Rotational Heisenberg Inequalities

Since their discovery in 1927, the Heisenberg Inequalities have become an icon of quantum mechanics. Often inappropriately referred to as the Uncertainty Principle, these inequalities relating the standard deviations of the position and momentum observables to Planck's constant are one of the cornerstones of the quantum formalism even if the physical interpretation of quantum mechanics remains still open to controversy nowadays. The Heisenberg Inequalities governing translational motion are well understood. However, the corresponding inequalities pertaining to rotational motion have not been established so far. To fill this gap, we present here the Rotational Heisenberg Inequalities relating the standard deviations of the orientation axis and orbital angular momentum observables of an isolated molecule. The reason for choosing this system is that a molecule separated from its environment corresponds to a bound system preserving the orbital angular momentum.Comment: 6 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1412.211

Evidence for a Magnetic Seebeck effect

The irreversible thermodynamics of a continuous medium with magnetic dipoles predicts that a temperature gradient in the presence of magnetisation waves induces a magnetic induction field, which is the magnetic analog of the Seebeck effect. This thermal gradient modulates the precession and relaxation. The Magnetic Seebeck effect implies that magnetisation waves propagating in the direction of the temperature gradient and the external magnetic induction field are less attenuated, while magnetisation waves propagating in the opposite direction are more attenuated

Relativistic thermodynamics of perfect fluids

The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the first and second laws of thermodynamics. The internal energy density and the pressure of a relativistic perfect fluid carry inertia, which leads to a relativistic coupling between heat and work. The relativistic continuity equation for the relativistic inertia is derived. The relativistic corrections in the Euler equation and in the continuity equations for the energy and momentum are identified. This relativistic theoretical framework allows a rigorous derivation of the relativistic transformation laws for the temperature, the pressure and the chemical potential based on the relativistic transformation laws for the energy density, the entropy density, the mass density and the number density.Comment: 62 page

Integrated modeling of friction stir welding of 6xxx series Al alloys: Process, microstructure and properties

International audienceCompared to most thermomechanical processing methods, friction stir welding (FSW) is a recent technique which has not yet reached full maturity. Nevertheless, owing to multiple intrinsic advantages, FSW has already replaced conventional welding methods in a variety of industrial applications especially for Al alloys. This provides the impetus for developing a methodology towards optimization, from process to performances, using the most advanced approach available in materials science and thermomechanics. The aim is to obtain a guidance both for process fine tuning and for alloy design. Integrated modeling constitutes a way to accelerate the insertion of the process, especially regarding difficult applications where for instance ductility, fracture toughness, fatigue and/or stress corrosion cracking are key issues. Hence, an integrated modeling framework devoted to the FSW of 6xxx series Al alloys has been established and applied to the 6005A and 6056 alloys. The suite of models involves an in-process temperature evolution model, a microstructure evolution model with an extension to heterogeneous precipitation, a microstructure based strength and strain hardening model, and a micro-mechanics based damage model. The presentation of each model is supplemented by the coverage of relevant recent literature. The "model chain" is assessed towards a wide range of experimental data. The final objective is to present routes for the optimization of the FSW process using both experiments and models. Now, this strategy goes well beyond the case of FSW, illustrating the potential of chain models to support a "material by design approach" from process to performances

Quantum description of a rotating and vibrating molecule

A rigorous quantum description of molecular dynamics with a particular emphasis on internal observables is developed accounting explicitly for kinetic couplings between nuclei and electrons. Rotational modes are treated in a genuinely quantum framework by defining a molecular orientation operator. Canonical rotational commutation relations are established explicitly. Moreover, physical constraints are imposed on the observables in order to define the state of a molecular system located in the neighborhood of the ground state defined by the equilibrium condition.Comment: 28 page

Planning complex engineer-to-order products

The design and manufacture of complex Engineer-to-Order products is characterised by uncertain operation durations, finite capacity resources and multilevel product structures. Two scheduling methods are presented to minimise expected costs for multiple products across multiple finite capacity resources. The first sub-optimises the operations sequence, using mean operation durations, then refines the schedule by perturbation. The second method generates a schedule of start times directly by random search with an embedded simulation of candidate schedules for evaluation. The methods are compared for industrial examples

Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid

A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1+3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular form for the space-time metric. The spin contributions to the field equations produce a bounce that averts an initial singularity, provided that the spin density exceeds the rate of shear. At later times, when the spin contribution can be neglected, a Weyssenhoff fluid reduces to a standard cosmological fluid in general relativity. Numerical solutions for the time evolution of the generalised scale factor in spatially-curved models are presented, some of which exhibit eternal oscillatory behaviour without any singularities. In spatially-flat models, analytical solutions for particular values of the equation-of-state parameter are derived. Although the scale factor of a Weyssenhoff fluid generically has a positive temporal curvature near a bounce, it requires unreasonable fine tuning of the equation-of-state parameter to produce a sufficiently extended period of inflation to fit the current observational data.Comment: 34 pages, 18 figure

Weyssenhoff fluid dynamics in general relativity using a 1+3 covariant approach

The Weyssenhoff fluid is a perfect fluid with spin where the spin of the matter fields is the source of torsion in an Einstein-Cartan framework. Obukhov and Korotky showed that this fluid can be described as an effective fluid with spin in general relativity. A dynamical analysis of such a fluid is performed in a gauge invariant manner using the 1+3 covariant approach. This yields the propagation and constraint equations for the set of dynamical variables. A verification of these equations is performed for the special case of irrotational flow with zero peculiar acceleration by evolving the constraints.Comment: 20 page

Traveling wave solutions in the Burridge-Knopoff model

The slider-block Burridge-Knopoff model with the Coulomb friction law is studied as an excitable medium. It is shown that in the continuum limit the system admits solutions in the form of the self-sustained shock waves traveling with constant speed which depends only on the amount of the accumulated stress in front of the wave. For a wide class of initial conditions the behavior of the system is determined by these shock waves and the dynamics of the system can be expressed in terms of their motion. The solutions in the form of the periodic wave trains and sources of counter-propagating waves are analyzed. It is argued that depending on the initial conditions the system will either tend to synchronize or exhibit chaotic spatiotemporal behavior.Comment: 12 pages (ReVTeX), 7 figures (Postscript) to be published in Phys. Rev.