Painlevé analysis and integrability of the damped anharmonic oscillator equation

The Painlevé analysis is applied to the anharmonic oscillator equation . The following three integrable cases are identified: (i)C=0,d ²=25A/6,A>0,B arbitrary, (ii)d ²=9A/2,B=0,A>0,C arbitrary and (iii)d ²=−9A/4,C=2B ²/(9A),A<0,C<0,B arbitrary. The first two integrable choices are already reported in the literature. For the third integrable case the general solution is found involving elliptic function with exponential amplitude and argument.     

Intramolecular surfaces for vicinal proton–proton coupling constants 3JHH

Equations for the intramolecular surfaces of the ³J_HH coupling constants in ethane, ethylene, and acetylene are formulated, and the corresponding coefficients are estimated from calculations at the DFT/B3LYP level. The chosen variables are changes in bond lengths, in the torsion angle φ between the coupled protons H_a and H_b, in bond angles, and in dihedral angles. The ³J_HH surface of ethane is formulated as an extended Karplus equation with the coefficients of a truncated Fourier series on the torsion angle φ expanded as second-order Taylor series in the chosen variables taking into account the invariance of ³J_HH under reflections and rotations of nuclear coordinates. Partial vibrational contributions from linear and square terms corresponding to changes in the geometry of the H_a ? C_a ? C_b ? H_b fragment are important while those from cross terms are small with a few exceptions. The ³J_HH surface of ethane is useful to predict contributions to ³J_HH from changes in local geometry of derivatives but vibrational contributions are predicted less satisfactorily. The predicted values at the B3LYP/BS2 level of the ³J_HH couplings (vibrational contributions at 300 K) from equilibrium geometries are 9.79 (?0.17) for acetylene, and 17.08 (1.93) and 10.73(0.93) for the trans and cis couplings of ethylene.     

Weak Neutrino-Lepton Annihilation into Hadrons

An exploratory study of weak neutrino-lepton annihilation into hadrons, v̄_l + l → hadrons is presented. Simple cross-section estimates indicate processes of this type may be observable in a large bubble chamber. We discuss the information one could hope to obtain from such experiments. General formulas for amplitudes and cross sections are given for v̄_l + l → hadrons assuming a point-like V – A interaction. To establish tests of the V – A interaction, we recalculate the annihilation amplitudes assuming a point-like scalar-pseudoscalar or tensor-pseudotensor interaction. The extension to theories with intermediate vector bosons is sketched. We discuss the connection between v̄_l + l → hadrons and e⁺e⁻ → hadrons implied by the conserved vector current hypothesis. We note that in v̄_l + l → rH, K⋆(890), A₁, B creation (these reactions enjoy comparatively large cross sections) the leptonic as well as hadronic couplings of these J = 1 , I = 1/2 or 1 mesons could be determined. A related possibility is the direct creation of new heavy charged J = 1 mesons. The normal J = 1 resonance region could be explored with neutrino energies of the order 500–2000 GeV. For this, and for higher-energy work, a TeV proton accelerator is clearly necessary.     

Thermal conductivity of fluids with steeply repulsive potentials

We consider the thermal conductivity of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, φ(r) = ε(σ/r)ⁿ. The time correlation function for the heat flux, C_λ(t), and the time average, C_λ(0) are calculated numerically by molecular dynamics simulations, and accurate expressions for these are also derived for the SRP fluid. We show, by molecular dynamics simulations, that close to the hard-sphere limit this time correlation function has the same analytic form as for the shear and pressure correlation functions for the shear and bulk viscosity, i.e. C_λ(t)/C_λ(0) = 1 ?T* (nt*)² + 0((nt*)⁴), where T* = k _B T/ε, is the reduced temperature, k _B is Boltzmann's constant and t* = (ε/σ²)^1/2 t is the reduced time. The thermal conductivity for the limiting case of hard spheres is numerically very close to that given by the traditional Enskog relation. At low densities the normalized relaxation times are typically largest for the thermal conductivity, followed by shear and then bulk viscosity. Close to the maximum fluid density, the latter two increase rapidly with density (especially for the shear) but continue a monotonic decline for the thermal conductivity. This reflects the relative insensitivity of the thermal conductivity to the approach to the fluid-solid phase boundary.     

Optical absorption studies on cobalt doped struvite

Abstract

Optical absorption spectrum of cobalt doped MgNH₄PO₄ · 6H₂O (struvite) is investigated in UV-VIS-NIR regions. The spectrum in UV-VIS-NIR region is attributed to Co²⁺ in octahedral symmetry whereas the IR spectrum is attributed to vibrations due to PO₄ ^3-, NH₄ ⁺ and H₂O. The following crystal field (Dq) and interelectronic repulsion (B, C) parameters are evaluated: Dq = 940cm^?1, B = 870cm^?1 and C = 3970cm^?1.     

