Theory of the Senftleben-Beenakker effects for NH3 and ND3: Collision integrals

The distorted wave Born approximation is used as a basis for understanding the cross sections which govern the production and relaxation of internal state polarizations, in gaseous ammonia, in the presence of shear flow or thermal gradients. For viscous flow, it is shown that the dominant dipole-dipole interaction leads to the production of [W]⁽²⁾J polarization, but not to any appreciable [J]⁽²⁾ polarization. The essential absence of the usual [J]⁽²⁾ polarization, as produced by the anisotropic dispersion interaction (P₂-potential), is consistent with the smallness of the anisotropy of the dipole polarizability in ammonia and with the suppression of the effect of such shorter ranged interactions (e.g. the P₂ potential) in the presence of a dominant longer ranged interaction (there the dipole-dipole potential). For thermal conduction, it is shown that the dominant dipole-dipole interaction apparently produces predominantly a $\text{WJ(W}{}^2\text{?}\text{5}\text{2}\text{)}$ polarization. The shorter ranged dipole-quadrupole interaction as well as higher multipole potentials produce a W[J]⁽²⁾ polarization, while a cross term between the dipole-dipole and quadrupole-dipole potentials can produce a velocity-independent dipolar polarization, denoted here as Jh¹.     

Steady flows in networks of microfluidic channels: building on the analogy with electrical circuits

This paper gathers comments and elaborations on the classical representation of networks of microfluidic channels in terms of equivalent electrical circuits. Basics on pressure-driven and electro-osmotic flows are first recalled. A unified formalism for hydrodynamic and electro-kinetic effects in networks of arbitary topology is then presented. Eventually, comments on the representation of pumps by generators are proposed. To cite this article: A. Ajdari, C. R. Physique 5 (2004).     

Improved higher order phase-integral approximations of the JWKB type in the vicinity of zeros and singularities of the “wave number”

This paper treats the local behaviour of certain phase-integral approximations (PIA) of arbitrary order. This is done for the vicinities of zeros and poles of the coefficient Q²(z) in the wave-equation d²ψ/dz²+Q²(z)ψ = 0. This coefficient can be complex on the real axis. A simple formula relating the cumulative error of PIA (μ-integral) to the first truncated correction in the phase-integral expansion is derived. For a simple model of a zero or pole of Q²(z), PIA of arbitrary order are determined explicitly. Their phase-integrals exhibit certain symmetry properties which justify the “loop integrals” often used in the JWKB formulae when applied in higher orders. We demonstrate the asymptotic character of the phase-integral expansion explicitly and determine its optimum order and accuracy. The well-known connection formulae are shown to retain their one-directional character in higher orders. Modifications which improve PIA at their critical points are also discussed in detail both at the modification point and elsewhere. Some quantum mechanical applications are also discussed.     

The photoelectron spectra of tricyclo[3.3.0.02,6]Octene and tricyclo[3.3.0.02,6]Octane

The photoelectron spectra of tricyclo[3.3.0.0^2,6]octene (1) and tricyclo[3.3.0.0^2,6]octane (2) have been recorded. The first bands in these spectra are correlated with orbitals which are linear combinations of the Walsh orbitals and of the olefinic π-orbital. This assignment is based on a zero differential overlap molecular orbital model as well as on the results of extended Hückel calculations. The resonance integral <π|H|W > for 1 is found to be ?1.34 eV.     

Phonons in the organic conductor TEA(TCNQ)2 studied by neutron inelastic scattering

The lattice dynamics of the one-dimensional organic conductor TEA(TCNQ)₂ is studied by inelastic neutron scattering at temperatures 77, 175 and 295 K. Special attention is paid to the phonons propagating along c¹ which is approximately along the conducting axis. These phonons show a well defined Kohn anomaly at 2k_F as well as gaps which we attribute to both the tetrametic structure of the crystals and to the electron- phonon coupling. The temperature variation of the phonons along c¹ is found to be typical for a system where electron-phonon coupling dominates.     

