Dual-lattice Model Research Articles

Hydromechanical couplings of reinforced tensioned members of steel fiber reinforced concrete by dual lattice model

AbstractThe durability of concrete structures strongly depends on the water and chloride penetration in cracked concrete during its service life. This work aims at modeling the damage effect of tension stiffening behavior on the permeability for concrete tie specimen under tensile load by a dual lattice model, which considers hydromechanical couplings. Three concrete materials, including normal strength concrete (NSC), steel fiber reinforced concretes (SFRC), and ultra high‐performance fiber reinforced concrete (UHPFRC), are considered. The hydromechanical lattice model is based on a dual element network modeling: the water transport and the mechanical response. The fiber bridging effect is considered by means of the cohesive law of Mazars. The water flow in the damaged conduit elements is proportional to the cube of the crack width, which results from the damage variable. Experimental results available in open literature for both NSC and SFRC tie specimens are used to analyze and validate the proposed model. Considering a UHPFRC tie specimen, the model well predicted the load drops due to macrocrack occurrence, load hardening, and permeability evolution. Based on the present results, the current lattice hydromechanical model is a useful tool for predicting the service life of steel bar reinforcing concrete structure with and without steel fiber reinforcement.

Generation of over 1000 Diffraction Spots from 2D Graded Photonic Super-Crystals

For the first time, we are able to generate over 1000 diffraction spots from a graded photonic super-crystal with a unit super-cell size of 12a × 12a where a is the lattice constant and hole radii are gradually changed in dual directions. The diffraction pattern from the graded photonic super-crystal reveals unique diffraction properties. The first order diffractions of (±1,0) or (0,±1) disappear. Fractional diffraction orders are observed in the diffraction pattern inside a square with vertices of (1,1), (1,−1), (−1,−1) and (−1,−1). The fractional diffraction can be understood from lattices with a period of a. However, a dual-lattice model is considered in order to explain higher-order diffractions. E-field intensity simulations show a coupling and re-distribution among fractional orders of Bloch waves. There are a total of 12 × 12 spots in E-field intensity in the unit supercell corresponding to 12 × 12 fractional diffraction orders in the diffraction pattern and 12 × 12 fractional orders of momentum in the first Brillouin zone in k-space.

Dual random lattice modeling of backward erosion piping

This manuscript provides a novel random lattice model to simulate the progressive degradation of soil embankments induced by the backward erosion piping (BEP) phenomenon. The progressive evolution of the piping process is described by expressing apparent diffusivity of the soil as a function of the local hydraulic gradient. In order to accurately compute local field gradients, a dual lattice approach that evaluates the response on both Delaunay and Voronoi nodes is formulated. The response computed at the Delaunay nodes is then employed to augment field gradient computation on the Voronoi grid. The proposed dual lattice model is numerically verified and validated by comparing numerical results with BEP experiments available in the literature.

Multiscale crystal defect dynamics: A coarse-grained lattice defect model based on crystal microstructure

Crystal defects have microstructure, and this microstructure should be related to the microstructure of the original crystal. Hence each type of crystals may have similar defects due to the same failure mechanism originated from the same microstructure, if they are under the same loading conditions. In this work, we propose a multiscale crystal defect dynamics (MCDD) model that models defects by considering its intrinsic microstructure derived from the microstructure or material genome of the original perfect crystal. The main novelties of present work are: (1) the discrete exterior calculus and algebraic topology theory are used to construct a scale-up (coarse-grained) dual lattice model for crystal defects, which may represent all possible defect modes inside a crystal; (2) a higher order Cauchy–Born rule (up to the fourth order) is adopted to construct atomistic-informed constitutive relations for various defect process zones, and (3) an hierarchical strain gradient theory based finite element formulation is developed to support an hierarchical multiscale cohesive (process) zone model for various defects in a unified formulation. The efficiency of MCDD computational algorithm allows us to simulate dynamic defect evolution at large scale while taking into account atomistic interaction. The MCDD model has been validated by comparing of the results of MCDD simulations with that of molecular dynamics (MD) in the cases of nanoindentation and uniaxial tension. Numerical simulations have shown that MCDD model can predict dislocation nucleation induced instability and inelastic deformation, and thus it may provide an alternative solution to study crystal plasticity.

Evolution of symbiosis with resource allocation from fecundity to survival.

Symbiosis is one of the most fundamental relationships between or among organisms and includes parasitism (which has negative effects on the fitness of the interacting partner), commensalism (no effect), and mutualism (positive effects). The effects of these interactions are usually assumed to influence a single component of a species’ fitness, either survival or fecundity, even though in reality the interaction can simultaneously affect both of these components. I used a dual lattice model to investigate the process of evolution of mutualistic symbiosis in the presence of interactive effects on both survival and fecundity. I demonstrate that a positive effect on survival and a negative effect on fecundity are key to the establishment of mutualism. Furthermore, both the parasitic and the mutualistic behaviour must carry large costs for mutualism to evolve. This helps develop a new understanding of symbiosis as a function of resource allocation, in which resources are shifted from fecundity to survival. The simultaneous establishment of mutualism from parasitism never occurs in two species, but can do so in one of the species as long as the partner still behaves parasitically. This suggests that one of the altruistic behaviours in a mutualistic unit consisting of two species must originate as a parasitic behaviour.Electronic supplementary materialThe online version of this article (doi:10.1007/s00114-014-1175-1) contains supplementary material, which is available to authorized users.

