EPR and optical spectra of Ni2+-VAg in silver chloride and silver bromide

The optical absorption and EPR spectra of Ni²⁺-V_Ag centres in the AgCl:Ni²⁺ and AgBr:Ni²⁺ systems have been investigated theoretically on the basis of the complete energy matrices including the electron–electron repulsion interaction, the ligand field interaction, the spin–orbit coupling interaction, and Zeeman interaction. Because the charge compensation forms a silver ion vacancy (V_Ag) which makes the attractive force acted on the each ligand ion different, it was determined that the Ni–X (X = Cl, Br) distance next to V_Ag is shorter than others for both AgCl:Ni²⁺ and AgBr:Ni²⁺ systems in the tetragonal symmetry. Besides, it was found that the local lattice structure of (NiX₆)^4? clusters in AgCl and AgBr crystals exhibit a compression distortion. This compression distortion may be ascribed to the fact that the Ni²⁺ ion has a smaller ionic radius and more effective charge than the Ag⁺ ion.     

Effect of local structure on electron paramagnetic resonance spectra for trigonal [Cr(H2O)6]3+coordination complex in the sulfate alums series: a ligand field theory study

A simple theoretical method is introduced for studying the interrelation between electronic and molecular structures.By diagonalizing the 120 × 120 complete energy matrices,the relationships between zero-field splitting(ZFS) parameter D and local distortion parameter △θ for Cr 3+ ions doped,separately,in α-and β-alums are investigated.Our results indicate that there exists an approximately linear relationship between D and △θ in a temperature range 4.2-297 K and the signs of D and △θ are opposite to each other.Moreover,in order to understand the contribution of spin-orbit coupling coefficient ζ to ZFS parameter D,the relation between D and ζ is also discussed.     

Investigation of local lattice structure around Cr3+ ions at the trigonal and tetragonal sites in RbCdF3: Cr3+ crystal

The local lattice structure and EPR, optical spectra for Cr³⁺ doped in RbCdF₃ crystal have been studied by diagonalizing the complete energy matrices. The results show that the local structure of the Cr³⁺ ions in RbCdF₃ exhibits a compressed distortion at the trigonal and tetragonal sites. The compressed distortion can be ascribed to the fact that the radius of Cr³⁺ ion is smaller than that of Cd²⁺ ion, and therefore Cr³⁺ ion will draw the fluorin ligands inwards. The variational ranges of the local structural parameters for Cr³⁺ doped in RbCdF₃ crystal R =?1.9491 Å ～?1.9814 Å, θ?= 55.234° ～?55.286° at the trigonal site and R ₁ =?1.8617 Å ～?1.8928 Å, R ₂ =?1.9527 Å ～?1.9851 Å at tetragonal site are obtained respectively, and the EPR and optical spectra agree well with the experimental results.     

Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls--Nabarro (P-N) theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.     

Numerical simulation of bubble dynamics in a Phan-Thien–Tanner liquid: Non-linear shape and size oscillatory response under periodic pressure

We study non-linear bubble oscillations driven by an acoustic pressure with the bubble being immersed in a viscoelastic, Phan-Thien–Tanner liquid. Solution is provided numerically through a method which is based on a finite element discretization of the Navier–Stokes flow equations. The proposed computational approach does not rely on the solution of the simplified Rayleigh–Plesset equation, is not limited in studying only spherically symmetric bubbles and provides coupled solutions for the velocity, stress fields and bubble interface. We present solutions for non-spherical bubbles, with asphericity being addressed by means of Legendre polynomials or associated Legendre functions. A parametric investigation of the bubble dynamical oscillatory response as a function of the fluid rheological properties shows that the amplitude of bubble oscillations drastically increases as liquid elasticity (quantified by the Deborah number) increases or as liquid viscosity decreases (quantified by the Reynolds number). Extensive numerical calculations demonstrate that increasing elasticity and/or viscosity of the surrounding liquid tend to stabilize the shape anisotropy of an initially non-spherical bubble. Results are shown for pressure amplitudes 0.2–2 MPa and Deborah, Reynolds numbers in the intervals of 1–8 and 0.094–1.256, respectively.     

