Asymptotic Behavior of Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum

In this paper, we study the one-dimensional Navier-Stokes equations connecting to vacuum state with a jump in density when the viscosity depends on the density. Precisely, when the viscosity coefficient μ(ρ) is proportional to ρ ^θ with θ > 0, where ρ is the density, we give the asymptotic behavior and the decay rate of the density function ρ(x, t). Furthermore, the behavior of the density function ρ(x, t) near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied. The analysis is based on some new mathematical techniques and some new useful estimates. This fills a final gap on studying Navier-Stokes equations with the viscosity coefficient μ(ρ) dependent on the density ρ.     

The Asymptotic Limits of Zero Modes of Massless Dirac Operators

Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q(x) are discussed, where α = (α₁, α₂, α₃) is the triple of 4 × 4 Dirac matrices, , and Q(x) = (q _jk (x)) is a 4 × 4 Hermitian matrix-valued function with | q _jk (x) | ≤ C 〈x〉^−ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of |x|² f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x).      

A study of the nuclear-medium influence on <Emphasis Type="Italic">ρ</Emphasis><Superscript>0</Superscript> neutrinoproduction

The nuclear effects in ρ ⁰-meson neutrino production are investigated using the data obtained with the SKAT bubble chamber. The nuclear-medium influence on the ρ ⁰ total yield and inclusive distributions on z = E _ρ /v and Feynman x _F variable is found to be approximately the same as for pions. It is shown that these distributions with increasing A tend to shift toward smaller values of z and x _F, thus indicating an increasing role of secondary intranuclear interactions. The predictions of a simple model incorporating the latter are found to be in qualitative agreement with experimental data. The text was submitted by the authors in English.     

Mixing and decays of ρ- and ω-mesons

Isospin-violating mixing of ρ- and ω-mesons is reconsidered in terms of propagators. Its influence on various pairs of (ρ,ω)-decays to the same final states is demonstrated. Some of them, (ρ,ω)↦π⁺π^- and (ρ,ω)↦πγ, have been earlier discussed in the literature, others (e.g., (ρ,ω)↦ηγ and (ρ,ω)↦e ⁺ e ^-) are new in this context. Changes in partial widths for all the decay pairs are shown to be correlated. The set of present experimental data, though yet inconclusive, provides some limits for the direct (ρω)-coupling and indirectly supports enhancement of ρ↦πγ in comparison with ρ^±↦π^±γ, though not so large as in some previous estimates. Received: 16 September 2002 / Accepted: 23 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: azimov@pa1400.spb.edu Communicated by V.V. Anisovich     

Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

The Landauer resistance of a one-dimensional metal with periodically spaced random impurities

We find the dependence of the ensemble-averaged resistance, 〈ρ _L〉, of a one-dimensional chain consisting of periodically spaced random delta-function potentials of the chain length L, the incident-electron energy, and the chain disorder parameter w. We show that generally the 〈ρ _L〉 vs L dependence can be written as a sum of three exponential functions, two of which tend to zero as L℩∞. Hence the asymptotic expression for 〈ρ _L〉 is always an exponential function of L. Such an expression for 〈ρ _L〉 means that the electronic states are indeed localized and makes it possible (which is important) to find the dependence of the localization radius on the incident-electron energy and the force with which an electron interacts with the sites of the chain. We also derive a recurrence representation for 〈ρ _L〉, which proves convenient in numerical calculations. Zh. éksp. Teor. Fiz. 111, 575–584 (February 1997)     

Equation for the Landauer resitivity in the case of multichannel scattering

Generalization of the Landauer resistivity ρ _N ^L is given for the case of multichannel scattering of a particle by the system of nonoverlapped N random potentials, depending on x − x _i and y, which are localized near the points x _i (i = 1,2,…N). It is shown that in this case a new resistivity ρ _N ^S appears, which is a power function of N. A recurrent equation is obtained for definition of the Landauer resistivity ρ _N ^L .     

Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature

We study the effect of an external field on (1 + 1) and (2 + 1) dimensional elastic manifolds, at zero temperature and with random bond disorder. Due to the glassy energy landscape the configuration of a manifold changes often in abrupt, “first order”-type of large jumps when the field is applied. First the scaling behavior of the energy gap between the global energy minimum and the next lowest minimum of the manifold is considered, by employing exact ground state calculations and an extreme statistics argument. The scaling has a logarithmic prefactor originating from the number of the minima in the landscape, and reads ΔE ₁∼L ^θ[ln(L _z L ^{- ζ})]^-1/2, where ζ is the roughness exponent and θ is the energy fluctuation exponent of the manifold, L is the linear size of the manifold, and L_z is the system height. The gap scaling is extended to the case of a finite external field and yields for the susceptibility of the manifolds ∼L ^{2D + 1 - θ}[(1 - ζ)ln(L)]^1/2. We also present a mean field argument for the finite size scaling of the first jump field, h ₁∼L ^{d - θ}. The implications to wetting in random systems, to finite-temperature behavior and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are discussed. Received December 2000 and Received in final form April 2001     

Experimental investigation of the angular dependence of photon-induced differential cross-sections of L X-rays from U,Th and Bi at 59.5 keV

Summary The differential cross-sections for the emission of L_ρ, L_α, L_β and L_γ groups of L X-ray lines from U, Th and Bi have been measured at different angles varying from 45° to 135° at intervals of 15°. The vacancies were created by 59.5 keV γ-rays from²⁴¹Am source and L X-rays were measured using a Si(Li) detector. It is found that the L_γ and L_β groups of L X-rays are isotropic, the L_ρ and L_α groups are anisotropic in the spatial distribution. The authors of this paper have agreed to not receive the proofs for correction.     

Frequency and spatial characteristics of the electrophysical parameters of a living tree trunk

The method of vertical electrical sounding is applied to derive the spatial characteristic of the dc resistivity ρ of a living pine trunk, ρ = L-0.85, and the frequency characteristic of the ac resistance R of the same pine trunk, R = f-0.053. The results are simulated by the methods of fractal geometry, according to which ρ = L ^{−h + 2} and $ R \sim f^{ - \tfrac{3} {h} + 1} $ R \sim f^{ - \tfrac{3} {h} + 1} , where h is the walk dimension of the electric current in the trunk. From comparison between the experimental and theoretical results, it follows that h = 2.85 and fractal dimension D = 1/h = 0.35. Since D = 1, conducting layers form a Cantor set.     

The energy—momentum tensor, the trace identity and the Casimir effect

The trace identity associated with the scale transformation x^Μ → x′^Μ = e^-ρx^Μ on the Lagrangian density for the noninteracting electromagnetic field in the co-variant gauge is shown to be violated on a single plate on which the Dirichlet boundary conditionA ^Μ(t, x¹, x², x³ = -a) = 0 is imposed. It is however respected in free space, i.e. in the absence of the plate. These results reinforce our assertions in an earlier paper where the same exercise was carried out using the Lagrangian density for the free, massive, real scalar field in 2 + 1 dimensions.     

Landauer resistance in the case of multichannel scattering

The Landauer resistance ρ _N ^L has been generalized to the case of multichannel scattering of a particle by the system of N nonoverlapping random potentials that are localized at the points x _i (i = 1, 2,..., N) and depend on x − x _i and y. It has been shown that, in this case, a new resistance ρ _N ^L appears, which is an exponential function of N. The recurrence equation for determining the Landauer resistance ρ _N ^L has been derived and its solution in the general case has been obtained.     

