The Parameter Planes of λz<Superscript><Emphasis Type="Italic">m</Emphasis></Superscript> exp(z) for <Emphasis Type="Italic">m</Emphasis> ≥ 2*

We consider the families of entire transcendental maps given by F _λ,m (z) = λz ^m exp(z), where m ≥ 2. All functions F _λ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A ^*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A ^*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of which serve as a model for F _λ,m , in the sense that they are related by means of quasiconformal surgery to F _λ,m . Both authors were supported by MTM2005-02139/Consolider (including a FEDER contribution) and CIRIT 2005 SGR01028. The first author was also supported by MTM2006-05849/Consolider (including a FEDER contribution).     

Determination of absorption cross sections for oxygen molecules in the Schumann-Runge band region at high temperatures

We have measured the absorption cross sections of oxygen molecules in oxygen and in an oxygen-argon mixture heated by a shock wave, in the wavelength range 190–250 nm at temperatures of 1500–7000 K, for thermal equilibrium conditions behind the shock wave front. Analysis of the absorption cross sections obtained allowed us to select a data set that adequately describes the absorption characteristics of the electronic transition X³Σ _g ⁻ → B³Σ _u ⁻ for the oxygen molecule. In order to approximate the temperature dependence of these cross sections at a temperature of 1500–4500 K, we chose the function σ(λ, T) = σ₀(λ)(1 − exp (−θ/T)) exp (− n*θ/T) where θ₀ = 1.4·10⁻¹⁷, 1.4·10⁻¹⁷, 1.2·10^{− 17}, and 1.3·10⁻¹⁷ cm², n* = 3.1, 4.1, 5.6, and 7.47 for wavelengths 190, 210, 230, and 250 nm, respectively; θ = 2240 K is the characteristic temperature of the O₂ molecules. The approximation error was 19–25% and did not exceed the experimental error. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 1, pp. 13–17, January–February, 2006.     

Measurement of OH spatially resolved spectrum in a wire-plate pulsed streamer discharge

In this study, spatially resolved measurements of the emission intensity of OH (A²Σ↦X²Π, 0-0) and the vibrational temperature of N₂ (C) have been performed during a positive pulsed streamer discharge with a wire-plate electrode configuration at atmospheric pressure. The effects of pulse peak voltage, pulse repetition rate and the added O₂ flow rate on the spatial distributions of the emission intensity of OH (A²Σ↦X²Π, 0-0) and the vibrational temperatures of N₂ (C) perpendicular to the wire in the direction towards the plate (in the radial direction) are investigated. It has been found that the emission intensity of OH (A²Σ↦X²Π, 0-0) increases with increasing pulse peak voltage and pulse repetition rate and decreases with increasing the distance from the wire electrode. When the different oxygen flows are added in N₂ and H₂O mixture gas, the emission intensity of OH (A²Σ↦X²Π, 0-0) decreases with increasing the flow rate of oxygen. The vibrational temperature of N₂ (C) is nearly independent of pulsed peak voltage and pulsed repetition rate, but increases with increasing the added O₂ flow rate and keeps almost constant in the radial direction under the present experimental conditions. This measurement plays a crucial role in understanding the discharge characters of pulsed streamer discharge and establishing the molecule reaction dynamics model of pulsed streamer discharge.     

Electromagnetic polarizabilities of the nucleon and properties of the σ-meson pole contribution

The t-channel contribution to the difference of electromagnetic polarizabilities of the nucleon, (α - β)^t, can be quantitatively understood in terms of a σ-meson pole in the complex t-plane of the invariant scattering amplitude A ₁(s, t) with properties of the σ-meson as given by the quark-level Nambu-Jona-Lasinio model (NJL). Equivalently, this quantity may be understood in terms of a cut in the complex t-plane where the properties of the σ-meson are taken from the ππ → σ → ππ, γγ → σ → ππ and Nˉ → σ → ππ reactions. This equivalence may be understood as a sum rule where the properties of the σ-meson as predicted by the NJL model are related to the f ₀(600) particle observed in the three reactions. In the following, we describe details of the derivation of (α - β)^t making use of predictions of the quark-level NJL model for the σ-meson mass. An erratum to this article is available at .     

Trapped modes in a T-shaped waveguide

We study the discrete spectrum of the Laplace operator with the Dirichlet boundary conditions in a plane waveguide made of a band of unit width and half-band of width h perpendicular to it. The existence of critical width h _* ∈ (1,2] is established: in the case of h ∈ (0, h_*), the discrete spectrum σ _d ^h of the problem contains only one eigenvalur λ₁ ^h , but σ _d ^h = ⊘ at h ≥ h _*. The asymptotics of the eigenvalue λ₁ ^h at h → + 0 is found.     