自由降落升降机中液滴的形状

定量讨论了自由降落升降机中实际液滴的形状.结果表明,在地球附近,液滴大小在1 m数量级时呈现明显的非球形,并与静态海潮形成的海洋表面形状相似.提供了一种在普通航天飞机中观察引力场非均匀效应的方法;给出了一种制造空间弯曲测量仪的设想.     

Effect of korteweg stress in miscible liquid two-layer flow in a microfluidic device

Miscible liquid two-layer flow in a Y-shaped microfluidic device, which consists of microchannels with 120 μm in width and 35 μm in depth, is investigated by particle image velocimetry (PIV) to clarify the flow characteristics at fluid interfaces. The obtained velocities with a spatial resolution of 5.9 x 1.5 μm² around the interface between water and ethanol indicate an imbalance in shear stress at interface. The reason of the imbalance is to be the Korteweg stress generated by interfacial tension gradient due to a concentration gradient by diffusion in a miscible two-layer flow. The stress may cause an interfacial instability and destroy a uniform mixing in two flowing fluids in the case of large concentration gradient.     

Lattice models of traffic flow considering drivers' delay in response

This paper proposes two lattice traffic models by taking into account the drivers' delay in response. The lattice versions of the hydrodynamic model are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained by using the linear stability theory. The modified KdV equation near the critical point is derived to describe the traffic jam by using the reductive perturbation method, and the kink--antikink soliton solutions related to the traffic density waves are obtained. The results show that the drivers' delay in sensing headway plays an important role in jamming transition.     

Asymmetry of the wall shear stress in a stimulated ascendant flow of a liquid with monodisperse bubbles

Results of an experimental investigation of the two-phase wall shear stress averaged over the tube perimeter and the pulsation of wall shear stress in a stimulated ascendant flow with monodisperse bubbles with an average diameter of 1.2 and 2.2 mm are presented. Regimes with various hydrodynamic parameters such as high shear stress on the wall, low and negative wall shear stress, a high level of shear stress pulsation on the wall, and possible decrease in this level of pulsation are found. An increase in the void gas fraction results in a monotonic increase of perturbation of the single-phase flow. The dependences of the ratio of two-phase and single-phase wall shear stresses for two average bubble diameters seem to be qualitatively similar. The analysis of data revealed a complex dependence of the shear stress pulsation on the bubble diameter. The averaged flow characteristics quantitatively change upon the decrease in the bubble diameter. A further decrease in the average bubble diameter at the same void gas fraction will probably increase the heat-and mass-transfer characteristics of the flow. This is an issue for the futures study.     

Investigations of the electron paramagnetic resonance parameters and the tetragonal local structure for (VCl6)4- coordination complex in MCl:V2+ (M=Na, K, Rb) systems

By simulating the electron paramagnetic resonance (EPR) and optical spectra on the basis of the 120×120 complete energy matrix, this paper determines the local lattice structure parameters R1 and R2 for MCl:V2+ (M=Na, K, Rb) systems at 77 K, 195 K and RT (room temperature 295 K or 302 K), respectively. The theoretical results indicate that there exists a compressed distortion in MCl:V2+ systems. Meanwhile, it finds that the structure parameters R1, R2 and |△R| (= R1-R2) increase with the rising temperature. Subsequently, from the analysis it concludes that the relation of EPR parameter D vs.△R is approximately linear. Finally, the effects of orbital reduction factor k on the g factors for the three systems have been discussed.     

