25,069 research outputs found
Problem of Time in Slightly Inhomogeneous Cosmology
The Problem of Time (PoT) is a multi-faceted conceptual incompatibility
between various areas of Theoretical Physics. Whilst usually stated as between
GR and QM, in fact 8/9ths of it is already present at the classical level. Thus
we adopt a `top-down' classical and then quantum approach. I consider a local
resolution to the Problem of Time that is Machian, which was previously
realized for relational triangle and minisuperspace models. This resolution has
three levels: classical, semiclassical and combined
semiclassical-histories-records. This article's specific model is a slightly
inhomogeneous cosmology considered for now at the classical level. This is
motivated by how the inhomogeneous fluctuations that underlie structure
formation - galaxies and CMB hotspots - might have been seeded by quantum
cosmological fluctuations, as magnified by some inflationary mechanism. In
particular, I consider the perturbations about case of this involving up
to second order, which has a number of parallels with the Halliwell-Hawking
model but has a number of conceptual differences and useful upgrades. The
article's main features are that the elimination part of the model's thin
sandwich is straightforward, but the modewise split of the constraints fail to
be first-class constraints. Thus the elimination part only arises as an
intermediate geometry between superspace and Riem. The reduced geometries have
surprising singularities influenced by the matter content of the universe,
though the N-body problem anticipates these with its collinear singularities. I
also give a `basis set' of Kuchar beables for this model arena.Comment: 15 pages including 4 figures. More self-contained explanations
include
Optimal design of sandwich plates with honeycomb core
This work deals with the problem of the optimum design of a sandwich structure composed of two laminated skins and a honeycomb core. The goal is to propose a numerical optimisation procedure that does not make any simplifying hypothesis in order to obtain a true global optimal solution for the considered problem. In order to face the design of the sandwich structure at both meso and macro scales, we use a two-level optimisation strategy. At the first level, we determine the optimum geometry of the unit cell together with the material and geometric parameters of the laminated skins, while at the second level we determine the optimal skins lay-up giving the geometrical and material parameters issued from the first level. We will illustrate the application of our strategy to the least-weight design of a sandwich plate submitted to several constraints: on the first buckling load, on the positive-definiteness of the stiffness tensor of the core, on the ratio between skins and core thickness and on the admissible moduli for the laminated skins
Constructing simply laced Lie algebras from extremal elements
For any finite graph Gamma and any field K of characteristic unequal to 2 we
construct an algebraic variety X over K whose K-points parameterise K-Lie
algebras generated by extremal elements, corresponding to the vertices of the
graph, with prescribed commutation relations, corresponding to the non-edges.
After that, we study the case where Gamma is a connected, simply laced Dynkin
diagram of finite or affine type. We prove that X is then an affine space, and
that all points in an open dense subset of X parameterise Lie algebras
isomorphic to a single fixed Lie algebra. If Gamma is of affine type, then this
fixed Lie algebra is the split finite-dimensional simple Lie algebra
corresponding to the associated finite-type Dynkin diagram. This gives a new
construction of these Lie algebras, in which they come together with
interesting degenerations, corresponding to points outside the open dense
subset. Our results may prove useful for recognising these Lie algebras.Comment: We made many corrections suggested by a referee, and extended our
results to positive characteristic greater than
A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part II: the optimisation strategy
This work deals with the problem of the optimum design of a sandwich panel. The design strategy that we propose is a numerical optimisation procedure that does not make any simplifying assumption to obtain a true global optimum configuration of the system. To face the design of the sandwich structure at both meso and macro scales, we use a two-level optimisation strategy: at the first level we determine the optimal geometry of the unit cell of the core together with the material and geometric parameters of the laminated skins, while at the second level we determine the optimal skins lay-up giving the geometrical and material parameters issued from the first level. The two-level strategy relies both on the use of the polar formalism for the description of the anisotropic behaviour of the laminates and on the use of a genetic algorithm as optimisation tool to perform the solution search. To prove its effectiveness, we apply our strategy to the least-weight design of a sandwich plate, satisfying several constraints: on the first buckling load, on the positive-definiteness of the stiffness tensor of the core, on the ratio between skins and core thickness and on the admissible moduli for the laminated skins
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