Group velocity of modes and pulse distortion in dielectric optical waveguides

After a brief summary of the main factors causing pulse distortion in optical fibres, expressions are derived for phase velocity, group velocity and dispersion, that is velocity variation with frequency, of each mode. The analysis is carried out by making extensive use of the functiony(x) (y andx being the arguments of the first and second kind Bessel functions that appear in the solutions of Maxwell equations), that we call characteristic function. By using this function we obtain particularly simple and compact formulas that make easier the analysis of the behaviour of velocity and dispersion near and far from cut-off. It will also be seen that the ratio between the power propagating in the core,W ₁, and the power in the cladding,W ₂, for each mode takes a very simple form if expressed by means of the characteristic function: this fact permits a direct relation to be found between group velocity and power flow in an optical fibre. The study of the ratioW ₁/W ₂ will show that, contrary to expectation, for some modes, a substantial fraction of energy travels inside the core, even near cut-off. Expressions are given forW ₁/W ₂ at cut-off, and far from cut-off. Plots of velocity and dispersion are shown. On the grounds of the obtained results pulse distortion in optical fibres is discussed.     

Charge-Conjugation Invariance of the Spectator Equations

 In response to recent criticism, we show how to define the spectator equations for negative energies so that charge-conjugation invariance is preserved. The result, which emerges naturally from the application of spectator principles to systems of particles with negative energies, is to replace all factors of the external energies W _i by W _i ², insuring that the amplitudes are independent of the sign of the energies W _i . Received August 30, 1999; accepted for publication February 24, 2000     

Simple-Complex Fluid Transition in Microemulsions

The aim of this work was to study the rheological behavior of water in-oil microemulsion formulated with AOT (sodium bis(2-ethylhexyl) sulfoccinate) in isooctane over a temperature range from 25°C to 55°C for the oil/AOT volume fraction φ _m =0.1 and various AOT and H₂O molar ratios, W₀, ranging from 0 to 45. The apparent viscosity was measured vs. shear rate by a rotational concentric cylinder viscometer. It was shown that above s^?1, the solutions utilized behaved as Newtonian liquids. The absolute viscosities were deduced from the shear stress- shear rate rheograms. For W₀ < 17, the solutions behaved as simple fluids, where the viscosities decrease as the temperature increases. However, an opposite behavior was observed for W₀ > 17; the viscosity remained constant and then increased above a critical temperature, T_c, depending on W₀. For the molar ratio W_0,c = 17; the studied viscosity remained constant, η(W_0,c) = (1.17 ± 0.04) cP, for the temperature range studied. Thus, a simple–complex fluid transition was evident in the studied system. For the simple fluids, W₀ < W_0,c, the total activation energy vs. W₀ showed three linear parts. The different slopes were attributed to the change of the microscopic structure of the formed micelles. For the critical molar ratio W_0,c = 17, the total activation energy vanished. So, according to the Eyring lattice model, the jump of the formed micelles from one site to another was not permitted and the entire molecular groups were in vibration and rotation motions. For W₀ > W_0,c, where the formed micelles were fully hydrated, the relative viscosity of the studied solutions vs. temperature was fitted according a polynomial law, where the exponent was found to be dependent on W₀.     

Reinterpretation of narrow bandwidths in a model for 5d electrons in the heavy rare-earth metals

The narrow widthsW(1 eV) of 5d subbands occurring in a model for 5d electrons in the heavy rare-earth metals are reinterpreted as effective bandwidths for the purpose of determining the equilibrium occupation numbers of 5d subbands. It is shown that, if explicit consideration of interactions between 5d electrons is limited to intraatomic Coulomb interactions without exchange, then, to first order in the intraatomic repulsion energyU between 5d electrons, these effective widths satisfyW=W ₁-FU. HereW ₁ is a rectangular-subband equivalent of the overall subband width, andF is a numerical factor, the value of which depends on the local basis states and number of 5d electrons per atom. For the model being discussed it is estimated thatF=0.6±0.4. A valueW ₁ ^B 4 eV is inferred forW ₁ in Gd from results of band-structure calculations. The termFU cannot account for all of the difference betweenW ₁ ^B andW; the discrepancy is attributed to effects of correlation onW ₁.     

