Internal waves in a compressible two-layer model atmosphere: Hamiltonian description

We consider slow, compared to the speed of sound, motions of an ideal compressible fluid (gas) in a gravitational field in the presence of two isentropic layers with a small specific-entropy difference between them. Assuming the flow to be potential in each of the layers (v _{1, 2} = ▿ϕ_{1, 2}) and neglecting the acoustic degrees of freedom (div($ \bar \rho $ \bar \rho (z)▿ϕ_{1, 2}) ≈ 0, where $ \bar \rho $ \bar \rho (z) is the average equilibrium density), we derive the equations of motion for the boundary in terms of the shape of the surface z = η(x, y, t) itself and the difference between the boundary values of the two velocity field potentials: ψ(x, y, t) = ψ₁ − ψ₂. We prove the Hamilto nian structure of the derived equations specified by a Lagrangian of the form ℒ = ∫$ \bar \rho $ \bar \rho (η)η _t ψdxdy − ℋ{η, ψ}. The system under consideration is the simplest theoretical model for studying internal waves in a sharply stratified atmosphere in which the decrease in equilibrium gas density due to gas compressibility with increasing height is essentially taken into account. For plane flows, we make a generalization to the case where each of the layers has its own constant potential vorticity. We investigate a system with a model dependence $ \bar \rho $ \bar \rho (z) ∝ e ^−2αz with which the Hamiltonian ℋ{η, ψ} can be represented explicitly. We consider a long-wavelength dynamic regime with dispersion corrections and derive an approximate nonlinear equation of the form u _t + auu _x − b[−$ \hat \partial _x^2 $ \hat \partial _x^2 + α²]^1/2 u _x = 0 (Smith’s equation) for the slow evolution of a traveling wave.     

Mechanism of the production of the <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) resonance in the γγ → π<Superscript>0</Superscript>η reaction

High-statistics Belle data on the γγ → π⁰η reaction have been analyzed in order to reveal the mechanism of two-photon production and the nature of the a ₀(980) resonance. The solution obtained for the γγ → π⁰η amplitude is in agreement with the predictions of the chiral theory for the πη-scattering length; with the strong coupling of the a ₀(980) resonance with the πη, K $ \bar K $ \bar K , and πη′ channels; and with the key role of the a ₀(980) → (K $ \bar K $ \bar K + π⁰η + π⁰η′) → γγ rescattering mechanisms in the a ₀(980) → γγ decay. This picture is much in favor of the q ² $ \bar q $ \bar q ² nature of a ₀(980) resonance and is consistent with the properties of its partners, σ₀(600) and f ₀(980) resonances, in particular, with those manifested in the γγ → ππ reactions. The important role of vector exchanges in the formation of the nonresonant background in the γγ → π⁰η reaction has been revealed. Preliminary information on the π⁰η → π⁰η reaction has been obtained.     

Mixing parameters of η and η′ mesons

Mixing angles of η and η′ mesons are obtained in the scheme of octet-singlet mixing θ_η = −15.4°, θ′_η = −17.9°, and in the scheme connected with expansion in the quark basis $ \bar q $ \bar q q − $ \bar s $ \bar s s φ = 39.3°. The constants gV _ηγ, g _η′ V _γ of radiative decays η′ → V _γ and V → ηγ (V ≡ ρ, ω, φ) and the ratios of constants of weak decays of η and η′ mesons are calculated. The numerical values that were found are in agreement with the experimental data.     

The model-independent analysis indications for spectroscopy of scalar mesons. Proof for the K0* (900)

In a model-independent approach the data on ππ → ππ, K $ \bar K $ \bar K , ηη, ηη′ in the I ^G J ^PC = 0⁺0⁺⁺ channel and on the Kπ scattering in the $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) channel are analyzed jointly for studying the status and QCD nature of the f ₀- and the K*₀-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q $ \bar q $ \bar q ). In the Kπ-scattering data analysis, the proof for the K*₀(900) is given.     

