Universal Scaling Properties Research Articles

Slip and flow in pastes of soft particles: Direct observation and rheology

Microgel pastes and concentrated emulsions are shown to exhibit a generic slip behavior at low stresses when sheared near smooth surfaces. The magnitude of slip depends on the applied stress. Well above the yield stress, slip is negligible compared to the bulk flow. Just above the yield stress, slip becomes significant and the total deformation results from a combination of bulk flow and slip. At and below the yield stress, the bulk flow is negligible and the apparent motion is entirely due to wall slip. By directly imaging the deformation of pastes and from rheological measurements, we show that slip is characterized by universal scaling properties, which depend on solvent viscosity, bulk shear modulus, and particle size. A model based on elastohydrodynamic lubrication between the squeezed particles and the shearing surface explains these properties quantitatively.

Universal features of JIMWLK and BK evolution at small x

In this paper we present the results of numerical studies of the JIMWLK and BK equations with a particular emphasis on the universal scaling properties and phase space structure involved. The results are valid for near zero impact parameter in DIS. We demonstrate IR safety due to the occurrence of a rapidity-dependent saturation scale Q s ( τ). Within the set of initial conditions chosen, both JIMWLK and BK equations show remarkable agreement. We point out the crucial importance of running coupling corrections to obtain consistency in the UV for both equations. Explicit studies of this have been performed with BK. Despite the scale breaking induced by the running coupling we find that evolution drives correlators towards an asymptotic form with near scaling properties. We discuss asymptotic features of the evolution, such as the τ- and A-dependence of Q s away from the initial condition.

Nonuniversality of invasion percolation in two-dimensional systems.

Employing highly efficient algorithms for simulating invasion percolation (IP) with trapping, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in a variety of two-dimensional lattices. The results indicate that these quantities are nonuniversal and vary with the coordination number Z of the lattices. In particular, while the fractal dimension D(f) of the sample-spanning cluster in lattices with low Z has the generally accepted value of about 1.82, it crosses over to the value of random percolation, D(f) approximately equal to 1.896, if Z is large enough. Since optimal paths in strongly disordered media and minimum spanning trees on random graphs are related to IP, the implication is that these problems do not also possess universal scaling properties.

Universal scaling properties of type-I intermittent chaos in isolated resistance arteries are unaffected by endogenous nitric oxide synthesis

Spontaneous fluctuations in flow in isolated rabbit ear resistance arteries may exhibit almost-periodic behavior interrupted by chaotic bursts that can be classified as type-I Pomeau-Manneville intermittency. This conclusion was supported by the construction of parabolic return maps and identification of the characteristic probability distributions for the number of oscillations per laminar segment (n) associated with the type-I scenario. Pharmacological inhibition of nitric oxide (NO) synthesis by the vascular endothelium modulated the dynamics of the reinjection mechanism, and thus the generic shape of the probability distribution for n. Nevertheless, average laminar length was related to a derived bifurcation parameter epsilon according to power-law scaling of the form <n> approximately epsilon(beta), where the estimated critical exponent beta was close to the theoretical value of -0.5 both in the presence and absence of NO synthesis.

Overscreened multichannelSU(N)Kondo model: Large-Nsolution and conformal field theory

The multichannel Kondo model with $\mathrm{SU}(N)$ spin symmetry and $\mathrm{SU}(K)$ channel symmetry is considered. The impurity spin is chosen to transform as an antisymmetric representation of $\mathrm{SU}(N),$ corresponding to a fixed number of Abrikosov fermions ${\ensuremath{\sum}}_{\ensuremath{\alpha}}{f}_{\ensuremath{\alpha}}^{\ifmmode\dagger\else\textdagger\fi{}}{f}_{\ensuremath{\alpha}}=Q.$ For more than one channel $(K&gt;1),$ and all values of $N$ and $Q,$ the model displays non-Fermi behavior associated with the overscreening of the impurity spin. Universal low-temperature thermodynamic and transport properties of this non-Fermi-liquid state are computed using conformal field theory methods. A large-$N$ limit of the model is then considered, in which $K/N\ensuremath{\equiv}\ensuremath{\gamma}$ and $Q/N\ensuremath{\equiv}{q}_{0}$ are held fixed. Spectral densities satisfy coupled integral equations in this limit, corresponding to a (time-dependent) saddle point. A low-frequency, low-temperature analysis of these equations reveals universal scaling properties in the variable $\ensuremath{\omega}/T,$ in agreement with conformal invariance. The universal scaling form is obtained analytically and used to compute the low-temperature universal properties of the model in the large-$N$ limit, such as the $T=0$ residual entropy and residual resistivity, and the critical exponents associated with the specific heat and susceptibility. The connections with the ``noncrossing approximation'' and the previous work of Cox and Ruckenstein are discussed.

