Critical scaling of shear viscosity at the jamming transition

We carry out numerical simulations to study transport behavior about the jamming transition of a model granular material in two dimensions at zero temperature. Shear viscosity eta is computed as a function of particle volume density rho and applied shear stress sigma, for diffusively moving particles with a soft core interaction. We find an excellent scaling collapse of our data as a function of the scaling variable sigma/|rho(c)-rho|(Delta), where rho(c) is the critical density at sigma=0 ("point J"), and Delta is the crossover scaling critical exponent. We define a correlation length xi from velocity correlations in the driven steady state and show that it diverges at point J. Our results support the assertion that jamming is a true second-order critical phenomenon.     

Holographic conductivity of holographic superconductors with higher-order corrections

We analytically and numerically disclose the effects of the higher-order correction terms in the gravity and in the gauge field on the properties of s-wave holographic superconductors. On the gravity side, we consider the higher curvature Gauss–Bonnet corrections and on the gauge field side, we add a quadratic correction term to the Maxwell Lagrangian. We show that, for this system, one can still obtain an analytical relation between the critical temperature and the charge density. We also calculate the critical exponent and the condensation value both analytically and numerically. We use a variational method, based on the Sturm–Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. For a fixed value of the Gauss–Bonnet parameter, we observe that the critical temperature decreases with increasing the nonlinearity of the gauge field. This implies that the nonlinear correction term to the Maxwell electrodynamics makes the condensation harder. We also study the holographic conductivity of the system and disclose the effects of the Gauss–Bonnet and nonlinear parameters \(\alpha \) and b on the superconducting gap. We observe that, for various values of \(\alpha \) and b, the real part of the conductivity is proportional to the frequency per temperature, \(\omega /T\), as the frequency is large enough. Besides, the conductivity has a minimum in the imaginary part which is shifted toward greater frequency with decreasing temperature.     

Magnetic hysteresis in the microwave surface resistance of Nb samples in the critical state

We discuss the hysteretic behavior of the field-induced variations of the microwave surface resistance in superconductors in the critical state. Measurements have been performed in a bulk sample of Nb and a powdered one at different values of the temperature. We discuss a model, based on the Coffey and Clem theory, in which we take into account the flux distribution inside the sample, due to the critical state. The experimental results are quite well justified in the framework of our model. We show that by fitting the experimental data it is possible to determine the value of the critical current density and its field dependence.     

The Kondo necklace model with planar anisotropy

We study the one-dimensional anisotropic Kondo necklace model at zero temperature through White's density matrix renormalization group technique. The ground state energy and the spin gap were calculated as a function of the exchange parameter for two anisotropy values. We found a finite critical point separating a Kondo singlet from an antiferromagnetic phase. The transition is highly congruent with a Kosterlitz–Thouless form. We observed that the critical point increases with the anisotropy.     

The functional renormalization group and O(4) scaling

The critical behavior of the chiral quark-meson model is studied within the Functional Renormalization Group (FRG). We derive the flow equation for the scale-dependent thermodynamic potential at finite temperature and density in the presence of a symmetry-breaking external field. We perform a set of approximations to formulate and solve the FRG flow equation in the presence of fermionic degrees of freedom and test their influence on the O(4) critical properties expected in the quark-meson model. Within this scheme, the critical scaling behavior of the order parameter, its transverse and longitudinal susceptibilities as well as the correlation lengths near the chiral phase transition are computed for vanishing baryon density. We focus on the scaling properties of these observables at non-vanishing external field when approaching the critical point from the symmetric as well as from the broken phase. We confront our numerical results with the Widom–Griffiths form of the magnetic equation of state, obtained by a systematic ε expansion of the scaling function.     

