Beam quality of radial Gaussian Schell-model array beams

Taking the Rayleigh range z_R and the M²-factor as the characteristic parameters of beam quality, the beam quality of radial Gaussian Schell-model (GSM) array beams is studied. The analytical expressions for the z_R and the M²-factor of radial GSM array beams are derived. It is shown that for the superposition of the cross-spectral density function z_R is longer and the M²-factor is lower than that for the superposition of the intensity. For the two types of superposition, z_R increases and the M²-factor decreases with increase in beam coherence parameter, and both z_R and the M²-factor increase with increase in inverse radial fill-factor. For the superposition of the cross-spectral density function, z_R increases and the M²-factor decreases with increase in beam number, while for the superposition of the intensity both the z_R and M²-factor are independent of the beam number.     

On the mass operator in a diagonally disordered binary alloy

It is shown that the multiple-occupancy corrections imply identities between skeleton diagrams generating a perturbation calculus for the mass operator M. Self-consistent equations for M_ii, M_i, i+1 are obtained. The corrections to the obtained M begin with terms of order z^-6 where z is the coordination number.     

Beam quality of truncated laser beams with amplitude modulations and phase fluctuations in turbulence

The closed-form expressions for the Rayleigh range z_R and the M²-factor of truncated laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) in turbulence are derived, and the beam quality is studied by taking the z_R and the M²-factor as the characteristic parameters of beam quality. The M²-factor of truncated laser beams with AMs and PFs is always larger than that of truncated Gaussian beams both in free space and in turbulence. However, in turbulence the beam quality of truncated laser beams with AMs and PFs may be better than that of truncated Gaussian beams if the z_R is taken as the characteristic parameter of beam quality. For laser beams with AMs and PFs in turbulence, the beam quality expressed in terms of z_R is consistent with that in terms of the M²-factor versus the phase fluctuation parameter α, but not versus the intensity modulation parameter σ_A. The beam quality of truncated laser beams with AMs and PFs is less sensitive to turbulence than that of truncated Gaussian beams. The beam quality of laser beams with smaller α and larger σ_A is less affected by turbulence than those with larger α and smaller σ_A.     

Molecular-weight scaling of coexistence curves for monodisperse polymer solutions

The available data for the polymer volume fraction along the coexistence curves for monodisperse solutions of polystyrene in methylcyclohexane are used to derive the exponent z ≈ 0.61 such that the “correct” order parameter is only a function of ?M^Z (M is the polymer's molecular weight while ? is the reduced temperature). It is shown that a knowledge of the “correct” order parameter is unnecessary for a determination of z which is expected to be universal, i.e. independent of the polymer-solvent system.     

Search for strong gravitational lensing effect in the current GRB data of BATSE

Because gamma-ray bursts(GRBs)trace the high-z universe,there is an appreciable probability for a GRB to be gravitational lensed by galaxies in the universe.Herein we consider the gravitational lensing effect of GRBs contributed by the dark matter halos in galaxies.Assuming that all halos have the singular isothermal sphere(SIS)mass profile in the mass range 1010h?1M?M2×1013h?1M?and all GRB samples follow the intrinsic redshift distribution and luminosity function derived from the Swift LGRBs sample,we calculated the gravitational lensing probability in BATSE,Swift/BAT and Fermi/GBM GRBs,respectively.With an derived probability result in BATSE GRBs,we searched for lensed GRB pairs in the BATSE5B GRB Spectral catalog.The search did not find any convincing gravitationally lensed events.We discuss our result and future observations for GRB lensing observation.     

Regular and chaotic motion of coupled rotators

We consider a classical Hamiltonian H = L_z+M_z+L_xM_x, where the components of L and M satisfy Poisson brackets similar to those of angular momenta. There are three constants of motion: H, L² and M². By studying Poincaré surfaces of section, we find that the motion is regular when L² or M² is very small or very large. It is chaotic when both L² and M² have intermediate values. The interest of this model lies in its quantization, which involves finite matrices only.     

