Dynamics and correlation length scales of a glass-forming liquid in quiescent and sheared conditions

We numerically study dynamics and correlation length scales of a colloidal liquid in both quiescent and sheared conditions to further understand the origin of slow dynamics and dynamic heterogeneity in glass-forming systems. The simulation is performed in a weakly frustrated two-dimensional liquid, where locally preferred order is allowed to develop with increasing density. The four-point density correlations and bond-orientation correlations, which have been frequently used to capture dynamic and static length scales ξ in a quiescent condition, can be readily extended to a system under steady shear in this case. In the absence of shear, we confirmed the previous findings that the dynamic slowing down accompanies the development of dynamic heterogeneity. The dynamic and static length scales increase with α-relaxation time τ(α) as a power law [Formula: see text], with μ?>?0. In the presence of shear, both viscosity and τ(α) have power-law dependences on shear rate in the marked shear-thinning regime. However, the dependence of correlation lengths cannot be described by power laws in the same regime. Furthermore, the relation [Formula: see text] between length scales and dynamics holds for not too strong shear where thermal fluctuations and external forces are both important in determining the properties of dense liquids. Thus, our results demonstrate a link between slow dynamics and structure in glass-forming liquids even under nonequilibrium conditions.     

Evidence of long-distance correlation of fluctuations during edge transitions to improved-confinement regimes in the TJ-II stellarator

Long-distance coupling between edge parameters' fluctuations has been investigated in the TJ-II stellarator. Results show long-range correlations in potential fluctuations, which are amplified by the development of radial electric fields during transitions to improved-confinement regimes, whereas there is no correlation between ion saturation current signals. These experimental findings suggest the importance of long-range correlations as a new fingerprint of the plasma behavior during the development of edge shear flows and the key role of electric fields to amplify them.     

Emergence of long-range correlations and rigidity at the dynamic glass transition

At the so-called dynamic glass transition predicted by the mean-field replica approach equilibrium liquid's translational symmetry is spontaneously broken, albeit at the microscopic level. We show that this fact implies the emergence of Goldstone modes and long-range density correlations. We derive and evaluate a new statistical mechanical expression for the glass shear modulus.     

Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with nondecaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in any dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.     

Emergent <Emphasis Type="Italic">SO</Emphasis>(3) Symmetry of the Frictionless Shear Jamming Transition

We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.     

Strong correlation, electron-phonon interaction and critical fluctuations: isotope effect, pseudogap formation, and phase diagram of the cuprates

Within the Hubbard-Holstein model with long-range Coulomb forces, we revisit the charge-ordering (CO) scenario for the superconducting cuprates and account for the presence or the absence of a formed stripe phase in different classes of cuprates. We also evaluate the mean-field and the fluctuation-corrected critical lines for CO and we relate them with the various pseudogap crossover lines occurring in the cuprates and we discuss a mechanism for their peculiar isotopic dependence. Considering the dynamical nature of the CO transition, we explain the spread of T∗ and of its isotopic shift, obtained with experimental probes with different characteristic time scales.     

无序度对一维长程关联无序系统中局域化-退局域化转变的影响

对长程幂律关联能量序列进行了修正,使其能体现出无序度在一维长程关联无序系统中的影响,并利用重正化群方法,计算了能反映该系统局域化-退局域化转变的Lyapunov指数.结果表明,在由于关联指数p的影响而在系统中出现的局域化向退局域化的转变中,无序度起着相反的作用.当关联指数p一定而无序度W增大时,系统中心能区范围内由于长程关联而引起的扩展态逐渐向局域态转变.当无序度W增大到某一临界值W_c时,系统中所有本征态均转变为局 关键词： 长程关联 Lyapunov指数 无序度 局域化-退局域化转变     

Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil

In this paper, we study the auto-correlations and cross-correlations of West Texas Intermediate (WTI) crude oil spot and futures return series employing detrended fluctuation analysis (DFA) and detrended cross-correlation analysis (DCCA). Scaling analysis shows that, for time scales smaller than a month, the auto-correlations and cross-correlations are persistent. For time scales larger than a month but smaller than a year, the correlations are anti-persistent, while, for time scales larger than a year, the series are neither auto-correlated nor cross-correlated, indicating the efficient operation of the crude oil markets. Moreover, for small time scales, the degree of short-term cross-correlations is higher than that of auto-correlations. Using the multifractal extension of DFA and DCCA, we find that, for small time scales, the correlations are strongly multifractal, while, for large time scales, the correlations are nearly monofractal. Analyzing the multifractality of shuffled and surrogated series, we find that both long-range correlations and fat-tail distributions make important contributions to the multifractality. Our results have important implications for market efficiency and asset pricing models.     

