Out-of-equilibrium kondo effect in double quantum dots

We present results of high resolution experiments on kinetic roughening of slow combustion fronts in paper, focusing on short length and time scales. Using three different grades of paper, we find that the combustion fronts show apparent spatial and temporal multiscaling at short scales. The scaling exponents decrease as a function of the order of the corresponding correlation functions. The noise affecting the fronts reveals short range temporal and spatial correlations, and non-Gaussian noise amplitudes. Our results imply that the overall behavior of slow combustion fronts cannot be explained by standard theories of kinetic roughening.     

Snell's law of refraction observed in thermal frontal polymerization

We demonstrate that Snell's law of refraction can be applied to thermal fronts propagating through a boundary between regions that support distinct frontal velocities. We use the free-radical frontal polymerization of a triacrylate with clay filler that allows for two domains containing two different concentrations of a peroxide initiator to be molded together. Because the polymerization reaction rates depend on the initiator concentration, the propagation speed is different in each domain. We study fronts propagating in two parallel strips in which the incident angle is 90 degrees. Our data fit Snell's law v(r)/v(i)=sin theta(r)/sin theta(i), where v(r) is the refracted velocity, v(i) is the incident velocity, theta(r) is the angle of refraction, and theta(i) is the incident angle. Further, we study circular fronts propagating radially from an initiation point in a high-velocity region into a low-velocity region (and vice versa). We demonstrate the close resemblance between the numerically simulated and experimentally observed thermal reaction fronts. By measuring the normal velocity and the angle of refraction of both simulated and experimental fronts, we establish that Snell's law holds for thermal frontal polymerization in our experimental system. Finally we discuss the regimes in which Snell's law may not be valid.     

Universal scaling of wave propagation failure in arrays of coupled nonlinear cells

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular coupling. We find the universal scaling of the field throughout the range of couplings and show that the field becomes exponentially small for large couplings. Our method is generic and applicable to a wide class of cellular dynamics in chemical, biological, and engineering systems. We confirm our results by direct numerical simulations.     

Coarsening kinetics with elastic effects

We discuss the coarsening process of melt inclusions inside a solid phase. Elastic effects lead to an oblate shape of the particles, resulting in a system with strong diffusional and elastic interactions between inclusions. The usual mean-field approximation breaks down and several independent length scales have to be taken into account. In a system of parallel oriented particles we find scaling laws for the coarsening of the different length scales involved. In particular, the lateral size of the particles obeys a nontrivial growth law, R approximately t(5/12).     

Effective-range approach and scaling laws for electromagnetic strength in neutron-halo nuclei

We study low-lying multipole strength in neutron-halo nuclei. The strength depends only on a few low-energy constants: the neutron separation energy, the asymptotic normalization coefficient of the bound-state wave function, and the scattering length that contains the information on the interaction in the continuum. The shape of the transition probability shows a characteristic dependence on few scaling parameters and the angular momenta. The total E1 strength is related to the root-mean-square radius of the neutron wave function in the ground state and shows corresponding scaling properties. We apply our approach to the E1 strength distribution of 11Be.     

Family-Vicsek scaling of detachment fronts in granular Rayleigh-Taylor instabilities during sedimentating granular/fluid flows

When submillimetric particles are confined in a fluid such that a compact cluster of particles lie above the clear fluid, particles will detach from the lower boundary of the cluster and form an unstable separation front giving rise to growing fingers of falling particles. We study this problem using both experiments and hybrid granular/fluid mechanics models. In the case of particles from 50 to 500 microns in diameter falling in air, we study the horizontal density fluctuations at early times: the amplitude of the density difference between two points at a certain horizontal distance grows as a power law of time. This happens up to a saturation corresponding to a power law of the distance. The way in which the correlation length builds up to this saturation also follows a power law of time. We show that these decompaction fronts in sedimentation problems follow a Family-Vicsek scaling, characterize the dynamic and Hurst exponent of the lateral density fluctuations, respectively z ∼ 1 and ζ ∼ 0.75, and show how the prefactors depend on the grain diameter. We also show from similar simulations with a more viscous and incompressible fluid, that this feature is independent of the fluid compressibility or viscosity, ranging from air to water/glycerol mixtures.     

