Scaling and universality in turbulent convection

Anomalous correlation functions of the temperature field in two-dimensional turbulent convection are shown to be universal with respect to the choice of external sources. Moreover, they are equal to the anomalous correlations of the concentration field of a passive tracer advected by the convective flow itself. The statistics of velocity differences is found to be universal, self-similar, and close to Gaussian. These results point to the conclusion that temperature intermittency in two-dimensional turbulent convection may be traced back to the existence of statistically preserved structures, as it is in passive scalar turbulence.     

Scaling and universality in rock fracture

We present a detailed statistical analysis of acoustic emission time series from laboratory rock fracture obtained from different experiments on different materials including acoustic emission controlled triaxial fracture and punch-through tests. In all considered cases, the waiting time distribution can be described by a unique scaling function indicating its universality. This scaling function is even indistinguishable from that for earthquakes suggesting its general validity for fracture processes independent of time, space, and magnitude scales.     

Scaling and universality in proportional elections

A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavor is to find regularities in data referring to large-scale social phenomena, such as scaling and universality. We show that, in proportional elections, the distribution of the number of votes received by candidates is a universal scaling function, identical in different countries and years. This finding reveals the existence in the voting process of a general microscopic dynamics that does not depend on the historical, political, and/or economical context where voters operate. A simple dynamical model for the behavior of voters, similar to a branching process, reproduces the universal distribution.     

Scaling and universality of the complexity of analog computation

We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We numerically analyze various ensembles of linear programming problems and obtain, for each of these ensembles, the probability distribution functions of certain quantities which measure the computational complexity, known as the convergence rate, the barrier and the computation time. We find that in the limit of very large problems these probability distributions are universal scaling functions. In other words, the probability distribution function for each of these three quantities becomes, in the limit of large problem size, a function of a single scaling variable, which is a certain composition of the quantity in question and the size of the system. Moreover, various ensembles studied seem to lead essentially to the same scaling functions, which depend only on the variance of the ensemble. These results extend analytical and numerical results obtained recently for the Gaussian ensemble, and support the conjecture that these scaling functions are universal.     

Scaling and universality in electrical failure of thin films

We describe the electrical failure of thin films as a percolation in two-dimensional random resistor networks. We show that the resistance evolution follows a scaling relation expressed as R approximately epsilon(-&mgr;) where epsilon = (1-t/tau), tau is the time of electrical failure of the film, and &mgr; is the same critical exponent appearing in the scaling relation between R and the defect concentration. For uniform degradation the value of &mgr; is universal. The validity of this scaling relation in the case of nonuniform degradation is proved by discussing the case in which the failure is due to a filamentary defect growth. The existence of this relation allows predictions of failure times from early time measurements of the resistance.     

Scaling behavior of the directed percolation universality class

In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling behavior, we present clear numerical evidence that all models belong to the universality class of directed percolation. Since the considered models are characterized by different interaction details the obtained universal scaling plots are an impressive manifestation of the universality of directed percolation.     

Scaling and universality of critical fluctuations in granular gases

The total energy fluctuations of a low-density granular gas in the homogeneous cooling state near the threshold of the clustering instability are studied by means of molecular dynamics simulations. The relative dispersion of the fluctuations is shown to exhibit a power-law divergent behavior. Moreover, the probability distribution of the fluctuations presents data collapse as the system approaches the instability, for different values of the inelasticity. The function describing the collapse turns out to be the symmetric of the one found in several molecular equilibrium and nonequilibrium systems.     

Scaling in the disordered quantum antiferromagnetic chain

Numerical calculations on the disordered quantum Heisenberg antiferromagnetic chain yield low-temperature behavior independent of the detailed form of the randomness. A simple scaling interpretation, which makes contact with earlier theoretical work, of these complicated calculations is presented. An analogy with a one-parameter scaling theory of localization is explored.     

Programming scale-free optics in disordered ferroelectrics

Using the history dependence of a dipolar glass hosted in a compositionally disordered lithium-enriched potassium tantalate niobate (KTN:Li) crystal, we demonstrate scale-free optical propagation at tunable temperatures. The operating equilibration temperature is determined by previous crystal spiralling in the temperature/cooling-rate phase space.     

Statistics of disordered chains

The statistical weights of the stationary states in various ensembles of isotopically disordered harmonic chains are compared. It is proven that the ensemble defined by boundary conditions at both ends of the chain is constructed with correct statistical weights as follows: One matches at sitei the stationary states of the ensemble defined by the boundary condition at one end and frequencyω with those of the ensemble defined by the boundary condition at the other end andω. Finally one integrates overω and sums over all sitesi. This confirms and substantiates the conjecture on the exponential localization of the eigenstates in one dimension. The matching procedure yields an equation for the density of states.     

