antiferromagnet

International Nuclear Information System (INIS)

Pereira, A R; Ercolessi, E; Pires, A S T

2007-01-01

Using the nonlinear σ model on a non-simply connected manifold, we consider the interaction effects between the elementary excitations (magnons and skyrmions) and static spin vacancy (hole) in two-dimensional quantum antiferromagnetic systems. Holes scatter magnons and trap skyrmions. The phase-shifts of the scattered magnons are obtained and used to calculate the zero point energy of spin waves measured with respect to the vacuum. It is suggested that this zero point energy lowers the energy cost of removing spins from the lattice. We also study the problems of the skyrmion-hole interactions and the skyrmion-hole (half-skyrmion-hole) bound states in the presence of magnons. We argue that two adjacent non-magnetic impurities are attracted when they are placed at the centre of half-skyrmions

A Review of Tensors and Tensor Signal Processing

Science.gov (United States)

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.

Skyrmion production on demand by homogeneous DC currents

Czech Academy of Sciences Publication Activity Database

Everschor-Sitte, K.; Sitte, M.; Valet, T.; Abanov, A.; Sinova, Jairo

2017-01-01

Roč. 19, Sep (2017), s. 1-5, č. článku 092001. ISSN 1367-2630 R&D Projects: GA ČR GB14-37427G; GA MŠk EF16_013/0001405 EU Projects: European Commission(XE) 610115 - SC2 Grant - others:OP VVV - LNSM(XE) CZ.02.1.01/0.0/0.0/16_013/0001405 Institutional support: RVO:68378271 Keywords : magnetization dynamics * micromagnetic simulations * skyrmions * thin films Subject RIV: BM - Solid Matter Physics ; Magnetism OBOR OECD: Condensed matter physics (including formerly solid state physics, supercond.) Impact factor: 3.786, year: 2016

Repulsive Casimir-Polder forces from cosmic strings

International Nuclear Information System (INIS)

Saharian, A.A.; Kotanjyan, A.S.

2011-01-01

We investigate the Casimir-Polder force acting on a polarizable microparticle in the geometry of a straight cosmic string. In order to develop this analysis we evaluate the electromagnetic field Green tensor on the imaginary frequency axis. The expression for the Casimir-Polder force is derived in the general case of anisotropic polarizability. In dependence on the eigenvalues for the polarizability tensor and of the orientation of its principal axes, the Casimir-Polder force can be either repulsive or attractive. Moreover, there are situations where the force changes the sign with separation. We show that for an isotropic polarizability tensor the force is always repulsive. At large separations between the microparticle and the string, the force varies inversely with the fifth power of the distance. In the non-retarded regime, corresponding to separations smaller than the relevant transition wavelengths, the force decays with the inverse fourth power of the distance. In the case of anisotropic polarizability, the dependence of the Casimir-Polder potential on the orientation of the polarizability tensor principal axes also leads to a moment of force acting on the particle. (orig.)

Tensor gauge condition and tensor field decomposition

Science.gov (United States)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

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

Tensor spherical harmonics and tensor multipoles. II. Minkowski space

International Nuclear Information System (INIS)

Daumens, M.; Minnaert, P.

1976-01-01

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

Monte Carlo Volcano Seismic Moment Tensors

Science.gov (United States)

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

2015-12-01

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

Interface-induced chiral domain walls, spin spirals and skyrmions revealed by spin-polarized scanning tunneling microscopy.

Science.gov (United States)

von Bergmann, Kirsten; Kubetzka, André; Pietzsch, Oswald; Wiesendanger, Roland

2014-10-01

The spin textures of ultra-thin magnetic layers exhibit surprising variety. The loss of inversion symmetry at the interface of the magnetic layer and substrate gives rise to the so-called Dzyaloshinskii-Moriya interaction which favors non-collinear spin arrangements with unique rotational sense. Here we review the application of spin-polarized scanning tunneling microscopy to such systems, which has led to the discovery of interface-induced chiral domain walls and spin spirals. Recently, different interface-driven skyrmion lattices have been found, and the writing as well as the deleting of individual skyrmions based on local spin-polarized current injection has been demonstrated. These interface-induced non-collinear magnetic states offer new exciting possibilities to study fundamental magnetic interactions and to tailor material properties for spintronic applications.

Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

Science.gov (United States)

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

2015-01-01

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

The metric theory of tensor products Grothendieck's resume revisited

CERN Document Server

Diestel, Joe; Swart, Johan; Swarte, Johannes Laurentius; Diestel, Joseph

2008-01-01

Grothendieck's Resumé is a landmark in functional analysis. Despite having appeared more than a half century ago, its techniques and results are still not widely known nor appreciated. This is due, no doubt, to the fact that Grothendieck included practically no proofs, and the presentation is based on the theory of the very abstract notion of tensor products. This book aims at providing the details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. Particular attention is paid to how the classical

Theory of high-resolution tunneling spin transport on a magnetic skyrmion

OpenAIRE

Palotás, Krisztián; Rózsa, Levente; Szunyogh, László

2018-01-01

Tunneling spin transport characteristics of a magnetic skyrmion are described theoretically in magnetic scanning tunneling microscopy (STM). The spin-polarized charge current in STM (SP-STM) and tunneling spin transport vector quantities, the longitudinal spin current and the spin transfer torque are calculated in high spatial resolution within the same theoretical framework. A connection between the conventional charge current SP-STM image contrasts and the magnitudes of the spin transport v...

Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes

Directory of Open Access Journals (Sweden)

Eloy Ayón-Beato

2016-01-01

Full Text Available We present a self-gravitating, analytic and globally regular Skyrmion solution of the Einstein–Skyrme system with winding number w=±1, in presence of a cosmological constant. The static spacetime metric is the direct product R×S3 and the Skyrmion is the self-gravitating generalization of the static hedgehog solution of Manton and Ruback with unit topological charge. This solution can be promoted to a dynamical one in which the spacetime is a cosmology of the Bianchi type-IX with time-dependent scale and squashing coefficients. Remarkably, the Skyrme equations are still identically satisfied for all values of these parameters. Thus, the complete set of field equations for the Einstein–Skyrme–Λ system in the topological sector reduces to a pair of coupled, autonomous, nonlinear differential equations for the scale factor and a squashing coefficient. These equations admit analytic bouncing cosmological solutions in which the universe contracts to a minimum non-vanishing size, and then expands. A non-trivial byproduct of this solution is that a minor modification of the construction gives rise to a family of stationary, regular configurations in General Relativity with negative cosmological constant supported by an SU(2 nonlinear sigma model. These solutions represent traversable AdS wormholes with NUT parameter in which the only “exotic matter” required for their construction is a negative cosmological constant.

Interlayer Exchange Coupling: A General Scheme Turning Chiral Magnets into Magnetic Multilayers Carrying Atomic-Scale Skyrmions.

Science.gov (United States)

Nandy, Ashis Kumar; Kiselev, Nikolai S; Blügel, Stefan

2016-04-29

We report on a general principle using interlayer exchange coupling to extend the regime of chiral magnetic films in which stable or metastable magnetic Skyrmions can appear at a zero magnetic field. We verify this concept on the basis of a first-principles model for a Mn monolayer on a W(001) substrate, a prototype chiral magnet for which the atomic-scale magnetic texture is determined by the frustration of exchange interactions, impossible to unwind by laboratory magnetic fields. By means of ab initio calculations for the Mn/W_{m}/Co_{n}/Pt/W(001) multilayer system we show that for certain thicknesses m of the W spacer and n of the Co reference layer, the effective field of the reference layer fully substitutes the required magnetic field for Skyrmion formation.

Extended skyrmion lattice scattering and long-time memory in the chiral magnet Fe1 -xCoxSi

Science.gov (United States)

Bannenberg, L. J.; Kakurai, K.; Qian, F.; Lelièvre-Berna, E.; Dewhurst, C. D.; Onose, Y.; Endoh, Y.; Tokura, Y.; Pappas, C.

2016-09-01

Small angle neutron scattering measurements on a bulk single crystal of the doped chiral magnet Fe1 -xCoxSi with x =0.3 reveal a pronounced effect of the magnetic history and cooling rates on the magnetic phase diagram. The extracted phase diagrams are qualitatively different for zero and field cooling and reveal a metastable skyrmion lattice phase outside the A phase for the latter case. These thermodynamically metastable skyrmion lattice correlations coexist with the conical phase and can be enhanced by increasing the cooling rate. They appear in a wide region of the phase diagram at temperatures below the A phase but also at fields considerably smaller or higher than the fields required to stabilize the A phase.

Dividing the Force Concept Inventory into two equivalent half-length tests

Directory of Open Access Journals (Sweden)

Jing Han

2015-05-01

Full Text Available The Force Concept Inventory (FCI is a 30-question multiple-choice assessment that has been a building block for much of the physics education research done today. In practice, there are often concerns regarding the length of the test and possible test-retest effects. Since many studies in the literature use the mean score of the FCI as the primary variable, it would be useful then to have different shorter tests that can produce FCI-equivalent scores while providing the benefits of being quicker to administer and overcoming the test-retest effects. In this study, we divide the 1995 version of the FCI into two half-length tests; each contains a different subset of the original FCI questions. The two new tests are shorter, still cover the same set of concepts, and produce mean scores equivalent to those of the FCI. Using a large quantitative data set collected at a large midwestern university, we statistically compare the assessment features of the two half-length tests and the full-length FCI. The results show that the mean error of equivalent scores between any two of the three tests is within 3%. Scores from all tests are well correlated. Based on the analysis, it appears that the two half-length tests can be a viable option for score based assessment that need to administer tests quickly or need to measure short-term gains where using identical pre- and post-test questions is a concern.