Two interacting particles in a random potential

We study the scaling of the localization length of two interacting bosons in a one-dimensional random lattice with the single particle localization length. We consider the short-range interaction assuming that the particles interact when located both on the same site. We discuss several regimes, among them one interesting weak Fock space disorder regime. In this regime we obtain a weak logarithmic scaling law. Numerical benchmark data support the absence of any strong enhancement of the two particle localization length.     

Stiffness scaling laws and vibration isolators

The variation in dynamic stiffness due to a geometrical shift of a cylindrical vibration isolator is predicted by a scaling law and compared to the results of a waveguide solution. The simple scaling law fails to model satisfactorily the stiffness variation due to a single length or radius shift, while predicting successfully the results of an isolator shape invariant shift. The small deviations arise from a disregarded material property shift.     

Power-law statistics of synchronous transition in inhibitory neuronal networks

We investigate the relationship between the synchronous transition and the power law behavior in spiking networks which are composed of inhibitory neurons and balanced by dc current. In the region of the synchronous transition, the avalanche size and duration distribution obey a power law distribution. We demonstrate the robustness of the power law for event sizes at different parameters and multiple time scales. Importantly, the exponent of the event size and duration distribution can satisfy the critical scaling relation. By changing the network structure parameters in the parameter region of transition, quasicriticality is observed, that is, critical exponents depart away from the criticality while still hold approximately to a dynamical scaling relation. The results suggest that power law statistics can emerge in networks composed of inhibitory neurons when the networks are balanced by external driving signal.     

Transition from static to kinetic friction: insights from a 2D model

We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic-slider-rigid-substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory microslip fronts are successfully reproduced. From the analysis of the interfacial stresses, we derive a prediction for the evolution of the precursor length as a function of the applied loads, as well as an approximate relationship between microscopic and macroscopic friction coefficients. We show that the stress buildup due to both elastic loading and microslip-related relaxations depends only weakly on the underlying shear crack propagation dynamics. Conversely, crack speed depends strongly on both the instantaneous stresses and the friction coefficients, through a nontrivial scaling parameter.     

Slow cracklike dynamics at the onset of frictional sliding

We propose a friction model which incorporates interfacial elasticity and whose steady state sliding relation is characterized by a generic nonmonotonic behavior, including both velocity weakening and strengthening branches. In 1D and upon the application of sideway loading, we demonstrate the existence of transient cracklike fronts whose velocity is independent of sound speed, which we propose to be analogous to the recently discovered slow interfacial rupture fronts. Most importantly, the properties of these transient inhomogeneously loaded fronts are determined by steady state front solutions at the minimum of the sliding friction law, implying the existence of a new velocity scale and a "forbidden gap" of rupture velocities. We highlight the role played by interfacial elasticity and supplement our analysis with 2D scaling arguments.     

Domain Branching in Uniaxial Ferromagnets: A Scaling Law for the Minimum Energy

We address the branching of magnetic domains in a uniaxial ferromagnet. Our thesis is that branching is required by energy minimization. To show this, we consider the nonlocal, nonconvex variational problem of micromagnetics. We identify the scaling law of the minimum energy by proving a rigorous lower bound which matches the already-known upper bound. We further show that any domain pattern achieving this scaling law must have average width of order L ^2/3, where L is the length of the magnet in the easy direction. Finally we argue that branching is required, by considering the constrained variational problem in which branching is prohibited and the domain structure is invariant in the easy direction. Its scaling law is different. Received: 15 April 1998 / Accepted: 14 August 1998     

Mechanism of branching in negative ionization fronts

When a strong electric field is applied to nonconducting matter, narrow channels of plasma called streamers may form. Branchlike patterns of streamers have been observed in anode directed discharges. We explain a mechanism for branching as the result of a balance between the destabilizing effect of impact ionization and the stabilizing effect of electron diffusion on ionization fronts. The dispersion relation for transversal perturbation of a planar negative front is obtained analytically when the ratio D between the electron diffusion coefficient and the intensity of the externally imposed electric field is small. We estimate the spacing lambda between streamers and deduce a scaling law lambda approximately D(1/3).     

