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We consider dynamics of charged solitons in branched conducting polymers. An effective model based on the sine-Gordon equation on metric graphs is used for computing the charge transport and scattering of charge carriers at the polymer…
The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice $\mathbb Z^d$, $d\ge1$, is a…
In random systems consisting of grains with size distributions the transport properties are difficult to explore by network models. However, the concentration dependence of effective conductivity and its critical properties can be…
Dispersion relations govern wave behaviors, and tailoring them is a grand challenge in wave manipulation. We demonstrate inverse design of phononic dispersion using non-local interactions on one-dimensional spring-mass chains. For both…
Quantum state transfer is investigated beyond the nearest-neighbour coupling scheme in long spin-$\frac{1}{2}$ linear chains. Exploiting the properties of the next-nearest neighbour Hamiltonian's dispersion relation, it is shown that with…
We consider distributed model-checking of Monadic Second-Order logic (MSO) on graphs which constitute the topology of communication networks. The graph is thus both the structure being checked and the system on which the distributed…
The transmission across a graphene bilayer region is calculated for two different types of connections to monolayer leads. A transfer matrix algorithm based on a tight binding model is developed to obtain the ballistic transmission beyond…
A new type of soliton with controllable speed is constructed generalizing the theory of slow-light propagation to an integrable regime of nonlinear dynamics. The scheme would allow the quantum-information transfer between optical solitons…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
Link prediction requires predicting which new links are likely to appear in a graph. Being able to predict unseen links with good accuracy has important applications in several domains such as social media, security, transportation, and…
In an isotopically disordered harmonic chain, phonon transmission attenuates exponentially with distance because of multiple scattering by the isotopic defects. We propose a simple method, which is based on the static structure factor, for…
The problem of link prediction has attracted considerable recent attention from various domains such as sociology, anthropology, information science, and computer sciences. A link prediction algorithm is proposed based on link similarity…
We introduce soliton percolation phenomena in the nonlinear transport of light packets in suitable optical lattices with random properties. Specifically, we address lattices with a gradient of the refractive index in the transverse plane,…
We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
We theoretically show the existence of cascaded second-order surface plasmon solitons propagating at the interface between metal and linear dielectric. Nonlocal multipole nonlinearities originating from free conduction electron plasma of a…
We calculate the plasmon dispersion relation for Coulomb coupled metallic armchair graphene nanoribbons and doped monolayer graphene. The crossing of the plasmon curves, which occurs for uncoupled 1D and 2D systems, is split by the…
We apply the linear response theory developed in \cite{Ruelle} to analyze how a periodic signal of weak amplitude, superimposed upon a chaotic background, is transmitted in a network of non linearly interacting units. We numerically compute…
It is clarified for the first time that solitons originating from the dipolar interaction in ferromagnetic nano-particle arrays are stably created. The characteristics can be well controlled by the strength of the dipolar interaction…
Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…