Correlation dimension of intermittent signals

We investigate the breaking of proper self-similarity of attractors in the presence of intermittency. We show that this can lead to dramatically too small values of the numerically estimated correlation dimension ${D}_{2}$, which we relate, in the case of type I intermittency, to universal scaling properties in the vicinity of the critical value of the control parameter. For spatially extended systems we study the influences of space-time intermittency on the correlation dimension.

Superconducting transition in Tl-2 2 1 2 thin films and polycrystals: Effect of the dimensionality of the sample

A former paper had shown that some Tl-2 2 1 2 thin films can be described as two-dimensional arrays of weakly coupled superconducting grains. We here report on a comparative study of the superconducting transition ( R = 0) in a Tl-2 2 1 2 thin film and a Tl-2 2 1 2 polycrystal. We find in this way rather striking evidence for two kinds of voltage-current behaviours respectively which places emphasis on the dimensionality of samples. We show that both these dissipative behaviours can quantatively be explained in terms of phase-coherence transitions predicted in D-dimensional arrays of superconducting grains. In particular, universal scaling properties of the three-dimensional phase-coherence transition and Kosterlitz-Thouless-like phase transition are found for the polycrystal and the film respectively.

Developed Turbulence: From Full Simulations to Full Mode Reductions.

Developed Navier-Stokes turbulence is simulated with varying wave-vector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents zeta p of the pth order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents rho p,q = ( zeta p- zeta 3p/3)/( zeta q- zeta 3q/3).

Dielectric dispersion in truely glassy system

Abstract It is examined whether or not the proton glass system has the universal scaling properties as observed for truely glass forming substances. The data of dielectric dispersion for the system are polydispersive and deviate considerably from the universal scaling curve. This deviation might be caused by the tunnelling motion of protons.

The cumulant approach for investigating the noise influence on mode-locking bifurcations

The influence of noise on mode-locking bifurcations is investigated for the circle map and for coupled logistic maps. The technique based on the cumulant expansion is used for the bifurcation analysis of these systems. It is shown that this cumulant analysis in Gaussian approximation provides a suitable description of the influence of weak noise. We find that the universal scaling properties for the circle map in the critical point for the golden-mean sequence are the same as those obtained analytically using the path integral technique. We find the same scaling behaviour in the case of weak multiplicative noise.

Can the light ion transport in heavy targets be characterized by a single parameter?

Based on parameter analysis for the linear Boltzmann equation of ion transport in solids, it has been found that the transport behaviour of low energy light ions in heavy targets possesses a universal scaling property. To test this interesting conclusion, accurate transport calculations based on the bipartition model of ion transport have been carried out for reflection coefficients, range distribution, radiation damage distribution and ionization distribution (namely, the energy deposition resulted by elastic collisions and inelastic collisions). The calculations show that these transport quantities can be characterized by a single parameter called the scaled transport cross section.

Magnetic shielding behavior of YBCO cylinders? A universal scaling property

Magnetic shielding studies have been carried out to investigate the usefulness of high-Tc YBCO ceramics for EMS applications. The starting materials were single-phase YBCO powder. The cylinders were prepared by uniaxial compresssion and isostatic compression, with and without Ag additive. The shielding fieldH*, defined as the value of the applied field at which a detectable field will be seen inside the superconducting shield, was 12 G for the shield prepared by uniaxial compression and around 17 G for shields prepared by isostatic compression. Measurements were done in both ac and dc fields. The field inside the shield for the sinusoidal ac applied field is highly distorted, showing the presence of three higher harmonics. The penetrated waveform was Fourier-analyzed to yield the rms value ofBin. When the normalized value ofB was plotted against the normalized value ofH with respect toH*, all the points corresponding to different shields fall on the same curve.

Universality and scaling in fully developed turbulence

Abstract The small scale velocity fluctuations in high Reynolds number incompressible fluid turbulence exhibit universal scaling properties independent of the large scale flow structures. The evidence for this universality and scaling from experiment and direct numerical simulation, which has considerably improved in recent years, is reviewed in this article. The emphasis is on those features which are independent of any particular statistical theory. Some attempt is made to link this phenomenological picture to Navier-Stokes dynamics, but this is necessarily quite incomplete since a fundamental theoretical understanding is still lacking.

Three-body halos: Gross properties.

Three-body bound systems are investigated in the limit of very weak binding by use of hyperspherical harmonics. The short-range two-body potentials are assumed to be unable to bind the binary subsystems. Then the mean square radius always converges for vanishing binding except for the most spherical wave function, where all angular momenta involved are zero, which diverges logarithmically. Universal scaling properties are suggested. Any additional long-range repulsive potential, like, for example, the Coulomb potential, leads to finite radial moments even for vanishing binding. Spatially extended charged halos are only possible for very low charges. The spatial extension of three-body systems is in the asymptotic region more confined than for corresponding two-body systems, where the divergences are stronger and more abundant. Numerical examples and transitions to the asymptotic region are shown for square well and Gaussian two-body potentials. The results are applied to several drip-line nuclei.

Nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices

We prove the moments of the directed polymer partition function GZ, using an exact position space renormalization group scheme on a hierarchical lattice. After sufficient iteration the characteristic functionf(n)=ln〈GZn〉 of the probability ℘(Z) converges to a stable limitf*(n). For smalln the limiting behavior is independent of the initial distribution, while for largen,f*(n) is completely determined by it and is thus nonuniversal. There is a smooth crossover between the two regimes for small effective dimensions, and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution. For large effective dimensions there is a sharp transition between the two regimes, and analytical continuation from integer moments ton→0 is not possible. Replica arguments can account for most features of the observed results.

Universality in quasiperiodic Rayleigh-Bénard convection.

We study universal scaling properties of quasiperiodic Rayleigh-Benard convection in a {sup 3}He--superfluid-{sup 4}He mixture. The critical line is located in a parameter space of Rayleigh and Prandtl numbers using a transient-Poincare-section technique to identify transitions from nodal periodic points to spiral periodic points within resonance horns. We measure the radial and angular contraction rates and extract the linear-stability eigenvalues (Flouquet multipliers) of the periodic point. At the crossings of the critical line with the lines of fixed golden-mean-tail winding number we determine the universality class of our experimental dynamics using {ital f}({alpha}) and trajectory-scaling-function analyses. A technique is used to obtain a robust five-scale approximation to the universal trajectory scaling function. Different methods of multifractal analysis are employed and an understanding of statistical and systematic errors in these procedures is developed. The power law of the inflection point of the map, determined for three golden-mean-tail winding numbers, is 2.9{plus minus}0.3, corresponding to the universality class of the sine-circle map.

Nonlinear dynamics of a forced thermoacoustic oscillation.

A spontaneous acoustic oscillation of a gas column induced by temparature gradients is periodically perturbed by an external force. Nonlinear coupling between two oscillating modes can generate abundant nonlinear phenomena, quasiperiodicity, frequency locking, onset of chaos, and quenching phenomenon. Adjusting the frequency ratio to the golden mean, we study the scaling universality for the quasiperiodic transition to chaos. The first experiment in acoustics demonstrates that thermoacoustic systems follow universal scaling properties of the circle map in spite of the complexity of the system.

Universal scaling properties of ballistic deposition and Eden growth on surfaces

The structures generated by ballistic deposition and Eden growth from a surface can be divided in a natural way (defined by the growth process) into 'trees' or clusters of connected sites or particles. The structure of these trees can be characterised by the exponents nu perpendicular to (=p) and nu /sub ///(=q) which describe how their heights (h) and widths (w) grow with increasing size s (w approximately sp, h approximately sq). In addition, the distribution of sizes can be described by the power law Ns approximately s- tau where Ns is the number of trees of size s. Both the individual trees and the complete deposit are compact so that the exponents p, q and tau satisfy the simple scaling relationships (d-1)p+q=1 and tau =2-q. The exponents p, q and tau seem to be universal for off-lattice ballistic deposition, on-lattice ballistic deposition and Eden growth models. However, the corresponding exponents for the river network model are different from those for Eden growth and ballistic deposition. From the two-dimensional Eden model and ballistic deposition models values of about 0.40, 0.60 and 1.40 were obtained for p, q and tau , respectively. In three dimensions p approximately=0.28, q approximately=0.46 and tau approximately=1.54.

Neutron Diffraction Study on the Kinetics of Non-Equilibrium Phase Transition in Ag3SI

The kinetics of the ordering process in the first order phase transition of superionic Ag 3 SI was investigated by neutron diffraction. α-Ag 3 SI was quenched to certain temperatures of T c - Δ T , and the time dependence of integrated intensities and line widths of 111 reflection were measured for various Δ T from 20 K to 75 K. The time development scheme of the intensities can be categorized into three ranges of \(\varDelta T:\varDelta T{\lesssim}32\,\text{K}\), \(35\,\text{K}{\lesssim}\varDelta T{\lesssim}42\,\text{K}\) and \(55\text{K}{\lesssim}\varDelta T\). In the first range data show the initial stage of domain nucleation. Relaxation time τ was estimated from the intensity data. The values thus obtained for \(\varDelta T{\gtrsim}32\,\text{K}\) were not explained from the measurement of line widths, especially for \(\varDelta T{\lesssim}55\,\text{K}\), though the time dependence of line widths followed nearly to the t -1/2 behavior. As a matter of course the validity of a universal scaling property...

Interference effects in the charge-density wave conductor NbSe 3

The nonlinear response of the charge-density wave (CDW) in NbSe 3 to combined ac + dc excitations is discussed. We analyze the harmonic and subharmonic steps appearing in the current-voltage characteristics and compare the experimental results to computer simulations. The effects of internal degrees of freedom and the relevance of some universal scaling properties, derived from the properties of the sine circle map, are investigated.