Iteration of the quadratic map produces sequences of polynomials whose degrees explode as the orbital period grows more and more. The polynomial mixing all 335 period-12 orbits has degree 4020, while for the 52 377 period-20 orbits the degree rises already to 1 047 540. Here, we show how to use preperiodic points to systematically extract exact equations of motion, one by one, without any need for

We present Star–Triangle Relations (STRs), a Mathematica® package designed to solve Feynman diagrams by means of the method of uniqueness in any Euclidean space-time dimension. The method of uniqueness is a powerful technique to solve multi-loop Feynman integrals in theories with conformal symmetry imposing some relations between the powers of propagators and the space-time dimension. In our algorithm

In this paper, we have a zeal for fulfilling the estimated scientific answers for the calculus of variations by using the Sumudu transform method (STM). The main target is to search the numerical arrangement of ordinary differential equations (ODEs) which emerge from the variational problems where first the fundamental condition for the arrangement of the issue is to fulfill the Euler–Lagrange condition

This paper addresses an autonomous facial expression recognition system using the feature selection approach of the Quantum-Inspired Binary Gravitational Search Algorithm (QIBGSA). The detection of facial features completely depends upon the selection of precise features. The concept of QIBGSA is a modified binary version of the gravitational search algorithm by mimicking the properties of quantum

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for Bangladesh, India, Pakistan and compared with that of China. Numerical solutions are used to obtain the value of parameters for the SIR model. It is predicted that the active case

In this paper, a mathematical model describing the transmission dynamics of onchocerciasis with distributed delays in infection incubation and recovery in humans and blackfly host population is formulated. We showed that the delayed model is positively invariant and bounded. Also, we obtain the onchocerciasis-free and endemic steady-state solutions as well as the basic reproduction number Rhb of the

When monolayer (ML) MoS2 is placed on a substrate, the proximity-induced interactions such as the Rashba spin-orbit coupling (RSOC) and exchange interaction (EI) can be introduced. Thus, the electronic system can behave like a spintronic device. In this study, we present a theoretical study on how the presence of the RSCO and EI can lead to the band splitting, the lifting of the valley degeneracy and

The exact controllability can be mapped to the problem of maximum algebraic multiplicity of all eigenvalues. In this paper, we focus on the exact controllability of deterministic complex networks. First, we explore the eigenvalues of two famous networks, i.e. the comb-of-comb network and the Farey graph. Due to their special structure, we find that the eigenvalues of each network are mutually distinct

From the stock markets of six countries with high GDP, we study the stock indices, S&P 500 (NYSE, USA), SSE Composite (SSE, China), Nikkei (TSE, Japan), DAX (FSE, Germany), FTSE 100 (LSE, Britain) and NIFTY (NSE, India). The daily mean growth of the stock values is exponential. The daily price fluctuations about the mean growth are Gaussian, but with a nonzero asymptotic convergence. The growth of

Segregation of granular particles affects the quality of end products in the pharmaceutical, chemical and food processing industries. Many researchers have worked on controlling the mechanical properties of granular particles to minimize segregation. In this paper, we studied different chute-related factors — inclination angle, friction, fill, channel geometry and base profile — and their effects on

In this paper, we study and simulate the effect of individual social responses, as a collective factor, on the epidemic spreading processes. We formally define the problem based on the traditional SI and SIR compartmental models considering the time-varying infection probability dependent on the social responses. In this study, models of generic and special case scenarios are developed. While in the

Modified three-derivative Runge–Kutta (MTHDRK) methods for the numerical solution of the resonant state for the Schrödinger equation are investigated. Order conditions are presented and oscillation-fitting conditions are derived. Two practical fifth-order explicit MTHDRK methods are constructed and the error analysis is carried out for large energy. The numerical results are presented for the numerical

In this work, theoretical analysis is carried out on fully developed hydromagnetic flow of heat generating/absorbing fluid in a vertical microchannel in the presence of Hall and ion-slip effects. The governing coupled flow equations are obtained in dimensional form and thereafter simplified by employing some similarity transformation variables and quantities. The transformed coupled equations are solved

The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely dimensional system. While it is well known that this approximation works surprisingly well for some CA, it is still not clear why it is the case, and which CA rules have this property. In order to shed some light on this problem, we present an example of a four input CA for which

Disordered traffic stream at the microscopic level can be described as a permeable medium. Each vehicle is considered to traverse through a series of lateral gaps created by other vehicles. We develop a multi-class traffic flow model that considers such viable and accessible gaps for individual vehicle classes to traverse downstream. The model accounts for the varying shares of different vehicle classes

