Regular Lattice Network Research Articles

Complex quasi-brittle fracture modelling using lattice particle method coupled with a local isotropic damage model

In this paper, a local isotropic damage model is incorporated into the lattice particle method (LPM) to model complex quasi-brittle fracture problems. The issue of particle-size dependency is addressed using fracture energy in the damage model regularized with characteristic length that is particle-size dependent. The characteristic lengths are first estimated from mode-I fracture test by ensuring the prescribed and calculated fracture energies match well for both 2D and 3D cases. Extensive validation against experimental data in terms of crack path and structural response is then carried out to assess the accuracy of the proposed model in 2D and 3D settings. Positive outcomes, in line with the experimental findings, have been obtained for both 2D and 3D problems covering mode I and mixed-mode fractures. Furthermore, by employing a regular lattice network, the present model, when integrated with more sophisticated yield surfaces, can address intricate 3D fracture problems that entail the twisting of crack surfaces. Convergence of structural response and crack path is obtained when the particle spacing is refined.

The emergence of rich complex dynamics in a spatial dyadic game with resource storage, participation cost, and agent interaction propensity

We present an evolutionary game model combining subordinate elements from several viewpoints to address whether a resource-storing mechanism promotes a society where the wealthy engage in or refrain from conflict. The model is based on the pairwise game, which incorporates the accumulation of payoffs over time and introduces the concept of participation probability based on wealthiness. Our study encompasses four distinct game classes: Prisoner's Dilemma, Trivial, Stag Hunt, and Chicken. By incorporating these diverse social dilemma structures, we strive to comprehensively understand the dynamics within different game scenarios. Additionally, we broaden the scope of our analysis by considering two network types: a regular lattice network and a Barabasi-Albert scale-free (BA-SF) graph. Through simulation results, we have discovered that the commonly held belief or human philosophical wisdom that “the wealthy do not fight” leads to the emergence of a cooperative society, depending on the intensity of the dilemma. In contrast, our findings strongly suggest that the prevailing notion of “the wealthy do fight” fosters an imbalanced exploitation-based society where defectors who exploit the poor cooperators thrive. Further analysis shows variations in beliefs and dynamics between cooperators and defectors, highlighting the emergence of social dilemmas and the impact of payoff storage. Our result reported here proves that the proposed model based on a minimal spatial game setting by 2-player & 2-strategy game just added several subordinate components can reproduce rich, complex scenarios likely observed in a real human society.

Long transients and dendritic network structure affect spatial predator-prey dynamics in experimental microcosms.

Spatial dynamics can promote persistence of strongly interacting predators and prey. Theory predicts that spatial predator-prey systems are prone to long transients, meaning that the dynamics leading to persistence or extinction manifest over hundreds of generations. Furthermore, the form and duration of transients may be altered by spatial network structure. Few empirical studies have examined the importance of transients in spatial food webs, especially in a network context, due to the difficulty in collecting the large scale and long-term data required. We examined predator-prey dynamics in protist microcosms using three experimental spatial structures: isolated, river-like dendritic networks and regular lattice networks. Densities and patterns of occupancy were followed for both predators and prey over a time scale that equates to >100 predator and >500 prey generations. We found that predators persisted in dendritic and lattice networks whereas they went extinct in the isolated treatment. The dynamics leading to predator persistence played out over long transients with three distinct phases. The transient phases showed differences between dendritic and lattice structures, as did underlying patterns of occupancy. Spatial dynamics differed among organisms in different trophic positions. Predators showed higher local persistence in more connected bottles while prey showed this in more spatially isolated ones. Predictions based on spatial patterns of connectivity derived from metapopulation theory explained predator occupancy, while prey occupancy was better explained by predator occupancy. Our results strongly support the hypothesized role of spatial dynamics in promoting persistence in food webs, but that the dynamics ultimately leading to persistence may occur with long transients which in turn may be influenced by spatial network structure and trophic interactions.

An enhanced FitzHugh–Nagumo neuron circuit, microcontroller-based hardware implementation: Light illumination and magnetic field effects on information patterns

This contribution introduced and investigated an improved photosensitive memristive FitzHugh–Nagumo (FHN) neural circuit. The mathematical equations of the model have been derived from Kirchhoff’s electrical circuit law. Based on Helmholtz’s theorem, the Hamilton statistical function that enables us to obtain the physical energy of the neuron necessary to sustain electrical activity has been established. Therefore, the energy dependency on the light intensity and the magnetic field has been provided. Using two-parameter diagrams, bifurcation diagrams, Lyapunov exponents, and time series, the window of parameters in which regular and irregular patterns of the neuron occur have been characterized. Besides, the proposed FHN neuron model is implemented using a simple microcontroller platform and various firing patterns are acquired experimentally to validate the numerical results. Furthermore, light and field-induced pattern formation in a chain regular lattice network made of 100 photosensitive memristive neurons is being studied. Numerical experiments are carried out to identify the effects of photocurrent and magnetic flux parameters on information coding patterns translated by the membrane potential from voltage output. The spatiotemporal patterns revealed that the network presents localized wave patterns with some features of synchronization, sensitive to parameter change. This confirms that information coding and other collective behaviors of the network could be efficiently controlled by taming the intensity of light illumination and magnetic field exposure.

