Two mutually-repelling self-avoiding walks: A Monte Carlo study

We consider two self-avoiding walks (SAWs) on a square lattice, beginning simultaneously from two arbitrary nearest neighbours. The walks cross neither themselves nor each other, and grow simultaneously. Using Monte Carlo technique we study the variation, with the length N of the walks, of the average end-to-end distance 〈R_N〉 of each walk and of their average separation 〈S_N〉. We find 〈R_N²〉∞N^2ν, 〈S_N²〉∞N^2λ, where ν ≈ λ ≈ 0.75 for two ordinary SAWs and ν ≈ λ ≈ 0.67 for two growing SAWs in two dimensions. For two directed SAWs, we find 〈R_N∥/⊥²〉 ∞ N^2ν∥/⊥ and 〈S_N∥/⊥² 〉 ∞ N^2λ_∥/⊥, where ν_∥ ≈ 1.00, ν_⊥ ≈ 0.56, λ_∥ ≈ 0.50 and λ_⊥ ≈ 0.59 in two dimensions. We thus find an indirect excluded volume effect on one directed SAW, due to the other.     

From random to self-avoiding walks

A brief review will be given of the current situation in the theory of self-avoiding walks (SAWs). The Domb-Joyce model first introduced in 1972 consists of a random walk on a lattice in which eachN step configuration has a weighting factor Π _i=0 ^N?2 Π_j=i+2/N(1?ωδ_ij). Herei andj are the lattice sites occupied by the ith and jth points of the walk. When ω=0 the model reduces to a standard random walk, and when ω=1 it is a self-avoiding walk. The universality hypothesis of critical phenomena will be used to conjecture the behavior of the model as a function ofω for largeN. The implications for the theory of dilute polymer solutions will be indicated.     

Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints

We introduce a new Monte Carlo algorithm for generating self-avoiding walks of variable length and free endpoints. The algorithm works in the unorthodox ensemble consisting of all pairs of SAWs such that the total number of stepsN _tot in the two walks is fixed. The elementary moves of the algorithm are fixed-N (e.g., pivot) moves on the individual walks, and a novel join- and-cut move that concatenates the two walks and then cuts them at a random location. We analyze the dynamic critical behavior of the new algorithm, using a combination of rigorous, heuristic, and numerical methods. In two dimensions the autocorrelation time in CPU units grows as N^1.5, and the behavior improves in higher dimensions. This algorithm allows high-precision estimation of the critical exponent.     

Numerical study on surface acoustic wave method for determining Young's modulus of low-k films involved in multi-layered structures

The surface acoustic waves (SAWs) technique is becoming an attractive tool for accurately and nondestructively characterizing the mechanical property of the brittle low dielectric constant (low-k) thin film. The theoretical equations for describing SAWs propagating on the multi-layered structure are derived in this study. The dispersion features of SAWs propagating on different structures of low-k/SiO₂/Si substrate, SiO₂/low-k/Si substrate, low-k/Si substrate, and low-k/Cu/Si substrate are investigated to instruct an accurate and facile fitting process for determining Young's modulus of low-k films. The dependence of dispersion relation on the film thickness, elastic modulus of low-k materials as well as frequency are provided and discussed in detail. The study shows an obvious influence of layered structure on the dispersion relation of SAWs. For a fixed structure, the dispersion curvature increases with the decrease of Young's modulus of low-k films.     

Different self-avoiding walks on percolation clusters: A small-cell real-space renormalization-group study

We calculate the average number of stepsN for edge-to-edge, normal, and indefinitely growing self-avoiding walks (SAWs) on two-dimensional critical percolation clusters, using the real-space renormalization-group approach, with small H cells. Our results are of the formN=AL ^D _SAW+B, whereL is the end-to-end distance. Similarly to several deterministic fractals, the fractal dimensionsD _SAW for these three different kinds of SAWs are found to be equal, and the differences between them appear in the amplitudesA and in the correction termsB. This behavior is atributed to the hierarchical nature of the critical percolation cluster.     

