Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.     

On the mixed nature of the 740 cm band in wurtzite GaN films: A polarized Raman scattering investigation

A detailed study of the polarized Raman scattering of wurtzite GaN films is presented, focusing on the nature of the band centered at 740 cm⁻¹ observed in the X(Z, Z)X configuration. The origin of this band is ascribed to the mixed contribution of the A₁ and E₁ longitudinal phonon modes coupled with the free carrier excitation. The spectral profile of the 740 cm⁻¹ Raman band has been successfully reconstructed through a linear combination of the A₁-E₁ longitudinal phonon plasmon-coupled modes, leading to a free carrier concentration in good agreement with Hall effect measurements.     

A kinetic study of the thermal decomposition process of potassium metabisulfite: Estimation of distributed reactivity model

The thermal decomposition kinetics of potassium metabisulfite was studied by thermogravimetric (TG) and differential thermogravimetric (DTG) techniques using non-isothermal experiments. The apparent activation energy (E_a) is determined using the differential (Friedman) isoconversional method. The results of the Friedman's isoconversional analysis of the TG data suggests that the investigated decomposition process follows a single-step reaction and the observed apparent activation energy was determined as 122.4±2.1 kJ mol⁻¹. A kinetic rate equation was derived for the decomposition process of potassium metabisulfite with contracting area model, f(α)=2(1−α)^1/2, which is established using the Malek's kinetic procedure. The value of pre-exponential factor (A) is also evaluated and was found to be A=1.37×10¹² min⁻¹. By applying the Miura's procedure the distributed reactivity model (DRM) for investigated decomposition process was established. From the dependence α versus E_a, the experimental distribution curve of apparent activation energies, f(E_a), was estimated. By applying the non-linear least-squares analysis, it was found that the Gaussian distribution model (with distribution parameters E₀=121.3 kJ mol⁻¹ and σ=1.5 kJ mol⁻¹) represents the best reactivity model for describing the investigated process. Using the Miura's method, the A values were estimated at five different heating rates and the average A values are plotted against E_a. The linear relationship between the A and E_a values was established (compensation effect). Also, it was concluded that the E_a values calculated by the Friedman's method and estimated distribution curve, f(E_a), are correct even in the case when the investigated decomposition process occurs through the single-step reaction mechanism.     

An analysis of the new pion form factor data

A form factor F(t) for the pion is constructed which is compatible with analyticity and the data in the space-like and time-like region. For the mean square pion radius 〈r²〉 = (0.46_?0.08^+0.06) fm² is obtained. Typical errors of the extrapolated F(t) are given (e.g. F(t =?8 GeV²/c²) = 0.07_?0.10^+0.04). Assuming F(t) ≈ β/(?t)^α at the end of the space-like data region we obtain β = 0.31, α = 0.81 for t in GeV²/c² together with the error contours of (α, β). No conclusive answer on the existence of zeroes of F(t) can be given.     

The AE-XA1 System of CaOCH3

We have recorded laser excitation spectra of the CaOCH₃ free radical in a laser ablation molecular beam apparatus, at a spectral resolution of about 0.010 cm⁻¹ and a rotational temperature estimated at 15 K. The two spin-orbit components of the A²E-X²A₁ 0₀⁰ origin band between 625 and 630 nm have been analyzed. Five main subbands were revealed, with ΔK=+1 and K″=0,±1,±2. There was clear evidence of lambda-doubling in the A²E_1/2-X²A₁ 0₀⁰ (F′₁) K′=+1←K″=0 component. A nonlinear least-squares fitting program based on the model developed by Endo et al. [Y. Endo, S. Saito, and E. Hirota, J. Chem. Phys.81, 122-135 (1984)] fit the experimental data (514 A-X lines, N″≤37) with a root mean square deviation of 0.003 cm⁻¹, using known molecular constants of the ground state. The main vibronic (T₀=15 925.1232(5) cm⁻¹), spin-orbit (aζ_ed=66.974 48(51) cm⁻¹), Coriolis (Aζ_t=5.437 30(24)) cm⁻¹, rotational (A=5.439 97(24) cm⁻¹, B=0.117 884(2) cm⁻¹), and fine structure constants (ε₁=−8.208(14)×10⁻³ cm⁻¹, h₁=1.50(12)×10⁻⁴ cm⁻¹, ε_aa=3.58(89)×10⁻³ cm⁻¹, ε_bc=3.20(76)×10⁻³ cm⁻¹) for the excited state have been obtained.     