Extracting the diffusion tensor from molecular dynamics simulation with Milestoning

International Nuclear Information System (INIS)

Mugnai, Mauro L.; Elber, Ron

2015-01-01

We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide

Vacuum stress tensor of a scalar field in a rectangular waveguide

International Nuclear Information System (INIS)

Rodrigues, R.B.; Svaiter, N.F.; Paola, R.D.M. de

2001-11-01

Using the heat Kernel method and the analytical continuation of the zeta function, we calculate the canonical and improved vacuum stress tensors, {T μν (vector x)} and {Θ μν (vector x)}, associated with a massless scalar field confined in the interior of an infinity long rectangular waveguide. The local depence of the renormalized energy for two special configurations when the total energy is positive and negative are presented using {T 00 (vector x)} and {Θ 00 (vector x)}. From the stress tensors we obtain the local casimir forces in all walls by introducing a particular external configuration. It is hown that this external configuration cannot give account of the edge divergences of the local forces. The local form of the forces is obtained for three special configurations. (author)

Diffusion tensor image registration using hybrid connectivity and tensor features.

Science.gov (United States)

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

2014-07-01

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

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

Science.gov (United States)

Li, Wei; Liu, Chunlei

2013-10-01

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

Statistics of Skyrmions and the ν=5/2 puzzle

International Nuclear Information System (INIS)

Dziarmaga, J.

1997-01-01

For the hard-core interaction there is some freedom left in the choice of the exact multi-Skyrmionic wave function close-quote s topology. The statistics of textured quasiholes, analyzed by calculation of the Berry phase, depends on this choice of topology. We find a class of textured two-hole eigenstates of the Coulomb interaction. There is no definite quantum statistics, but there is a definite rule of how to construct Coulomb eigenstates out of the hard-core wave functions. A wave function for the 5/2 state is constructed according to this rule. copyright 1997 The American Physical Society

Molecular beam epitaxy growth of [CrGe/MnGe/FeGe] superlattices: Toward artificial B20 skyrmion materials with tunable interactions

Science.gov (United States)

Ahmed, Adam S.; Esser, Bryan D.; Rowland, James; McComb, David W.; Kawakami, Roland K.

2017-06-01

Skyrmions are localized magnetic spin textures whose stability has been shown theoretically to depend on material parameters including bulk Dresselhaus spin orbit coupling (SOC), interfacial Rashba SOC, and magnetic anisotropy. Here, we establish the growth of a new class of artificial skyrmion materials, namely B20 superlattices, where these parameters could be systematically tuned. Specifically, we report the successful growth of B20 superlattices comprised of single crystal thin films of FeGe, MnGe, and CrGe on Si(1 1 1) substrates. Thin films and superlattices are grown by molecular beam epitaxy and are characterized through a combination of reflection high energy electron diffraction, X-ray diffraction, and cross-sectional scanning transmission electron microscopy (STEM). X-ray energy dispersive spectroscopy (XEDS) distinguishes layers by elemental mapping and indicates good interface quality with relatively low levels of intermixing in the [CrGe/MnGe/FeGe] superlattice. This demonstration of epitaxial, single-crystalline B20 superlattices is a significant advance toward tunable skyrmion systems for fundamental scientific studies and applications in magnetic storage and logic.

Killing tensors and conformal Killing tensors from conformal Killing vectors

International Nuclear Information System (INIS)

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

2003-01-01

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

Tensors for physics

CERN Document Server

Hess, Siegfried

2015-01-01

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

Effect of Tensor Correlations on Gamow-Teller States in 90Zr and 208Pb

International Nuclear Information System (INIS)

Bai, C. L.; Zhang, H. Q.; Zhang, X. Z.

2009-01-01

The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF-RPA) model. The Gamow-Teller (GT) strength functions of 9 0Z r and 2 08P b is calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA. A microscopic origin of the quenching of GT sum rule due to the tensor force is discussed.(author)

Anisotropic magnetocrystalline coupling of the skyrmion lattice in MnSi

Science.gov (United States)

Luo, Yongkang; Lin, Shi-Zeng; Fobes, D. M.; Liu, Zhiqi; Bauer, E. D.; Betts, J. B.; Migliori, A.; Thompson, J. D.; Janoschek, M.; Maiorov, B.

2018-03-01

We investigate the anisotropic nature of magnetocrystalline coupling between the crystallographic and skyrmion crystal (SKX) lattices in the chiral magnet MnSi by magnetic field-angle resolved resonant ultrasound spectroscopy. Abrupt changes are observed in the elastic moduli and attenuation when the magnetic field is parallel to the [011] crystallographic direction. These observations are interpreted in a phenomenological Ginzburg-Landau theory that identifies switching of the SKX orientation to be the result of an anisotropic magnetocrystalline coupling potential. Our paper sheds new light on the nature of magnetocrystalline coupling potential relevant to future spintronic applications.

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

Science.gov (United States)

Gurau, Razvan

2018-06-01

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

Charge- and parity-projected Hartree-Fock method for the strong tensor correlation and its application to the alpha particle

International Nuclear Information System (INIS)

Sugimoto, Satoru; Ikeda, Kiyomi; Toki, Hiroshi

2004-01-01

We propose a new mean-field-type framework which can treat the strong correlation induced by the tensor force. To treat the tensor correlation we break the charge and parity symmetries of a single-particle state and restore these symmetries of the total system by the projection method. We perform the charge and parity projections before variation and obtain a Hartree-Fock-like equation, which is solved self-consistently. We apply the Hartree-Fock-like equation to the alpha particle and find that by breaking the parity and charge symmetries, the correlation induced by the tensor force is obtained in the projected mean-field framework. We emphasize that the projection before the variation is important to pick up the tensor correlation in the present framework

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.

Forces in General Relativity

Science.gov (United States)

Ridgely, Charles T.

2010-01-01

Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced…

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

OpenAIRE

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

2016-01-01

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

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

International Nuclear Information System (INIS)

Gandy, Silvia; Yamada, Isao; Recht, Benjamin

2011-01-01

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

Tensor eigenvalues and their applications

CERN Document Server

Qi, Liqun; Chen, Yannan

2018-01-01

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

Tensor Transpose and Its Properties

OpenAIRE

Pan, Ran

2014-01-01

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

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

OpenAIRE

Chen, Lin; Friedland, Shmuel

2017-01-01

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

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

Science.gov (United States)

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

2017-05-01

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

Bowen-York tensors

International Nuclear Information System (INIS)

Beig, Robert; Krammer, Werner

2004-01-01

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

2D massless QED Hall half-integer conductivity and graphene

International Nuclear Information System (INIS)

Martínez, A Pérez; Querts, E Rodriguez; Rojas, H Pérez; Gaitan, R; Rodriguez-Romo, S

2011-01-01

Starting from the photon self-energy tensor in a magnetized medium, the 3D complete antisymmetric form of the conductivity tensor is found in the static limit of a fermion system C-non-invariant under fermion–antifermion exchange. The massless relativistic 2D fermion limit in QED is derived by using the compactification along the dimension parallel to the magnetic field. In the static limit and at zero temperature, the main features of the quantum Hall effect (QHE) are obtained: the half-integer QHE and the minimum value proportional to e 2 /h for the Hall conductivity. For typical values of graphene the plateaus of the Hall conductivity are also reproduced. (paper)

The dynamics of aloof baby Skyrmions

Energy Technology Data Exchange (ETDEWEB)

Salmi, Petja; Sutcliffe, Paul [Department of Mathematical Sciences, Durham University,Durham DH1 3LE (United Kingdom)

2016-01-25

The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)-dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-described by a simple binary species particle model. In this paper we present the first results on soliton dynamics in the aloof baby Skyrme model. Numerical field theory simulations reveal that the lightly bound cluster structure results in a variety of exotic soliton scattering events that are novel in comparison to standard Skyrmion scattering. A dynamical version of the binary species point particle model is shown to provide a good qualitative description of the dynamics.

The dynamics of aloof baby Skyrmions

Science.gov (United States)

Salmi, Petja; Sutcliffe, Paul

2016-01-01

The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)-dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-described by a simple binary species particle model. In this paper we present the first results on soliton dynamics in the aloof baby Skyrme model. Numerical field theory simulations reveal that the lightly bound cluster structure results in a variety of exotic soliton scattering events that are novel in comparison to standard Skyrmion scattering. A dynamical version of the binary species point particle model is shown to provide a good qualitative description of the dynamics.

Forces in general relativity

International Nuclear Information System (INIS)

Ridgely, Charles T

2010-01-01

Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced by an observer in general coordinates. The general force is then applied to the local co-moving coordinate system of a uniformly accelerating observer, leading to an expression of the inertial force experienced by the observer. Next, applying the general force in Schwarzschild coordinates is shown to lead to familiar expressions of the gravitational force. As a more complex demonstration, the general force is applied to an observer in Boyer-Lindquist coordinates near a rotating, Kerr black hole. It is then shown that when the angular momentum of the black hole goes to zero, the force on the observer reduces to the force on an observer held stationary in Schwarzschild coordinates. As a final consideration, the force on an observer moving in rotating coordinates is derived. Expressing the force in terms of Christoffel symbols in rotating coordinates leads to familiar expressions of the centrifugal and Coriolis forces on the observer. It is envisioned that the techniques presented herein will be most useful to graduate level students, as well as those undergraduate students having experience with general relativity and tensor analysis.

Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics

Energy Technology Data Exchange (ETDEWEB)

Klima, Matej [Czech Technical Univ. in Prague, Praha (Czech Republic); Kucharik, MIlan [Czech Technical Univ. in Prague, Praha (Czech Republic); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Velechovsky, Jan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-01-06

We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J₂ invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J₂ invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.

Harmonic d-tensors

Energy Technology Data Exchange (ETDEWEB)

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

2016-07-01

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

Current density tensors

Science.gov (United States)

Lazzeretti, Paolo

2018-04-01

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

Nucleon-delta mass difference in the chiral bag plus skyrmion hybrid model

International Nuclear Information System (INIS)

Kusaka, K.; Toki, H.

1988-01-01

We study the nucleon-delta isobar mass difference in the chiral bag plus skyrmion hybrid model (CSH). While in the Skyrme model the collective rotation solely provides the mass difference, in the CSH model the one-gluon exchange process also contributes in addition to the collective rotation due to the broken symmetry restoration. We study the one-gluon exchange contribution using the collective coordinate projection method. We find that the one-gluon exchange energy tends to compensate for the decreasing tendency of the rotational energy in the large bag region. (orig.)

TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow

OpenAIRE

Hafner, Danijar; Davidson, James; Vanhoucke, Vincent

2017-01-01

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

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

OpenAIRE

SASAKURA, NAOKI

2010-01-01

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

Observation of Various and Spontaneous Magnetic Skyrmionic Bubbles at Room Temperature in a Frustrated Kagome Magnet with Uniaxial Magnetic Anisotropy

KAUST Repository

Hou, Zhipeng; Ren, Weijun; Ding, Bei; Xu, Guizhou; Wang, Yue; Yang, Bing; Zhang, Qiang; Zhang, Ying; Liu, Enke; Xu, Feng; Wang, Wenhong; Wu, Guangheng; Zhang, Xixiang; Shen, Baogen; Zhang, Zhidong

2017-01-01

to various external stimuli acting as information carriers in spintronic devices. Here, the first observation of skyrmionic magnetic bubbles with variable topological spin textures formed at room temperature in a frustrated kagome Fe3 Sn2 magnet with uniaxial

Time integration of tensor trains

OpenAIRE

Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart

2014-01-01

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

Tensor spaces and exterior algebra

CERN Document Server

Yokonuma, Takeo

1992-01-01

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

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

NARCIS (Netherlands)

Akkerman, Erik M.

2010-01-01

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

Research in theoretical nuclear physics

International Nuclear Information System (INIS)

Liu, Keh-Fei.

1989-01-01

This paper discusses: the role of nuclear binding in EMC effect; skyrmion quantization and phenomenology; lattice gauge Monte Carlo calculations; identification of tensor glueball; evidence of mesoniums in bar pm annihilation and γγ reactions; Skyrme-Landau parameterization of effective NN interactions; and quark-gluon plamsa

Tensor structure for Nori motives

OpenAIRE

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

2018-01-01

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

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

Science.gov (United States)

Iwasaki, Tohru; Furukawa, Tetsuo

2016-05-01

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

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

OpenAIRE

Loveridge, Lee C.

2004-01-01

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

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

Science.gov (United States)

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

2008-01-01

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

Development of the Tensoral Computer Language

Science.gov (United States)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

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

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

Science.gov (United States)

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

2017-08-02

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

Killing-Yano tensors and Nambu mechanics

International Nuclear Information System (INIS)

Baleanu, D.

1998-01-01

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

Brane-induced Skyrmion on S3: Baryonic matter in holographic QCD

International Nuclear Information System (INIS)

Nawa, Kanabu; Suganuma, Hideo; Kojo, Toru

2009-01-01

We study baryonic matter in holographic QCD with D4/D8/D8 multi-D brane system in type IIA superstring theory. The baryon is described as the 'brane-induced Skyrmion', which is a topologically nontrivial chiral soliton in the four-dimensional meson effective action induced by holographic QCD. We employ the ''truncated-resonance model'' approach for the baryon analysis, including pion and ρ meson fields below the ultraviolet cutoff scale M KK ∼1 GeV, to keep the holographic duality with QCD. We describe the baryonic matter in large N c as single brane-induced Skyrmion on the three-dimensional closed manifold S 3 with finite radius R. The interactions between baryons are simulated by the curvature of the closed manifold S 3 , and the decrease of the size of S 3 represents the increase of the total baryon-number density in the medium in this modeling. We investigate the energy density, the field configuration, the mass and the root-mean-square radius of single baryon on S 3 as the function of its radius R. We find a new picture of 'pion dominance' near the critical density in the baryonic matter, where all the (axial) vector meson fields disappear and only the pion fields survive. We also find the swelling phenomena of the baryons as the precursor of the deconfinement, and propose the mechanism of the swelling in the general context of QCD. The properties of the deconfinement and the chiral symmetry restoration in the baryonic matter are examined by taking the proper order parameters. We also compare our truncated-resonance model with another instanton description of the baryon in holographic QCD, considering the role of cutoff scale M KK .

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.

Half-maximal supersymmetry from exceptional field theory

Energy Technology Data Exchange (ETDEWEB)

Malek, Emanuel [Arnold Sommerfeld Center for Theoretical Physics, Department fuer Physik, Ludwig-Maximilians-Universitaet Muenchen (Germany)

2017-10-15

We study D ≥ 4-dimensional half-maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half-maximal Minkowski{sub D} and AdS{sub D} vacua. We then show how to obtain consistent truncations of type II / 11-dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised SO(d - 1 - N) structures, where d = 11 - D, and N is the number of vector multiplets obtained in the lower-dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half-maximal gauged SUGRA. We use this to prove that all D ≥ 4 half-maximal warped AdS{sub D} and Minkowski{sub D} vacua of type II / 11-dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M-theory / heterotic duality. In five dimensions, we find a new SO(5, N) double field theory with a (6 + N)-dimensional extended space. Its section condition has one solution corresponding to 10-dimensional N = 1 supergravity and another yielding six-dimensional N = (2, 0) SUGRA. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Tensor Permutation Matrices in Finite Dimensions

OpenAIRE

Christian, Rakotonirina

2005-01-01

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

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 independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...

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

International Nuclear Information System (INIS)

Senovilla, Jose M M

2010-01-01

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

Symmetric Tensor Decomposition

DEFF Research Database (Denmark)

Brachat, Jerome; Comon, Pierre; Mourrain, Bernard

2010-01-01

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

The tensor part of the Skyrme energy density functional. I. Spherical nuclei

Energy Technology Data Exchange (ETDEWEB)

Lesinski, T.; Meyer, J. [Universite de Lyon, F-69003 Lyon (France)]|[Institut de Physique Nucleaire de Lyon, CNRS/IN2P3, Universite Lyon 1, F-69622 Villeurbanne (France); Bender, M. [DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette Cedex (France)]|[Universite Bordeaux, CNRS/IN2P3, Centre d' Etudes Nucleaires de Bordeaux Gradignan, UMR5797, Chemin du Solarium, BP120, F-33175 Gradignan (France); Bennaceur, K. [Universite de Lyon, F-69003 Lyon (France)]|[Institut de Physique Nucleaire de Lyon, CNRS/IN2P3, Universite Lyon 1, F-69622 Villeurbanne (France)]|[DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette Cedex (France); Duguet, T. [National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States)

2007-04-15

We perform a systematic study of the impact of the J-vector{sup 2} tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations which cover a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of radii. The major findings of our study are (i) tensor terms should not be added perturbatively to existing parameterizations, a complete refit of the entire parameter set is imperative. (ii) The free variation of the tensor terms does not lower the {chi}{sup 2} within a standard Skyrme energy functional. (iii) For certain regions of the parameter space of their coupling constants, the tensor terms lead to instabilities of the spherical shell structure, or even the coexistence of two configurations with different spherical shell structure. (iv) The standard spin-orbit interaction does not scale properly with the principal quantum number, such that single-particle states with one or several nodes have too large spin-orbit splittings, while those of node-less intruder levels are tentatively too small. Tensor terms with realistic coupling constants cannot cure this problem. (v) Positive values of the coupling constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the evolution of spin-orbit splittings in chains of Ca, Ni and Sn isotopes. (vi) For the same values of the tensor term coupling constants, however, the overall

Monograph On Tensor Notations

Science.gov (United States)

Sirlin, Samuel W.

1993-01-01

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

Cartesian tensors an introduction

CERN Document Server

Temple, G

2004-01-01

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

MATLAB tensor classes for fast algorithm prototyping.

Energy Technology Data Exchange (ETDEWEB)

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

2004-10-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2007-02-15

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

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

International Nuclear Information System (INIS)

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

2007-01-01

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

Skyrmions and vector mesons: a symmetric approach

International Nuclear Information System (INIS)

Caldi, D.G.

1984-01-01

We propose an extension of the effective, low-energy chiral Lagrangian known as the Skyrme model, to one formulated by a non-linear sigma model generalized to include vector mesons in a symmetric way. The model is based on chiral SU(6) x SU(6) symmetry spontaneously broken to static SU(6). The rho and other vector mesons are dormant Goldstone bosons since they are in the same SU(6) multiplet as the pion and other pseudoscalars. Hence the manifold of our generalized non-linear sigma model is the coset space (SU(6) x SU(6))/Su(6). Relativistic effects, via a spin-dependent mass term, break the static SU(6) and give the vectors a mass. The model can then be fully relativistic and covariant. The lowest-lying Skyrmion in this model is the whole baryonic 56-plet, which splits into the octet and decuplet in the presence of relativistic SU(6)-breaking. Due to the built-in SU(6) and the presence of vector mesons, the model is expected to have better phenomenological results, as well as providing a conceptually more unified picture of mesons and baryons. 29 references

Tensor-based spatiotemporal saliency detection

Science.gov (United States)

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

2018-03-01

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

Skyrmions and nuclear forces

International Nuclear Information System (INIS)

Saito, Sakae

1987-01-01

It is shown that the Skyrme model underlied by the large-N c limit of the QCD has a qualitative success in describing the static properties of nucleon and the NN and the πN interactions. Despite this, no medium-range attraction in the central NN potential and no Yukawa πN interaction term are serious. I will talk about how they are. (orig.)

Generalized dielectric permittivity tensor

International Nuclear Information System (INIS)

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

1986-01-01

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

Tensor analysis for physicists

CERN Document Server

Schouten, J A

1989-01-01

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

Sparse alignment for robust tensor learning.

Science.gov (United States)

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

2014-10-01

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

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

International Nuclear Information System (INIS)

Huf, P A; Carminati, J

2015-01-01

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

Spin Modes in Nuclei and Nuclear Forces

International Nuclear Information System (INIS)

Suzuki, Toshio; Otsuka, Takaharu

2011-01-01

Spin modes in stable and unstable exotic nuclei are studied and important roles of tensor and three-body forces on nuclear structure are discussed. New shell model Hamiltonians, which have proper tensor components, are shown to explain shell evolutions toward drip-lines and spin properties of both stable and exotic nuclei, for example, Gamow-Teller transitions in 12 C and 14 C and an anomalous M1 transition in 17 C. The importance and the necessity of the repulsive monopole corrections in isospin T = 1 channel to the microscopic two-body interactions are pointed out. The corrections are shown to lead to the proper shell evolutions in neutron-rich isotopes. The three-body force, in particular the Fujita-Miyazawa force induced by Δ excitations, is pointed out to be responsible for the repulsive corrections among the valence neutrons. The important roles of the three-body force on the energies and transitions in exotic oxygen and calcium isotopes are demonstrated.