Pattern formation in a thermosensitive neural network

Pattern formation and synchronization stability in the network are dependent on cooperation between nodes and the local kinetics as well. Temperature has a significant effect on the membrane potential by regulating the channel conductance and excitability of neurons. Thermistor is a smart sensor and its resistance value changes with temperature. A nonlinear circuit composed of thermistors is effective to detect the changes in surroundings temperature. In this paper, a temperature-induced pattern formation in a two-dimensional regular lattice network composed of thermosensitive neurons is studied. Numerical simulations are performed to research the effect of parameters (coupling amplitude) and temperature spatial gradient distribution of neural network on pattern formation and synchronization stability. The bifurcation analysis of the membrane potential reveals the conversion in electrical activity and pattern selection. The results show that neural membrane potential can present distinct firing patterns with the change of temperature. The electrical synapse coupling between neurons promotes effective signals propagation in the network. It is found that the collective dynamic behavior of the network is changed by taming the coupling intensity. The Hamilton energy is estimated to predict the mode selection in neural activities. The energy can be ordered in the network under the temperature gradient distribution. Our results confirm that electrical synapse coupling and temperature spatial gradient distribution can be controlled to affect the neural activities in nervous system.

A Proportional-Egalitarian Allocation Policy for Public Goods Problems with Complex Network

How free-riding behavior can be avoided is a constant topic in public goods problems, especially in persistent and complex resource allocation situations. In this paper, a novel allocation policy for public goods games with a complex network, called the proportional-egalitarian allocation method (PEA), is proposed. This allocation rule differs from the well-studied redistribution policies by following a two-step process without paying back into the common pool. A parameter is set up for dividing the total income into two parts, and then they are distributed by following the egalitarianism and proportional rule, respectively. The first part of total income is distributed equally, while the second part is allocated proportionally according to players’ initial payoffs. In addition, a new strategy-updating mechanism is proposed by comparing the average group payoffs instead of the total payoffs. Compared with regular lattice networks, this mechanism admits the difference of cooperative abilities among players induced by the asymmetric network. Furthermore, numerical calculations show that a relatively small income for the first distribution step will promote the cooperative level, while relatively less income for the second step may harm cooperation evolution. This work thus enriches the knowledge of allocation policies for public goods games and also provides a fresh perspective for the strategy-updating mechanism.

Phase connectivity in pore-network models for capillary-driven flow

Pore-network representations of permeable media provide the framework for explicit simulation of capillary-driven immiscible displacement governed by invasion-percolation theory. The most demanding task of a pore-network flow simulation is the identification of trapped defending phase clusters at every displacement step, i.e. the phase connectivity problem. Instead of employing the conventional adjacency list we represent the connectivity of a phase cluster as a tree accompanied by a set of adjacent non-tree edges. In this graph representation, a decrease in phase connectivity due to a pore displacement event corresponds to deletion of either a tree or a non-tree edge. Deletion of a tree edge invokes a computationally intensive search for a possible reconnection of the resulting subtrees by an adjacent non-tree edge. The tree representation facilitates a highly efficient execution of the reconnection search. Invasion-percolation simulations of secondary water floods under different wetting conditions in pore-networks of different origin and size confirm the efficiency of the proposed phase connectivity algorithm. Moreover, a systematic simulation study of runtime growth with increasing model size on regular lattice networks demonstrates a consistent orders-of-magnitude speed-up compared to conventional simulations. Consequently, the proposed algorithm proves to be a powerful tool for invasion-percolation simulations on large multi-scale networks and for extensive stochastic analysis of typical single-scale pore-networks.

Emergence of spatially periodic diffusive waves in small-world neuronal networks.

It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.

A Century of Topological Coevolution of Complex Infrastructure Networks in an Alpine City

In this paper, we used complex network analysis approaches to investigate topological coevolution over a century for three different urban infrastructure networks. We applied network analyses to a unique time‐stamped network data set of an Alpine case study, representing the historical development of the town and its infrastructure over the past 108 years. The analyzed infrastructure includes the water distribution network (WDN), the urban drainage network (UDN), and the road network (RN). We use the dual representation of the network by using the Hierarchical Intersection Continuity Negotiation (HICN) approach, with pipes or roads as nodes and their intersections as edges. The functional topologies of the networks are analyzed based on the dual graphs, providing insights beyond a conventional graph (primal mapping) analysis. We observe that the RN, WDN, and UDN all exhibit heavy tailed node degree distributions [P(k)] with high dispersion around the mean. In 50 percent of the investigated networks, P(k) can be approximated with truncated [Pareto] power‐law functions, as they are known for scale‐free networks. Structural differences between the three evolving network types resulting from different functionalities and system states are reflected in the P(k) and other complex network metrics. Small‐world tendencies are identified by comparing the networks with their random and regular lattice network equivalents. Furthermore, we show the remapping of the dual network characteristics to the spatial map and the identification of criticalities among different network types through co‐location analysis and discuss possibilities for further applications.