Effect of kink-rounding barriers on step edge fluctuations

The effect that an additional energy barrier E_kr for step adatoms moving around kinks has on equilibrium step edge fluctuations is explored using scaling arguments and kinetic Monte Carlo simulations. When mass transport is through step edge diffusion, the time correlation function of the step fluctuations behaves as C(t)=A(T)t^1/4. At low temperatures the prefactor A(T) shows Arrhenius behavior with an activation energy (E_det+3?)/4 if E_kr<? and (E_det+E_kr+2?)/4 if E_kr>?, where ? is the kink energy and E_det is the barrier for detachment of a step adatom from a kink. We point out that the assumption of an Einstein relation for step edge diffusion has lead to an incorrect interpretation of step fluctuation experiments, and explain why such a relation does not hold. The theory is applied to experimental results on Pt(1 1 1) and Cu(1 0 0).     

Optical and electrical characterization of cadmium selenide doped with cobalt

The optical and electrical properties of Co²⁺ ions in CdSe have been investigated. Absorption, photoluminescence, electron paramagnetic resonance, and Hall measurements were used to characterize a cobalt-doped (1×10¹⁹ cm⁻³) single crystal. Infrared absorption and emission spectra associated with transitions between the ⁴A₂(F) ground state and the ⁴T₁(F) and ⁴T₂(F) excited states are described. At 10 K, spin-orbit splittings result in three structured absorption bands associated with the ⁴A₂(F) to ⁴T₁(F) transition having zero-phonon lines at 4926, 5101, and 5724 cm⁻¹. The ⁴A₂(F) to ⁴T₂(F) transition shows two zero-phonon lines at 2874 and 3286 cm⁻¹, also accompanied by vibronic structure. Intrinsic lattice modes explain most of the sharp-line structure observed at low temperature, except for a subset of peaks where local modes (25-30 cm⁻¹) are invoked. Using below-band-gap light, selective excitation allows detection of the ⁴T₁(F) to ⁴A₂(F) recombination at liquid-helium temperatures. The activation of free carriers in our n-type material containing shallow donors is affected by the presence of cobalt, and we find the Co^+/++ level to be about 34 meV below the conduction band of CdSe.     

Fluctuations of trading volume in a stock market

We consider the probability distribution function of the trading volume and the volume changes in the Korean stock market. The probability distribution function of the trading volume shows double peaks and follows a power law, P(V/〈V〉)∼(V/〈V〉)^−α at the tail part of the distribution with α=4.15(4) for the KOSPI (Korea composite Stock Price Index) and α=4.22(2) for the KOSDAQ (Korea Securities Dealers Automated Quotations), where V is the trading volume and 〈V〉 is the monthly average value of the trading volume. The second peaks originate from the increasing trends of the average volume. The probability distribution function of the volume changes also follows a power law, , where V_r=V(t)−V(t−T) and T is a time lag. The exponents β depend on the time lag T. We observe that the exponents β for the KOSDAQ are larger than those for the KOSPI.     

Spectroscopy of AlO: Combined analysis of the AΠi → XΣ and BΣ → XΣ transitions

A combined analysis of the A²Π_i → X²Σ⁺ and B²Σ⁺ → X²Σ⁺ band systems of AlO, involving 21,500 line assignments, has been performed. The analysis indicates that the previously reported γ values of the B²Σ⁺ state are questionable. The present analysis shows that γ(B²Σ⁺) ≈ 0.014 cm⁻¹, essentially independent of the vibrational level. The positive sign is consistent with second order interaction with the higher-lying C²Π_r and lower-lying A²Π_i states. It also appears that many of the previously reported γ and γ_D values of X²Σ⁺ (v > 0) are doubtful. In fact, γ(X²Σ⁺) is observed to become increasingly negative for v″ > 1, due to second order interaction with the low-lying A²Π_i state. The present results are based on models where the hyperfine structure of the ²Σ⁺ states has been taken into account explicitly. Intensity patterns of the branches of the B²Σ⁺ → X²Σ⁺ system have been shown to be influenced by the case bβ_S coupling in the ground state v = 0,1 levels. This gives rise to intensity differences of around 10 percent in the R₁/R₂ and P₁/P₂ doublet components. The synthesized intensity patterns are fully in accord with the F₁/F₂ assignments of the present work.     