Unique characterization of the Bel-Robinson tensor

International Nuclear Information System (INIS)

Bergqvist, G; Lankinen, P

2004-01-01

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

Nonlocal elasticity tensors in dislocation and disclination cores

International Nuclear Information System (INIS)

Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.

2017-01-01

We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.

Tensor Product of Polygonal Cell Complexes

OpenAIRE

Chien, Yu-Yen

2017-01-01

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

Mean template for tensor-based morphometry using deformation tensors.

Science.gov (United States)

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

2007-01-01

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

Notes on super Killing tensors

Energy Technology Data Exchange (ETDEWEB)

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

2016-03-14

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

Making nuclei by using nuclear forces. Overwhelming power and difficulties of π mesons

International Nuclear Information System (INIS)

Toki, Hiroshi

2013-01-01

This paper is contributed to the planed title of 'Thirty Years History of The Playing Fields of Physics'. These thirty years are exactly the period while the author has devoted himself to the research and study of physics. The title is centered on the papers on experiments. He wishes, however, to write based on his experience as a theoretical physicist on the nuclear physics as it should be and in which direction to be developed. He would like to dedicate this paper to the late Professors M. Muraoka and K. Sugimoto of Osaka University. In the section 2 of 'Overwhelming Power and Difficulty of π Mesons', the fundamental pictures of '2.1 Start of the Yukawa's π Meson theory', '2.2 Mayer-Jensen's shell model', '2.3 Nambu's chiral symmetry and its spontaneous breaking' are introduced briefly. In the section 3 of 'Physics Lead by the Nuclear Forces Including π Mesons', the subsection '3.1 Phenomenological nuclear force' is taken up at first, then '3.2 Structure of D and tensor forces', '3.3 Structure of triton and three body forces', '3.4 Tensor forces in α-particles' and '3.5 Shell structure of light nuclei developed by the Argonne group' are explained successively. In section 4 of 'Tensor Best Fitting Shell-Model', problems on '4.1 Halo structure of 11 Li brought about by the tensor force' and '4.2 Strong tensor correlated Hartree-Fock theory' are explained. In section 5 of 'Nuclear Structure in the age of K computer', present and future view is given in '5.1 Nuclear forces described on Quantum Chromo Dynamics', '5.2 Present status of the nuclear structure derived on the lattice QCD', '5.3 Three-body forces created by π mesons' and '5.4 Role of K computer in nuclear physics'. In section 6 of 'Fusion of D', a new way to reconsider this problem as one of the nuclear physics is presented. In the final section 7 of 'Exciting Nuclear Physics' a short summary and memories of Professor Sugimoto are given. (S. Funahashi)

Tensor Train Neighborhood Preserving Embedding

Science.gov (United States)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

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

The Topology of Symmetric Tensor Fields

Science.gov (United States)

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

1997-01-01

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

Theory of the Maxwell pressure tensor and the tension in a water bridge.

Science.gov (United States)

Widom, A; Swain, J; Silverberg, J; Sivasubramanian, S; Srivastava, Y N

2009-07-01

A water bridge refers to an experimental "flexible cable" made up of pure de-ionized water, which can hang across two supports maintained with a sufficiently large voltage difference. The resulting electric fields within the de-ionized water flexible cable maintain a tension that sustains the water against the downward force of gravity. A detailed calculation of the water bridge tension will be provided in terms of the Maxwell pressure tensor in a dielectric fluid medium. General properties of the dielectric liquid pressure tensor are discussed along with unusual features of dielectric fluid Bernoulli flows in an electric field. The "frictionless" Bernoulli flow is closely analogous to that of a superfluid.

Topological Aspects of Solitons in Ferromagnets

International Nuclear Information System (INIS)

Ren Jirong; Wang Jibiao; Li Ran; Xu Donghui; Duan Yishi

2008-01-01

Two kinds of topological soliton (skyrmion and magnetic vortex ring) in ferromagnets are studied. They have the common topological origin, a tensor H αβ = n-vector · (∂ α n-vector x ∂ β n-vector ), which describes the non-trivial distribution of local orientation of magnetization n-vector at large distances in space. The topological stability of skyrmion is protected by the winding number. Knot-like topological defect as magnetic vortex rings is also studied. On the assumption that magnetic vortex rings are geometric lines, we present their δ-function distribution in ferromagnetic materials. Furthermore, it is briefly shown that Hopf invariant is a proper topological invariant to describe the topology of magnetic vortex rings

Random SU(2) invariant tensors

Science.gov (United States)

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

2018-04-01

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

The Armory Chamber and Armed Forces of Russia in the Second Half of 17th - Early 18th Century

Directory of Open Access Journals (Sweden)

Orlenko Sergey P.

2016-06-01

Full Text Available The article is devoted to the insufficiently studied aspect of the activities of the Armory chamber in the second half of 17th - beginning of 18th centuries – supplying the needs of the Russian armed forces. Political and military realities of the first half of the seventeenth century revealed the need for the modernization and transformation of the armed forces of Russia. Military reform required a massive amount of combat weapons and equipment made by Western European standard. The middle of the 17th century was the times of a search for an optimal algorithm which would provide the armed forces with weapons and equipment. The integration in this process of the court gunsmith and Armory was an effective solution. The content of the Inventory of the Armory Chamber in 1647 can be divided into two parts: 1 parade and ceremonial weapons and armor, designed for the sovereign and court 2 a huge number of combat weapons deposed in a different storages. The research is based on the complex of archival documents showing the role of the Armory chamber officials in organizing the purchase of combat weapons, its testing, preserving, repairing and transfer to the troops. The author also observed the changes in the activities of the institution in the last quarter of the century – when craftspeople of the court Armory workshop participated in the manufacturing of some special types of combat arms and service as a military gunsmith directly in troops and provincial armories.

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

Reisert, Marco; Burkhardt, Hans

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

Improved tensor multiplets

International Nuclear Information System (INIS)

Wit, B. de; Rocek, M.

1982-01-01

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

The evolution of tensor polarization

International Nuclear Information System (INIS)

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

1993-01-01

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

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

CERN Document Server

Itskov, Mikhail

2015-01-01

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

Extension of Hartree-Fock theory including tensor correlation in nuclear matter

Science.gov (United States)

Hu, Jinniu; Toki, Hiroshi; Ogawa, Yoko

2013-10-01

We study the properties of nuclear matter in the extension of Hartree-Fock theory including tensor correlation using a realistic nucleon-nucleon (NN) interaction. The nuclear wave function consists of the Hartree-Fock and two-particle-two-hole (2p-2h) states, following the concept of the tensor-optimized shell model (TOSM) for light nuclei. The short range repulsion and strong tensor force of realistic NN interaction provide high momentum components, which are taken into account in a many-body framework by introducing 2p-2h states. Single particle states are determined by the variational principle of the total energy with respect to 2p-2h amplitudes and Hartree-Fock (HF) single-particle states. The resulting differential equation is almost identical with that of Brueckner-Hartree-Fock (BHF) theory by taking two-body scattering terms only. We calculate the equation of state (EOS) of nuclear matter in this framework with the Bonn potential as a realistic NN interaction. We found similar results to BHF theory with slightly repulsive effects in the total energy. The relativistic effect is discussed for the EOSs of nuclear matter in both non-relativistic and relativistic frameworks. The momentum distribution has large components at high momenta due to 2p-2h excitations. We also obtain the EOSs of pure neutron matter, where the tensor effect is small in the iso-vector channel.

Exotic Nuclei and Yukawa's Forces

International Nuclear Information System (INIS)

Otsuka, Takaharu; Suzuki, Toshio; Utsuno, Yutaka

2008-01-01

In this plenary talk, we will overview the evolution of the shell structure in stable and exotic nuclei as a new paradigm of nuclear structure physics. This shell evolution is primarily due to the tensor force. The robust mechanism and some examples will be presented. Such examples include the disappearance of existing magic numbers and the appearance of new ones. The nuclear magic numbers have been believed, since Mayer and Jensen, to be constants as 2, 8, 20, 28, 50, ... This turned out to be changed, once we entered the regime of exotic nuclei. This shell evolution develops at many places on the nuclear chart in various forms. For example, superheavy magic numbers may be altered. Thus, we are led to a new paradigm as to how and where the nuclear shell evolves, and what consequences arise. The evolution of the shell affects weak process transitions, and plays a crucial role in deformation. The π and ρ mesons generate tensor forces, and are the fundamental elements of such intriguing phenomena. Thus, physics of exotic nuclei arises as a manifestation of Yukawa's forces

Potential implementation of reservoir computing models based on magnetic skyrmions

Science.gov (United States)

Bourianoff, George; Pinna, Daniele; Sitte, Matthias; Everschor-Sitte, Karin

2018-05-01

Reservoir Computing is a type of recursive neural network commonly used for recognizing and predicting spatio-temporal events relying on a complex hierarchy of nested feedback loops to generate a memory functionality. The Reservoir Computing paradigm does not require any knowledge of the reservoir topology or node weights for training purposes and can therefore utilize naturally existing networks formed by a wide variety of physical processes. Most efforts to implement reservoir computing prior to this have focused on utilizing memristor techniques to implement recursive neural networks. This paper examines the potential of magnetic skyrmion fabrics and the complex current patterns which form in them as an attractive physical instantiation for Reservoir Computing. We argue that their nonlinear dynamical interplay resulting from anisotropic magnetoresistance and spin-torque effects allows for an effective and energy efficient nonlinear processing of spatial temporal events with the aim of event recognition and prediction.

