Search results for "SCALAR"
showing 10 items of 1002 documents
The Boson Fermion Correspondence
1989
In 1932 Louis de Broglie suggested that photons could be constructed from pairs of neutrinos [de Broglie, 1932]. Both are massless particles (except for some recent unconfirmed experiments according to which the neutrino could have a very small mass) and are electrically neutral. The main difference between free photons and free neutrinos is that the former obeys Bose statistics and the second Fermi statistics. The spin of a photon is 1 and the spin of a neutrino is 1/2 and therefore kinematically it should be possible to think of a photon as a neutrino pair. However, this old formulation of boson fermion equivalence has not been very fruitful in particle physics. Instead, there has been a …
Nonlinear frequency conversion in a birefringent microstructured fiber tuned by externally applied hydrostatic pressure.
2013
We studied vector frequency conversion in externally tuned microstructured fibers for applications as a novel, nonlinear fiber-optic sensor. We investigated both experimentally and numerically a possibility of shifting vector and scalar modulation instability gain bands by pressure-induced changes in the linear properties of a microstructured fiber. Our results show that polarization-dependent vector nonlinear processes sensitive to variation of fiber group velocity difference (group birefringence) exhibit a clear advantage for pressure-sensing applications compared with scalar nonlinear processes only sensitive to group velocity dispersion changes. Analytical predictions and numerical simu…
Stand-Off Magnetometry with Directional Emission from Sodium Vapors
2021
International audience; Stand-off magnetometry allows measuring magnetic field at a distance, and can be employed in geophysical research, hazardous environment monitoring, and security applications. Stand-off magnetometry based on resonant scattering from atoms or molecules is often limited by the scarce amounts of detected light. The situation would be dramatically improved if the light emitted by excited atoms were to propagate towards the excitation light source in a directional manner. Here, we demonstrate that this is possible by means of mirrorless lasing. In a tabletop experiment, we detect free-precession signals of ground-state sodium spins under the influence of an external magne…
Mixed Mode Delamination Analysis by a Thermodynamically Consistent Cohesive Interface Model with Independent Mode I and Mode II Fracture Energies
2015
Abstract In the present paper a new thermodynamically consistent cohesive interface model is proposed; it based on a predefined Helmhotz free energy with a single scalar damage variable and produces two independent fracture energies, in pure mode I and pure mode II debonding conditions. The proposed model can also take in to account the frictional effects with a smooth transition of the mechanical behaviour, from the initial cohesive one of the sound material, to the frictional one of the fully debonded interface. The cohesive-frictional behaviour is based on the mesoscale geometric interpretation of the scalar damage variable, which distinguish sound and debonded fractions of a representat…
Multi-scenario multi-objective robust optimization under deep uncertainty: A posteriori approach
2021
This paper proposes a novel optimization approach for multi-scenario multi-objective robust decision making, as well as an alternative way for scenario discovery and identifying vulnerable scenarios even before any solution generation. To demonstrate and test the novel approach, we use the classic shallow lake problem. We compare the results obtained with the novel approach to those obtained with previously used approaches. We show that the novel approach guarantees the feasibility and robust efficiency of the produced solutions under all selected scenarios, while decreasing computation cost, addresses the scenario-dependency issues, and enables the decision-makers to explore the trade-off …
Representation of capacity drop at a road merge via point constraints in a first order traffic model
2018
We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower than the receiving capacity of the outgoing road, as too many vehicles trying to access the junction from the incoming roads hinder each other. In this paper, we first construct an enhanced version of the locally constrained model introduced by Haut et al. (Proceedings 16th IFAC World Congress. Prague, Czech Republic 229 (2005) TuM01TP/3), then we propose its counterpart featuring a non-local constraint and finally we compare numerically the two models by c…
Necessary conditions for extremality and separation theorems with applications to multiobjective optimization
1998
The aim of this paper is to give necessary conditions for extremality in terms of an abstract subdifferential and to obtain general separation theorems including both finite and infinite classical separation theorems. This approach, which is mainly based on Ekeland's variational principle and the concept of locally weak-star compact cones, can be considered as a generalization f the notions of optima in problems of scalar or vector optimization with and without constraints. The results obtained are applied to derive new necessary optimality conditions for Pareto local minimum and weak Pareto minimum of nonsmooth multlobjectivep rogramming problems.
The Riemannian manifold of all Riemannian metrics
1991
In this paper we study the geometry of (M, G) by using the ideas developed in [Michor, 1980]. With that differentiable structure on M it is possible to use variational principles and so we start in section 2 by computing geodesics as the curves in M minimizing the energy functional. From the geodesic equation, the covariant derivative of the Levi-Civita connection can be obtained, and that provides a direct method for computing the curvature of the manifold. Christoffel symbol and curvature turn out to be pointwise in M and so, although the mappings involved in the definition of the Ricci tensor and the scalar curvature have no trace, in our case we can define the concepts of ”Ricci like cu…
The Light Ray transform in Stationary and Static Lorentzian geometries
2019
Given a Lorentzian manifold, the light ray transform of a function is its integrals along null geodesics. This paper is concerned with the injectivity of the light ray transform on functions and tensors, up to the natural gauge for the problem. First, we study the injectivity of the light ray transform of a scalar function on a globally hyperbolic stationary Lorentzian manifold and prove injectivity holds if either a convex foliation condition is satisfied on a Cauchy surface on the manifold or the manifold is real analytic and null geodesics do not have cut points. Next, we consider the light ray transform on tensor fields of arbitrary rank in the more restrictive class of static Lorentzia…
Non-preserved curvature conditions under constrained mean curvature flows
2014
We provide explicit examples which show that mean convexity (i.e. positivity of the mean curvature) and positivity of the scalar curvature are non-preserved curvature conditions for hypersurfaces of the Euclidean space evolving under either the volume- or the area preserving mean curvature flow. The relevance of our examples is that they disprove some statements of the previous literature, overshadow a widespread folklore conjecture about the behaviour of these flows and bring out the discouraging news that a traditional singularity analysis is not possible for constrained versions of the mean curvature flow.