Data Assimilation: A Mathematical Introduction

These notes provide a systematic mathematical treatment of the subject of data assimilation

Loss of purity by wave packet scattering at low energies

We study the quantum entanglement produced by a head-on collision between two gaussian wave packets in three-dimensional space. By deriving the two-particle wave function modified by s-wave scattering amplitudes, we obtain an approximate analytic expression of the purity of an individual particle. The loss of purity provides an indicator of the degree of entanglement. In the case the wave packets are narrow in momentum space, we show that the loss of purity is solely controlled by the ratio of the scattering cross section to the transverse area of the wave packets.Comment: 7 pages, 1 figur

S-wave quantum entanglement in a harmonic trap

We analyze the quantum entanglement between two interacting atoms trapped in a spherical harmonic potential. At ultra-cold temperature, ground state entanglement is generated by the dominated s-wave interaction. Based on a regularized pseudo-potential Hamiltonian, we examine the quantum entanglement by performing the Schmidt decomposition of low-energy eigenfunctions. We indicate how the atoms are paired and quantify the entanglement as a function of a modified s-wave scattering length inside the trap.Comment: 10 pages, 5 figures, to be apear in PR

Replacement of PBNA in HB and HC polymers used in SRM propellant and liner

The antioxidant phenyl-beta-naphthylamine (PBNA) was used in both HB and HC polymers. The sole (domestic) supplier of PBNA has withdrawn this product from the market, primarily because of suspected health hazards. Commercially available substitute(s) were selected and qualified for use in the two polymers

Production of photons by the parametric resonance in the dynamical Casimir effect

We calculate the number of photons produced by the parametric resonance in a cavity with vibrating walls. We consider the case that the frequency of vibrating wall is $n \omega_1 (n=1,2,3,...)$ which is a generalization of other works considering only $2 \omega_1$, where $\omega_1$ is the fundamental-mode frequency of the electromagnetic field in the cavity. For the calculation of time-evolution of quantum fields, we introduce a new method which is borrowed from the time-dependent perturbation theory of the usual quantum mechanics. This perturbation method makes it possible to calculate the photon number for any $n$ and to observe clearly the effect of the parametric resonance.Comment: 15 pages, RevTeX, no figure

Optimizing photon indistinguishability in the emission from incoherently-excited semiconductor quantum dots

Most optical quantum devices require deterministic single-photon emitters. Schemes so far demonstrated in the solid state imply an energy relaxation which tends to spoil the coherent nature of the time evolution, and with it the photon indistinguishability. We focus our theoretical investigation on semiconductor quantum dots embedded in microcavities. Simple and general relations are identified between the photon indistinguishability and the collection efficiency. The identification of the key parameters and of their interplay provides clear indications for the device optimization

Design approaches and materials processes for ultrahigh efficiency lattice mismatched multi-junction solar cells

In this study, we report synthesis of large area (>2cm^2), crack-free GaAs and GaInP double heterostructures grown in a multi-junction solar cell-like structure by MOCVD. Initial solar cell data are also reported for GaInP top cells. These samples were grown on Ge/Si templates fabricated using wafer bonding and ion implantation induced layer transfer techniques. The double heterostructures exhibit radiative emission with uniform intensity and wavelength in regions not containing interfacial bubble defects. The minority carrier lifetime of ~1ns was estimated from photoluminescence decay measurements in both double heterostructures. We also report on the structural characteristics of heterostructures, determined via atomic force microscopy and transmission electron microscopy, and correlate these characteristics to the spatial variation of the minority carrier lifetime