Self-dual Skyrmions on the spheres S2 N +1

Science.gov (United States)

Amari, Y.; Ferreira, L. A.

2018-04-01

We construct self-dual sectors for scalar field theories on a (2 N +2 )-dimensional Minkowski space-time with the target space being the 2 N +1 -dimensional sphere S2 N +1. The construction of such self-dual sectors is made possible by the introduction of an extra functional in the action that renders the static energy and the self-duality equations conformally invariant on the (2 N +1 )-dimensional spatial submanifold. The conformal and target-space symmetries are used to build an ansatz that leads to an infinite number of exact self-dual solutions with arbitrary values of the topological charge. The five-dimensional case is discussed in detail, where it is shown that two types of theories admit self-dual sectors. Our work generalizes the known results in the three-dimensional case that lead to an infinite set of self-dual Skyrmion solutions.

Tensor Calculus: Unlearning Vector Calculus

Science.gov (United States)

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

2018-01-01

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

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....

Energy-momentum tensor of the electromagnetic field

International Nuclear Information System (INIS)

Horndeski, G.W.; Wainwright, J.

1977-01-01

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

A new Weyl-like tensor of geometric origin

Science.gov (United States)

Vishwakarma, Ram Gopal

2018-04-01

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

Tensor calculus for physics a concise guide

CERN Document Server

Neuenschwander, Dwight E

2015-01-01

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

Casimir-Lifshitz force for nonreciprocal media and applications to photonic topological insulators

Science.gov (United States)

Fuchs, Sebastian; Lindel, Frieder; Krems, Roman V.; Hanson, George W.; Antezza, Mauro; Buhmann, Stefan Yoshi

2017-12-01

Based on the theory of macroscopic quantum electrodynamics, we generalize the expression of the Casimir force for nonreciprocal media. The essential ingredient of this result is the Green's tensor between two nonreciprocal semi-infinite slabs, including a reflexion matrix with four coefficients that mixes optical polarizations. This Green's tensor does not obey Lorentz's reciprocity and thus violates time-reversal symmetry. The general result for the Casimir force is analyzed in the retarded and nonretarded limits, concentrating on the influences arising from reflections with or without change of polarization. In a second step, we apply our general result to a photonic topological insulator whose nonreciprocity stems from an anisotropic permittivity tensor, namely InSb. We show that there is a regime for the distance between the slabs where the magnitude of the Casimir force is tunable by an external magnetic field. Furthermore, the strength of this tuning depends on the orientation of the magnetic field with respect to the slab surfaces.

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 norms and operator ideals

CERN Document Server

Defant, A; Floret, K

1992-01-01

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

Shape anisotropy: tensor distance to anisotropy measure

Science.gov (United States)

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

2011-03-01

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

Tensors and their applications

CERN Document Server

Islam, Nazrul

2006-01-01

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

Tensor Completion Algorithms in Big Data Analytics

OpenAIRE

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

2017-01-01

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

Efficient MATLAB computations with sparse and factored tensors.

Energy Technology Data Exchange (ETDEWEB)

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

2006-12-01

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

Reciprocal mass tensor : a general form

International Nuclear Information System (INIS)

Roy, C.L.

1978-01-01

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

A new deteriorated energy-momentum tensor

International Nuclear Information System (INIS)

Duff, M.J.

1982-01-01

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

Antisymmetric tensor generalizations of affine vector fields.

Science.gov (United States)

Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

2016-02-01

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

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

International Nuclear Information System (INIS)

Manoff, S.; Dimitrov, B.

1998-01-01

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

The Riemann-Lovelock Curvature Tensor

OpenAIRE

Kastor, David

2012-01-01

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

Nuclear reaction matrix and nuclear forces

International Nuclear Information System (INIS)

Nagata, Sinobu; Bando, Hiroharu; Akaishi, Yoshinori.

1979-01-01

An essentially exact method of solution is presented for the reaction- matrix (G-matrix) equation defined with the orthogonalized plane-wave intermediate spectrum for high-lying two-particle states. The accuracy is examined for introduced truncations and also in comparison with the Tsai-Kuo and Sauer methods. Properties of the G-matrix are discussed with emphasis on the relation with the saturation mechanism, especially overall saturation from light to heavy nuclei. Density and starting-energy dependences of the G-matrix are separately extracted and discussed. It is demonstrated that the triplet-even tensor component of the nuclear force is principally responsible for these dependences and hence for the saturation mechanism. In this context different nuclear potentials are used in the renormalized Brueckner calculation for energies of closed-shell nuclei in the harmonic oscillator basis. A semi-phenomenological ''two-body potential'' is devised so that it can reproduce the saturation energies and densities of nuclear matter and finite nuclei in the lowest-order Brueckner treatment. It is composed of a realistic N-N potential and two additional parts; one incorporates the three-body force effect and the other is assumed to embody higher-cluster correlations in G. The tensor component in the triplet-even state of this potential is enhanced by the three-body force effect. The G-matrix is represented in the effective local form and decomposed into central, LS and tensor components. (author)

The Physical Interpretation of the Lanczos Tensor

OpenAIRE

Roberts, Mark D.

1999-01-01

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

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

Science.gov (United States)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

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

3D reconstruction of tensors and vectors

International Nuclear Information System (INIS)

Defrise, Michel; Gullberg, Grant T.

2005-01-01

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

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

Science.gov (United States)

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

2012-01-01

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

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

Science.gov (United States)

Alam, Meheboob; Saha, Saikat

2014-11-01

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

Weyl tensors for asymmetric complex curvatures

International Nuclear Information System (INIS)

Oliveira, C.G.

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

Tensor voting for robust color edge detection

OpenAIRE

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

2014-01-01

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

Should I use TensorFlow

OpenAIRE

Schrimpf, Martin

2016-01-01

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

Dictionary-Based Tensor Canonical Polyadic Decomposition

Science.gov (United States)

Cohen, Jeremy Emile; Gillis, Nicolas

2018-04-01

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

Bayesian regularization of diffusion tensor images

DEFF Research Database (Denmark)

Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif

2007-01-01

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

Energy-momentum tensor in the fermion-pairing model

International Nuclear Information System (INIS)

Kawati, S.; Miyata, H.

1980-01-01

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

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

Science.gov (United States)

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

2017-08-01

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

Theory of high-resolution tunneling spin transport on a magnetic skyrmion

Science.gov (United States)

Palotás, Krisztián; Rózsa, Levente; Szunyogh, László

2018-05-01

Tunneling spin transport characteristics of a magnetic skyrmion are described theoretically in magnetic scanning tunneling microscopy (STM). The spin-polarized charge current in STM (SP-STM) and tunneling spin transport vector quantities, the longitudinal spin current and the spin transfer torque, are calculated in high spatial resolution within the same theoretical framework. A connection between the conventional charge current SP-STM image contrasts and the magnitudes of the spin transport vectors is demonstrated that enables the estimation of tunneling spin transport properties based on experimentally measured SP-STM images. A considerable tunability of the spin transport vectors by the involved spin polarizations is also highlighted. These possibilities and the combined theory of tunneling charge and vector spin transport pave the way for gaining deep insight into electric-current-induced tunneling spin transport properties in SP-STM and to the related dynamics of complex magnetic textures at surfaces.

The Einstein tensor characterizing some Riemann spaces

International Nuclear Information System (INIS)

Rahman, M.S.

1993-07-01

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

Radiative corrections in a vector-tensor model

International Nuclear Information System (INIS)

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

2006-01-01

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

Transposes, L-Eigenvalues and Invariants of Third Order Tensors

OpenAIRE

Qi, Liqun

2017-01-01

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

Joint Tensor Feature Analysis For Visual Object Recognition.

Science.gov (United States)

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

2015-11-01

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

Graded tensor calculus

International Nuclear Information System (INIS)

Scheunert, M.

1982-10-01

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

On deriving the Maxwell stress tensor method for calculating the optical force and torque on an object in harmonic electromagnetic fields

Science.gov (United States)

Ye, Qian; Lin, Haoze

2017-07-01

Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.

On deriving the Maxwell stress tensor method for calculating the optical force and torque on an object in harmonic electromagnetic fields

International Nuclear Information System (INIS)

Ye, Qian; Lin, Haoze

2017-01-01

Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space , if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function. (paper)

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

International Nuclear Information System (INIS)

Manoff, S.; Dimitrov, B.

1998-01-01

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

Tensor network method for reversible classical computation

Science.gov (United States)

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

2018-03-01

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

Robust estimation of adaptive tensors of curvature by tensor voting.

Science.gov (United States)

Tong, Wai-Shun; Tang, Chi-Keung

2005-03-01

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

On the concircular curvature tensor of Riemannian manifolds

International Nuclear Information System (INIS)

Rahman, M.S.; Lal, S.

1990-06-01

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

Generalized force in classical field theory. [Euler-Lagrange equations

Energy Technology Data Exchange (ETDEWEB)

Krause, J [Universidad Central de Venezuela, Caracas

1976-02-01

The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.

Glyph-Based Comparative Visualization for Diffusion Tensor Fields.

Science.gov (United States)

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

2016-01-01

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

Tensoral for post-processing users and simulation authors

Science.gov (United States)

Dresselhaus, Eliot

1993-01-01

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

Ab initio study of {sup 2}H(d,{gamma}){sup 4}He, {sup 2}H(d,p){sup 3}H, and {sup 2}H(d,n){sup 4}He reactions and the tensor force

Energy Technology Data Exchange (ETDEWEB)

Arai, K.; Aoyama, S.; Suzuki, Y.; Descouvemont, P.; Baye, D. [Division of General Education, Nagaoka National College of Technology, 888 Nishikatakai, Nagaoka, Niigata, 940-8532 (Japan); Center for Academic Information Service, Niigata University, Niigata 950-2181 (Japan); Department of Physics, Niigata University, Niigata 950-2181, Japan and RIKEN Nishina Center, Wako 351-0198 (Japan); Physique Nucleaire Theorique et Physique Mathematique, C.P.229, Universite Libre de Bruxelles, B 1050 Brussels (Belgium); Physique Quantique, CP165/82, Universite Libre de Bruxelles, B-1050 Brussels (Belgium)

2012-11-12

The {sup 2}H(d,p){sup 3}H, {sup 2}H(d,n){sup 3}He, and {sup 2}H(d,{gamma}){sup 4}He reactions at low energies are studied with realistic nucleon-nucleon interactions in an ab initio approach. The obtained astrophysical S-factors are all in very good agreement with experiment. The most important channels for both transfer and radiative capture are all found to dominate thanks to the tensor force.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

Science.gov (United States)

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

2018-05-01

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

Applications of tensor functions in creep mechanics

International Nuclear Information System (INIS)

Betten, J.