Note on the calculation of electrostatic lattice potentials

We reconsider the problem of calculating electrostatic lattice potentials, or in fact potentials of the type |r|^βφ_l(r), where φ_l(r) is the lth derivative of the l/|r|^p potential. According to Ewald, and generalized by Nijboer and de Wette, the slowly converging potential can be expressed in two screened potentials, one on the original lattice and the other on the reciprocal lattice, which are rapidly converging. In general these screenings are related by a type of Hankel transform. The request of (asymptotic) symmetry between the screenings then leads to the well-known screenings as the best possible. Detailed formula needed for calculations are given.     

Ultrasound-assisted synthesis of water-soluble monosubstituted diruthenium compounds

The elusive monosubstituted diruthenium complexes [Ru₂Cl(DAniF)(O₂CMe)₃] (1), [Ru₂Cl(DPhF)(O₂CMe)₃] (2), [Ru₂Cl(D-p-CNPhF)(O₂CMe)₃] (3), [Ru₂Cl(D-o-TolF)(O₂CMe)₃] (4), [Ru₂Cl(D-m-TolF)(O₂CMe)₃] (5), [Ru₂Cl(D-p-TolF)(O₂CMe)₃] (6) and [Ru₂Cl(p-TolA)(O₂CMe)₃] (7) have been synthesized using for the first time ultrasound-assisted synthesis to carry out a substitution reaction in metal–metal bonded dinuclear compounds (DAniF⁻ = N,N′-bis(4-anisyl)formamidinate; DPhF⁻ = N,N′-diphenylformamidinate; D-p-CNPhF⁻ = N,N′-bis(4-cyanophenyl)formamidinate; D-o/m/p-TolF⁻ = N,N′-bis(2/3/4-tolyl)formamidinate; p-TolA⁻ = N-4-tolylamidate). This is a simpler and greener method than the tedious procedures described in the literature, and it has permitted to obtain water-soluble complexes with good yields in a short period of time. A synthetic study has been implemented to find the best experimental conditions to prepare compounds 1–7. Two different types of ligands, formamidinate and amidate, have been used to check the generality of the method for the preparation of monosubstituted complexes. Five new compounds (2–6) have been obtained using a formamidinate ligand, the synthesis of the previously described compound 1 has been improved, and an unprecedented monoamidate complex has been achieved (7). The crystal structures of compounds 3 and 7 have been solved by single crystal X-ray diffraction. These compounds show the typical paddlewheel structure with three acetate ligands and one formamidinate (3) or amidate (7) bridging ligand at the equatorial positions. The axial positions are occupied by the chloride ligand giving rise to one-dimensional polymer structures that were previously unknown for monosubstituted compounds.     

Ab initio SCF-Cl studies on the large amplitude bending motion of the water molecule: Rigid,semirigid, and nonrigid bender models for the Hamiltonian

Self-Consistent Field (SCF) and Configuration Interaction (CI) studies are performed on the bending mode of the water molecule using a double zeta plus polarization basis set. The ab initio points are fitted to a three-parameter double minimum potential consisting of a quadratic plus Lorentzian terms. The vibration-rotation energies are then evaluated using the large amplitude Hamiltonian developed by P. R. Bunker and co-workers at various levels of approximations. It is found that the calculated frequencies improve significantly as one proceeds from approximate H_b⁰⁰(ρ) to rigid bender H_b⁰(ρ) [P. R. Bunker and J. M. R. Stone, J. Mol. Spectrosc.41, 310–332 (1972)] to semirigid bender H_b⁰(r, ρ) [P. R. Bunker and P. M. Landsberg, J. Mol. Spectrosc.67, 374–385 (1977)] Hamiltonian. With H_b⁰(r, ρ), the ab initio calculated bending frequency ν₂ differs from the observed value (1595 cm^?1) by 30 cm^?1 and the barrier height is 12 229 cm^?1. It is also shown that ν₂ and its first four overtones are better calculated by 45–98 cm^?1 when the ab initio potential is used directly instead of the three-parameter analytic potential fitted to ab initio data. Finally, rotation bending energy levels are calculated for v₂ ≤ 3 and J ≤ 10 on the basis of a nonrigid bender Hamiltonian of A. R. Hoy and P. R. Bunker [J. Mol. Spectrosc.74, 1–8 (1979)], using the ab initio quadratic force field of P. Hennig, W. P. Kraemer, G. H. F. Diercksen, and G. Strey, [Theor. Chim. Acta47, 233–248 (1978)]. These results show that the accuracy of calculated force constants and frequencies is critically dependent not only on the size of the basis set but also on the number and spacing of the ab initio points used to derive the force field.     