Coexistence of mutualists and non-mutualists in a dual-lattice model

Evolution and maintenance of mutualism have been one of the major questions in evolutionary ecology, because it is often susceptible of invasion of non-mutualistic strategy. Some previous studies using dual-lattice model suggest that spatial structures of habitat can prevent non-mutualism from prevailing over mutualism, while the detail of the dynamics is not fully revealed. Here we explore population dynamics of the two strategies (mutualism and non-mutualism) in two species engaged in Prisoner's Dilemma game on a dual-lattice space, especially focusing on whether mutualists and non-mutualists can coexist in long-term dynamics. The habitat consists of two layers, each of which a population of species inhabits, and interspecific interaction is restricted between two corresponding sites of the layers. Each individual of the both species is either a mutualist or a non-mutualist and only the former pay cost c for benefit of the partner b. The payoff of the game affects the individuals' fecundity, while the mortality is constant. Reproduction is restricted to neighboring vacant sites of the focal individuals. Our computer simulations of the model show that even if b/c ratio remains constant, mutualists become dominant in both species over wider ranges of basic reproduction rate (reproduction rate without interspecific interaction) as b and c increase. If basic reproduction rates are asymmetric between the species or basic reproduction rates were sufficiently large, mutualists and non-mutualists can coexist in one or both species, while their population sizes often fluctuate. Transition of the final state between mutualism and non-mutualism happens rather discontinuously, then total population sizes change drastically at the transition. Moreover, we also find paradoxical cases of unilateral exploitation, i.e. one species consists of mutualists and other species non-mutualists. Additional simulations reveal that accidental extinction of the non-mutualists of one species can result in extinction of mutualist of the other species.

Evolution of situation-dependent mutualism

In nature, we can find an organism plays a mutualistic role on its partner species in a particular situation even though it is parasite in essence. What condition realizes such a flexible symbiotic system? To answer this question, we conducted the simulation using dual-lattice model.

Phenotypic variation in nurse traits and community feedbacks define an alpine community

Much is known about facilitation, but virtually nothing about the underlying genetic and evolutionary consequences of this important interaction. We assessed the potential of phenotypic differences in facilitative effects of a foundation species to determine the composition of an Alpine community in Arizona. Two phenotypes of Geum rossii occur along a gradient of disturbance, with 'tight' competitive cushions in stable conditions and 'loose' facilitative cushions in disturbed conditions. A common-garden study suggested that field-based traits may have a genetic basis. Field experiments showed that the reproductive fitness of G. rossii cushions decreased with increasing facilitation. Finally, using a dual-lattice model we showed that including the cost and benefit of facilitation may contribute to the co-occurrence of genotypes with contrasting facilitative effects. Our results indicate that changes in community composition due to phenotypic differences in facilitative effects of a foundation species may in turn affect selective pressures on the foundation species.

Dual lattice model of the evolution of facultative symbiosis with continuous Prisoner's Dilemma game

Mutualism is ubiquitous in nature and is thought to have played a key role in the history of life. However, how mutualism could evolve despite being prone to unilateral exploitation is a puzzling question in evolutionary ecology. Some theoretical studies have shown that spatial structure of habitat can facilitate the emergence and maintenance of mutualism. However, they are based on the simple assumption that the trait in question is discrete: each individual is either a mutualist or a non-mutualist. In this article I develop a simple simulation model of coevolution of facultative symbiosis using a one-shot continuous Prisoner's Dilemma game to investigate the evolutionary dynamics of mutualism between two species. In this model I assume continuous traits for both species from - 1 (fully deceptive) to 1 (fully cooperative). The habitat has a dual-lattice structure, each layer is inhabited by one species. Interspecific interaction is restricted between two corresponding sites of the two layers. Without limitation on the magnitude of a single mutation, I find that mutualism can arise and persist when the intrinsic reproduction rate is low (but is above a threshold) and the benefit/cost ratio of the cooperative strategy is large, which is consistent with Yamamura et al. [2004. Evolution of mutualism through spatial effects. J. Theor. Biol. 226, 421–428]. In these cases, extreme antagonism often evolves starting from a neutral population that seems nearly stable, but once mutualism arises, the cooperative individuals quickly increase and both the populations eventually become mutualistic on average, although they are polymorphic. However, when the effect of a single mutation was limited to be small, extreme antagonism is much likely to dominate unless the intrinsic reproduction rate is low. When only one species is allowed to evolve, mutualism arises when the initial strategy of the other species is cooperative. Otherwise, excessive deception evolves in the former, and the latter often becomes driven to extinction.

The distribution of positive and negative species interactions across environmental gradients on a dual-lattice model

There has been considerable recent interest in understanding the role of positive inter-specific interactions within ecology, and significant progress has been made both empirically and theoretically. Similarly, considerable progress has been made in improving our understanding of the mechanisms that limit species’ ranges. In this contribution, we seek to understand the setting of species’ borders when some species within the assemblage exhibit positive inter-specific interactions. We use a spatially explicit dual-lattice simulation model to explore the distribution of different interactions across environmental gradients. We first simulate community dynamics when there is either a gradient in reproductive rate or in mortality. We then consider what happens when gradients in reproduction and mortality run in parallel or perpendicular to one another. If the stress gradient impacts on reproductive potential, positive interactions are found where there is high abiotic stress. In this instance, the mutualists are able to tolerate an environment that the cheaters cannot. However, when the stress gradient influences mortality, we find that the mutualists occur as a stripe surrounded by cheaters both towards the better and the harsher ends of the gradient. Previous theory and most empirical evidence tend to indicate that net positive interactions are likely to occur in environments characterized by high abiotic stress. However, evidence from some stress gradients suggests that the distribution of positive and negative interactions can be more complex, with the most stressful environments being occupied by individuals engaging in negative rather than positive interactions. Our results provide a potential theoretical explanation for these recent field observation, and highlight the need for further theoretical and empirical work to better our understanding of how positive and negative interactions act to determine the limits to species’ ranges.