Rovibrational spectrum and potential energy surface of the N2-N2O van der Waals complex

The rovibrational spectrum of the N₂-N₂O van der Waals complex has been recorded in the N₂O ν₁ region (∼1285 cm⁻¹) using a tunable diode laser spectrometer to probe a pulsed supersonic slit jet. The observed transitions together with the data observed previously in the N₂O ν₃ region are analyzed using a Watson S-reduced asymmetric rotor Hamiltonian. The rotational and centrifugal distortion constants for the ground and excited vibrational states are accurately determined. The band-origin of the spectrum is determined to be 1285.73964(14) cm⁻¹. A restricted two-dimensional intermolecular potential energy surface for a planar structure of N₂-N₂O has been calculated at the CCSD(T) level of theory with the aug-cc-pVDZ basis sets and a set of mid-bond functions. With the intermolecular distance fixed at the ground state value R = 3.6926 Å, the potential has a global minimum with a well depth of 326.64 cm⁻¹ at θ_N2 = 11.0° and θ_N2O = 84.3° and has a saddle point with a barrier height of 204.61 cm⁻¹ at θ_N2 = 97.4° and θ_N2O = 92.2°, where θ_N2(θ_N2O) is the enclosed angle between the N-N axis (N-N-O axis) and the intermolecular axis.     

Central limit theorem in quantum field theory,generalized partons and application to deep-inelastic scattering

We prove the following elementary theorem. Ifφ ¹,...,φ ^N is a sequence of fields having identical, thougharbitrary, interactions but not interacting with each other and 〈φ _n 〉0,i=1,...,N then the generating functional of the «average» field φ^(N) may be explicitly obtained and may be written in terms of the two-point function of any of the fields φ _i . The theorem is then applied to define generalized parton fields \(\psi _j = \sum\limits_{i = 1}^N {\psi _{ij} } /\sqrt N \) as «averages» of basic fieldsψ _ij havingarbitrary interactions but not interacting with each other. We show that in the limitN→∞ Bjorken scaling, as observed at energies not too high, may be obtained if only quanta associated with generalized parton fields are excited in the hadron by the virtual photonwith no reference to the details of the underlying dynamics. ForN<∞, and the excitation of other quanta as well lead to a systematic breaking of scale invariance and the details of the dynamics are necessarily recovered which are expected to be applicable at higher energy regimes.     

Electromigration and permeation of hydrogen and deuterium in silver

A steady state flow technique was used to measure the effective charge number (Z*) and permeability (N) of hydrogen and deuterium in silver. Over the range of temperature (485–720°C) and pressure (220–750 torr) the effective charge number is a constant. The interstitial impurity migrates in the direction of the electron wind with Z_H* = ?6·8 and Z_D* = ? 18. The values of Z* are of the same order as self-electromigration but the size of the isotope effect is surprising. The quantum theories used to explain the isotope effect for hydrogen electromigration in Fe and Ni appear to fail here. In order to determine the effective charge number is was necessary to measure the permeability. For both H₂ and D₂, the permeability in silver follows the equation N = N_O exp(? Q/RT) where N_0D = 2·39 ± 0·40, Q_D = 14400 ± 300, N_OH = 2·86 ± 0·70 and Q_H = 14200 ± 500. Here Q is in units of cal/mol and N is in units of cc(ntp)/(sec - atm² - cm) The isotope effect ratio N_H/N_D = 1·25 was smaller than the classically expected value of (2)^1/2, but could be explained by the theory of Ebisuzaki, Kass and O'Keeffe.     

Specific heat of NaNO2 near its transition points

Using an a.c. technique, the specific heat of NaNO₂ was measured as a function of temperature near its antiferroelectric-to-paraelectric phase transition point (T_N). The transition was found to be of the second order. The critical exponents are; α = 0·38 for ? = 2 × 10^?4 ～ 1 × 10^?1, and α′ = 0·18 for ? = ?2 × 10^?4 ～ ?3 × 10^?3. The critical exponents deduced from the scaling-law relations are roughly close to the values obtained from a random phase approximation for a system with an isotropic interaction. However, a difference was recognized between the observed exponent for the specific heat and the values theoretically given for T > T_N by the random phase approximation for a system with a short-range interaction or for a system with a long-range dipolar interaction. A thermodynamical analysis was made by using the generalized Pippard relation, and the present result was found to be consistent with the pressure dependence of the antiferroelectric transition point.     

