Bidirectional highly-efficient quantum routing in a T-bulge-shaped waveguide

Quantum routing in a T-bulge-shaped waveguide system coupled with a driven cyclic three-level atom and a twolevel atom is investigated theoretically.By employing the discrete-coordinate scattering method,exact expressions of the transport coefficients along three ports of the waveguide channels are derived.Our results show that bidirectional high transfer-rate single-photon routing between two channels can be effectively implemented,with the help of the effective potential generated by two atoms and the external driving.Moreover,multiple band zero-transmission emerges in the scattering spectra,arising from the quantum interferences among photons scattered by the boundary and the bulged resonators.The proposed system may suggest an efficient duplex router with filtering functions.     

Statistical mechanics of linear molecules II: Density expansions,intermolecular potentials and virial coefficients

In the Percus-Yevick and convolution-hypernetted-chain equations obtained in the previous paper, a density expansion for the correlation functions is introduced. To first order in the density, the so-obtained equations are identical and exact. By solving these, the pair correlation functions for linear molecules are obtained explicitly to first order in the density and for arbitrary order in the potential perturbation expansion. From these, the second and third virial coefficients can be extracted for all orders. A generalized charge is defined and used to give generalized multipole expansions for the intermolecular potential. Explicit expressions for this potential model are given up to fourth order. It is shown how the correlation functions, and second and third virial coefficients can be obtained to fourth order for any intermolecular potential with the same perturbation structure.     

Slow-neutron scattering by molecules

We have explicitly calculated the experimental scattering cross-section for homonuclear diatomic molecular perfect gases using virtually exact expressions for the scattering law. These recoil and detector corrections are illustrated for a series of molecules at various temperatures on various instruments. We have shown that the conventional Placzek corrections are quite inadequate for vibrating molecules and we propose a simple recipe which leads to readily calculable expressions which give good agreement with the ‘exact’ results even for nuclei as light as deuterium. This recipe can be generalized for use for almost any nucleus in any molecule and may be expected to materially improve the accuracy of structure determination in molecular gases and liquids. In particular it is found that the Debye-Waller coefficient is very dependent on the experimental parameters. The generalization to time-of-flight experiments is given in the following paper.     

Exact results for anomalous transport in one-dimensional hamiltonian systems

Anomalous transport in one-dimensional translation invariant hamiltonian systems with short range interactions is shown to belong in general to the Kardar-Parisi-Zhang universality class. Exact asymptotic forms for density-density and current-current time correlation functions and their Fourier transforms are given in terms of the Pr?hofer-Spohn scaling functions, obtained from their exact solution for the polynuclear growth model. The exponents of corrections to scaling are found as well, but not so the coefficients. Mode coupling theories developed previously are found to be adequate for weakly nonlinear chains but in need of corrections for strongly anharmonic interparticle potentials. A simple condition is given under which Kardar-Parisi-Zhang behavior does not apply, sound attenuation is only logarithmically superdiffusive, and heat conduction is more strongly superdiffusive than under Kardar-Parisi-Zhang behavior.     

Losses and nonlinear steady-state particle distribution functions for fully ionized tokamak-plasmas in the collisional transport regimes

Fully ionized L-mode tokamak plasmas in the fully collisional (Pfirsch-Schlüter) and in the low-collisional (banana) nonlinear transport regimes are analyzed. We derive the expressions for particles and heat losses together with the steady-state particle distribution functions in the several collisional transport regimes. The validity of the nonlinear closure equations, previously derived, has been indirectly tested by checking that the obtained particle distribution functions are indeed solutions of the nonlinear, steady-state, Vlasov-Landau gyro-kinetic equations. A quite encouraging result is the fact that, for L-mode tokamak plasmas a dissymmetry appears between the ion and electron transport coefficients: the latter submits to a nonlinear correction, which makes the radial electron coefficients much larger than the former. In particular we show that when the L-mode JET plasma is out of the linear region, the Pfirsch-Schlüter electron transport coefficients are corrected by an amplification factor, which may reach values of order 10². Such a correction is absent for ions. On the contrary, in the banana regime, the ion transport coefficients are increased by a factor 2 and the nonlinear corrections for electrons are negligible. These results are in line with experiments.     

The coupling between translational and rotational motions

The coupling between molecular reorientation and translational displacement is studied in a fluid of rough spheres. The correlation functions frequently encountered in thermal neutron scattering and laser light scattering are computed using a binary collision approximation. These are compared with the corresponding uncoupled results. In the diffusion limit coupled and uncoupled diffusion coefficients are found. The Hubbard relation is generalized. The maximum deviation between the coupled and uncoupled results occur for wavenumbers commonly found in thermal neutron scattering. The ratio of uncoupled and coupled correlation times displays regions where translation-rotation coupling is clearly important. In these regions there are important differences in the computed coupled and uncoupled correlation functions.     

