On the theory of conductivity of anisotropic composites: A weakly inhomogeneous medium

The conductivity of a weakly inhomogeneous anisotropic medium is considered. The effective conductivity tensor $ \hat \sigma _e $ \hat \sigma _e is determined in the approximation quadratic in deviation of local conductivity $ \hat \sigma $ \hat \sigma (r) from mean value 〈$ \hat \sigma $ \hat \sigma 〉 for an arbitrary anisotropy of the composite.     

Mimicking diffuse supernova antineutrinos with the sun as a source

Measuring the $ \bar \nu _e $ \bar \nu _e component of the cosmic diffuse supernova neutrino background (DSNB) is the next ambitious goal for low-energy neutrino astronomy. The largest flux is expected in the lowest accessible energy bin. However, for E ≲ 15 MeV a possible signal can be mimicked by a solar $ \bar \nu _e $ \bar \nu _e flux that originates from the usual ⁸B neutrinos by spin-flavor oscillations. We show that such an interpretation is possible within the allowed range of neutrino electromagnetic transition moments and solar turbulent field strengths and distributions. Therefore, an unambiguous detection of the DSNB requires a significant number of events at E ≳ 15 MeV.     

The conductivity of a 2D system with a doubly periodic arrangement of circular inclusions

We present a scheme for the evaluation of the conductivity and other effective properties of a model composite with a regular anisotropic structure, namely, a 2D system with circular inclusions forming a rectangular array. Exact expressions for the electric potential and the effective conductivity tensor [^(s)] _e\hat \sigma _e were obtained in the form of infinite series. For small inclusion densities, a virial expansion for [^(s)] _e\hat \sigma _e was derived from the general formulas and its applicability conditions were found. The first terms of this expansion yield the well-known Rayleigh result for the isotropic model (square array).     

Spin correlations in the ΛΛ and Λ$$ \bar \Lambda $$ systems generated in relativistic heavy-ion collisions

Spin correlations for the ΛΛ and Λ$ \bar \Lambda $ \bar \Lambda pairs, generated in relativistic heavy-ion collisions, and related angular correlations at the joint registration of hadronic decays of two hyperons, in which space parity is not conserved, are analyzed. The correlation tensor components can be derived from the double angular distribution of products of two decays by the method of “moments”. The properties of the “trace” of the correlation tensor (a sum of three diagonal components), determining the relative fractions of the triplet states and singlet state of respective pairs, are discussed. Spin correlations for two identical particles (ΛΛ) and two nonidentical particles (Λ$ \bar \Lambda $ \bar \Lambda ) are considered from the viewpoint of the conventional model of one-particle sources. In the framework of this model, correlations vanish at sufficiently large relative momenta. However, under these conditions, in the case of two nonidentical particles (Λ$ \bar \Lambda $ \bar \Lambda ) a noticeable role is played by two-particle annihilation (two-quark, two-gluon) sources, which lead to the difference of the correlation tensor from zero. In particular, such a situation may arise when the system passes through the “mixed phase.”     

Electrical conductivity of a two-dimensional model for a composite material with structural anisotropy

The electrical conductivity of a structurally anisotropic two-dimensional model for a composite material is considered. The model represents an isotropic matrix with a system of nonconducting inclusions in the form of mutually perpendicular scratches of various lengths. The centers of the scratches are chaotically distributed in plane (x, y). The approximate effective medium method is used to derive an expression for effective conductivity tensor $\hat \sigma _e$ that satisfactorily describes the electrical conductivity of this model over a wide concentration range. The model conductivity in the critical region is considered in terms of the similarity hypothesis.     

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.     

On the possibilities for studying the electromagnetic properties of monoenergetic solar neutrinos in the borexino experiments

Electroweak (EW) and electromagnetic (EM) scattering of solar beryllium neutrinos by electrons are analyzed. An analysis of the influence of the mean-square charge radius of an electron neutrino $ r_{\nu _e } = \sqrt {\left\langle {r_{_{\nu _e } }^2 } \right\rangle } $ r_{\nu _e } = \sqrt {\left\langle {r_{_{\nu _e } }^2 } \right\rangle } on differential and total cross sections is performed. The possibility of measuring the magnetic moment of an electron neutrino (μ_v) on the basis of isolating its contribution to the section of the discussed processes is considered.     

