Stabilization of mode-locked trains,and dark resonance of two-photon lambda-level structures

Our ultimate objective is to design a combined frequency standard for optical as well as radio frequencies. A mode-locked laser provides frequency components that can be used as a ruler to measure any unknown optical source through direct beating. The frequency spacing of a pair of teeth of this comb is in itself a radio frequency reference. Fast control and correction for both the average frequency and the repetition rate of a mode-locked Ti : sapphire laser are achieved by locking the laser to a reference cavity of ultra-low expansion quartz with equal mode spacing. We measure an optical frequency with a mean square deviation of 700 Hz, instability limited by the radio-frequency sources used to count the repetition rate. As a reference standard to achieve absolute accuracy, we use the Λ transition 5S^1/2 (F = 1) → 5D^5/2 (F = 3) → 5S^1/2 (F = 2) of rubidium. The theory for this coherent interaction shows that, with one mode resonant with the two-photon 5S^1/2 (^F = 1) → 5D^5/2 (^F = 3) transition, the fluorescence goes through a resonance for a change in repetition rate of less than 10 kHz. These results suggest that, by locking to the peak of that resonant feature, optical stability and absolute accuracy better than 1 kHz can easily be achieved.     

The modulation instability of dispersed electromagnetic waves in the Josephson junction with nonlocal interaction

The modulation instability of dispersed electromagnetic waves propagating in the Josephson junction between massive superconductors has been studied. A dispersion equation for the increment of small perturbations of the wave amplitude is obtained. It is shown that the spatial nonlocality produces a stabilizing influence with respect to the development of modulation instability in a long-wavelength region of the perturbation wavevectors 0≤Q≤Q _B1(k). The region of modulation instability Q _B1(k)<Q<Q _B2(k, A, L) can be controlled by the dispersion parameter—the wavevector k (or the frequency ω(k)) of the carrier wave in the linear approximation.     

Deviation from the Lambert-Beer Law in the Transmittance of a Light Beam Through Diffusing Media: Experimental Results

Abstract

Attenuation measurements of an He-Ne laser beam in suspensions of polystyrene latex spheres are presented. Measurements were performed with a transmissometer having a receiver with a variable field of view (FOV) in a lenspinhole geometry. Attenuation measurements taken with different fields of view for any fixed optical depth, enabled us to separate the scattered received power P _s and the beam-attenuated power P ₀ from the total received power P. In this way the true value τ of the optical depth was obtained from P ₀ and compared with the apparent optical depth τ_A obtained from P. Thus the error ? = (τ ? τ_A)/τ due to the contribution of scattered received power in attenuation measurements was investigated. Many measurements were taken in order to see how τ_A and ? vary with the optical depth, with the size of the diffusing spheres and with geometric arrangement (radius and angular FOV of the receiver, distance between scattering cell and receiver).     

Gelation theory for solutions of polymers with loci of strong interaction

This paper presents a statistical mechanical analysis of gelation in certain solutions ofA/B copolymers. Repeat unitsA, the major units, must constitute about 90 mole% or more of the copolymer, and are compatible with the solvent. Repeat unitsB, the minor units, must be totally incompatible with the solvent and represent loci of strong interaction between the macromolecular chains. If these interactions are sufficiently strong they can lead to gelation of the mixture. The following simplifications of the model afford results that can be expressed in simple, closed form: (1) TheB units are uniformly distributed along the chain backbone. (2) Polymer concentration must be greater then that for chain overlap. (3)B–B interactions lead to dimerization ofB units only. Examples include: (1) Any aqueous polymer solution where theA repeat units are hydrophilic and theB repeat units are hydrophobic;B–B interactions are thus by hydrophobic bonding. (2) Neutralized acrylic acid/acrylamide copolymers where theB are acrylamide repeat units which associate by hydrogen bonds. (3) Ionomer solutions whereB–B bonding is by dipole-dipole interaction. The results show that there is a critical copolymer concentration for gel formation, C _c . It turns out that C _c decreases withB content for low dimerization energies and increases withB content for higher dimerization energies. At intermediate dimerization energies, C _c is insensitive to theB content. The two extreme regimes of behavior are similar to contradictory predictions of previously published theories. Received: 18 September 2000 / Reviewed and accepted: 20 September 2000     