Neutron diffraction studies of the negative thermal expansion in a layered indium selenide crystal

The neutron diffraction patterns have been analyzed for a layered single crystal and a powder of the γ-polytype of indium selenide in the temperature range 10–300 K. In the temperature range 10–50 K, the excitation of bending vibrations due to the charge density waves changes the phonon spectrum and gives rise to a negative thermal expansion in the plane of layers, i.e., α_‖c = −2.2 × 10⁻⁶ K⁻¹, which is characteristic of two-dimensional structures. The average (over the range T = 50–300 K) coefficients of thermal expansion along the principal crystallographic directions have been calculated: $ \bar \alpha _{ \bot c} $ \bar \alpha _{ \bot c} = 10.48 × 10⁻⁶ K⁻¹ and $ \bar \alpha _{\parallel c} $ \bar \alpha _{\parallel c} = 12.97 × 10⁻⁶ K⁻¹, which agree with the X-ray diffraction data previously obtained by the authors at T = 290 K.     

Contribution of semi-hadronic states <Emphasis Type="Italic">P</Emphasis>γ, <Emphasis Type="Italic">S</Emphasis>γ, π<Superscript>+</Superscript>π<Superscript>−</Superscript>γ to amm of muon in the framework of the Nambu-Jona-Lasinio model

We calculate the contribution of semi-hadronic states with the pseudoscalar P = π⁰, η and scalar (σ(550)) meson accompanied with a real photon as an intermediate state of a heavy photon to the anomalous magnetic moment of the muon. We consider the intermediate states with π⁰ and σ as hadrons in the frame-work of the Nambu-Jona-Lasinio (NJL) model. The contribution of the π⁰γ state is in agreement with results obtained in previous theoretical considerations as well as with the experimental data $ a_\mu ^{\pi _0 \gamma } \approx 4.5 \times 10^{ - 10} $ a_\mu ^{\pi _0 \gamma } \approx 4.5 \times 10^{ - 10} , besides we estimate a _μ^ηγ = 0.7 × 10⁻¹⁰, a _μ^σγ ∼ 1.5 × 10⁻¹¹, $ a_\mu ^{\pi ^ + \pi ^ - \gamma } \sim 3.2 \times 10^{ - 10} $ a_\mu ^{\pi ^ + \pi ^ - \gamma } \sim 3.2 \times 10^{ - 10} . We also discuss the light-by-light (LbL) mechanism with a _μ ^lbl = 10.5 × 10⁻¹⁰.     

The p/π ratio pT dependence in the RHIC range of baryo-chemical potential

The BRAHMS measurement of proton-to-pion ratios in Au+Au and p+p collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 62.4 GeV and $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV is presented as a function of transverse momentum and collision centrality within the pseudorapidity range 0 ≤ η ≤ 3. The baryo-chemical potential, μ _B , for the indicated data spans from μ _B ≈ 26 MeV ($ \sqrt {s_{NN} } $ \sqrt {s_{NN} } 200 GeV, η ≈ 0) to μ _B ∼ 260 MeV ($ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 62.4 GeV, η ≈ 3) [1]. The p/πratio measured for Au+Au system at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } 62.4 GeV, η ≈ 3 reaches astounding value of 8–10 at p _T > 1.5 GeV/c. For these energy and pseudorapidity interval no centrality dependency of p/π ratio is observed. Moreover, the baryon-to-meson ratio of nucleus-nucleus data are consistent with results obtained for p+p interactions.     

The property of maximal transcendentality in the N \mathcal{N} = 4 SYM

We show results for the universal anomalous dimension γ_uni(j) of Wilson twist-2 operators in the $ \mathcal{N} $ \mathcal{N} = 4 Supersymmetric Yang-Mills theory in the first three orders of perturbation theory. These expressions are obtained by extracting the most complicated contributions from the corresponding anomalous dimensions in QCD.     

Directed flow of identified particles from Au+Au collisions at RHIC

We present the measurement of directed flow (v ₁) for the identified particles, namely, Λ, $ \bar \Lambda $ \bar \Lambda and K _s ⁰, as a function of rapidity and centrality in Au+Au collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV and 62.4 GeV. The measurement is based on the run IV data obtained by the STAR experiment at RHIC. In order to enhance event plane resolution, we use tracks reconstructed from the Forward Time Projection Chambers (FTPCs), together with the sideward deflection of spectator neutrons measured by the STAR’s Shower Maximum Detector at Zero Degree Calorimeters (ZDC-SMDs). We find that for 200 GeV, proton and antiproton v ₁ is less than 1%, the K _s ⁰ Λ, $ \bar \Lambda $ \bar \Lambda v ₁ is less than 2%; for 62 GeV, proton v ₁ is less than 1% and antiproton is less than 2%, v ₁ for K _s ⁰, Λ, $ \bar \Lambda $ \bar \Lambda is less than 2% in Au+Au collisions at 200 GeV.     

