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In this research paper, the authors wish to examine the effects of couple stress on hybrid nanofluid considering magnetohydrodynamic three-dimensional transient flow between two parallel plates. Stretching of the lower plate causes fluid flow in the channel. The fluid flow model is shown in mathematical form using a set of coupled nonlinear partial differential equations, which are then translated into coupled nonlinear ordinary differential equations using the proper transformation. The authors used the spectral quasi linearization method (SQLM), an effective numerical technique, to solve the updated equations and study the effects of various flow parameters on fluid temperature and velocity. The Nusselt number and skin friction coefficients were also investigated from an engineering standpoint. The generated solutions are verified using the residual analysis. Statistical analysis is performed on the skin-friction coefficients and the Nusselt number using quadratic regression models. [ABSTRACT FROM AUTHOR]

This paper is a key contribution with respect to the applications of solitary wave solutions to the unique solution in the presence of the auxiliary data. Hence, this study provides an insight for the unique selection of solitons for the physical problems. Additionally, the novel numerical scheme is developed to compare the result. Further, this paper deals with the stochastic Fisher-type equation numerically and analytically with a time noise process. The nonstandard finite difference scheme of stochastic Fisher-type equation is proposed. The stability analysis and consistency of this proposed scheme are constructed with the help of Von Neumann analysis and Itô integral. This model is applicable in the wave proliferation of a viral mutant in an infinitely long habitat. Additionally, for the sake of exact solutions, we used the Riccati equation mapping method. The solutions are constructed in the form of hyperbolic, trigonometric and rational forms with the help of Mathematica 11.1. Lastly, the graphical comparisons of numerical solutions with exact wave solution with the help of Neumann boundary conditions are constructed successfully in the form of 3D and line graphs by using different values of parameters. [ABSTRACT FROM AUTHOR]

Gyrotactic microorganisms may be mobile ones that exist in surroundings, for instance oceans, pools, and reservoirs. The convective heat transfer due to the movement of these microorganisms in the base fluids is known as bio-convection. In this paper, the analysis of MHD bio-convection of nanofluid in the Γ -shaped enclosure with gyrotactic microorganisms inside is conducted. The effect of thermal Rayleigh number Rat (104–105), bio-convection Rayleigh number (10–100), Lewis number (0.1–0.9), and Peclet number (10 − 3 –10 − 1 ) on the natural convection (NC) and concentration of the micro-organisms (C) is investigated. The Navier–Stokes equations are used as the governing equations and are solved by Finite Element Method. The results reveal that Le may have a reverse impact on Nuavg (upto 42%); however, Pe has a positive impact on both Nuavg (upto 10%) and Shavg (upto 12%) and enhances heat transfer performance. [ABSTRACT FROM AUTHOR]

The goal of this paper is to identify the consequences of Darcy–Forchheimer flow (DFF) on electromagnetohydrodynamic flow of graphene oxide–iron oxide hybrid nanofluid over a rotating disk in a porous medium with viscous dissipation. The set of obtained ordinary differential equations had been solved with the corresponding boundary conditions using a numerical method called fourth-order Runge–Kutta method along with the shooting technique. The impact of the pertinent parameters on the dimensionless flow and temperature field profiles is shown using graphs. Also the nondimensional skin friction factor is stated in tabular form. The results state that as there is an increase in the value of porosity parameter, the velocity profile then diminishes. As shown in the outcomes, we accomplish that in this modeling, platelets have higher influence than the blade, brick, and cylinder. Due to nanoparticles, graphene oxide–iron oxide nanocomposite exhibits anti-microbial capabilities. These studies suggest that graphene oxide–iron oxide nanocomposite may be used to remove natural solvents and water filter. [ABSTRACT FROM AUTHOR]

In this paper, an investigation into Williamson nanofluid stagnation point flow of nano-biofilm over a stretching/ shrinking sheet with chemical reaction is performed. Moreover, the impact of cylindrical-shaped nanoparticles, activation energy, and bioconvection has been considered. The fluid's fluctuating transport properties (dynamic viscosity, heat conductivity, nanoparticle mass diffusivity) and microorganism diffusivity are evaluated. The nonlinear systems of partial differential equations are transformed into nonlinear differential equations via the implementation of similarity transformations. The shooting approach and RK-4 technique are used for this investigation. The impacts of various fluid transport characteristics and various factors on patterns of velocity, temperature, the concentration of nanoparticles, and motile density are described. The Brownian motion, heat source and thermophoresis parameters all lead to a more consistent temperature profile being observed. It is seen that concentration-dependent properties decrease the velocity profile while the temperature, concentration, and motile density profiles increase. Also, the physical quantities decrease with the rising values of concentration-dependent properties. [ABSTRACT FROM AUTHOR]