Thiolated cyclodextrin self-assembled monolayer-like characterized with secondary ion mass spectrometry

In the work the focus is on the preparation of self-assembled monolayer-like films consisting of thiolated cyclodextrin on gold substrate and a characterization by using secondary ion mass spectrometry. The short (1 min) and long (1 h) time preparations of self-assembled monolayer-like films, resulting in submonolayer and monolayer regimes, are investigated, respectively. The observed species of thiolated cyclodextrin (M as molecular ion) self-assembled monolayer-like films are assigned to three groups: Au_xH_yS_z clusters, fragments with origin in cyclodextrin molecule associated with Au, and molecular ions. The group of Au_xH_yS_z (x = 2-17, y = 0-2, z = 1-5) clusters have higher intensities than other species in the positive and even more in negative mass spectra. Interestingly, the dependence between the number of Au and S atoms shows that with the increasing size of Au_xH_yS_z clusters up to 11 Au atoms, the number of associated S atoms is also increasing and then decreasing. Molecular species as (M−S+H)Na⁺, (M+H)Na⁺, AuMNa⁺, (M₂−S)Na⁺, and M₂Na⁺ are determined, and also in cationized forms with K⁺. The intensities of thiolated cyclodextrin fragments at the long time preparation are approximately 10 times higher than the intensities of the same fragments observed at the short time. The largest observed ions in thiolated cyclodextrin self-assembled monolayer-like films are AuM₂ and Au₂M. The thiolated cyclodextrin molecular ions are compared with hexadecanethiol molecular ions in the form of Au_xM_w where the values of x and w are smaller for thiolated cyclodextrin than for hexadecanethiol. This result is supported with larger, more compact, and more stabile thiolated cyclodextrin molecule.     

The exact solution of an elimination problem in kinetic theory: I. The one-dimensional hard sphere gas

A class of initial value problems for a one-dimensional hard sphere gas is considered where a specified particle has a given distribution f⁽¹⁾(z₁; 0) and the rest are in equilibrium at t=0. An exact expansion is obtained for a certain n-particle reduced distribution function f⁽ⁿ⁾(z₁;…;z_n; t) in terms of the 1-particle reduced distribution function f⁽¹⁾(z₁; t) for the specified particle by starting with separate expressions for these functions in terms of f⁽¹⁾(z₁; 0). Expansions for the corresponding cluster functions are first obtained and then graph theoretic methods applied to obtain a solution.     

QCD predictions for the Q2 dependence of quark and gluon fragmentation functions using Altarelli-Parisi type equations

In the leading logarithmic approximation, the fragmentation functions of quarks and gluons are investigated using Altarelli-Parisi type equations. Using a new method to make the Mellin transformation, the equation is solved. Analytic expressions for the fragmentation functions near z = 0 and z = 1 are also given. Finally, numerical results for the fragmentation functions D_q^π, D_q^K are presented for different Q².     

Weak-coupling expansion of the low-lying energy values in the SU(2) gauge theory on a torus

Relying on analytic results obtained previously, we complete the one-loop computation of the low-lying energy values of the SU(2) gauge theory in an L × L × L periodic box. The expansions are then rewritten in terms of the universal parameter z = M(0⁺) · L (M(0⁺): energy gap in the J^p = 0⁺ sector). We find that the crossover from small-volume to large-volume behaviour is likely to take place at z ? 2. Furthermore, near the crossover, the lowest energy levels (above the ground state) in the 0⁺ sector and the 2⁺ sector are practically degenerate. In each of these sectors there is one more state at about 1.5 · M(0⁺). In the 0^? sector, on the other hand, the lowest energy value is greater than 3 · M(0⁺).     

Higher order field equations II; Limit properties of green's functions

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions G^M_R(x) and G^M_A(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions G^M_R(x) and G^M_A(x) approach the Green's functions Δ_R(x) and Δ_A(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of G^M_A(x) and G^M_A(x) is the same as of Δ_R(x) and Δ_A(x) - and also the same as for D_R(x) and D_A(x) for t→ ± ∞, where D_R and D_A are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense.     

Etude en fonction du temps de l'oxydation des magnetites substituees a l'aluminium et au chrome au moyen de la conductivite electrique

The oxidation of substituted magnetites (Fe²⁺Fe_2?x³⁺M_x³⁺O₄^2?(O < x < 2) into the lacunar phase γ(Fe_1?z³⁺M_z³⁺)O₃^{2 ?} (x = 3z) was followed over time by electrical conductivity over the temperature r Curves σ = f(t) are different according to whether we deal with an n or p-type spinel. However, for intermediate substitution rates (1,1 < x < 1,8), n-type ferrichromites are oxidized after an initial period in the same way as p-type semi-conductors.For the initial period, the chemisorption kinetics of oxygen upon these n-type samples, reduced under vacuum, was found to follow Elovich's law with an activation energy depending on the degree of coverage.     

