8,870 research outputs found
The Torsion of Members Having Sections Common in Aircraft Construction
Within recent years a great variety of approximate torsion formulas and drafting-room processes have been advocated. In some of these, especially where mathematical considerations are involved, the results are extremely complex and are not generally intelligible to engineers. The principal object of this investigation was to determine by experiment and theoretical investigation how accurate the more common of these formulas are and on what assumptions they are founded and, if none of the proposed methods proved to be reasonable accurate in practice, to produce simple, practical formulas from reasonably correct assumptions, backed by experiment. A second object was to collect in readily accessible form the most useful of known results for the more common sections. Formulas for all the important solid sections that have yielded to mathematical treatment are listed. Then follows a discussion of the torsion of tubular rods with formulas both rigorous and approximate
Elastic Instability of Members Having Sections Common in Aircraft Construction
Two fundamental problems of elastic stability are discussed in this report. In part one formulas are given for calculating the critical stress at which a thin, outstanding flange of a compression member will either wrinkle into several waves or form into a single half wave and twist the member about its longitudinal axis. A mathematical study of the problem, which together with experimental work has led to these formulas, is given in an appendix. Results of test substantiating the recommended formulas are also presented. In part two the lateral buckling of beams is discussed. The results of a number of mathematical studies of this phenomenon have been published prior to this writing, but very little experimentally determined information relating to the problem has been available heretofore. Experimental verification of the mathematical deductions is supplied
Ab initio wavefunction based methods for excited states in solids: correlation corrections to the band structure of ionic oxides
Ab initio wavefunction based methods are applied to the study of electron
correlation effects on the band structure of oxide systems. We choose MgO as a
prototype closed-shell ionic oxide. Our analysis is based on a local
Hamiltonian approach and performed on finite fragments cut from the infinite
solid. Localized Wannier functions and embedding potentials are obtained from
prior periodic Hartree-Fock (HF) calculations. We investigate the role of
various electron correlation effects in reducing the HF band gap and modifying
the band widths. On-site and nearest-neighbor charge relaxation as well as
long-range polarization effects are calculated. Whereas correlation effects are
essential for computing accurate band gaps, we found that they produce smaller
changes on the HF band widths, at least for this material. Surprisingly, a
broadening effect is obtained for the O 2p valence bands. The ab initio data
are in good agreement with the energy gap and band width derived from
thermoreflectance and x-ray photoemission experiments. The results show that
the wavefunction based approach applied here allows for well controlled
approximations and a transparent identification of the microscopic processes
which determine the electronic band structure
Spatial fluctuations in an optical parametric oscillator below threshold with an intracavity photonic crystal
We show how to control spatial quantum correlations in a multimode degenerate
optical parametric oscillator type I below threshold by introducing a spatially
inhomogeneous medium, such as a photonic crystal, in the plane perpendicular to
light propagation. We obtain the analytical expressions for all the
correlations in terms of the relevant parameters of the problem and study the
number of photons, entanglement, squeezing, and twin beams. Considering
different regimes and configurations we show the possibility to tune the
instability thresholds as well as the quantumness of correlations by breaking
the translational invariance of the system through a photonic crystal
modulation.Comment: 12 pages, 7 figure
Kinetic Energy Density Study of Some Representative Semilocal Kinetic Energy Functionals
There is a number of explicit kinetic energy density functionals for
non-interacting electron systems that are obtained in terms of the electron
density and its derivatives. These semilocal functionals have been widely used
in the literature. In this work we present a comparative study of the kinetic
energy density of these semilocal functionals, stressing the importance of the
local behavior to assess the quality of the functionals. We propose a quality
factor that measures the local differences between the usual orbital-based
kinetic energy density distributions and the approximated ones, allowing to
ensure if the good results obtained for the total kinetic energies with these
semilocal functionals are due to their correct local performance or to error
cancellations. We have also included contributions coming from the laplacian of
the electron density to work with an infinite set of kinetic energy densities.
