524 research outputs found
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
Exporting unemployment? Assessing the impact of German import competition on regional manufacturing employment in France
This paper assesses the extent to which German import competition has contributed to the observed differential decline in manufacturing employment across French regions. The study employs an exposure research design that exploits differences in regional manufacturing specialisation across French départements combined with an instrumental variable strategy. The analysis does not establish a connection between German import competition and differential changes in regional French manufacturing employment. This result suggests that German import competition has neither driven nor halted the overall decline of French manufacturing employment. It also indicates that the sizeable and long-lasting negative regional employment effects of trade between China and developed countries do not necessarily generalise
Port-Hamiltonian systems on graphs
In this paper we present a unifying geometric and compositional framework for
modeling complex physical network dynamics as port-Hamiltonian systems on open
graphs. Basic idea is to associate with the incidence matrix of the graph a
Dirac structure relating the flow and effort variables associated to the edges,
internal vertices, as well as boundary vertices of the graph, and to formulate
energy-storing or energy-dissipating relations between the flow and effort
variables of the edges and internal vertices. This allows for state variables
associated to the edges, and formalizes the interconnection of networks.
Examples from different origins such as consensus algorithms are shown to share
the same structure. It is shown how the identified Hamiltonian structure offers
systematic tools for the analysis of the resulting dynamics.Comment: 45 pages, 2 figure
Magnetohydrodynamic equilibria of a cylindrical plasma with poloidal mass flow and arbitrary cross section shape
The equilibrium of a cylindrical plasma with purely poloidal mass flow and
cross section of arbitrary shape is investigated within the framework of the
ideal MHD theory. For the system under consideration it is shown that only
incompressible flows are possible and, conscequently, the general two
dimensional flow equilibrium equations reduce to a single second-order
quasilinear partial differential equation for the poloidal magnetic flux
function , in which four profile functionals of appear. Apart from
a singularity occuring when the modulus of Mach number associated with the
Alfv\'en velocity for the poloidal magnetic field is unity, this equation is
always elliptic and permits the construction of several classes of analytic
solutions. Specific exact equlibria for a plasma confined within a perfectly
conducting circular cylindrical boundary and having i) a flat current density
and ii) a peaked current density are obtained and studied.Comment: Accepted to Plasma Physics & Controlled Fusion, 14 pages, revte
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
Robust Aeroelastic Control of Very Flexible Wings using Intrinsic Models
This paper explores the robust control of large exible wings when their dynamics are written in terms of intrinsic variables, that is, velocities and stress resultants. Assuming 2-D strip theory for the aerodynamics, the resulting nonlinear aeroelastic equations of motion are written in modal coordinates. It is seen that a system which experiences large displacements can nonetheless be accurately described by a system with only weak nonlinear couplings in this description of the wing dynamics. As result, a linear robust controller acting on a control surface is able to effectively provide gust load alleviation and flutter suppression even when the wing structure undergoes large deformations. This is numerically demonstrated on various representative test cases. © 2013 by Yinan Wang, Andrew Wynn and Rafael Palacios
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