Translation–rotation coupling in the self–diffusion of fluids: molecular dynamic investigation and a generalized exponential approach

Detailed molecular dynamics simulations are carried out to investigate the translation–rotation coupling in linear molecules. We calculated the moment of inertia ratio dependence of the self–diffusion coefficients D, the so–called dynamic isotope effect on the self–diffusion, in pure fluids. Our model systems consist of linear homonuclear pseudo–triatomic rigid molecules for three different molecular sizes over a wide range of density for a given temperature. For a compact representation of our results an exponential approach is employed, which demonstrates a strong translation–rotation coupling on the self–diffusion coefficient in a linear molecule. We find as a main result that in contrast to the low density behaviour at high densities the change of the rotation–translation coupling as a function of the moments of inertia is quite similar for all investigated molecules and we could explain this finding by a careful inspection of the corresponding velocity autocorrelation functions. Finally we present a comparison of experimental data for 20 neat molecular liquids and the corresponding theoretical predictions based on our findings for linear molecules. The good overall agreement indicates that our approach can be generalized and is therefore not only a compact representation of the calculated data but has also large predictive capabilities.     

Application of stereo vision to the study of mixed-mode crack-tip deformations

A stereo vision is applied to evaluate crack-tip parameters for fracture specimens subjected to a mixed-mode loading (tension and shear). By using a special loading device, the applied remote loading is oriented at an angle with respect to the axis of the crack. At each loading angle, the calibrated vision system was rotated so that the axis of the crack is parallel to the horizontal or vertical axis of the image frame. At a load close to the crack initiation, the displacement field around the crack-tip region of the fracture specimen was measured relative to a specimen coordinate system located at the crack tip of the fracture specimen. During the experiment, the fracture specimen was subjected to rigid body translation and rotation. Hence, the displacement fields are affected by the rigid body translation and rotation. Using the experimentally determined displacements and the analytically determined displacements with several higher order terms being included, the stress intensity factors and the amount of rigid body translation and rotation were calculated through a least-squares fit. The effect of the rigid body motion on the measured displacements was then eliminated using the computed rigid body translation and rotation. Experimental results indicate that a K_I and K_II dominant region is observed in the corrected displacement fields.     

Thermal averaging of the spin-rotation coupling in small molecules leads to an isotropic NMR shielding

It has been known for over 70 years that nuclear spins couple to molecular rotation via a Zeeman interaction. This spin–rotation coupling can be observed as a discrete splitting in molecular beam magnetic resonance experiments, but is quenched by molecular collisions at higher pressures. We show that because of differential thermal population of M_J levels at high magnetic fields, the spin rotation coupling retains a small isotropic component at high field. For all but the smallest molecules at very low temperature, the residual coupling is temperature independent and linear in the magnetic field; it therefore closely mimics the chemical shift. The ‘super spin rotation’ shift may in the future be a necessary correction to ultra – high precision computations of the NMR chemical shielding of small molecules in gases and liquids.     

The effect of out-of-plane motion on 2D and 3D digital image correlation measurements

The effect of out-of-plane motion (including out-of-plane translation and rotation) on two-dimensional (2D) and three-dimensional (3D) digital image correlation measurements is demonstrated using basic theoretical pinhole image equations and experimentally through synchronized, multi-system measurements. Full-field results obtained during rigid body, out-of-plane motion using a single-camera vision system with (a-1) a standard f55mm Nikon lens and (a-2) a single Schneider–Kreuznach Xenoplan telecentric lens are compared with data obtained using a two-camera stereovision system with standard f55mm Nikon lenses.Results confirm that the theoretical equations are in excellent agreement with experimental measurements. Specifically, results show that (a) a single-camera, 2D imaging system is sensitive to out-of-plane motion, with in-plane strain errors (a-1) due to out-of-plane translation being proportional to ΔZ/Z, where Z is the distance from the object to the pin hole and ΔZ the out-of-plane translation displacement, and (a-2) due to out-of-plane rotation are shown to be a function of both rotation angle and the image distance Z; (b) the telecentric lens has an effective object distance, Z_eff, that is 50× larger than the 55 mm standard lens, with a corresponding reduction in strain errors from 1250 μs/mm of out-of-plane motion to 25 μs/mm; and (c) a stereovision system measures all components of displacement without introducing measurable, full-field, strain errors, even though an object may undergo appreciable out-of-plane translation and rotation.     

