Conditional statistics of inert droplet effects on turbulent combustion in reacting mixing layers

Direct numerical simulation (DNS) of turbulent reacting mixing layers laden with evaporating inert droplets is used to assess the droplet effects in the context of the conditional moment closure (CMC) for multiphase turbulent combustion. The temporally developing mixing layer has an initial Reynolds number of 1000 based on the vorticity thickness with more than 16 million Lagrangian droplets traced. An equivalent mixture fraction incorporating the inert vapour mass fractions clearly demonstrates the effects of vapour dilution on the mixture. Instantaneous fields and conditional statistics, such as the singly conditioned scalar dissipation rate, the gas temperature 〈 T _g|η 〉, conditional variance of the gas temperature 〈 T _g ^”2|η 〉 and conditional covariance between the fuel mass fraction and gas temperature 〈 Y _f ^” T _g ^”|η 〉 show considerable droplet effects. Comparison between the droplet-free and droplet-laden reacting mixing layer cases suggests significant extinction in the latter case. The resulting large conditional fluctuations around the conditional means contradict the basic assumption behind the first-order singly conditioned CMC. More sophisticated CMC approaches, such as doubly conditioned or second-order CMCs are, in principle, better able to incorporate the effects of evaporating droplets, but significant modelling challenges exist. The scalar dissipation rate doubly conditioned on the mixture fraction and a normalized gas temperature 〈 χ | η, ζ 〉 exemplifies the modelling complexity in the CMC of multiphase combustion.     

Determining the KS→3π amplitude in pp(OR e+e−)→K0K0

The amplitude ratio 〈3π|T|K_S〉/〈3π|T|K_L〉 can be well determined in e⁺e^? (or low energy $\text{p}\text{p}\text{)→K}{}^{\mathrm{o}}\text{K}{}^{\mathrm{o}}$ from the decay time-distribution when each produced kaon→3π, other unknown parameters of the distribution being obtainable from corresponding observations involving known channels like ππ.     

Study of data on the associated momentum on the trigger side in highP T hadron production

The British-French-Scandinavian collaboration has recently studied the non trigger charged mean momentum in different rapidity regions on the trigger hemisphere, 〈p _x〉, in the collision of two hadrons at the CERN Intersecting Storing Rings (ISR). In particular, they give for the rapidity regions |y|<0.5 and |y|<1 the values of the slope, α, of 〈p _x〉 with the trigger momentum,p _T ^t . Several authors have analysed those values of α in the framework of hard scattering models which predict values independent ofp _T ^t for 〈z _c〉, the longitudinal momentum fraction of the outgoing hard scattered system taken by the trigger. From this analysis they give estimates of 〈z _c〉 of very difficult reconcilliation with those calculated in the Feynman, Field and Fox hard scattering model or in the QCD treatment of highp _T hadron production. The authors of the present paper have looked for, and found, other data whose model independent analysis is more feasible than that of the data mentioned above. More specifically, we analyse in the framework of the hard scattering models, but otherwise model independently, data on 〈p _x〉 in two other rapidity regions (|y|<3, 2<|y|<3) and find that consistence of the average slopes, α, in these two regions is only achieved with mean values of 〈z _c〉 significantly, increasing withp _T ^t and close in value to those obtained by Feynman et al. [6, 7].     

A note on the mean square deviation of the voltage of a resistively shunted Josephson junction in the running state

We show that a resistively shunted Josephson junction, in steady state, satisfies the relation 〈V²〉_T = IR〈V_T〉, where V is the voltage, I is the bias current, R is the junction resistance, and 〈 〉_T is a time average.     

Statistical properties of volatility return intervals of Chinese stocks

The statistical properties of the return intervals τ_q between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τ_q for different thresholds q. Furthermore, the KS test and weighted KS test show that the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function with γ≈0.31 under the significance level of 5%, where is the mean return interval. The investigation of the conditional probability distribution P_q(τ|τ₀) and the mean conditional return interval 〈τ|τ₀〉 demonstrates the existence of short-term correlation between successive return interval intervals. We further study the mean return interval 〈τ|τ₀〉 after a cluster of n intervals and the fluctuation F(l) using detrended fluctuation analysis, and find that long-term memory also exists in the volatility return intervals.     

