International Journal of Modern Physics C

In this paper, we present a dynamical system based on the Langevin equation without stochastic term and using fractional derivatives that exhibit properties of Brownian motion, i.e. a deterministic model to generate Brownian motion is proposed. The stochastic process is replaced by considering an additional degree of freedom in the second-order Langevin equation. Thus, it is transformed into a system of three first-order linear differential equations, additionally $\alpha$-fractional derivative are considered which allow us to obtain better statistical properties. Switching surfaces are established as a part of fluctuating acceleration. The final system of three $\alpha$-order linear differential equations does not contain a stochastic term, so the system generates motion in a deterministic way. Nevertheless, from the time series analysis, we found that the behavior of the system exhibits statistics properties of Brownian motion, such as, a linear growth in time of mean square displacement, a Gaussian distribution. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion.

The lattice Boltzmann method (LBM) has been widely used in the simulation of particulate flows involving complex moving boundaries. Due to the kinetic background of LBM, the bounce-back (BB) rule and the momentum exchange (ME) method can be easily applied to the solid boundary treatment and the evaluation of fluid–solid interaction force, respectively. However, recently it has been found that both the BB and ME schemes may violate the principle of Galilean invariance (GI). Some modified BB and ME methods have been proposed to reduce the GI error. But these remedies have been recognized subsequently to be inconsistent with Newton’s Third Law. Therefore, contrary to those corrections based on the BB and ME methods, a unified iterative approach is adopted to handle the solid boundary in the present study. Furthermore, a direct force (DF) scheme is proposed to evaluate the fluid–particle interaction force. The methods preserve the efficiency of the BB and ME schemes, and the performance on the accuracy and GI is verified and validated in the test cases of particulate flows with freely moving particles.

With the increase of buses and bus lines, a negative effect on road section capacity is made by the prolonged delay and queuing time at bus stops. However, existing methods of measuring the negative effect pay little attention to different bus stop types in the curb lanes. This paper uses Gap theory and Queuing theory to build models for effect-time and potential capacity in different conditions, including curbside bus stops, bus bays with overflow and bus bays without overflow. In order to make the effect-time models accurate and reliable, two types of probabilities are introduced. One is the probability that the dwell time is less than the headway of curb lane at curbside bus stops; the other is the overflow probability at bus bays. Based on the fundamental road capacity model and effect-time models, potential capacity models of curb lane are designed. The new models are calibrated by the survey data from Changchun City, and verified by the simulation software of VISSIM. Furthermore, with different arrival rates of vehicles, the setting conditions of bus stops are researched. Results show that the potential capacity models have high precision. They can offer a reference for recognizing the effect of bus stops on the capacity of curb lane, which can provide a basis for planning, design and management of urban roads and bus stops.

We analyze the patterns like synchrony, desynchrony, and Drum head mode in a network of Hindmarsh–Rose (HR) neurons interacting via chemical synapse in unidirectional and bidirectional star topology. A two-coupled system has been studied for synchronization by varying the coupling strength and the parameter describing the activation and inactivation of the fast ion channel. The transverse Lyapunov exponent spectrum is plotted to observe the point of transition from desynchrony to synchrony. The synchronized, desynchronized, and drum head mode regions are observed when the neurons are connected in unidirectional and bidirectional coupling configurations. A detailed analysis about the time evolution of membrane potential corresponding to each region is presented. The annihilation of synchronized region and the expansion of drum head mode region in bidirectional coupling is discussed using parameter space. Our work provides finer insight into the existence and stability of Drum head mode and is useful for designing communication networks.

A study of the crystal structure, mechanical and acoustic properties of two $P{2}_1∕a$ and $P{2}_1∕c$ monoclinic phases of naphthalene and anthracene was performed using ab initio method of linear combination of atomic orbitals (LCAO) and basis sets: C_6-21G*, H_3-1p1G. The method was implemented in the CRYSTAL${}^{\prime }$14,${}^{\prime }$17 software package using electron density functional theory including van der Waals interactions (DFT-D2 and DFT-D3 (BJ)), in the local density approximation (LDA) with VWN exchange-correlation potential, gradient approximation PBE exchange-correlation functional and B3LYP hybrid functional. The calculated elastic constants for the first time are in moderate agreement with experimental data. Bulk modulus $B$, shear modulus $G$, Young’s modulus $E$ and the Poisson’s ratio $\mu$, as well as acoustic properties (average velocity of sound $〈v〉$, the Debye temperature ${\mathrm{\Theta }}_D$, and acoustic Grüneisen parameter ${\gamma }_a$) were obtained using the Voigt–Reuss–Hill model.

