Fluid-dynamical representations of the Dirac equation

A relative kinetic mass operator is defined bym =c ⁻²·(E −eΦ), and it is shown that bt using it in a symmetric form one can correlate the (charge) velocity operatorα in the Dirac theory exactly with the general quantum mechanical momentum —ih∇. Then the net force, defined as the rate of change of the relative momentum with time, is exactly equal to the Lorentz force. The contribution due to the time variation of mass equals the negative of space variation of the scalar potential, the Newtonian force, whereas the time variation of the charge current absorbs the entire vector potential dependence. The analogous Euler equations can be written either in terms of the charge current or in terms of the mass current. For a many particle system one needs the usual net single particle parameters and the consideration of both the direct and exchange contributions of the two particle interaction. These Euler equations yield two different conditions of the stationary state. It is shown that the charge-current condition is necessary but not sufficient, whereas the mass-current condition retains the appropriate scalar potential dependence. These two conditions are compared for the spherically symmetric case. The charge density, charge current and relative mass current are tabulated for atomic spinors. Differences between the quantum and classical forces for the H ₂ ⁺ molecular ion exhibit the inadequacy of ordinary atomic spinor basis in forming molecular spinors.     

Contribution to the theory of Lorentzian ionization

The probability w _L of Lorentzian ionization, which arises when an atom or ion moves in a constant magnetic field, is calculated in the quasiclassical approximation. The nonrelativistic (v≲e ²/ℏ=1, v is the velocity of the atom) and ultrarelativistic (v→c=137) cases are examined and the stabilization factor S, which takes account of the effect of the magnetic field on tunneling of an electron, is found. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 391–396 (10 March 1997)     

Kinematics of Cherenkov’s effect with noninvariant velocity of light

The kinematics of Cherenkov’s effect is considered for an electron moving in the Minkowski space with universal time and velocity of light c = c ₀ (1 + v ²/c ₀²)^1/2, where c ₀ = 3⋅10 m/s is the invariant constant and v is the particle velocity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 47–50, January, 2009.     

Field theoretic calculation of energy cascade rates in non-helical magnetohydrodynamic turbulence

Energy cascade rates and Kolmogorov’s constant for non-helical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimensiond = 3, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov’s constant for magnetohydrodynamics is approximately equal to that for fluid turbulence (≈ 1.6) for Alfvén ratio 05 ≤r _A ≤ ∞. For higher space-dimensions, the energy fluxes are qualitatively similar, and Kolmogorov’s constant varies asd ^1/3. For the normalized cross helicity σ_c →1, the cascade rates are proportional to (1 − σ_c)/(1 + σ_c , and the Kolmogorov’s constants vary significantly with σ_cc.     

Magnetotransport properties of a layered La1.6Ca1.4Mn2O7 polycrystal

Magnetotransport properties of a two-layered La_1.6Ca_1.4Mn₂O₇ polycrystal have been examined as a function of temperature and applied field. It was found that the magnetic transition temperature (T_c) is about 70 K higher than the insulator–metal transition temperature (T_p). Two peaks were observed on both the temperature dependence of the imaginary part of the ac magnetic susceptibility χ^′′(T ) and that of the magnetoresistance MR(T). One is slightly below T_p∼107 K and the other is near T_c∼170 K. Below 70 K, the MR ratio increases with decreasing temperature. Around and above T_p but below T_c, the magnetization shows some indication of saturation, whereas the MR ratio shows no indication of saturation. The magnetotransport properties can be explained by considering the anisotropy exchange interactions along the a–b plane and the c direction, and the low-temperature MR can be attributed to the effects of the nearly fully spin-polarized carriers’ tunneling through the insulating (La,Ca)₂O₂ layers between the adjacent MnO₂ bilayers. Received: 18 September 2000 / Accepted: 20 February 2001 / Published online: 26 April 2001     

Spatial parity violation in Mössbauer transition of Np-237 nucleus

The measurements of 59.6 keV γ-radiation circular polarization of Np-237 unpolarized oxcited nuclei gave the value P_c=(−1.23±0.25)·10⁻³. It characterizes P-parity violation in this transition. The matrix element of the weak NN-interaction <v>=(0.92±0.25)·10⁻¹ eV was obtained from this experimental data.     

Brownian motion in a classical ideal gas: A microscopic approach to Langevin’s equation

We present an insightful ‘derivation’ of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton’s law of motion (mx = F) for the heavy particle reduces to a Langevin equation (valid on a coarser time-scale) with the assumption that the lighter gas particles follow a Boltzmann velocity distribution. Starting from the kinematics of the random collisions we show that (1) the average force 〈F〉 ∞ −x and (2) the correlation function of the fluctuating forceη = F — 〈F〉 is related to the strength of the average force. Deceased     

Calculation of spectroscopic constants and radiative parameters for A1Σ u+ -X1Σ g+ and B1Πu-X1Σ g+ electronic transitions of sodium dimer

Vibrational, rotational, and centrifugal spectroscopic constants and radiative parameters, i.e., the Einstein coefficients, oscillator strengths, and wave numbers for vibrational transitions in electronic systems of bands A ¹Σ _u ⁺-X ¹Σ _g ⁺ (0 ≤ v′ ≤ 25; 0 ≤ v″ ≤ 44), B ¹Π _u -X ¹Σ _g ⁺ (0 ≤ v′ ≤ 29; 0 ≤ v″ ≤ 47), and the radiative lifetimes for the vibrational levels of excited states of the sodium dimer, are calculated. The calculations are carried out based on semiempirical potential curves constructed in this study. The calculated spectroscopic constants and radiative lifetimes are compared to the experimental values.     