For all the functionals but one we have found that their success in the
evaluation of the total kinetic energy are due to global error cancellations,
whereas the local behavior of their kinetic energy density becomes worse than
that corresponding to the Thomas-Fermi functional.Comment: 12 pages, 3 figure
Thermodynamical Scaling of the Glass Transition Dynamics
Classification of glass-forming liquids based on the dramatic change in their
properties upon approach to the glassy state is appealing, since this is the
most conspicuous and often-studied aspect of the glass transition. Herein, we
show that a generalized scaling, log tau proportional to T^(-1)V^(-gamma),
where gamma is a material-constant, yields superpositioning for ten
glass-formers, encompassing van der Waals molecules, associated liquids, and
polymers. The exponent gamma reflects the degree to which volume, rather than
thermal energy, governs the temperature and pressure dependence of the
relaxation times.Comment: 12 page, 4 figure
A Liquid Model Analogue for Black Hole Thermodynamics
We are able to characterize a 2--dimensional classical fluid sharing some of
the same thermodynamic state functions as the Schwarzschild black hole. This
phenomenological correspondence between black holes and fluids is established
by means of the model liquid's pair-correlation function and the two-body
atomic interaction potential. These latter two functions are calculated exactly
in terms of the black hole internal (quasilocal) energy and the isothermal
compressibility. We find the existence of a ``screening" like effect for the
components of the liquid.Comment: 20 pages and 6 Encapsulated PostScript figure
Gaussian density fluctuations and Mode Coupling Theory for supercooled liquids
The equations of motion for the density modes of a fluid, derived from
Newton's equations, are written as a linear generalized Langevin equation. The
constraint imposed by the fluctuation-dissipation theorem is used to derive an
exact form for the memory function. The resulting equations, solved under the
assumption that the noise, and consequently density fluctuations, of the liquid
are gaussian distributed, are equivalent to the random-phase-approximation for
the static structure factor and to the well known ideal mode coupling theory
(MCT) equations for the dynamics. This finding suggests that MCT is the
canonical mean-field theory of the fluid dynamics.Comment: 4 pages, REVTE
Two-particle photoemission from strongly correlated systems: A dynamical-mean field approach
We study theoretically the simultaneous, photo-induced two-particle
excitations of strongly correlated systems on the basis of the Hubbard model.
Under certain conditions specified in this work, the corre- sponding transition
probability is related to the two-particle spectral function which we calculate
using three different methods: the dynamical-mean field theory combined with
quantum Monte Carlo (DMFT- QMC) technique, the first order perturbation theory
and the ladder approximations. The results are analyzed and compared for
systems at the verge of the metal-insulator transitions. The dependencies on
the electronic correlation strength and on doping are explored. In addition,
the account for the orbital degeneracy allows an insight into the influence of
interband correlations on the two particle excitations. A suitable experimental
realization is discussed.Comment: 25 pp, 10 figs. to be published in PR
Dynamics of supercooled liquids: density fluctuations and Mode Coupling Theory
We write equations of motion for density variables that are equivalent to
Newtons equations. We then propose a set of trial equations parameterised by
two unknown functions to describe the exact equations. These are chosen to best
fit the exact Newtonian equations. Following established ideas, we choose to
separate these trial functions into a set representing integrable motions of
density waves, and a set containing all effects of non-integrability. It
transpires that the static structure factor is fixed by this minimum condition
to be the solution of the Yvon-Born-Green (YBG) equation. The residual
interactions between density waves are explicitly isolated in their Newtonian
representation and expanded by choosing the dominant objects in the phase space
of the system, that can be represented by a dissipative term with memory and a
random noise. This provides a mapping between deterministic and stochastic
dynamics. Imposing the Fluctuation-Dissipation Theorem (FDT) allows us to
calculate the memory kernel. We write exactly the expression for it, following
two different routes, i.e. using explicitly Newtons equations, or instead,
their implicit form, that must be projected onto density pairs, as in the
development of the well-established Mode Coupling Theory (MCT). We compare
these two ways of proceeding, showing the necessity to enforce a new equation
of constraint for the two schemes to be consistent. Thus, while in the first
`Newtonian' representation a simple gaussian approximation for the random
process leads easily to the Mean Spherical Approximation (MSA) for the statics
and to MCT for the dynamics of the system, in the second case higher levels of
approximation are required to have a fully consistent theory
- …