Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice

We experimentally investigate diffraction of a Rb-87 Bose-Einstein condensate from a 1D optical lattice. We use a range of lattice periods and timescales, including those beyond the Raman-Nath limit. We compare the results to quantum mechanical and classical simulations, with quantitative and qualitative agreement, respectively. The classical simulation predicts that the envelope of the time-evolving diffraction pattern is shaped by caustics: singularities in the phase space density of classical trajectories. This behavior becomes increasingly clear as the lattice period grows.Comment: 7 pages, 6 figure

On the chromatic diffusion halo and other optical effects exhibited by pearls

The paper discusses the origin and character of the coloured diffusion halo exhibited by pearls surrounding the reflected image of a light source seen at their surface. Twelve photographs illustrative of various types of halo are reproduced. Other aspects of the optical behaviour of pearls are also described and discussed with illustrative photographs

On the iridescence of potassium chlorate crystals. Part I. Its spectral characters

This article does not have an abstract

Optics of the pearl

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Evaluation of the four elastic constants of some cubic crystals

This article does not have an abstract

On the iridescence of potassium chlorate crystals. Part III. Some general observations

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The structure and optical behaviour of iridescent shells

Some remarkable optical effects exhibited by nacreous shells have been observed and reported, the following amongst others: The monochromatic reflections and extinctions split into two polarised components at oblique incidences as a result of the birefringence of the material. Light traversing the stratifications obliquely suffers extinction by reason of diffusion by the crystallites of aragonite, this being most rapid for the component of vibration in the plane of incidence. Striking changes are also observed in the character of the diffusion haloes with increasing obliquity of observation, a particularly noteworthy feature being that the different parts of the diffusion field are differently polarised

The structure and optical behaviour of pearls

The paper embodies a study of the structure of the material composing pearls and of the optical effects which they display. The following topics are dealt with: (1) Birefringence, (2) X-ray-diffraction patterns, (3) The reflection-diffraction spectra, (4) The diffusion haloes of reflection and transmission, (5) The whispering-gallery effect, (6) The spectral character of iridescence and the influence of birefringence thereon, (7) The transmission spectra. The most noteworthy result of the investigation is to show that the diffusive properties of nacre play a major role no less important than that of the reflection by its stratifications in the optics of pearls

The eigenspectra of Indian musical drums

In a family of drums used in the Indian subcontinent, the circular drum head is made of material of non-uniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the non-uniform membrane are harmonic. In this work we model the drum head by a non-uniform membrane whose density varies smoothly between two prescribed values. Using a Fourier-Chebyshev spectral collocation method we obtain the eigenmodes and eigenvalues of the drum head. For a suitable choice of parameters, which we find by optimising a cost function, the eigenspectra obtained from our model are in excellent agreement with experimental values. Our model and the numerical method should find application in numerical sound synthesis

A multienvironment conditional probability density function model for turbulent reacting flows

The multienvironment conditional probability density function (MECPDF) model was first proposed by Fox [Computational Models for Turbulent Reacting Flows (Cambridge University Press, Cambridge, 2003)] as a simple extension of multienvironment probability density function models for turbulent reacting flows. Like the conditional moment closure (CMC) and the laminar flamelet model (LFM), the MECPDF model describes the reacting scalars conditioned on the value of the mixture fraction. However, unlike CMC and LFM, the new model provides a consistent description of conditional fluctuations in both the scalar dissipation rate and the reacting scalars, and hence can be used to model partial extinction and reignition in homogeneous turbulent reacting flows. In this work, a general derivation of the MECPDF model is presented for a single reaction-progress variable using the direct quadrature method of moments. Extensions of the model to multiple reaction-progress variables and conditioning on the mixture-fraction vector are also discussed. After deriving the model, the closure assumptions are validated using direct simulations for pure diffusion of two randomly distributed, initially correlated scalar fields. Two homogeneous applications are then considered: nonreactive mixing starting from nontrivial initial conditions, and reactive mixing with partial extinction and reignition