活性浴中非活性棒的扩散动力学模拟研究：非单调尺寸依赖和反常平动-转动耦合

本文采用Langevin动力学模拟二维刚性棒状示踪粒子在活性浴中的扩散动力学,主要关注示踪粒子平动(转动)扩散系数随其棒长和背景粒子的活性强度如何变化. 本文发现示踪粒子在小时间尺度显示出超扩散行为,并在大时间尺度下恢复到正常扩散,同时平动扩散系数和转动扩散系数均随背景粒子的活性强度增加单调增加,但呈现出与棒长的非单调依赖. 在研究棒的平动-转动耦合时发现这种平衡系统中不存在反直觉现象,即棒在一定参数下会表现出负的平动-转动耦合,表明示踪粒子在平行于棒方向上的扩散比在垂直方向上更慢. 这种异常(扩散)行为随背景粒子的活性强度增加具有重入行为,表明背景粒子的活性导致了两种扩散行为存在竞争关系的效应.     

Phonon-assisted spin diffusion in solids

The spin flip-flop transition rate is calculated for the case of spectral spin diffusion within a system of dipolarly coupled spins in a solid where the lattice vibrations are present. Long-wavelength acoustic phonons time-modulate the interspin distance r_ij and enhance the transition rate via the change of the 1/r³_ij term in the coupling dipolar Hamiltonian. The phonon-assisted spin diffusion rate is calculated by the golden rule in the Debye approximation of the phonon density of states. The coupling of the spins to the phonons introduces temperature dependence into the transition rate, in contrast to the spin diffusion in a rigid lattice, where the rate is temperature-independent. The direct (one-phonon absorption or emission) processes introduce a linear temperature dependence into the rate at temperatures not too close to T = 0. Two-phonon processes introduce a more complicated temperature dependence that again becomes simple analytical for temperatures higher than the Debye temperature, where the rate is proportional to T², and in the limit T → 0, where the rate varies as T⁷. Raman processes (one-phonon absorption and another phonon emission) dominate by far the phonon-assisted spin flip-flop transitions.     

Bose–Einstein condensates in concentrically coupled annular traps with spin–orbit coupling and rotation

We investigate Bose–Einstein condensates in concentrically coupled annular traps with spin–orbit coupling and rotation. The ground state wave functions are computed by minimizing the Gross–Pitaevskii energy functional, and the combined effects of system?s parameters, especially the spin–orbit coupling and rotating, are investigated. The results show that for a finite fixed spin–orbit coupling, with increasing the angular frequency of rotation, the system is always in phase coexistence. Moreover, phase transitions between different ground state phases can be induced not only by spin–orbit coupling, but also rotation, which resembles very much the one where the s-wave interactions are varied.     

Revised molecular constants and term values for the XΣ and AΠ states of NH

The vibration–rotation spectra of NH have been reinvestigated using laboratory spectra and infrared solar spectra recorded from orbit by the ACE and ATMOS instruments. In addition to identifying the previously unobserved 6–5 vibration–rotation band in the laboratory spectra, many additional high N rotational lines have been observed. By combining the new observations with the previously published data and recent far infrared data, an improved set of molecular constants and term values have been derived for the X³Σ⁻ and A³Π states.     

Higher dimensional charged rotating dilaton black holes

In this paper, we present the metric for the n-dimensional charged slowly rotating dilaton black hole with N = [(n −1)/2] independent rotation parameters, associated with N orthogonal planes of rotation in the background of asymptotically flat and asymptotically (anti)-de Sitter spacetime. The mass, angular momentum and the gyromagnetic ratio of such a black hole are determined for the arbitrary values of the dilaton coupling constant. We find that the gyromagnetic ratio crucially depends on the dilaton coupling constant, α, and decreases with increasing α in any dimension.     

Mechanical analogues of spin Hamiltonians and dynamics

Bloch et al. mapped the precession of the spin-half in a magnetic field of variable magnitude and direction to the rotations of a rigid sphere rolling on a curved surface utilizing SU(2)–SO(3)$\mathit{SU}(2)\text{–}\mathit{SO}(3)$ isomorphism. This formalism is extended to study the behaviour of spin–orbit interactions and the mechanical analogy for Rashba–Dresselhauss spin–orbit interaction in two dimensions is presented by making its spin states isomorphic to the rotations of a rigid sphere rolling on a ring. The change in phase of spin is represented by the angle of rotation of sphere after a complete revolution. In order to develop the mechanical analogy for the spin filter, we find that perfect spin filtration of down spin makes the sphere to rotate at some unique angles and the perfect spin filtration of up spin causes the rotations with certain discrete frequencies.     

