ﻻ يوجد ملخص باللغة العربية
We view a complex liquid as a network of bonds connecting each particle to its nearest neighbors; the dynamics of this network is a chain of discrete events signaling particles rearrangements. Within this picture, we studied a two-dimensional complex liquid and found a stretched-exponential decay of the network memory and a power-law for the distribution of the times for which a particle keeps its nearest neighbors; the dependence of this distribution on temperature suggests a possible dynamical critical point. We identified and quantified the underlying spatio-temporal phenomena. The equilibrium liquid represents a hierarchical structure, a mosaic of long-living crystallites partially separated by less-ordered regions. The long-time dynamics of this structure is dominated by particles redistribution between dynamically and structurally different regions. We argue that these are generic features of locally ordered but globally disordered complex systems. In particular, these features must be taken into account by any coarse-grained theory of dynamics of complex fluids and glasses.
We study transient behaviour in the dynamics of complex systems described by a set of non-linear ODEs. Destabilizing nature of transient trajectories is discussed and its connection with the eigenvalue-based linearization procedure. The complexity is
We consider a class of random block matrix models in $d$ dimensions, $d ge 1$, motivated by the study of the vibrational density of states (DOS) of soft spheres near the isostatic point. The contact networks of average degree $Z = z_0 + zeta$ are rep
We use a simple model to extend network models for activated dynamics to a continuous landscape with a well-defined notion of distance and a direct connection to many-body systems. The model consists of a tracer in a high-dimensional funnel landscape
In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we fi
We derive the spectral properties of adjacency matrix of complex networks and of their Laplacian by the replica method combined with a dynamical population algorithm. By assuming the order parameter to be a product of Gaussian distributions, the pres