Nahm dualities on the torus - a synthesis

We give a unified description of self-dual SU(2) gauge fields on tori of size lt x ls^3 based on a mixture of analytical and numerical methods using the Nahm transformation, extended to the case of twisted boundary conditions. We show how torus calorons (lt/ls small) are Nahm dual to the torus instantons (lt/ls large). Holonomies are dual to the locations of constituents, this duality becoming exact in the limiting cases ls or lt --> infinity. Implications for the moduli spaces are discussed.Comment: Latex, 22 pages, 8 figures in 11 postscript file

Self-similar solutions and collective coordinate methods for Nonlinear Schrodinger Equations

In this paper we study the phase of self-similar solutions to general Nonlinear Schr\"odinger equations. From this analysis we gain insight on the dynamics of nontrivial solutions and a deeper understanding of the way collective coordinate methods work. We also find general evolution equations for the most relevant dynamical parameter $w(t)$ corresponding to the width of the solution. These equations are exact for self-similar solutions and provide a shortcut to find approximate evolution equations for the width of non-self-similar solutions similar to those of collective coordinate methods

Multi-Caloron solutions

We discuss the construction of multi-caloron solutions with non-trivial holonomy, both as approximate superpositions and exact self-dual solutions. The charge k SU(n) moduli space can be described by kn constituent monopoles. Exact solutions help us to understand how these constituents can be seen as independent objects, which seems not possible with the approximate superposition. An "impurity scattering" calculation provides relatively simple expressions. Like at zero temperature an explicit parametrization requires solving a quadratic ADHM constraint, achieved here for a class of axially symmetric solutions. We will discuss the properties of these exact solutions in detail, but also demonstrate that interesting results can be obtained without explicitly solving for the constraint.Comment: 31 pages, 7 figures (in 19 parts

On the applicability of the classical dipole-dipole interaction for polar Bose-Einstein condensates

We argue that the classical form of the dipole-dipole interaction energy cannot be used to model the interaction of the bosons in a dilute Bose-Einstein condensate made of polar atoms. This fact is due to convergence of integrals, if no additional restrictions are introduced. The problem can be regularized, in particular, by introducing a hard sphere model. As an example we propose a regularization consistent with the long range behavior of the effective potential and with the scattering amplitude of the fast particles.Comment: submitted to Phys. Re

Fixed point actions and on-shell tree-level Symanzik improvement

In this paper it is argued that the properties of the fixed point action of a renormalization group transformation can be used to implement the on-shell tree-level Symanzik improvement of lattice actions to any given order in the expansion in the lattice spacing, in a way which does not involve any perturbative calculations. In particular, a well-known technique for the lowest order improvement of SU(N) lattice gauge theories is revisited from the point of view of fixed point actions, which allows to shed light on some subtle points.Comment: 14 pages, LaTeX, 1 TeX figur

The Relationship Between Various Filter Notions on aGL-Monoid

AbstractThe notion of a generalised filter is extended to the setting of aGL-monoid. It is shown that there exists a one-to-one correspondence between the collection of generalised filters on a setXand the collection of strongly stratifiedL-filters onX. Specialising to the case whereLis the closed unit interval [0,c] viewed as a Heyting algebra, we show that any strongly stratified [0,c]-filter onXcan be uniquely identified with a saturated filter onIXwith characteristic valuec. In this way, the notion of a generalised filter unifies various filter notions. In particular, necessity measures and finitely additive probability measures are specific examples of generalised filters

Note on Scalar Fields Non-Minimally Coupled to (2+1)-Gravity

Scalar fields non--minimally coupled to (2+1)-gravity, in the presence of cosmological constant term, are considered. Non-minimal couplings are described by the term $\zeta R \Psi^2$ in the Lagrangian. Within a class of static circularly symmetric space-times, it is shown that the only existing physically relevant solutions are the anti-de Sitter space-time for $\zeta=0$, and the Martinez-Zanelli black hole for $\zeta=1/8$. We obtain also two new solutions with non-trivial scalar field, for $\zeta=1/6$ and $\zeta=1/8$ respectively, nevertheless, the corresponding space-times can be reduced, via coordinate transformations, to the standard anti-de Sitter space.Comment: 5 pages, RevTe

Study of SU(3) vortex-like configurations with a new maximal center gauge fixing method

We present a new way of fixing the gauge to (direct) maximal center gauge in SU(N) Yang-Mills theory and apply this method to SU(3) configurations which are vortex-like. We study the structure of the Z_3 configurations obtained after center-projecting the SU(3) ones.Comment: 11 pages, 2 figures. To appear in PL

Flow injection determination of total catechins and procyanidins in white and red wines

An easily automatable flow-injection (FI) method for the determination of total catechins is reported. The method is based on the reaction of vanillin in acid medium to yield a coloured product with maximum absorption at 500 nm. After optimisation by the univariate and multivariate approaches as required, the linear range was established (between 10 and 90 mgL-1 and 10 and 250 mgL-1 for white and red wines, respectively). Then, the assessment of the proposed versus the reference method was studied in terms of repeatability (2.57 mgL-1), reproducibility (3.56 mgL-1) (no significant differences were found), detection and quantification limits (not far from those of the reference method and always sufficient for the determination of catechins in any type of wine), traceability (excellent correlation under all conditions) and sample throughput (23 samples h-1 for the proposed method versus 3 samples h-1 for the reference method)

Comments on the Instanton Size Distribution

By studying the non-linear effects of overlapping instanton pairs we address difficulties in the identification of instanton distributions when the average instanton size is comparable to the average distance. For the exact charge two solution, we study how its parametrisation relates to a description in terms of individual instantons. There exist two dual sets of parameters describing the same charge two instanton solution. This duality implies the existence of a minimal separation between two instantons. Conventionally used lattice instanton finder algorithms based on the assumption of diluteness tend to underestimate instanton sizes. Finally we numerically confirm this for realistic parameters of the instanton liquid. The effect is enhanced by parallel orientation in group space.Comment: LaTeX, 15 pages, 3 figure