Measurement of the coupling strength distribution in ferromagnetic (F)/antiferromagnetic (AF) exchange bias systems

We propose a method for determination of the distribution function P(j) of the coupling energy density j in polycrystalline textured ferromagnetic (F)/antiferromagnetic (AF) film systems. P(j) governs the entire film coupling J and the exchange bias field H_e and was not measurable until now. The method is verified by torquemetry in a high magnetic field and by reversing its rotation sense. The transition to a new magnetic steady state after rotation reversal is analyzed within a Stoner–Wohlfarth model including thermal relaxation. This transition is completed earlier for strongly coupled grains than for grains with smaller j, which is reflected in the torque curves. We determined P(j) for a sputtered NiFe(16 nm)/IrMn(0.8 nm) film at T=50 K in the hysteretic range of coupling energies and found that P strongly decreases for increasing j.     

The thermoelastic behaviour of the orientationally disordered ionic crystals in two dimensions

The anomalous temperature dependence of the elastic constantsc ₁₁ andc ₆₆ and the elastic instability temperatureT _c are obtained in the two-dimensional microscopic model of the alkali cyanides crystals. It has been found, by means of the Michel and Naudts' theory of the translation rotation coupling, that the orientational disorder in the high-temperature phase leads to the critical softening of the shear elastic constantc ₆₆.     

Superconductivity and normal state resistivity of Ba0.6K0.4BiO3: an optical phonon approach

We discuss the nature of the pairing mechanism and the physical properties associated with the normal as well as the superconducting state of cubic perovskites Ba_0.6K_0.4BiO₃using the strong coupling theory. An interaction potential which includes the Coulomb, electron–optical phonon and electron–plasmon interactions is developed to elucidate the superconducting state. A model dielectric function is constructed with these interactions fulfilling thef-sum rule. The screening parameter (μ^* = 0.26) infers the poor screening of charge carriers. The electron–optical phonon strength (λ) estimated as 0.98 is consistent with an attractive electron–electron interaction and supports the moderate to strong coupling theory. The superconducting transition temperature of Ba_0.6K_0.4BiO₃is then estimated as 32 K. Ziman's formula of resistivity is employed to analyse and compare this with the temperature-dependent resistivity of a single crystal. The estimated contribution from the electron–optical phonon together with the residual resistivity clearly infers a difference when a comparison is made with experimental data. The subtracted data infer a quadratic temperature dependence in the temperature domain (30 ≤ T ≤ 200 K). The quadratic temperature dependence of ρ [ = ρ_exp − (ρ₀ + ρ_e–ph)] is understood in terms of 3D electron–electron inelastic scattering. The presence of these el–el and el–ph interactions allows a coherent interpretation of the physical properties. Analysis reveals that a moderate to strong coupling exists in the Ba_0.6K_0.4BiO₃system and the coupling of electrons with the high-energy optical phonons of the oxygen breathing mode will be a reason for superconductivity. The implications of the above analysis are discussed.     

Vortex rings and plasma toroidal vortices in homogeneous infinite media. III. Diffusion anisotropy effect in vortices

The effect of diffusion anisotropy of material particles in toroidal vortices (TVs) is experimentally studied in plasma TVs in air, in vortex rings in air and water. The essence of this effect consists in the fact that diffusion coefficients of material particles in TVs in the direction perpendicular to the rotation axis D _⊥ are much lower than in the direction parallel to this axis D _‖. The coefficient D _⊥ is determined for propane molecules in air TVs, and the dependence of the coefficient D _⊥ of ink particles in water TVs on the rotation angular velocity ω is studied. It is shown that the coefficient D _⊥ can decrease with increasing ω by a factor of 10–25 in comparison with the coefficient D _‖.     