Car-following is an approach to understand traffic behavior restricted to pairs of cars, identifying a “leader” moving in front of a “follower”, which at the same time, it is assumed that it does not surpass to the first one. From the first attempts to formulate the way in which individual cars are affected in a road through these models, linear differential equations were suggested by author like Pipes or Helly. These expressions represent such phenomena quite well, even though they have been overcome by other more recent and accurate models. However, in this paper, we show that those early formulations have some properties that are not fully reported, presenting the different ways in which they can be expressed, and analyzing them in their stability behaviors. Pipes’ model can be extended to what it is known as Helly’s model, which is viewed as a more precise model to emulate this microscopic approach to traffic. Once established some convenient forms of expression, two control designs are suggested herein. These regulation schemes are also complemented with their respective stability analyses, which reflect some important properties with implications in real driving. It is significant that these linear designs can be very easy to understand and to implement, including those important features related to safety and comfort.

In this paper, we propose a stochastic cellular automata model to study the traffic behavior at a single-lane roundabout. Vehicles can enter the interior lane or exit from it via $N$ intersecting lane, the boundary conditions are stochastic. The traffic is controlled by a self-organized scheme. It has turned out that depending on the rules of insertion to the roundabout, five distinct traffic phases can appear, namely, free flow, congestion, maximum current, jammed and gridlock. The transition between the free flow and the gridlock is forbidden. The density profiles are used to study the traffic pattern at the interior lane of the roundabout. In order to quantify the interactions between vehicles in the interior lane of the roundabout, the velocity correlation coefficient (VCC) is also studied. Besides, the spatiotemporal diagrams corresponding to the entry/exit lanes are derived numerically. Furthermore, we have investigated the effect of displaying signal ($P_{\mathrm{\text{In}}})$, as the $P_{\mathrm{\text{In}}}$ decreases, the maximum current increases at the expense of the free flow and the jamming phase. Finally, we have investigated the effect of the braking probability $P$ on the interior lane of the roundabout. We have found that the increase of $P$ raises the spontaneous jam formation on the ring. Thus, enlarges the maximum current and the jamming phase while the free flow phase decreases.

To understand crowd evacuation, a model based on a bacterial foraging algorithm (BFA) is proposed in this paper. Considering dynamic and static factors, the probability of pedestrian movement is established using cellular automata. In addition, given walking and queue times, a target optimization function is built. At the same time, a BFA is used to optimize the objective function. Finally, through real and simulation experiments, the relationship between the parameters of evacuation time, exit width, pedestrian density, and average evacuation speed is analyzed. The results show that the model can effectively describe a real evacuation.

We discuss thermodynamic stability of neutral real (quantum) matter from the point of view of a computer experiment at finite, nonzero, temperature. We perform (restricted) path integral Monte Carlo simulations of the two component plasma where the two species are both bosons, both fermions, and one boson and one fermion. We calculate the structure of the plasma and discuss about the formation of binded couples of oppositely charged particles. The purely bosonic case is thermodynamically unstable. In this case we find an undetermined size-dependent contact value unlike partial radial distribution function. For the purely fermionic case, we find a demixing transition with binding also of like species.

In this paper, we present a method for portfolio selection based on the consideration on deformed exponentials in order to generalize the methods based on the gaussianity of the returns in portfolio, such as the Markowitz model. The proposed method generalizes the idea of optimizing mean-variance and mean-divergence models and allows a more accurate behavior for situations where heavy-tails distributions are necessary to describe the returns in a given time instant, such as those observed in economic crises. Numerical results show the proposed method outperforms the Markowitz portfolio for the cumulated returns with a good convergence rate of the weights for the assets which are searched by means of a natural gradient algorithm.