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.     

Production of strange secondaries in high-energy Σ<Superscript>−</Superscript><Emphasis Type="Italic">A</Emphasis> collisions

The WA89 Collaboration experimental data on production of Λ, Σ⁻, Σ⁺, Ξ⁻, Ω⁻ baryons, $ \bar \Lambda $ \bar \Lambda and $ \bar \Xi ^ + $ \bar \Xi ^ + antibaryons in Σ⁻ collisions with C and Cu targets at 345 GeV/c ($ \sqrt {s_{\Sigma N} } $ \sqrt {s_{\Sigma N} } ≈ 25.5 GeV) in the frame of the Quark-Gluon String Model is described. The comparison of the theoretical results with the experimental data is discussed. Finally, some relations among the values of the model parameters obtained with the help of quark combinatorics are presented.     

Parity nonconservation in deuteron photoreactions

We calculate the asymmetries in parity-nonconserving deuteron photodisintegration due to circularly polarized photons $ \vec \gamma d \to np $ \vec \gamma d \to np with the photon laboratory energy ranging from the threshold up to 10MeV and the radiative capture of thermal polarized neutrons by protons $ \vec np \to \gamma d $ \vec np \to \gamma d . We use the leading-order electromagnetic Hamiltonian neglecting the smaller nuclear exchange currents. Comparative calculations are done by using the Reid93 and Argonne v₁₈ potentials for the strong interaction and the DDH and FCDH “best” values for the weak couplings in a weak one-meson exchange potential. A weak NΔ transition potential is used to incorporate also the Δ(1232) -isobar excitation in the coupled-channels formalism.     

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.     

Energy gaps at neutrality point in bilayer graphene in a magnetic field

Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the ν = 0 quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane ($ \bar \Delta _0 $ \bar \Delta _0 , B), where $ \bar \Delta _0 $ \bar \Delta _0 is a top-bottom gates voltage imbalance, is described. It is shown that the energy gap scales linearly, ΔE ∼ 14B [T] K, with magnetic field.     

Reconstruction of $$ \tilde \tau _1 $$ mass at the LHC

The cascade mass reconstruction approach was used for mass reconstruction of the lightest $ \tilde \tau $ \tilde \tau produced at the LHC in the cascade decay $ \tilde g \to \tilde bb \to \tilde \chi _2^0 bb \to \tilde \tau _1 \tau bb \to \tilde \chi _1^0 \tau \tau bb $ \tilde g \to \tilde bb \to \tilde \chi _2^0 bb \to \tilde \tau _1 \tau bb \to \tilde \chi _1^0 \tau \tau bb . The $ \tilde \tau _1 $ \tilde \tau _1 mass was reconstructed assuming that masses of gluino, bottom squark, and two lightest neutralinos were reconstructed in advance. SUSY data sample sets for the SU(3) model point containing 160k events each were generated which corresponded to an integrated luminosity of about 8 fb⁻¹ at 14 TeV. These events were passed through the AcerDET detector simulator, which parametrized the response of a generic LHC detector. The mass of the $ \tilde \tau _1 $ \tilde \tau _1 was reconstructed with a precision of about 20% on average.     

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.     

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.     

On the theory of galvanomagnetic properties of composites

The conductivity of composites in the presence of a magnetic field H is considered. The galvanomagnetic characteristics for a weakly inhomogeneous medium are determined in explicit form in an approximation quadratic in the deviations of conductivity tensor $\hat \sigma $ (r) from its mean value 〈 $\hat \sigma $ 〉. The contribution to the effective conductivity tensor $\hat \sigma _e $ linear in concentration c of inclusions for a composite with a small value of c is expressed in terms of the dipole polarizability of an individual inclusion, which is defined in the transformed system in which it is surrounded by an isotropic matrix with a scalar conductivity. Transition to this system is performed using a symmetry transformation that does not change the dc equations. An approximate approach proposed for describing the galvanomagnetic properties of composites in the wide range of parameters appearing in the problem generalizes the standard theory of an effective medium to the case of anisotropic systems with inclusions of arbitrary shape in field H ≠ 0.     