1991-01-01

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

Tensor interaction in heavy-ion scattering. Pt. 1

International Nuclear Information System (INIS)

Nishioka, H.; Johnson, R.C.

1985-01-01

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

On Lovelock analogs of the Riemann tensor

Science.gov (United States)

Camanho, Xián O.; Dadhich, Naresh

2016-03-01

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

The simplicial Ricci tensor

International Nuclear Information System (INIS)

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

2011-01-01

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

The simplicial Ricci tensor

Science.gov (United States)

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

2011-08-01

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

Beyond Low Rank: A Data-Adaptive Tensor Completion Method

OpenAIRE

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

2017-01-01

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

Exploring the tensor networks/AdS correspondence

Energy Technology Data Exchange (ETDEWEB)

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

2016-08-11

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

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.

Differential invariants for higher-rank tensors. A progress report

International Nuclear Information System (INIS)

Tapial, V.

2004-07-01

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

Energy-momentum tensor in scalar QED

International Nuclear Information System (INIS)

Joglekar, S.D.; Misra, A.

1988-01-01

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

Calculus of tensors and differential forms

CERN Document Server

Sinha, Rajnikant

2014-01-01

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

Tensor Galileons and gravity

Energy Technology Data Exchange (ETDEWEB)

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

2017-03-13

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

Algebraic and computational aspects of real tensor ranks

CERN Document Server

Sakata, Toshio; Miyazaki, Mitsuhiro

2016-01-01

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

Decomposition of a symmetric second-order tensor

Science.gov (United States)

Heras, José A.

2018-05-01

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

Efficient Low Rank Tensor Ring Completion

OpenAIRE

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2017-01-01

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

Colored Tensor Models - a Review

Directory of Open Access Journals (Sweden)

Razvan Gurau

2012-04-01

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

Efficient Tensor Strategy for Recommendation

Directory of Open Access Journals (Sweden)

Aboagye Emelia Opoku

2017-07-01

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

Ponderomotive forces in electrodynamics of moving media: The Minkowski and Abraham approaches

Science.gov (United States)

Nesterenko, V. V.; Nesterenko, A. V.

2016-09-01

In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive relations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive forces in the Abraham and Minkowski approaches as the Abraham force not only under consideration of media at rest but also in the case of moving media. The Lorentz force is found which is exerted by external electromagnetic field on the conduction current in a medium, the covariant Ohm law, and the constitutive Minkowski relations being taken into account. The physical argumentation is traced for the definition of the 4-vector of the ponderomotive force as the 4-divergence of the energy-momentum tensor of electromagnetic field in a medium.

Conformal field theories and tensor categories. Proceedings

Energy Technology Data Exchange (ETDEWEB)

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

2014-08-01

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

On improving the efficiency of tensor voting.

Science.gov (United States)

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

2011-11-01

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

Reduction schemes for one-loop tensor integrals

International Nuclear Information System (INIS)

Denner, A.; Dittmaier, S.

2006-01-01

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

Conformal field theories and tensor categories. Proceedings

International Nuclear Information System (INIS)

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

2014-01-01

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

Loop optimization for tensor network renormalization

Science.gov (United States)

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

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

The Twist Tensor Nuclear Norm for Video Completion.

Science.gov (United States)

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

2017-12-01

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

Composite Fermi surface in the half-filled Landau level with anisotropic electron mass

Science.gov (United States)

Ippoliti, Matteo; Geraedts, Scott; Bhatt, Ravindra

We study the problem of interacting electrons in the lowest Landau level at half filling in the quantum Hall regime, when the electron dispersion is given by an anisotropic mass tensor. Based on experimental observations and theoretical arguments, the ground state of the system is expected to consist of composite Fermions filling an elliptical Fermi sea, with the anisotropy of the ellipse determined by the competing effects of the isotropic Coulomb interaction and anisotropic electron mass tensor. We test this idea quantitatively by using a numerical density matrix renormalization group method for quantum Hall systems on an infinitely long cylinder. Singularities in the structure factor allow us to map the Fermi surface of the composite Fermions. We compute the composite Fermi surface anisotropy for several values of the electron mass anisotropy which allow us to deduce the functional dependence of the former on the latter. This research was supported by Department of Energy Office of Basic Energy Sciences through Grant No. DE-SC0002140.

Skyrmion formation and optical spin-Hall effect in an expanding coherent cloud of indirect excitons.

Science.gov (United States)

Vishnevsky, D V; Flayac, H; Nalitov, A V; Solnyshkov, D D; Gippius, N A; Malpuech, G

2013-06-14

We provide a theoretical description of the polarization pattern and phase singularities experimentally evidenced recently in a condensate of indirect excitons [H. High et al., Nature 483, 584 (2012)]. We show that the averaging of the electron and hole orbital motion leads to a comparable spin-orbit interaction for both types of carriers. We demonstrate that the interplay between a radial coherent flux of bright indirect excitons and the Dresselhaus spin-orbit interaction results in the formation of spin domains and of topological defects similar to Skyrmions. We reproduce qualitatively all the features of the experimental data and obtain a polarization pattern as in the optical spin-Hall effect despite the different symmetry of the spin-orbit interactions.

Off-shell N = 2 tensor supermultiplets

International Nuclear Information System (INIS)

Wit, Bernard de; Saueressig, Frank

2006-01-01

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

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

OpenAIRE

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

2008-01-01

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

Tensors, relativity, and cosmology

CERN Document Server

Dalarsson, Mirjana

2015-01-01

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

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

Science.gov (United States)

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

2016-08-01

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

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

Science.gov (United States)

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

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

Dislocations, the elastic energy momentum tensor and crack propagation

International Nuclear Information System (INIS)

Lung, Chi-wei

1979-07-01

Based upon dislocation theory, some stress intensity factors can be calculated for practical cases. The results obtained by this method have been found to agree fairly well with the results obtained by the conventional fracture mechanics. The elastic energy momentum tensor has been used to calculate the force acting on the crack tip. A discussion on the kinetics of migration of impurities to the crack tip was given. It seems that the crack tip sometimes may be considered as a singularity in an elastic field and the fundamental law of classical field theory is applicable on the problem in fracture of materials. (author)

Tucker tensor analysis of Matern functions in spatial statistics

KAUST Repository

Litvinenko, Alexander

2018-04-20

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

Poisson-Jacobi reduction of homogeneous tensors

International Nuclear Information System (INIS)

Grabowski, J; Iglesias, D; Marrero, J C; Padron, E; Urbanski, P

2004-01-01

The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold M, homogeneous with respect to a vector field Δ on M, and first-order polydifferential operators on a closed submanifold N of codimension 1 such that Δ is transversal to N. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on M to the Schouten-Jacobi bracket of first-order polydifferential operators on N and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can also be understood as a sort of reduction; in the standard case-a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between Δ-homogeneous symplectic structures on M and contact structures on N

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

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

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

2015-01-01

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

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

Science.gov (United States)

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

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

A recursive reduction of tensor Feynman integrals

International Nuclear Information System (INIS)

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

2009-07-01

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

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

Science.gov (United States)

Dibb, Russell; Liu, Chunlei

2017-06-01

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

Anode wire in cylindrical cathode tube : destabilizing electrostatic force

CERN Document Server

Wertelaers, P

2017-01-01

A two-dimensional -- cross-sectional -- discussion suffices. The tube is offset, and the electrostatic potential is found analytically with perturbative methods. Then, the force is established with the Maxwell stress tensor. Alternatively, trying to find the force with energy methods, fails. Finally, finite element tests are performed in order to report on the degree of non-linearity for large offsets.

Tensor-based Dictionary Learning for Spectral CT Reconstruction

Science.gov (United States)

Zhang, Yanbo; Wang, Ge

2016-01-01

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

Tensor-Based Dictionary Learning for Spectral CT Reconstruction.

Science.gov (United States)

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

2017-01-01

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

Typesafe Abstractions for Tensor Operations

OpenAIRE

Chen, Tongfei

2017-01-01

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

Tensor network state correspondence and holography

Science.gov (United States)

Singh, Sukhwinder

2018-01-01

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

Concatenated image completion via tensor augmentation and completion

OpenAIRE

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

2016-01-01

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

General projective relativity and the vector-tensor gravitational field

International Nuclear Information System (INIS)

Arcidiacono, G.

1986-01-01

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

Tensor harmonic analysis on homogenous space

International Nuclear Information System (INIS)

Wrobel, G.

1997-01-01

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

Tensor estimation for double-pulsed diffusional kurtosis imaging.

Science.gov (United States)

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

2017-07-01

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

Tensor network decompositions in the presence of a global symmetry

International Nuclear Information System (INIS)

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

2010-01-01

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

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

Science.gov (United States)

Marin Quintero, Maider J.

2013-01-01

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

Indicial tensor manipulation on MACSYMA

International Nuclear Information System (INIS)

Bogen, R.A.; Pavelle, R.

1977-01-01

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

Tensor based structure estimation in multi-channel images

DEFF Research Database (Denmark)

Schou, Jesper; Dierking, Wolfgang; Skriver, Henning

2000-01-01

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

On energy-momentum tensors of gravitational field

International Nuclear Information System (INIS)

Nikishov, A.I.

2001-01-01

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

Spectral Tensor-Train Decomposition

DEFF Research Database (Denmark)

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

2016-01-01

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

Importance of Force Decomposition for Local Stress Calculations in Biomembrane Molecular Simulations.