In this paper, a novel meshless numerical scheme to solve the time-fractional Oskolkov–Benjamin–Bona–Mahony–Burgers-type equation has been proposed. The proposed numerical scheme is based on finite difference and Kansa-radial basis function collocation approach. First, the finite difference scheme has been employed to discretize the time-fractional derivative and subsequently, the Kansa method is utilized to discretize the spatial derivatives. The stability and convergence analysis of the time-discretized numerical scheme are also elucidated in this paper. Moreover, the Kudryashov method has been utilized to acquire the soliton solutions for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]

Human survival is purely based on the environment. Through natural calamities or man-made depredation, the pleasant existence is disturbed. Trees provide not just foliage for the environment but also a pleasant atmosphere for the human population. One of the most serious threats to the forest and ecology is the pine wilt disease (PWD). It is a devastating disease that kills pine trees in a matter of weeks. The pine-wood nematode Bursaphelenchus Xylophilus causes PWD. This study emphasises on the infectious model of PWD engaging the q -homotopy analysis transform method (q -HATM) to a leading fractional operator Caputo–Fabrizio fractional time derivative to arrive for superior understanding. The denouements are presented in the forms of plots and tables. At last the paper supports to examine the real-world models and helps to forecast their behavior that communicate the instructions considered in the models. [ABSTRACT FROM AUTHOR]

The study of multiphase flows gained much importance because of its extensive applications in nature and industry. These flows possess two or more thermodynamic phases, for example, one component phase (e.g., water vapors and water flow) or several components phase (e.g., water and oil flow). The most common example of multiphase flow in the context of the oil industry is petroleum. Further blood flow, porous structures, fluidized bed, bubbly flow in nuclear reactors, and fiber suspension in the paper industry are some significant examples of multiphase flows. In this paper, we considered the Couette flow of non-Newtonian (couple stress) fluid with variable magnetic field and thermal conductivity effects between parallel walls of the channel. The upper wall of the channel is in constant motion while the lower wall is in a fixed position. The variable viscosity effects with the suspension of hafnium particles are also discussed by taking Vogel's viscosity case. The shooting method based on the R–K method is applied to obtain the numerical solution of the current problem. A comparison between Newtonian and non-Newtonian fluids is presented by sketching graphs. The variations in flow and temperature of fluid against various involved factors, including variable viscosity, wall temperature, thermal radiations, variable magnetic field, and thermal conductivity are sketched and also physically described. It is observed that variable viscosity parameter elevated both velocity and temperature profiles while wall temperature parameter decelerated both fields. Further, noticed that the variable thermal conductivity and variable magnetic field impede the velocity of the fluid and also retarded the temperature field. Our attempt is not just useful to investigate the mechanical and industrial multiphase flows but also delivers important results to fill the gap in the existing literature. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the time-dependent stagnation point flow of an Oldroyd-B fluid subjected to the modified Fourier law. The flow into a vertically stretched cylinder at the stagnation point is discussed. The heat flux model of a non-Fourier is intended for the transfer of thermal energy in fluid flow. The study is carried out on the surface heating source, namely the surface temperature. The developed nonlinear partial differential equation for regulating fluid flow and heat transport is transformed via appropriate similarity variables into a nonlinear ordinary differential equation. The development and analysis of convergent series solutions were considered for velocity and temperature. Prandtl number numerical values are computed and investigated. This study's findings are compared to the previous findings. By making use of the bvp4c Matlab method, numerical solutions are obtained. Besides, high buoyancy parameter values are found to increase the fluid velocity for the stimulating approach. By improving the thermal relaxation time parameter values, heat transfer in the fluid flow decreases. The temperature field effects are displayed graphically. [ABSTRACT FROM AUTHOR]

