International Journal of Modern Physics C

Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder–Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel–Bulkley, Ellis, Ree–Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

It is shown that the single relaxation time (SRT) version of the Lattice Boltzmann (LB) equation permits to compute the permeability of Darcy’s flows in porous media within a few percent accuracy. This stands in contrast with previous claims of inaccuracy, which we relate to the lack of recognition of the physical dependence of the permeability on the Knudsen number.

In this research, we propose a practical method for simulating the financial return series whose distribution has a specific heaviness. We employ the Ising model for generating financial return series to be analogous to those of the real series. The similarity between real financial return series and simulated one is statistically verified based on their stylized facts including the power law behavior of tail distribution. We also suggest the scheme for setting the parameters in order to simulate the financial return series with specific tail behavior. The simulation method introduced in this paper is expected to be applied to the other financial products whose price return distribution is fat-tailed.

We propose and study the competitiveness of a class of adaptive zero-determinant strategies (ZDSs) in a population with spatial structure against four classic strategies in iterated prisoner’s dilemma. Besides strategy updating via a probabilistic mechanism by imitating the strategy of a better performing opponent, players using the ZDSs can also adapt their strategies to take advantage of their local competing environment with another probability. The adapted ZDSs could be extortionate-like to avoid being continually cheated by defectors or to take advantage of unconditional cooperators. The adapted ZDSs could also be a compliance strategy so as to cooperate with the conditionally cooperative players. This flexibility makes adaptive ZDSs more competitive than nonadaptive ZDSs. Results show that adaptive ZDSs can either dominate over other strategies or at least coexist with them when the ZDSs are allowed to adapt more readily than to imitate other strategies. The effectiveness of the adaptive ZDSs relies on how fast they can adapt to the competing environment before they are replaced by other strategies. The adaptive ZDSs generally work well as they could adapt gradually and make use of other strategies for suppressing their enemies. When adaptation happens more readily than imitation for the ZDSs, they outperform other strategies over a wide range of cost-to-benefit ratios.

In this paper, a robust nonlinear feedback control scheme with adaptive gain is proposed to control the chaotic behavior in a Bose–Einstein condensate (BEC). The control goal concerns the track or regulation purposes. The BEC system is represented as stochastic ordinary differential equations with measured output perturbed by Gaussian noise, which represents the nature of the quantum systems. The convergence of the BEC control law is analyzed under the frame of the Lyapunov stability theory. Numerical experiments show an adequate performance of the proposed methodology under the required conditions. The results are applicable when the shape of the condensate is sufficiently simple.

A sampling procedure for the transition matrix Monte Carlo method is introduced that generates the density of states function over a wide parameter range with minimal coding effort.

In this paper, we numerically study an anisotropic shape transformation of membranes under external forces for two-dimensional triangulated surfaces on the basis of Finsler geometry. The Finsler metric is defined by using a vector field, which is the tangential component of a three-dimensional unit vector $\sigma$ corresponding to the tilt or some external macromolecules on the surface of disk topology. The sigma model Hamiltonian is assumed for the tangential component of $\sigma$ with the interaction coefficient $\lambda$. For large (small) $\lambda$, the surface becomes oblong (collapsed) at relatively small bending rigidity. For the intermediate $\lambda$, the surface becomes planar. Conversely, fixing the surface with the boundary of area A or with the two-point boundaries of distance L, we find that the variable $\sigma$ changes from random to aligned state with increasing of A or L for the intermediate region of $\lambda$. This implies that an internal phase transition for $\sigma$ is triggered not only by the thermal fluctuations, but also by external mechanical forces. We also find that the frame (string) tension shows the expected scaling behavior with respect to $A∕N$ ($L∕N$) at the intermediate region of A (L) where the $\sigma$ configuration changes between the disordered and ordered phases. Moreover, we find that the string tension $\gamma$ at sufficiently large $\lambda$ is considerably smaller than that at small $\lambda$. This phenomenon resembles the so-called soft-elasticity in the liquid crystal elastomer, which is deformed by small external tensile forces.

In this paper, we present an analysis and modeling of the interaction of electromagnetic fields with metallic nanostructures using computational tools that allow us to study the phenomena that are produced as an electromagnetic field interacts with the nanostructure. The analysis of dielectric systems including metals can be very complicated because of the metal parameters. For this reason, we propose to integrate the dielectric function of the Lorentz-Drude model with the finite difference time-domain (FDTD) method, which will permit to study the surface and internal effects within the metal nanostructure system added to the dielectric system, and the interaction of electromagnetic fields with atoms, ions or molecules excited up to their resonant frequency, which causes transitions among atomic energy levels. We solved the system and showed the results of the simulation for the following case studies, silver nanosphere of 100nm in diameter, gold nanorod of 12nm in thickness and 30nm in length and gold nanogroove of 70nm.

The traffic dynamics of multi-layer networks has become a hot research topic since many networks are comprised of two or more layers of subnetworks. Due to its low traffic capacity, the traditional shortest path routing (SPR) protocol is susceptible to congestion on two-layer complex networks. In this paper, we propose an efficient routing strategy named improved global awareness routing (IGAR) strategy which is based on the betweenness centrality of nodes in the two layers. With the proposed strategy, the routing paths can bypass hub nodes of both layers to enhance the transport efficiency. Simulation results show that the IGAR strategy can bring much better traffic capacity than the SPR and the global awareness routing (GAR) strategies. Because of the significantly improved traffic performance, this study is helpful to alleviate congestion of the two-layer complex networks.

Urban traffic flows are inherently repeated on a daily or weekly basis. This repeatability can help improve the traffic conditions if it is used properly by the control system. In this paper, we propose a novel iterative learning control (ILC) strategy for traffic signals of urban road networks using the repeatability feature of traffic flow. To improve the control robustness, the ILC strategy is further integrated with an error feedback control law in a complementary manner. Theoretical analysis indicates that the ILC-based traffic signal control methods can guarantee the asymptotic learning convergence, despite the presence of modeling uncertainties and exogenous disturbances. Finally, the impacts of the ILC-based signal control strategies on the network macroscopic fundamental diagram (MFD) are examined. The results show that the proposed ILC-based control strategies can homogenously distribute the network accumulation by controlling the vehicle numbers in each link to the desired levels under different traffic demands, which can result in the network with high capacity and mobility.

Community structure detection is of great significance for better understanding the network topology property. By taking into account the neighbor degree information of the topological network as the link weight, we present an improved Nonnegative Matrix Factorization (NMF) method for detecting community structure. The results for empirical networks show that the largest improved ratio of the Normalized Mutual Information value could reach $63.21\%$. Meanwhile, for synthetic networks, the highest Normalized Mutual Information value could closely reach 1, which suggests that the improved method with the optimal $\lambda$ can detect the community structure more accurately. This work is helpful for understanding the interplay between the link weight and the community structure detection.

The modified Schrödinger equation obtained by Costa Filho et al. [Phys. Rev. A 84, 050102(R) (2011)] is shown to be a Sturm–Liouville problem. This demonstration guarantees that Hamiltonian eigenvalues obtained in this formalism are real. It also allows us to show that, regardless of the non-Hermitian characteristic of the Hamiltonian operator in the Hilbert space, its time evolution remains unitary.