Research on heterodyne efficiency of laser Doppler velocimeter

Heterodyne efficiency is a very important factor in a laser Doppler velocimeter (LDV). Gaussian-Airy mode is put forward to analyze the heterodyne efficiency. And the calculate formulas and results of simulation of heterodyne efficiency are given. The results of numerical analysis show that heterodyne efficiency of LDV depends on the parameters—x₀, A, θ and x_a. Heterodyne efficiency can reach 81.45%, when x₀ = 3.59, A = 5.04 and θ = x_a = 0. At last, the antenna theorem of LDV is derived, and a defocused telescope system is used to adjust the waist's position and radius of the reference beam to match the signal beam.     

Algebraic determination of the metric from the curvature in general relativity

The general solution for a symmetric second-order tensorX of the equationX _e(a R ^e _b cd=0 whereR is the Riemann tensor of a space-time manifold, andX is obtained in terms of the curvature 2-form structure ofR by a straightforward geometrical technique, and agrees with that given by McIntosh and Halford using a different procedure. Two results of earlier authors are derived as simple corollaries of the general theorem.     

Cosmological constraints on the graviton mass in RTG

The Friedmann cosmological scenario in RTG (without inflation) is considered. The joint maximum-likelihood analysis of data on type Ia supernovae, the shift parameter of microwave radiation, and baryon acoustic oscillations from the Sloan catalogue of red galaxies provided tight fit constraints on the graviton mass and the space curvature in GR. It is demonstrated that the confidence interval for the graviton mass extends indefinitely if the quintessence parameter tends to zero. These conclusions are valid if the present scale factor a ₀ >(2)^?1/6= 0.89. At a ₀ <(2)^?1/6, a tight constraint on the graviton mass was derived from these observational data: m < 10^–83 g. This implies that terms with the graviton mass may be neglected (with the exception of solutions of the black-hole type) in the gravitational field equations in a broad range of redshifts (0 < z < 10¹⁵).     

Near-surface turbulence in the atmospheric boundary layer

Measurements of the near-surface turbulence in the atmospheric boundary layer have been made using hot-wire probes above the salt flats of northwestern Utah, where the momentum thickness Reynolds number, R_θ, is O(10⁶), and the surface is smooth and nearly devoid of flow obstructions. The measurements were made with arrays of up to 24 parallel straight sensors and with a modular 12-sensor probe capable of measuring all of the components of the instantaneous velocity vector and velocity gradient tensor. Measurements were also made in a laboratory wind tunnel at R_θ=1730 using 22 straight sensors. The data analysis focuses on the effects of the Reynolds number on turbulence properties and on the physics of the dissipation rate of turbulent kinetic energy.Some properties are found to be dependent on the Reynolds number when normalized with inner variables, while others are not. Among those that show the significant Reynolds number dependence are the rms and the skewness factor of the streamwise velocity fluctuations.Significant differences in flow structure, particularly those related to high rates of dissipation, are implied by the data. The joint PDF and covariance integrand of streamwise and wall normal vorticity fluctuations show less preferred orientation of the vorticity vector in the buffer layer at R_θ of O(10⁶) than at R_θ=1070. The largest contribution to the dissipation rate, at O(10⁶) is by the ∂w/∂z velocity gradient, while this term makes a quite small contribution to the dissipation rate at low R_θ. Here w and z are the spanwise velocity fluctuations and direction, respectively. Conditional analysis in the streamwise-wall normal (x−y) plane based on high instantaneous dissipation rate shows that the typical high dissipation rate events are generally similar at high and low Reynolds numbers, but display some significant differences.     

Laser excitation spectrum of PbO: Rotational analysis of the a(1)-X(0+) system

A flashlamp-pumped tunable dye laser has been used to investigate the a-X band system of PbO. Spectra with resolution adequate for rotational analysis were obtained by exciting a-X photoluminescence with the laser operating at a bandwidth of 0.2 cm^?1. The (3,1) and (4,1) bands have been rotationally analyzed, providing the rotational constants B₃ = 0.2389 ± 0.0002 cm^?1 and B₄ = 0.2374 ± 0.0002 cm^?1 for the a state. Observation of P, Q, and R branch structure confirms the assignment of the a state as a Hund's case (c), $\text{Ω}\text{= 1}$ state of PbO. Calculated combination defects having positive algebraic sign support the presence of a b(0^?) state approximately 350 cm^?1 above the a(1) state.     