Main objective of this paper is to investigate comparative analysis of Copper-water and Copper Oxide-Water nanofluids flow due to a stretchable plate. Magnetic field is applied in transverse direction. Energy equation contains impacts of viscous dissipation and Joule heating. Appropriate dimensionless variables are used to transform the nonlinear PDEs system into dimensionless form. The dimensionless PDEs system is solved numerically by FDM (Finite difference method). Impacts of flow variables including Reynolds number, nanoparticles fraction, Hartmann number and Eckert number on velocity, surface drag force, Nusselt number and temperature are analyzed. Obtained outcomes show that velocity increases through Reynolds number and time while it decreases with Hartmann number. Temperature enhances with Eckert number while it decays with time. Skin friction increases for both Hartmann number and Reynolds number. Nusselt number decreases through nanopartical fraction. Comparative analysis of Copper-water and Copper Oxide-Water nanofluids shows that velocity and temperature are higher in Copper-water when compared with Copper Oxide-Water. For higher nanopartical fraction, the velocity and temperature decrease. [ABSTRACT FROM AUTHOR]

Understanding the spatial correlation of urban traffic state is essential for identifying the evolution patterns of urban traffic state. However, the distribution of traffic state always has characteristics of large spatial span and heterogeneity. This paper adapts the concept of community detection to the correlation network of urban traffic state and proposes a new perspective to identify the spatial correlation patterns of traffic state. In the proposed urban traffic network, the nodes represent road segments, and an edge between a pair of nodes is added depending on the result of significance test for the corresponding correlation of traffic state. Further, the process of community detection in the urban traffic network (named GWPA- K-means) is applied to analyze the spatial dependency of traffic state. The proposed method extends the traditional K-means algorithm in two steps: (i) redefines the initial cluster centers by two properties of nodes (the GWPA value and the minimum shortest path length); (ii) utilizes the weight signal propagation process to transfer the topological information of the urban traffic network into a node similarity matrix. Finally, numerical experiments are conducted on a simple network and a real urban road network in Beijing. The results show that GWPA- K-means algorithm is valid in spatial correlation analysis of traffic state. The network science and community structure analysis perform well in describing the spatial heterogeneity of traffic state on a large spatial scale. [ABSTRACT FROM AUTHOR]

Link prediction in complex networks has become a common focus of many researchers. But most existing methods concentrate on neighbors, and rarely consider degree heterogeneity of two endpoints. Node degree represents the importance or status of endpoints. We describe the large-degree heterogeneity as the nonequilibrium between nodes. This nonequilibrium facilitates a stable cooperation between endpoints, so that two endpoints with large-degree heterogeneity tend to connect stably. We name such a phenomenon as the nonequilibrium cooperation effect. Therefore, this paper proposes a link prediction method based on the nonequilibrium cooperation effect to improve accuracy. Theoretical analysis will be processed in advance, and at the end, experiments will be performed in 12 real-world networks to compare the mainstream methods with our indices in the network through numerical analysis. [ABSTRACT FROM AUTHOR]

A novel plate-type acoustic metamaterial with a high sound transmission loss (STL) in the low-frequency range (1000 Hz) is designed, theoretically proven and then experimentally verified. The thin plates with large modulus used in this paper mean that we do not need to apply tension to the plates, which is more applicable to practical engineering, the achievement of noise reduction is better and the installation of plates is more user-friendly than that of the membranes. The effects of different structural parameters of the plates on the sound-proofed performance at low-frequencies were also investigated by experiment and finite element method (FEM). The results showed that the STL can be modulated effectively and predictably using vibration theory by changing the structural parameters, such as the radius and thickness of the plate. Furthermore, using unit cells of different geometric sizes which are responsible for different frequency regions, the stacked panels with thickness 16 mm and weight 5 kg/m2 showed high STL below 2000 Hz. The acoustic metamaterial proposed in this study could provide a potential application in the low-frequency noise insulation. [ABSTRACT FROM AUTHOR]

