Controlled transitions between phyllotactic states of repulsive particles confined on the surface of a cylinder

Phyllotaxis is a botanical classification scheme that can describe regular lattice-like structures on cylinders, often as a set of helical chains. In this letter, we study the general properties of repulsive particles on cylindrical geometries and demonstrate that this leads to a model which allows one to predict the minimum energy configuration for any given combination of system parameters. We are able to predict a sequence of transitions between phyllotactic ground states at zero temperature. Our results are understood in terms of a newly identified global scale invariant, \(\alpha\), dependent on circumference and density, which \emph{alone} determines the ground state structure. This representation provides a framework within which to understand and create lattice structures on more complex curved surfaces, which occur in both biological and nanoscale experimental settings.

Lattice-Based 3-Dimensional Wireless Sensor Deployment

With the wide application of wireless sensor networks (WSNs) in real space, there are numerous studies on 3D sensor deployments. In this paper, the k -connectivity theoretical model of fixed and random nodes in regular lattice-based deployment was proposed to study the coverage and connectivity of sensor networks with regular lattice in 3D space. The full connectivity range and cost of the deployment with sensor nodes fixed in the centers of four regular lattices were quantitatively analyzed. The optimal single lattice coverage model and the ratio of the communication range to the sensing range r c / r s were investigated when the deployment of random nodes satisfied the k -connectivity requirements for full coverage. In addition, based on the actual sensing model, the coverage, communication link quality, and reliability of different lattice-based deployment models were determined in this study.

A Markov Chain Monte Carlo Algorithm for Spatial Segmentation

Spatial data are very often heterogeneous, which indicates that there may not be a unique simple statistical model describing the data. To overcome this issue, the data can be segmented into a number of homogeneous regions (or domains). Identifying these domains is one of the important problems in spatial data analysis. Spatial segmentation is used in many different fields including epidemiology, criminology, ecology, and economics. To solve this clustering problem, we propose to use the change-point methodology. In this paper, we develop a new spatial segmentation algorithm within the framework of the generalized Gibbs sampler. We estimate the average surface profile of binary spatial data observed over a two-dimensional regular lattice. We illustrate the performance of the proposed algorithm with examples using artificially generated and real data sets.

Spatial patterns emerging from a stochastic process near criticality

There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration and local jumps on a regular lattice. We study its properties when the system is close to its critical point. Even if this model violates detailed balance, within a physically relevant regime dominated by fluctuations, it is possible to calculate analytically the probability density function of the number of individuals living in a given volume, which captures the close-to-critical behavior of the community across spatial scales. We find that the resulting distribution satisfies an equation where spatial effects are encoded in appropriate functions of space, which we calculate explicitly. The validity of the analytical formulæ is confirmed by simulations in the expected regimes. We finally discuss how this model in the critical-like regime is in agreement with several biodiversity patterns observed in tropical rain forests.

FRACTAL AGGREGATES ON GEOMETRIC GRAPHS

We study the aggregation process on the geometric graph. The geometric graph is composed by sites randomly distributed in space and connected locally. Similar to the regular lattice, the network possesses local connection, but the randomness in the spatial distribution of sites is considered. We show that the correlations within the aggregate patterns fall off with distance with a fractional power law. The numerical simulation results indicate that the aggregate patterns on the geometric graph are fractal. The fractals are robust against the randomness in the structure. A remarkable new feature of the aggregate patterns due to the geometric graph is that the fractal dimension can be adjusted by changing the connection degree of the geometric graph.