The Electronic Transition Moment Function for the BΠ-XΔ System of TiO

Several vibronic bands associated with v′=0, 1, and 2 for the B³Π-X³Δ transition of TiO have been observed using a dispersed laser induced fluorescence (DLIF) technique. From intensity distributions of the DLIF spectra, the dependence of the electronic transition moment R_e(r) for the B³Π-X³Δ system was determined as a function of the internuclear distance r. For the determination of the R_e(r) function, a merged fit of the observed distributions, the reported radiative lifetimes of three vibrational levels in the B³Π state, and the reported value of R_e(r) for the (0, 0) band were performed; R_e(r) was determined as R_e(r)=1.3723(79)[1−0.316(81)(r−r₀)+2.0(10)(r−r₀)²](r₀=1.6648 Å and 1.5131 Å≤r≤1.8636 Å). The r-dependence of R_e(r) was much smaller than the reported theoretical predictions. The obtained values of R_e(r) were analyzed simultaneously with the hyperfine coupling constants for the X³Δ state and the spin-orbit constants for the X³Δ and B³Π states to assess the ionic and orbital characters. It was found that the r-dependence of R_e(r) could be accounted for by both the configuration interaction in the B³Π state and the polarization in the unpaired 9σ and 4π orbitals.     

Fourier transform emission spectroscopy of the EΠ-XΣ transition of CaH and CaD

The emission spectra of CaH and CaD have been recorded at high resolution using a Fourier transform spectrometer and bands belonging to the E²Π-X²Σ⁺ transition have been measured in the 20 100-20 700 cm⁻¹ region. A rotational analysis of 0-0 and 1-1 bands of both the isotopologues has been carried out. The present measurements have been combined with the previously available pure rotation and vibration-rotation data to provide improved spectroscopic constants for the E²Π state. The constants ΔG(½) = 1199.8867(34) cm⁻¹, B_e = 4.345032(49) cm⁻¹, α_e = 0.122115(92) cm⁻¹, r_e = 1.986633(11) Å for CaH, and ΔG(½)=868.7438(46) cm⁻¹, B_e = 2.212496(51) cm⁻¹, α_e = 0.036509(97) cm⁻¹, r_e = 1.993396(23) Å for CaD have been determined.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

Type I FA (Rb, Cs) and II FA (Li, Na) tunable laser activities and donor-acceptor properties of O and O at KCl (001) surface: first principle calculations

Type I F_A (Rb⁺, Cs⁺) and II F_A (Li⁺, Na⁺) tunable laser activities, adsorptivity and donor-acceptor properties of O and O⁻ adsorbates at the flat surface of KCl crystal were investigated using an embedded cluster model and ab initio methods of molecular electronic structure calculations. Ion clusters were embedded in a simulated Coulomb field that closely approximates the Madelung field of the host surface, and the nearest neighbor ions to the defect site were allowed to relax to equilibrium. Based on the calculated Stokes shifted optical transition bands, F_A tunable laser activities were found to be inversely proportional to the size of the dopant cation (Li⁺, Na⁺, Rb⁺, Cs⁺) relative to the host cation (K⁺). This relation was explained in terms of the axial perturbation of the impurity cation. The probability of orientational bleaching attributed to the RES saddle point ion configuration along the 〈110〉 axis was found to be inversely proportional to the size of the dopant cation, with activation energy barriers of ca. 0.44-3.34 eV. Surface relaxation energies of type II F_A centers were more important than those of type I F_A centers. In terms of defect formation energies, the products of type II F_A center imperfection were more stable than those of type I F_A. The difference between F or F_A band energies and exciton bands depended almost exclusively on the size of the positive ion species. As far as the adsorptivity of O and O⁻ is concerned, the results confirm that surface imperfection enhances the adsorption energies by ca. 4.38-16.37 eV. O and O⁻ penetrate through the defect-containing surface. The energy gap between the adsorbate and the defect containing surface and the donor-acceptor property of adsorbate play the dominant role in the course of adsorbate substrate interactions and the results were explained in terms of electrostatic potential curves and Mulliken population analysis.     

On directly measuring relative Fermi energies of noble metals and their alloys

We present the first evidence of direct measurement of relative Fermi energies in alloys and between pure metals. From applying the “atomic” concept of core hole final state screening, the Auger energy shift of noble metal A equals E_F^A?E_F(x). High resolution Auger shifts in P_1?x^tCu_x,Au_xCu_1?x and Au_xAg_1?x demonstrate experimental verification of this simple relation. We find E_F^CuE_F^Au ? ? 0.2 eV, and E_F^Pt ? E_F^Cu and E_F^Ag ? E_F^Au.     