Conservation laws for classical and relativistic collisions. I

On the basis of simple kinematic arguments it is shown that any quantity, depending only on the nature and velocity of a particle, that is conserved in a collision must, in classical mechanics, be of the form λ+Σ_iμ_iυ_i+1/2vυ ² or in relativistic mechanics of the form λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc [1−(υ ²/c ²)]^−1/2 where λ,μ _i, andν are particle parameters.     

A Way To Discover Maxwell's Equations Theoretically

The Coulomb force, established in the rest frame of a source-charge Q, when transformed to a new frame moving with a velocity V has a form F = q E + q v × B, where E = E′_∥ + γE′_⊥ and B = (1/c ²)v × E and E′ is the electric field in the rest frame of the source. The quantities E and B are then manifestly interdependent. We prove that they are determined by Maxwell's equations, so they represent the electric and magnetic fields in the new frame and the force F is the well known from experiments Lorentz force. In this way Maxwell's equations may be discovered theoretically for this particular situation of uniformly moving sources. The general solutions of the discovered Maxwell's equations lead us to fields produced by accelerating sources.     

The wideband attenuation of short radio waves on mid-latitude paths during X-ray flares in January 2005

We present the results of the ionosphere oblique chirp sounding on the Cyprus—Nizhny Novgorod, Cyprus—Rostov-on-Don, and Moscow—Rostov-on-Don mid-latitude paths during X-ray flares in January 17, 19, and 20, 2005. It is found that during strong flares the blackout of short radio waves was observed over the entire frequency range of chirp sounding on the Cyprus—Nizhny Novgorod and Cyprus—Rostov-on-Don paths. Modeling of the electron-density profiles in the lower ionosphere based on absorption of short radio waves on the Moscow—Rostov-on-Don path at different stages of the decay of the X-ray radiation intensity is carried out. It is shown that at the instant corresponding to the maximum value of the flare radiation flux, the electron density in the lower ionosphere at altitudes 60–80 km increased by a factor of about 10 and 100 for flares with radiation flux densities 5·10⁻² and 3·10⁻¹ erg/(cm ²·s) in the wavelength range 0.5–4.0 Å which took place in January 19 and 20, respectively. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 1, pp. 1–8, January 2007.     

Heat capacity of MnBr2·4H2O near the antiferromagnetic transition temperature

Heat capacity of MnBr₂·4H₂O has been measured in the critical region around the Neel temperature. The data can be fitted, over a restricted range of |t|⩽10⁻², to the asymptotic power law. The critical exponents and the amplitudesA andA′ are not consistent with any theoretic predictions. However when scaling constraints are imposed, their values agree with the parameters of Ising model. Corrections to scaling are necessary to extend the range of the fit to |t|>10⁻². The correction terms are asymmetric giving −1·15±0·25 as the ratio of the amplitudes of the lowest order correction terms,D andD′ above and belowT _c. This value is in agreement with the recent predictions of the renormalisation group theory.     

Anharmonic force constants of GaSb from the measured third order elastic constants at 300°K

The third-order elastic constants of single crystal GaSb are determined using ultrasonic pulse interferometer at 10 MHz. The constants at 300°K, in units of 10¹¹ N.m.⁻², are C_l11 = ™ 4 ·75 ± 0·06 C₁₄₄ = + 0·50 ± 0·25 C₁₁₃ = ™ 3 ·08 ± 0·02 C₁₆₆ = ™ 2·16 ± 0·13 C₁₂₃ = ™ 0 ·44 ± 0·29 C₄₅₆ = ™ 0·25 ± 0·15 These constants are used to evaluate the three anharmonic first and second neighbour force constants based on modified Keating’s model. The constants are (in units of 10¹¹ N.m⁻²)γ=− 2·406;δ=0·407;ε=−0·222.     

Plane and cylindrical shock waves in magnetogasdynamics

Summary The Chisnell-Chester-Whitham method has been used to study the propagation of diverging plane and cylindrical shock waves through an ideal gas in the presence of a magnetic field having only constant axial and azimuthal components, simultaneously for both weak and strong cases. By assuming an initial density distribution ϱ₀ = ϱ′r ^−W , where ϱ′ is the density at the plane/axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strength have been obtained. The expressions for the pressure, the density and the particle velocity immediately behind the shock have been derived for both the cases.

