International Journal of Modern Physics C

This work explores the synchronization behavior in discrete systems with both discrete time and discrete state. In order to describe the self-driven function of the node’s state, a state transfer matrix is introduced. Three typical network structures (random network, small-world network and scale-free network) are numerically studied in order to investigate the impact of network structure. Simulation results show that, according to the phase synchronization index, the coupling strength is divided into four regions: the increasing region, the maximum region, the decreasing region and the oscillation region. Moreover, the size of the oscillation region seems to be changeless, independent of the network structure and a parameter describing the number of total node’s states.

The Earth radiation and energy budget is calculated by a manifold of rather complex Global Circulation Models. Their outcome mostly cannot identify integral radiation or energy budget relations. Therefore it is reasonable to look at more basic models to identify the main aspects of the model results. The simplest one of all of those is a one-dimensional one-layer model. However, most of these models — two are discussed here — suffer the drawback that they do not include essential contributions and relations between the atmospheric layer and the Earth. The one-dimensional one-layer model presented here integrates sensible and latent heat, the absorption of solar radiation and the direct emission of the long wave radiation to space in addition to the standard correlations. For the atmospheric layer two different long wave fluxes are included, top of atmosphere to space and bulk emission to Earth. The reflections of long wave radiation are taken into account. It is shown that this basic model is in excellent agreement with the observed integrated global energy budget.

This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics. The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was developed by Sekora and Stone 2009, 2010. The earlier one-dimensional technique was shown to preserve certain asymptotic limits and be uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. This paper gives the algorithmic details for constructing a multidimensional method. A future paper will present numerical tests that demonstrate the robustness of the computational technique across a wide-range of parameter space.

A modified Olami–Feder–Christensen (OFC) earthquake model on scale-free networks with assortative mixing is introduced. In this model, the distributions of avalanche sizes and areas display power-law behaviors. It is found that the period distribution of avalanches displays a scale-invariant law with the increment of range parameter d. More importantly, different assortative topologies lead to different dynamical behaviors, such as the distribution of avalanche size, the stress evolution process, and period distribution.

We investigate how humans visually perceive and approximate area or space allocation through visual area experiments. The participants are asked to draw a circle concentric to the reference circle on the monitor screen using a computer mouse with area measurements relative to the area of the reference circle. The activity is repeated for triangle, square and hexagon. The area estimated corresponds to the area estimates of a participant (perceived) for a corresponding requested area to be drawn (stimulus). The area estimated fits very well (goodness of fit R² > 0.97) to a power law given by r^2α where r is the radius of the circle or the distance of the edge for triangle, square and hexagon. The power law fit demonstrates that for all shapes sampled, participants underestimated area for stimulus that are less than ~100% of the reference area and overestimated area for stimulus greater than ~100% of the reference area. The value of α is smallest for the circle (α_∘ ≈ 1.33) and largest for triangle (α_△ ≈ 1.56) indicating that in the presence of a reference area with the same shape, circle is perceived to be smallest among the figures considered when drawn bigger than the reference area, but largest when drawn smaller than the reference area. We also conducted experiments on length estimation and consistent with the results of Dehaene et al., Science 2008, we recover a linear relationship between the perceived length and the stimulus. We show that contrary to number mapping into space and/or length perception, human's perception of area is not corrected by the introduction of cultural interventions such as formal education.

We present a Monte Carlo study of the effects of elastic anisotropy on the textures of nematic films with specific random hybrid boundary conditions. The polarized microscopy images and their evolution are analyzed in uniaxial systems for different values of the elastic constants.

A hybrid method is developed based on the spectral and finite-difference methods for solving the inhomogeneous Zerilli equation in time-domain. The developed hybrid method decomposes the domain into the spectral and finite-difference domains. The singular source term is located in the spectral domain while the solution in the region without the singular term is approximated by the higher-order finite-difference method.

The spectral domain is also split into multi-domains and the finite-difference domain is placed as the boundary domain. Due to the global nature of the spectral method, a multi-domain method composed of the spectral domain only does not yield the proper power-law decay unless the range of the computational domain is large. The finite-difference domain helps reduce boundary effects due to the truncation of the computational domain. The multi-domain approach with the finite-difference boundary domain method reduces the computational cost significantly and also yields the proper power-law decay.

Stable and accurate interface conditions between the finite-difference and spectral domains and the spectral and spectral domains are derived. For the singular source term, we use both the Gaussian model with various values of full width at half-maximum and a localized discrete δ-function. The discrete δ-function was generalized to adopt the Gauss–Lobatto collocation points of the spectral domain.

The gravitational waveforms are measured. Numerical results show that the developed hybrid method accurately yields the quasi-normal modes and the power-law decay profile. The numerical results also show that the power-law decay profile is less sensitive to the shape of the regularized δ-function for the Gaussian model than expected. The Gaussian model also yields better results than the localized discrete δ-function.

In this paper we adopt a phenomenological approach in order to develop a suitable Cellular Automata (CA) model capable to satisfactory mimic city growth and urban sprawl. The use of CA in urban expansion modeling is well known since many years, but very rarely it has been related with a down-top approach which considers inhabitants' preferences as a driving tool to characterize the CA algorithm. In addition, we consider as a control mechanism of the cell conversion rate (i.e. the number of cells experiencing conversion into urban use) the logistic function. This function is tuned on the free space (cells) at disposal for the urban development.

In this paper we present the basics of the model and we perform a simple simulation in the case of a generic geographic pattern.