This paper concerns the vibrational behavior of concentric double-walled and triple-walled carbon and boron nitride nanotubes using the finite element method. Armchair and zigzag nanotubes with different lengths and diameters are considered. Moreover, different boundary conditions are applied on the nanotubes. It is observed that in double-walled nanotubes, when the inner and outer layers are respectively from boron nitride and carbon, the frequencies are larger than those in the reverse arrangement. Investigating the effect of diameter on the first 10 natural frequencies of double-walled and triple-walled nanotubes showed that nanotubes with larger diameters possess smaller frequencies. The effect of diameter is more significant for higher modes. Finally, comparisons are made between the vibrational behavior of concentric carbon and boron nitride double-walled and triple-walled nanotubes. Considering the effect of vacancy defect on the vibrational characteristics of the nanotubes revealed that when all of the walls of the nanotubes are defective, the largest diminish occurs for the fundamental natural frequencies. [ABSTRACT FROM AUTHOR]

The predictions of the Quantum Theory have been verified so far with astonishingly high accuracy. Despite of its impressive successes, the theory still presents mysterious features such as the border line between the classical and quantum world, or the deep nature of quantum nonlocality. These open questions motivated in the past several proposals of alternative and/or generalized approaches. We shall discuss in the present paper alternative theories that can be infered from a reconsideration of the status of time in quantum mechanics. Roughly speaking, quantum mechanics is usually formulated as a memory free (Markovian) theory at a fundamental level, but alternative, nonMarkovian, formulations are possible, and some of them can be tested in the laboratory. In our paper we shall give a survey of these alternative proposals, describe related experiments that were realized in the past and also formulate new experimental proposals. [ABSTRACT FROM AUTHOR]

Recently, Majorana fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation. They are proposed to exist in various two-dimensional (2D) topological systems, such as topological superconductor (SC) and nanowire-superconducting hybridization system. In this paper, we point out that Majorana fermions in different topological systems obey different types of polygon sign rules. A numerical approach is described to identify the type of polygon sign rule of the Majorana fermions. Applying the approach to study two 2D topological systems, we find that vortex-induced Majorana fermions obey topological polygon sign rule and line-defect-induced Majorana fermions obey normal polygon sign rule. [ABSTRACT FROM AUTHOR]

Because of the importance of second harmonic generation (SHG) in some nonlinear media, in this paper, we investigated induced SHG in diamond where there is no intrinsic second-order susceptibility, . The electric field is proposed to introduce moving susceptibility of the second-order and induce second harmonic generation. Then, spatiotemporal quasi-phase matching (QPM) is applied to optimize the induced SHG. Numerical results reveal that in this way, the induced second harmonic is found at the frequency of rather than . [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze a new extragradient method for solving the general variational inequalities involving two operators. We also prove the global convergence of the proposed modified method under certain mild conditions. We used a self-adaptive technique to adjust parameter ρ at each iteration. It is proved theoretically that the lower-bound of the progress obtained by the proposed method is greater than that by the extragradient method. An example is given to illustrate the efficiency and its comparison with the extragradient method. Since the general variational inequalities include the classical variational inequalities and complementarity problems as special cases, our results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this field. [ABSTRACT FROM AUTHOR]

The flows around a typical open cavity with a store are numerically simulated in this paper. A fully implicit unfactored method is employed in the solver of RANS equations, where the S-A turbulent model is implemented to calculate the turbulent eddy viscosity. The flow-induced oscillation of the free shear layer around the cavity lip is captured and analyzed. Comparisons for the different cases of the cavity flow are made. The calculated results show that the pressure fluctuation is pertinent to the different positions of the store inside the cavity. The power spectral density (PSD) of the pressure by fast Fourier transformations (FFT) is also displayed in the paper. For the Rossiter's oscillatory mode, the numerical results compare well with the experimental data. [ABSTRACT FROM AUTHOR]

This paper studies chaos synchronization via unidirectional coupling. The self-synchronization of Lorenz systems, modified coupled dynamos systems and hyperchaotic Chen systems is studied by three methods: the Lyapunov function method, the global synchronization method and the numerical calculation of the largest Lyapunov exponent method. In regard to application to communication, we show that via transmitting single signal the synchronization of the drive system and the response system can be achieved. An example of applying self-synchronization of hyperchaotic Chen systems to chaotic masking secure communication is presented in this paper. Simulation results show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, a new type of honeycomb structure is proposed to enhance the energy absorption capacity for a honeycomb structure, and investigated its energy absorption efficiency (absorbed energy per unit volume) by finite element method (FEM). This model has small arc-shaped parts on the double cell wall, and can be manufactured by a similar way of standard honeycomb structures. Also, the proposed structure has large rigidity of plastic bending without increasing the mass. In this paper, effects of geometrical properties on the energy absorption characteristics are discussed. [ABSTRACT FROM AUTHOR]

