Noise characteristics of upper surface blown configurations: Analytical Studies

Noise and flow results of upper surface blown configurations were analyzed. The dominant noise source mechanisms were identified from experimental data. From far-field noise data for various geometric and operational parameters, an empirical noise prediction program was developed and evaluated by comparing predicted results with experimental data from other tests. USB aircraft compatibility studies were conducted using the described noise prediction and a cruise performance data base. A final design aircraft was selected and theory was developed for the noise from the trailing edge wake assuming it as a highly sheared layer

Phase Diagram of the Holstein-Hubbard Two-Leg Ladder

Using a functional renormalization group method, we obtain the phase diagram of the two-leg ladder system within the Holstein-Hubbard model, which includes both electron-electron and electron-phonon interactions. Our renormalization group technique allows us to analyze the problem for both weak and strong electron-phonon coupling. We show that, in contrast results from conventional weak coupling studies, electron-phonon interactions can dominate electron-electron interactions because of retardation effects.Comment: 4 page

Nonresonant EFISH and THG studies of nonlinear optical property and molecular structure relations of benzene, stilbene, and other arene derivatives

D.c. elec. field induced 2nd-harmonic generation (EFISH) and 3rd-harmonic generation (THG) measurement results are reported on the intrinsic mol. hyperpolarizabilities of benzenes, stilbenes, and other arene derivs. Structure-property relations, as revealed by a comprehensive set of systematic measurements, are discussed. Issues concerning donor-acceptor strength; charge-transfer; transparency trade-off; conjugation planarity, length, and aromaticity; and heteroatom and side-group substitution effects are included

String Indexing for Patterns with Wildcards

We consider the problem of indexing a string $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $\sigma$ the size of the alphabet. We obtain the following results. - A linear space index with query time $O(m+\sigma^j \log \log n + occ)$. This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time $\Theta(jn)$ in the worst case. - An index with query time $O(m+j+occ)$ using space $O(\sigma^{k^2} n \log^k \log n)$, where $k$ is the maximum number of wildcards allowed in the pattern. This is the first non-trivial bound with this query time. - A time-space trade-off, generalizing the index by Cole et al. [STOC 2004]. We also show that these indexes can be generalized to allow variable length gaps in the pattern. Our results are obtained using a novel combination of well-known and new techniques, which could be of independent interest

Cosmic axion thermalization

Axions differ from the other cold dark matter candidates in that they form a degenerate Bose gas. It is shown that their huge quantum degeneracy and large correlation length cause cold dark matter axions to thermalize through gravitational self-interactions when the photon temperature reaches approximately 500 eV. When they thermalize, the axions form a Bose-Einstein condensate. Their thermalization occurs in a regime, herein called the `condensed regime', where the Boltzmann equation is not valid because the energy dispersion of the particles is smaller than their interaction rate. We derive analytical expressions for the thermalization rate of particles in the condensed regime, and check the validity of these expressions by numerical simulation of a toy model. We revisit axion cosmology in light of axion Bose-Einstein condensation. It is shown that axions are indistinguishable from ordinary cold dark matter on all scales of observational interest, except when they thermalize or rethermalize. The rethermalization of axions that are about to fall in a galactic potential well causes them to acquire net overall rotation as they go to the lowest energy state consistent with the total angular momentum they acquired by tidal torquing. This phenomenon explains the occurrence of caustic rings of dark matter in galactic halos. We find that photons may reach thermal contact with axions and investigate the implications of this possibility for the measurements of cosmological parameters.Comment: 38 pages, 1 figur

Division of labour and the evolution of multicellularity

Understanding the emergence and evolution of multicellularity and cellular differentiation is a core problem in biology. We develop a quantitative model that shows that a multicellular form emerges from genetically identical unicellular ancestors when the compartmentalization of poorly compatible physiological processes into component cells of an aggregate produces a fitness advantage. This division of labour between the cells in the aggregate occurs spontaneously at the regulatory level due to mechanisms present in unicellular ancestors and does not require any genetic pre-disposition for a particular role in the aggregate or any orchestrated cooperative behaviour of aggregate cells. Mathematically, aggregation implies an increase in the dimensionality of phenotype space that generates a fitness landscape with new fitness maxima, and in which the unicellular states of optimized metabolism become fitness saddle points. Evolution of multicellularity is modeled as evolution of a hereditary parameter, the propensity of cells to stick together, which determines the fraction of time a cell spends in the aggregate form. Stickiness can increase evolutionarily due to the fitness advantage generated by the division of labour between cells in an aggregate.Comment: 28 pages, 2 figure