Anomalies of attenuation and phase velocity of surface acoustic waves in YBa2Cu3O7‒δ thin films in the vicinity of Tc

We present measurements of the attenuation and phase velocity of surface acoustic waves in thin YBa₂Cu₃O films as a function of temperature, in magnetic fields up to 3.6 T applied parallel to the c-axis of the films. We have observed anomalies in both, the attenuation and the phase velocity in the vicinity of the superconducting critical temperature which do not depend on the magnetic field. Possible origins of these anomalies, observed, to our knowledge, for the first time in YBa₂Cu₃O thin films, are discussed and compared to bulk acoustic wave experiments. We present a kind of feedback technique for surface acoustic waves which improves the sensitivity of this type of measurement. The actual sensitivity limits are mentioned. Received: 7 August 1997 / Revised: 7 November 1997 / Accepted: 17 November 1997     

Phase diagram in the quantum XY model with long-range interactions

We study the d-dimensional quantum XY model with ferromagnetic long-range interaction decaying as r-p in terms of boson operators, by employing the coherent state path integral approach. We have obtained a finite critical temperature as a function of the dimension (d) for d2d the system becomes disordered at all temperatures. For the particular values p=3/2 and d=1 our theoretical calculations are comparable to those from Monte Carlo simulations.     

Solitary modes of bacterial culture in a temperature gradient

We study the behavior of a bacterial culture in a one-dimensional temperature gradient. The bacteria first accumulate near their natural temperature due to thermotaxis. The maximum of the bacterial density profile then drifts to lower temperature with a velocity proportional to the initial concentration of bacteria (typical velocity 0.5 microm/sec). Above a critical concentration of 10(8) cells/cm(3), a new mode develops from the initial accumulation in the form of a sharp pulse moving at a faster velocity ( approximately 3.5 microm/sec). The time of development of this mode diverges as the concentration approaches its critical value. This mode is a result of a positive feedback mechanism provided by interbacterial communication. A theoretical model shows good agreement with the experimental results.     

Transport properties of the two-dimensional electron gas in wide AlP quantum wells including temperature and correlation effects

We investigate the mobility, magnetoresistance and scattering time of a quasi-two-dimensional electron gas in a GaP/AlP/GaP quantum well of width L>L_c=45.7 Å at zero and finite temperatures. We consider the interface-roughness and impurity scattering, and study the dependence of the mobility, the resistance and scattering time ratio on the carrier density and quantum well width for different values of the impurity position and temperature using different approximations for the local-field correction. In the case of zero temperature and Hubbard local-field correction our results reduce to those of Gold and Marty (Phys. Rev. B. 76 (2007) 165309) [3]. We also study the correlation and multiple scattering effects on the total mobility and the critical density for a metal–insulator transition.     

Asymptotic Models of Diffusion Effects due to Nonlinear Resonant Interaction of Waves with Flows

We develop an asymptotic theory describing nonlocal effects caused by weak-diffusion processes in the case of resonant interaction of quasi-harmonic waves of small but finite amplitudes with flows of various physical nature in the case of an arbitrary relation between the nonlinearity and diffusion.We analyze the interaction of internal gravity waves with plane-parallel stratified shear flows in the nonlinearly-dissipative critical layer (CL) formed in the vicinity of the resonance level where the flow velocity is equal to the phase velocity of the wave. It is shown that the combined effect of the radiation force in the inner region of the CL and vorticity diffusion to the outer region results in the formation of a flow in which the asymptotic values of average vorticity at different sides of the CL are constant but different. If the criterion of the linear dynamic stability is satisfied (the Richardson number Ri>1/4), the resulting vorticity steps are comparable to the unperturbed vorticity. As a result, a wave reflected from the vorticity inhomogeneity in the CL is formed. As the amplitude of the incident wave increases, the average vorticity at the incidence side approaches the linear-stability threshold (Richardson number Ri > 1/4), and the reflection coefficient tends to -1.In the regime of nonlinear dissipative CL, we study the quasi-stationary asymptotic behavior of the flow formed by an internal gravity wave incident on a dynamically stable flow with velocity and density stratification, whose velocity at some level is equal to the phase velocity of the wave. It is shown that the vorticity diffusion results in the formation of a nonlocal transition region between the CL and the unperturbed flow, which we call the diffusive boundary layer (DBL). In this case, the CL is shifted toward the incident wave. We obtain a self-similar solution for the average fields, which is valid in the case of a constant vorticity step in the CL, and determine its parameters depending on the inner Reynolds number in the CL which describes the relation between the nonlinear and diffusive effects for the wave field in the resonance region. We determine the structure and temporal dynamics of the DBL formed by a rough surface streamlined by a stratified fluid whose velocity changes direction at some level.It is shown that in the case of the nonlinear resonance interaction of plasma electrons with a Langmuir wave, the electron diffusion in the velocity space leads to a significant nonlocal distortion of the electron distribution function outside the trapping region. We determine the distorted distribution function and calculate the rate of the nonlinear Landau damping of a finite-amplitude wave for an arbitrary ratio of the electron collision rate and the oscillation period of trapped electrons.     