Non-steady-state photo-EMF in nanostructured GaN and polypyrrole within porous matrices

We report an experimental investigation of the non-steady-state photoelectromotive force in nanostructured GaN within porous glass and polypyrrole within chrysotile asbestos. The samples are illuminated by an oscillating interference pattern created by two coherent light beams and the alternating current is detected as a response of the material. Dependences of the signal amplitude versus temporal and spatial frequencies, light intensity, and temperature are studied for two wavelengths λ=442 and 532 nm. The conductivity of the GaN composite is measured: σ=(1.1–1.6)×10⁻¹⁰ Ω⁻¹ cm⁻¹ (λ=442 nm, I ₀=0.045–0.19 W/cm², T=293 K) and σ=(3.5–4.6)×10⁻¹⁰ Ω⁻¹ cm⁻¹ (λ=532 nm, I ₀=2.3 W/cm², T=249–388 K). The diffusion length of photocarriers in polypyrrole nanowires is also estimated: L _D=0.18 μm.     

The Discrete Spectrum in the Gaps of the Continuous One for Non-Signdefinite Perturbations with a Large Coupling Constant

Given two selfadjoint operators A and V=V ₊ -V _-, we study the motion of the eigenvalues of the operator A(t)=A-tV as t increases. Let α>0 and let λ be a regular point for A. We consider the quantities N ₊(λ,α), N _-(λ,α), N ₀(λ,α) defined as the number of the eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right or change the direction of their motion exactly at point λ, respectively, as t increases from 0 to α>0. An abstract theorem on the asymptotics for these quantities is presented. Applications to Schr?dinger operators and its generalizations are given. Received: 9 April 1997 / Accepted: 26 August 1997     

Chain orientation in natural rubber,Part I: The inverse yielding effect

Inhomogeneous deformations are observed in stretched natural rubber of different crosslink density; the conditions of observation, nucleation and propagation are given in the first part of the paper. In samples of low crosslink density these inhomogeneities recall necking observed in others materials and in glassy polymers when the materials are drawn above a critical draw ratio. The difference is that in natural rubbers, NR, they nucleate and propagate at constant stress during unloading. This phenomenon, called inverse yielding appears during recovery only if the samples have been drawn previously in the hardening domain. During necking propagation the stress is constant. The mechanical and crystallinity properties of samples with and without inverse yielding are studied as a function of draw ratio, crosslink density and temperature. In the second part of the paper this transition zone (neck) of thickness 2 mm is studied by WAXS at the synchrotron source. From the orientation of NR crystallites and from the orientation of the stearic acid (2%, present in this type of rubber) we conclude that the deformation in the neck follows the flow lines. From the local crystallinity of the NR crystallites one deduces the local draw ratio across this transition zone. We suggest that in all these rubbers, which present a plateau of the recovery stress strain curve, micronecking exists. This effect is discussed in the framework of the Flory theory.-1     

Charge distribution studies in the fast-neutron-induced fission of <Superscript>232</Superscript>Th, <Superscript>238</Superscript>U, <Superscript>240</Superscript>Pu and <Superscript>244</Superscript>Cm

Charge distribution studies for heavy-mass fission products were carried out in the fast-neutron-induced fission of ²³²Th, ²³⁸U, ²⁴⁰Pu and ²⁴⁴Cm using radiochemical and gamma-ray spectrometric techniques. The width parameter( σ_Z/σ_A), the most probable charge/mass ( Z _P/A _P), the charge polarization (ΔZ) and the slope of charge polarization [ δ(ΔZ)/δA ^′] as a function of the fragment mass (A ^′) were deduced. The average charge dispersion parameter ( 〈σ_Z〉) and proton odd-even effect ( δ_p) were also obtained for these fissioning systems. The 〈σ_Z〉 and δ_p values in the fissioning systems ²⁴¹Pu ^* and ²⁴⁵Cm ^* were determined for the first time. The δ(ΔZ)/δA ^′ value is also determined for the first time in the fissioning systems ²³⁹U ^* , ²⁴¹Pu ^* and ²⁴⁵Cm ^* . These data along with the literature data for even-Z fissioning systems such as ²³⁰Th ^* , ²³²Th ^* , ²³³U ^* , ²³⁴U ^* , ²³⁶U ^* , ²³⁸U ^* , ²³⁹Pu ^* , ²⁴⁰Pu*, ²⁴²Pu ^* , ²⁴⁶Cm ^* , ²⁵⁰Cf ^* and ²⁵²Cf(SF) are discussed in terms of nuclear structure effect and dynamics of descent from the saddle to the scission point. The role of the excitation energy in low-energy fission is also discussed. Received: 26 July 2002 / Accepted: 3 December 2002 / Published online: 3 April 2003 RID="a" ID="a"Present address: Emeritus Scientist (CSIR) Bhabha Atomic Research Centre, Nuclear Recycle Group, WIP Building, Trombay, Mumbai-400085, India; e-mail: rhiyer@magnum. barc.ernet.in Communicated by D. Schwalm     

