Computer-Aided Derivation of Multi-scale Models: A Rewriting Framework

We introduce a framework for computer-aided derivation of multi-scale models. It relies on a combination of an asymptotic method used in the field of partial differential equations with term rewriting techniques coming from computer science. In our approach, a multi-scale model derivation is characterized by the features taken into account in the asymptotic analysis. Its formulation consists in a derivation of a reference model associated to an elementary nominal model, and in a set of transformations to apply to this proof until it takes into account the wanted features. In addition to the reference model proof, the framework includes first order rewriting principles designed for asymptotic model derivations, and second order rewriting principles dedicated to transformations of model derivations. We apply the method to generate a family of homogenized models for second order elliptic equations with periodic coefficients that could be posed in multi-dimensional domains, with possibly multi-domains and/or thin domains.Comment: 26 page

Abelian simply transitive affine groups of symplectic type

We construct a model space C(\gsp(\bR^{2n})) for the variety of Abelian simply transitive groups of affine transformations of type {\rm Sp}(\bR^{2n}). The model is stratified and its principal stratum is a Zariski-open subbundle of a natural vector bundle over the Grassmannian of Lagrangian subspaces in \bR^{2n}. \noindent Next we show that every flat special K\"ahler manifold may be constructed locally from a holomorphic function whose third derivatives satisfy some algebraic constraint. In particular global models for flat special K\"ahler manifolds with constant cubic form correspond to a subvariety of C(\gsp(\bR^{2n})).Comment: corrected typos, updated reference

Towards Functional Flows for Hierarchical Models

The recursion relations of hierarchical models are studied and contrasted with functional renormalisation group equations in corresponding approximations. The formalisms are compared quantitatively for the Ising universality class, where the spectrum of universal eigenvalues at criticality is studied. A significant correlation amongst scaling exponents is pointed out and analysed in view of an underlying optimisation. Functional flows are provided which match with high accuracy all known scaling exponents from Dyson's hierarchical model for discrete block-spin transformations. Implications of the results are discussed.Comment: 17 pages, 4 figures; wording sharpened, typos removed, reference added; to appear with PR

The Role of the Academic Reference Librarian in the Learning Commons

Frontline reference librarians purvey their skills in a variety of reference service models. These range from the traditional to the tiered to the information commons (IC) to the learning commons (LC). Libraries might use one pure form of any model, a hybrid model, or a model in the process of transformation. A few libraries with space and funding have fully adopted the latest model, the LC. An examination of transformations to the LC indicates that frontline reference librarians can to some extent effect changes in their professional environments

The Role of the Academic Reference Librarian in the Learning Commons

Frontline reference librarians purvey their skills in a variety of reference service models. These range from the traditional to the tiered to the information commons (IC) to the learning commons (LC). Libraries might use one pure form of any model, a hybrid model, or a model in the process of transformation. A few libraries with space and funding have fully adopted the latest model, the LC. An examination of transformations to the LC indicates that frontline reference librarians can to some extent effect changes in their professional environments

Navier-Stokes-alpha model: LES equations with nonlinear dispersion

We present a framework for discussing LES equations with nonlinear dispersion. In this framework, we discuss the properties of the nonlinearly dispersive Navier-Stokes-alpha model of incompressible fluid turbulence --- also called the viscous Camassa-Holm equations and the LANS equations in the literature --- in comparison with the corresponding properties of large eddy simulation (LES) equations obtained via the approximate-inverse approach. In this comparison, we identify the spatially filtered NS-alpha equations with a class of generalized LES similarity models. Applying a certain approximate inverse to this class of LES models restores the Kelvin circulation theorem for the defiltered velocity and shows that the NS-alpha model describes the dynamics of the defiltered velocity for this class of generalized LES similarity models. We also show that the subgrid scale forces in the NS-alpha model transform covariantly under Galilean transformations and under a change to a uniformly rotating reference frame. Finally, we discuss in the spectral formulation how the NS-alpha model retains the local interactions among the large scales, retains the nonlocal sweeping effects of large scales on small scales, yet attenuates the local interactions of the small scales amongst themselves.Comment: 15 pages, no figures, Special LES volume of ERCOFTAC bulletin, to appear in 200

A hierarchy of exactly solvable spin-1/2 chains with so(N)_1 critical points

We construct a hierarchy of exactly solvable spin-1/2 chains with so(N)_1 critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We employ this framework to construct a Hamiltonian term that couples N transverse field Ising chains such that the resulting theory is critical and described by the so(N)_1 conformal field theory. By employing spin duality transformations, we then cast these spin chains for arbitrary N into translationally invariant forms that all allow exact solution by the means of a Jordan-Wigner transformation. For odd N our models generalize the phase diagram of the transverse field Ising chain, the simplest model in our hierarchy. For even N the models can be viewed as longer ranger generalizations of the XY chain, the next model in the hierarchy. We also demonstrate that our method of constructing spin chains with given critical points goes beyond exactly solvable models. Applying the same strategy to the Blume-Capel model, a spin-1 generalization of the Ising chain in a generic magnetic field, we construct another critical spin-1 chain with the predicted CFT describing the criticality.Comment: 24 pages, 5 figures; v2: minor changes and added reference