Reaction-diffusion in a simple pooled chemical system

The reaction scheme based on the cubic autocatalator A + 2B→ 3B B → C is considered in a closed vessel with the reactant Abeing replenished by the slow decay of a precursor Pvia the simple step P→A The concentration of Pis assumed to be very much larger than that of the intermediates Aand Bso that the pooled chemical approximation can be made. Spatial variations are allowed for within the vessel and it is assumed that initially the vessel contains only the reactant Pand that at time ? = 0 a quantity of B,characterized by the parameter β_o; is introduced into some localized region. The long-time behaviour is discussed and it is shown that this depends on the parameters β_oand μ(where μis a non-dimensional parameter representing the reaction rates) with the value of the diffusion parameter λ effectively controlling the form of the transient path leading to the final behaviour. Analytic solutions are derived for the cases when β_ois small and λ is large. These are complemented by numerical solutions for general values of the parameters. It is found that there are three possibilities: a finite equilibrium may be reached with Aand Bhaving constant concentrations, the concentrations of Aand Bmay oscillate, or Bmay die away leaving just the conversion of P to AIn the first two cases it is found that this behaviour is left behind a propagating reaction-diffusion front. The nature of this front is analysed in detail.     

The high-field thermal and electrical magnetoconductivities of Pb

The limiting high-magnetic-field behavior of the electrical and thermal magnetoconductivities of a Pb single crystal withB along [001] have been extracted from data taken in fields of up to 4.3 T in the liquid ⁴ He temperature range. The electrical conductivity varies asB ^–2 in the limit of high fields, with the coefficient exhibiting aT ⁵ dependence, the same as is found for the zero-field resistivity. The analogous coefficient for the thermal magnetoconductivity shows aT ³ dependence, but there are no zero-field data available for comparison. The lattice conductivity has also been determined and is shown to obey aT ² dependence only below 3 K, with a more rapid dependence between 3 and 4 K.     

Stress-driven diffusion in a deforming and evolving elastic circular tube of single component solid with vacancies

The title problem is considered for an elastic circular tube of inner radius A and outer radius B. The tube is made of a single component solid with vacancies as its second component. The mole fraction of the massive species is denoted by x ¹, while that of the vacancies by x ⁰ = 1 – x ¹. The tube is completely surrounded by vacuum, serving as a reservoir of vacancies. One of the standard elasticity boundary conditions is applied at time t = 0, when the composition is uniform. The ensuing coupled deformation and diffusion leads to the evolving of A(t), B(t) and x ¹(R, t) as functions of time. Since the single component solid is not in contact with its vapor or liquid, the diffusion boundary condition is always tied to the elasticity problem through a surface condition that involves the normal configurational traction. Our chemical potential has an energy density term that serves as a source in the interior and the boundary conditions for the diffusion problem are such that the time rates of boundary accretion Ȧ(t) and Ḃ(t) must simultaneously satisfy two dissipative inequalities, one governed by the gradient of the internal chemical potential and the other by the normal configurational traction.     

Cyclodextrin Inclusion Complexes of the Central Analgesic Drug Nefopam

ABSTRACT

Inclusion complexes of nefopam base (NEF) with various β‐cyclodextrins (βCDs) were investigated. All tested βCDs increased the apparent solubility of NEF according to a Higuchi A_L type plot (except βCD: A_N type plot), which indicates the formation of 1:1 stoichiometry inclusion complexes. ¹H-NMR and ¹³C-NMR experiments showed that complexation by CDs allowed an easy separation of the R and S enantiomers. Based on spectral data obtained from the two-dimensional rotating frame nuclear Overhauser effect spectroscopy (2D-ROESY), a reasonable geometry for the complexes could be proposed implicating the insertion of the benzoxazocine ring into the wide end of the torus cavity.     

Simple instability criteria for a family of complex‐coefficient polynomials

Abstract

In this paper, the A[r, R) stability and A[r, R) instability are introduced. The instability of a family of complex‐coefficient polynomials is investigated. Simple instability criteria are derived to guarantee the instability of such polynomials. Finally, a numerical example is provided to illustrate the main results.     

A Relationship between Vernier Acuity and Intersaccadic Interval

Measurements of vernier acuity V and intersaccadic interval (T _is) on a number of subjects are consistent with the relation V ²= A(T _is + B), where A and B are constants. This suggests that an integration period determined by the length of the intersaccadic interval is significant in vernier acuity performance.     

