Electronic shot noise in fractal conductors

By solving a master equation in the Sierpiński lattice and in a planar random-resistor network, we determine the scaling with size L of the shot noise power P due to elastic scattering in a fractal conductor. We find a power-law scaling P proportional, variantL;{d_{f}-2-alpha}, with an exponent depending on the fractal dimension d_{f} and the anomalous diffusion exponent alpha. This is the same scaling as the time-averaged current I[over ], which implies that the Fano factor F=P/2eI[over ] is scale-independent. We obtain a value of F=1/3 for anomalous diffusion that is the same as for normal diffusion, even if there is no smallest length scale below which the normal diffusion equation holds. The fact that F remains fixed at 1/3 as one crosses the percolation threshold in a random-resistor network may explain recent measurements of a doping-independent Fano factor in a graphene flake.     

Scaling of the shear viscosity of the system nitrobenzene —n-heptane in the critical region

The temperature dependence of shear viscosity of the system nitrobenzene-n-heptane has been studied near the critical concentration. The critical exponent of the shear viscosity Φ was calculated from the empirical formula and compared with the theoretical and experimental results obtained for other critical systems. The shear viscosity satisfies scaling law relations similar to those previously established for equilibrium properties.     

Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')infinity limit, we show that lambda(')(c)=d+2 and phi=z/2. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.     

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.     

Translocation of closed polymers through a nanopore under an applied external field

The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics simulations. The power-law scaling of the translocation time τ with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be τ～ N α , with the exponent α varying from α = 0.71 for relatively short chains to α = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α = 1.27 for the translocation of double-strand DNA. The distribution of translocation time D(τ) is close to a Gaussian function for duration time τ < τ p and follows a falling exponential function for duration time τ > τ p . For closed knotted polymers, the scaling exponent α is 1.27 for small field force (F = 5) and 1.38 for large field force (F = 10). The distribution of translocation time D(τ) remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.     

Anomalous Hall effect of facing-target sputtered ferrimagnetic Mn4N epitaxial films with perpendicular magnetic anisotropy

Epitaxial Mn$_{4}$N films with different thicknesses were fabricated by facing-target reactive sputtering and their anomalous Hall effect (AHE) is investigated systematically. The Hall resistivity shows a reversed magnetic hysteresis loop with the magnetic field. The magnitude of the anomalous Hall resistivity sharply decreases with decreasing temperature from 300 K to 150 K. The AHE scaling law in Mn$_{4}$N films is influenced by the temperature-dependent magnetization, carrier concentration and interfacial scattering. Different scaling laws are used to distinguish the various contributions of AHE mechanisms. The scaling exponent $\gamma > 2$ for the conventional scaling in Mn$_{4}$N films could be attributed to the residual resistivity $\rho_{xx0}$. The longitudinal conductivity $\sigma_{xx}$ falls into the dirty regime. The scaling of $\rho_{\rm AH}=\alpha \rho_{xx0} +b\rho_{xx}^{n}$ is used to separate out the temperature-independent $\rho_{xx0}$ from extrinsic contribution. Moreover, the relationship between $\rho_{\rm AH}$ and $\rho_{xx}$ is fitted by the proper scaling to clarify the contributions from extrinsic and intrinsic mechanisms of AHE, which demonstrates that the dominant mechanism of AHE in the Mn$_{4}$N films can be ascribed to the competition between skew scattering, side jump and the intrinsic mechanisms.     

Anomalous roughening of viscous fluid fronts in spontaneous imbibition

We report experiments on spontaneous imbibition of a viscous fluid by a model porous medium in the absence of gravity. The average position of the interface satisfies Washburn's law. Scaling of the interface fluctuations suggests a dynamic exponent z approximately 3, indicative of global dynamics driven by capillary forces. The complete set of exponents clearly shows that interfaces are not self-affine, exhibiting distinct local and global scaling, both for time (beta = 0.64 +/- 0.02, beta(*) = 0.33 +/- 0.03) and space (alpha = 1.94 +/- 0.20, alpha(loc) = 0.94 +/- 0.10). These values are compatible with an intrinsic anomalous scaling scenario.     

On the scaling of probability density functions with apparent power-law exponents less than unity

We derive general properties of the finite-size scaling of probability density functions and show that when the apparent exponent of a probability density is less than 1, the associated finite-size scaling ansatz has a scaling exponent τ equal to 1, provided that the fraction of events in the universal scaling part of the probability density function is non-vanishing in the thermodynamic limit. We find the general result that τ≥1 and . Moreover, we show that if the scaling function approaches a non-zero constant for small arguments, , then . However, if the scaling function vanishes for small arguments, , then τ= 1, again assuming a non-vanishing fraction of universal events. Finally, we apply the formalism developed to examples from the literature, including some where misunderstandings of the theory of scaling have led to erroneous conclusions.     

