Minimum state for high Reynolds and Péclet number turbulent flows

Direct numerical simulations (DNS) or experiments for the very high Reynolds (Re) and Péclet (Pe) number flows commonly exceed the resolution possible even when use is made of the most advanced computer capability or most sophisticated diagnostics and physical capabilities of advanced laboratory facilities. In practice use is made of statistical flow data bases developed at the highest Re and Pe levels achievable within the currently available facility limitations. In addition, there is presently no metric to indicate whether and how much of the fully resolved physics of the flow of interest has been captured within the facilities available. In this Letter the authors develop the necessary metric criteria for homogeneous, isotropic and shear layer flows. It is based on establishing a smaller subset of the total range of dynamic scale interactions that will still faithfully reproduce all of the essential, significant, influences of the larger range of scale interactions. The work identifies a minimum significant Re and Pe level that must be obtained by DNS or experiment in order to capture all of the significant dynamic influences in data which is then scaleable to flows of interest. Hereafter this is called the minimum state. Determination of the minimum state is based on finding a minimum scale separation for the energy-containing scales of the flow and scalar fields sufficient to prevent contamination by interaction with the (non-universal) velocity dissipation and scalar diffusivity inertial range scale limits.     

Anisotropic strain effects on light emission characteristics of CdZnO/ZnO quantum well structures

Anisotropic strain effects by strain relaxation on TE-polarized light emission characteristics of c-plane CdZnO/ZnO quantum well (QW) structures were theoretically investigated by using the multiband effective-mass theory. The CdZnO/ZnO QW structure with anisotropic strain has much larger emission intensity than conventional CdZnO/ZnO QW structure without the strain relaxation. In the case of the strain relaxation along x(or y)-direction, the x(or y)-polarized light emission is observed to be larger than the x(or y)-polarized light emission. In particular, in the case of the strain relaxation along both x- and y-directions, the increase in the spontaneous emission peak is significant. This can be explained by the fact that the internal field is reduced owing to the decrease in the piezoelectric field by the strain relaxation.     

Preserving some numerical correspondencesbetween Hilbert space effects

In this paper we introduce some natural numerical quantities which measure differentkinds of correspondences between Hilbert space effects. We show that every objective map of the space ?(H) of all effects on the Hilbert space H which preserves any of these quantities is implemented by a unitary or antiunitary operator on H.     

Compensation temperature of 3d mixed ferro-ferrimagnetic ternary alloy

In this study, we have considered the three dimensional mixed ferro-ferrimagnetic ternary alloy model of the type AB_pC_1-p where the A and X (X=B or C) ions are alternately connected and have different Ising spins S^A=3/2, S^B=1 and S^C=5/2, respectively. We have investigated the dependence of the critical and compensation temperatures of the model on concentration and interaction parameters by using MC simulation method. We have shown that the behavior of the critical temperature and the existence of compensation points strongly depend on interaction and concentration parameters. In particular, we have found that the critical temperature of the model is independent on concentration of different types of spins at a special interaction value and the model has one or two compensation temperature points in a certain range of values of the concentration of the different spins.     

A dynamically adaptive wavelet approach to stochastic computations based on polynomial chaos – capturing all scales of random modes on independent grids

In stochastic computations, or uncertainty quantification methods, the spectral approach based on the polynomial chaos expansion in random space leads to a coupled system of deterministic equations for the coefficients of the expansion. The size of this system increases drastically when the number of independent random variables and/or order of polynomial chaos expansions increases. This is invariably the case for large scale simulations and/or problems involving steep gradients and other multiscale features; such features are variously reflected on each solution component or random/uncertainty mode requiring the development of adaptive methods for their accurate resolution. In this paper we propose a new approach for treating such problems based on a dynamically adaptive wavelet methodology involving space-refinement on physical space that allows all scales of each solution component to be refined independently of the rest. We exemplify this using the convection–diffusion model with random input data and present three numerical examples demonstrating the salient features of the proposed method. Thus we establish a new, elegant and flexible approach for stochastic problems with steep gradients and multiscale features based on polynomial chaos expansions.     

Comments on employing the Riesz-Feller derivative in the Schrödinger equation

In this paper, we deal with a fractional Schrödinger equation that contains the quantum Riesz-Feller derivative instead of the Laplace operator in the case of a particle moving in a potential field. In particular, this equation is solved for a free particle in terms of the Fox H-function. On the other hand, we show that from physical viewpoint, the fractional Schrödinger equation with the quantum Riesz-Feller derivative of order α, 0 < α ≤ 2 and skewness θ makes sense only if it reduces to the Laplace operator (α = 2) or to the quantum Riesz fractional derivative (θ = 0). The reason is that the quantum Riesz-Feller derivative is a Hermitian operator and possesses real eigenvalues only when α = 2 or θ = 0. We then focus on the time-independent one-dimensional fractional Schrödinger equation with the quantum Riesz derivative in the case of a particle moving in an infinite potential well. In particular, we show that the explicit formulas for the eigenvalues and eigenfunctions of the time-independent fractional Schrödinger equation that some authors recently claimed to receive cannot be valid. The problem to find right formulas is still open.     

