Vortices, circumfluence, symmetry groups and Darboux transformations of the (2+1)-dimensional Euler equation

The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, oceanic and atmospheric dynamics. A symmetry group theorem of the (2+1)-dimensional EE is obtained via a simple direct method which is thus utilized to find \em exact analytical \rm vortex and circumfluence solutions. A weak Darboux transformation theorem of the (2+1)-dimensional EE can be obtained for \em arbitrary spectral parameter \rm from the general symmetry group theorem. \rm Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.Comment: 25 pages, 9 figure

The spectrum of states with one current acting on the adjoint vacuum of massless QCD2

We consider a ``one current'' state, which is obtained by the application of a color current on the ``adjoint'' vacuum. This is done in $QCD_2$, with the underlying quarks in the fundamental representation. The quarks are taken to be massless, in which case the theory on the light-front can be ``currentized'', namely, formulated in terms of currents only. The adjoint vacuum is shown to be the application of a current derivative, at zero momentum, on the singlet vacuum. We apply the operator $M^2=2P^+P^-$ on these states and find that in general they are not eigenstates of $M^2$ apart from the large $N_f$ limit. Problems with infra-red regularizations are pointed out. We discuss the fermionic structure of these states.Comment: 18 pages, no figures. v2: minor corrections. v3: added some clarifications and remarks, mainly on the contribution of zero modes. Typos corrected, references added. To appear in Nuclear Physics

Modeling electrolytically top gated graphene

We investigate doping of a single-layer graphene in the presence of electrolytic top gating. The interfacial phenomena is modeled using a modified Poisson-Boltzmann equation for an aqueous solution of simple salt. We demonstrate both the sensitivity of graphene's doping levels to the salt concentration and the importance of quantum capacitance that arises due to the smallness of the Debye screening length in the electrolyte.Comment: 7 pages, including 4 figures, submitted to Nanoscale Research Letters for a special issue related to the NGC 2009 conference (http://asdn.net/ngc2009/index.shtml

Global anisotropy of arrival directions of ultra-high-energy cosmic rays: capabilities of space-based detectors

Planned space-based ultra-high-energy cosmic-ray detectors (TUS, JEM-EUSO and S-EUSO) are best suited for searches of global anisotropies in the distribution of arrival directions of cosmic-ray particles because they will be able to observe the full sky with a single instrument. We calculate quantitatively the strength of anisotropies associated with two models of the origin of the highest-energy particles: the extragalactic model (sources follow the distribution of galaxies in the Universe) and the superheavy dark-matter model (sources follow the distribution of dark matter in the Galactic halo). Based on the expected exposure of the experiments, we estimate the optimal strategy for efficient search of these effects.Comment: 19 pages, 7 figures, iopart style. v.2: discussion of the effect of the cosmic magnetic fields added; other minor changes. Simulated UHECR skymaps available at http://livni.inr.ac.ru/UHECRskymaps

Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras

This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice), reflection group $W\subset W(S)$, fundamental polyhedron \Cal M of $W$ and an acceptable (corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors orthogonal to faces of \Cal M (simple roots). One can construct the corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by $M$. We show that \goth g has good behavior of imaginary roots, its denominator formula is defined in a natural domain and has good automorphic properties if and only if \goth g has so called {\it restricted arithmetic type}. We show that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus, Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a natural class to study. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the best automorphic properties for the denominator function if they have {\it a lattice Weyl vector $\rho$}. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type with generalized lattice Weyl vector $\rho$ are called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on results and ideas. 31 pages, no figures. AMSTe