Renormalization in theories with modified dispersion relations: Weak gravitational fields

We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes, within the framework of Einstein–Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion of 〈?²〉$〈{?}^2〉$ and 〈T_μν〉$〈T_{\mu \nu }〉$, working in the weak field approximation. We show that for dispersion relations containing up to 2s powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on s   in a qualitatively different way: while 〈?²〉$〈{?}^2〉$ becomes convergent for a sufficiently large value of s  , the number of divergent terms in the adiabatic expansion of 〈T_μν〉$〈T_{\mu \nu }〉$ increases with s. This property was not apparent in previous results for spatially homogeneous backgrounds.     

Vacuum polarization in the field of a multidimensional global monopole

An approximate expression for the Euclidean Green function of a massless scalar field in the spacetime of a multidimensional global monopole has been derived. Expressions for the vacuum expectation values 〈?²〉_ren and 〈T ₀₀〉_ren have been derived by the dimensional regularization method. Comparison with the results obtained by alternative regularization methods is made.     

Temperature quenching of luminescence for linear and derivative nuclear operators

An earlier study of the thermal quenching of luminescence using the single-configurational-coordinate model is extended from Condon-approximation overlap integrals 〈u_n|v_m〉² to the linear and derivative integrals 〈u_n|z_v|v_m〉² and 〈u_n|?/?z_v|v_m〉². For non-radiative transitions, the thermally weighted nuclear factor in the transition rate is, for the linear and derivative integrals, the corresponding factor for 〈u_n|v_m〉² integrals multiplied by 2E_Xv/?ω_v and $\text{2[E}{}_{\mathrm{Xv}}\text{- E}{}_{\mathrm{p}}{}_{\mathrm{U}}\text{(T)]/}\text{h}\text{?}\text{ω}{}_{\mathrm{v}}$, respectively. E_Xv is the energy of the crossover above the initial- v-parabola minimum, and E_pU(T) is the single activation energy fitted to the nuclear factor's temperature dependence for 〈u_n|v_m〉² integrals. These multiplying factors are exact for equal parabola force constants and good approximations for unequal force constants. These multiplying factors will be difficult to distinguish experimentally. The more important considerations for fitting the model to thermal-quenching data are the parabola placement and the Condon-approximation integrals described previously.     

Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions

We present analytically the exact solutions of the Schrödinger equation in the N-dimensional spaces for the pseudoharmonic oscillator potential by means of the ansatz method. The energy eigenvalues of the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained. A realization of the ladder operators for the wavefunctions is studied and we deduced that these operators satisfy the commutation relations of the generators of the dynamical group SU(1,1). Some expectation values for 〈r ^?2〉, 〈r ²〉, 〈T〉, 〈V〉, 〈H〉, 〈p ²〉 and the virial theorem for the pseudoharmonic oscillator potential in an arbitrary number of dimensions are obtained by means of the Hellmann–Feynman theorems. Each solution obtained is dimensions and parameters dependent.     

Charged hadron production ine + e − annihilation in the Υ and Υ′ region

Charged hadron production ine ⁺ e ^? annihilation is studied in the 7 to 10 GeV CM energy region and at the Υ (9.46) and Υ′ (10.01) resonances with the LENA detector at DORIS. The statistical moments of the charged multiplicities are studied. The data show KNO scaling behaviour and suggest the presence of long range correlations. An average charged multiplicityrise of Δn(Υ)=0.55±0.19 and Δn(Υ′)=1.26±0.29 over the continuum is observed for the Υ and Υ′ direct decays. The jet structure of the Υ and Υ′ direct decays is investigated using the charged particles. The polar angular distributions of the jet axis behave like 1+α(T) cos²θ with 〈α(T)〉_Υ=0.7±0.3 and 〈α(T)〉_Υ′=0.6±0.4. The 〈α(T)〉_Υ value is in agreement with the QCD vector gluon assignment and excludes scalar gluons by more than four standard deviations.     