Field theoretic calculation of energy cascade rates in non-helical magnetohydrodynamic turbulence

Energy cascade rates and Kolmogorov’s constant for non-helical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimensiond = 3, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov’s constant for magnetohydrodynamics is approximately equal to that for fluid turbulence (≈ 1.6) for Alfvén ratio 05 ≤r _A ≤ ∞. For higher space-dimensions, the energy fluxes are qualitatively similar, and Kolmogorov’s constant varies asd ^1/3. For the normalized cross helicity σ_c →1, the cascade rates are proportional to (1 − σ_c)/(1 + σ_c , and the Kolmogorov’s constants vary significantly with σ_cc.     

Laser dye stability. Part 5

Photodegradation parameters that relate bleaching and absorption at the lasing wavelength λ_l have been examined for over 30 different coumarin and quinolone laser dyes in a number of solvents. Quinolone dyes were found to bleach faster than the coumarin dyes. The effect of chemical substituents was found to affect bleaching of the coumarin dyes only to a small (20%) extent in ethanol. The major effect of chemical substituents was in the conversion of a dye to products absorbing at λ_l. Effects of solvent, cover gas, and changes in fluorescent quantum yields are discussed. Of particular interest is the photodegradation parameterA, the ratio of the percent absorption at λ_l to the total input energy per dm³. Combined with τ, the total input energy per dm³ required for a laser to reach half its original intensity, it was found thatAτ=1.2±0.9 for all of the dyes independent of dye concentration in all of the solvents tested. It appears that where bleaching of the dye is only of the order of 10–20%, the absorption at λ_l is 1.2% when our dye laser has reached one-half of its initial output. It is consequently possible to estimate τ values of new dyes by the use ofA terms through the relationshipA ₁τ₁=A ₂τ₂ where τ₁ of Dye 1 has been calibrated in the same dye laser system.     

Saturation in diffractive deep inelastic eA scattering

In this paper, we investigate the saturation physics in diffractive deep inelastic electron-ion scattering. We estimate the energy and nuclear dependence of the ratio σ^diff/σ^tot and predict the x_ℙ and β behavior of the nuclear diffractive structure function F_2,A^D(3)(Q²,β,x_ℙ). Moreover, we analyze the ratio R^diff_A1,A2(Q²,β,x_ℙ)=F_2,A1^D(3)/F_2,A2^D(3), which probes the nuclear dependence of the structure of the pomeron. We show that saturation physics predicts that approximately 37% of the events observed at eRHIC should be diffractive.     

Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces

We consider continuous-spin models on the d-dimensional hypercubic lattice with the spins σ _x a priori uniformly distributed over the unit sphere in ℝ ⁿ (with n≥2) and the interaction energy having two parts: a short-range part, represented by a potential Φ, and a long-range antiferromagnetic part λ|x−y|^−s σ _x ⋅σ _y for some exponent s>d and λ≥0. We assume that Φ is twice continuously differentiable, finite range and invariant under rigid rotations of all spins. For d≥1, s∈(d,d+2] and any λ>0, we then show that the expectation of each σ _x vanishes in all translation-invariant Gibbs states. In particular, the spontaneous magnetization is zero and block-spin averages vanish in all (translation invariant or not) Gibbs states. This contrasts the situation of λ=0 where the ferromagnetic nearest-neighbor systems in d≥3 exhibit strong magnetic order at sufficiently low temperatures. Our theorem extends an earlier result of A. van Enter ruling out magnetized states with uniformly positive two-point correlation functions.     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.     

