Wind on the boundary for the Abelian sandpile model

We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge c=-2, by introducing two new boundary conditions. These have two unusual features: they carry an intrinsic orientation, and, more strangely, they cannot be imposed uniformly on a whole boundary (like the edge of a cylinder). They lead to seven new boundary condition changing fields, some of them being in highest weight representations (weights -1/8, 0 and 3/8), some others belonging to indecomposable representations with rank 2 Jordan cells (lowest weights 0 and 1). Their fusion algebra appears to be in full agreement with the fusion rules conjectured by Gaberdiel and Kausch.Comment: 26 pages, 4 figure

Factorizable ribbon quantum groups in logarithmic conformal field theories

We review the properties of quantum groups occurring as Kazhdan--Lusztig dual to logarithmic conformal field theory models. These quantum groups at even roots of unity are not quasitriangular but are factorizable and have a ribbon structure; the modular group representation on their center coincides with the representation on generalized characters of the chiral algebra in logarithmic conformal field models.Comment: 27pp., amsart++, xy. v2: references added, some other minor addition

Analysis of phenolic compounds in black walnut (Juglans nigra L.) fruit extract using high-performance liquid chromatography

Black walnut (Juglans nigra L.), which belongs to the Nut family (Juglandaceae), is a valuable raw material for the production of phytopreparations. The extract from the fruits of Juglans nigra L. has immunomodulating and antioxidant properties, which is primarily due to the presence of a large amount of phenolic compounds in the plant. But the phytochemical composition and pharmacological properties of Juglans nigra L. have not been sufficiently studied. The aim of our work was to study the optimal conditions for the extraction of Juglans nigra L. fruits, followed by the identification of its quantitative and qualitative composition. The main criterion for evaluating optimal extraction conditions was the quantitative content of phenolic compounds, which was determined spectrophotometrically by the Folin–Chocalteu method. The analysis of polyphenolic compounds was carried out by the method of high performance liquid chromatography. On the basis of experimental studies, the optimal conditions for extracting the fruits of Juglans nigra L. by maceration method conditions were selected. According to the results of the comparative analysis, it is shown that for the maximum extraction of phenolic compounds, it is advisable to use a 70% water-ethanol mixture as an extractant with a raw material to solvent ratio of 1:9. The method of high-performance liquid chromatography showed that the total content of phenolic compounds in the fruits of Juglans nigra L. is 2 327.09 μg/ml. Analysis of the extract of Juglans nigra L. by high-performance liquid chromatography method showed the presence of such phenolic compounds in plant material samples as catechins, catechin-like substances, flavonols (rutin, quercetin, myricetin), flavanones (naringin, naringenin) and phenolic acids. It should be noted, that the presence of such substances as chlorogenic acid, caffeic acid, kaempferol, hesperidin, genistein and daidzein glycosides, luteolin and apigenin glycosides, luteolin and apigenin in the extract of Juglans nigra L. was not detected. A high content of compounds of polyphenolic nature in the fruits of Juglans nigra L. was established. Therefore, this medicinal plant material is promising for further research, in particular, for the development of medicines based on the extract with potential anti-inflammatory, analgesic and antioxidant activity

Fusion algebra of critical percolation

We present an explicit conjecture for the chiral fusion algebra of critical percolation considering Virasoro representations with no enlarged or extended symmetry algebra. The representations we take to generate fusion are countably infinite in number. The ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of these representations decomposes into a finite direct sum of these representations. The fusion rules are commutative, associative and exhibit an sl(2) structure. They involve representations which we call Kac representations of which some are reducible yet indecomposable representations of rank 1. In particular, the identity of the fusion algebra is a reducible yet indecomposable Kac representation of rank 1. We make detailed comparisons of our fusion rules with the recent results of Eberle-Flohr and Read-Saleur. Notably, in agreement with Eberle-Flohr, we find the appearance of indecomposable representations of rank 3. Our fusion rules are supported by extensive numerical studies of an integrable lattice model of critical percolation. Details of our lattice findings and numerical results will be presented elsewhere.Comment: 12 pages, v2: comments and references adde