Scaling and universality of integer quantum Hall plateau-to-plateau transitions

We have investigated the integer quantum Hall plateau-to-plateau transition in two-dimensional electrons confined to AlxGa(1-x)As-Al0.33Ga0.67As heterostructures over a broad range of Al concentration x. For x between 0.65% and 1.6%, where the dominant contribution to disorder is from the short-range alloy potential fluctuations, we observe a perfect power-law scaling in the temperature range from 30 mK to 1 K with a critical exponent kappa = 0.42 +/- 0.01.     

On the theory of wannier exciton in a disordered structure

The motion of the optically excited coulomb-bounded electron-hole pair in a random gaussian potential has been investigated by using the Feynman path integral method. The motion of the mass center shows the same hopping character as a single particle. The coupling of the mass center motion and of the internal motion of the pair depends on the difference of the effective masses; ifm _e =m _h or ifm _e ?m _h the coupling tends to zero. A characteristic function \(F(\omega ) = \left( {1 - \frac{{\omega _c^2 }}{{2\omega ^2 }}\frac{{\phi \hbar \beta }}{{tg\frac{{\phi \hbar \beta }}{2}}}} \right)^{ - 1} \) has been found which determines the influence of the disorder on the internal motion of the pair. IfF(ω)→ 0 the motion is hydrogen-like, ifF(ω)→∞ the pair dissociates. The conditions for dominancy of the localizing influence of the random field or of the hydrogenlike motion due to the coulombic bound has been found. It has been shown that at high temperatures one can speak about the Wannier exciton at the same sense as in periodic lattices.     

Perfectly conducting channel and universality crossover in disordered graphene nanoribbons

The band structure of graphene ribbons with zigzag edges have two valleys well separated in momentum space, related to the two Dirac points of the graphene spectrum. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at the band center. This feature gives rise to a perfectly conducting channel in the disordered system, if the impurity scattering does not connect the two valleys, i.e., for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through intervalley scattering display ordinary localization behavior. The two regimes belong to different universality classes: unitary for long-range impurities and orthogonal for short-range impurities.     

Exciton optics of a disordered semiconductor

Interband light absorption in a disordered semiconductor is considered with due allowance for exciton effects. Allowance is made for the scattering of the electron and hole in a weak static random field and also for collisions of the second kind experienced by the exciton on interaction with a random field. It is shown that the contribution of these latter to the half width of the absorption line of the exciton spectrum (even at temperatures of the order of the exciton ionization energy) is considerably smaller than the contribution arising from the scattering of the particles forming the exciton.     

New universality class in spin-one-half Fibonacci Heisenberg chains

Low energy properties of the S=1/2 antiferromagnetic Heisenberg chains with Fibonacci exchange modulation are studied using the real space renormalization group method for strong exchange modulation. Using the analytical solution of the recursion equation, the true asymptotic behavoir is revealed, which was veiled by the finite size effect in the previous numerical works. It is found that the ground state of this model belongs to a new universality class with a logarithmically divergent dynamical exponent which is neither like Fibonacci XY chains nor like XY chains with relevant aperiodicity.     

Density of exciton states in one-dimensional disordered molecular crystals

We investigate the effects of structural disorder on the exciton density of states of molecular crystals, utilizing an exact soluble model which involves correlated Lorentzian distributions of both the site-excitation energies and the transfer integrals. Off-diagonal disorder results in asymmetric density of states functions, the asymmetry being prominent for one-dimensional exciton band structure.     

Scaling and universality of self-organized patterns on unstable vicinal surfaces

We propose a unified treatment of the step bunching instability during epitaxial growth. The scaling properties of the self-organized surface pattern are shown to depend on a single parameter, the leading power in the expansion of the biased diffusion current in powers of the local surface slope. We demonstrate the existence of universality classes for the self-organized patterning appearing in models and experiments.     

Crossover between universality classes in the statistics of rare events in disordered conductors

The crossover from orthogonal to the unitary universality classes in the distribution of the anomalously localized states (ALS) in two-dimensional disordered conductors is traced as a function of magnetic field. We demonstrate that the microscopic origin of the crossover is the change in the symmetry of the underlying disorder configurations that are responsible for ALS. These disorder configurations are of weak magnitude (compared to the Fermi energy) and of small size (compared to the mean free path). We find their shape explicitly by means of the direct optimal fluctuation method.