Subdiffusion and cage effect in a sheared granular material

We investigate experimentally the diffusion properties of a bidimensional bidisperse dry granular material under quasistatic cyclic shear. The comparison of these properties with results obtained both in computer simulations of hard spheres systems and Lennard-Jones liquids and experiments on colloidal systems near the glass transition demonstrates a strong analogy between the statistical behavior of granular matter and these systems, despite their intrinsic microscopic differences (thermal vs athermal). More specifically, we study in detail the cage dynamics responsible for the subdiffusion in the slow relaxation regime, and obtain the values of relevant time and length scales.     

Multiscale entropy analysis of complex physiologic time series

There has been considerable interest in quantifying the complexity of physiologic time series, such as heart rate. However, traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long-range correlations. This paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics. We introduce a method to calculate multiscale entropy (MSE) for complex time series. We find that MSE robustly separates healthy and pathologic groups and consistently yields higher values for simulated long-range correlated noise compared to uncorrelated noise.     

Effect of shear strain on the α-ε phase transition of iron: a new approach in the rotational diamond anvil cell

The effect of shear strain on the iron α-ε phase transformation has been studied using a rotational diamond anvil cell (RDAC). The initial transition is observed to take place at the reduced pressure of 10.8?GPa under pressure and shear operation. Complete phase transformation was observed at 15.4?GPa. The rotation of an anvil causes limited pressure elevation and makes the pressure distribution symmetric in the sample chamber before the phase transition. However, it causes a significant pressure increase at the centre of the sample and brings about a large pressure gradient during the phase transformation. The resistance to the phase interface motion is enhanced due to strain hardening during the pressure and shear operations on iron and this further increases the transition pressure. The work of macroscopic shear stress and the work of the pressure and shear stress at the defect tips account for the pressure reduction of the iron phase transition.     

Multifractal properties of Chinese stock market in Shanghai

In this article, we apply three methods of multifractal analysis, partition function method, singular spectrum method and multifractal detrended fluctuation analysis method, to analyze the closing index fluctuations of Shanghai stock market during the past seven years. We have found that Shanghai stock market has weak multifractal features and there are long-range power-law correlations between index series. The shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten. But when the orders of partition function increase, the strengths of multifractal increase, the singular spectrums become rougher and the general Hurst exponents decrease. These results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation.     

Long-range boundary effects in simple fluids

We discuss long-range boundary effects in simple two- or three-dimensional fluids. These boundary effects are due to the existence of long-range correlations in nonequilibrium fluids and can be computed either by means of kinetic theory or phenomenological mode-coupling theories. In particular, we use kinetic theory to compute the stress tensor and heat flux vector for a fluid in a nonequilibrium steady state in a finite geometry and show that both the effective shear viscosity and effective heat conductivity have contributions due to the walls of the container that influence the behavior of the system far into the fluid. We also show that the mechanocaloric effect is present in the bulk of a three-dimensional fluid and that there are normal stresses in a fluid whenever the temperature gradient is nonzero.Work performed under National Science Foundation grant No. CHE 77-16308.     

Strongly interacting low-viscosity matter created in relativistic nuclear collisions

Substantial collective flow is observed in collisions between large nuclei at BNL RHIC (Relativistic Heavy Ion Collider) as evidenced by single-particle transverse momentum distributions and by azimuthal correlations among the produced particles. The data are well reproduced by perfect fluid dynamics. A calculation of the dimensionless ratio of shear viscosity eta to entropy density s by Kovtun, Son, and Starinets within anti-de Sitter space/conformal field theory yields eta/s=variant Planck's over 2pi/4pikB, which has been conjectured to be a lower bound for any physical system. Motivated by these results, we show that the transition from hadrons to quarks and gluons has behavior similar to helium, nitrogen, and water at and near their phase transitions in the ratio eta/s. We suggest that experimental measurements can pinpoint the location of this transition or rapid crossover in QCD.     

一维扩展量子罗盘模型的拓扑序和量子相变

应用矩阵乘积态表示的无限虚时间演化块算法,研究了扩展的量子罗盘模型.为了深入研究该模型的长程拓扑序和量子相变,基于奇数键和偶数键,引入了奇数弦关联和偶数弦关联,计算了保真度、奇数弦关联、偶数弦关联、奇数弦关联饱和性与序参量.弦关联表现出三种截然不同的行为:衰减为零、单调饱和与振荡饱和.基于弦关联的以上特征,给出了量子罗盘模型的基态序参量相图.在临界区,局域磁化强度和单调奇弦序参量的临界指数β=1/8表明:相变的普适类是Ising类型.此外,保真度探测到的相变点、连续性与非连续性和序参量的结果一致.     