Testing the minimal supersymmetric standard model with the mass of the <Emphasis Type="Italic">W</Emphasis> boson

We review the currently most accurate evaluation of the W boson mass, M _W , in the minimal supersymmetric standard model (MSSM). It consists of a full one-loop calculation, including the complex phase dependence, all available MSSM two-loop corrections as well as the full standard model result. We analyse the impact of the phases in the scalar quark sector on M _W and compare the prediction for M _W based on all known higher-order contributions with the experimental results.      

The sign of interband interaction and stability of the superconducting ground state in the multiband model

Summary It is stressed that the stability of the superconducting ground state in the two-band model is guaranteed for both signs of the leading interband interactionW. Thereby the requirement for the energy minimum fixed the phase differences of two order parameters as |ϕ₁-ϕ₂|=0,2π, … ifW<0 and |ϕ₁-ϕ₂|=π 3π, … ifW>0, and this difference is reflected in the ground-state wave function.     

Normal and antinormal ordering of field operators in quantum optics

The relations between the probability distributionp n _vt of the number of photonsn _vt in a volumeV at timet and the probability distributions P_N(W) and P_A(W) of the integrated intensityW related to the normal and antinormal ordering of field operators and the relations between corresponding moments are studied for a field containingM modes. As the normally ordered correlations are measured with photodetectors and the antinormally ordered correlations are measured with quantum counters the relations betweenn _vt , P_N(W) and P_A(W) permit the statistical behaviour of light to be determined from measurements with photodetectors and quantum counters. The results obtained here are used for the superposition of coherent and thermal fields. It is also shown that the antinormal correlations depend explicitly on the number of modes and that in the classical limit, when the average photon occupation number per mode becomes large, the distributionsn _vt , P_N(W) and P_A(W) become equal.     

Magnetic and non-magnetic ground states of the Kondo lattice

We use the variational method to investigate the ground state phase diagram of the Kondo lattice Hamiltonian for arbitraryJ/W, and conduction electron concentrationn _c (J is the Kondo coupling andW the bandwidth). We are particularly interested in the question under which circumstances the globally singlet (collective Kondo) Fermi liquid type ground state becomes unstable against magnetic ordering. For the collective Kondo singlet we use the lattice generalization of Yosida's wavefunction which implies the existence of a large Fermi volume, in accordance with Luttinger's theorem. Using the Gutzwiller approximation, we derive closed-form results for the ground state energy at arbitraryJ/W andn _c, and for the Kondo gap atn _c=1. We introduce simple trial states to describe ferromagnetic, antiferromagnetic, and spiral ordering in the small-J (RKKY) regime, and Nagaoka type ferromagnetism at largeJ/W. We study three particular cases: a band with a constant density of states, and the (tight binding) linear chain, and square lattice periodic Kondo models. We find that the lattice enhancement of the Kondo effect, which is described in our theory of the Fermi liquid state, pushes the RKKY-to-nonmagnetic phase boundary to much smaller values ofJ/W than it was previously thought. In our study of the square lattice case, we also find a region of itinerant, Nagaoka-type ferromagnetism at largeJ/W forn _c 1/3.     

Wn (n= 1–6)团簇吸附CO的密度泛函研究

采用密度泛函理论(density functional theory, DFT) 在B3LYP/LANL2DZ基组水平上对钨团簇吸附CO分子进行了系统研究. 结果表明, W_nCO团簇的基态结构是在W_n团簇中性或阴离子基态结构的基础上吸附CO生长而成; CO的吸附以端位吸附为主,桥位吸附为辅; CO分子在W_n团簇表面发生的是非解离性吸附. 与优化的CO键长(0.116 nm)相比,吸附后C-O键长变长(0.120–0.123 nm), 表明吸附后C-O键被削弱, CO分子被活化了.稳定性分析表明,在所研究的团簇中, W₃CO和W₅CO团簇的稳定性较强;自然键轨道(NBO)分析表明, W原子与CO分子相互作用的本质是CO分子内的杂化轨道与W原子6s, 5d, 6p和6d轨道相互作用的结果. 关键词： nCO (n= 1–6)团簇')" href="#">W_nCO (n= 1–6)团簇 基态构型 稳定性 电子性质     

Classical and thermodynamic work fluctuations

We have studied the nature of classical work (W _c ) and thermodynamic work (W) fluctuations in systems driven out of equilibrium both in transient and time periodic steady state. As the observation time of a large number of trajectories increases, the fraction of trajectories which exhibit excursions away from the typical behaviour, namely, W _c < 0, W < Δ F and dissipated heat Q < 0 decreases as anticipated for macroscopic time scales. An analytical expression for such trajectories is obtained. Trajectory for which W _c < 0 may not correspond to W < Δ F or Q < 0. The applicability of steady state fluctuation theorems is discussed in our linear as well as nonlinear models.     

