Serre duality for polarised symplectic manifolds

Let F be a polarisation, in the sense of Kostant, of a 2n-dimensional symplectic manifold M, and let L be a complex line bundle with flat connection along F. We prove, under suitable conditions, that the r-dim. cohomology of C^∞L-valued half forms normal to F with forms on F as coefficients, has as dual space the (n?r)-dim. cohomology of compactly supported distributional L¹-valued half forms normal to F with forms on F as coefficients. We deduce that the spectrum of an F-preserving function ? is the same when quantised on the highest C^∞ cohomology as when quantised on the compactly supported distributional sections.     

Generalizing some properties of short range classical solutions to Yang-Mills theory

We extend a theorem which states that for classical solutions of Yang-Mills theory, the field G_μν has to decrease at least as fast as the source S_μ at spatial infinity, provided G_μν decreases exponentially [G_μν ～ exp(?Mr)]. This generalization encompasses all decreases G_μν ～ exp(?Mr^η) with η > 0, r→∞. This is done by assuming an integral representation for A_μ, the vector potential, and imposing some regularity conditions on A_μ, valid as r→∞.     

The effect of screening on the x and Q2 behaviour of F2 slopes

A systematic study of ϖF₂(x, Q²)/ϖ ln Q² and ϖ ln F₂(x, Q²)/ϖ ln(1/x) is carried out in pQCD taking screening corrections into account. The result of calculations, which are different from the non-screened DGLAP prediction, are compared and shown to agree with the available experimental data as well as a pseudo data base generated from the ALLM'97 parameterization. This pseudo data base allows us to study in detail our predictions over a wider kinematic region than is available experimentally, and allows us to make suggestions for future experiments. Our results are compared with the GRV'94 parameterization (which is used as an input for our calculations) as well as the recently proposed MRST structure functions.     

A local-world node deleting evolving network model

A new type network growth rule which comprises node addition with the concept of local-world connectivity and node deleting is studied. A series of theoretical analysis and numerical simulation to the LWD network are conducted in this Letter. Firstly, the degree distribution p(k) of this network changes no longer pure scale free but truncates by an exponential tail and the truncation in p(k) increases as pa decreases. Secondly, the connectivity is tighter, as the local-world size M increases. Thirdly, the average path length L increases and the clustering coefficient 〈C〉 decreases as generally node deleting increases. Finally, 〈C〉 trends up when the local-world size M increases, so as to kmax. Hence, the expanding local-world can compensate the infection of the node deleting.     

Majority-vote on directed Erd?s-Rényi random graphs

Through Monte Carlo Simulation, the well-known majority-vote model has been studied with noise on directed random graphs. In order to characterize completely the observed order-disorder phase transition, the critical noise parameter q_c, as well as the critical exponents β/ν, γ/ν and 1/ν have been calculated as a function of the connectivity z of the random graph.     

The ν9 + ν11 − ν11, ν10 + ν11 − ν11 hot band system in allene-d4

The hot band system ν₉ + ν₁₁ ? ν₁₁, ν₁₀ + ν₁₁ ? ν₁₁ in allene-d₄ was studied at a resolution near 0.010 cm^?1. About 1500 partly overlapped hot band rotational lines were assigned and fitted to a model taking into account z-Coriolis resonance between the combination levels ν₉ + ν₁₁ and ν₁₀ + ν₁₁ as well as vibrational l-type resonances within these levels. Upperstate constants have been derived from an analysis in which the constants for the ν₁₁ level were constrained. A detailed study of rotational as well as vibrational l-type doublings occurring in the KΔK = ?1 subband is presented, and the sign of vibrational l-type doubling constants for the ν₁₀ + ν₁₁ level is determined. A localized (x, y)-Coriolis resonance between ν₁₀ + ν₁₁ and ν₄(B₁) + ν₁₁ is discussed and the interaction parameter is obtained as well as some constants for ν₄ + ν₁₁.     

Nuclear Quadrupole Interactions in Nuclear Quadrupole Resonance Detection of Energetic and Controlled Materials: Theoretical Study

There has been a growing interest in nuclear quadrupole resonance (NQR) techniques useful for the detection of explosives and drugs in solid state systems. This paper uses the first-principles one-electron Hartree?CFock theoretical method to study the nuclear quadrupole interaction parameters e ² qQ and ?? for the ¹⁴N nuclei in the explosives RDX and ??-HMX as well as the drugs cocaine and heroin. It has been found in our earlier published investigations reviewed here that there is very good agreement for our calculated e ² qQ and ?? for ¹⁴N, for all these four systems, and experiment. We also present our unpublished theoretical results for cocaine with an HCl molecule attached. We successfully explain quantitatively the drastic decrease in e ² qQ in going to cocaine-HCl from cocaine-free base as well as the observed substantial increase in ?? and discuss the implications of these dramatic changes for NQR detection in general.     