Statistics of reaction progress variable and mixture fraction gradients of a pulverised coal jet flame using Direct Numerical Simulation data

The statistical behaviour of the variances, covariance and gradients of the reaction progress variable (c), and the mixture fraction (ξ) have been analysed in a pulverised coal jet flame using a three-dimensional carrier phase direct numerical simulation (DNS) dataset. It has been observed that the Favre-probability density functions (PDFs) of c and ξ can be parametrised by the standard β function. Furthermore, the log-normal distribution has been found to accurately represent |?c| and |?ξ|. It is also found that ?c and ?ξ remain aligned throughout the flame brush. Finally the joint PDF of |?c| and |?ξ| has been compared with the product of the PDF of |?c| and PDF of |?ξ| extracted from carrier phase DNS, and it has been found that |?c| and |?ξ| are not statistically independent in the case investigated.The bivariate log-normal distributions with and without correlation have also been considered, and the former is found to be in better agreement with the carrier phase DNS data.     

Laser fluctuation studies in intensity dependent absorption of light

The interaction of a laser with an intensity-dependent absorber has been analysed for discrete regions of operations of the laser. It is shown that the beam is thermally defocused due to absorption for the values of intensity under consideration. The fluctuation properties have been analysed by evaluating 〈I〉,〈I ²〉 and 〈(ΔI)²〉/〈I〉².     

Statistical mechanics of a bounded,ideal magnetofluid

A statistical model of a three-dimensional, incompressible, cylindrically bounded, current-bearing magnetofluid is presented for the purpose of gaining insight into the nonlinear relaxation process routinely observed in reversed-field-pinch experiments. An absolute equilibrium ensemble is utilized that incorporates energy, magnetic helicity, and magnetic flux constraints. Results are extracted only after an extensive mathematical treatment of the properties of poloidal and toroidal fields. The model predicts the presence of magnetic fluctuations about a cylindrically symmetric, Bessel-function-model, mean magnetic field, which satisfies ▽ × 〈B〉 = μ〈B〉. As Taylor's ∵-parameter approaches 1.56, the model predicts that the significant region of the fluctuation spectrum narrows down to a single (coherent) m = 1 mode. An analogy between the Debye length of an electrostatic plasma and μ^?1 suggests the physical validity of the model's prediction of the magnetic-field-fluctuation autocorrelation tensor 〈δB(r) δB(r′)〉, when |;r ? r′| ≥ μ^?1.     

Averaged local field intensities in composite films

The photophysical properties of molecules adsorbed in composite films (e.g. surface island films) depend on the local electromagnetic field within the film. The ratio between the average field intensity 〈|E|²〉 in the film and the intensity |E_I|² associated with the incident field is a measure of the electromagnetic contribution to the surface influence on molecular photophysical phenomena. This ratio depends on the film composition and morphology, on the dielectric properties of the pure components making the film and on the frequency, direction and polarization of the incident radiation. Calculations of this ratio as a function of these parameters for several models of composite films are presented. Image interactions and retardation effects as well as radiative damping and finite size contributions to the dielectric response of the films are taken into account. In addition, an estimate of the field inhomogeneity within the film is obtained by calculating also the ratio 〈|E|²〉_shell/|E_I|² associated with the field in thin shells surrounding the dielectric particles which constitute the film.     

一维分子晶体系统的极化子-孤子压缩态、系统基态性质和量子涨落

基于一维分子晶体系统的 Holstein 模型,采用压缩-相干态展开方法,计及电子-声子间量子关联和重整化平移修正,分析和研究电子-双声子相互作用对极化子-孤子系统基态性质和量子涨落的影响.推导了一维极化子-孤子系统的封闭形式非线性方程.应用非线性项展开方法,给出非线性方程的解析解和相关基态特性结果.研究表明,仅当电子-双声子耦合强度 g₁<0时非线性方程才有孤波解,此时声子量子涨落效应随着压缩的增加,极化子-孤子系统基态能量变得更负,孤子局域减少,孤子态更加稳定;另一方面,电子密度涨落〈Δ²n〉和声子坐标-动量的不确定量〈Δ²p〉〈Δ²q〉比无声子压缩效应的大,极化子结合能变得更负.特别是,当g₁<0时,双声子效应的量子涨落〈Δ²n〉与〈Δ²p〉〈Δ²q〉的值比单声子情况有明显增加. 关键词： 压缩-相干态展开 极化子-孤子态与量子涨落 电子-双声子相互作用 非线性薛定谔方程     