Critical temperature and energy gap in superconductors with singular density of states

The influence of-functional (symmetric as well as asymmetric) singularities in density of states (DOS) on the critical temperature and zero temperature energy gap is calculated. Surprisingly, we have obtained the same function for the off-symmetry of the peak position in DOS on the corresponding critical temperature as for the temperature dependence of the energy gap in the strong-coupling limit. The enhancement of the critical temperature due to the singularity (compared with the constant DOS near the Fermi surface) is much lower for strong-coupling superconductors than in the weak-coupling limit. Hence, the singularity in DOS cannot be the exclusive reason for large values of critical temperatures in highTc superconductors.This work was supported by the grant GA SAV 188/1991.     

Determination of the critical current density and the flux pinning force in single crystals YBa2Cu3O7-δ from the magnetization hysteresis cycles

In this study, the magnetization measurements have been performed on high-temperature superconductor's single crystals YBa₂Cu₃O_7-δ at large ranges of temperature T (15-85 K) and in magnetic fields up to 6T at different values of the angle θ between the applied magnetic field and c-axis. The critical current density Jc deduced from the magnetic hysteresis loops by the Bean formula for H parallel to the c-axis (θ=0°), our results have shown that the critical current density Jc was strongly dependent on the applied magnetic field. The pinning force Fp=Jc×μ₀H was determined from magnetization for H//c, however, a plot of the normalized pinning force density fp= Fp/Fpmax as a function of the reduced magnetic field h= H/Hirr at different temperatures have shown good scaling with the form fp ~h^p(1-h)^q, where p and q are scaling parameters. We also found that the point pinning is more dominant than surface pinning under high temperatures.     

Temperature dependence of the upper critical field in the model of a superconductor with singular points near the Fermi surface

We consider a generalization of BCS theory to the case where the energy spectrum of parent charge carriers near the Fermi energy has a nonlinear character. This nonlinearity can cause an abrupt decrease in the coherence length, growth of the density of states and transition temperature, and non-analyticity of the vertex part as a function of the momentum. As the density of states increases the model exhibits a tendency toward negative curvature of the critical field at the transition point (although a sign change of the curvature is possible near it). Positive curvature can show up upon depletion of the density of states, which in fact corresponds to a departure of the crystal parameters from the conditions maximizing the transition temperature. Fiz. Tverd. Tela (St. Petersburg) 41, 975–978 (June 1999)     

Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model

Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerically in the past. Here, we present an analytical study for the optimal velocity model with a stepwise specification of the optimal velocity function and a simple kind of perturbation. Despite various approximations, the analytical results are shown to reproduce numerical results very well.     

