The Schro¨\ddot{o}dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics

In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schr$\ddot{o}$dinger-Poisson equations in the large $N$ limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as $\hbar \sim M^{5/3} G^{1/2} (N/)^{1/6}$, where is $G$ the gravitational constant, $N$ and $M$ are the number and the mass of the bodies, and $$ is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schr$\ddot{o}$dinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales.Comment: Accepted for publication in the Euro. Phys. J.

Structure of a GH51 α- L -arabinofuranosidase from Meripilus giganteus : Conserved substrate recognition from bacteria to fungi

α-l-Arabinofuranosidases from glycoside hydrolase family 51 use a stereochemically retaining hydrolytic mechanism to liberate nonreducing terminal α-l-arabinofuranose residues from plant polysaccharides such as arabinoxylan and arabinan. To date, more than ten fungal GH51 α-l-arabinofuranosidases have been functionally characterized, yet no structure of a fungal GH51 enzyme has been solved. In contrast, seven bacterial GH51 enzyme structures, with low sequence similarity to the fungal GH51 enzymes, have been determined. Here, the crystallization and structural characterization of MgGH51, an industrially relevant GH51 α-l-arabinofuranosidase cloned from Meripilus giganteus, are reported. Three crystal forms were grown in different crystallization conditions. The unliganded structure was solved using sulfur SAD data collected from a single crystal using the I23 in vacuo diffraction beamline at Diamond Light Source. Crystal soaks with arabinose, 1,4-dideoxy-1,4-imino-l-arabinitol and two cyclophellitol-derived arabinose mimics reveal a conserved catalytic site and conformational itinerary between fungal and bacterial GH51 α-l-arabino­furanosidases

A guide to the Choquard equation

We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$-\Delta u + V(x)u = \bigl(|x|^{-(N-\alpha)} * |u|^p\bigr)|u|^{p - 2} u \qquad \text{in $\mathbb{R}^N$},$$ and some of its variants and extensions.Comment: 39 page

Promoter Complexity and Tissue-Specific Expression of Stress Response Components in Mytilus galloprovincialis, a Sessile Marine Invertebrate Species

The mechanisms of stress tolerance in sessile animals, such as molluscs, can offer fundamental insights into the adaptation of organisms for a wide range of environmental challenges. One of the best studied processes at the molecular level relevant to stress tolerance is the heat shock response in the genus Mytilus. We focus on the upstream region of Mytilus galloprovincialis Hsp90 genes and their structural and functional associations, using comparative genomics and network inference. Sequence comparison of this region provides novel evidence that the transcription of Hsp90 is regulated via a dense region of transcription factor binding sites, also containing a region with similarity to the Gamera family of LINE-like repetitive sequences and a genus-specific element of unknown function. Furthermore, we infer a set of gene networks from tissue-specific expression data, and specifically extract an Hsp class-associated network, with 174 genes and 2,226 associations, exhibiting a complex pattern of expression across multiple tissue types. Our results (i) suggest that the heat shock response in the genus Mytilus is regulated by an unexpectedly complex upstream region, and (ii) provide new directions for the use of the heat shock process as a biosensor system for environmental monitoring

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In this paper, we extend our previous template analysis of a self-exciting Faraday disc dynamo with a linear series motor to the case of a nonlinear series motor. This introduces two additional nonlinear symmetry-breaking terms into the governing dynamo equations. We investigate the consequences for the identification of a possible template on which the unstable periodic orbits (UPOs) lie. By computing Gauss linking numbers between pairs of UPOs, we show that their values are not incompatible with those for a template for the Lorenz attractor for its classic parameter values. © 2011 The Royal Society

Template analysis of a Faraday disk dynamo

In a recent paper Moroz [1] returned to a nonlinear three-dimensional model of dynamo action for a self-exciting Faraday disk dynamo introduced by Hide et al. [2]. Since only two examples of chaotic behaviour were shown in [2], Moroz [1] performed a more extensive analysis of the dynamo model, producing a selection of bifurcation transition diagrams, including those encompassing the two examples of chaotic behaviour in [2]. Unstable periodic orbits were extracted and presented in [1], but no attempt was made to identify the underlying chaotic attractor. We rectify that here. Illustrating the procedure with one of the cases considered in [1], we use some of the unstable periodic orbits to identify a possible template for the chaotic attractor, using ideas from topology [3]. In particular, we investigate how the template is affected by changes in bifurcation parameter. © EDP Sciences and Springer 2008

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In this paper, we extend our previous template analysis of a self-exciting Faraday disc dynamo with a linear series motor to the case of a nonlinear series motor. This introduces two additional nonlinear symmetry-breaking terms into the governing dynamo equations. We investigate the consequences for the identification of a possible template on which the unstable periodic orbits (UPOs) lie. By computing Gauss linking numbers between pairs of UPOs, we show that their values are not incompatible with those for a template for the Lorenz attractor for its classic parameter values. © 2011 The Royal Society

Self-exciting Faraday disk homopolar dynamos

In this paper we present an overview of recently published work on the Faraday disk self-exciting homopolar dynamos. We also extend the analysis of two such coupled self-exciting disk dynamos with linear series motors [Moroz et al., 1998a; Moroz et al., 1998b] to the situation where one or both dynamo subunits incorporate nonlinear motors. We examine the differences in some of the bifurcation transition sequences between the various cases and consider whether the nonlinear quenching of oscillatory solutions can occur [Hide, 1998]

The Kadomtsev-Petviashvili equation under rapid forcing

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data. © 1997 American Institute of Physics