Science.gov (United States)

Vanegas, Juan M; Torres-Sánchez, Alejandro; Arroyo, Marino

2014-02-11

Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.

Scalable Tensor Factorizations with Missing Data

DEFF Research Database (Denmark)

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

2010-01-01

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

Scalable tensor factorizations for incomplete data

DEFF Research Database (Denmark)

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

2011-01-01

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

On improving the efficiency of tensor voting

OpenAIRE

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

2011-01-01

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

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

Science.gov (United States)

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

2014-01-01

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

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...

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

Science.gov (United States)

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

2017-10-12

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

The tensor bi-spectrum in a matter bounce

Energy Technology Data Exchange (ETDEWEB)

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

2015-11-01

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

Endoscopic Anatomy of the Tensor Fold and Anterior Attic.

Science.gov (United States)

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

2018-02-01

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

Potentials for transverse trace-free tensors

International Nuclear Information System (INIS)

Conboye, Rory; Murchadha, Niall Ó

2014-01-01

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

Gauge theories, duality relations and the tensor hierarchy

International Nuclear Information System (INIS)

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

2009-01-01

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

Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

Science.gov (United States)

Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming

1996-01-01

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.

Reconstruction of convex bodies from surface tensors

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus

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

Relativistic particles with spin and antisymmetric tensor fields

International Nuclear Information System (INIS)

Sandoval Junior, L.

1990-09-01

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

Prescribed curvature tensor in locally conformally flat manifolds

Science.gov (United States)

Pina, Romildo; Pieterzack, Mauricio

2018-01-01

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

Algebraic Rainich conditions for the fourth rank tensor V

International Nuclear Information System (INIS)

So, Lau Loi

2011-01-01

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

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

OpenAIRE

Hadjesfandiari, Ali R.

2013-01-01

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

Tensor products of higher almost split sequences

OpenAIRE

Pasquali, Andrea

2015-01-01

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

Tensor-optimized antisymmetrized molecular dynamics as a successive variational method in nuclear many-body system

Energy Technology Data Exchange (ETDEWEB)

Myo, Takayuki, E-mail: takayuki.myo@oit.ac.jp [General Education, Faculty of Engineering, Osaka Institute of Technology, Osaka 535-8585 (Japan); Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Toki, Hiroshi [Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Ikeda, Kiyomi [RIKEN Nishina Center, Wako, Saitama 351-0198 (Japan); Horiuchi, Hisashi [Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Suhara, Tadahiro [Matsue College of Technology, Matsue 690-8518 (Japan)

2017-06-10

We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, {sup 3}H and {sup 4}He, using the nucleon–nucleon interaction AV8′. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions.

The 'gravitating' tensor in the dualistic theory

International Nuclear Information System (INIS)

Mahanta, M.N.

1989-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-01-07

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

Reconstruction of convex bodies from surface tensors

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus

2016-01-01

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

The Riemann-Lovelock curvature tensor

International Nuclear Information System (INIS)

Kastor, David

2012-01-01

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

A General Expression for the Quartic Lovelock Tensor

OpenAIRE

Briggs, C. C.

1997-01-01

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

Tensor-GMRES method for large sparse systems of nonlinear equations

Science.gov (United States)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

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

Tensor Network Quantum Virtual Machine (TNQVM)

Energy Technology Data Exchange (ETDEWEB)

2016-11-18

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

A Tour of TensorFlow

OpenAIRE

Goldsborough, Peter

2016-01-01

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

Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.

Science.gov (United States)

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

2016-03-01

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

Abelian gauge theories with tensor gauge fields

International Nuclear Information System (INIS)

Kapuscik, E.

1984-01-01

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

Theoretical study of lithium clusters by electronic stress tensor

International Nuclear Information System (INIS)

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

2012-01-01

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

First Half Of CMS Hadron Calorimeter Completed

CERN Multimedia

2001-01-01

CMS HCAL electronics coordinator John Elias from Fermilab inspecting the assembled first half of the calorimeter. The first half barrel of the CMS hadron calorimeter was completed last month and assembly work on the elements of the second half commenced just last week. This is not a simple task considering the fact that the constructed half-barrel consists of eighteen 30 tonne segments each made with 0.15 mm tolerance. But through the work of everyone on the CMS hadron calorimeter team it is all moving forward. In the LHC, detection of particles produced in collisions of two proton beams requires measurement of their energy. To do this, the particle energy has to be changed into a form that can be easily measured. This is achieved by stopping the initial particles in a dense medium, where they create a shower of secondary particles. While particles that interact through electromagnetic forces (electrons and positrons) create relatively small showers, the size of showers created by hadrons, particles that i...

Aspects of the Antisymmetric Tensor Field

Science.gov (United States)

Lahiri, Amitabha

1991-02-01

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

Tensor hypercontraction. II. Least-squares renormalization

Science.gov (United States)

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

2012-12-01

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

Ryu-Takayanagi formula for symmetric random tensor networks

Science.gov (United States)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

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

Visualizing Tensor Normal Distributions at Multiple Levels of Detail.

Science.gov (United States)

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

2016-01-01

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

Energy-momentum tensor in quantum field theory

International Nuclear Information System (INIS)

Fujikawa, K.

1981-01-01

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

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

Science.gov (United States)

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

2016-10-01

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

Local Tensor Radiation Conditions For Elastic Waves

DEFF Research Database (Denmark)

Krenk, S.; Kirkegaard, Poul Henning

2001-01-01

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

Exact tensor network ansatz for strongly interacting systems

Science.gov (United States)

Zaletel, Michael P.

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

The normal conformal Cartan connection and the Bach tensor

International Nuclear Information System (INIS)

Korzynski, Mikolaj; Lewandowski, Jerzy

2003-01-01

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

An introduction to tensors and group theory for physicists

CERN Document Server

Jeevanjee, Nadir

2011-01-01

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

Dispersive force between dissimilar materials: Geometrical effects

International Nuclear Information System (INIS)

Noguez, Cecilia; Roman-Velazquez, C.E.

2004-01-01

We calculate the Casimir force or dispersive van der Waals force between a spherical nanoparticle and a planar substrate, both with arbitrary dielectric properties. We show that the force between the sphere and half-space can be calculated through the interacting surface plasmons of the bodies. Using a Spectral Representation formalism, we show that the force of a sphere made of a material A and a half-space made of a material B differs from the case when the sphere is made of B, and the half-space is made of A. We find that the difference depends on the plasma frequency of the materials, the geometry, and the distance of separation between the sphere and half-space. The differences show the importance of the geometry, and make evident the necessity of realistic descriptions of the system beyond the Derjaguin Approximation or Proximity Theorem Approximation

Tensor Excitations in Nambu - Jona-Lasinio Model

CERN Document Server

Chizhov, M V

1996-01-01

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

On the energy-momentum tensor in Moyal space

International Nuclear Information System (INIS)

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

2015-01-01

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

Residual stresses relaxation in surface-hardened half-space under creep conditions

Directory of Open Access Journals (Sweden)

Vladimir P. Radchenko

2015-09-01

Full Text Available We developed the method for solving the problem of residual stresses relaxation in surface-hardened layer of half-space under creep conditions. At the first stage we made the reconstruction of stress-strain state in half-space after plastic surface hardening procedure based on partial information about distribution for one residual stress tensor component experimentally detected. At the second stage using a numerical method we solve the problem of relaxation of self-balanced residual stresses under creep conditions. To solve this problem we introduce the following Cartesian system: x0y plane is aligned with hardened surface of half-space and 0z axis is directed to the depth of hardened layer. We also introduce the hypotheses of plane sections parallel to x0z and y0z planes. Detailed analysis of the problem has been done. Comparison of the calculated data with the corresponding test data was made for plane specimens (rectangular parallelepipeds made of EP742 alloy during T=650°C after the ultrasonic hardening with four hardening modes. We use half-space to model these specimens because penetration's depth of residual stresses is less than specimen general size in two digit exponent. There is enough correspondence of experimental and calculated data. It is shown that there is a decay (in modulus of pressing residual stresses under creep in 1.4–1.6 times.

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

International Nuclear Information System (INIS)

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

1993-01-01

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

Quantum mechanics of Yano tensors: Dirac equation in curved spacetime

International Nuclear Information System (INIS)

Cariglia, Marco

2004-01-01

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

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

Science.gov (United States)

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

2017-05-01

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

Tensor meson dominance and e+e--physics

International Nuclear Information System (INIS)

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

1983-01-01

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

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

African Journals Online (AJOL)

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

Holographic stress tensor for non-relativistic theories

International Nuclear Information System (INIS)

Ross, Simon F.; Saremi, Omid

2009-01-01

We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.

Unsupervised Tensor Mining for Big Data Practitioners.

Science.gov (United States)

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.

Correlators in tensor models from character calculus

Directory of Open Access Journals (Sweden)

A. Mironov

2017-11-01

Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.

Scalar-tensor linear inflation

Energy Technology Data Exchange (ETDEWEB)

Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)

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 (φ) 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.

Superconformal tensor calculus and matter couplings in six dimensions

International Nuclear Information System (INIS)

Bergshoeff, E.; Sezgin, E.; Proeyen, A. van

1986-01-01

Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. We also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet. (orig.)

Genten: Software for Generalized Tensor Decompositions v. 1.0.0

Energy Technology Data Exchange (ETDEWEB)

2017-06-22

Tensors, or multidimensional arrays, are a powerful mathematical means of describing multiway data. This software provides computational means for decomposing or approximating a given tensor in terms of smaller tensors of lower dimension, focusing on decomposition of large, sparse tensors. These techniques have applications in many scientific areas, including signal processing, linear algebra, computer vision, numerical analysis, data mining, graph analysis, neuroscience and more. The software is designed to take advantage of parallelism present emerging computer architectures such has multi-core CPUs, many-core accelerators such as the Intel Xeon Phi, and computation-oriented GPUs to enable efficient processing of large tensors.

A tensor-based dictionary learning approach to tomographic image reconstruction

DEFF Research Database (Denmark)

Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian

2016-01-01

We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion...... coefficients in that dictionary. Our approach differs from past approaches in that (a) we use a third-order tensor representation for our images and (b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem...... with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images...