New data for the 197Au(γ, nX) and 197Au(γ, 2nX) reaction cross sections

The results from experimental and theoretical studies of the total and partial cross sections of photoneutron reactions on the ¹⁹⁷Au isotope were analyzed. The cross sections for reactions σ(γ, nX) = σ(γ, n) + σ(γ, np) + … + σ(γ, 2nX) = σ(γ, 2n) + σ(γ, 2np) + … were evaluated in the energy range 7 ≤ E _γ ≤ 30 MeV using an approach free of the shortcomings of experimental photoneutron multiplicity sorting methods. The total photoneutron reaction cross sections σ^exp(γ, xn) = σ^exp(γ, nX) + 2σ^exp(γ, 2nX) + … = σ^exp(γ, n) + σ^exp(γ, np) + 2σ^exp(γ, 2n) + 2σ^exp(γ, 2np) + … were used as the initial experimental data. The contributions from the cross sections σ(γ, nX) and σ(γ, 2nX) to the cross sections σ^exp(γ, xn) were separated using the multiplicity transition functions F ₁ ^theor = σ^theor(γ, 1nX)/σ^theor(γ, xn) and F ₂ ^theor = σ^theor(γ, 2nX)/σ^theor(γ, xn), calculated within an updated version of the pre-equilibrium model of photonuclear reactions. New evaluated data for both partial reaction cross sections, i.e., σ^eval (γ, 1nX) = F ₁ ^theorσ^exp(γ, xn) and σ^eval(γ, 2nX) = F ₂ ^theorσ^exp(γ, xn), were obtained. The cross sections σeval(γ, nX) and σ^eval.(γ, 2nX) evaluated using the theoretically calculated functions F _1,2^theor are consistent with the Livermore data, but substantially contradict the Saclay data.     

Saturable absorbers for passive Q-switching of erbium lasers emitting in the region of 3 μm

The phototropic properties of Fe:ZnSe, Co:ZnSe, and Co:ZnS single crystals have been investigated. It is shown that these crystals can be used to advantage as the saturable absorbers in solid-state erbium lasers emitting in the region of the 3-μm range. The absorption cross sections of the ground states of the Co²⁺ ion in the ZnSe (σ_GSA = 11·10⁻²⁰ cm²) and ZnS (σ_GSA = 5.6·10⁻²⁰ cm²) crystals and of the Fe²⁺ ion in the ZnSe (σ_GSA = 50·10⁻²⁰ cm²) crystal at λ = 2.79 μm were determined experimentally. It has been established that the above-indicated crystals in the excited state absorb light weakly. The use of these crystals as passive Q switches made it possible to realize, for the first time, the regime of Q-switching of a Cr,Er:YSGG laser emitting at a wavelength of 2.79 μm. Single pulses with an energy of 60 mJ and a duration of 170 nsec were obtained in the regime of passive Q-switching. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 747–751, November–December, 2005.     

The superconducting properties of YBa2(Cu1−xMx)3O7 for M=Zn and Ni

Transverse and zero-field μSR measurements were made on YBa₂(Cu_1−xNi_x)₃O_7−y withx=0.1 and 0.2, and YBa₂(Cu_1−x Zn _x )₃O_7−y withx=0.03, 0.06, 0.1, and 0.16, wherey≈0.1. Since doping may lead to magnetic ordering this was searched for with both zero and transverse field μSR, but no evidence was found over the temperature range studied: 10–100 K. However, depolarization rates as functions of temperature were obtained, and the low temperature values of these are σ=3.2 μs⁻¹.1.6μs⁻¹, and 1 μs⁻¹ forx=0.01, and 0.2 Ni, respectively, and σ=0.8 μs⁻¹, 0.75 μs⁻¹, 0.65 μs⁻¹, and 0.4 μs⁻¹ forx=0.03, 0.06, 0.1, and 0.16 Zn, respectively. Estimates for the effect of decreasing electron concentration for Zn are made, but these alone do not account for the drop in σ. Estimates for the effect of scattering on λ and hence σ are made. The reduction in σ for Ni dopant is in surprisingly good agreement with these estimates. For Zn the order of magnitude is correct, but the relative lack of further change in σ after the effect of the first 0.03 addition seems to imply a saturation of the effect of scattering.     

Unparticle physics in the Moller scattering

We investigate the virtual effects of vector unparticles in Moller scattering. We derive the analytic expression for scattering amplitudes with unpolarized beams. We obtain 95% confidence level limits on the unparticle couplings λ_V and λ_A with integrated luminosity of L_int=50, 500 fb^-1 and , 300 and 500 GeV energies. We show that limits on λ_V are more sensitive than λ_A. PACS  14.80.-j; 12.90.+b; 13.66.-a     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.