scholarly journals The Eshelby stress tensor, angular momentum tensor and dilatation flux in gradient elasticity

2007 ◽  
Vol 44 (7-8) ◽  
pp. 2477-2486 ◽  
Author(s):  
Markus Lazar ◽  
Helmut O.K. Kirchner
Keyword(s):  
Angular Momentum ◽  
Stress Tensor ◽  
Gradient Elasticity ◽  
Momentum Tensor ◽  
Eshelby Stress

scholarly journals Crystal plasticity: The Hamilton-Eshelby stress in terms of the metric in the intermediate configuration

2012 ◽  
Vol 39 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Paolo Mariano
Keyword(s):  
Free Energy ◽  
Energy Momentum Tensor ◽  
Large Strain ◽  
Momentum Tensor ◽  
Classical Field ◽  
Field Theories ◽  
Relative Power ◽  
Eshelby Stress ◽  
Classical Field Theories ◽  
Intermediate Configuration

The Hamilton-Eshelby stress is a basic ingredient in the description of the evolution of point, lines and bulk defects in solids. The link between the Hamilton-Eshelby stress and the derivative of the free energy with respect to the material metric in the plasticized intermediate configuration, in large strain regime, is shown here. The result is a modified version of Rosenfeld-Belinfante theorem in classical field theories. The origin of the appearance of the Hamilton-Eshelby stress (the non-inertial part of the energy-momentum tensor) in dissipative setting is also discussed by means of the concept of relative power.

scholarly journals Observables for Quarks and Gluons Orbital Angular Momentum Distributions

2015 ◽  
Vol 37 ◽  
pp. 1560039
Author(s):  
Simonetta Liuti ◽  
Aurore Courtoy ◽  
Gary R. Goldstein ◽  
J. Osvaldo Gonzalez Hernandez ◽  
Abha Rajan
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Spin Asymmetry ◽  
Energy Momentum Tensor ◽  
Deeply Virtual Compton Scattering ◽  
Virtual Compton Scattering ◽  
Momentum Tensor ◽  
Transverse Momentum Distribution ◽  
Kinetic Term ◽  
Momentum Distributions

We discuss the observables that have been recently put forth to describe quarks and gluons orbital angular momentum distributions. Starting from a standard parameterization of the energy momentum tensor in QCD one can single out two forms of angular momentum, a so-called kinetic term – Ji decomposition – or a canonical term – Jaffe-Manohar decomposition. Orbital angular momentum has been connected in each decomposition to a different observable, a Generalized Transverse Momentum Distribution (GTMD), for the canonical term, and a twist three Generalized Parton Distribution (GPD) for the kinetic term. While the latter appears as an azimuthal angular modulation in the longitudinal target spin asymmetry in deeply virtual Compton scattering, due to parity constraints, the GTMD associated with canonical angular momentum cannot be measured in a similar set of experiments.

The Maxwell equations

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Variational Principle ◽  
Maxwell Equations ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Field Energy ◽  
Total Charge ◽  
Faraday’S Law ◽  
System Energy

This chapter presents Maxwell equations determining the electromagnetic field created by an ensemble of charges. It also derives these equations from the variational principle. The chapter studies the equation’s invariances: gauge invariance and invariance under Poincaré transformations. These allow us to derive the conservation laws for the total charge of the system and also for the system energy, momentum, and angular momentum. To begin, the chapter introduces the first group of Maxwell equations: Gauss’s law of magnetism, and Faraday’s law of induction. It then discusses current and charge conservation, a second set of Maxwell equations, and finally the field–energy momentum tensor.

Multivector Fields of Noether Symmetries in the Lagrangian Formalism and Belinfante Tensor

2021 ◽  
Vol 61 ◽  
pp. 53-78
Author(s):  
Halima Loumi-Fergane ◽  
Keyword(s):  
Angular Momentum ◽  
Energy Momentum Tensor ◽  
Internal Symmetry ◽  
Momentum Tensor ◽  
Gauge Fields ◽  
Lagrangian Formalism ◽  
Order Partial Differential Equation ◽  
Spin Angular Momentum ◽  
Relativistic Mechanic ◽  
Invariant Gauge

Elsewhere, we gave the explicit expressions of the multivectors fields associated to infinitesimal symmetries which gave rise to Noether currents for classical field theories and relativistic mechanic using the Second Order Partial Differential Equation SOPDE condition for the Poincar\'e-Cartan form.\\ The main objective of this paper is to reformulate the multivector fields associated to translational and rotational symmetries of the gauge fields in particular those of the electromagnetic field which gave rise to symmetrical and invariant gauge energy-momentum tensor and the orbital angular momentum. The spin angular momentum appears however because of the internal symmetry inside the fiber.

scholarly journals Stress Tensor of Free Maxwell Field in Friedmann-Robertson-Walker Universe

1970 ◽  
Vol 7 (7) ◽  
pp. 1-2 ◽  
Author(s):  
SK Sharma ◽  
PR Dhungel ◽  
U Khanal
Keyword(s):  
Energy Density ◽  
Key Words ◽  
Stress Tensor ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Anisotropic Pressure ◽  
Translational Energy ◽  
Closed Universe ◽  
Scientific World ◽  
Friedmann Robertson Walker

The solutions of the Maxwellian field in FRW spacetime, found by using the Newman Penrose formalism, is used to determine the energy-momentum tensor. The tensor is obviously traceless, with the energy density equal to the sum of the radial and the two tangential pressures. But it turns out that the radial and tangential pressures are not equal, giving rise to anisotropy. Such anisotropy can be the origin of the rotation of galaxies. Another result is that the photon energy in a closed universe are quantized in units of one from the lowest value of two upwards. The lowest quantum of two can be interpreted as one unit of spin energy and one of translational energy. Key words: Galactic structure; Maxwellian field; Anisotropic pressure. DOI: 10.3126/sw.v7i7.3814 Scientific World Vol.7(7) 2009 pp.1-2

scholarly journals Eshelbian mechanics of novel materials: Quasicrystals

2016 ◽  
Vol 01 (03n04) ◽  
pp. 1640008 ◽  
Author(s):  
Markus Lazar ◽  
Eleni Agiasofitou
Keyword(s):  
Material Balance ◽  
Momentum Tensor ◽  
Configurational Forces ◽  
Dislocation Loops ◽  
One Dimensional ◽  
Novel Materials ◽  
Eshelby Stress ◽  
Rotational Vector ◽  
Quasicrystalline Structure ◽  
Eshelbian Mechanics

In this work, the so-called Eshelbian or configurational mechanics of quasicrystals is presented. Quasicrystals are considered as a prototype of novel materials. Material balance laws for quasicrystalline materials with dislocations are derived in the framework of generalized incompatible elasticity theory of quasicrystals. Translations, scaling transformations as well as rotations are examined; the latter presents particular interest due to the quasicrystalline structure. This derivation provides important quantities of the Eshelbian mechanics, as the Eshelby stress tensor, the scaling flux vector, the angular momentum tensor, the configurational forces (Peach–Koehler force, Cherepanov force, inhomogeneity force or Eshelby force), the configurational work, and the configurational vector moments for dislocations in quasicrystals. The corresponding [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-integrals for dislocation loops and straight dislocations in quasicrystals are derived and discussed. Moreover, the explicit formulas of the [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-integrals for parallel screw dislocations in one-dimensional hexagonal quasicrystals are obtained. Through this derivation, the physical interpretation of the [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-integrals for dislocations in quasicrystals is revealed and their connection to the Peach–Koehler force, the interaction energy and the rotational vector moment (torque) of dislocations in quasicrystals is established.

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