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...

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 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...

A general closed expression is given for the isothermal minimum free energy of a linear viscoelastic material in terms of Fourier-transformed quantities. A oneparameter family of free energies is constructed, ranging continuously from the maximum to the minimum free energies. The simplest case of single component stress and strain tensors and a single viscoelastic function is considered in this...

We describe an analytical form of the Wulff plot construction procedure and derive a general expression for the surface energy from the three-dimensional equilibrium crystal shape in generalized orthogonal curvilinear coordinates. Particular expressions in Cartesian, spherical polar, and circular cylindrical coordinates are also presented. Corresponding results for a two-dimensional (2D) island...

Two possibile applications of the optimized expansion for the free energy of the quantum-mechanical anharmonic oscillator are discussed. The first method is for the finite temperature effective potential; the second one, for the classical effective potential. The results of both methods show a quick convergence and agree well with the exact free energy in the whole range of temperatures.

We present a calculation of the change of free energy of a solid surface upon bending of the solid. It is based on extracting the surface stress through a molecular dynamics simulation of a bent slab by using a generalized stress theorem formula, and subsequent integration of the stress with respect to strain as a function of

The strong coupling behavior of finite temperature free energy in N = 4 supersym-metric SU (N) Yang-Mills theory has been recently discussed by Gubser, Klebanov and Tseytlin in the context of AdS-SYM correspondence. In this note, we focus on the weak coupling behavior. As a result of a two-loop computation we obtain, in the large N 't Hooft limit, F (g 2 N → 0) ≈ − π 2 6 N 2 V 3 T 4 (1 − 3 2π 2...

A new method is proposed which enables one to convert the formulae for a uniform multi-component system to those for a non-uniform one. As an application of the method, the expansion formulae of. the free energy, potentials of average force and distribution functions for a non-uniform multi-component system are derived in a simple and systematic way. The formulae are obtained both for a continu...