Hydrodynamic coarsening of binary fluids

By suitable interpretation of results from the linear analysis of interface dynamics, it is found that the hydrodynamic growth of the size L of domains that follow spinodal decomposition in fluid mixtures scales with time as L approximately t(alpha), with alpha = 4/7 in the inertial regime. The previously proposed exponent alpha = 2/3 is shown to indicate only the scaling of the oscillatory frequency omega(-2/3) approximately L of the largest structures of the system. The viscous dissipation in the system occurs within a layer of thickness L(d) that also follows a power law of the form L(d) approximately L3/4 in the inertial regime. In the viscous regime the growth is linear in time L approximately t and the dissipative region remains constant L(d) approximately L0.     

Crossover from attractive to repulsive Casimir forces and vice versa

Systems described by an O(n) symmetrical varphi;{4} Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes B_{j}, j=1,2, are investigated as functions of film thickness L for generic symmetry-preserving boundary conditions partial differential_{n}phi=c[over composite function]_{j}phi. The L-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form f_{res} approximately D(c_{1}L;{Phi/nu},c_{2}L;{Phi/nu})/L;{d-1} when d<4, where c_{i} are scaling fields associated with the variables c[over composite function]_{i} and Phi is a surface crossover exponent. Explicit two-loop renormalization group results for the function D(c_{1},c_{2}) at d=4- dimensions are presented. These show that (i) the Casimir force can have either sign, depending on c_{1} and c_{2}, and (ii) for appropriate choices of the enhancements c[over composite function]_{j}, crossovers from attraction to repulsion and vice versa occur as L increases.     

Spherical top-hat collapse of a viscous unified dark fluid

In this paper, we test the spherical collapse of a viscous unified dark fluid (VUDF) which has constant adiabatic sound speed and show the nonlinear collapse for VUDF, baryons, and dark matter, which are important in forming the large-scale structure of our Universe. By varying the values of the model parameters $\alpha $ and $\zeta _{0}$ , we discuss their effects on the nonlinear collapse of the VUDF model, and we compare its result to the $\Lambda $ CDM model. The results of the analysis show that, within the spherical top-hat collapse framework, larger values of $\alpha $ and smaller values of $\zeta _{0}$ make the structure formation earlier and faster, and the other collapse curves are almost distinguished with the curve of $\Lambda $ CDM model if the bulk viscosity coefficient $\zeta _{0}$ is less than $10^{-3}$ .     

Current relaxation in nonlinear random media

We study the current relaxation of a wave packet in a nonlinear random sample coupled to the continuum and show that the survival probability decays as P(t) approximately 1/t(alpha). For intermediate times tt(*) and chi>chi(cr) we find a universal decay with alpha=2/3 which is a signature of the nonlinearity-induced delocalization. Experimental evidence should be observable in coupled nonlinear optical waveguides.     

Defect production in nonlinear quench across a quantum critical point

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.     

Preferential attachment network model with aging and initial attractiveness

In this paper, we generalize the growing network model with preferential attachment for new links to simultaneously include aging and initial attractiveness of nodes. The network evolves with the addition of a new node per unit time, and each new node has m new links that with probability Π_i are connected to nodes i already present in the network. In our model, the preferential attachment probability Π_i is proportional not only to k_i + A, the sum of the old node i's degree k_i and its initial attractiveness A, but also to the aging factor ${\tau }_{i}^{-\alpha }$, where τ_i is the age of the old node i. That is, ${{\rm{\Pi }}}_{i}\propto ({k}_{i}+A){\tau }_{i}^{-\alpha }$. Based on the continuum approximation, we present a mean-field analysis that predicts the degree dynamics of the network structure. We show that depending on the aging parameter α two different network topologies can emerge. For α < 1, the network exhibits scaling behavior with a power-law degree distribution P(k) ∝ k^−γ for large k where the scaling exponent γ increases with the aging parameter α and is linearly correlated with the ratio A/m. Moreover, the average degree k(t_i, t) at time t for any node i that is added into the network at time t_i scales as $k({t}_{i},t)\propto {t}_{i}^{-\beta }$ where 1/β is a linear function of A/m. For α > 1, such scaling behavior disappears and the degree distribution is exponential.     