Eigenvalues of damped structures: Vectoriteration in the original space of DOF

The equations of motion in structural dynamics as well as the corresponding eigenvalue problem are governed by 3 matrices for mass, damping and stiffness of order n which equals the number of degrees of freedom. High-performance eigenvalue-solvers are developed for only pairs A, B of matrices. Nevertheless, to benefit from these solvers, the original eigenvalue problem (λ² M+λD+K)x=0 is transformed into a linear eigenvalue representation with only two hypermatrices of double order 2n. Consequently the total numerical effort depends on this order 2n. This paper presents a vectoriteration process which actually works in the original space of order n and which needs no special actions like simultaneous iteration if complex conjugate eigenvalues λ, λˉ with identical norm have to be calculated. The theoretical foundation of this process still goes back to the pair of hypermatrices.     

Thermelectric power in ultrathin films ofA 3 II B 2 V semiconductors in the presence of a quantizing magnetic field

An attempt is made to study theoretically the thermoelectric power in ultrathin films ofA ₃ ^II B ₂ ^V semiconductors in the presence of a quantizing magnetic field by formulating a new magneto-dispersion law, within the framework ofk · p formalism incorporating the anisotropies in the band parameters. It is found, taking ultrathin films ofn-Cd₃P₂ as an example, that the same power decreases with increasing surface electron concentration and changes in an oscillatory manner with film thickness and quantizing magnetic field. In addition, the well-known results for parabolic energy bands have also obtained from our expressions as special cases.     

Les pyrochlores AIB2X6: Mise en evidence de l'occupation par le cation AI de nouvelles positions cristallographiques dans le groupe d'espace fd3m

In A^IB₂X₆ pyrochlores—A^I = Pb, Tl; X = O, F— the A^I ions occupe 32e positions with a probability of 25% instead of the 8b positions as it was previously described; this results from the observations of very weak X-diffraction peaks provided by planes such as h = 4n, k = 4n, l = 4n + 2, visible on single crystals photographs of RbCoCrF₆, RbNb₂O₅F, TlNb₂O₅F; this displacement of A^I with respect to the 8b position -about 0,6 Å for Tl⁺ and 0,4 Å for Rb⁺ - is in agreement with the great size of the 8b cavity -about 1,80 Å-. However Cs⁺, the radius of which is well adapted to this cavity, is not significantly displaced in homologous compounds.     

Measurement of the Boltzmann Constant <Emphasis Type="Italic">k</Emphasis><Subscript>B</Subscript> Using a Quasi-Spherical Acoustic Resonator

There is currently great interest in the international metrological community for new accurate determinations of the Boltzmann constant k _B, with the prospect of a new definition of the unit of thermodynamic temperature, the kelvin. In fact, k _B relates the unit of energy (the joule) to the unit of the thermodynamic temperature (the kelvin). One of the most accurate ways to access the value of the Boltzmann constant is from measurements of the velocity of the sound in a noble gas. In the method described here, the experimental determination has been performed in a closed quasi-spherical cavity. To improve the accuracy, all the parameters in the experiment (purity of the gas, static pressure, temperature, exact shape of the cavity monitored by EM microwaves, etc.) have to be carefully controlled. Correction terms have been computed using carefully validated theoretical models, and applied to the acoustic and microwave signals. We report on two sets of isothermal acoustic measurements yielding the value k _B = 1.380 647 74(171) × 10⁻²³ J · K⁻¹ with a relative standard uncertainty of 1.24 parts in 10⁶. This value lies 1.9 parts in 10⁶ below the 2006 CODATA value (Mohr et al., Rev. Mod. Phys. 80, 633 (2008)), but, according to the uncertainties, remains consistent with it.     

B111, B112, B113, and B114: The most stable core-shell borospherenes with an icosahedral B12 core at the center exhibiting superatomic behaviors

