On the classical WN(l)W_N^{(l)} algebras

We analyze the W_N^l algebras according to their conjectured realization as the second Hamiltonian structure of the integrable hierarchy resulting from the interchange of x and t in the l^{th} flow of the sl(N) KdV hierarchy. The W_4^3 algebra is derived explicitly along these lines, thus providing further support for the conjecture. This algebra is found to be equivalent to that obtained by the method of Hamiltonian reduction. Furthermore, its twisted version reproduces the algebra associated to a certain non-principal embedding of sl(2) into sl(4), or equivalently, the u(2) quasi-superconformal algebra. The general aspects of the W_N^l algebras are also presented.Comment: 28 page

Discrete Geometric Structures in Homogenization and Inverse Homogenization with application to EIT

We introduce a new geometric approach for the homogenization and inverse homogenization of the divergence form elliptic operator with rough conductivity coefficients $\sigma(x)$ in dimension two. We show that conductivity coefficients are in one-to-one correspondence with divergence-free matrices and convex functions $s(x)$ over the domain $\Omega$. Although homogenization is a non-linear and non-injective operator when applied directly to conductivity coefficients, homogenization becomes a linear interpolation operator over triangulations of $\Omega$ when re-expressed using convex functions, and is a volume averaging operator when re-expressed with divergence-free matrices. Using optimal weighted Delaunay triangulations for linearly interpolating convex functions, we obtain an optimally robust homogenization algorithm for arbitrary rough coefficients. Next, we consider inverse homogenization and show how to decompose it into a linear ill-posed problem and a well-posed non-linear problem. We apply this new geometric approach to Electrical Impedance Tomography (EIT). It is known that the EIT problem admits at most one isotropic solution. If an isotropic solution exists, we show how to compute it from any conductivity having the same boundary Dirichlet-to-Neumann map. It is known that the EIT problem admits a unique (stable with respect to $G$-convergence) solution in the space of divergence-free matrices. As such we suggest that the space of convex functions is the natural space in which to parameterize solutions of the EIT problem

X rays from old open clusters: M 67 and NGC 188

We have observed the old open clusters M 67 and NGC 188 with the ROSAT PSPC. In M 67 we detect a variety of X-ray sources. The X-ray emission by a cataclysmic variable, a single hot white dwarf, two contact binaries, and some RS CVn systems is as expected. The X-ray emission by two binaries located below the subgiant branch in the Hertzsprung Russell diagram of the cluster, by a circular binary with a cool white dwarf, and by two eccentric binaries with orbital period > 700 d is puzzling. Two members of NGC 188 are detected, including the FK Com type star D719. Another possible FK Com type star, probably not a member of NGC 188, is also detected.Comment: 10 pages, 5 figures. Accepted for publication on Astronomy & Astrophysic

The Boltzmann Equation in Classical Yang-Mills Theory

We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang-Mills theory. Our method is not relied on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.Comment: 24 pages, 7 figures; v2: typos corrected, reference added, published in Eur. Phys. J.

Integrability of the quantum KdV equation at c = -2

We present a simple a direct proof of the complete integrability of the quantum KdV equation at $c=-2$, with an explicit description of all the conservation laws.Comment: 9 page

Phase field simulations of coupled phase transformations in ferroelastic-ferroelastic nanocomposites

We use phase field simulations to study composites made of two different ferroelastics (e.g., two types of martensite). The deformation of one material due to a phase transformation can elastically affect the other constituent and induce it to transform as well. We show that the phase transformation can then occur above its normal critical temperature and even higher above this temperature in nanocomposites than in bulk composites. Microstructures depend on temperature, on the thickness of the layers, and on the crystal structure of the two constituents -- certain nanocomposites exhibit a great diversity of microstructures not found in bulk composites. Also, the periodicity of the martensite twins may vary over 1 order of magnitude based on geometry. keywords: Ginzburg-Landau, martensitic transformation, multi-ferroics, nanostructure, shape-memory alloyComment: 8 pages, 15 figure