A mathematical electron

A particle (m) is represented by a Ricci-flat Schwarzschild-basedanalytic enerel (“energy+ ixelectric charge”) geometry X with fundamental form:ds ²=g _αβ dx ^β =(1-2m/r)dt²?(1?2m/r)^?1 dr ² ?r ²(dθ²+sin²θd?²), wherex ^γ=(t, r, θ,?), m=m+ie isenerel, m is rest energy (or mass), and e is electric charge. A unitary vectoru _α and a scalarφ are defined inX by means of the postulated constitutive equation: φu _αβ u ^β+φ_α=0. The normalization condition is postulated as: $$m = \kappa \smallint _0^\pi \smallint _0^\pi \smallint _{ - a}^a \phi \rho g^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} u^0 dr{\text{ }}d\theta {\text{ }}d\varphi $$ whereρ=(R _αβγδ R ^αβγδ )^1/2 is an enerel density function,?=m ²/?c is a normalization constant and also a fine-structure constant,gdetg _αβ =?r ⁴sin² θ, andR _αβγδ is the Riemann curvature tensor formed with complexg _αβ . These equations yield the charge e=0.0855115... of a purely mathematicaleltron (m)=(ie) of radiusa.     

How to compare the SU(5) value of sin2θw with experiments?

We establish the relation between κsin²θ_w to be found from neutral-current experiments and sin²θ_w(Q) for Q=M_W predicted by grand unified theories. We then calculate sin²θ_W(M_W) in the minimal SU(5) model taking the M_W as well as M_x threshold effects into account. We find that these two threshold effects on sin²θ_W(M_W) cancel with each other and sin²θ_W(M_W)=0.211± 0.005.     

Excitation spectrum of a paramagnetic-superconducting contact

A calculation of the bound states in a paramagnetic-superconducting contact, valid at any temperature belowT _c, is performed by using a recently developed method of solving the Bogoliubov equations. The problem of self-consistency of the pair-potentialΔ(x) is being avoided by leaving open the detailed form ofΔ(z), introducing instead the characteristic lenghth for the spatial variation of the pair-potential,d=_O∫ ^D (1?Δ(z)/Δ)dz, as a fit parameter. The energies, the quasiparticle wave-functions and the density of the bound states are calculated for negligible impurity scattering. The energy gap of the excitation spectrum reduces from about one third of its bulk value to practically zero as the thicknessa of the normal film increases froma?d toa?d.     

激光束在漫射表面上的散射(Ⅱ)

首先在前文的基础上,对于用激光根据“光核、光带比”(D₂/D₁)来测定磨削工件表面光洁度的原理加以系统总结,然后按照经验关系R_x=5R_a(对于▽7以上光洁度),确定了表面随机高度的概率密度函数中的衰减系数。对于有限负指数型函数P₁(h)={e^{(-b(|h|/h_m))} 当|h|≤h_m; 0 当|h|>h_m, 定出b=1.23,对于正则型函数P₂(h)=e^{(-a2(h/h_m)2)} 定出a²=2.分别讨论了以上两种函数中h_m的物理意义(皆对应于1/2R_z)将前文中公式加以精确改进后,对P₁(h)和P₂(h)分别计算了D₂/D₁与R_x的关系曲线,即绝对定标曲线。最后还计算了衍射图样半强度宽与R_x的关系曲线。 关键词：     

de Broglie’s wave hypothesis from Fisher information

Seeking the unknown dynamics obeyed by a particle gives rise to the de Broglie wave representation, without the need for physical assumptions specific to quantum mechanics. The only required physical assumption is conservation of momentum μ. The particle, of mass m, moves through free space from an unknown source-plane position a to an unknown coordinate x in an aperture plane of unknown probability density p_X(x), and then to an output plane of observed position y=a+z. There is no prior knowledge of the probability laws or , with the particle momentum at the source. It is desired to (i) optimally estimate a, in the sense of a maximum likelihood (ML) estimate. The estimate is further optimized, by minimizing its error through (ii) maximizing the Fisher information about a that is received at y. Forming the ML estimate requires (iii) estimation of the likelihood law p_Z(z), which (iv) must obey positivity. The relation p_Z(z)≡|u(z)|²≥0 satisfies this. The same u(z) conveniently defines the Fisher channel capacity, a concept central to the principle of Extreme physical information (EPI). Its output u(z) achieves aims (i)-(iv). The output is parametrized by a free parameter K. For a choice K=0, the result is u(z)=δ(z), indicating classical motion. Or, for a finite, empirical choice K=? (Planck’s constant), u(z) obeys the familiar de Broglie representation as the Fourier transform of the particle’s probability amplitude function P(μ) on momentum μ. For a definite momentum μ,u(z) becomes a sinusoid of wavelength λ=h/μ, the de Broglie result.     