Spin-lattice relaxation in 13CH3 compounds: application to 13C enriched aspirin

Spin-lattice relaxation processes in ¹³CH₃ groups in methyl compounds are studied both theoretically and experimentally. The four spin-½ nuclei in such methyl groups give rise to 16 spin-rotational states, which are split by rotational tunnelling. From the corresponding populations (15 independent) five long lived combinations are formed: the ¹³C magnetization M _C, proton magnetization M _H, tunnelling energy TE, rotational polarization RP and dipolar energy DE. Their spin-lattice relaxation via the transitions induced by the ¹³C-proton dipolar interaction is studied in detail. Direct relaxation rates and coupling terms between these combinations are derived. Predictions are compared with experimental data for ¹³C spin-lattice relaxation at 75.4 MHz in 99% enriched (only methyl carbons enriched) single crystal of aspirin. Above 40 K, the M _C recovery is exponential and describable in terms of the direct relaxation transitions without couplings. The same is true for the initial relaxation in the region of non-exponential relaxation between 30 K and 40 K. The orientation dependence of the initial relaxation rate agrees with the theoretical calculations. The non-exponentiality is related to resonant level-crossing transitions with ω_t, + ω_C = ω_H, where the angular frequencies represent rotational tunnelling and carbon and proton resonances, respectively. The resonant transitions produce couplings between M _C, M _H and TE that are described quite accurately by the present model.     

A many-body calculation of the hyperfine interaction in the lowest2S and2P states of li-like systems

A non-relativistic perturbation method of Brueckner-Goldstone type is used to calculate the hyperfine interactions in the lowest² S and² P states of the Li-like systems, Li, Be⁺, B²⁺, C³⁺, N⁴⁺, O⁵⁺ and F⁶⁺. The effect of the polarization of the closed shell is treated to all orders of perturbation, while the correlation effect is calculated in the lowest order, i.e. in the third order of the perturbation expansion. Experimental data are at present available only for Li, Be⁺ and F⁶⁺, and the agreement with the calculated values is in these cases very good, usually within the experimental uncertainties. This implies that the predictions made in the remaining cases should be quite reliable, which may simplify the experimental determination of these quantities. Theoretical values are also given for the quadrupole interaction, which can be used to determine the nuclear quadrupole moments, when accurate experimental information becomes available.     

Perturbations of Magnetic Schrödinger Operators

We study Schrödinger operators H(a, V): = (P – a)² + V acting in L ²(³). We assume that the magnetic field B = rot a may be decomposed as B = B ⁰ + B, where B ⁰ is a very general field having constant direction. The perturbations B and V will be small in a certain sense in the direction of B ⁰, but in the orthogonal plane they may even grow for certain fields B ⁰. Commutator methods are used to derive spectral properties of H(a, V).     

Determination of the Splitting of the 6a0 and 6b0 Bands of C-Hexadeuterobenzene in a Supersonic Jet

By using resonance-enhanced two-photon ionization, rotationally resolved spectra of the 6¹₀ band of ¹²C₆D₆ and (¹³C¹²C₅D₆ molecules have been obtained for the first time at a rotational temperature of 0.7 K in a pulsed supersonic beam. From the former, the values of B″ = 0.1573 ± 0.0008 cm⁻¹, B′ = 0.1508 ± 0.0008 cm⁻¹, and ξ′ = −0.412 ± 0.050 have been derived for rotational and Coriolis constants in the lower and upper levels of ¹²C₆D₆. Also, the spectra corresponding to ¹²C₆H₆ and ¹³C¹²C₅H₆ have been measured and the values B″ = 0.1892 ± 0.0008 cm⁻¹, B′ = 0.1815 ± 0.0008 cm⁻¹, and ξ′ = −0.586 ± 0.050 have been obtained for ¹²C₆H₆, in agreement with previous results. Rotational constants of ¹³C labeled benzene molecules have been geometrically deduced from the constants obtained. Experimental isotopic shifts of the vibronic origins of the 6a¹₀ and 6b¹₀ bands have been determined. There is agreement with previous ¹³C-benzene-h₆ data. The present results are −0.91 ± 0.05 and 3.09 ± 0.05 cm⁻¹ for ¹³C¹²C₅D₆ and −1.64 ± 0.05 and 2.64 ± 0.05 cm⁻¹ for ¹³C¹²C₅H₆. The splittings of vibrational modes 6b and 6a in the ¹B_2u state are 4.00 ± 0.10 cm⁻¹ for ¹³C¹²C₅D₆ and 4.28 ± 0.10 cm⁻¹ for ¹³C¹²C₅H₆.     