Structure, dsingle-particle and many-particle coefficients of Lennard—Jones liquid Al

We investigate the effects of temperature and density on the single-particle and many-particle coefficients as well as on the structures of homogenous systems in which the particles are assumed to interact via a continuous soft sphere potential in the microcanonical ensemble. The pair distribution function and therefore the structures of the systems studied are affected by temperature close to and above the melting point through migrations of atoms from the first shell in the pair distribution function. The dynamics of atomic pairs in the short-time regime in liquid aluminium may be said to be governed by the potential of mean force, which depends on the static structure of liquid Al at all investigated temperatures. A polynomial dependence ofD on density and temperature was observed in contradiction to Arrhenius law. The shear viscosities of the systems studied are largely nonlinear. It was observed that the soft sphere potential used in our calculations overestimates the Stoke-Einstein relation.     

Multifractal method for the instantaneous evaluation of the stream function in geophysical flows

Multifractal or multiaffine analysis is a promising new branch of methods in nonlinear physics for the study of turbulent flows and turbulentlike systems. In this Letter we present a new method based on the multifractal singularity extraction technique, the maximum singular stream-function method (MSSM), which provides a first order approximation to the stream function from experimental data in 2D turbulent systems. The essence of MSSM relies in relating statistical properties associated with the energy cascade in flows with geometrical properties. MSSM is a valuable tool to process sparse collections of data and to obtain instant estimates of the velocity field. We show an application of MSSM to oceanography as a way to obtain the current field from sea surface temperature satellite images; we validate the result with independent dynamical information obtained from sea level measurements.     

Multiscaling at Point J: jamming is a critical phenomenon

We analyze the jamming transition that occurs as a function of increasing packing density in a disordered two-dimensional assembly of disks at zero temperature for "Point J" of the recently proposed jamming phase diagram. We measure the total number of moving disks and the transverse length of the moving region, and find a power law divergence as the packing density increases toward a critical jamming density. This provides evidence that the T=0 jamming transition as a function of packing density is a second order phase transition. Additionally, we find evidence for multiscaling, indicating the importance of long tails in the velocity fluctuations.     

Metal-insulator transition in two dimensions: experimental test of the two-parameter scaling

We report a detailed scaling analysis of resistivity rho(T,n) measured for several high-mobility 2D electron systems in the vicinity of the 2D metal-insulator transition. We analyzed the data using the two-parameter scaling approach and general scaling ideas. This enables us to determine the critical electron density, two critical indices, and temperature dependence for the separatrix in the self-consistent manner. In addition, we reconstruct the empirical scaling function describing a two-parameter surface which fits well the rho(T,n) data.     

Ordered and disordered dynamics in monolayers of rolling particles

We consider the ordered and disordered dynamics for monolayers of rolling self-interacting particles modeling water molecules. The rolling constraint represents a simplified model of a strong, but rapidly decaying bond with the surface. We show the existence and nonlinear stability of ordered lattice states, as well as disturbance propagation through and chaotic vibrations of these states. We study the dynamics of disordered gas states and show that there is a surprising and universal linear connection between distributions of angular and linear velocity, allowing definition of temperature.     

Experimental study of the Doppler shift generated by a vibrating scatterer

We report an experimental study of the backscattering of a sound wave of frequency f by a surface vibrating harmonically at frequency F (F < f) and amplitude A in the regime where the Doppler effect overcomes bulk nonlinear effects. When the duration to of the analyzed time series of the scattered wave is small compared to the vibration period, the power spectrum of the backscattered wave is proportional to the probability density function of the scatterer velocity, which presents two peaks shifted from f by roughly 2fAomega/c (omega = 2piF). On the contrary, when t0 > F(-1), sidebands at frequencies f +/- nF (n integer) appear in the power spectrum, which are due to the phase modulation of the backscattered wave induced by its reflection on a moving boundary. We use the backscattered power spectrum to validate the phase modulation theory of the Doppler effect in the latter case for 2kA < 1 and 2kA approximately > 1 (k = 2pif/c, where c is the wave velocity) and we test the validity of an acoustic nonintrusive estimator of A as a function of power spectrum bandwidth and of A itself.