The structural, electronic, dielectric and vibrational properties of zinc-blende (ZB) InAs were studied within the framework of density functional theory (DFT) by employing local density approximation and norm-conserving pseudopotentials. The optimal lattice parameter, direct band gap, static dielectric constant, phonon frequencies and Born effective charges calculated by treating In-4d electrons as

The extortion strategy can let its surplus exceed its opponents by a fixed percentage, hence the influence of extortion strategy in a population games has drawn wide attention. In this paper, we study the evolution of extortion strategy with unconditional cooperation and unconditional defection strategies in the Kagome lattice with abundant triangles. Our investigation shows that the extortion strategy

A novel median dual finite volume lattice Boltzmann method (FV-LBM) for the accurate simulation of incompressible flows on unstructured grids is presented in this paper. The finite volume method is adopted to discretize the discrete velocity Boltzmann equation (DVBE) on median dual control volumes (CVs). In the previous studies on median dual FV-LBMs, the fluxes for each partial face have to be computed

In this study, the incentive is defined based on feedback mechanism promoting propagation, and a novel model of behavior propagation is proposed based on feedback mechanism to investigate behavior propagation. In this model, the incentive includes the distance among individuals and the set of state and the influence of node is decided by the incentive and node degree, which explore the propagation

By comparing with symplectic different methods, the quadratic element is an approximately symplectic method which can keep high accuracy approximate of symplectic structure for Hamiltonian chaos, and it is also energy conservative when there have chaos phenomenon. We use the quadratic finite element method to solve the Hênon–Heiles system, and this method was never used before. Combining with Poincarê

This work considers the displacement of a resident fluid in a radial Hele-Shaw cell by an invading low viscosity fluid driven by time-dependent injection rates. Finger formation in the circular interface through a sequence of bifurcations may be minimized by the optimal choice of a time-dependent injection rate. Approximate solutions of fluid equations predict how bifurcations can be suppressed or

In this paper, we present a detailed study of the electronic dynamics in systems with correlated disorder generated from the Ornstein–Uhlenbeck process (OU). In short, we used numeric methods for solving the time-dependent Schrödinger equation. We apply a Taylor’s expansion of the evolution operator in order to solve the differential equation. We calculate some typical tools, such as the participation

In this paper, we propose a cellular automaton model to simulate traffic flow controlled by a series of traffic lights. The synchronized traffic light and the green wave light strategies were investigated. The spatiotemporal diagrams, energy dissipation, and CO2 emission of the system were presented. Our simulations are conducted to clarify the difference between both strategies and their effects on

This study examines the cellular automata traffic flow model, which considers the asynchronous update of vehicles’ velocities. Computer simulations are used to identify three typical phases: linear free flow phase, nonlinear moving phase and traffic jam phase. Compared to the original NaSch model, the system of the present model can reach the maximum flow when the vehicle density is higher. The influence

The generalized windmill graphs are good models for many real-world networks. In this paper, we obtain analytic expressions for the eigenvalues of the adjacency matrices and of the Laplacian matrices of the generalized windmill graphs. Using this information, we study some structural and dynamical properties of these graphs. To the end, we investigate the metro networks of four France cities and propose

In this paper, the flapping dynamics and wake flow characteristics in the nonlinear hysteresis region are investigated experimentally by immersing a cantilevered flexible plate in uniform airflow. The experimental results show that the flapping mode of a cantilevered flexible plate in hysteresis region will be transited from periodical traveling wave mode to limited cantilever-like mode with the variation

This paper was aimed to study of the wetting angle (Θ) of Sn–Ag–Cu, Sn–(3−x)Ag–0.5Cu–(x)Bi and Sn–(3−x)Ag–0.5Cu–(x)In (x=0.5, 1 and 2 in wt.%) Pb-free solder alloy systems at various temperatures (250, 280 and 310∘C) on Cu substrate in Ar atmosphere. The new Sn–(3−x)Ag–0.5Cu–xBi and Sn–(3−x)Ag–0.5Cu−(x) In systems, low Ag content quaternary Pb-free solder alloys, were produced by adding 0.5%, 1% and

Pedestrian counter flows widely exist in public pedestrian facilities such as corridors, sidewalks, signalized crossings and so on. There is one specific flow in real life, namely counter flow with conflicting walking preference which often occurs in the case of presence of one-sidedly asymmetry due to shadows, light, snow and so on. It is often overlooked in practice and the related studies are still

As an effective method to remove fine particulate matter (FPM) in coal-fired industries, the aerodynamic agglomeration has recently received increasing attention due to its application value. In this paper, a CFD–PBM coupled model of the particle agglomeration for industrial application was developed to predict the particle size distributions (PSDs) using Eulerian multiphase approach and Population

