Search results for " Tensor"

showing 10 items of 210 documents

Module categories of finite Hopf algebroids, and self-duality

2017

International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.

Self-duality[ MATH ] Mathematics [math]Finite tensor categoryGeneral MathematicsDuality (mathematics)Representation theory of Hopf algebrasBimodulesQuasitriangular Hopf algebra01 natural sciencesMonoidal CategoriesMathematics::Category TheoryMathematics::Quantum Algebra0103 physical sciencesRings0101 mathematicsAlgebra over a fieldAbelian group[MATH]Mathematics [math]Fusion categoryHopf algebroidMSC: Primary 16T99 18D10SubfactorsMathematicsQuantum groupApplied Mathematics010102 general mathematicsMathematics::Rings and AlgebrasTensor CategoriesTheorem16. Peace & justiceHopf algebraDual (category theory)Algebra010307 mathematical physicsWeak Hopf algebra
researchProduct

The nonabelian tensor product of two soluble minimax groups

2010

Settore MAT/02 - AlgebraChernikov groups soluble minimax groups nonabelian tensor productsSettore MAT/03 - Geometria
researchProduct

Studio di parcellizzazione talamica per l’identificazione del target di trattamento applicato alle talamotomie trans-craniche mediante ultrasuoni foc…

2019

SCOPO DEL LAVORO: La tcMRgFUS consente di effettuare una vera e propria esplorazione neurofunzionale per confermare ed ottimizzare il target lesionale prima di indurre una lesione cerebrale permanente. La scelta del target di trattamento si basa tuttavia su coordinate stereotassiche che non tengono conto delle diversità anatomiche di ciascun individuo. Essendo il paziente vigile durante tutta la durata della procedura, l'ottimizzazione del target di trattamento viene effettuata sulla base del feedback del paziente nel corso della procedura utilizzando sonicazioni di potenza sub-lesionale. Scopo di questo lavoro è valutare retrospettivamente il possibile ruolo della parcellizzazione talamica…

Settore MED/27 - NeurochirurgiaSettore FIS/01 - Fisica SperimentaleSettore MED/37 - NeuroradiologiaSettore MED/26 - Neurologiaultrasuoni focalizzati risonanza magnetica tensore di diffusione trattografia parcellizzazione talamotomia tremore essenziale parkinsonSettore MED/36 - Diagnostica Per Immagini E Radioterapia
researchProduct

Studio preliminare di parcellizzazione talamica per l’identificazione del target di trattamento applicato alle talamotomie trans-craniche mediante ul…

2018

Introduzione La tcMRgFUS consente di effettuare una vera e propria esplorazione neurofunzionale per confermare ed ottimizzare il target lesionale prima di indurre una lesione cerebrale permanete. La scelta del target di trattamento si basa tuttavia su coordinate stereotassiche che non tengono conto delle diversità anatomiche di ciascun individuo. L'ottimizzazione del target di trattamento viene effettuata sulla base del feedback del paziente durante la procedura stessa. Materiali e metodi È’ stato utilizzato uno scanner RM da 1.5T per acquisire sequenze morfologiche 3D e ultrastrutturali (DTI) in pazienti successivamente sottoposti a tcMRgFUS. È stata effettuata una segmentazione delle aree…

Settore MED/27 - NeurochirurgiaSettore MED/37 - NeuroradiologiaSettore MED/26 - NeurologiaSettore MED/36 - Diagnostica Per Immagini E Radioterapiatrattografia tensore di diffusione segmentazione morfovolumetrica parcellizzazione talamica
researchProduct

Thalamic parcellation for target identification in trans-cranial MR-guided Focused UltraSound (tcMRgFUS) thalamotomies: a preliminary probabilistc tr…

2018

Background: Trans-cranial MR-guided Focused UltraSound (tcMRgFUS) allows a neurofunctional exploration of thalamic nuclei to confirm and optimize the target before inducing a permanent brain lesion. However, the choice of the target is based on stereotactic coordinates that do not take into account the anatomical variability of each single patient. Thus, the optimization of the treatment target is based on the patient's feedback during lower power sonications. The aim of this work is to retrospectively evaluate the possible role of thalamic parcellation for the identification of the intermediate ventral nucleus (VIM) in patients undergoing tcMRgFUS. Materials and Methods: A 1.5T MR scanner …

Settore MED/37 - Neuroradiologiathalamic parcellizzation diffusion tensor imaging tractography segmentationSettore MED/36 - Diagnostica Per Immagini E RadioterapiaSettore FIS/07 - Fisica Applicata(Beni Culturali Ambientali Biol.e Medicin)
researchProduct

The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

2021

The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the $O(3)$ non-linear sigma model in $1+1$ dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in $3+1$ dimensio…