The primary order parameter in antiferroelectric NaNbO3

X-ray scattering experiments on NaNbO₃ near the transition to antiferroelectric phase R indicate that the mode that softens — the primary mode or order parameter — is an octahedral rotational mode. It is argued that the antiferroelectric array of static Nb displacements present in phase R constitute the secondary order parameter; in other words non-zero values of the Nb displacements are induced through anharmonic coupling to the soft mode or primary mode. In current terminology, phase R is an improper antiferroelectric.     

The relationship between measured activation enthalpy and pre-exponential factor: Rate processes in ionic crystals in the intrinsic-extrinsic region

In measurement of activated processes, such as diffusion, ionic conduction, creep and sintering, it is common to use Arrhenius plots of the measured quantity, A(T), to give the logarithm of the pre-exponential factor, logA₀, and the experimental activation enthalpy, h. It is shown that, in the cases of conduction and diffusion in ionic crystals, well-defined relationships can exist between the values of logA₀, logA and h, measured on similar samples with differing doping or impurity levels. These relationships are derived for ionic crystals showing either Frenkel, Schottky, or interstitial disorder. In the resulting plots of logA₀ versus h, approximately linear regions are shown to exist, similar to those described by the compensation law for glasses and by the Meyer-Neldel rule for semiconductors.     

Dispersion properties of hollow-core photonic bandgap fibers based on a square lattice cladding

In this paper the dispersion properties and confinement loss of hollow-core photonic bandgap fibers (PBGFs) based on a square lattice (SL) with rounded square air-holes was investigated for the first time, by using a full-vector finite element method (FEM). The waveguide group velocity dispersion (GVD) curves with different core diameter D, air hole size d, rounded diameter d_c and hole pitch Λ are presented. The influence of the number of cladding rings on dispersion and confinement loss were also calculated. It was found that as Λ or d increases, the width of PBG becomes wider, and that D and the number of cladding rings have a smaller influence on waveguide GVD. The ratio between bandgap width and central wavelength in our simulation is about 38.1%, which is larger than that of hollow-core PBGFs with triangular lattice (TL) (∼25%). By simulation, the desired zero dispersion wavelength or desired dispersion slope could be obtained by properly choosing the value of d_c or Λ. Compared to TL PBGF, at least nine cladding rings is needed to achieve the confinement loss less than 0.1 dB/m for future application.     

Infrared spectra of solid germane

An IR spectroscopic study has shown that GeH₄ molecules are situated on one set of sites of C, symmetry in phase IV. The III–IV transition at 63 K is apparently a second-order phase transition. In phases II and III the molecules are on sites of C_3v. or C₃ symmetry. The II–III phase transition was observed at 67 K. In solid GeD₄, phase transitions were observed at 68.5 and 77 K. In phases II and III the site symmetry is C_I. The II–III phase transition in GeD₄ is apparently second order. There is evidence that the ν₁, vibration of GeD₄ is IR active in the solid state.     

Exceptional points of a Hamiltonian and phase transitions in finite systems

For a model Hamiltonian which describesN interacting Fermions and which is typical for systems that undergo phase transitions it is shown that for finiteN the transitional point is associated with exceptional points of the Hamiltonian. In the limit of largeN these singularities move down to the real axis. The nature of the limit turns out to be quite different depending on whether it is taken for interaction strengths smaller or larger than the critical value.     

Synchronization, multistability and basin crisis in coupled pendula

The synchronization dynamics of two linearly coupled pendula is studied in this paper. Based on the Lyapunov stability theory and Linear matrix inequality (LMI); some necessary and sufficient conditions for global asymptotic synchronization are derived from which an estimated threshold coupling k_th, for the on-set of full synchronization is obtained. The numerical value of k_th determined from the average energies of the systems is in good agreement with theoretical analysis. Prior to the on-set of synchronization, the boundary crisis of the chaotic attractor is identified. In the bistable states, where two asymmetric periodic attractors co-exist, it is shown that the coupled pendula can attain multistable states via a new dynamical transition—the basin crisis that occur prior to the on-set of stable synchronization. The essential feature of basin crisis is that the two co-existing attractors are destroyed while new three or more co-existing attractors of the same or different periodicity are created. In addition, the linear perturbation technique and the Routh-Hurwitz criteria are employed to investigate the stability of steady states, and clearly identify the different types of bifurcations likely to be encountered. Finally, two-parameter phase plots, show various regions of chaos, hyperchaos and periodicity.     