In nature, many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex motion of these systems, we study the Vicsek model of self-propelled particles (SPP) which is an important tool to investigate the behavior of collective motion of live organisms. This model reproduces the biological behavior patterns in the two-dimensional (2D) space. Within the framework of this model, the particles move with the same absolute velocity and interact locally in the zone of orientation by trying to align their direction with that of the neighbors. In this paper, we model the collective movement of SPP using an agent-based model which follows biologically motivated behavioral rules, by adding a second region called the attraction zone, where each particles move towards each other avoiding being isolated. Our main goal is to present a detailed numerical study on the effect of the zone of attraction on the kinetic phase transition of our system. In our study, the consideration of this zone seems to play an important role in the cohesion. Consequently, in the directional orientation, the zone that we added forms the compact particle group. In our simulation, we show clearly that the model proposed here can produce two collective behavior patterns: torus and dynamic parallel group. Implications of these findings are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient and fast numerical method of finding a stationary solution of large systems of aggregation-fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable when the stationary concentrations steeply decrease with increasing aggregate size, which is fulfilled for the most important cases. We show that under rather mild restrictions, imposed on the kernel of the Smoluchowski equation, the following numerical procedure may be used: First, a complete solution for a relatively small number of equations (a 'seed system') is generated and then the result is exploited in a fast iterative scheme. In this way the new approach allows to obtain a steady-state solution for rather large systems of equations, by orders of magnitude faster than the standard schemes. [ABSTRACT FROM AUTHOR]

Predicting missing links in networks plays a significant role in modern science. On the basis of structural similarity, our paper proposes a new node-similarity-based measure called biased resource allocation (BRA), which is motivated by the resource allocation (RA) measure. Comparisons between BRA and nine well-known node-similarity-based measures on five real networks indicate that BRA performs no worse than RA, which was the best node-similarity-based index in previous researches. Afterwards, based on localPath (LP) and Katz measure, we propose another two improved measures, named Im-LocalPath and Im-Katz respectively. Numerical results show that the prediction accuracy of both Im-LP and Im-Katz measure improve compared with the original LP and Katz measure. Finally, a new path-similarity-based measure and its improved measure, called LYU and Im-LYU measure, are proposed and especially, Im-LYU measure is shown to perform more remarkably than other mentioned measures. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, we have used a more precise Hamiltonian matrix based on first nearest neighbor (1NN) and third nearest neighbor (3NN) carbon-carbon interactions to simulate carbon nanotube field effect transistors (CNTFETs). By taking the interactions with more distant neighbors into account, an improvement in tight-binding picture is gained. A self-consistent solution of Schrodinger equation based on nonequilibrium Green's function (NEGF) formalism coupled to a two-dimensional Poisson's equation for treating the electrostatics of the device has been employed to simulate CNTFETs. A tight-binding Hamiltonian with an atomistic (pz orbitals) mode space basis in the ballistic limits has been used to describe the carbon nanotube (CNT) region. Simulations show that in the presence of 3NN, the energy bandgap of the CNT decreases and consequently the simulated device has lower threshold voltage compared to a simulated device with just 1NN. Short channel effects study demonstrates that neglecting 3NN underestimates the subthreshold swing and overestimates ON/OFF current ratio. All these investigations show that for simulating a CNTFET more precisely, the 3NN interactions can be taken into account in addition to the 1NN. [ABSTRACT FROM AUTHOR]

The paper reviews the entanglement behavior of a 2-qubit system in a quantum spin glass using the Heisenberg XX model and the interaction of the system with a spin glass bath environment. In the first part, we study the entanglement (concurrence) for a 3- and 4-qubit with nearest neighbor interaction. With a fixed mean and varying standard deviation for the J coupling, the concurrence is numerically plotted with temperature for the different configurations. A general formula for the concurrence is given for n qubits at low temperature. In the second part, we study the concurrence of a 2-qubit system coupled to a spin glass bath environment with n = 2 to ≥ 4 qubits. The bath sites are coupled with random J coupling and varying applied magnetic field. A general formula for concurrence is given for mean J = 0 and B = 0 for n bath sites. For small random J and magnetic field B, a steady state is obtained with an approximate concurrence of 0.5, showing that the entanglement is preserved. [ABSTRACT FROM AUTHOR]

