Quantum transport on honeycomb networks.

We study the transport properties on honeycomb networks motivated by graphene structures by using the continuous-time quantum walk (CTQW) model. For various relevant topologies we consider the average return probability and its long-time average as measures for the transport efficiency. These quantities are fully determined by the eigenvalues and the eigenvectors of the connectivity matrix of the network.

Mechanisms to decrease the diseases spreading on generalized scale-free networks.

In this work, an epidemiological model is constructed based on a target problem that consists of a chemical reaction on a lattice. We choose the generalized scale-free network to be the underlying lattice. Susceptible individuals become the targets of random walkers (infectious individuals) that are moving over the network.

Relaxation dynamics of semiflexible treelike small-world polymer networks.

We study the relaxation dynamics of the polymer networks that are constructed based on a degree distribution specific to small-world networks. The employed building algorithm generates polymers with a large variety of architectures, thus allowing for a detailed study of the structural transition from a pure linear chain to dendritic polymer networks. This is done by varying a single parameter p, which measures the randomness in the degree of the network's nodes.

Dynamics of a Polymer Network Modeled by a Fractal Cactus.

In this paper, we focus on the relaxation dynamics of a polymer network modeled by a fractal cactus. We perform our study in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. By performing real-space renormalization transformations, we determine analytically the whole eigenvalue spectrum of the connectivity matrix, thereby rendering possible the analysis of the Rouse-dynamics at very large generations of the structure.

Relaxation dynamics of generalized scale-free polymer networks.

We focus on treelike generalized scale-free polymer networks, whose geometries depend on a parameter, γ, that controls their connectivity and on two modularity parameters: the minimum allowed degree, K , and the maximum allowed degree, K . We monitor the influence of these parameters on the static and dynamic properties of the achieved generalized scale-free polymer networks. The relaxation dynamics is studied in the framework of generalized Gaussian structures model by employing the Rouse-type approach.

Dynamics of a Complex Multilayer Polymer Network: Mechanical Relaxation and Energy Transfer.

In this paper, we focus on the mechanical relaxation of a multilayer polymer network built by connecting identical layers that have, as underlying topologies, the dual Sierpinski gasket and the regular dendrimer. Additionally, we analyze the dynamics of dipolar energy transfer over a system of chromophores arranged in the form of a multilayer network. Both dynamical processes are studied in the framework of the generalized Gaussian structure (GSS) model.

Dynamics of Dual Scale-Free Polymer Networks.

We focus on macromolecules which are modeled as sequentially growing dual scale-free networks. The dual networks are built by replacing star-like units of the primal treelike scale-free networks through rings, which are then transformed in a small-world manner up to the complete graphs. In this respect, the parameter γ describing the degree distribution in the primal treelike scale-free networks regulates the size of the dual units.

Relaxation dynamics of Sierpinski hexagon fractal polymer: Exact analytical results in the Rouse-type approach and numerical results in the Zimm-type approach.

In this paper, we focus on the relaxation dynamics of Sierpinski hexagon fractal polymer. The relaxation dynamics of this fractal polymer is investigated in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. In the Rouse-type approach, by performing real-space renormalization transformations, we determine analytically the complete eigenvalue spectrum of the connectivity matrix.

Relaxation dynamics of multilayer triangular Husimi cacti.

We focus on the relaxation dynamics of multilayer polymer structures having, as underlying topology, the Husimi cactus. The relaxation dynamics of the multilayer structures is investigated in the framework of generalized Gaussian structures model using both Rouse and Zimm approaches. In the Rouse type-approach, we determine analytically the complete eigenvalues spectrum and based on it we calculate the mechanical relaxation moduli (storage and loss modulus) and the average monomer displacement.

Continuous-time quantum walks on multilayer dendrimer networks.

We consider continuous-time quantum walks (CTQWs) on multilayer dendrimer networks (MDs) and their application to quantum transport. A detailed study of properties of CTQWs is presented and transport efficiency is determined in terms of the exact and average return probabilities. The latter depends only on the eigenvalues of the connectivity matrix, which even for very large structures allows a complete analytical solution for this particular choice of network.

Complex quantum networks: From universal breakdown to optimal transport.

We study the transport efficiency of excitations on complex quantum networks with loops. For this we consider sequentially growing networks with different topologies of the sequential subgraphs. This can lead either to a universal complete breakdown of transport for complete-graph-like sequential subgraphs or to optimal transport for ringlike sequential subgraphs.

Dynamics of semiflexible scale-free polymer networks.

Scale-free networks are structures, whose nodes have degree distributions that follow a power law. Here we focus on the dynamics of semiflexible scale-free polymer networks. The semiflexibility is modeled in the framework of [M.

Spectra of Husimi cacti: exact results and applications.

Starting from exact relations for finite Husimi cacti we determine their complete spectra to very high accuracy. The Husimi cacti are dual structures to the dendrimers but, distinct from these, contain loops. Our solution makes use of a judicious analysis of the normal modes.