Temperature dependence of liquid volume

It is shown that the temperature dependence of the liquid volume is well described by the equation $ V = A + BT + CT^2 + V_e \exp ( - E/RT), $ V = A + BT + CT^2 + V_e \exp ( - E/RT), where A, B, C, V _e , and E are constants. This equation reflects two processes owing to which the liquid volume increases with temperature, namely, anharmonic oscillations of molecules and formation of “holes.”     

L-dependent heavy ion fusion potentials

The energyE and angular momentuml dependence of optical potential for fusion of¹⁶O+²⁰⁸Pb system, observed by Christleyet al [5], is expressed as a function of radial kinetic energy (ɛ) instead of explicitE andl dependence. It is shown that the effects of different channel couplings, which result in different effective potentials, can also be parametrized as a function ofɛ. A correlation is obtained between the energy dependent part of this effective potential and the maximum of the spin enhancement around the Coulomb barrier and both these quantities depend on the details of the channel couplings.     

CaCuMn<Subscript>6</Subscript>O<Subscript>12</Subscript> vs. CaCu<Subscript>2</Subscript>Mn<Subscript>5</Subscript>O<Subscript>12</Subscript>: A comparative study

The ferrimagnetic compounds Ca(Cu_xMn_3?x)Mn₄O₁₂ of the double distorted perovskites AC₃B₄O₁₂ family exhibit a rapid increase of the ferromagnetic component in magnetization at partial substitution of square coordinated (Mn³⁺)_C for (Cu²⁺)_C. In the transport properties, this is seen as a change of the semiconducting type of resistivity for the metallic one. The evolution of magnetic properties of Ca(Cu_xMn_3?x)Mn₄O₁₂ is driven by strong antiferromagnetic exchange interaction of (Cu²⁺)_C with (Mn³⁺/Mn⁴⁺)_B coordinated octahedra. The competing interactions of (Mn³⁺)_C with (Mn³⁺/Mn⁴⁺)_B lead to the formation of noncollinear magnetic structures that can be aligned by magnetic fields.     

Measurement of charged current triple gauge boson couplings using W pairs at LEP

Triple gauge boson couplings are measured from W-pair events recorded by the OPAL detector at LEP at centre-of-mass energies of 183 - 209 GeV with a total integrated luminosity of 680 pb^-1. Only CP-conserving couplings are considered and SU(2) x U(1) relations are used, resulting in four independent couplings, and g^z₅. Determining each coupling in a separate fit, assuming the other couplings to take their Standard Model values, we obtain , g^z₁ = 0.987 ^{+ 0.034}_-0.033, and g^z₅ = -0.04 ^{+ 0.13}_-0.12, where the errors include both statistical and systematic uncertainties. Fits are also performed allowing some of the couplings to vary simultaneously. All results are consistent with the Standard Model predictions.Received: 14 July 2003, Published online: 9 March 2004     

Survival and extinction in cyclic and neutral three-species systems

We study the ABC model ( A + B↦2B, B + C↦2C, C + A↦2A), and its counterpart: the three-component neutral drift model ( A + B↦2A or 2B, B + C↦2B or 2C, C + A↦2C or 2A.) In the former case, the mean-field approximation exhibits cyclic behaviour with an amplitude determined by the initial condition. When stochastic phenomena are taken into account the amplitude of oscillations will drift and eventually one and then two of the three species will become extinct. The second model remains stationary for all initial conditions in the mean-field approximation, and drifts when stochastic phenomena are considered. We analyzed the distribution of first extinction times of both models by simulations of the master equation, and from the point of view of the Fokker-Planck equation. Survival probability vs. time plots suggest an exponential decay. For the neutral model the extinction rate is inversely proportional to the system size, while the cyclic model exhibits anomalous behaviour for small system sizes. In the large system size limit the extinction times for both models will be the same. This result is compatible with the smallest eigenvalue obtained from the numerical solution of the Fokker-Planck equation. We also studied the behaviour of the probability distribution. The exponential decay is found to be robust against certain changes, such as the three reactions having different rates. Received 14 August 2002 and Received in final form 14 February 2003 / Published online: 1 April 2003 RID="a" ID="a"e-mail: ita@physics.ubc.ca     

On the Spectral Theory of Operator Pencils in a Hilbert Space

Abstract

Consider the operator pencil L _λ = A ? λB ? λ ² C, where A, B, and C are linear, in general unbounded and nonsymmetric, operators densely defined in a Hilbert space H. Sufficient conditions for the existence of the eigenvalues of L _λ are investigated in the case when A, B and C are K-positive and K-symmetric operators in H, and a method to bracket the eigenvalues of L _λ is developed by using a variational characterization of the problem (i) L _λ u = 0. The method generates a sequence of lower and upper bounds converging to the eigenvalues of L _λ and can be considered an extension of the Temple-Lehman method to quadratic eigenvalue problems (i).     