First-principles study of the local structure and crystal field of Yb2+ in sodium and potassium halides

The local coordination structures around the doping Yb²⁺ ions in sodium and potassium halides were calculated by using the first-principles supercell model. Both the cases with and without the charge compensation vacancy in the local environment of the doping Yb²⁺ were calculated to study the effect of the doping on the local coordination structures of Yb²⁺. Using the calculated local structures, we obtained the crystal-field parameters for the Yb²⁺ ions doped in sodium and potassium halides by a method based on the combination of the quantum-chemical calculations and the effective Hamiltonian method. The calculated crystal-field parameters were analyzed and compared with the fitted results.     

Exact second order formalism for the study of electro-acoustic properties in piezoelectric structures under an initial mechanical stress

In this study we develop the exact second order formalism of piezoelectric structures under an external mechanical stress. Indeed, previous models are approximated since they consist in deriving all the equations in the natural coordinate system (corresponding to the pre-stress free case). Hence, our exact formalism proposes to obtain the whole of equations in the current coordinate system (which is the coordinate system after the pre-deformation). Then, this exact formalism is used to derive the modified Christoffel equations and the modified KLM model. Finally, we quantify the correction with the approximate formalism on several transfer functions and electro-mechanical parameters for a non hysteretic material (lithium niobate). In conclusion, we show that for this material, significant corrections are obtained when studying the plane wave velocities and the electrical input impedance (about 4%), whereas other parameters such as coupling coefficient and impulse response are less influenced by the choice of coordinate systems (corrections less than 0.5%).     

Electrical discharge characteristics of a dielectric liquid under external flow in a microchannel with planar electrode configuration

The effect of fluid flow on discharge characteristics in a dielectric liquid was determined. Tests were performed for flow in a 100 micron high, 5 mm wide, 50 mm long microchannel at Reynolds numbers up to 13 and applied DC potentials up to 1.5 kV through 100 micro planar electrode pairs along the floor of the channel. The current within the conduction regime increased as the flow rate increased for the case where the flow was in the same direction as the applied electric field. In the injection regime, there was an optimum flow rate for maximum current.     

Numerical simulation of the ignition of liquid fuel with a limited-energy source under turbulent flow conditions

The ignition of a typical liquid fuel with a limited-energy source, a small metal particle heated to high temperature is numerically simulated with consideration given to the possible turbulization of the fuel vapor flow. The dependences of the integral ignition characteristics on the key parameters of the local heat source are established. The integral ignition characteristics, as well as the fields of fuel vapor concentrations and velocities predicted by models accounting for the laminar and turbulent modes of the vapor-oxidizer mixture flow are compared.     

Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles

This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics ofn×n random matrices within spectral intervals ofO(n ^–1) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions.     

Study of mass transport in rotating couple stress liquid under concentration modulation

A weakly non-linear stability analysis has been performed to examine the effect of time-periodic concentration modulation on the mass transport. We consider an infinite horizontal fluid layer is rotating with angular velocity Ω₁ about Z-axis subjected to an imposed time-periodic boundary concentration (ITBC). The concentration gradient between the plates of the fluid layer consists of a steady part and a time-dependent oscillatory part. The concentration of both walls is modulated in this case. We have expanded the infinitesimal disturbances in terms of power series of amplitude of modulation, which is assumed to be small. Ginzburg–Landau equation is obtained to find the rate of mass transfer. It is found that, the effect of Taylor number is to stabilize the system. Effect of Schmidt number and Couple stress parameter on mass transfer are also discussed. Further, it is found that the mass transport can be controlled by suitably adjusting the frequency and amplitude of modulation .     

Experimental study of a textural transition in liquid crystals under shear stress induced by surface friction

Results of a study of the optical response of liquid crystals with helical supramolecular structure to surfacefriction-induced shear stress in aerodynamic experiments are reported. The effect of re-orientation of molecules from confocal (light-scattering) to planar (selectively reflecting light) texture is considered. The textural transition is examined by the spectral and colorimetric methods. Dependences of the reflection spectra of the formed planar texture on time and on the mean shear-stress level were obtained. It is shown that the dependence of the texture transition time on the shear-stress level can be approximated, in a logarithmic scale, with a linear dependence; this allows using the effect for flow diagnostics.