Pipe network model for scaling of dynamic interfaces in porous media

We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E 52, 5166 (1995)]. Using simple scaling arguments, we derive a new identity among the scaling exponents in agreement with the experimental results.     

Nonlocal dynamics of spontaneous imbibition fronts

We have studied spontaneous imbibition fronts generated by capillary rise between two roughened glass plates, the separation d of which varied between 10 and 50 microm. Perfect agreement with Washburn's law was obtained. We have determined the roughness exponent chi of the fronts, and found chi=0.81+/-0.01 for small length scales. Above a certain crossover length xi, it reached chi=0.58+/-0.04, as predicted by the quenched noise Kardar-Parisi-Zhang equation. The crossover length is found to scale with the plate separation as sqrt[d], as predicted by recent models which properly include nonlocal dynamics effects on the front. We believe this to be the first clear identification of crossover from nonlocal to local dynamics.     

Performance limitations of flat-histogram methods

We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based upon the exact density of states of 2D Ising models. The typical tunneling time needed to sample the entire bandwidth does not scale with the number of spins N as the minimal N2 of an unbiased random walk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the +/-J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Fréchet extremal value distribution that obeys exponential scaling. Furthermore, the shape parameters of these distributions indicate that statistical sample means become ill defined already for moderate system sizes within these complex energy landscapes.     

Dynamical scaling: the two-dimensional XY model following a quench

To sensitively test scaling in the two-dimensional XY model quenched from high temperatures into the ordered phase, we study the difference between measured correlations and the (scaling) results of a Gaussian-closure approximation. We also directly compare various length scales. All of our results are consistent with dynamical scaling and an asymptotic growth law L approximately (t/ln[t/t(0)])(1/2), though with a time scale t(0) that depends on the length scale in question. We then reconstruct correlations from the minimal-energy configuration consistent with the vortex positions, and find them significantly different from the "natural" correlations - though both scale with L. This indicates that both topological (vortex) and nontopological "spin-wave" contributions to correlations are relevant arbitrarily late after the quench. We also present a consistent definition of dynamical scaling applicable more generally, and emphasize how to generalize our approach to other quenched systems where dynamical scaling is in question. Our approach directly applies to planar liquid-crystal systems.     

Relaxation timescales for conformational substates in disordered polymers

We study the kinetics of interconversion of conformational substates in RNA folding by means of a Monte-Carlo simulation. We establish a scaling law relating the size of the barriers with the length of a random uncorrelated RNA chain. The way the relaxation timescales diverge in the thermodynamic limit coincides with the behavior of nonergodic relaxation timescales for spin glasses.     

Scaling of hysteresis in a multi-dimensional all-optical bistable system

We analyse the hysteresis enlargements of an optical bistable system involving three dynamical variables. We investigate, both experimentally and numerically, the local dynamics of the up- and down-switching process versus the sweeping frequency of the control parameter. In particular, we delineate the domain of validity of the scaling law predicted for one-dimensional systems. At high sweeping frequency, we show the appearance of another asymptotic scaling low in . Thereafter, we analyse the global evolution of the hysteresis loop induced by these processes. At low frequency, a scaling law is retrieved, whereas at high frequency, the dynamical behaviour is shown to strongly depend on the particular shape of the bistability curve. Received: 14 September 1998 / Received in final form: 15 February 1999