International Journal of Modern Physics C

A nanofluid saturated porous medium is used for cooling purposes of a plane electronic device contained in the base of a hemispherical cavity. According to the intended application in embarked electronics, the base could be tilted with respect to the horizontal plane by an angle ranging from 0${}^{\circ }$ to 180${}^{\circ }$ (horizontal disc with cupola facing upwards and downwards, respectively). The volume fraction of the considered monophasic water-based ZnO nanofluid varies between 0% (pure water) and 10%, while the Rayleigh number based on the radius of the cavity ranges from $5.21\times 10^7$ to $7.29\times 10^{10}$. The ratio between the thermal conductivity of the porous medium solid matrix and that of the base fluid varies between 0 and 70. Influence of these four parameters on the average temperature of the active electronic device is presented and commented. The work shows that the saturated porous medium has a significant effect on the thermal state of the electronic device. A correlation is proposed to easily calculate this temperature for any combination of these parameters, which allows thermal sizing for optimal cooling of this assembly used in electronics engineering.

Rule 136 and its equivalents, rules 192, 238 and 252, are not number conserving rules. Out of these four, 136 and 192 are number nonincreasing rules, whereas 238 and 252 are number nondecreasing rules. However, when a non-uniform cellular automation (CA) is formed with rules 136 and 252, or 192 and 238 in alternate positions, the CA becomes conservative. This paper studies these non-uniform CAs. It is further shown that, except rules 136, 192, 238 and 252, no other number nonincreasing and nondecreasing rules can participate in a non-uniform CA to form a conservative system.

A modified kinetic Ising model with Metropolis dynamics, so-called $q$-neighbor Ising model, is investigated on random graphs. In this model, each spin interacts only with $q$ spins randomly chosen from its neighborhood. Investigations are performed by means of Monte Carlo (MC) simulations and the analytic pair approximation (PA). The range of parameters such as the size of the $q$-neighborhood and the mean degree of nodes of the random graph is determined for which the model exhibits continuous or discontinuous ferromagnetic (FM) phase transition with decreasing temperature. It is also shown that, in the case of discontinuous transition for large enough and fixed mean degree of nodes, the width of the hysteresis loop oscillates with the parameter $q$, expanding for even and shrinking for odd values of $q$. Predictions of the PA show satisfactory quantitative agreement with results of MC simulations.

As one type of lip-driven wind instruments, although flutes have a very long history, the acoustics of flutes is still unclear. Here, using the admittance matching method, the resonance frequencies of different tones for a flute are calculated with the precise correction for geometrical sizes. The result shows that the given frequency spectra of the flute are almost the same as the designed values.

In the present paper, a novel perspective fundamentally focused on the differential quadrature method using modified cubic B-spline basis functions are going to be applied for obtaining the numerical solutions of the complex modified Korteweg–de Vries (cmKdV) equation. In order to test the effectiveness and efficiency of the present approach, three test problems, that is single solitary wave, interaction of two solitary waves and interaction of three solitary waves will be handled. Furthermore, the maximum error norm $L_{\infty }$ will be calculated for single solitary wave solutions to measure the efficiency and the accuracy of the present approach. Meanwhile, the three lowest conservation quantities will be calculated and also used to test the efficiency of the method. In addition to these test tools, relative changes of the invariants will be calculated and presented. In the end of these processes, those newly obtained numerical results will be compared with those of some of the published papers. As a conclusion, it can be said that the present approach is an effective and efficient one for solving the cmKdV equation and can also be used for numerical solutions of other problems.

To control the spread of cascading failure on scale-free networks, we propose a new model with the betweenness centrality and the degrees of the nodes which are combined. The effects of the parameters of the edge weight on cascading dynamics are investigated. Five metrics to evaluate the robustness of the network are given: the threshold parameter ($T_C$), the proportion of collapsed edges ($C{F}_E$), the proportion of collapsed nodes ($C{F}_N$), the number of nodes in the largest connected component ($S_G$) and the number of the connected component ($S_C$). Compared with the degrees of nodes’ model and the betweenness of the nodes’ model, the new model could control the spread of cascading failure more significantly. This work might be helpful for preventing and mitigating cascading failure in real life, especially for small load networks.

In this paper, we consider a nonlinear control problem for one-dimensional viscous Burgers’ equation associated with a controlled linear heat equation by means of the Hopf–Cole transformation. The control is carried out by the time-dependent intensity of a distributed heat source influencing the heat equation. The set of admissible controls consists of compactly supported $L^{\infty }$ functions. Using the Green’s function approach, we analyze the possibilities of exact and approximate establishment of a given terminal state for the associated nonlinear Burgers’ equation within a desired amount of time. It is shown that the exact controllability of the associated Burgers’ equation and the heat equation are equivalent. Furthermore, sufficient conditions for the approximate controllability are derived. The set of resolving controls is constructed in both cases. The determination of the resolving controls providing exact controllability is reduced to an infinite-dimensional system of linear algebraic equations. By means of the heuristic method of resolving control determination, parametric hierarchies of solutions providing approximate controllability are constructed. The results of a numerical simulation supporting the theoretical derivations are discussed.

Community detection offers an important way to understand the structures and functions of social network. The label propagation algorithm has attracted vast attention since it is very suitable for discovering communities from large-scale networks. However, the algorithm suffers from the instability and inefficiency problem caused by the random policies it adopted. In this paper, we propose a novel label propagation approach based on local optimization to deal with the problem. The approach introduces a pre-propagation mechanism to optimize randomly initialized labels according to special factors, for example, node compactness. After that, it traverses and relabels nodes in the descending order of aggregate influence. The experiment results demonstrate the usefulness and effectiveness of our approach.

Based on the simplified Lorenz multiwing attractor and the generalized Jerk multiscroll attractor, the grid compound chaotic systems are designed via state variables exchanging, state variables scale transformation, coordinate transformation and switching control. By designing different switching controllers, four kinds of grid compound attractors are realized. Dynamical characteristics of these grid compound systems are analyzed by the means of phase diagram, Poincaré section, bifurcation diagram and the largest Lyapunov exponent (LLE). The digital circuit and analog circuit are designed, which verify the feasibility of the circuit implement of the compound chaotic system.

Many real-world complex systems consist of a set of basic units that are connected by different kinds of relationships. All types of such systems can be described by a multilayer network, where each link represents different types of interaction among the same set of nodes. In this paper, we present a general framework to characterize the influences (centrality) of layers. Furthermore, we propose two measures for layer centrality in terms of network connectivity under this framework. The basic idea of our measures consists in assigning more centrality value to layers that contribute more connectivity in a multilayer network. In other words, layers are more influential if more centrality values of links are assigned to them. We validate the measures on a real-world dataset of air transportation multilayer network and find that the measures are able to extract novel and useful information from the dataset.