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We examine how the distribution of contour lengths and the high-stretch stiffening of individual chain segments affect the macroscopic shear modulus of flexible polymer gels, using a 2D numerical model, in which polymer segments form a…

Based on a recent simulation study [Masubuchi et al., Macromolecules, 56, 9359 (2023)], the cycle rank plays a significant role in determining the fracture characteristics of network polymers. However, the study only considered…

We study the effects of adding loops to a critical percolation cluster on the diffusional, and equivalently, (scalar) elastic properties of the fractal network. From the numerical calculations of the eigenspectrum of the transition…

Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…

The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…

The elastic modulus $G$ of a polymer network depends notably on parameters such as the initial concentration of the monomers before the synthesis ($\rho_0$), the density of the cross-linker, or the topology of the network. Understanding how…

Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…

Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an…

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…

We analyze a simple network where a source and a receiver are connected by a line of erasure channels of different reliabilities. Recent prior work has shown that random linear network coding can achieve the min-cut capacity and therefore…

We study theoretically the transfer of quantum information along bends in two-dimensional discrete lattices. Our analysis shows that the fidelity of the transfer decreases considerably, as a result of interactions in the neighbourhood of…

We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the…

The non-linear stress-strain relation for crosslinked polymer networks is studied using molecular dynamics simulations. Previously we demonstrated the importance of trapped entanglements in determining the elastic and relaxational…

Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional…

Tightening performance bounds of ring networks with cyclic dependencies is still an open problem in the literature. In this paper, we tackle such a challenging issue based on Network Calculus. First, we review the conventional timing…

We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties…

In many cases of attacks or failures, memory effects play a significant role. Therefore, we present a model that not only considers the dependencies between nodes but also incorporates the memory effects of attacks. Our research…

Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…

We study a number of domain wall forming models where various types of defect junctions can exist. These illustrate some of the mechanisms that will determine the evolution of defect networks with junctions. Understanding these mechanisms…

Disordered filamentous networks with compliant crosslinks exhibit a low linear elastic shear modulus at small strains, but stiffen dramatically at high strains. Experiments have shown that the elastic modulus can increase by up to three…