Attenuation and scattering of axisymmetrical modes in a fluid-filled round pipe with internally rough walls

The attenuation of axisymmetric eigenmodes in a cylindrical, elastic, fluid-filled waveguide with a statistically rough elastic wall is studied. It is shown that small perturbation theory can be used to relate explicitly the statistical characteristics of the internal wall surface roughness of an elastic pipe to the attenuation and scattering coefficients of the acoustic modes in the filling fluid. Analytical expressions for modal attenuation coefficients are obtained. The analysis of the frequency dependent attenuation coefficients and the ratio between the roughness correlation length and the inner radius of the pipe is made for different correlation functions of the roughness. It is shown that two scale parameters control the overall behavior of the modal attenuation coefficients. These are the ratios of the roughness correlation length and the inner pipe radius to the acoustic wavelength. The numerical results for sound propagation in a pipe and in a borehole with statistically rough, elastic walls are obtained and discussed.     

Numerical simulations of random sound waves

We perform one-dimensional numerical simulations of both driven and impulsively generated sound waves propagating through a medium whose mass density admits time-independent, random fluctuations. While the amplitude of both types of wave is always attenuated, driven sound waves can be either retarded or speeded up depending on their wavenumber and amplitude and on the strength of the random field. The speed of a pulse propagating in the random medium is also altered, in agreement with the findings for the driven waves. The concomitant action of nonlinearity and randomness results in wave speeding for wavenumbers which are of the order of the size of an average random density fluctuation, whereas it gives retardation for larger wavenumbers.     

Renormalized cluster expansion for multiple scattering in disordered systems

We study wave propagation in a disordered system of scatterers and derive a renormalized cluster expansion for the optical potential or self-energy of the average wave. We show that in the problem of multiple scattering a repetitive structure of Ornstein-Zernike type may be detected. We derive exact expressions for two elementary constituents of the renormalized scattering series, called the reaction field operator and the short-range connector. These expressions involve sums of integrals of a product of a chain correlation function and a nodal connector. We expect that approximate calculation of the reaction field operator and the short-range connector allows one to find a good approximation to the self-energy, even for high density of scatterers. The theory applies to a wide variety of systems.     

Efficient transmission calculations for polydisperse water sprays using spectral scaling

Analytical expressions are developed to scale the extinction, scattering and absorption coefficients as a function of the Sauter mean diameter for polydisperse water sprays in fire suppression systems. A scaling procedure is introduced to avoid prohibitive exact integration of the functions obtained from Mie theory resulting in several orders in magnitude of computational savings. Spectral-based and total transmission of real spray distributions using the scaling procedure are compared to exact results and experimental data. Results show the proposed scaling procedure yields significant computational savings with little loss in accuracy for predictions of spectral and total transmission.     

基于优选NIR光谱波数的绿豆产地无损检测方法

产地是影响农作物生产的重要环境因素,产地溯源对于食品安全具有重要意义。针对传统农产品产地检测一般采用化学分析法,其操作繁琐且存在破坏性和耗时较长等不足的问题,以北方寒地绿豆为研究对象,分别在白城、杜蒙、泰来等优质绿豆主产区,获取绿豆的籽粒和粉末两种状态的近红外光谱数据（NIR）,利用优选NIR光谱特征波数,建立了绿豆产地无损检测的新方法。首先在吸光度值较强的10 105.37~4 078.655 cm-1波数范围内,采用多元散射校正法（MSC）,对不同产地的绿豆原始光谱数据进行预处理,以消除光谱干扰信息。应用竞争性自适应重加权采样算法（CARS）,优选不同产地绿豆籽粒和粉末状态的光谱特征波数,以减少光谱曲线的特征向量维度。最后利用前馈神经网络（BP）自适应推理机制,建立了绿豆产地与其光谱特征波数之间非线性映射模型,并将网络输出的编码向量解析至产地名称,作为绿豆产地检测的输出结果。研究结果表明：（1）原始光谱经过多元散射校正预处理后,绿豆粉末光谱曲线的误差从12.87降到3.20,绿豆籽粒光谱曲线的误差从153.04降到27.73,提供有效可靠的光谱数据。（2）通过竞争性自适应重加权采样算法,提取绿豆光谱曲线的重要特征波数,从籽粒和粉末状态原始2 114个波数中,分别优化为61个和107个特征波数,波段总数目减少了94.94%以上,并将其作为绿豆产地识别的特征指标。（3）创新性提出了MSC-CARS-BP绿豆产地检测模型,以优选出的光谱特征波数为定量依据,分别对绿豆籽粒和粉末进行产地检测,预测集准确率为92.59%和98.63%,相关系数均达到0.99以上。该方法能够利用近红外光谱处理技术,实现绿豆产地无损检测的目标,为农产品产地自动快速溯源提供了技术支持和参考。     