N/V-limit for Langevin dynamics in continuum

We construct an infinite particle/infinite volume Langevin dynamics on the space of configurations in $\R^d$ having velocities as marks. The construction is done via a limiting procedure using $N$-particle dynamics in cubes $(-\lambda,\lambda]^d$ with periodic boundary conditions. A main step to this result is to derive an (improved) Ruelle bound for the canonical correlation functions of $N$-particle systems in $(-\lambda,\lambda]^d$ with periodic boundary conditions. After proving tightness of the laws of finite particle dynamics, the identification of accumulation points as martingale solutions of the Langevin equation is based on a general study of properties of measures on configuration space (and their weak limit) fulfilling a uniform Ruelle bound. Additionally, we prove that the initial/invariant distribution of the constructed dynamics is a tempered grand canonical Gibbs measure. All proofs work for general repulsive interaction potentials $\phi$ of Ruelle type (e.g. the Lennard-Jones potential) and all temperatures, densities and dimensions $d\geq 1$

Quantum-sl(2) action on a divided-power quantum plane at even roots of unity

We describe a nonstandard version of the quantum plane, the one in the basis of divided powers at an even root of unity $q=e^{i\pi/p}$. It can be regarded as an extension of the "nearly commutative" algebra $C[X,Y]$ with $X Y =(-1)^p Y X$ by nilpotents. For this quantum plane, we construct a Wess--Zumino-type de Rham complex and find its decomposition into representations of the $2p^3$-dimensional quantum group $U_q sl(2)$ and its Lusztig extension; the quantum group action is also defined on the algebra of quantum differential operators on the quantum plane.Comment: 18 pages, amsart++, xy, times. V2: a reference and related comments adde

Using Rheo-Small-Angle Neutron Scattering to Understand How Functionalised Dipeptides Form Gels

We explore the use of rheo-small-angle neutron scattering as a method to collect structural information from neutron scattering simultaneously with rheology to understand how low-molecular-weight hydrogels form and behave under shear. We examine three different gelling hydrogel systems to assess what structures are formed and how these influence the rheology. Furthermore, we probe what is happening to the network during syneresis and why the gels do not recover after an applied strain. All this information is vital when considering gels for applications such as 3D-printing and injection

Ultra-High Energy Neutrino Fluxes: New Constraints and Implications

We apply new upper limits on neutrino fluxes and the diffuse extragalactic component of the GeV gamma-ray flux to various scenarios for ultra high energy cosmic rays and neutrinos. As a result we find that extra-galactic top-down sources can not contribute significantly to the observed flux of highest energy cosmic rays. The Z-burst mechanism where ultra-high energy neutrinos produce cosmic rays via interactions with relic neutrinos is practically ruled out if cosmological limits on neutrino mass and clustering apply.Comment: 10 revtex pages, 9 postscript figure

Ab-initio Quantum Enhanced Optical Phase Estimation Using Real-time Feedback Control

Optical phase estimation is a vital measurement primitive that is used to perform accurate measurements of various physical quantities like length, velocity and displacements. The precision of such measurements can be largely enhanced by the use of entangled or squeezed states of light as demonstrated in a variety of different optical systems. Most of these accounts however deal with the measurement of a very small shift of an already known phase, which is in stark contrast to ab-initio phase estimation where the initial phase is unknown. Here we report on the realization of a quantum enhanced and fully deterministic phase estimation protocol based on real-time feedback control. Using robust squeezed states of light combined with a real-time Bayesian estimation feedback algorithm, we demonstrate deterministic phase estimation with a precision beyond the quantum shot noise limit. The demonstrated protocol opens up new opportunities for quantum microscopy, quantum metrology and quantum information processing.Comment: 5 figure

Time separation as a hidden variable to the Copenhagen school of quantum mechanics

The Bohr radius is a space-like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time-like separation linearly mixed with the Bohr radius. Indeed, the time-separation is one of the essential variables in high-energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman's rest of the universe. It is noted first that Feynman's Lorentz-invariant differential equation for the bound-state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two-mode squeezed states in quantum optics, where both photons are observable, but one of them can be treated a variable hidden in the rest of the universe. The physics of this two-mode state can then be translated into the time-separation variable in the quark model. As in the case of the un-observed photon, the hidden time-separation variable manifests itself as an increase in entropy and uncertainty.Comment: LaTex 10 pages with 5 figure. Invited paper presented at the Conference on Advances in Quantum Theory (Vaxjo, Sweden, June 2010), to be published in one of the AIP Conference Proceedings serie