Infinite-order phase transition in a classical spin system

For an exactly soluble classical spin model with long-range inhomogeneous coupling it is proved that in the absence of external magnetic field the free energy is aC function of the temperature at the critical point.     

Diffusion coefficient measurement in a microfluidic analyzer using dual-beam microscale-refractive index gradient detection. Application to on-chip molecular size determination

We report a microchip-based detection scheme to determine the diffusion coefficient and molecular mass (to the extent correlated to molecular size) of analytes of interest. The device works by simultaneously measuring the refractive index gradient (RIG) between adjacent laminar flows at two different positions along a microchannel. The device, referred to as a microscale molecular mass sensor (micro-MMS), takes advantage of laminar flow conditions where the mixing of two streams occurs essentially by diffusion across the boundary between the two streams. Two flows merge on the microchip, one containing solvent only, referred to as the mobile phase stream and one which contains the analyte(s) of interest in the solvent, i.e. the sample stream. As these two streams merge and flow parallel to each other down the microchannel a RIG is created by the concentration gradient. The RIG is further influenced by analyte diffusion from the sample stream into the mobile phase stream. Measuring the RIG at a position close to the merging point (upstream signal) and simultaneously a selected distance further down the microchannel (downstream signal) provides real-time data related to the extent a given analyte has diffused, which can be readily correlated to analyte molecular mass by taking the ratio of the downstream-to-upstream signals. For the dual-beam RIG measurements, a diode laser output is coupled to a single mode fiber optic splitter with two output fibers. Light from each fiber passes through a graded refractive index (GRIN) lens forming a collimated beam that then passes through the microchannel and then on to a position sensitive detector (PSD). The RIG at both detection positions deflects the two collimated probe beams. The deflection angle of each beam is then measured on two separate PSDs. The micro-MMS was evaluated using polyethylene glycols (PEGs), sugars, and as a detector for size-exclusion chromatography (SEC). Peak purity can be readily identified using the micro-MMS with SEC. The limit of detection was 0.9 ppm (PEG at 11 840 g/mol) at the upstream detection position corresponding to a RI limit of detection (LOD) (3sigma) of 7-10(-8) RI. The pathlength for the RIG measurement was 200 microm and the angular LOD was 0.23 micro(rad) with a detection volume of 8 nl at both positions. The average molecular mass resolution was 9% (relative standard deviation) for a series of PEGs ranging in molecular mass from 106 to 22 800 g/mol. With this excellent mass resolution, small molecules such as monosaccharides, disaccharides, and so on, are readily distinguished. The sensor is demonstrated to readily determine unknown diffusion coefficients.     

Determination of selected neurotransmitter metabolites using monolithic column chromatography coupled with chemiluminescence detection

The oxidation of selected clinically important neurotransmitter metabolites with acidic potassium permanganate in the presence of polyphosphates evokes chemiluminescence of sufficient intensity to enable the sensitive determination of these species. Limits of detection for 5-hydroxyindole-3-acetic acid (5-HIAA), vanilmandelic acid (VMA; α,4-dihydroxy-3-methoxybenzeneacetic acid), 4-hydroxy-3-methoxyphenylglycol (MHPG), homovanillic acid (HVA, 4-hydroxy-3-methoxyphenylacetic acid) and 3,4-dihydroxyphenylacetic acid (DOPAC) were between 5 × 10⁻⁹ and 4 × 10⁻⁸ M, using flow-injection analysis methodology. In addition, we demonstrate the rapid determination of homovanillic acid and 5-hydroxyindole-3-acetic acid in human urine - without the need for extraction procedures - using monolithic column chromatography with chemiluminescence detection.     

Borel Summability and Lindstedt Series

Resonant motions of integrable systems subject to perturbations may continue to exist and to cover surfaces with parametric equations admitting a formal power expansion in the strength of the perturbation. Such series may be, sometimes, summed via suitable sum rules defining C ^∞ functions of the perturbation strength: here we find sufficient conditions for the Borel summability of their sums in the case of two-dimensional rotation vectors with Diophantine exponent τ =1 (e.g. with ratio of the two independent frequencies equal to the golden mean).     

Criteria for farthest points on convex surfaces

We provide a sharp, sufficient condition to decide if a point y on a convex surface S is a farthest point (i.e., is at maximal intrinsic distance from some point) on S, involving a lower bound π on the total curvature ω_y at y, ω_y ≥ π. Further consequences are obtained when ω_y > π, and sufficient conditions are derived to guarantee that a convex cap contains at least one farthest point. A connection between simple closed quasigeodesics O of S, points y ∈ S\O with ω_y > π, and the set ?? of all farthest points on S, is also investigated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

What do cylinders look like?

The farthest point mapping is bijective and involutive on any right circular cylinder of radius r and height h ≤ r(π ? 2). For any right cylinder C over a typical convex body K, most points in bd(K) are endpoints of C.     

On typical degenerate convex surfaces

Various properties are given concerning geodesics on, and distance functions from points in, typical degenerate convex surfaces; i.e., surfaces obtained by gluing together two isometric copies of typical (in the sense of Baire category) convex bodies, by identifying the corresponding points of their boundaries.     

Gamow Vectors and Borel Summability in a Class of Quantum Systems

We analyze the detailed time dependence of the wave function ψ(x,t) for one dimensional Hamiltonians \(H=-\partial_{x}^{2}+V(x)\) where V (for example modeling barriers or wells) and ψ(x,0) are compactly supported.We show that the dispersive part of ψ(x,t) is the Borel sum of its asymptotic series in powers of t ^?1/2, t→∞. The remainder, the difference between ψ and the Borel sum, i.e., the exponential part of the transseries of ψ, is a convergent expansion of the form \(\sum_{k=0}^{\infty}g_{k}\Gamma_{k}(x)e^{-\gamma_{k} t}\), where Γ _k are the Gamow vectors of H, and iγ _k are the associated resonances; generically, all g _k are nonzero. For large k, γ _k ～const?klog?k+k ² π ² i/4. The effect of the Gamow vectors is visible when time is not very large, and the decomposition defines rigorously resonances and Gamow vectors in a nonperturbative regime, in a physically relevant way.The decomposition allows for calculating ψ for moderate and large t, to any prescribed exponential accuracy, using optimal truncation of power series plus finitely many Gamow vectors contributions.The analytic structure of ψ is perhaps surprising: in general (even in simple examples such as square wells), ψ(x,t) turns out to be C ^∞ in t but nowhere analytic on ?⁺. In fact, ψ is t-analytic in a sector in the lower half plane and has the whole of ?⁺ a natural boundary. In the dual space, we analyze the resurgent structure of ψ.     

Einzelschicten aus zwei Komponenten. I. Experimentelle Verfahren und die Auswahl eines Systems

Ohne Zusammenfassung