A generalization of the inhomogeneity measure for point distributions to the case of finite size objects

The statistical measure of spatial inhomogeneity for n points placed in χ cells each of size k×k is generalized to incorporate finite size objects like black pixels for binary patterns of size L×L. As a function of length scale k, the measure is modified in such a way that it relates to the smallest realizable value for each considered scale. To overcome the limitation of pattern partitions to scales with k being integer divisors of L, we use a sliding cell-sampling approach. For given patterns, particularly in the case of clusters polydispersed in size, the comparison between the statistical measure and the entropic one reveals differences in detection of the first peak while at other scales they well correlate. The universality of the two measures allows both a hidden periodicity traces and attributes of planar quasi-crystals to be explored.     

Optical experimental evidence for a universal length scale for the dynamic charge inhomogeneity of cuprate superconductors

Time-resolved optical experiments can give unique information on the characteristic length scales of dynamic charge inhomogeneity on femtosecond time scales. From data on the effective quasiparticle relaxation time tau(r) in La(2-x)SrxCuO4 and Nd(2-x)Ce(x)CuO4, we derive the temperature and doping dependence of the intrinsic phonon escape length l(e), which can be a direct measure of charge inhomogeneity. Remarkably, a common feature of both p- and n-type cuprates is that, as T --> Tc, l(e) approaches the superconducting coherence length l(e) --> xi(s)0. In the normal state l(e) is found to be in excellent agreement with the mean free path l(m) obtained from the resistivity data and structural coherence lengths l(s) from neutron scattering experiments, implying the existence of complex intrinsic textures on different length scales which may have a profound effect on the functional properties of these materials.     

Vortices in superfluid fermi gases through the BEC to BCS crossover

We have analyzed a single vortex at T=0 in a 3D superfluid atomic Fermi gas across a Feshbach resonance. On the BCS side, the order parameter varies on two scales: k(F)(-1)and the coherence length xi, while only variation on the scale of xi is seen away from the BCS limit. The circulating current has a peak value jmax which is a nonmonotonic function of 1/k(F)a(s) implying a maximum critical velocity approximately v(F) at unitarity. The number of fermionic bound states in the core decreases as we move from the BCS to the BEC regime. Remarkably, a bound state branch persists even on the BEC side reflecting the composite nature of bosonic molecules.     

SrTiO3 displacive transition revisited via coherent X-ray diffraction

We present a coherent x-ray diffraction study of the antiferrodistortive displacive transition of SrTiO3, a prototypical example of a phase transition for which the critical fluctuations exhibit two length scales and two time scales. From the microbeam x-ray coherent diffraction patterns, we show that the broad (short-length scale) and the narrow (long-length scale) components can be spatially disentangled, due to 100-microm-scale spatial variations of the latter. Moreover, both components exhibit a speckle pattern, which is static on a approximately 10 mn time scale. This gives evidence that the narrow component corresponds to static ordered domains. We interpret the speckles in the broad component as due to a very slow dynamical process, corresponding to the well-known central peak seen in inelastic neutron scattering.     

Multiple scaled disorder in the photonic structure of Morpho rhetenor butterfly

The iridescence of Morpho rhetenor butterfly is known to result from a photonic structure on wing scales, where multilayer interference and grating diffraction occur simultaneously. We characterize the disorder at the photonic structure length scale and at the butterfly scale. We measure the scattering pattern of the wing. Through RCWA and 1st Born approximation models, we link the different disorders to different features in the scattering patterns.     

Nonlinear cyclotron resonant wave-particle interaction in a nonuniform magnetic field

Quasilinear analysis of wave-particle interactions is presented for plasma flowing in a weakly nonuniform magnetic field configuration. The method presented is based on a scale separation between the length scales of quasilinear relaxation and the magnetic field inhomogeneity, allowing one to obtain large scale solutions for both particle distribution functions and wave spectra, without going into the details of the small scale quasilinear relaxation. The numerical example shows the existence of a secondary instability for an initially stable particle distribution function.     

Analysis of the spectral variation of a dye laser by gain medium inhomogeneity

In this paper, an analysis of spectral variation of a high repetition rate dye laser by an optical inhomogeneity developed inside the gain medium is presented. The passive band-pass, responsible for bandwidth, set (in homogeneous medium) by dispersive optical element in its resonator is modulated by scale length of the inhomogeneity introduced in the gain medium. Inhomogeneities, introduced by temperature in laminar flow (at low Reynolds number) and fractional change in flow-induced scale length (at higher Reynolds number) have an effect on the wavelength of dye laser.     