In this paper, on the basis of the Laypunov stability and the cascade synchronization approach, an effectual scroll controller and improving cascade synchronization approach are derived. The chaotic attractor can be displayed to be lopsided, till to be 1-scroll and periodic via the different scroll controller. And the proposed synchronization technique is applied to the new system, which the synchronization controller obtained by improving cascade method and adaptive functions. Numerical results are used to verify the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

This paper further investigates the adaptive full state hybrid projective synchronization (FSHPS) of hyper-chaotic systems - CYQY system with fully unknown parameters and perturbations. Based on the Lyapunov stability theory, adaptive controllers and updating laws of parameters can be designed for achieving the FSHPS of the CYQY hyper-chaotic systems with the same and different structures. Two groups numerical simulations are provided to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper studies the problem of chaos synchronization between two different hyperchaotic systems with uncertain parameters. Based on the Lyapunov stability theory, we obtain the sufficient condition of synchronization between two different hyperchaotic systems with uncertain parameters. A new adaptive controller with parameter update laws is designed to synchronize these chaotic systems. We proved it in theory with an uncertain hyperchaotic Lorenz system and an uncertain hyperchaotic Rössler system. Numerical results verified the validation of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor-corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system is realized using active control method. Numerical simulations indicated that the scheme was always effective and efficient. [ABSTRACT FROM AUTHOR]

This paper investigates the global synchronization problem of master-slave coupled multi-scroll saturated chaotic systems via single-state linear feedback control. An algebraic criterion for global synchronization is rigorously proven by means of the absolute stability theory. The obtained algebraic criterion is then optimized thereby deriving a less-conservative result, which is finally verified by numerical examples. [ABSTRACT FROM AUTHOR]

Based on the stability theory of fractional order systems and the pole placement technique, this paper designs a synchronization scheme with the state observer method and achieves the projective synchronization of a class of fractional order chaotic systems. Taking an example for the fractional order unified system by using this observer controller, and numerical simulations of fractional order Lorenz-like system, fractional order Lü system and fractional order Chen system are provided to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, an image encryption algorithm based on couple multiple chaotic systems is presented. It made the one-dimensional Coupled Map Lattice (CML) formed by Skew Tent map as spatiotemporal chaotic system and made its output sequence as the initial value of logistic and meanwhile did iterative of specific times to get the final key sequence, and then did XOR operations with corresponding pixels to finish the encryption. Numerical analysis expresses that this algorithm has large enough space and high security. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, we consider theoretically all the potential orientations of dipoles for second harmonic generation (SHG) under crystallized type I collagen fiber. With high numerical aperture (NA = 14), the effect of dipole orientation angle Φ on the SHG intensity, on the maximum SHG emergence angles (θmax, &#966max) and the action of these dipole sources on the ratio of forward to backward (F/B) SHG have been studied under different cases of fibrils diameter d1 and the QPM order (m, l) in the crystallized collagen fiber, and it is found that the influential patterns of the same Φ on SHG at different fibrils diameter d1 and the QPM order (m, l) are different. The dipoles arrangement is related to the characteristic changes in biological tissue so that our work may provide a helpful theoretical tool for pathological status detecting. [ABSTRACT FROM AUTHOR]

It is important to magnify natural stochastic resonance of nonlinear systems. In this paper, positive feedback is proposed to enhance stochastic resonance of those nonlinear systems whose internal parameters are difficult or impossible to be adjusted. The method can be used to improve the response of these nonlinear systems to external stimulus or strengthen the effect of target manipulation. At first, theoretical analysis based on adiabatic approximation method is presented, and then numerical simulations for both hard potential system and soft potential system are conducted to demonstrate the proposed method. Both theoretical analysis and numerical simulation indicate that stochastic resonance of these systems can be magnified by positive feedback. [ABSTRACT FROM AUTHOR]