This paper presents an accurate numerical algorithm to solve the space fractional-order Fisher’s equation where the derivative operator is described in the Caputo derivative sense. In the presented discretization process, first, we use the compact finite difference (CFD) for a semi-discrete occurrence in time derivative and implement the Chebyshev spectral collocation method (CSCM) of the third-kind

To avoid social and economic losses, governments need to control rumor propagation by releasing official rumor-refuting information (ORI) to dispel the rumors. Therefore, understanding the complex competition mechanism between ORI and rumors is key to successfully refuting rumors. This paper presents an in-depth analysis of the function of ORI in suppressing and quashing rumors. First, the influencing

In this work, we have performed Monte Carlo simulations to study phase transitions in a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on the square and cubic lattices and with two different single-ion anisotropies. These lattices are divided in two interpenetrating sublattices with spins SA=1 (states ±1 and 0) on the sublattice A and SB=3∕2 (states ±3∕2, ±1∕2) on the sublattice B. We have used

MHD viscoelastic (Walters’-B) fluid flow close to the stagnation point region along an extending plate with the changeable fluid properties’ influences has been debated. Heat transfer’s features are scrutinized via Cattaneo–Christov (CC) theory. The mathematical model for the physical problem is tackled numerically via Chebyshev pseudospectral (CPS) technique. The existing outcomes are supported by

Linux operating system (LOS) represents one of the most complex human-made systems, and it acts as an important function between software and hardware. In recent years, a large number of related works treat Linux operating system as a complex network and explore some of the unique characteristics of the network. However, there is little research on the execution process of LOS in terms of networks

The paper modeled a leader’s opinion transmission in a population. The proposed model develops the cooperation agent-based continuous model in which the cooperation of individuals is based on the similarity of evolved “tags” which are relative to evolved tag-difference tolerances. In proposed model, an individual’s opinion and the individual’s tolerance are specified as variables in the model. During

The study of advection–diffusion equation has relatively became an active research topic in the field of uncertainty quantification (UQ) due to its numerous real life applications. In this paper, Hermite polynomial chaos is united with summation-by-parts (SBP) – simultaneous approximation terms (SATs) technique to solve the advection–diffusion equations with random Dirichlet boundary conditions (BCs)

We introduce a minesweeper percolation model, in which the system configuration is obtained via an automatic minesweeper process. For a variety of candidate networks with different lattice configurations, our process gives rise to a second-order phase transition. Using Monte Carlo simulation, we identify the critical points implied by giant components. A set of critical exponents are extracted to characterize

We study the estimated investigative answers for one of the popular models in biomathematics, in particular, the nonlinear Anopheles mosquito model numerically. The optimal control (OC) for nonlinear Anopheles mosquito model is examined. Important and adequate conditions to ensure the presence and singularity of the arrangements of the control issue are assumed. Two control factors are suggested to

We aim to compute the discrete energy spectrum for two-body scattering in a three-dimensional box under periodic boundary conditions. The spectrum in the center of mass is obtained by solving the Schödinger equation in a test potential using the Fourier basis. The focus is on how to project the spectrum into the various irreducible representations of the symmetry groups of the box. Four examples are

Cooperate epidemic spreading dynamics has attracted much attention from the field of network science. In this paper, we study the cooperate epidemic spreading dynamics on multiplex networks with heterogeneous populations, which induces the heterogeneous coinfection susceptibility. We propose a spreading model to describe the evolution mechanisms. To predict the final state of the epidemic outbreak

In this work, the structural, electronic and absorption properties of 2-methyl-2H-naphtho-[1,8-de]triazine in the pressure ranges of 0–250GPa are studied in detail (hereinafter referred to as 2-methyl crystal). Density functional theory (DFT) is used to calculate the lattice constants, bond lengths and bond angles of 2-methyl under different pressures. The results show that the crystals undergo complex

Based on first-principles calculations, we studied the magnetic properties of ultrathin Fe film on a nonmagnetic substrate Ta(001). We found that the perpendicular magnetocrystalline anisotropy (PMA) of Fe/Ta(001) system with only one or two Fe atomic layer(s) can be enhanced significantly, and the corresponding magnetocrystalline anisotropy energy is enlarged tos about 3 times of that in pure ultrathin

A space-time collocation method (STCM) using asymptotically-constant basis functions is proposed and applied to the quantum Hamiltonian constraint for a loop-quantized treatment of the Schwarzschild interior. Canonically, these descriptions take the form of a partial difference equation (PDE). The space-time collocation approach presents a computationally efficient, convergent, and easily parallelizable

Originally, we would like to use traffic modeling for car-following model to recover the individual difference of driving behavior corresponding to honk effect under V2X environment. Traffic stability is related to the individual difference resulting from the honk effect, which states that the individual difference of honk effect plays a different significant impact on the traffic stability. Furthermore