The bΣ(b0) → XΣ(X10,X21) and aΔ(a2) → X21 transitions of AsBr

Emission spectra of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺,X₂1) and a¹Δ(a2) → X₂1 transitions of AsBr have been measured in the near-infrared spectral region with a Fourier-transform spectrometer. The arsenic bromide radicals were generated in fast-flow systems by reaction of arsenic vapor (As_x) with bromine and were excited by microwave-discharged oxygen. The most prominent features in the spectrum are the Δv = +1,0,−1, and −2 band sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺) transition in the range 11 700-12 700 cm⁻¹. With lower intensities, the Δv = 0 and −1 sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₂1) sub-system show up in the same range. Further to the red, between 6000 and 6700 cm⁻¹, the Δv = 0, +1, and −1 sequences of the hitherto unknown a¹Δ(a2) → X₂1 transition are observed. Analyses of medium- and high-resolution spectra have yielded improved molecular constants for the X₁0⁺, X₂1, and b0⁺ states and first values of the electronic energy and the vibrational constants of the a2 state.     

Messung der Winkelverteilung der Neutronenpolarisation bei Streuung von 15,85 MeV-Neutronen am Kohlenstoff

AtE _n=15.85 MeV the angular distributions of neutron polarizationP(θ) for¹²C(n, n)¹²C and of scattering asymmetry A(θ) for¹² C(n,n′)¹² C ^*(Q=?4.43 MeV) have been measured. In a neutron time-of-flight method with a plastic scintillator as scatterer carbon recoil nuclei were used for detection. Polarized neutrons were produced in thed-t reaction atE _d=1.90 MeV at a reaction angle of 70° (lab.). WithP _n=?0.135 scattering polarizations P(θ) are forθ _lab=30, 40, 50, 60, 70, and 80° respectively ?27.0±2.1, ?48.4±2.7, ?68.7±3.6, ?20.7±6.2, +5.3±3.9, and +2.1±4.5%.     

Elasticp+12C scattering between 0.3 and 2 MeV

Absolute differential cross-sections ofp+¹²C elastic scattering have been measured atθ _cm=89.1°, 118.7°, 146.9° for bombarding energies between 0.3 and 2.0 MeV. Revised level parameters of the first three excited states in¹³N have been extracted with aR-matrix analysis. It is shown that the influence of the bound ground-state of¹³N has an appreciable effect on low-energy scattering. Recent predictions concerning Mott-Schwinger polarization are also discussed.     

Doppler-limited spectroscopy of the AΠ1 ← XΣ system of ICl in the 0.8 μm region using a Ti:sapphire ring laser

Doppler-limited vib-rotational absorption spectra of the A ← X electronic transition of I^35/37Cl are measured in the range 11,352-13,507 cm⁻¹ using a Ti:sapphire ring laser. The P-, Q-, and R-branch lines belonging to the v ← v″ = (0-7) ← (0-7) transition in I³⁵Cl and the v ← v″ = (0-6) ← (2-6) transition in I³⁷Cl are assigned. Under Doppler-limited conditions, the P- and R-branch lines are split into doublets by the nuclear quadrupole coupling effect of the I atom. The unperturbed positions of these lines are correctly calculated, whereas splitting in the Q-branch lines was not observed. The mass-reduced Dunham expansion coefficients U_l,m of the A and X states and the spectroscopic constants , and H_v^′ of the A state are determined using a global least-squares fitting procedure.     

Dissociative excitation of odd sextet levels of the manganese atom in the e-MnCl2 collisions

The dissociative excitation of odd sextet levels of the manganese atom in collisions between slow electrons and manganese dichloride molecules was studied experimentally. The cross sections for the population of the metastable a ⁶ D levels (the lower levels of the laser transitions) by cascade transitions have been determined. It is established that for the z ⁶ F° and z ⁶ D° levels, the cross sections for both the dissociative and direct excitation, Q _m and Q _a , respectively, differ only slightly in absolute value. For the x ⁶ P° levels, the ratio Q _a /Q _m amounts to 9–11, but for the upper laser levels it is much larger: 33 for the z ⁶ P° level and 240 for the y ⁶ P° level.     

