Recent work in the literature has identi ed a new heating mechanism during induction processing of carbon thermoplastic prepreg stacks: contact resistance between bers of adjacent plies. An experimental methodology has been developed to estimate the contact resistance through heating tests based on the properties of the composite and geometry of the specimen. Measured values indicate comparable resistance values at the contact region, compared to resistance in the ber direction, for AS-4 / PEI prepreg stacks under vacuum pressure. The measured values can serve as inputs for induction heating models and process models of carbon thermoplastic prepreg stacks.
In this paper, we show that the Glauber dynamics for the Ising model on a complete multipartite graph Knp 1 ,...,npm has cutoff at tn := αn ln n with window size O(n) in the high temperature regime β < 1 where α is a constant only depending on β, p 1 , . . . , pm.
We study the Lévy spin glass model, a fully connected model on N vertices with heavy-tailed interactions governed by a power law distribution of order 0 < α < 2. Our investigation focuses on two domains 0 < α < 1 and 1 < α < 2. When 1 < α < 2, we identify a high temperature regime, in which the limit and fluctuation of the free energy are explicitly obtained and the site and bound overlaps are shown to exhibit concentration, interestingly, while the former is concentrated around zero, the latter obeys a positivity behavior. At any temperature, we further establish the existence of the limiting free energy and derive a variational formula analogous to Panchenko's framework in the setting of the Poissonian Viana-Bray model. In the case of 0 < α < 1, we show that the Lévy model behaves differently, where the proper scaling for the free energy is N 1/α instead of N and the normalized free energy converges weakly to the sum of a Poisson Point Process at any temperature. Additionally, we show that the Gibbs measure carries its weight on polynomially many heaviest edges.
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