In some research involving opinion formation, there are some details that have not been studied deeply, just as the role of a person’s self-confidence in opinion dynamics. This small but important detail needs to be cleared up. Hence, in this paper, we want to discuss the self-confidence in opinion dynamics with regard to some common linear and nonlinear models: DeGroot, Friedkin–Johnsen, Deffuant–Weisbuch

Link prediction has been widely applied in social network analysis. Existing studies on link prediction assume the network to be undirected, while most realistic social networks are directed. In this paper, we design a simple but effective method of link prediction in directed social networks based on common interest and local community. The proposed method quantifies the contributions of neighbors

The study of community structure is of great significance when analyzing the structural and functional characteristics of networks. Attractor is a fast community detection method with the advantage of high accuracy for complex networks. However, in the connected nodes interaction model proposed by the Attractor algorithm, there is a problem with slow convergence during the distance updating process

Current continuation describes the computational study concerning with the unsteady flow of Eyring–Powell magneto nanoliquid over a bidirectionally deformable surface. Transference of activation energy is used in the improvement of binary chemical reaction. Nonlinear significance of thermal radiation is also incorporated in the energy equation. Investigation has been carried out through convective

Link prediction based on node similarity has become one of the most effective prediction methods for complex network. When calculating the similarity between two unconnected endpoints in link prediction, most scholars evaluate the influence of endpoint based on the node degree. However, this method ignores the difference in contribution of neighbor (NC) nodes for endpoint. Through abundant investigations

The growth and development of COVID-19 transmission have significantly attracted the attention of many societies, particularly Iran, that have been struggling with this contagious, infectious disease since late February 2020. In this study, the known “Susceptible-Infectious-Recovered (SIR)” and some other mathematical approaches were used to investigate the dynamics of the COVID-19 epidemic to provide

The fluid flow over three staggered square cylinders at two symmetrical arrangements has been numerically investigated in this study. The numerical calculations are carried out for several values of the Reynolds number (Re) ranging from 1 to 180. The results are presented in the form of vorticity contours and temporal histories of drag and lift coefficients. Furthermore, the physical parameters, namely

The evolution of cultural diversity in some social systems can be observed as the oppositional patterns in different levels, namely, the directions of the trends of diversity in different levels are opposite. In this paper, we propose a payoff-driven metapopulation modeling framework to investigate the origin of the oppositional patterns in the trends of cultural diversity. This model considers the

Recent work on the cascading failure of networks with dependence groups assumes that the number of nodes in each dependence group is equal. In this paper, we construct a model on interdependent networks with dependence groups against cascading failure. The size of dependence group is supposed to obey the Poisson Distribution and the Truncated Normal Distribution, respectively. By applying the tools

With the deepening of research on complex networks, many properties of complex networks are gradually studied, for example, the mean first-passage times, the average receive times and the trapping times. In this paper, we further study the average trapping time of the weighted directed treelike network constructed by an iterative way. Firstly, we introduce our model inspired by trade network, each

Electronic structure, X-ray absorption, and magnetic circular dichroism (XMCD) spectra in the CoFeMnSi Heusler alloy were studied from first principles. Fully relativistic Dirac linear muffin-tin orbital band structure method was implemented with various exchange–correlation functionals tested. The supercell approach was used to study the influence of intersite disorder, at the levels of 6.25%, 12

We introduce a new opinion model to study the opinion evolving in three typical networks (small-world network, scale-free network and highly clustered scale-free network) by employing Monte Carlo numerical simulation. To consider important social influence, we propose a heat bath like optimized opinion model that includes both local and global social impacts. By employing the new opinion model into

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for various infected countries. Numerical solutions are used to obtain the value of parameters for the SIR model. The maximum and minimum basic reproduction number (14.5 and 2.3) are

Macroscopic growth laws describe in an effective way the underlying complex dynamics of the spreading of infections, as in the case of Covid-19, where the counting of the cumulative number N(t) of detected infected individuals is a generally accepted variable to understand the epidemic phase. However, N(t) does not take into account the unknown number of asymptomatic cases A(t). The considered model

Lateral intakes are hydraulic structures used for domestic, agricultural and industrial water conveyance, characterized by a very complex three-dimensional morphodynamic behavior: since streamlines near the lateral intake are deflected, some vortices form, pressure gradient, shear and centrifugal forces at the intake generate flow separation and a secondary movement, responsible for local scour and

The main purpose of this article is to apply response surface method to analyze the residual dyes removal independent variables from the experimental data for dye adsorption onto alkali-activated sand as natural adsorbent from textile wastewater. The independent variables are contact time (3–30min) and adsorbent dosage (12.5–100g) and the dependent variables are percentage of dye removal and dye adsorbed