A role of the axial-vector mesons on the photon production in heavy-ion collisions and their relevant decays

A role of the axial-vector mesons, such as K₁ and a₁, on the emitted-photon spectrum in hot hadronic matter is studied through the channels πρ→a ₁→πγ and Kρ→K ₁→Kγ. Both channels could be dominant over the region lower than E _γ∼ 0.5 GeV, while the role of the K₁ meson is diminished in the higher E _γ region. This study is carried out with an SU _L(3) ⊗SU _R(3) effective chiral Lagrangian which includes vector and axial-vector mesons systematically and explains well their hadronic and radiative decays simultaneously. Received: 8 August 2001 / Accepted: 4 February 2002     

Photoproduction of baryons decaying into Nπ and Nη

A combined analysis of photoproduction data on γp↦ πN, ηN was performed including the data on KΛ and KΣ. The data are interpreted in an isobar model with s-channel baryon resonances and π, ρ (ω), K, and K ^* exchange in the t-channel. Three baryon resonances have a substantial coupling to ηN, the well-known N(1535)S ₁₁, N(1720)P ₁₃, and N(2070)D ₁₅. The inclusion of data with open strangeness reveals evidence for further new resonances, N(1840)P ₁₁, N(1875)D ₁₃ and, with weaker evidence, for N(2170)D ₁₃.     

Ubiquitousness of link-density and link-pattern communities in real-world networks

Many networks are characterized by the presence of communities, densely intra-connected groups with sparser inter-connections between groups. We propose a community overlay network representation to capture large-scale properties of communities. A community overlay G _o can be constructed upon a network G, called the underlying network, by (a) aggregating each community in G as a node in the overlay G _o ; (b) connecting two nodes in the overlay if the corresponding two communities in the underlying network have a number of direct links in between, (c) assigning to each node/link in the overlay a node/link weight, which represents e.g. the percentage of links in/between the corresponding underlying communities. The community overlays have been constructed upon a large number of real-world networks based on communities detected via five algorithms. Surprisingly, we find the following seemingly universal properties: (i) an overlay has a smaller degree-degree correlation than its underlying network ρ _o (D _l+, D _l−) < ρ(D _l+, D _l−) and is mostly disassortative ρ _o (D _l+, D _l−) < 0; (ii) a community containing a large number W _i of nodes tends to connect to many other communities ρ _o (W _i , D _i ) > 0. We explain the generic observation (i) by two facts: (1) degree-degree correlation or assortativity tends to be positively correlated with modularity; (2) by aggregating each community as a node, the modularity in the overlay is reduced and so is the assortativity. The observation (i) implies that the assortativity of a network depends on the aggregation level of the network representation, which is illustrated by the Internet topology at router and AS level.     

Shubnikov-de Haas effect in tricrystals of the system of alloys Bi1−x Sbx (x=0.1; 0.13) with n-type conductivity

The Shubnikov-de Haas effect has been investigated in tricrystals of the alloy system Bi_1−x Sb_x (x=0.1; 0.13) with n-type conductivity in stationary (up to 14 T) and pulsed (up to 40 T) magnetic fields. Reconstruction of the internal boundary of the tricrystals was observed, along with a number of new component oscillations of ρ(B) indicating a rotation of the constant-energy surfaces of the L electrons on the intercrystallite boundary at an angle of ∼74° in the binary-trigonal plane. Fiz. Tverd. Tela (St. Petersburg) 41, 991–993 (June 1999)     

f-α Spectrum of circle map

We present an analytic perturbative method for calculatingf(α) and the generalized dimensionD _q of the critical invariant circle of the polynomial circle map. The scaling behaviour is found to depend onz, the exponent defining the map. The asymptotic bounds of the scaling constantsα(z) andδ(z) are verified analytically.     

Equation of state of fluid helium at high temperatures and densities

Helium, hydrogen, and their isotopes are the simplest monoatomic and diatomic molecules. It is relatively easy to describe their properties using the basic principles of quantum mechanics. In condensed matter physics, hydrogen and helium serve as the models for the condensed matter properties at extreme conditions so that both experi- mental and theoretical physicists pay much attention to the study of their properties[1], especially the insulator-metal transition of hydrogen[2]. The aim to st…