Order-disorder transition in conflicting dynamics leading to rank-frequency generalized beta distributions

The behavior of rank-ordered distributions of phenomena present in a variety of fields such as biology, sociology, linguistics, finance and geophysics has been a matter of intense research. Often power laws have been encountered; however, their validity tends to hold mainly for an intermediate range of rank values. In a recent publication (Martínez-Mekler et al., 2009 [7]), a generalization of the functional form of the beta distribution has been shown to give excellent fits for many systems of very diverse nature, valid for the whole range of rank values, regardless of whether or not a power law behavior has been previously suggested. Here we give some insight on the significance of the two free parameters which appear as exponents in the functional form, by looking into discrete probabilistic branching processes with conflicting dynamics. We analyze a variety of realizations of these so-called expansion-modification models first introduced by Wentian Li (1989) [10]. We focus our attention on an order-disorder transition we encounter as we vary the modification probability p. We characterize this transition by means of the fitting parameters. Our numerical studies show that one of the fitting exponents is related to the presence of long-range correlations exhibited by power spectrum scale invariance, while the other registers the effect of disordering elements leading to a breakdown of these properties. In the absence of long-range correlations, this parameter is sensitive to the occurrence of unlikely events. We also introduce an approximate calculation scheme that relates this dynamics to multinomial multiplicative processes. A better understanding through these models of the meaning of the generalized beta-fitting exponents may contribute to their potential for identifying and characterizing universality classes.     

Bosonization and quantum hydrodynamics

It is shown that it is possible to bosonize fermions in any number of dimensions using the hydrodynamic variables, namely the velocity potential and density. The slow part of the Fermi field is defined irrespective of dimensionality and the commutators of this field with currents and densities are exponentiated using the velocity potential as conjugate to the density. An action in terms of these canonical bosonic variables is proposed that reproduces the correct current and density correlations. This formalism in one dimension is shown to be equivalent to the Tomonaga-Luttinger approach as it leads to the same propagator and exponents. We compute the one-particle properties of a spinless homogeneous Fermi system in two spatial dimensions with long-range gauge interactions and highlight the metal-insulator transition in the system. A general formula for the generating function of density correlations is derived that is valid beyond the random phase approximation. Finally, we write down a formula for the annihilation operator in momentum space directly in terms of number conserving products of Fermi fields.     

Dynamic stimulation of quantum coherence in systems of lattice bosons

Thermal fluctuations tend to destroy long-range phase correlations. Consequently, bosons in a lattice will undergo a transition from a phase-coherent superfluid as the temperature rises. Contrary to common intuition, however, we show that nonequilibrium driving can be used to reverse this thermal decoherence. This is possible because the energy distribution at equilibrium is rarely optimal for the manifestation of a given quantum property. We demonstrate this in the Bose-Hubbard model by calculating the nonequilibrium spatial correlation function with periodic driving. We show that the nonequilibrium phase boundary between coherent and incoherent states at finite bath temperatures can be made qualitatively identical to the familiar zero-temperature phase diagram, and we discuss the experimental manifestation of this phenomenon in cold atoms.     

He superfluidity in the presence of aerogel

Aerogels introduce disorder into the p-wave-paired superfluid ³He and suppress T_c. Quantifiable (by small angle X-ray scattering) differences in the long-range structure of two identical density aerogels are primarily responsible for their different transition temperatures. We also demonstrate that alteration of the short-range correlations by the addition of ⁴He does not strongly affect T_c. Acoustic measurements of the fast and slow modes of ³He in aerogel are described. These can be used to explore the superfluid component. We also outline future prospects.     

Commentary on "Solid-like rheological response of non-entangled polymers in the molten state" by H. Mendil et al

We discuss the rheology experiments on classical and liquid crystal polymer melts by Mendil et al., in the light of the old and new piezorheometry experiments we have carried out on both types of melt. The mechanical behavior we have observed in the linear and non-linear regimes are independent of the melt studied (classical or liquid crystal), and of their nature (siloxane-type, acrylate-type and styrene-type). In the linear regime, the mechanical behavior of the melts presents two components: the first one is the conventional contribution. It is due to polymer chains, and is independent of sample thickness. The second one, which can be observed only when a strong interaction between the compound and the substrate exists, is associated with the glass transition. This component displays an elastic response depending on the sample thickness, and disappears at high temperature. It can be explained by assuming the presence of long-range density fluctuations, which are associated with the glass transition, and frozen at the frequencies used in the experiments. The experiments as a function of the applied strain show that the value of the elastic component decreases when the applied strain increases. This slipping transition occurs progressively, which highlights the heterogeneous nature of the anchoring. The results on the classical polymer by Mendil et al. can be considered to be consistent with ours. In contrast, their results on the liquid crystal polymer differ markedly from ours, showing that the elastic response of this sample has not the same origin.