Fluctuations and pseudo long range dependence in network flows: A non-stationary Poisson process model

In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) < F_i> of the i-th node and its variance σ_i as F_{i ∝ <Fi^α. Such scaling laws are found to be prevalent both in natural and man-made network systems, but the understanding of their origins still remains limited. This paper proposes a non-stationary Poisson process model to give an analytical explanation of the non-universal scaling phenomenon: the exponent α varies between 1/2 and 1 depending on the size of sampling time window and the relative strength of the external/internal driven forces of the systems. The crossover behaviour and the relation of fluctuation scaling with pseudo long range dependence are also accounted for by the model. Numerical experiments show that the proposed model can recover the multi-scaling phenomenon.}     

Critical collapse of a complex scalar field with angular momentum

We report a new critical solution found at the threshold of axisymmetric gravitational collapse of a complex scalar field with angular momentum. To carry angular momentum the scalar field cannot be axisymmetric; however, its azimuthal dependence is defined so that the resulting stress-energy tensor and spacetime metric are axisymmetric. The critical solution found is nonspherical, discretely self-similar with an echoing exponent Delta=0.42(+/-4%), and exhibits a scaling exponent gamma=0.11(+/-10%) in near-critical collapse. Our simulations suggest that the solution is universal (within the imposed symmetry class), modulo a family-dependent constant, complex phase.     

Ferromagnetic phase transition in a Heisenberg fluid: Monte Carlo simulations and Fisher corrections to scaling

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent alpha. The appearance of such new corretions to scaling is a general feature of systems with constraints.     

Radiating gravitational collapse with shear viscosity revisited

A new model is proposed to a collapsing radiating star consisting of an isotropic fluid with shear viscosity undergoing radial heat flow with outgoing radiation. In a previous paper we have introduced a function time dependent into the g _rr , besides the time dependent metric functions and . The aim of this work is to generalize this previous model by introducing shear viscosity and compare it to the non-viscous collapse. The behavior of the density, pressure, mass, luminosity and the effective adiabatic index is analyzed. Our work is compared to the case of a collapsing shearing fluid of a previous model, for a star with 6 . The pressure of the star, at the beginning of the collapse, is isotropic but due to the presence of the shear the pressure becomes more and more anisotropic. The black hole is never formed because the apparent horizon formation condition is never satisfied. An observer at infinity sees a radial point source radiating exponentially until reaches the time of maximum luminosity and suddenly the star turns off. The effective adiabatic index has a very unusual behavior because we have a non-adiabatic regime in the fluid due to the heat flow.     

Analytic Representation of Critical Equations of State

A new form is proposed for equations of state (EOS) of thermodynamic systems in the 3-dimensional Ising universality class. The new EOS guarantees the correct universality and scaling behavior close to critical points and is formulated in terms of the scaling fields only—unlike the traditional Schofield representation, which uses a parametric form. Close to a critical point, the new EOS expresses the square of the strong scaling field $\Sigma $ as an explicit function $\Sigma ^2=D^{2e_{-1}}W(D^{-e_0}\Theta )$ of the thermal scaling field $\Theta $ and the dependent scaling field $D>0$ , with a smooth, universal function $W$ and the universal exponents $e_{-1}=\delta /(\delta +1)$ , $e_0=1/(2-\alpha )$ . A numerical expression for $W$ is derived, valid close to critical points. As a consequence of the construction it is shown that the dependent scaling field can be written as an explicit function of the relevant scaling fields without causing strongly singular behavior of the thermodynamic potential in the one-phase region. Augmented by additional scaling correction fields, the new EOS also describes the state space further away from critical points. It is indicated how to use the new EOS to model multiphase fluid mixtures, in particular for vapor–liquid–liquid equilibrium where the traditional revised scaling approach fails.     

Maximal height scaling of kinetically growing surfaces

The scaling properties of the maximal height of a growing self-affine surface with a lateral extent L are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: h*(L) approximately L alpha. For large values its distribution obeys logP(h*(L)) approximately (-)A(h*(L)/L(alpha))(a). In the early-time regime where the roughness grows as t(beta), we find h*(L) approximately t(beta)[lnL-(beta/alpha)lnt+C](1/b), where either b = a or b is the corresponding exponent of the velocity distribution. These properties are derived from scaling and extreme-value arguments. They are corroborated by numerical simulations and supported by exact results for surfaces in 1D with the asymptotic behavior of a Brownian path.