Spontaneous and stimulated emission in the mid-ultraviolet range of quantum-well heterostructures based on AlGaN compounds grown by molecular beam epitaxy on c-sapphire substrates

This paper reports on the results of investigations of the spontaneous and stimulated luminescence in AlGaN heterostructures with a single quantum well and a high Al content (up to ～80 mol % in barrier layers), which were grown by plasma assisted molecular beam epitaxy (PAMBE) on c-sapphire substrates. It has been demonstrated that the stimulated emission occurs in the mid-ultraviolet range of the spectrum at wavelengths of 259, 270, and 289 nm with threshold excitation power densities of 1500, 900, and 700 kW/cm², respectively. It has been shown that there exists a possibility of TE polarization (E ⊥ c) of both stimulated and spontaneous luminescence down to wavelengths of 259 nm.     

A Pulsed EPR and DFT Investigation of the Stabilization of Coordinated Phenoxyl Radicals in a Series of Cobalt Schiff-Base Complexes

We recently demonstrated how the aerobic addition of acetic acid to N,N′-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexane-diamino Co^II, [Co(1)], leads to the formation of an unusual coordinated Co^III-phenoxyl radical. In this work, some of the structural aspects associated with the Schiff-base-derived ligand (1) that are crucial for the acid-mediated formation of the phenoxyl radical are investigated. For comparison with [Co(1)], we therefore studied the influence of acetic acid on two complexes: (1) the N,N′-bis(3,5-di-tert-butylsalicylidene)-1,2-ethane-diamino Co^II complex, [Co(2)], that lacks the cyclohexyl group of [Co(1)], and (2) the N′-disalicylidene-ethylenediamine Co^II salen complex, [Co(3)], that lacks both the tertiary butyl groups and the cyclohexyl groups. It is shown that the cyclohexyl group of [Co(1)] is not involved in the formation or stabilization of the phenoxyl radical, whereas the tertiary butyl groups of [Co(1)] play a crucial role. In addition, the characteristics of the phenoxyl radical, formed after aerobic addition of acetic acid to [Co(2)], are analyzed in detail by pulsed electron paramagnetic resonance, in combination with isotopic labeling. The experimental data are compared to density functional theory computations and to previous data on the acid-mediated phenoxyl radical of [Co(1)].     

Measurement of Δ1J(199Hg, 31P) in [HgPCy3(OAc)2]2 and relativistic ZORA DFT investigations of mercury–phosphorus coupling tensors

Using ³¹P solid-state NMR spectroscopy, anisotropy in the indirect ¹⁹⁹Hg-³¹P spin–spin coupling tensor (ΔJ) for powdered [HgPCy₃(OAc)₂]₂ (1) has been measured as 4700±300 Hz. Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations, including scalar and spin-orbit relativistic effects, performed on 1 and a series of other related compounds show that ΔJ(¹⁹⁹Hg, ³¹P) arises entirely from the ZORA Fermi-contact–spin-dipolar cross term. The calculations validate assumptions made in the spectral analysis of 1 and in previous determinations of ΔJ in powder samples, namely that J is axially symmetric and shares its principal axis system with the direct dipolar coupling tensor (D). Agreement between experiment and theory for various ¹⁹⁹Hg, ³¹P spin–spin coupling anisotropies is reasonable; however, experimental values of ¹J(¹⁹⁹Hg, ³¹P)_iso are significantly underestimated by the calculations. The most important improvements in the agreement were obtained as a result of including more of the crystal lattice in the model used for the calculations, e.g., a change of 43% was noted for ¹J(¹⁹⁹Hg, ³¹P)_iso in [HgPPh₃(NO₃)₂]₂ depending on whether the two or three nearest nitrate ions are included in the model. Finally, we have written a computer program to simulate the effects of non-axial symmetry in J and of non-coincidence of the J and D on powder NMR spectra. Simulations clearly show that both of these effects have a pronounced impact on the ³¹P NMR spectrum of ¹⁹⁹Hg–³¹P spin pairs, suggesting that the effects should be observable experimentally if a suitable compound can be identified.     