Optimal bounds for the pion form factor from analyticity and experimental data

Optimal bounds for the pion electromagnetic form factor F(t) below threshold and on the pion mean-square charge radius 〈r_π²〉 = 6F'(0) are derived. Use is made of analyticity arguments and of experimental data on F(t) from e⁺e^? → π⁺π^? as well as e^?p → e^?nπ⁺. The method accounts in an approximate way for the statistical errors of the experimental information. Numerical results for F(t) are calculated for the CEA as well as the DESY electroproduction data.     

Statistics of event by event fluctuations

Following Hwa and Wu [R.C. Hwa, Y. Wu, Phys. Rev. C 60 (1999) 0544904], we characterize the fluctuation behavior of the hadron density produced during quark-hadron phase transition, as modeled by a 2D Ising model. Using a recently developed discrete wavelet based approach, the scaling behavior is studied at temperatures below, at and above T_c. At T_c, we find the Hurst exponent H?1, as observed in a recent experimental finding [L. Qin, M. Ta-chung, Phys. Rev. D 72 (2005) 014011]. However, as compared to the R/S analysis, which yields only the Hurst exponent, our local approach finds a correlation behavior and multifractal properties at temperatures below, at and above T_c. We find evidence for a transition from Brownian to fractional Browian motion near T_c. The correlation behavior compares well with the results obtained from a continuous wavelet based average wavelet co-efficient method, as well as with Fourier power spectral analysis.     

A string-like self-dual solution of Yang-Mills theory

We attempt to obtain Nielsen-Olesen strings in pure Yang-Mills theory without Higgs scalars. This is inspired by recent work interpreting the Prasad-Sommerfield monopole as a static self-dual Yang-Mills solution in which A₄^a plays the role of the Higgs field. In similar fashion, we make A₃^aA₄^a serve as the two required isovector fields in an ansatz independent of x₃ and x₄. The condition of self-duality results in a single Painlevé equation of the third kind (or equivalently, a radial sinh-Gordon equation in 2 + 0 dimensions), the solution of which determines A_μ^a. We make use of the extensive analysis of the former equation carried out by Wu, McCoy and collaborators in the context of the scaling limit of the two-dimensional Ising model. Their simplest solution yields a flux value of ?2π/e just as in the Nielsen-Olesen model and flux is quantized in multiples of this unit. The string tension (action per unit time per unit distance) diverges as r^?2 (In r)^?2 as r → 0 for the same Wu-McCoy solution.     

The kinetics of vacancy annihilation and short range order formation in Ni 11.4 at % Cr

In Ni-Cr alloys annealing after quenching from high temperatures leads to an increase of electrical resistivity which is attributed to a short range order state often denoted as K-state. Here the kinetics of the formation of the K-state in a Ni 10% Cr alloy is investigated by resistivity measurements for different quenching and annealing temperatures. The measurements are analyzed by an extended Schulze-Lücke method [22] which assumes that the rate of resistivity change is proportional to the vacancy concentration and that this rate as well as the rate of vacancy annihilation is described by a chemical rate equation.This analysis allowed a quantitative determination of the parameters determining the kinetics of short range order formation under different vacancy concentrations as well as the kinetics of annealing out of the quenched-in surplus vacancies. Among other quantities this treatment yielded the activation energies for vacancy formation H_F = 1.16 eV, for vacancy migration H_M = 1.56 eV and, as an independent cross check, for self diffusion H_D = 2.73 eV in good agreement with H_F + H_M = 2.72 eV.     

Composition law of cardinal ordering permutations

In this paper the theorems that determine composition laws both cardinal ordering permutations and their inverses are proven. So, the relative position of points in an hs-periodic orbit is completely known as well as which order those points are visited, no matter how the hs-periodic orbit emerges, be it through a period doubling cascade (s=2ⁿ) of as the h-periodic orbit or a primary window (like saddle-node bifurcation cascade with h=2ⁿ) or a secondary window (the birth of an s-periodic window inside the h-periodic one). Certainly, period doubling cascade orbits are particular cases with h=2 and s=2ⁿ. Both composition laws are also shown in algorithmic way for easy use.     

Theory of the period-doubling phenomenon of one-dimensional mappings based on the parameter dependence

A theory is presented of the period-doubling phenomenon of one-dimensional mappings of the form x_n+1 = F(x_n, r), which is different from that of Feigenbaum mainly in that it is based on the r dependence of various quantities rather than on their x dependence. Consequently, it enables us to evaluate, for example, the Lyapunov numbers of periodic orbits as a function of r as well as the Feigenbaum ratio. It is shown that the results of our theory are in good agreement with those of numerical simulations.     

Luminescence of MeFX : Eu2+ (Me = Sr,Ba; X = Cl,Br)

Compounds of the type MeFX : Eu²⁺ with Me = Sr, Ba and X = C1, Br are efficient phosphors. Emission consists of both a 5d-4f band as well as 4f-4f lines, their relative intensities being strongly dependent on host lattice and temperature.     