In this paper, we use the decomposition technique of Noor and Noor [M. A. Noor and K. I. Noor, Three-step iterative methods for nonlinear equations, preprint (2006)] to suggest and analyze a new iterative methods for solving the integral equations. Our method of developing this new method is very simple as compared with other methods. Several numerical examples are given to illustrate the efficiency and performance of the new method. Results reveal that the proposed method is very effective and simple. Our method can be considered as an improvement of the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we have proposed a novel three-dimensional Lorenz-like chaotic system. Some basic properties of the system, such as dynamical behaviors, bifurcation diagram. Lyapunov exponents and Poincare mapping are investigated either analytically or numerically. Furthermore, the control problem of the new chaotic system was studied via nonlinear backstepping method. The single backstepping control input was designed according to Lyapunov stability criterion. Numerical simulations are carried out in order to demonstrate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

In the present paper, a technique is presented for obtaining estimates for the natural frequencies of axisymmetric vibration for transversely isotropic material. The wave propagation of harmonic waves in hollow cylinder of transversely isotropic materials subjected to certain boundary conditions is studied. The two-dimensional equations of elastodynamic are solved in terms of displacement by using the technique of variables separation. The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained. The natural frequencies are calculated numerically and the effects of rotation is discussed. The numerical results obtained have been illustrated graphically to understand the behavior of natural frequency versus the ratio h. Comparisons are made with the result in the absence of rotation. [ABSTRACT FROM AUTHOR]

The Šil'nikov homoclinic theorem provides one analytic criterion for proving the existence of chaos in three-dimensional autonomous nonlinear systems. In applications of the theorem, however, the existence of a homoclinic orbit that usually determines the geometric structure of the chaotic attractor is not easily verified mainly because there are no available efficient methods. In this paper, based on the undetermined coefficient approach we present a framework of how to find homoclinic orbits in two classes of three-dimensional autonomous nonlinear systems of normal forms, including how to set a reasonable form of expanding series of the homoclinic orbit, how to determine all coefficients in the expansion, and how to find a numerical homoclinic orbit. Numerical examples show that the proposed framework in combination with computer simulation is very efficient. [ABSTRACT FROM AUTHOR]

In the present paper, we have studied the propagation of axial symmetric cylindrical surface waves through rotating cylindrical bore in a micropolar porous medium of infinite extent possessing cubic symmetry. The frequency equation for surface wave propagation in the micropolar porous medium has been derived and liquid filled bore are derived. The effect of the rotation on phase velocity of surface wave has been studied in detail. Radius of bore and other material parameters for empty and liquid filled bore are derived. A particular case of interest has been deduced. Numerical results have been obtained and illustrated graphically to understand the behavior of phase velocity versus wave number of a wave. The results have indicated that the effect of rotation on phase velocity is highly pronounced. Comparisons are made in the absence of rotation. [ABSTRACT FROM AUTHOR]

Synchronization of multiple identical chaotic systems, coupled in a ring structure, was studied in this paper. Ueda attractor was used as an example to perform the synchronization of several chaotic systems. The bound of the Ueda attractor was also estimated by numerical simulation. The above results were also adopted to design a controller to synchronize chaotic systems. The stability of the synchronization of multiple identical chaotic systems was investigated using Lyapunov's direct method. Some sufficient conditions of asymptotical synchronization were attained from rigorous mathematical theory. Further, numerical results were also demonstrated in order to validate the proposed synchronization approach. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a master-slave synchronization scheme of two n-dimensional nonautonomous chaotic systems coupled by sinusoidal state error feedback control, where parameter mismatch exists between the external harmonic excitation of master system and that of slave one. A concept of synchronization with error bound is introduced due to parameter mismatch, and then the bounds of synchronization error are estimated analytically. Some synchronization criteria are firstly obtained in the form of matrix inequalities by the Lyapunov direct method, and then simplified into some algebraic inequalities by the Gerschgorin disc theorem. The relationship between the estimated synchronization error bound and system parameters reveals that the synchronization error can be controlled as small as possible by increasing the coupling strength or decreasing the magnitude of mismatch. A three-dimensional gyrostat system is chosen as an example to verify the effectiveness of these criteria, and the estimated synchronization error bounds are compared with the numerical error bounds. Both the theoretical and numerical results show that the present sinusoidal state error feedback control is effective for the synchronization. Numerical examples verify that the present control is robust against amplitude or phase mismatch. [ABSTRACT FROM AUTHOR]