Higher-twist effects in QCD,deep inelastic scattering,and the Drell-Yan process

Inclusion of specific effects associated with constituent binding in hadronic wave functions is shown to lead to important non-scaling, nonfactorizing 1/Q ² contributions to cross sections for semi-inclusive deep-inelastic scattering, the Drell-Yan process, and other hard scattering reactions. These 1/Q ² higher-twist terms are predicted to be dominant in well defined kinematic regions such as largex and/or largez. The provide angular distributions typical of longitudinally polarized virtual photons andW's, including sin² θ terms in meson induced Drell-Yan processes and ine ⁺ e ^?→πX, as well as unusual (1?y) terms in deep-inelastic scattering. Calculations are also presented of the quark structure functions of the pionq _π(x, Q ²) and for the quark to pion fragmentation functionD _π(z, Q ²). Predictions are made for the azimuthal angle dependence of the cross sections for \(\pi N \to \mu {\text{ }}\bar \mu X\) andlN→l′πX.     

EPR theoretical study of local lattice structure in Al2O3:Fe system

By analyzing the EPR spectrum of transition-metal ion Fe³⁺ in Al₂O₃:Fe³⁺ system, the local lattice structure around impurity Fe³⁺ ion in the crystal has been studied by means of the diagonalization of the energy matrices of the electron-electron repulsion, the ligand-field and the spin-orbit coupling for a d⁵ configuration ion in a trigonal ligand-field. Both the second-order and fourth-order EPR parameters D and (a−F) are taken simultaneously in the structural investigation. The results indicate that the two three-edge-pyramids elongated obviously along C₃ axis. The two distortion angles Δθ₁=−1.1±0.1°,Δθ₂=−1.8° as well as the two Fe-O bond lengths R₁=2.016 A, R₂=1.907 A are determined, respectively.     

Electrical Conductivity Measurement Through the Loaded Q Factor of a Resonant Cavity

We present a method for measuring the electrical conductivity of metallic materials that relies on the ratio of two loaded Q factors, Q_R/Q_X, with Q_R corresponding to a TE₀₁₁-mode reference cavity made of aluminum, and Q_X the Q that results upon replacing the aluminum plate with the one fabricated from the material to be examined. Electrical conductivity is mathematically inferred from the ratio Q_R/Q_X where the loaded Q factors are measured by using the transmission-type method. Within a 3.0 percent accuracy, conductivities determined at 8.7 GHz for electrolytic copper (5.6 times 10⁷ S/m) and brass (1.6 times 10⁷ S/m) show to be in good agreement with those reported in the literature.     

Synthesis and characterization of Co7(OH)12(C2H4S2O6)(H2O)2—a single crystal structural study of a ferrimagnetic layered cobalt hydroxide

A novel layered hydrotalcite-like material, Co₇(H₂O)₂(OH)₁₂(C₂H₄S₂O₆), has been prepared hydrothermally and the structure determined using single crystal X-ray diffraction (a=6.2752(19) Å, b=8.361(3) Å, c=9.642(3) Å, α=96.613(5)°, β=98.230(5)°, γ=100.673(5)°, R1=0.0551). The structure consists of brucite-like sheets where 1/6 of the octahedral sites are replaced by two tetrahedrally coordinated Co(II) above and below the plane of the layer. Ethanedisulfonate anions occupy the space between layers and provide charge balance for the positively charged layers. The compound is ferrimagnetic, with a Curie temperature of 33 K, Curie-Weiss θ of −31 K, and a coercive field of 881 Oe at 5 K.     

Integrals involving Euler-Bernoulli flexure and Saint-Venant torsion eigenfunctions

Tables of the integral ∝₀^LX_i(x)θ_j(x) dx where X_i(x) and θ_j(x) are Euler-Bernoulli and Saint-Venant eigenfunctions respectively are presented for 1?i, j?5 for beams with combinations of clamped, pinned and free ends. These integrals arise in application of the Rayleigh-Ritz and Ritz-Galerkin methods to free vibration and dynamic stability problems involving coupled torsion and bending.