Measurements and theoretical calculations of N2-broadening and N2-shift coefficients in the ν2 band of CH3D

In this paper, we report measured Lorentz N₂-broadening and N₂-induced pressure-shift coefficients of CH₃D in the ν₂ fundamental band using a multispectrum fitting technique. These measurements were made by analyzing 11 laboratory absorption spectra recorded at 0.0056 cm⁻¹ resolution using the McMath-Pierce Fourier transform spectrometer located at the National Solar Observatory on Kitt Peak, Arizona. The spectra were obtained using two absorption cells with path lengths of 10.2 and 25 cm. The total sample pressures ranged from 0.98 to 402.25 Torr with CH₃D volume mixing ratios of 0.01 in nitrogen. We have been able to determine the N₂ pressure-broadening coefficients of 368 ν₂ transitions with quantum numbers as high as J″ = 20 and K = 16, where K″ = K′ ≡ K (for a parallel band). The measured N₂-broadening coefficients range from 0.0248 to 0.0742 cm⁻¹ atm⁻¹ at 296 K. All the measured pressure-shifts are negative. The reported N₂-induced pressure-shift coefficients vary from about −0.0003 to −0.0094 cm⁻¹ atm⁻¹. We have examined the dependence of the measured broadening and shift parameters on the J″, and K quantum numbers and also developed empirical expressions to describe the broadening coefficients in terms of m (m = −J″, J″, and J″ + 1 in the ^QP-, ^QQ-, and ^QR-branch, respectively) and K. On average, the empirical expressions reproduce the measured broadening coefficients to within 4.7%. The N₂-broadening and pressure-shift coefficients were calculated on the basis of a semiclassical model of interacting linear molecules performed by considering in addition to the electrostatic contributions the atom-atom Lennard-Jones potential. The theoretical results of the broadening coefficients are in good overall agreement with the experimental data (8.7%). The N₂-pressure shifts whose vibrational contribution is derived from parameters fitted in the ^QQ-branch of self-induced shifts of CH₃D, are also in reasonable agreement with the scattered experimental data (20% in most cases).     

Different types of self-avoiding walks on deterministic fractals

Normal and indefinitely-growing (IG) self-avoiding walks (SAWs) are exactly enumerated on several deterministic fractals (the Manderbrot-Given curve with and without dangling bonds, and the 3-simplex). On then th fractal generation, of linear sizeL, the average number of steps behaves asymptotically as N=AL ^D _saw+B. In contrast to SAWs on regular lattices, on these factals IGSAWs and normal SAWs have the same fractal dimensionD _saw. However, they have different amplitudes (A) and correction terms (B).     

Application of a microscopic interacting boson model to single-closed-shell nuclei

The microscopic treatment of an extended IBM including the pairing vibrational modes is applied to single-closed-shell nuclei with N = 50 or Z = 50. The low-lying spectra in the N = 50 isotones are well described in terms of the quadrupole phonon and the pairing vibration. The Sn isotopes roughly resemble the N = 50 isotones. The behavior of the 0₂⁺, 0₃⁺ and 2₁⁺ levels can be explained fairly well by the present model. Introduction of the pairing-vibrational modes into the IBM is essential for describing the single-closed-shell nuclei.     

Quark microscopic picture for vector and pseudoscalar mesons in the nucleon and their quasielastic knockout by high-energy electrons

A technique for projecting a multiquark wave function in the microscopic model of a ³P⁰ scalar fluctuation onto the virtual-decay channels N → N + ρ and N → N + π is formulated (at a more general level for the latter than previously). The amplitude for the electromagnetic transition ρ + γ _T ^* → π in electron-induced quasielastic rho-meson knockout followed by rho-meson conversion to a pion is considered. Theoretical results obtained in this way are contrasted against available experimental data, and reasonable agreement is found for cross-section values. This confirms a universal character of the ³P₀ model. The precision of relevant experiments is as yet insufficient for comparing the momentum distribution of the rho meson from the channel N → N + ρ with its theoretical counterpart.     

Statistics of self-avoiding walks on random lattices

The statistics of directed self-avoiding walks (SAWs) on randomly bond diluted square lattices have been solved exactly and a computer simulation study of the statistics of ordinary SAWs on diluted square lattices has also been performed. The configurational averaging has been performed here over the logarithms of the distribution functions. We find that the critical behaviour remains unchanged below a certain dilution concentrationp ^*, dependent on the length of the chains considered (p ^*=0 forN), and a crossover to a higher order critical behaviour occurs beyond that point.     

Finite energy sum rules for π-N backward scattering

Finite energy sum rules for the A and S,π-N scattering amplitudes are saturated in the region ?0.4 GeV²< u <0 with a number of s andt channel resonances. It turns out that one needs a rather large π—π s wave contribution, to get agreement with the high energy Regge pole analysis, which explains the dip structure in π⁺p scattering atu ₀=?0.15 GeV² by a zero in theN _α contribution. The coupling of theN _α trajectory seems to be much stronger than the coupling of theN _γ andΔ _δ trajectories.     