Boron allotropes are known to be predominately constructed by icosahedral B₁₂ cages, while icosahedral-B₁₂ stuffing proves to effectively improve the stability of fullerene-like boron nanoclusters in the size range between B₉₈–B₁₀₂. However, the thermodynamically most stable core-shell borospherenes with a B₁₂ icosahedron at the center still remains unknown. Based on the structural motif of D_5h C₇₀ and extensive first-principles theory calculations, we predict herein the high-symmetry C_5v B₁₁₁⁺ (3) which satisfies the Wade’s n+1 and n+2 skeletal electron counting rules exactly and the approximately electron sufficient C_s B₁₁₁ (4), C_s B₁₁₂ (5), C_s B₁₁₃ (6), and C_s B₁₁₄ (7) which are the most stable neutral core-shell borospherenes with a B₁₂ icosahedron at the center reported to date in the size range between B₆₈–B₁₃₀, with C_s B₁₁₂ (5) being the thermodynamically most favorite species in the series. Detailed orbital and bonding analyses indicate that these spherically aromatic species all contain a negatively charged icosahedral B₁₂²⁻ core at the center which exhibits typical superatomic behaviors in the electronic configuration of 1S²1P⁶1D¹⁰1F⁸, with its dangling valences saturated by twelve radial B-B 2c-2e σ bonds between the B₁₂ inner core and the B₇₀ outer shell. The infrared (IR) and Raman spectra of the concerned species are computationally simulated to facilitate their future characterizations.

     

Ferroelectricity and antiferroelectricity in tellurium containing compounds with perovskite structure

A number of the Te-containing perovskite compounds (about 50) with compositions A²⁺₂B²⁺Te⁶⁺O₆, (A²⁺A³⁺)B¹⁺Te⁶⁺O₆ and (A³⁺A¹⁺)B²⁺TeO₆, where A²⁺ = Ba, Pb, Sr, Ca or Cd; A³⁺ = Bi or La; A¹⁺ = Na or Li; B¹⁺ = Na or Li, B²⁺ = Mg, Co, Zn, Mn, Cd or Ca were synthesized and a thorough investigation of their crystal structure and dielectric properties has been carried out. It was found that these compounds are ferro-, ferri- or antiferroelectrics. It is concluded that the sublattice of small and high charged Te⁶⁺ cations, is ferroelectric activity and that the Curie-temperatures of the investigated compounds are inversely proportional to the unit cell volumes and directly proportional to the degree of “rattling” of the small Te-cations in the oxygen octahedron.     

Disintegration of dextran sulfate tablet products: Effect of physicochemical properties

Abstract

Disintegration characteristics of three lots of enteric-coated dextran sulfate tablets (250 or 300 mg dosage formulations) from two manufacturers (A and B) were determined in 0.1M phosphate buffer at various pH levels between 5.0 and 7.5. Differences in disintegration times within- and between-lots were observed and appear to relate to differences in the nature and thickness of their enteric coatings. The composition of tablets and coatings was examined by Fourier-transform infrared spectroscopy. Lactose and a form of cellulose were the predominant excipients in the A and B formulations, respectively. The yellow coating on A tablets consisted mainly of a phthalic alkyd polyester modified with soya oil, whereas the white coating on B tablets contained mostly hydroxypropyl methylcellulose, modified with di-2-ethylhexylphthalate. Some yellow tablets appeared darker than the rest, attributable to the larger film thickness of dark yellow tablets (0.14 mm) compared with that of lighter tablets (0.06 mm). The more than twofold greater film thickness of dark yellow tablets was consistent with the near doubling of disintegration times at pH 6.8, from about 62 minutes for light yellow tablets to about 109 minutes for dark yellow tablets.     

Physical Chemistry of the Compounds AI I(BVUO6)2·nH2O (AI I = Mn, Ni, Co, Zn, Cd; BV = P, As)

The ion exchange between an aqueous solution of a bivalent metal chloride (A^{I I} = Mn, Ni, Co, Zn, Cd) and crystalline phases HB^VUO₆·4H₂O (B^V = P, As) was studied. The exchange constants and standard Gibbs energies of formation of the crystalline compounds A^{I I}(B^VUO₆)₂·nH₂O were calculated.     

Correction to the formula for the London moment of a rotating superconductor

This paper gives a full quantum mechanical analysis of the magnetic field (first discussed by London) that appears spontaneously when a sample of superconductor is set into rotation. It is shown that, for slow rotation velocities and using certain approximations, the fieldB threading a cavity within a superconductor that rotates at angular velocity is given bye B=2(m _o–W/c ²), where — e is the charge on the electron,m _o is the free electron mass,W is the work function of the superconductor, andc is the velocity of light. In this calculation effects that are second order in the rotation velocity have been ignored, and the result is only strictly valid at the zero of temperature. The application of this result to experiments using practical, nonideal apparatus is then illustrated for a simple geometry.This work was supported in turn by the Science Research Council; Trinity College, Cambridge; and the U. S. Department of Commerce under contract number NB81RAC10026.