Field of linear frames as a fundamental self-interacting system

We present some philosophical and physical arguments supporting the hypothesis that the most fundamental self-interacting field in an amorphous space-time is the field of linear frames, i.e. the quadruple of vector bosons. We construct a wide class of Lagrangian dynamical models invariant under the total group of diffeomorphisms and under the natural action of the proper linear group GL⁺ (4, R) on the tetrad field. There exist some links between these models and the Hamiltonian dynamical systems on GL⁺ (3, R) (the mechanics of affinely-rigid bodies [23] [27]). We present the general form of field equations, conservation laws and Bianchi identities. There exist some formal similarities between our Lagrangians and those used in non-linear electrodynamics, in particular in the Born–Infeld theory [21]. We also give a few rough remarks concerning models invariant under natural subgroups of GL⁺ (4, R), i.e. under SL(4, R) and SO(1, 3; R) (special linear group and Lorentz group). The latter class includes the conventional Einstein relativity and the more general metrical-parallelism models. It turns out that there are GL⁺ (4, R)-invariant Lagrangians which are structurally alike the conventional Einstein Lagrangian.We have not derived as yet either mathematical or physical consequences of the presented model. Nevertheless, it seems to follow from our discussion that, a priori, the GL⁺ (4, R)-invariant tetrad models could be competitive with the Einstein theory. The next thing to be done would be a careful mathematical analysis of these models and attempts to compare their consequences with those of the Einstein relativity and of other field theories.     

On dielectric and magnetic relaxation phenomena and vectorial internal degrees of freedom in thermodynamics

It has been shown by the author in a previous paper that thermodynamic vectorial internal degrees of freedom which influence the polarization or the magnetization of a medium may give rise to dielectric or magnetic relaxation phenomena. Snoek's equation for magnetic relaxation phenomena was derived and it was shown that Debye's theory for dielectric after-effects in polar liquids is a special case of the developed theory. In this paper it is shown that if Z is some vectorial internal degree of freedom which influences the polarization a new internal degree of freedom bip^(int) may be defined which is a function of biZ, which may replace biZ as vectorial internal degree of freedom and which is a part of the total specific polarization. Furthermore, p^(int) may be introduced in such a way that the remaining part of the polarization, p^(el) (defined by $\text{p}{}^{\mathrm{<mtext>(</mtext><mtext>el</mtext><mtext>)</mtext>}}\text{=}\text{p}\text{?}\text{p}{}^{\mathrm{<mtext>int</mtext><mtext>)</mtext>}}$, where p is the total polarization per unit of mass), has the property that it vanishes for all values of p^(int) if the medium is in a state where the electric field E and the mechanical elastic stresses vanish and the temperature of the medium equals some reference temperature. If the equations of state are linearized the latter result implies for an isotropic medium $\text{E}\text{=ρa}{}^{\mathrm{(0,0)}}{}_{\mathrm{(bdp)}}\text{p}{}^{\mathrm{<mtext>(</mtext><mtext>el</mtext><mtext>)</mtext>}}$, where ρ is the mass density and a^(0,0)_(P) a constant. On the other hand p^(int) satifies a relaxation equation. It is seen that the use of p^(int) as an internal degree of freedom is of great advantage. This is connected with the fact that p^(int) is a measurable quantity in contradistinction to an arbitrary “hidden” vectorial internal degree of freedom. Analogous results may be obtained for magnetic after-effects.     