Vibration-rotation bands of nitrous oxide: 4.1 micron region

The infrared spectrum of nitrous oxide has been measured and analyzed from 2265 cm^?1 to 2615 cm^?1. Newly refined effective rotational constants for twenty-one vibrational states of ¹⁴N₂O, three vibrational states each of ¹⁴N₂¹⁸O and ¹⁵N¹⁴N¹⁶O, two states of ¹⁴N¹⁵N¹⁶O and one state of ¹⁴N₂¹⁷O have been calculated.The most interesting features observed are two Δ-Σ “forbidden” bands, 04^2c0-00⁰0 and 12^2c0-00⁰0. These bands occur because of Coriolis interaction between unperturbed vibrational states having l = 0 and l = 2.     

Dynamic 13C NMR spectroscopy

Dynamic ¹³C NMR spectroscopy is a recent addition to the tools available to chemists to investigate dynamic processes in molecules. The ¹³C spectra are not complicated by coupling and separation of the signals is the order of five times as large (in Hz). Consequently the temperature range over which meaningful measurements can be obtained is increased. There is therefore a marked increase in the dynamic range and accuracy of the measurements. Both very slow processes, e.g. 0.017 s^?1 for N,N-dimethylformamide and very fast processes, e.g. ΔG³ = 17.6 kJ mol^?1 for cycloocta-1,3,5-triene can be examined. In addition the technique is becoming very important in observing dynamic processes in metal carbonyls.     

Multispectrum analysis of the ν4 band of CH3CN: Positions, intensities, self- and N2-broadening, and pressure-induced shifts

A multispectrum nonlinear least-squares fitting technique was applied to measure accurate zero-pressure line center positions, Lorentz self- and nitrogen (N₂)-broadened half-width coefficients, and self- and N₂-pressure-induced shift coefficients for over 700 transitions in the parallel ν₄ band of CH₃CN near 920 cm⁻¹. Fifteen high-resolution (0.0016 cm⁻¹) laboratory absorption spectra of pure and N₂-broadened CH₃CN recorded at room temperature using the Bruker IFS 125HR Fourier transform spectrometer located at the Pacific Northwest National Laboratory (PNNL) in Richland, Washington, USA, were analyzed simultaneously assuming standard Voigt line shapes. Short spectral intervals containing manifolds of transitions from the same value of J were fitted together. In all, high-precision line parameters were obtained for P(44)-P(3) and R(0)-R(46) manifolds. As part of the analysis, quantum assignments were extended, and the total internal partition function sum was calculated for four isotopologs: ¹²CH₃¹²CN, ¹³CH₃¹²CN, ¹²CH₃¹³CN, and ¹³CH₃¹³CN. Measurements of N₂ broadening, self-broadening, N₂-shift, and self-shift coefficients for transitions with J up to 48 and K up to 12 were measured for the first time in the mid-infrared. Self-broadened half-width coefficients were found to be very large (up to ∼2 cm⁻¹ atm⁻¹ at 296 K). Ratios of self-broadened half-width coefficients to N₂-broadened half-width coefficients show a compact distribution with rotational quantum number in both the P and R branches that range from ∼4.5 to 14 with maxima near ∣m∣=24, where m=−J″, J″, and J″+1 for P, Q, and R lines, respectively. Pressure-induced shifts for N₂ are small (few exceed ±0.006 cm⁻¹ atm⁻¹ at 294 K) and are both positive and negative. In contrast, self-shift coefficients are large (maxima of about ±0.08 cm⁻¹ atm⁻¹ at 294 K) and are both positive and negative as a function of rotational quantum numbers. The present measured half-widths and pressure shifts in ν₄ were compared with corresponding measurements of rotational transitions.     

A study of meson-baryon couplings in the constituent quark model

Within the framework of the constituent quark model we discuss the effects of different types of meson-baryon-baryon vertex operators on the form factors and the coupling strengths of the lowest-lying positive and negative parity non-strange baryons. We compare the quark pair creation model (³P₀-model) with the SU(6)-model in which mesons are treated as elementary fields that directly couple to the quarks. The latter model is employed both in the so-called static limit and in a modification motivated by Galilei invariance. It is demonstrated that the inclusion of non-static effects simulates some features of the³P₀ vertex. Especially the reaction πN→ππN is found to be very sensitive to the different assumptions on the dynamics of theq¯q pair creation process. More indirect hints for the internal structure of the mesons might be obtained from the predicted asymmetry for the two form factors ofN→Δ+π andΔ→N+π, which occurs in the³P₀-model, only.