几种三元过渡金属碳化物弹性及电子结构的第一性原理研究

基于密度泛函理论平面波方法研究了六方WC型Re_xW_1－xC(x=1, 0.25, 0.75, 0),Re_0.5Os_0.5C和Os_0.5W_0.5C的晶体结构、弹性和电子结构性质.研究发现Re_0.25W_0.75C晶体具有优异的弹性性能及稳定性,其剪切模量(312 GPa)超过了所有其他实验合成和     

Precipitation kinetics of W2B5 in (Ti0.4W0.5Cr0.1)B2 solid solutions

The isothermal precipitation kinetics of W₂B₅ secondary phase from supersaturated polycrystalline (Ti_0.4W_0.5Cr_0.1)B₂ solid solutions were investigated with X-ray diffractometry and scanning electron microscopy in the temperature range between 1500 and 1700°C. The precipitate formation is described by a modified Johnson–Mehl–Avrami–Kolmogorov (JMAK) model, where W₂B₅ particles nucleate preferentially at grain boundaries and subsequently grow into the volume by a two-dimensional process controlled by volume diffusion of the transition metals. Numerical calculations are used to describe quantitatively the time dependence of the precipitated fraction and to determine a differential JMAK exponent n _diff which gives information on the nucleation and growth modes. n _diff decreases during the precipitation process from 2 to about 0.8 for all temperatures investigated. The first limit corresponds to the classical JMAK model (two-dimensional diffusional growth and constant nucleation rate) and the decrease in n _diff is the consequence of an impingement of the nucleating and growing particles in the late stages of the process. Nucleation and growth rates are determined as functions of reciprocal temperature, where the first quantity shows a non-monotonic behaviour with a maximum at about 1650°C and the second quantity exhibits an Arrhenius behaviour with an activation enthalpy of 3.6?eV. From this it can be concluded that the overall precipitate formation is dominated by the kinetics of atomic motion at low temperatures and by the thermodynamics of nucleation at high temperatures.     

Physical states and BRST operators for higher-spin <Emphasis Type="Italic">W</Emphasis> strings

In this paper, we mainly investigate the W _2,s ^M ⊗ W _2,s ^L system, in which the matter and the Liouville subsystems generate the W _2,s ^M and W _2,s ^L algebras, respectively. We first give a brief discussion of the physical states for the corresponding W strings. The lower states are given by freezing the spin-2 and spin-s currents. Then, introducing two pairs of ghost-like fields, we give the realizations of the W _1,2,s algebras. Based on these linear realizations, the BRST operators for the W _2,s algebras are obtained. Finally, we construct new BRST charges of the Liouville system for the W _2,s ^L strings at the specific values of the central charges c: for the W _2,3^L algebra, c=−24 for the W _2,4^L algebra and for the W _2,6^L algebra, at which the corresponding W _2,s ^L algebras are singular.     

弹性矩形板方程在非线性边界条件下整体解的存在唯一性

考虑了在非线性边界条件下的弹性矩形板方程.利用Galerkin方法,首先证明了该方程在非线性边界(a)及初值w⁰∈W,w¹∈W的条件下初边值问题存在唯一整体弱解w(t).其次证明了该方程在非线性边界(b)及初值w⁰∈W₁,w¹∈W₁的条件 关键词： 弹性矩形板方程 非线性边界条件 初边值问题 整体解     

The algebra of differential operators on the circle and W KP (q)

Radul has recently introduced a map from the Lie algebra of differential operators on the circle of W _n . In this Letter, we extend this map to W _KP ^(q) , a recently introduced one-parameter deformation of W_KP - the second Hamiltonian structure of the KP hierarchy. We use this to give a short proof that W is the algebra of additional symmetries of the KP equation.     