Infrared Transitions of HCN and HCN between 500 and 10 000 cm

We have measured the Fourier transform spectrum (FTS) of two isotopomers of hydrogen cyanide (H¹²C¹⁴N and H¹²C¹⁵N) from 500 to 10 000 cm⁻¹. The infrared data have been combined with earlier published microwave and submillimeter-wave measurements. From this analysis new vibration–rotation energy levels and constants are given, based on the observation of a number of new vibrational levels, especially for H¹²C¹⁵N. The Coriolis interaction involving Δv₃= −1, Δv₂= 3, and Δl= ±1 has been observed for a great many levels and in some cases the assignments of laser transitions allowed by this interaction are more clearly shown. New vibration–rotation constants are given that allow one to predict the transition wavenumbers for most of the transitions below 10 000 cm⁻¹with accuracies of about 0.5 cm⁻¹or better. Values are given for the power series expansion of thel-type resonance constants and for the centrifugal distortion constants, as well as the usual vibrational and rotational constants.     

Effect of the ambient field on the I–V characteristics of nanowire resistors and junctions—A simulation study

Ambient field refers to the field lines outside the semiconductor that are caused by the potential difference between points on the semiconductor. We present a TCAD study of the effects of the ambient field on the I–V characteristics of NanoWire (NW) resistors and junctions. The study covers different contact geometries, hi–lo as well as p–n junctions, and practical bias range including the equilibrium condition; effects of varying the wire radius, length, doping and ambient dielectric constant are brought out. The NWs studied have radii≥15 nm and length≥500 nm for which classical models based on drift–diffusion transport are applicable. Simple qualitative explanations for various non-linear shapes of the I–V characteristics are provided using field lines. An appealing analogy is presented for the rise in the carrier concentration of an undoped NW grown on a heavily doped substrate. The study is aimed at improving the understanding of nanoscale devices and proper interpretation of their experimental data.     

Laser Spectroscopy of the CCO Radical in the 0.77-μm Region: Analysis of theÃ(020)κΠ andÃΠi(001) States

TheÃ(020)κ³Π–X³Σ⁻(000) andóΠ_i(001)–X³Σ⁻(000) bands of the CCO radical have been investigated by laser spectroscopy with two types of tunable laser system. An analysis was made simultaneously for both the bands to establish line assignments and determine molecular constants for both theÃ(020) andÃ(001) states. A coupling constant between these two states was also determined by assuming the interaction to be of Fermi type.     

Theory of bending of polycrystalline beams by creep at low stress

Attempts to extend diffusion creep theory from simple grain geometries to more complex polycrystalline structures generally make the assumptions that the vacancy creation (or annihilation) rate is constant over each grain face and that the volume of each grain is conserved. These assumptions do not permit grain rotation, a common feature of polycrystalline creep, nor is diffusion allowed to occur between individual grains. These two aspects are investigated theoretically in this paper, for the specific case of the grain boundary diffusion controlled bending of a polycrystalline beam consisting of a set of orthorhombic grains of dimensions X, Y and Z, with the Z dimension, parallel to the axis of bending, assumed large such that two-dimensional diffusion predominates. The grains are aligned with continuous boundaries across the beam height. For grains highly elongated along the beam length (X???Y), the derived rotation rate is identical to that for a bicrystal having the same height as the beam. For smaller X, diffusion in boundaries along the beam length make increasing contributions and the rotation rate increases. The novel prediction is made that the non-conservation of grain volume is an inevitable consequence of the grain boundary diffusion controlled deformation of this particular polycrystalline configuration.     

Theory of diffusional rotation about the common boundary of a bicrystal

During the creep of polycrystals, individual grains may undergo shape changes, grain boundary sliding and grain rotation. Theoretical studies have focused on the first two of these processes but only recently has the theory of rotation received detailed attention. Diffusional rotation was analysed by Burton [Phil. Mag. A 82 51 (2002); Phil. Mag. 83 2715 (2003)], for a bicrystal with orthorhombic grains of dimensions X, Y and Z with the common boundary in the yz plane and with Z???X,Y. Rate equations were derived and the stress profile over the common boundary predicted, for cases where grain boundary and lattice diffusion predominate. In this paper, the analyses are extended using numerical methods, to the full two- and three-dimensional cases for boundary and lattice diffusion, respectively. For boundary diffusion, the results for Z/Y???1 reproduce those obtained by analytical means and this is regarded as a verification of the numerical method. When Z/Y?=?1, the rotation rates are shown to be about 30% faster, due to the additional diffusion contribution in the z direction. This contribution increases with decreasing values of Z/Y. The stress patterns at the rotating boundary are derived. For lattice diffusion, the stress pattern at the boundary, the shapes of the vacancy potential contours and the variation of the rotation rate with the ratios X/Y and Z/Y are presented.