Acoustic radiation from shear deformable stiffened laminated cylindrical shells

An analytical model of acoustic radiation from shear deformable laminated cylindrical shells with initial axial loadings and doubly periodic rings is presented. The shear deformation and rotary inertia of the rings are taken into account and the rings interact with the cylindrical shell only through the normal forces. The far-field sound pressure is found by using the Fourier wavenumber transform and stationary phase method. High frequency limitation issues of the first-order shear deformation theory are discussed and the effects of the second set of rings, axial initial loadings and multiple external loadings on the far-field acoustic radiation are explored. Further, the helical wave spectra of the radial displacement and sound pressure are used to study the vibrational and acoustic characteristics of the laminated shells. Above the ring frequency, the profile of the helical wave spectra of the far-field sound pressure induced by the cylindrical shell is an ellipse and the patterns of the helical wave spectra of the far-field sound pressure keep unchanged. Moreover, the ellipse distinguishes the supersonic wavenumbers and subsonic wavenumbers from the helical wave spectra of the radial displacement and surface sound pressure in the wavenumber domain. The bright spots and highlights of the helical wave spectra show that the corresponding waves are dominant.     

Mobility matrix for arbitrary spherical particles in solution

We review the theory of the extended mobility matrix for N arbitrary, spherically symmetric particles immersed in an incompressible fluid. The two-particle mobility functions can be evaluated to any desired order in the inverse interparticle distance by means of an algebraic computer program implementing exact recursion relations. We correct some earlier published expressions and summarize known results for the scattering coefficients which characterize the hydrodynamic properties of the particles. Explicit results are presented for stick and slip hard spheres, for permeable spheres and for fluid droplets.     

Chapman–Enskog solutions to arbitrary order in Sonine polynomials I: Simple,rigid-sphere gas

The Chapman–Enskog solutions of the Boltzmann equations provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosities, the thermal conductivities, and diffusion coefficients. The Chapman–Enskog solutions are also useful for computation of the associated slip and jump coefficients near surfaces. Generally, these solutions are expressed in terms of Sonine polynomial expansions. While it has been found that relatively, low-order expansions (of order 4) can provide reasonable precision in the computation of the transport coefficients (to about 1 part in 1000), the adequacy of the low-order expansions for computation of the slip and jump coefficients still needs to be explored. Also of importance is the fact that such low-order expansions do not provide good convergence (in velocity space) for the actual Chapman–Enskog solutions even though the transport coefficients derived from these solutions appear to be reasonable. Thus, it is of some interest to explore Sonine polynomial expansions to higher orders. It is our purpose in this paper to report the results of our investigation of high-order, standard, Sonine polynomial expansions for the viscosity and the thermal conductivity related Chapman–Enskog solutions for a simple, rigid-sphere gas where we have carried out our calculations using expansions to order 150 and where our reported values for the transport coefficients have been demonstrated to converge to at least 25 significant digits. We note that, for a rigid-sphere gas, all of the relevant integrals needed for these solutions are evaluated analytically as pure fractions and, thus, results to any desired precision may be obtained. This work also indicates how results may be obtained in a similar fashion for realistic intermolecular potential models, and how gas-mixture problems may also be addressed with some additional effort.     

Nonlinear transport in the Boltzmann limit

Formal expressions for the irreversible fluxes of a simple fluid are obtained as functionals of the thermodynamic forces and local equilibrium time correlation functions. The Boltzmann limit of the correlation functions is shown to yield expressions for the irreversible fluxes equivalent to those obtained from the nonlinear Boltzmann kinetic equation. Specifically, for states near equilibrium, the fluxes may be formally expanded in powers of the thermodynamic gradients and the associated transport coefficients identified as integrals of time correlation functions. It is proved explicitly through nonlinear Burnett order that the time correlation function expressions for these transport coefficients agree with those of the Chapman-Enskog expansion of the nonlinear Boltzmann equation. For states far from equilibrium the local equilibrium time correlation functions are determined in the Boltzmann limit and a similar equivalence to the Boltzmann equation solution is established. Other formal representations of the fluxes are indicated; in particular, a projection operator form and its Boltzmann limit are discussed. As an example, the nonequilibrium correlation functions for steady shear flow are calculated exactly in the Boltzmann limit for Maxwell molecules.Research supported in part by NSF grant PHY 76-21453.