In search of scalar gluonium

We discuss a scalar meson coupled strongly to gluons. Radiative decays of the J/ψ are taken as a source of gluons so that our aim is to calculate Γ(J/ψ→σγ), where σ is the presumed scalar gluonium. We use QCD sum rules to find both 〈0|α_sG_μν^aG_μν^a|σ〉 (where G_μν^a is the gluon field strength tensor) and Γ(J/ψ→σγ) in terms of 〈0|α_sG_μν^aG_μν^a|σ〉. The final prediction for the width is expected to be valid within a factor of two and gives $\text{Γ(}\text{J}\text{/ψ→σγ→}\text{two pions in S-wave}\text{+ γ) ? 25}\text{eV for}\text{m}{}_{\mathrm{\sigma }}\text{= 700}\text{MeV}$. Non-perturbative QCD naturally explains the observed asymmetry between scalar and pseudoscalar states in the radiative decays of the J/ψ. Some general remarks on gluonium in QCD are made.     

Partial virial theorems for atomic-molecular systems

New virial relations for three-and four-particle atomic-molecular systems are proposed. Using operators of extension or squeezing of interparticle distances, it is shown that, for all pairs of j and k particles in S states of these systems, the following partial virial relations are valid: 〈2T _jk 〉+〈 V _jk 〉=0, where 〈V _jk 〉 is the average Coulomb interaction energy for a pair of particles and 〈T _jk 〉 is a part of the average kinetic energy of the system. There are three and six such relations for three-and four-particle systems, respectively. The conventional virial theorem (〈 2T〉+〈V〉=0) for the average total kinetic and potential energies of the system (〈 T〉 and 〈V〉, respectively) corresponds to the summation of partial virial relations over all pairs of particles. It is shown by an example of variational calculations of the helium atom ⁴He²⁺ e ^? e ^? and the helium muon-electron mesoatom ⁴He²⁺μ^? e ^? that partial virial relations are a highly sensitive indicator of the accuracy of wave functions.     

The nature of the rectilinear diameter singularity

The rigorous explanation for the term |t|^2β in the rectilinear diameter equation is given (t=(T_c−T)/T_c, β is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for which the branches of binodal are symmetric, is constructed within the canonical formalism. It is shown that the ratio of the amplitudes for the diameter singularity of the order parameter before |t|^1−α and |t|^2β, where α determines the behavior of the heat capacity and β is the critical exponent of the order parameter, takes the universal character modulo non-universal factor which depends on the thermodynamic class of the corresponding states. The analysis of entropy for argon and water leads to β=0.33 and the corresponding amplitude ratio .     

Anomalous fluctuations of 2D-electron recombination radiation intensity in the quantum Hall regime

Anomalous intensity fluctuations are observed in the spectrum of radiative ecombination of quasi-two-dimensional (2D) electrons with photoexcited holes in a single quantum well. The fluctuations are observed exclusively under the conditions of the quantum Hall effect (QHE). It is shown that, if the QHE conditions are not fulfilled, the radiation intensity fluctuates strictly following the Poisson distribution 〈δN ²〉/〈N〉= 1), whereas in the QHE regime the fluctuation amplitude increases by several orders of magnitude (〈δ N ²〉/〈N〉～10²). It is demonstrated that the maxima of the emission noise amplitude coincide with the maxima of inverse magnetoresistance of 2D electrons in the QHE regime and correspond to establishing an anomalously high uniformity of the system.     

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V_j(x) can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k₀²±i0)|k′〉, |k| = |k′| = k₀, then each t_j is also on-shell.