Localized ferromagnetic resonance in inhomogeneous thin films

The effect of sample inhomogeneity on the ferromagnetic resonance linewidth is determined by diagonalization of a spin wave Hamiltonian for ferromagnetic thin films with inhomogeneities spanning a wide range of characteristic length scales. A model inhomogeneity is used that consists of size D grains and an anisotropy field H(p) that varies randomly from grain to grain in a film with thickness d and magnetization M(s). The resulting linewidth agrees well with the two-magnon model for small inhomogeneity, H(p)DpiM(s)d, the precession becomes localized and the spectrum approaches that of local precession on independent grains.     

Anomalous scaling of a passive scalar in turbulence and in equilibrium

We analyze the multipoint correlation functions of a tracer in an incompressible flow at scales far exceeding the scale L at which fluctuations are generated (quasiequilibrium domain) and compare them with the correlation functions at scales smaller than L (turbulence domain). We demonstrate that scale invariance can be broken in the equilibrium domain and trace this breakdown to the statistical integrals of motion (zero modes) as has been done before for turbulence. Employing the Kraichnan model of short-correlated velocity we identify the new type of zero modes, which break scale invariance and determine an anomalously slow decay of correlations at large scales.     

Imageless microscopy of surface patterns using optical waveguides

Recent experiments using a grating coupled low-index nanoporous silica supported monomode waveguide have demonstrated that living cells can cause heavy distortion of the grating coupler resonance lines, in some cases even leading to a separation into two resonance peaks. These findings stand in contrast to previously reported data, where simple peak broadening was observed during cell attachment and spreading using less sensitive waveguide designs. In order to explain these observations, we apply the local interference method to simulate the effects of inhomogeneity patterns on the surface of grating coupled planar optical waveguides and obtain the resonant peaks for the modes. It is shown that analyte inhomogeneities affect both the position and shape of the resonant peaks. Depending on the deposited cell or domain size, refractive index contrast and waveguide design, peak shift, peak deformations or peak splitting can be observed. On the basis of simulation data, characteristic parameters of the resonant peaks such as peak width at half maxima, overall width, central position and peak integral are connected for the first time to quantitative parameters of the inhomogeneity patterns; like analyte covered sensor area, surface averaged effective refractive index and domain size. Our results indicate that by careful investigations of the incoupling resonant peaks, quantitative information about sample inhomogeneities at the micrometer scale can be obtained, thus allowing for a new generation of simple, low cost, label free and imageless optical sensors, which are well suited for high throughput screening applications. PACS 42.82.Et     

Magnetosheath plasma turbulence and its spatiotemporal evolution as observed by the cluster spacecraft

We study the plasma turbulence, at scales larger than the ion inertial length scale, downstream of a quasiparallel bow shock using Cluster multispacecraft measurements. We show that turbulence is intermittent and well described by the extended structure function model, which takes into account the spatial inhomogeneity of the cascade rate. For the first time we use multispacecraft observations to characterize the evolution of magnetosheath turbulence, particularly its intermittency, as a function of the distance from the bow shock. The intermittency significantly changes over the distance of the order of 100 ion inertial lengths, being increasingly stronger and anisotropic away from the bow shock.     

Multifractal modelling and 3D lacunarity analysis

This study presents a comparative evaluation of lacunarity of 3D grey level models with different types of inhomogeneity. A new method based on the “Relative Differential Box Counting” was developed to estimate the lacunarity features of grey level volumes. To validate our method, we generated a set of 3D grey level multifractal models with random, anisotropic and hierarchical properties. Our method gives a lacunarity measurement correlated with the theoretical one and allows a better model classification compared with a classical approach.     

Coarsening of fractal viscous fingering patterns

We have measured the coarsening due to surface tension of radially grown fractal viscous fingering patterns. The patterns at late times depend on the structural form at the onset of coarsening, providing information on the age of the fractal. The coarsening process is not dynamically scale invariant, exhibiting two dynamic length scales that grow as L1(t) approximately t(0.22+/-0.02) and L2(t) approximately t(0.31+/-0.02). The measured exponents are in agreement with the results of recent numerical studies of diffusion-controlled coarsening of a diffusion-limited aggregation fractal [Phys. Rev. E 65, 050501 (2002)]].     