A Model of spin catalysis in bacterial photosynthetic reaction centres

A model of influence of non-heme Fe²⁺ ion on kinetics of electron transfer between quinone anion-radicals Q_A⁻ and Q_B⁻ in bacterial reaction centres is proposed and investigated. Physical mechanism of the influence is associated with singlet-triplet transitions in Q_A⁻Q_B⁻ Pair caused by interactions with paramagnetic Fe²⁺. The model incorporates exchange couplings between the particles and zero-field splittings in high-spin Fe²⁺. These interactions are shown to catalyze electron transfer in triplet pairs and alter the reaction yield significantly.     

The effects of high-energy ion irradiations on the I–V characteristics of silicon NPN transistors

The silicon NPN rf power transistors were irradiated with different linear energy transfer (LET) ions such as 50?MeV Li³⁺, 80?MeV C⁶⁺ and 150?MeV Ag¹²⁺ ions in the dose range of 1–100?Mrad. The SRIM simulation was used to understand the energy loss and range of these ions in the transistor structure. The different electrical parameters such as Gummel characteristics, excess base current (ΔI_B), DC current gain (h_FE), displacement damage factor (K) and output characteristics were systematically studied before and after irradiation. The ion irradiation results were compared with ⁶⁰Co-gamma irradiation result in the same dose range. A considerable increase in base current (I_B) and a decrease in h_FE and I_CSat were observed after irradiation. The degradation in the electrical parameters was comparably very high for Ag¹²⁺ ion-irradiated transistor when compared to other ion-irradiated transistors, whereas the degradation in the electrical parameters for Li³⁺ and C⁶⁺ ion-irradiated transistors was comparable with gamma-irradiated transistor. The isochronal annealing study was conducted on the 100?Mrad irradiated transistors up to 500°C to analyze the recovery in different electrical parameters. The h_FE and other electrical parameters of irradiated transistors were almost recovered after 500°C for 50?MeV Li³⁺, 80?MeV C⁶⁺ ion and ⁶⁰Co-gamma-irradiated transistors, whereas for 150?MeV Ag¹²⁺ ion-irradiated transistor, the recovery in electrical characteristics is not complete.     

Complements to various Stone-Weierstrass theorems forC *-algebras and a theorem of Shultz

J. Glimm's Stone-Weierstrass theorem states that ifA is aC ^*-algebra,P(A) is the set of pure states ofA, andB is aC ^*-subalgebra which separates , thenB=A. We show that ifB is aC ^*-subalgebra ofA andx an element ofA such that any two elements of which agree onB agree also onx, thenxB. Similar complements are given to other Stone-Weierstrass theorems. A theorem of F. Shultz states that ifxA ^**, the enveloping von Neumann algebra ofA, and ifx, x ^*, x, andxx ^* are uniformly continuous onP(A){0}, then there is an element ofA which agrees withx onP(A). We show that the hypotheses onx ^*x andxx ^* can be dropped.     

Electron-impact ionization and dissociation of C<Subscript>2</Subscript>D<Superscript>+</Superscript>

Absolute cross sections for electron-impact single ionization, dissociative excitation and dissociative ionization of the ethynyl radical ion (C₂D⁺)^+) have been measured for electron energies ranging from the corresponding reaction thresholds to 2.5 keV. The animated crossed electron-ion beam experiment is used and results have been obtained for the production of C₂D²⁺, C²⁺, C₂⁺_2^+ , CD⁺, C⁺ and D⁺. The maximum of the cross section for single ionization is found to be (2.01 ± 0.02) × 10^-17 cm², at the incident electron energy of 105 eV. Absolute total cross sections for the various singly charged fragments production are observed to decrease by a factor of almost three, from the largest cross-section measured for C⁺, over C₂⁺_2^+ and CD⁺ down to that of D⁺. The maxima of the cross sections are obtained to be (14.5 ± 0.5) × 10^-17 cm² for C₂⁺_2^+, (12.1 ± 0.1) × 10^-17 cm² for CD⁺, (27.7 ± 0.2) × 10^-17 cm² for C⁺ and (11.1 ± 0.8) × 10^-17 cm² for D⁺. The smallest cross section is measured to be (1.50 ± 0.04) × 10^-18 cm² for the production of the doubly charged ion C²⁺. Individual contributions for dissociative excitation and dissociative ionization are determined for each singly-charged product. The cross sections are presented in closed analytic forms convenient for implementation in plasma simulation codes. Kinetic energy release distributions of dissociation fragments are seen to extend from 0 to 6 eV for the heaviest fragment C₂⁺_2^+, up to 11.0 eV for CD⁺, 14.2 eV for C⁺ and 11.2 eV for D⁺ products.