Impurity-ligand distances derived from magnetic resonance and optical parameters

Non empirical methods for obtaining information from EPR, ENDOR and optical data on the true impurity-ligand distance,R, as well as on the true variations, ΔR, induced by chemical and hydrostatic pressures, phase transitions in the host material and temperature changes are discussed through this work. Special attention is addressed to spectroscopic parameters of d-impurities whose dependence onR can reasonably be calculated theoretically for the superhyperfine (shf) tensor or the lowest optical transitions but not for fine structure terms. In the case of impurities with unpaired σ-electrons it is shown that the isotropic shf constant,A _s, is specially sensitive toR changes. The microscopic origin of this fact is discussed in detail. Determination of trueR values from experimentalA _s has been carried out for impurities like Mn²⁺ or Ni⁺ with encouraging results. In the case of Mn²⁺ in fluorides, results obtained by this method coincide with those reached through EXAFS and the analysis of the experimental 10 Dq. Finally, for some selected complexes, a view is offered on the dependence of several EPR and optical parameters upon metal-ligand distances. The main conclusion is that ΔR values of the order of 0.1 pm can be detected using EPR and optical parameters thus improving by an order of magnitude the sensitivity reached through EXAFS. In particular the use of ENDOR allows one to measure ΔR values close to 0.01 pm.     

Generalized projective synchronization between two different general complex dynamical networks with delayed coupling

In this Letter, generalized projective synchronization (GPS) between two different complex dynamical networks with delayed coupling is investigated. Two complex networks are distinct if they have diverse node dynamics, or different number of nodes, or different topological structures. By using the adaptive control scheme, a sufficient synchronization criterion for this GPS is derived based on the LaSalle invariance principle. Three corollaries are also obtained. It is noticed that the synchronization speed sensitively depends on the adjustable positive constants μi. Furthermore, the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. In addition, the node dynamic need not satisfy the very strong and conservative uniformly Lipschitz condition. Numerical simulations further demonstrate the feasibility and effectiveness of the theoretical results.     

Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality

In order to study the effect of diffraction focusing characteristics of microlens arrays on the parallel laser direct writing quality, we use nonparaxial approximation to analyze the diffraction focus characteristic of a single microlens, take into consideration the cross-talk effect of a number of microlenses on the diffraction focusing characteristics of an array, and establish a theoretical focusing intensity model of a microlens array to describe the influence of a change in F-number and/or center distance on the diffraction focusing characteristics of a parallel laser direct writing system while incident writing laser is normal. Numerical simulation results indicate that there is a cross-talk effect among microlenses which increases as the F-number increases when the center distance is the same as the smaller aperture, and parallel writing quality can be improved by reducing or totally eliminating the cross-talk effect by reducing F-number and/or increasing center distance.     

DCCA cross-correlation coefficient apply in time series of air temperature and air relative humidity

In this paper we propose, analyze and also quantify cross-correlations between climatological data. For this purpose we adopt the DCCA cross-correlation coefficient ρ_DCCA. In order to accomplish this goal, we calculate the cross-correlation between time series of air temperature and relative humidity. This analysis was performed taking into account several stations (cities) around the world. The results found here, depending on the station location, may exhibit one of the following behaviors, i.e., negative, positive, or null cross-correlations. It is noteworthy that, the level of cross-correlation between air temperature and relative humidity is quantified in these cases. Finally, DCCA cross-correlation coefficients show that, in general, the data are influenced by seasonal components.     

Symmetry breaking in τ decay

In view of the recent attempts to detect theG-parity violating decay τ→πηv _τ which may have bearing on the presence of the second class current, we discuss the isospin symmetry breaking effects in the processes of τ→δv, Bv, and ηπv from a dynamical point of view. It is shown that all the symmetry breaking effects are proportional to theu?d quark mass difference. Depending on whether the current or the constituent quark masses are used, the decay τ→πηv _τ via δ is either of the same order or three orders of magnitude smaller than the upper limit set by the latest experiments. This is in agreement with the other theoretical estimates.     

Electronic and magnetic states in metallic compound—II: Electron transport and magnetic susceptibility in NiAl and FeAl

Electron transport and magnetic properties were investigated in NiAl and FeAl alloys in the vicinity of exact stoichiometry. The results as well as those of other workers were compared with recent augmented-plane-wave band calculations for NiAl, and semiquantitative agreement was found. With respect to impurity states in NiAl, it was concluded that transport anomalies, though definitely magnetic in origin, were not due to localized-magnetic moments on excess Ni atoms on Al sites. It was suggested that the anomalies may be due to subtle structural defects or such defects in combination with one of several intrinsic (non-impurity or defect) mechanisms. In the FeAl alloys, it was concluded that excess Fe atoms on Al sites (Fe_x atoms) carry a moment in the paramagnetic state of 7·8 μ_B. Negative magneto-resistance but no resistance minima effects were observed. The data, similar in several respects to those for dilute Rh(Fe) alloys, were interpreted in terms of antiferromagnetically coupled Fe_x atoms which lead to magnetic transitions of a spin-glass or mictomagnetic nature, that is, having no long-range order.