Localized electron states in the continuous spectrum of the Cu(001) monolayer

The results of the calculation of electron bands of bound states that cross the edge of the continuous spectrum for the (001) fcc copper monolayer are presented for the first time. The calculations are performed in the local approximation for the exchange and correlations using the film variant of the Green’s function technique. Symmetry of electron states near the edge of the continuous spectrum is explored. It is found that there are bound states along the $ \bar \sum $ \bar \sum direction of the two-dimensional Brillouin zone of the Cu(001) monolayer that are embedded in the continuum of delocalized states of the continuous spectrum. Along the $ \bar \Delta $ \bar \Delta and $ \bar Y $ \bar Y directions, bands of bound states turn into resonance states after crossing the edge of the continuous spectrum.     

On the theory of conductivity of anisotropic composites: A linear-concentration approximation of inclusions

A general approach is proposed for calculating the conductivity of anisotropic composites with a low concentration of inclusions of an arbitrary shape. The contribution to effective conductivity [^(s)] _e\hat \sigma _e, which is linear in concentration, is expressed in terms of the polarizability of the inclusion defined in a certain transformed system in which the inclusion is surrounded by an isotropic matrix. A transition to this system is performed using a symmetry transformation that does not change the equations for direct current.     

“Magic numbers” in the melting of a cluster of point charges on a sphere

The thermodynamic properties of a cluster of point Coulomb charges on a sphere have been analyzed using the Monte Carlo method for the number of charges 20 ≤ N ≤ 90. The ground state of the system of charges is described in the model of a closed quasi-two-dimensional triangular lattice with topological defects. We have determined the dependence of the Lindeman parameter δ_L of this system on N and on the dimensionless parameter $ \tilde T $ \tilde T , which is proportional to the temperature T and to the radius R of the cluster: $ \tilde T = {{k_B T\varepsilon R} \mathord{\left/ {\vphantom {{k_B T\varepsilon R} {e^2 }}} \right. \kern-\nulldelimiterspace} {e^2 }} $ \tilde T = {{k_B T\varepsilon R} \mathord{\left/ {\vphantom {{k_B T\varepsilon R} {e^2 }}} \right. \kern-\nulldelimiterspace} {e^2 }} , where ∈ is the dielectric constant of the medium and e is the charge of a particle. The “magic numbers,” i.e., the N values, for which the melting point of the closed triangular lattice of charges is much higher than those for neighboring N values, have been found. The evolution of the lattice-melting mechanisms with an increase in the number of charges N in a mesoscopic cluster has been analyzed. For N ≤ 32, the melting of the lattice does not involve dislocations (nontopological melting); this behavior of the mesoscopic system of charges on the sphere differs from the behavior of the extended planar two-dimensional system. At N ≳ 50, melting is accompanied by the formation of dislocations. The mechanism of dislocation-free non-topological melting of a closed lattice, which occurs at small N values and is associated with the cooperative rotational motion of “rings” of particles, has been analyzed. The model has various implementations in the mesoscopic region; in particular, it describes the system of electrons over the liquid-helium cluster, the liquid-helium cluster with incorporated charged particles, a multielectron bubble in liquid helium, a charged quantum dot, etc.     

Confinement singularities in two-pion decays of mesons

We consider as an example the two-pion decay of the ρ meson, the ³ S ₁ q $ \bar q $ \bar q state of the constituent quarks—the decay being determined by the transition q $ \bar q $ \bar q → ππ contains information about confinement interactions. One can specify in this decay two types of transitions: (i) the bremsstrahlung radiation of a pion q → q + π (or $ \bar q $ \bar q → $ \bar q $ \bar q + π) with a subsequent fusion q $ \bar q $ \bar q → π, and (ii) the direct transition q $ \bar q $ \bar q → ππ. We demonstrate how in the amplitudes of the corresponding transitions the quark singularities have to disappear, i.e., what is the way the quark confinement at relatively short distances can be realized. We calculate and estimate the contributions of processes with bremsstrahlung radiation of the pion and of the direct transition q $ \bar q $ \bar q → ππ. The estimates demonstrate that the processes involving the direct transition q $ \bar q $ \bar q → ππ are necessary, but they cannot be determined unambiguously by the decay ρ(775) → ππ. We conclude that for the determination of the q $ \bar q $ \bar q → ππ transition more complete data on the resonance decays into the ππ channels are needed than those available at the moment.