Birkhoff Strata of Sato Grassmannian and Algebraic Curves

Algebraic and geometric structures associated with Birkhoff strata of Sato Grassmannian are analyzed. It is shown that each Birkhoff stratum Σ_S contains a subset W_? of points for which each fiber of the corresponding tautological subbundle TB_WS is closed with respect to multiplication. Algebraically TB_WS is an infinite family of infinite-dimensional commutative associative algebras and geometrically it is an infinite tower of families of algebraic curves. For the big cell the subbundle TBW_? represents the tower of families of normal rational (Veronese) curves of all degrees. For W₁ such tautological subbundle is the family of coordinate rings for elliptic curves. For higher strata, the subbundles TBW_1,2,..,n represent families of plane (n + 1, n + 2) curves (trigonal curves at n = 2) and space curves of genus n. Two methods of regularization of singular curves contained in TBW_?, namely, the standard blowing-up and transition to higher strata with the change of genus are discussed.     

Analysis of temperature and concentration dependence of flow stress in KCl–KBr single crystals with special reference to solute distribution

Available data on the temperature and concentration dependence of critical resolved shear stress (CRSS) of KCl–KBr solid-solution crystals containing 9, 17, 27 and 45?mol% KBr in the temperature range 77–230?K have been analyzed within the framework of the kink-pair nucleation model of plastic flow in solid- solution crystals. It is found that CRSS τ decreases with increasing temperature T in accordance with the model relation lnτ?=?A???BT, where A and B are positive constants. The CRSS τ at a given temperature depends on solute concentration c as τ?∝?c^p , where exponent p has a value between 0.33 and 0.57 as temperature T rises from 0 to 230?K. The model parameter W _o, i.e. binding energy between the edge-dislocation segment L _o involved in the unit activation process and the solute atoms close to it (T?→?0?K), which is inversely proportional to B, increases with solute concentration c monotonically as W _o?∝?c ^0.33 up to a critical value c _m?=?35?mol% KBr, which is in reasonable agreement with the model prediction W _o?∝?c ^0.25. However, W _o decreases with an increase in c beyond c _m, which indicates somewhat ordered distribution of solute in the host lattice of concentrated KCl–KBr solid solutions with c?>?c _m.     

Re-evaluation of the LHC potential for the measurement of <Emphasis Type="Italic">m</Emphasis><Subscript><Emphasis Type="Italic">W</Emphasis></Subscript>

We present a study of the LHC sensitivity to the W boson mass based on simulation studies. We find that both experimental and phenomenological sources of systematic uncertainties can be strongly constrained with Z measurements: the lineshape, dσ _Z /dm, is robustly predicted, and its analysis provides an accurate measurement of the detector resolution and absolute scale, while the differential cross-section analysis, d² σ _Z /dydp _T , absorbs the strong interaction uncertainties. A sensitivity δ m _W ∼7 MeV for each decay channel (W→e ν, W→μ ν), and for an integrated luminosity of 10 fb⁻¹, appears as a reasonable goal.     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002     

Growth defect W<Superscript>3+</Superscript>-W<Superscript>2+</Superscript> of CdWO<Subscript>4</Subscript> crystals

CdWO₄ crystals grown by the Czochralski method at the low-temperature gradient were investigated with electron spin resonance (ESR) spectroscopy. ESR spectra did not contain the spectra of impurity ions typical for the CdWO₄ structure, i.e., Fe³⁺, Mn²⁺, and Cr³⁺. At the same time, in the studied crystals a complex ESR spectrum having the hyperfine structure due to two nonequivalent tungsten atoms was observed (W¹⁸³;I=1/2; natural abundance, 14.28%). Angular dependence analysis and simulation of ESR spectra have shown that this novel spectrum is described by a spin-Hamiltonian with the following parameters:D=839 G,E=80 G,g _xx=2.01,g _yy=1.97,g _zz=1.987 and electron spinS=7/2. There is one magnetically nonequivalent position of the center in the crystal structure and the direction ofD _zz andg _zz corresponds to the direction of W_n-W_n+2 (or Cd_n-Cd_n+2) in the crystal structure. Because of the fact that it is in principle impossible to achieve the electron stateS=7/2 for the d-shell of one transition metal ion and taking into account the fact that such electron state is realized for two nonequivalent tungsten atoms, we suppose the defect structure to be the chain W²⁺-M⁺-W³⁺. In the structure of this defect the ion M⁺ is diamagnetic, the ions W²⁺ and W³⁺ have electron spinS=2 andS=3/2, respectively. The necessary condition for such defect to exist is to place this chain of ions in cadmium positions for the charge compensation. the reason for such defects to form is supposed to be the incorporation of M⁺ ions into the CdWO₄ lattice. The presence of W²⁺ and W³⁺ in Cd positions in the defect structure provides the charge compensation and the lowering of the lattice stress.