Measurement of ω/? → e+e? in proton + proton collisions at ?s \sqrt s = 200 GeV at RHIC-PHENIX

The PHENIX experiment at RHIC has measured ω and ϕ meson production using di-electron decay mode over a psude-rapidity range of |η| ≤ 0.35 and a transverse momentum range of 0 < p _T < 5 GeV/c in proton + proton collisions at $ \sqrt s $ \sqrt s = 200 GeV. The spectra of production cross section as a function of p _T for ω and ϕ → e ⁺ e ⁻ show good agreement with other hadornic decay channels ω → π ⁰ γ, ω ⁰ π ⁺ π ⁻ and ϕ → K ⁺ K ⁻, respectively.     

Designing Klod detector prototypes and results of their experimental tests

The projected KLOD facility is intended for finding and investigating the ultrarare decay K _L ⁰ → π⁰ν$ \bar \nu $ \bar \nu ; its branching ratio predicted by the Standard Model is Br = (3.0 ± 0.6) × 10⁻¹¹. Designing and testing the prototype of the decay-volume veto system and beam veto calorimeter, which are the most important detectors of the facility, are considered. It is shown that the proposed beam veto calorimeter is able to detect γ rays with a high efficiency at the neutron flux of 300 MHz.     

On the high-statistics investigation of the <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) resonance in the γγ → π<Superscript>0</Superscript>η reaction

High-statistics data on the γγ → π⁰η reaction will make it possible to conclude whether the K ⁺ K ⁻-loop rescattering mechanism, γγ → K ⁺ K ⁻ → a ₀(980) → π⁰η, is the main mechanism of the production of a ₀(980) isovector resonance. This mechanism provides a reasonable value of 20–30 nb at the maximum for the manifestation of a ₀(980) in the γγ → π⁰η cross section. It also gives rise to a noticeable narrowing of the a ₀(980) peak to its effective (observed) width ≈20–30 MeV in the γγ → π⁰η channel. The decay width averaged over the resonance mass distribution is 〈Γ_{α 0} → K ⁺ K ⁻ → γγ〉_πη ≈ 0.13 keV. The experimental confirmation of this scenario would be important evidence in favor of the q ² $ \bar q $ \bar q ² nature of light scalar mesons.     

Finite-size scaling and power law relations for dipole-quadrupole interaction on Blume-Emery-Griffiths model

The Blume-Emery-Griffiths model with the dipole-quadrupole interaction ($ \ell = \frac{I} {J} $ \ell = \frac{I} {J} ) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (χ) are proposed for the dipole-quadrupole interaction (ℓ). The dipole-quadrupole critical exponent δ_χ has been estimated from the data of the order parameter (M) and the susceptibility (χ). The simulations have been done in the interval $ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 $ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 for $ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 $ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 and $ h = \frac{H} {J} = 0 $ h = \frac{H} {J} = 0 parameter values on a face centered cubic (fcc) lattice with periodic boundary conditions. The results indicate that the effect of the ℓ parameter is similar to the external magnetic field (h). The critical exponent δ_ℓ are in good agreement with the universal value (δ _h = 5) of the external magnetic field.     

Vorticity waves in problems of hydrodynamic stability

The known problem of flow transition near a circular cylinder at Re = 40 from a symmetrical form to the Karman vortex street can be considered as the problem of vortex wave development and intensification. Development of three bundles of vortex waves of low intensity is observed in a wake of a cylinder; these bundles are easily visualized as the structures of relative vorticity $ \bar \Omega $ \bar \Omega = Ω(t ₁) − Ω(t ₀): difference of vorticity Ω at two time moments, t ₀ being fixed. In the field of $ \bar \Omega $ \bar \Omega the alternating structure of quadrupoles is characterized by linear parameter l = h/d: the ratio of the width of the central bundle of vortex waves to the distance between the centers of quadrupoles of a “single sign”. When l = 0.281 is achieved, which coincides with the value of the same parameter of a stable Karman street, the transition from symmetrical streamlining by viscous incompressible liquid to the vortex street occurs.     