Pearson-walk visualization of the characteristic function of the invariant measure for 1-d chaos

The Pearson-walk visualization of one-dimensional (1-d) chaos, which has been proposed in a qualitative fashion by the same authors recently (Physica 134A (1985) 123) is treated quantitatively. Continuity of the Pearson image is deduced for a map f(x) whose kth iterate f^k(x) is continuous for any k. Then the Lyapunov exponent is used to describe the length of the Pearson image. The normalized Pearson-walk visualization is introduced to show that it can be related to the existence of the invariant measure. For a 1-d map that has a definite invariant measure it is shown that the characteristic function of the invariant measure is represented by a unique point in the normalized Pearson plane for a large iteration-number limit.     

Magnetic Resonance Imaging of Diffusion in the Presence of Background Gradients and Imaging of Background Gradients

The measurement of the self-diffusion coefficient D by an NMR technique that uses an applied gradient G_A can be corrupted by systems that have a background magnetic field gradient G₀ and also by imaging gradients G₁, when used in an imaging mode. In a nonimaging mode, the corrupting cross term G_A · G₀can be eliminated in the diffusion measurement by use of an alternating-pulse-field-gradient (APFG) sequence that allows an accurate and uncorrupted measurement of D. A Carr-Purcell echo train enables the measurement of the expectation value, 〈DG²₀〉; assuming D and G₀ to be uncorrelated will allow 〈G²₀〉 to be determined. An image of D or of 〈DG²₀〉 may be obtained without the corrupting G_A · G₀ and G_A · G_I terms by appending a standard imaging sequence to an APFG sequence or a Carr-Purcell sequence, respectively; assuming D and G₀ to be uncorrelated will allow (〈G²₀〉 to be determined within each pixel. Measurements of D and 〈G²₀〉 and their images are made in apple flesh in which minute air bubbles are shown to produce the large 〈G²₀〉. Their values in an 81 g Golden Delicious apple at a measuring frequency of 100 MHz were D = 1.42 × 10⁻⁵ cm²/s and [formula] = 8.9 G/cm.     

States on the current algebra

We introduce the field algebra Σ$\text{D}$(M;ⁿ?ⁿ$\text{g}$) associated with the current algebra $\text{D}$_r(M;$\text{g}$) for the Lie algebra $\text{g}$ over physical space M. The Heisenberg magnet model is generalized to this continuum. It is shown that the Hamiltonian can be given meaning as implementing a derivation of the field algebra in certain representations.We introduce new representations of the current algebra. For example, if G = SU(2), a representation in L²(R³)?³ is [σ(?)F]^j = ε^jkl?_kψ_l for (?_k) = ? in $\text{D}$_r(M;$\text{g}$)(ψ_l = F. This has cyclic subrepresentations with prime parts.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Study on spin configuration in photoresponsive iron mixed-valence complexes by Mössbauer spectroscopy

We have investigated magnetic properties in a series of photoresponsive dithiooxalato (dto)-bridged iron mixed-valence complexes, (SP-R)[Fe^IIFe^III(dto)₃] (SP-R = R-substituted pyridospiropyran cation; R = Me, Et, and Pr; abbreviated as 1 ^Me, 1 ^Et, and 1 ^Pr, respectively). As for our previous reports, 1 ^Me and 1 ^Et show two-step succeeding ferromagnetic transitions at T _C?=?25 & 8 K and 22 & 5 K, respectively. However, 1 ^Et has no hysteresis in the magnetic susceptibility, while 1 ^Me undergoes the charge transfer phase transition with thermal hysteresis around 75 K. To elucidate the two-step transitions of them, we measured ⁵⁷Fe Mössbauer spectra of 1 ^Et. The spectra of Fe^II (S?=?2) and Fe^III (S?=?1/2) in the HTP were observed in the magnetically ordered state as well as the paramagnetic state, and revealed that only HTP exists in a temperature range up to 5 K. The result is consistent with that of 1 ^Pr, where one ferromagnetic phase transition occurs at T _C?=?10 K. ⁵⁷Fe Mössbauer spectroscopy is useful to clarify the origin of the succeeding magnetic transition for these systems.