Dark energy in scalar-tensor theories

International Nuclear Information System (INIS)

Moeller, J.

2007-12-01

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 σ-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.)

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.)

Tensor completion for PDEs with uncertain coefficients and Bayesian Update

KAUST Repository

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.

Tensor completion for PDEs with uncertain coefficients and Bayesian Update

KAUST Repository

Litvinenko, Alexander

2017-01-01

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.

Skyrmions, dense matter and nuclear forces

International Nuclear Information System (INIS)

Pethick, C.J.

1984-12-01

A simple introduction to a number of properties of Skyrme's chiral soliton model of baryons is given. Some implications of the model for dense matter and for nuclear interactions are discussed. (orig.)

The impact of the tensor interaction on the β-delayed neutron emission of the neutron-rich Ni isotopes

Directory of Open Access Journals (Sweden)

Sushenok E.O.

2018-01-01

Full Text Available The neutron emission of the β-decay of 74;76;78;80Ni are studied within the quasiparticle random phase approximation with the Skyrme interaction. The coupling between one- and two-phonon terms in the wave functions of the low-energy 1+ states of the daughter nuclei is taken into account. It is shown that the strength decrease of the neutronproton tensor interaction leads to the increase of the half-life and the neutron-emission probability.

The matter Lagrangian and the energy-momentum tensor in modified gravity with nonminimal coupling between matter and geometry

International Nuclear Information System (INIS)

Harko, T.

2010-01-01

We show that in modified f(R) type gravity models with nonminimal coupling between matter and geometry, both the matter Lagrangian and the energy-momentum tensor are completely and uniquely determined by the form of the coupling. This result is obtained by using the variational formulation for the derivation of the equations of motion in the modified gravity models with geometry-matter coupling, and the Newtonian limit for a fluid obeying a barotropic equation of state. The corresponding energy-momentum tensor of the matter in modified gravity models with nonminimal coupling is more general than the usual general-relativistic energy-momentum tensor for perfect fluids, and it contains a supplementary, equation of state dependent term, which could be related to the elastic stresses in the body, or to other forms of internal energy. Therefore, the extra force induced by the coupling between matter and geometry never vanishes as a consequence of the thermodynamic properties of the system, or for a specific choice of the matter Lagrangian, and it is nonzero in the case of a fluid of dust particles.

Tensor squeezed limits and the Higuchi bound

Energy Technology Data Exchange (ETDEWEB)

Bordin, Lorenzo [SISSA, via Bonomea 265, 34136, Trieste (Italy); Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Mirbabayi, Mehrdad [Institute for Advanced Study, Princeton, NJ 08540 (United States); Noreña, Jorge, E-mail: lbordin@sissa.it, E-mail: creminel@ictp.it, E-mail: mehrdadm@ias.edu, E-mail: jorge.norena@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Universidad 330, Curauma, Valparaíso (Chile)

2016-09-01

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 consistency 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 has a privileged direction.

Massless and massive quanta resulting from a mediumlike metric tensor

International Nuclear Information System (INIS)

Soln, J.

1985-01-01

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

Superconformal tensor calculus and matter couplings in six dimensions

International Nuclear Information System (INIS)

Bergshoeff, E.; Sezgin, E.; van Proeyen, A.

1989-01-01

Using superconformal tensor calculus the authors construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. They start from the superconformal algebra which they realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. The authors also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet

Tensor product varieties and crystals. GL case

OpenAIRE

Malkin, Anton

2001-01-01

The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.

Gravitational Metric Tensor Exterior to Rotating Homogeneous ...

African Journals Online (AJOL)

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

Hybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction

Science.gov (United States)

Lyu, Mengjiao; Isaka, Masahiro; Myo, Takayuki; Toki, Hiroshi; Ikeda, Kiyomi; Horiuchi, Hisashi; Suhara, Tadahiro; Yamada, Taiichi

2018-01-01

Many-body correlations play an essential role in the ab initio description of nuclei with nuclear bare interactions. We propose a new framework to describe light nuclei by the hybridization of the tensor-optimized antisymmetrized molecular dynamics (TOAMD) and the high-momentum AMD (HM-AMD), which we call "HM-TOAMD." In this framework, we describe the many-body correlations in terms of not only the correlation functions in TOAMD, but also the high-momentum pairs in the AMD wave function. With the bare nucleon-nucleon interaction AV8^', we sufficiently reproduce the energy and radius of the {^3}H nucleus in HM-TOAMD. The effects of tensor force and short-range repulsion in the bare interaction are nicely described in this new framework. We also discuss the convergence in calculation and flexibility of the model space for this new method.

Atomic-batched tensor decomposed two-electron repulsion integrals

Science.gov (United States)

Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove

2017-04-01

We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.

Inflationary tensor fossils in large-scale structure

Energy Technology Data Exchange (ETDEWEB)

Dimastrogiovanni, Emanuela [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Fasiello, Matteo [Department of Physics, Case Western Reserve University, Cleveland, OH 44106 (United States); Jeong, Donghui [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Kamionkowski, Marc, E-mail: ema@physics.umn.edu, E-mail: mrf65@case.edu, E-mail: duj13@psu.edu, E-mail: kamion@jhu.edu [Department of Physics and Astronomy, 3400 N. Charles St., Johns Hopkins University, Baltimore, MD 21218 (United States)

2014-12-01

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-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.

Properties of the tensor correlation in He isotopes

International Nuclear Information System (INIS)

Myo, Takayuki; Sugimoto, Satoru; Kato, Kiyoshi; Toki, Hiroshi; Ikeda, Kiyomi

2006-01-01

We investigate the roles of the tensor correlation on the structures of 4,5 He. For 4 He, we take the high angular momentum states as much as possible with the 2p2h excitations of the shell model type method to describe the tensor correlation. Three specific configurations are found to be favored for the tensor correlation. This correlation is also important to describe the scattering phenomena of the 4 He+nsystem including the higher partial waves consistently

Energy-momentum tensor in the quantum field theory

International Nuclear Information System (INIS)

Azakov, S.I.

1977-01-01

An energy-momentum tensor in the scalar field theory is built. The tensor must satisfy the finiteness requirement of the Green function. The Green functions can always be made finite by renormalizations in the S-matrix by introducing counter terms into the Hamiltonian (or Lagrangian) of the interaction. Such a renormalization leads to divergencies in the Green functions. Elimination of these divergencies requires the introduction of new counter terms, which must be taken into account in the energy-momentum tensor

Tensor product of quantum logics

Science.gov (United States)

Pulmannová, Sylvia

1985-01-01

A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A ``tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.

A Closed-Form Solution to Tensor Voting: Theory and Applications

OpenAIRE

Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gerard

2016-01-01

We prove a closed-form solution to tensor voting (CFTV): given a point set in any dimensions, our closed-form solution provides an exact, continuous and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence...

Superconformal tensor calculus in five dimensions

International Nuclear Information System (INIS)

Fujita, Tomoyuki; Ohashi, Keisuke

2001-01-01

We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)

The tensor distribution function.

Science.gov (United States)

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

2009-01-01

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

Inductive Framework for Multi-Aspect Streaming Tensor Completion with Side Information

OpenAIRE

Nimishakavi, Madhav; Mishra, Bamdev; Gupta, Manish; Talukdar, Partha

2018-01-01

Low-rank tensor completion is a well-studied problem and has applications in various fields. However, in many real-world applications the data is dynamic, i.e., the tensor grows as new data arrives. Besides the tensor, in many real-world scenarios, side information is also available in the form of matrices which also grow. Existing work on dynamic tensor completion do not incorporate side information and most of the previous work is based on the assumption that the tensor grows only in one mo...

The classification of the Ricci tensor in the general theory of relativity

International Nuclear Information System (INIS)

Cormack, W.J.

1979-10-01

A comprehensive classification of the Ricci tensor in General Relativity using several techniques is given and their connection with existing classification studied under the headings; canonical forms for the Ricci tensor, invariant 2-spaces in the classification of the Ricci tensor, Riemannian curvature and the classification of the Riemann and Ricci tensors, and spinor classifications of the Ricci tensor. (U.K.)

Susceptibility Tensor Imaging (STI) of the Brain

Science.gov (United States)

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

2016-01-01

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

Singular Poisson tensors

International Nuclear Information System (INIS)

Littlejohn, R.G.

1982-01-01

The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular

The footprint of Alaskan tundra fires during the past half-century: implications for surface properties and radiative forcing

International Nuclear Information System (INIS)

Rocha, Adrian V; Loranty, Michael M; Higuera, Phil E; Mack, Michelle C; Hu Fengsheng; Jones, Benjamin M; Breen, Amy L; Rastetter, Edward B; Shaver, Gus R; Goetz, Scott J

2012-01-01

Recent large and frequent fires above the Alaskan arctic circle have forced a reassessment of the ecological and climatological importance of fire in arctic tundra ecosystems. Here we provide a general overview of the occurrence, distribution, and ecological and climate implications of Alaskan tundra fires over the past half-century using spatially explicit climate, fire, vegetation and remote sensing datasets for Alaska. Our analyses highlight the importance of vegetation biomass and environmental conditions in regulating tundra burning, and demonstrate that most tundra ecosystems are susceptible to burn, providing the environmental conditions are right. Over the past two decades, fire perimeters above the arctic circle have increased in size and importance, especially on the North Slope, indicating that future wildfire projections should account for fire regime changes in these regions. Remote sensing data and a literature review of thaw depths indicate that tundra fires have both positive and negative implications for climatic feedbacks including a decadal increase in albedo radiative forcing immediately after a fire, a stimulation of surface greenness and a persistent long-term (>10 year) increase in thaw depth. In order to address the future impact of tundra fires on climate, a better understanding of the control of tundra fire occurrence as well as the long-term impacts on ecosystem carbon cycling will be required. (letter)

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

Energy Technology Data Exchange (ETDEWEB)

Krause, J [Universidad Central de Venezuela, Caracas

1976-04-11

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

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.