Vol. 7, No. 3 (2018): Regular Issue

The understanding of droplets is important to different applications, ranging from wetting to diagnosis of airways condition in the lung. In this work, we performed molecular dynamics and Monte Carlo simulations to solve the displacement of center of mass (CM) of droplets, in order to calculate the Hurst exponent in z-coordinate and in the xy-plane. Depending on the confinement condition, the CM motion, can be persistent, anti-persistent, Brownian or confined.

Magnetohydrodynamics is an important tool to study the dynamics of Space Physics. In this context, we introduce a three-dimensional magnetohydrodynamic solver with divergence-cleaning in the adaptive multiresolution CARMEN code. The numerical scheme is based on a finite volume discretization that ensures the conservation of physical quantities. The adaptive multiresolution approach allows for automatic identification of local structures in the numerical solution and thus provides an adaptive mesh refined only in regions where the solution needs more improved resolution. We assess the threedimensional magnetohydrodynamic CARMEN code and compare its results with the ones from the well-known FLASH code.

The coupling strength of a real-world network is studied to gain insight into the dynamics of state consensus. Real-world networks such as AUV fleets and bird flocks are highly nonlinear on the node level while environmental disturbance and communication error an aggravate the dynamic state of nonlinearity and non-stationarity on the network level. It is therefore necessary that a comprehensive consensus control methodology be developed so as to help hold the network together as a whole in an energy efficient way. However, the significance of coupling strength in affecting state consensus is usually ignored in the literature. This article investigates the issue with a focus on the impact of coupling strength.

We will consider two models describing certain market structures: (i) a domestic market in which a public firm (whose objective is to maximize social welfare) competes with two private firms (whose objective is to maximize their own profits); and (ii) an international market in which a domestic public firm competes with one domestic private firm and one foreign private firm. In both situations, firms decide simultaneously the price for their substitutable goods. We compare the maximum-revenue tariff with the optimum-welfare tariff, and also the other output equilibria obtained in each case. Furthermore, we also compare the results in the domestic competition with the ones in the international competition.

We study how effectively edge-centric dynamics solve semi-supervised learning tasks. The Edge Domination System is an algorithm to reveal patterns and obtain information of the underlying complex network. The algorithm consists of the simulation of a collective dynamical system based on particle competition for the dominance of edges. In this paper, we propose a vertex-centric version of this model and assess the differences between the edge-centric model. The edge-centric system offers better features in semi-supervised learning tasks, such as greater exploration behavior and faster convergence.

For adaptive multiresolution schemes we propose a local timestepping scheme based on natural extensions of Runge–Kutta methods. We consider reaction-diffusion equations in two space dimensions and assess the precision and efficiency of the new method. The obtained results are compared with those using classical finite volume schemes on a uniform grid and multiresolution schemes with global time stepping. It is shown that both CPU time and precision of the adaptive solutions are improved.

We will consider a mixed Bertrand duopoly model (that means, two firms decide simultaneously their prices for a substitutable good) to study the relationship between the privatization of a state-owned public firm and government preferences for tax revenue. In the model, we assume that the government imposes a specific tax rate on the quantity produced by each firm. The public firm aims to maximize social welfare, whereas the government’s objective function is a weighted sum between social welfare and tax revenue. Of course, the private firm aims to maximize its own profit. Furthermore, we also present the results for the Cournot duopoly model with differentiated goods, and we do a comparison between both models. We also present comparative static results.

Ballistic calculations were the first attempt where computers were used for, and the oblique launching of objects when studied at an ideal approach is quite simple with a parabolic trajectory of particles. The same motion could become intrinsically difficult to solve when dissipative forces are considered at the model. The present work shows a brief theoretical review on the motion of a spinning spherical particle under the influence of the gravitational field, the drag force and the Magnus effect. The drag forces can alter the translation speed and the angular velocity. We determined the profiles of the trajectories, velocity field and the modifications of frequency in two scenarios, first when the particle is moving across one medium and second when it pass through one medium to another. The results, trajectories obtained are in agreement the predictions for the cases where non continuous and non uniform forces are acting on a body.

Lyapunov dimension formula for Lorenz system is obtained. The methods of attractors localization and Lyapunov functions are developed.