Entropy and diffuse scattering: comparison of NbTiVZr and CrMoNbV

The chemical disorder intrinsic to high entropy alloys inevitably creates diffuse scattering in their x-ray or neutron diffraction patterns. Through first principles hybrid Monte Carlo/molecular dynamics simulations of two BCC high entropy alloy forming compounds, CrMoNbV and NbTiVZr, we identify the contributions of chemical disorder, atomic size and thermal fluctuations to the diffuse scattering. As a side benefit, we evaluate the reduction in entropy due to pair correlations within the framework of the cluster variation method. Finally, we note that the preference of Ti and Zr for HCP structures at low temperature leads to a mechanical instability reducing the local BCC character of NbTiVZr, while preserving global BCC symmetry.Comment: Submitted to Met Mat Trans A: TMS Symposium on High Entropy Alloys (2015

Some Classes of Solutions to the Toda Lattice Hierarchy

We apply an analogue of the Zakharov-Shabat dressing method to obtain infinite matrix solutions to the Toda lattice hierarchy. Using an operator transformation we convert some of these into solutions in terms of integral operators and Fredholm determinants. Others are converted into a class of operator solutions to the $l$-periodic Toda hierarchy.Comment: LaTeX file, 18 pages. Results generalized and applications to the Toda equations adde

Free Fermions Violate the Area Law For Entanglement Entropy

We show that the entanglement entropy associated to a region grows faster than the area of its boundary surface. This is done by proving a special case of a conjecture due to Widom that yields a surprisingly simple expression for the leading behaviour of the entanglement entropy.Comment: Proceedings of the 9th Hellenic School on Elementary Particle Physics and Gravity, Corfu 2009. 4 page

Geometric view of the thermodynamics of adsorption at a line of three-phase contact

We consider three fluid phases meeting at a line of common contact and study the linear excesses per unit length of the contact line (the linear adsorptions Lambda_i) of the fluid's components. In any plane perpendicular to the contact line, the locus of choices for the otherwise arbitrary location of that line that makes one of the linear adsorptions, say Lambda_2, vanish, is a rectangular hyperbola. Two of the adsorptions, Lambda_2 and Lambda_3, then both vanish when the contact line is chosen to pass through any of the intersections of the two corresponding hyperbolas Lambda_2 = 0 and Lambda_3 = 0. There may be two or four such real intersections. It is required, and is confirmed by numerical examples, that a certain expression containing \Lambda_{1(2,3)}, the adsorption of component 1 in a frame of reference in which the adsorptions Lambda_2 and Lambda_3 are both 0, is independent of which of the two or four intersections of Lambda_2 = 0 and Lambda_3 = 0 is chosen for the location of the contact line. That is not true of Lambda_{1(2,3)} by itself; while the adsorptions and the line tension together satisfy a linear analog of the Gibbs adsorption equation, there are additional, not previously anticipated terms in the relation that are required by the line tension's invariance to the arbitrary choice of location of the contact line. The presence of the additional terms is confirmed and their origin clarified in a mean-field density-functional model. The additional terms vanish at a wetting transition, where one of the contact angles goes to 0