We present a method, based on loop equations, to compute recursively, all the terms in the large N topological expansion of the free energy for the 2-hermitian matrix model. We illustrate the method by computing the first subleading term, i.e. the free energy of a statistical physics model on a discretized torus.

In an important recent paper, [2], S. Franz and M. Leone prove rigorous lower bounds for the free energy of the diluted p-spin model and the K-sat model at any temperature. We show that the results for these two models are consequences of a single general principle. Our calculations are significantly simpler than those of [2], even in the replica-symmetric case.

Supercoiling is introduced into DNAmolecules when the double helix is twisted around its own axis in three-dimensional space. Generally, DNAmolecules are negatively supercoiled inside cells, although the level of supercoiling is not equal throughout the genome and many supercoils may be constrained by bound proteins. Supercoiling increases the free energy of DNA and influences DNA metabolism by...

We consider an aggregation equation in Rd, d ≥ 2 with fractional dissipation: ut +∇ · (u∇K ∗ u) = −νΛγu, where ν ≥ 0, 0 < γ < 1 and K(x) = e−|x|. We prove a refined blowup criteria by which the global existence of solutions is controlled by its Lx norm, for any d d−1 ≤ q ≤ ∞. We prove for a general class of nonsymmetric initial data the finite time blowup of the corresponding solutions. The arg...

The strain rate sensitivity (SRS) of Mg–1.5 wt% Gd processed by conventional extrusion and 2 passes of simple shear extrusion (SSE) was investigated by shear punch testing. Shear punch tests were conducted at initial shear strain rates in the range of 0.003–0.3 s-1 and at temperatures in the range of 573–773 K. A fine-grained microstructure with an average grain size of about 2.5 µm, obtained a...

We study the behaviour of free energies of baryonic systems composed of three heavy quarks on the lattice in SU(3) pure gauge theory at finite temperature. For all temperatures above Tc we find that the connected part of the singlet (decuplet) free energy of the three quark system is given by the sum of the connected parts of the free energies of qq-triplets (-sextets). Using renormalized free ...

Chemically induced grain boundary structural transitions are well documented in a number of ceramic systems. It has been hypothesized that transitions between distinct structural states, referred to as complexions, are driven by a reduction in the free energy of the grain boundaries. The current work tests this hypothesis by measuring the relative energies of boundaries on normal grains and abn...

The resolution of the protein folding problem has been tied to the development of a detailed understanding of the configurational energy or of the free energy landscape associated with these molecules. Using the activation-relaxation technique and a simplified energy model, we present here a detailed analysis of the energy landscape of 16-residue peptide that folds into a beta-hairpin. Our resu...

The energy balance associated with the transmission of cleavage front across high angle grain boundary is analysed theoretically. On the one hand, if the distance between adjacent breakthrough points is small, their crack trapping effect tends to be pronounced. On the other hand, decreasing this distance promotes the separation of persistent grain boundary areas. The effective grain boundary to...