Lambda polarization in inclusive K−p interactions at 10 and 16 GeV/c

A strong negative transverse polarization P_z is found for forward produced lambdas observed in 10 and 16 GeV/c K^?p interactions. This indicates that exchanges of natural spin-parity are dominant in the production process. Using the polarization results, the $\text{d}\text{σ}\text{d}\text{u′}$ distributions for natural and unnatural spin-parity exchanges are derived. For unnatural exchanges, a dip is observed at u′?0.3 GeV², which can be explained as a nonsense-wrong-signature zero of the N_β trajectory. The value of P_z for forward producted lambdas is constant with energy. This is in agreement with the triple-Regge model prediction, as is the fact that P_z is constant as a function of $\text{M}{}^2\text{s}$. The two non-transverse polarization components, P_x and P_y, have been measured and are found to be consistent with zero for all x values, unlike P_z.     

The higgs boson mass from precision electroweak data

We present a new global fit to precision electroweak data, including new low- and high-energy data and analyzing the radiative corrections arising from the minimal symmetry breaking sectors of the Standard Model (SM) and its supersymmetric extension (MSSM). It is shown that present data favor a Higgs mass ofO(M _z):M _H=76 _?50 ⁺¹⁵² GeV. We confront our analysis with (meta) stability and perturbative bounds on the SM Higgs mass, and the theoretical upper bound on the MSSM Higgs mass. Present data do not discriminate significantly between the SM and MSSM Higgs mass ranges. We comment in passing on the sensitivity of the Higgs mass determination to the values ofα(M _z) andα _s(M _z).     

Equation of state and quantal crossover of the XY model in a longitudinal magnetic field

The equation of state of the XY model in a longitudinal (Γ) and transverse field (B) is investigated in the vicinity of a multicritical point (Γ_c, T =0) using the renormalization group method developed recently by the author and K. Walasek. For Γ = Γ_c a quantal crossover behaviour of the form H = M_{R³ψ (z)} is obtained, where H ～ B, M_R denotes the transverse magnetization, z ～ TM_R^?/βq, while ?,β_q are crossover and multicritical exponents, respectively.     

Measuring entanglement-induced quantum correlations in the oscillatory motion of a trapped ion

The preparation of a wide class of entangled vibrational states involving two or three phononic modes of a three-dimensional trapped ion has been reported in the literature from both theoretical and experimental points of view. Here, the time evolution of such a system from an initial condition wherein two oscillatory modes (M _x, M _y) are reciprocally entangled and both are disentangled to the third mode (M _z) is studied. By coupling one of the entangled oscillators (M _x) with the third oscillator (M _z), a correlation between the two uncoupled modes (M _y, M _z) is induced, well visible when the mean value of a suitable operator is considered. A method of measuring the expectation value of a vibrational observable is briefly sketched and then exploited in order to reveal such nonclassical behavior.     

Period doubling in maps with a maximum of order z

We consider the scaling behaviour in period-doubling systems, exemplified by the one-dimensional map χ_n+1 = 1 − λ|χ_n|^z, which has a maximum of order z (z > 1). The Feigenbaum scaling factors α and δ are studied as functions of z, and more generally the scaling functions 1/σ and ƒ(a). In particular, using the universal functions g(x) and h(x) we establish the inequality δ < α^z, which implies that δ remains finite (≲ 30) in the limit z → ∞.     

Haldane gap in a S=1 exchange model with long-range interactions

The ground-state properties of the S = 1 Haldane- Shastry model are studied using a modified Lanczos algorithm and diagonalizing exactly small chains. We find evidence that, as for the antiferromagnetic Heisenberg model, the spectrum shows a gap, in contrast to the {ie1-1} case. The correlation functions < S ^z(0)S ^z(m) > decay exponentially for large m. We find that the correlation functions for the Haldane-Shastry model decay faster than for the Heisenberg model. We estimate the infinite system limit for the groundstate energy, value of the gap and correlation functions.     

Heavy particles and the ϱ parameter in the standard model

A new formalism is presented for the calculation of the contribution δ? to ? = M_w²/M_z²cos²θ_w from heavy particles transforming according to arbitrary representations of SU(2) × U(1). A conjecture for the necessary and sufficient conditions that δ??0 for all values of masses and mixing angles within a particular multiplet is formulated. A number of examples are given (all consistent with the conjecture) and the significance of improved knowledge of ? vis à vis the possible existence of undiscovered heavy particles discussed.