Suggested approaches to writing songs at the primary and elementary levels

Thesis (M.Ed.)--Boston Universit

Condensers and or evaporators in convective and radiative environments

Condensers and/or evaporators in convective and radiative environment

Stationary and moving breathers in a simplified model of curved alpha--helix proteins

The existence, stability and movability of breathers in a model for alpha-helix proteins is studied. This model basically consists a chain of dipole moments parallel to it. The existence of localized linear modes brings about that the system has a characteristic frequency, which depends on the curvature of the chain. Hard breathers are stable, while soft ones experiment subharmonic instabilities that preserve, however the localization. Moving breathers can travel across the bending point for small curvature and are reflected when it is increased. No trapping of breathers takes place.Comment: 19 pages, 11 figure

Universal diffusion near the golden chaos border

We study local diffusion rate $D$ in Chirikov standard map near the critical golden curve. Numerical simulations confirm the predicted exponent $\alpha=5$ for the power law decay of $D$ as approaching the golden curve via principal resonances with period $q_n$ ($D \sim 1/q^{\alpha}_n$). The universal self-similar structure of diffusion between principal resonances is demonstrated and it is shown that resonances of other type play also an important role.Comment: 4 pages Latex, revtex, 3 uuencoded postscript figure

Renormalization and Quantum Scaling of Frenkel-Kontorova Models

We generalise the classical Transition by Breaking of Analyticity for the class of Frenkel-Kontorova models studied by Aubry and others to non-zero Planck's constant and temperature. This analysis is based on the study of a renormalization operator for the case of irrational mean spacing using Feynman's functional integral approach. We show how existing classical results extend to the quantum regime. In particular we extend MacKay's renormalization approach for the classical statistical mechanics to deduce scaling of low frequency effects and quantum effects. Our approach extends the phenomenon of hierarchical melting studied by Vallet, Schilling and Aubry to the quantum regime.Comment: 14 pages, 1 figure, submitted to J.Stat.Phy

The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results

The problem of finding the exact energies and configurations for the Frenkel-Kontorova model consisting of particles in one dimension connected to their nearest-neighbors by springs and placed in a periodic potential consisting of segments from parabolas of identical (positive) curvature but arbitrary height and spacing, is reduced to that of minimizing a certain convex function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6 Postscript figures, accepted by Phys. Rev.

Community Detection as an Inference Problem

We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that this leads to fast, accurate algorithms for community detection.Comment: 4 pages, 2 figure

Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in $\epsilon$ as $\epsilon\rightarrow 0$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse.Comment: 21 page

Depolarization regions of nonzero volume in bianisotropic homogenized composites

In conventional approaches to the homogenization of random particulate composites, the component phase particles are often treated mathematically as vanishingly small, point-like entities. The electromagnetic responses of these component phase particles are provided by depolarization dyadics which derive from the singularity of the corresponding dyadic Green functions. Through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. We present an extension to the strong-property-fluctuation theory in which depolarization regions of nonzero volume and ellipsoidal geometry are accommodated. Therein, both the size and spatial distribution of the component phase particles are taken into account. The analysis is developed within the most general linear setting of bianisotropic homogenized composite mediums (HCMs). Numerical studies of the constitutive parameters are presented for representative examples of HCM; both Lorentz-reciprocal and Lorentz-nonreciprocal HCMs are considered. These studies reveal that estimates of the HCM constitutive parameters in relation to volume fraction, particle eccentricity, particle orientation and correlation length are all significantly influenced by the size of the component phase particles

Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we compute the Melnikov function for a perturbation of a three-dimensional map that has a heteroclinic connection between a pair of invariant circles. The intersection curves of the manifolds are shown to undergo bifurcations in homologyComment: LaTex with 10 eps figure