Peak effect in polycrystalline vortex matter

We report a study of the peak-effect phase diagram of a strongly disordered type-II superconductor V-21 at. %Ti using ac magnetic susceptibility and small-angle neutron scattering (SANS). In this system, the peak effect appears only at fields higher than 3.4 T. The sample is characterized by strong atomic disorder. Vortex states with field-cooled thermal histories show that both deep in the mixed state, as well as close to the peak effect, there exist no long-range orientationally ordered vortex lattices. The SANS scattering radial widths reveal vortex states ordered in the sub-mum scale. We conjecture that the peak effect in this system is a remnant of the Bragg glass disordering transition, but occurs on submicron length scales due to the presence of strong atomic disorder on larger length scales.     

Paramagnetic relaxation in sandstones: distinguishing T1 and T2 dependence on surface relaxation, internal gradients and dependence on echo spacing

This work provides a generalized theory of proton relaxation in inhomogeneous magnetic fields. Three asymptotic regimes of relaxation are identified depending on the shortest characteristic time scale. Numerical simulations illustrate that the relaxation characteristics in the regimes such as the T(1)/T(2) ratio and echo spacing dependence are determined by the time scales. The theoretical interpretation is validated for fluid relaxation in porous media in which field inhomogeneity is induced due to susceptibility contrast of fluids and paramagnetic sites on pore surfaces. From a set of measurements on model porous media, we conclude that when the sites are small enough, no dependence on echo spacing is observed with conventional low-field NMR spectrometers. Echo spacing dependence is observed when the paramagnetic materials become large enough or form a 'shell' around each grain such that the length scale of the region of induced magnetic gradients is large compared to the diffusion length during the time of the echo spacing. The theory can aid in interpretation of diffusion measurements in porous media as well as imaging experiments in presence of contrast agents used in MRI.     

Atoms in a radio-frequency-dressed optical lattice

We load cold atoms into an optical lattice dramatically reshaped by radio-frequency coupling of state-dependent lattice potentials. This radio-frequency dressing changes the unit cell of the lattice at a subwavelength scale, such that its curvature and topology departs strongly from that of a simple sinusoidal lattice potential. Radio-frequency dressing has previously been performed at length scales from mm to tens of mum, but not at the single-optical-wavelength scale. At this length scale significant coupling between adiabatic potentials leads to nonadiabatic transitions, which we measure as a function of lattice depth and dressing amplitude. We also investigate the dressing by measuring changes in the momentum distribution of the dressed states.     

The vibrations of glasses near the end of acoustic branches

The interest in measuring acoustic and optic vibrations of glasses at terahertz frequencies is explained. Techniques used for Brillouin spectroscopy at scattering vectors Q⩾1 nm⁻¹ are briefly described and compared. Experimental results, for example on vitreous silicas or glassy selenium, show that plane-wave acoustic excitations exhibit a crossover from propagation to strong scattering as Q is increased. Optical excitations at similar frequencies form a ‘boson peak’. These fairly local excitations can obey ‘molecular-like’ selection rules. The findings reveal a somewhat unexpected strong elastic inhomogeneity in the structure of glasses at the extended length scale of ∼5 nm, about which so little is known otherwise.     

CX2+CH2O (X=F, Cl, Br)环加成反应的密度泛函理论计算

用密度泛函理论,在B3LYP/6-311 G(d)水平上研究了CX2 CH2O(X=F,Cl,Br)环加成反应一条三过渡态三中间体路径的反应机理,全参数优化了反应势能面各驻点的几何构型,用内禀反应坐标(IRC)和频率分析方法,对过渡态进行了验证.用高级电子相关校正的耦合簇[CCSD(T)/6-311 G(d)]方法对优化构型进行了单点能计算.采用经Wigner校正的Eyring过渡态理论和热力学方法,研究了该反应通道的热力学及动力学性质.从热力学和动力角度综合分析,该途径CF2与GH2O的环加成反应难以发生,而CCl2及CBr2与CH2O反应的适宜温度范围均为400～1000K,如此,反应既具有较大的自发趋势和平衡常数,又具有较快的反应速率.     

The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.