Binding energies of hypernuclei and ΛN interaction

A central ΛN potential V _ΛN that describes, in the limits of experimental errors, the binding energies of three-, four-, and five-particle ground and excited states of hypernuclei, as well as energy and angular dependence of Λp scattering cross sections, is found on the basis of a conjoint analysis of binding energies of 1s-shell hypernuclei and Λp scattering. The reliability and accuracy of three-, four-, and five-particle calculations of hypernuclei and related nuclear systems are assured by the estimation of, an upper, as well as a lower bound of energy. In the framework of the model Λ+core, V _ΛN agrees with binding energies of heavy hypernuclei.     

Quark trapping for lattice U(1) gauge fields

We show for lattice U(1) gauge fields in d = 3 dimensions, that 〈exp(i∮_CAdx)〉 ? exp (? const.T lnL), where C is a rectangle of dimension T × L, T ? L. This indicates quark trapping, by a potential at least as strong as Coulomb.     

Azimuthal correlations in 40 GeV/c π−p collisions and the independent cluster model

Data on azimuthal correlations and their rapidity dependence are presented in inclusive and semi-inclusive reactions π^?p → π⁺π⁺X,→ π^?π^?X and π⁺π^?X at 40 GeV/c. They show a long range as well as a short range effect. The short range effect, leading to different behaviour of dN/dφ near φ = 0 of like and unlike pion pairs is explained by identical and unidentical particle statistics. The predictions of the independent cluster model for the azimuthal asymmetry are in qualitative agreement with data of this experiment as well as those at 102 and 205 GeV/c.     

Semiconducting properties of pure and Mn-doped chromium disilicides

The phase analysis was carried out for the system (l?x) CrSi₂ + xMnSi₂ in the range 0?x?0.5 by X-ray technique. The solid solution Cr_1?xMn_xSi₂ was identified in the composition range 0?x?0.225, where the added Mn-atoms occupied substitutionally the Cr-atom sites in the CrSi₂ structure. Resistivity, Hall coefficient as well as thermoelectric power were measured as functions of temperature in the range, 80–1200 K and composition x in the single phase region, 0 ?x?0.225. The pure CrSi₂ (x = 0) was a p-type degenerate semiconductor, whose hole concentration was determined to be 7.7 × 10²⁰ cm^?3 at room temperature. Mn-atoms introduced in the CrSi₂ crystal were found to act as donors. The forbidden energy gap was determined to be 0.30 eV from the Hall-data in the intrinsic region. With increasing x, a conversion from p- into n-type semiconductor took place in Cr_1?xMn_xSi_y. From the analysis of Hall- as well as resistivity-data, the mobility ratio b was obtained as a function of composition x. It was revealed that b increased with increasing x from 0.01 for x = 0 to 0.12 for x = 0.182. The electron-hole concentration product could be expressed as $\text{np = 1.2 × 10}{}^{35}\text{T}{}^{35}\text{exp}\text{(?}\text{3480}\text{T}\text{)}$, and the hole mobility as $\text{μ}{}_{\mathrm{p}}\text{= 7.0 × 10}{}^4\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>3</mtext><mtext>2</mtext>}}$ in the acoustic scattering region. The effective mass of hole was found out to be 3.2 m₀ and independent of x, whereas that of electron varied from 20.2 m₀ for x = 0 to 7.5 m₀ for x = 0.182. When these parameters are used, the theoretical temperature variation of the thermoelectric power curve was found out to be in good agreement with the measurement.     

Possible reference method of total excitation energy partition between complementary fission fragments

A method of total excitation energy (TXE) partition between fully-accelerated fission fragments based exclusively on the systematic behaviour of experimental ν(A) (νH/νpair as a function of AH being parameterized) is proposed. This TXE partition method has the advantage to be not dependent on models and assumptions made at scission and in this sense it can be taken as a possible reference method. From this TXE partition applied on many fissioning systems a general parameterization of the fragment residual temperature ratio RT=TL/TH as a function of AH is obtained, giving the possibility to predict prompt fission quantities as a function of fragment. Other TXE partition methods (based on models and assumptions at scission or on equal residual temperatures of complementary fragments at full acceleration) are compared to this one, revealing limits of applicability as well as the sensibility of prompt neutron emission models to the TXE partition. The behaviour of experimental ν(A) with the increase of incident energy consisting in the multiplicity increase for heavy fragments only, is argued and entirely supported by the quantitative Point-by-Point model results of ν(A) describing very well the experimental ν(A) of ²³⁷Np(n, f) at 0.8 and 5.5 MeV incident energies.     

Doped graphene as a superconductor

We study s-wave superconductivity state in doped graphene within the extended attractive Hubbard model and BCS theory. We use the Green's function approach and coherent potential approximation. We obtain critical temperature of graphene, Tc, as a function of the impurity concentration, c, as well as impurity strength, δ. The results show that when c and δ, are increased, Tc remains finite and doped graphene can be a superconductor.