Chaos in collective health: Fractal dynamics of social learning

Physiology often exhibits non-linear, fractal patterns of adaptation. I show that such patterns of adaptation also characterize collective health behavior in a model of collective health protection in which individuals use highest payoff biased social learning to decide whether or not to protect against a spreading disease, but benefits of health are shared locally. This model results in collectives of protectors with an exponential distribution of sizes, smaller ones being much more likely. This distribution of protecting collectives, in turn, results in incidence patterns often seen in infectious disease which, although they seem to fluctuate randomly, actually have an underlying order, a fractal time trend pattern. The time trace of infection incidence shows a self-similarity coefficient consistent with a fractal distribution and anti-persistence, reflecting the negative feedback created by health protective behavior responding to disease, when the benefit of health is high enough to stimulate health protection. When the benefit of health is too low to support any health protection, the self-similarity coefficient shows high persistence, reflecting positive feedback resulting the unmitigated spread of disease. Thus the self-similarity coefficient closely corresponds to the level of protection, demonstrating that what might otherwise be regarded as “noise” in incidence actually reflects the fact that protecting collectives form when the spreading disease is present locally but drop protection when disease subsides locally, mitigating disease intermittently. These results hold not only in a deterministic version of the model in a regular lattice network, but also in small-world networks with stochasticity in infection and efficacy of protection. The resulting non-linear and chaotic patterns of behavior and disease cannot be explained by traditional epidemiological methods but a simple agent-based model is sufficient to produce these results.

Noise-induced enhancement of network reciprocity in social dilemmas

The network reciprocity is an important dynamic rule fostering the emergence of cooperation among selfish individuals. This was reported firstly in the seminal work of Nowak and May, where individuals were arranged on the regular lattice network, and played the prisoner’s dilemma game (PDG). In the standard PDG, one often assumes that the players have perfect rationality. However, in reality, we human are far from rational agents, as we often make mistakes, and behave irrationally. Accordingly, in this work, we introduce the element of noise into the measurement of fitness, which is determined by the parameter α controlling the degree of noise. The considered noise-induced mechanism remarkably promotes the behavior of cooperation, which may be conducive to interpret the emergence of cooperation within the population.

Application of GA in optimization of pore network models generated by multi-cellular growth algorithms

In pore network modeling, the void space of a rock sample is represented at the microscopic scale by a network of pores connected by throats. Construction of a reasonable representation of the geometry and topology of the pore space will lead to a reliable prediction of the properties of porous media. Recently, the theory of multi-cellular growth (or L-systems) has been used as a flexible tool for generation of pore network models which do not require any special information such as 2D SEM or 3D pore space images. In general, the networks generated by this method are irregular pore network models which are inherently closer to the complicated nature of the porous media rather than regular lattice networks. In this approach, the construction process is controlled only by the production rules that govern the development process of the network. In this study, genetic algorithm has been used to obtain the optimum values of the uncertain parameters of these production rules to build an appropriate irregular lattice network capable of the prediction of both static and hydraulic information of the target porous medium.

Explosive Growth in Biased Dynamic Percolation on Two-Dimensional Regular Lattice Networks

The growth of two-dimensional lattice bond percolation clusters through a cooperative Achlioptas type of process, where the choice of which bond to occupy next depends upon the masses of the clusters it connects, is shown to go through an explosive, first-order kinetic phase transition with a sharp jump in the mass of the largest cluster as the number of bonds is increased. The critical behavior of this growth model is shown to be of a different universality class than standard percolation.

Improved Lattice Model for Concrete Fracture

An improved regular lattice network model is developed and validated for fracture of concrete structures. The improvements pertain to the inclusion of the tension softening response of the matrix phase, and of the modelling of structural response by incrementing the deformation rather than the load. A further development is the use of a regular square rather than a triangular lattice network to speed up the computations. These improvements eliminate the need for the introduction of arbitrary scaling parameters in the beam element failure criteria. Validation checks on notched three-point bend concrete specimens confirm the predictive capabilities of the improved lattice model with regard to both the load-deformation behavior and the energy dissipation mechanisms.

A new Monte Carlo method for percolation problems on a lattice

AbstractA new and general Monte Carlo technique is described for solving some well-known percolation and cluster-size problems on regular lattice networks. The method has been applied to ten two-dimensional structures.