Sigma modelSpontaneous symmetry breakingQC1-999Lattice (group)General Physics and AstronomyFOS: Physical sciencesClassical Heisenberg modelQuantum Materials53001 natural sciences010305 fluids & plasmasTheoretical physicsHigh Energy Physics - Lattice0103 physical sciencesSymmetric tensorTensorQuantum field theory010306 general physicsclassical Heisenberg modelCondensed Matter - Statistical MechanicsPhysicsQuantum PhysicsStatistical Mechanics (cond-mat.stat-mech)Heisenberg modelPhysics500 Naturwissenschaften und Mathematik::530 Physik::530 PhysikHigh Energy Physics - Lattice (hep-lat)magnetismstatistical and condensed matter physicsQuantum Physics (quant-ph)
researchProduct

Rovibrational spectroscopy of ethylene : Stark effect : Application to ethylene in zeolites

2010

The objective of this report is to present a study as complete as possible of the Stark effect in the asymmetric top molecules of X2Y4 type possessing the D2h symmetry group and to apply it to the problem of the spectroscopy of the ethylene molecule trapped in a zeolite. For the first time, a tensorial formalism adapted to the study of the Stark effect for the O(3) D2h group chain was developed. In parallel, a computer package was worked out as a new generation of software called D2hTDS-ST using a simpler basis, allowing an economy in the calculation time. On the basis of the theoretical and computing tools as well as from the experimental spectra, recorded in the laboratory, we made a firs…

Spectroscopie moléculaireD2h point groupNanoporous solidsFormalisme tensorielStark effectZéolithesTensorial formalismSolides nanoporeux[ PHYS.COND.CM-GEN ] Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]Effet StarkGroupe ponctuel D2hMolecular spectroscopy[PHYS.COND.CM-GEN] Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other][PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]Zeolites
researchProduct

ROVIBRATIONAL AND STARK SPECTROSCOPY OF THE X2Y4MOLECULES. APPLICATION TO ETHYLENE

2005

This thesis is devoted to the spectroscopy of ethylene in the aim of studying the molecule trapped in zeolites. The first part deals with the tensorial model adapted to the symmetry of the isolated molecule: formalism, Hamiltonian and transition moments. To take the strong electric fields existing into zeolites into account, an extension of the model to the Stark effect is proposed in the second part. The third part describes the programs of the D2hTDS software which have been built for the calculation and analysis of X2Y4-type molecule spectra. The fourth part presents applications to the calculation and analysis of zero-field and Stark ethylene spectra. In particular, the model has been t…

Spectroscopie moléculaire[PHYS.PHYS.PHYS-ATOM-PH]Physics [physics]/Physics [physics]/Atomic Physics [physics.atom-ph]Formalisme tensorielAlignementPositions et intensités[ PHYS.PHYS.PHYS-ATOM-PH ] Physics [physics]/Physics [physics]/Atomic Physics [physics.atom-ph]EthylèneEffet Stark[PHYS.PHYS.PHYS-ATOM-PH] Physics [physics]/Physics [physics]/Atomic Physics [physics.atom-ph]
researchProduct

Mohr-cyclides, a 3D representation of geological tensors: The examples of stress and flow

2008

Mohr-circles are commonly used to represent second-rank tensors in two dimensions. In geology, this mainly applies to stress, flow, strain and deformation. Three-dimensional second rank tensors have been represented by sets of three Mohr-circles, mainly in the application of stress. This paper demonstrates that three-dimensional second rank tensors can in fact be represented in a three-dimensional reference frame by Mohr surfaces, which are members of the cyclide family. Such Mohr-cyclides can be used to represent any second rank tensor and are exemplified with the stress and flow tensors.

Stress (mechanics)Pure mathematicsRank (linear algebra)Flow (mathematics)Invariants of tensorsMohr's circleGeologyGeometryMaxwell stress tensorTensorPhysics::GeophysicsMathematicsPlane stressJournal of Structural Geology
researchProduct

A nonlocal strain gradient plasticity theory for finite deformations

2009

Abstract Strain gradient plasticity for finite deformations is addressed within the framework of nonlocal continuum thermodynamics, featured by the concepts of (nonlocality) energy residual and globally simple material. The plastic strain gradient is assumed to be physically meaningful in the domain of particle isoclinic configurations (with the director vector triad constant both in space and time), whereas the objective notion of corotational gradient makes it possible to compute the plastic strain gradient in any domain of particle intermediate configurations. A phenomenological elastic–plastic constitutive model is presented, with mixed kinematic/isotropic hardening laws in the form of …

Stress (mechanics)Strain rate tensorClassical mechanicsMechanics of MaterialsMechanical EngineeringFinite strain theoryConstitutive equationInfinitesimal strain theoryGeneral Materials ScienceLevy–Mises equationsStrain rateElastic and plastic strainMathematicsInternational Journal of Plasticity
researchProduct