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Riassunto Il metodo di Chisnell-Chester-Whitham è stato usato per studiare la propagazione di onde d’urto divergenti cilindriche e piane attraverso un gas ideale in presenza di un campo magnetico che ha solo componenti costanti assiali e azimutali, contemporaneamente per casi deboli e forti. Assumendo una distribuzione di densità iniziale ϱ₀ = ϱ′r ^−W , dove ϱ′ è la densità al piano/asse di simmetria ew è una costante, si sono ottenute le espressioni analitiche per la velocità d’urto e la forza d’urto. Le espressioni per la pressione, la densità e la velocità delle particelle immediatamente dopo l’urto sono state determinate per entrambi i casi.

     

Charge-separated-state enhancement of the third-order optical nonlinearity of a photosensitizer-electron acceptor triad assembly

′ ,4^′′,4^′′′-tetrasulfonato-phthalocyanine/N-butyl-N^′-methylanthraquinone-4,4^′-bipyridinum dibromide assembly (ZnTsPc-V-AQ), was observed to be enhanced by ten times when the sample was optically pumped by a 355 nm pump beam. The enhancement of the nonlinearity was found to be due predominantly to the charge transfer between the two monomers of the supramolecule after optical excitation. Received: 2 July 1996     

Chemical, morphological and chromatic behavior of mural paintings under Er:YAG laser irradiation

Several pigments (malachite CuCO₃⋅Cu(OH)₂, azurite 2CuCO₃⋅Cu(OH)₂, yellow ochre (goethite α-FeOOH, gypsum CaSO₄⋅2H₂O), St. John’s white CaCO₃ formed from slaked lime) and respective mural paintings specimens were subjected to the free-running Er:YAG laser radiation in order to study their damage thresholds, in a broad range of laser fluences, both in dry and wet conditions. The specimens’ damage thresholds were evaluated by spectroscopic methods, colorimetric measurements and microscopic observation. The pigments containing –OH groups were found to be more sensitive than St. John’s white; hence the most sensitive paint layers in dry conditions are those containing malachite, azurite (both 1.3 J/cm²) and yellow ochre (2.5 J/cm²) as compared to the ones containing St. John’s white (15.2 J/cm²). The presence of wetting agents (w.a.) attenuated the pigments chemical alteration. The damage thresholds of all the paint layers, in presence of w.a., were found to be around 2.5 J/cm². The alteration was caused by thermo-mechanical damage and by binding medium ablation of a fresco and a secco prepared specimens, respectively.     

Critical point phenomena in the electrical resistivity of binary liquid systems: CS2 + CH3CN and CS2 + CH3NO2

Electrical resistance measurements are reported on the binary liquid mixtures CS₂ + CH₃CN and CS₂ + CH₃NO₂ with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport. For the liquid mixture filled at the critical composition, the resistance of the system aboveT _c follows the relationR=R _c−A(T−T _c) ^b withb=0·6±0·1. BelowT _c the conductivities of the two phases obey a relation σ₂−σ₁=B(T _c−T)^β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium property.     

Calculation of radiative parameters for the $$ {A^1}\sum\nolimits_u^{+} {{X^1}} \sum\nolimits_g^{+} {} $$-transition of cesium dimer

Radiative parameters for vibrational bands (0 ≤ v′ ≤ 30, 0 ≤ v′′ ≤ 59) of the A¹?_u⁺ X¹ ?_g⁺ {A^1}\sum\nolimits_u^{+} {{X^1}} \sum\nolimits_g^{+} {} -electronic transition of a cesium dimer are calculated. These include vibronic band wavenumbers, Franck–Condon factors, Einstein coefficients for spontaneous emission, absorption band oscillator strengths, and radiative lifetimes for vibrational levels of the excited electronic state. Vibrational energies and wave functions for the ground and excited electronic states were found by a numerical solution of the radial wave equation based on potential curves plotted during the course of the study.     

Non-unitary minimal models,Bailey's Lemma and <Emphasis Type="Italic">N</Emphasis>=1,2 Superconformal algebras

Using the Bailey flow construction, we derive character identities for the N=1 superconformal models SM(p′,2p+p′) and SM(p′,3p′−2p), and the N=2 superconformal model with central charge c=3 from the nonunitary minimal models M(p,p′). A new Ramond sector character formula for representations of N=2 superconformal algebras with central element c=3 is given. Supported in part by NSF grant DMS-0200774.     

Search for a fourth generation b’-quark at LEP-II at ?s= \sqrt{s}=\,196–209?GeV

A search for the pair production of fourth generation b’-quarks was performed using data taken by the DELPHI detector at LEP-II. The analysed data were collected at centre-of-mass energies ranging from 196 to 209 GeV, corresponding to an integrated luminosity of 420 pb^-1. No evidence for a signal was found. Upper limits on BR(b’→bZ) and BR(b’→cW) were obtained for b’ masses ranging from 96 to 103 GeV/c ². These limits, together with the theoretical branching ratios predicted by a sequential four generations model, were used to constrain the value of , where V_cb′, V_tb′ and V_tb are elements of the extended CKM matrix.