Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model

Morphological properties of strained epitaxial films are examined through a mesoscopic approach developed to incorporate both the film crystalline structure and standard continuum theory. Film surface profiles and properties, such as surface energy, liquid-solid miscibility gap and interface thickness, are determined as a function of misfit strains and film elastic modulus. We analyze the stress-driven instability of film surface morphology that leads to the formation of strained islands. We find a universal scaling relationship between the island size and misfit strain which shows a crossover from the well-known continuum elasticity result at the weak strain to a behavior governed by a "perfect" lattice relaxation condition. The strain at which the crossover occurs is shown to be a function of liquid-solid interfacial thickness, and an asymmetry between tensile and compressive strains is observed. The film instability is found to be accompanied by mode coupling of the complex amplitudes of the surface morphological profile, a factor associated with the crystalline nature of the strained film but absent in conventional continuum theory.Comment: 16 pages, 10 figures; to be published in Phys. Rev.

How well are the states of the Eighth Federal Reserve District prepared for the next recession?

Economic downturns often force state policymakers to enact sizable tax increases or spending cuts to close budget shortfalls. In this paper the authors make use of a Markov-switching regression model to empirically describe the expansions and contractions in the states of the Eighth Federal Reserve District. They use the estimated parameters from the switching regressions to form probability distributions of the revenue shortfalls states are likely to encounter in future slowdowns. This allows them to estimate the probability that each state's projected fiscal-year-end balances will be sufficient to offset the fiscal stress from a recession.Business cycles ; Recessions ; Federal Reserve District, 8th

An experimental model of a 2kw, 2500 volt power converter for ion thrustors using gate controlled switches in two phase-shifted parallel inverters summary report

Power converter for ion thrustors using electronic gate controlled switches in two phase-shifted parallel inverter

On trivial words in finitely presented groups

We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups whose cogrowth series are known exactly. Further, we add to the set of such groups by finding the cogrowth series for Baumslag-Solitar groups $\mathrm{BS}(N,N) =$ and prove that their cogrowth rates are algebraic numbers.Comment: This article has been rewritten as two separate papers, with improved exposition. The new papers are arXiv:1309.4184 and arXiv:1312.572