Related papers: Behavior of the scaling correlation functions unde…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…
Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations…
We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible uncertainty in a system performing…
We report two-dimensional phase-field simulations of locally-conserved coarsening dynamics of random fractal clusters with fractal dimension D=1.7 and 1.5. The correlation function, cluster perimeter and solute mass are measured as…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Motivated by interest in the geometry of high intensity events of turbulent flows, we examine spatial correlation functions of sets where turbulent events are particularly intense. These sets are defined using indicator functions on…
Entanglement patterns reveal essential information on many-body states and provide a way to classify quantum phases of matter. However, experimental studies of many-body entanglement remain scarce due to their unscalable nature. The present…
We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system…
The models of $k$-core percolation and interdependent networks (IN) have been extensively studied in their respective fields. A recent study has revealed that they share several common critical exponents. However, several newly discovered…
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…
The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian,…
When assessing spatially-extended complex systems, one can rarely sample the states of all components. We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagating…
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…
Fractal structures appear in a vast range of physical systems. A literature survey including all experimental papers on fractals which appeared in the six Physical Review journals (A-E and Letters) during the 1990's shows that experimental…
Under decompression, disordered solids undergo an unjamming transition where they become under-coordinated and lose their structural rigidity. The mechanical and vibrational properties of these materials have been an object of theoretical,…
We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal…
Many physical and physiological signals exhibit complex scale-invariant features characterized by $1/f$ scaling and long-range power-law correlations, suggesting a possibly common control mechanism. Specifically, it has been suggested that…
The prospects for a determination of the strong coupling constant $\alpha_s$ via scaling violations of fragmentation functions in deeply inelastic scattering are studied. The statistical error in the case of an integrated luminosity of $250…