A Laser-Induced Fluorescence Study of the Visible Spectrum of Rhodium Monoxide

A first analysis of an electronic spectrum of RhO is presented. The molecular species has been produced in a jet-cooled molecular beam following reaction in a laser ablation plasma. Laser excitation spectra have been recorded between 600 and 640 nm at 200 MHz resolution. Two transitions have been identified of ²Π_r(a)-X⁴Σ⁻(b) type and six subbands have been rotationally analyzed, four being (0,0) components. Molecular parameters for the X⁴Σ ⁻ state are B₀=0.41320 cm⁻¹, λ₀=−0.5733 cm⁻¹, γ₀=−0.10276 cm⁻¹, and r₀=0.1717 nm. An analysis of the hyperfine structure involving the ¹⁰³Rh nucleus has been made. It shows that the ground state of RhO conforms to Hund's coupling case b_βJ with b=− 0.0203 cm⁻¹. Hyperfine effects in the excited states are negligible.     

Evolution of the nucleon structure in the lightest nuclei

We show that the pattern of the oscillation of the structure functions ratio r^A(x)=F₂^A/F₂^N(D) varies with A by changing the position of the cross-over point x₃ in which r^A(x)=1, unlike the pattern for nuclei with masses A>4, where only the amplitude of the oscillation changes. In particular we find that the pattern of F₂(x) modifications is controlled with the values (1−x₃)=0.32 (D/N), 0.16 (³He/D) and 0.08 (⁴He/D). The obtained results follow from the relativistic approach and allow one to define the class of modifications of the bound nucleon structure.     

Fourier Transform Emission Spectroscopy of the FΣ-XΣ System of RuN

Emission spectra of RuN have been recorded at high resolution in the region 12 000-35 000 cm⁻¹ using a Fourier transform spectrometer. The molecules were excited in a ruthenium hollow cathode lamp in the presence of about 2.5 Torr of Ne and 5 m Torr of N₂. New bands with origins near 17 758.1, 18 866.4, 19 800.4 and 20 721.5 cm⁻¹ have been assigned as the 0-1, 0-0, 1-0, and 2-0 bands of a new ²Σ⁺-²Σ⁺ system with the lower state as the ground state. This transition has been labeled as F²Σ⁺-X²Σ⁺, with the F²Σ⁺ state arising from the 1σ²2σ²1π⁴1δ⁴4σ¹ configuration. A rotational analysis of these bands has been carried out and spectroscopic constants have been extracted. The principal equilibrium constants for the ground state of RuN are ΔG(1/2)″=1108.3235(22) cm⁻¹, B_e″=0.5545023(42) cm⁻¹, α_e″=0.0034468(57) cm⁻¹, r_e″=1.5714269(60) Å, while the equilibrium constants for the excited state are ω_e′=946.8471(40) cm⁻¹, ω_ex_e′=6.4229(14) cm⁻¹, B_e′=0.50085(21) cm⁻¹, α_e′=0.00375(10) cm⁻¹, r_e′=1.65345(34) Å. This transition is analogous to the E²Σ⁺-X²Σ⁺ system of RhC (W. J. Balfour et al., J. Mol. Spectrosc.198, 393 (1999)).     

The high-resolution infrared spectrum of pyrrole between 900 and 1500 cm revisited

The Fourier transform gas-phase infrared spectrum of pyrrole, C₄H₅N, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 900-1500 cm⁻¹ spectral region. Four fundamental bands, ν₈(A₁; 1016.9 cm⁻¹), ν₂₃(B₂; 1049.1 cm⁻¹), ν₇(A₁; 1074.6 cm⁻¹), ν₂₀(B₂; 1424.4 cm⁻¹) and the overtone band 2ν₁₆(A₁; 962.7 cm⁻¹) have been analysed using the Watson model. The ν₈ and 2ν₁₆ bands are unperturbed; the ν₇ and ν₂₃ bands are locally perturbed, while the ν₂₀ band is globally perturbed by weak c-Coriolis resonance. Upper state vibrational term values, and rotational and centrifugal distortion constants, have been obtained from fits using S-reduction and I^r-representation as well as A-reduction and III^r-representation. A set of ground state rotational and centrifugal distortion constants using A-reduction was obtained from a simultaneous fit of ground state combination differences from all five bands and previous microwave and millimetre-wave data.     

Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(S_α(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)^2H+σX(τ)dB_H(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.