Two-photon decays of pseudotensor mesons <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(1670), <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(2250), and <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(2510)

In terms of relativistic and gauge-invariant spectral-integral technique, we calculate amplitude for the π ₂ → γγ decay as a three-step transition π ₂ → q $ \bar q $ \bar q (2⁻⁺) → γ + q $ \bar q $ \bar q (1⁻⁻) → γγ. Using wave functions of the q $ \bar q $ \bar q components of photon (hep-ph/0406320) and those of pseudotensor mesons π ₂(1670), π ₂(2000), π ₂(2250), and π ₂(2510) (hep-ph/0511109), we obtain the following values for partial widths: Γ _{π2(1670)→γγ} = 0.072 ± 0.007 keV, Γ _{π2(2000)→γγ} = 0.037 ± 0.004 keV, Γ _{π2(2250)→γγ} = 0.027 ± 0.003 keV, and Γ _{π2(2510)→γγ} = 0.022 ± 0.002 keV. In the calculations, we use the momentum operator expansion, and, in this connection, discuss the problem of nilpotent operators inherent in the considered amplitude. It should be emphasized that measurement of two-photon decays of the π ₂ states can give valuable information about the long-range quark-antiquark forces which, as one may guess, are related to the quark confinement.     

Trajectory attractor of a reaction-diffusion system with a series of zero diffusion coefficients

We study a reaction-diffusion system of N equations with k nonzero and N − k zero diffusion coefficients. More exactly, the first k equations of the system contain the terms a _i Δu _i − f _j (u, v), i = 1, …, k, with the diffusion coefficient a _i > 0. The right-hand sides of the other N − k equations contain only nonlinear interaction functions −h _j (u, v), j = k + 1, …, N, with zero diffusion. Here u = (u ₁, …, u _k ) and v = (υ _k+1, …, υ _N ) are unknown concentration vectors. Under appropriate assumptions on the interaction functions f(·) and h(·), we construct the trajectory attractor of this reaction-diffusion system. We also find the trajectory attractors , δ = (δ ₁, …, δ _k ), for the analogous reaction-diffusion systems having the terms δ _j Δυ _j − h _j (u, v), j = k + 1, …, N, with small diffusion coefficients δ _j ⩾ 0 in the last N − k equations. We prove that the trajectory attractors converge to (in an appropriate topology) as δ → 0+. Dedicated to the memory of Vladimir Borovikov Partially supported by the Russian Foundation for Basic Research (projects nos. 08-01-00784 and 07-01-00500).     

Neutral meson oscillations and equivalence principle for particles and antiparticles

Oscillations of neutral meson (K ⁰-$ \overline {K^0 } $ \overline {K^0 } , D ⁰-$ \overline {D^0 } $ \overline {D^0 } , and B ⁰-$ \overline {B^0 } $ \overline {B^0 } are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc ²—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field of the galaxy center, we obtain the estimate from experimental data on K ⁰-$ \overline {K^0 } $ \overline {K^0 } oscillations:

Laser-induced optical activity in range of Rydberg autoionizing states of xenon

Optical activity of xenon atoms in the vacuum UV range induced by circularly polarized laser light is studied theoretically. The optical activity arises in the vicinity of the autoionizing state 5p ⁵(² P _1/2)8s′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 as a result of its coupling via the laser field with the discrete state 5p ⁵(² P _3/2)7p $ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 . Polarization variations of the vacuum UV radiation upon its propagation through the atomic medium are calculated, and the possibility of controlling this polarization is discussed. Manifestations of nonresonant coupling of the discrete state with the broad autoionizing state 5p ⁵(² P _1/2)6d′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 induced by the overlap of the Rydberg autoionizing series in xenon are studied.     

Pre-exponential factor of the hopping conductivity in disordered carbon films

The conductivity of carbon films grown by polymethylphenylsiloxane vapor decomposition in stimulated dc discharge plasma was studied. It is found that the Mott hopping conductivity $ \sigma \left( T \right) = \sigma _0 \left( T \right)\exp \left\{ { - \frac{{T_0 }} {T}^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} } \right\} $ \sigma \left( T \right) = \sigma _0 \left( T \right)\exp \left\{ { - \frac{{T_0 }} {T}^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} } \right\} is characteristic of the samples under study in the temperature range of 80–400 K in the electric field E to 5 · 10⁴ V/cm. An analysis of the pre-exponential factor σ ₀(T) = σ ₀₀(T ₀)T ^α allowed the conclusion that the hopping transport is most adequately described in the model with the exponential energy dependence of the density of localized states for which α = −1/2 and the universal relation ln σ ₀₀ −T ₀^1/4 0 is valid, which is satisfied in the range where the parameter σ ₀₀ varies by eight orders of magnitude.