In this paper, a novel approach for generating multi-wing chaotic attractors via switching control is proposed. By using a switching controller, multi-wing chaotic attractors can be generated from a double-wing system. The presented method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. Furthermore, the basic dynamical behaviors, including equilibrium points, maximum Lyapunov exponents and bifurcations, are further investigated. An improved module-based unified circuit is designed for realizing 4, 6, 8 and 10-wing chaotic attractors, and the experimental result is also demonstrated, which is consistent with the numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, due to the effect of positively-charged screening holes, Coulomb potential energy 1/r is modified to be 1/rp, which is assumed to deviate slightly from the former. Using many-body perturbation theory, we obtain a simple analytic representation of the ground-state energy and correlation energy for a uniform electron gas. Our results agree with those obtained by the numerical and semi-analytic methods at low-density limit. Higher ground-state energies at high-density limit are calculated from our model. High order r expansion terms are found at high-density region. A curve of transition density versus p is drawn via the Misawa spin-scaling relation, which is in consistent with Perdew's study at low-density limit. [ABSTRACT FROM AUTHOR]

This paper investigates antisynchronization of identical and nonidentical Φ6 Van der Pol oscillators (VDPOs) and Φ6 Duffing oscillators (DOs) with both parametric and external excitations based on adaptive backstepping technique. The technique is applied to achieve complete antisynchronization between identical Φ6 (VDPOs), identical Φ6 (DOs), and nonidentical Φ6 oscillators comprising the Φ6 (VDPO) and Φ6 (DO). Numerical simulations are implemented to verify the feasibility and effectiveness of the antisynchronization technique. [ABSTRACT FROM AUTHOR]

In this paper, we provide a new approach to create weighted scale-free networks by the method of weight redistribution. In our model, from an Erdös and Rényi random graph, with every edge having the same weight one, along with the total number of vertices and the total weight of all edges constant, we redistribute the weight based on our rules. When the network is dynamically stabilized, we find that both the degree and the strength distributions of our model satisfy the power-law form respectively, with the exponents approximating one. To have the power-law exponents tunable, we give each vertex an intrinsic strength initially. When the improved model is dynamically stabilized, we find the power-law exponents become tunable. Numerical results verify our theoretical analysis. [ABSTRACT FROM AUTHOR]

We used numerical simulations of a continuous model and the molecular dynamics model to understand the particle instability, formation of island-like structures and existence of one critical particle concentration of 1% (v/v) for formation of island-like structures in the suspension in a gradient AC electric field reported in Paper I. The simulations of the continuous model show that the critical concentration of 1% (v/v) is the concentration of which the particles of a suspension are just fully filling the lower field region finally. According to the MD simulations, the particles instability does exist in the corn oil in a gradient AC electric field, anisotropic polarization interactions among the particles are responsible for the particle instability and have memory, and the memory is still kept even when the particles are transported by a dielectrophoresis force. The island-like structures can be regarded as signature of the memory. We explored possibilities to apply our findings in biomedical fields. [ABSTRACT FROM AUTHOR]

The lattice BGK method is a recently developed numerical scheme for simulating a variety of physical systems in recent years. In this paper, a four-speed lattice BGK model is given for simulating KdV-Burgers equation ut+uux-αuxx+βuxxx = 0. Simulating results are compared with the analytical solution of the KdV-Burgers equation and they are in excellent agreement with each other. [ABSTRACT FROM AUTHOR]

This paper studies the global synchronization of a new hyperchaotic Lorenz system proposed by Wang et al. Based on the Lyapunov stability theory, the coupled control matrix is discussed when either knowing or unknowing the system boundary, respectively. The analysis of theory and numerical simulations show that the synchronization of hyperchaos Lorenz system can be realized effectively with the methods. [ABSTRACT FROM AUTHOR]

The inverse problem of the initial condition about the boundary value of the chord vibration equation is ill-posed. First, we transform it into a Fredholm integral equation. Second, we discretize it by the trapezoidal formula method, and then obtain a severely ill-conditioned linear equation, which is sensitive to the disturbance of the data. In addition, the tiny error of right data causes the huge concussion of the solution. We cannot obtain good results by the traditional method. In this paper, we solve this problem by the Tikhonov regularization method, and the numerical simulations demonstrate that this method is feasible and effective. [ABSTRACT FROM AUTHOR]