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We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection) under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration. [ABSTRACT FROM AUTHOR]

One-dimensional fourth-order boundary value problems (BVPs) play a critical role in engineering applications, particularly in the analysis of beams. Current numerical investigations primarily concentrate on homogeneous boundary conditions. In addition to its high precision advantages, the Hermite finite element method (HFEM) is capable of directly computing both the function value and its derivatives. In this paper, both the cubic and quintic HFEM are employed to address two prevalent non-homogeneous fourth-order BVPs. Furthermore, a priori error estimations are established for both BVPs, demonstrating the optimal error convergence order in H 2 semi-norm and L 2 norm. Finally, a numerical simulation is presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we treat the problem of constructing secure communication systems using chaotic synchronization of distributed parameter systems. In particular, we concentrate on the chaotic vibration of a wave equation with a van der Pol boundary condition. In general, a secure communication system consists of three components, a synchronization system, and modulation and demodulation components. In the present work, a wave equation generating non-isotropic spatiotemporal chaotic vibration is used. The non-isotropic characteristic makes it harder for the mechanism behind the synchronization system to be detected. To simulate the chaotic vibration accurately, a numerical algorithm is also developed. Finally, through security analysis by numerical simulations, it is shown that the introduction of non-isotropy makes one of the system parameters more sensitive. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for a piston flow reactor based on the material balance law using partial differential equations. A more general, nondimensional variant of the model is also derived. The finite difference method and coupled map lattice are used to create numerical algorithms to simulate spatio-temporal behavior in the stud- ied system. The paper also includes a stability analysis of the proposed algorithms and results of numerous numerical simulations, done in order to compare both methods and to visualize the spatio-temporal behavior of the reactor and the effects of different model parameters. Discussion of the obtained results and comparison of both algorithms is also provided. [ABSTRACT FROM AUTHOR]

In this paper, we consider a coupled snap system in a fractional G -Caputo derivative sense with integral boundary conditions. Hyers-Ulam stability criterion is investigated, and a numerical simulation will be supplied to some applications. Some numerical simulations are presented to guarantee the theoretical results. [ABSTRACT FROM AUTHOR]

With the excavation of underground opening, the roof rock block may fall under external dynamic disturbance. In this paper, the roof rock mass was simplified as a rock block system composed of trapezoidal rock blocks. A series of experiments and numerical simulations were performed to study the sliding process of the key block under the horizontal static clamping load and vertical impact disturbance. The propagation of stress wave in the block system were captured and analyzed by using high-speed camera and digital image correlation technique. The results reveal that a pendulum-type wave was generated due to the propagation and superposition of stress waves in the block system. Therefore, the governing mechanism of the sliding displacement of the key block was clarified based on the propagation of incident stress waves or pendulum-type waves. Meanwhile, it is found that the sliding distance of the key block decreases in a power function with the increasing friction coefficient, or decreases in a parabolic function with the increasing trapezoid internal angle. Finally, a case study on the roof block sliding of the roadway at a gold mine was conducted, and it is concluded that the sliding of the key block resulted from the coupled effects of "shear driving" and "low friction" driven by stress wave propagation, regardless of a single or multilayer rock block system. These results may provide technical guideline for preventing rock-falling accidents caused by blasting disturbances in underground mining. [ABSTRACT FROM AUTHOR]

In Papers I and II, we developed new shifted potential, gradient shifted force, and Taylor shifted force real-space methods for multipole interactions in condensed phase simulations. Here, we discuss the dielectric properties of fluids that emerge from simulations using these methods. Most electrostatic methods (including the Ewald sum) require correction to the conducting boundary fluctuation formula for the static dielectric constants, and we discuss the derivation of these corrections for the new real space methods. For quadrupolar fluids, the analogous material property is the quadrupolar susceptibility. As in the dipolar case, the fluctuation formula for the quadrupolar susceptibility has corrections that depend on the electrostatic method being utilized. One of the most important effects measured by both the static dielectric and quadrupolar susceptibility is the ability to screen charges embedded in the fluid. We use potentials of mean force between solvated ions to discuss how geometric factors can lead to distance-dependent screening in both quadrupolar and dipolar fluids. [ABSTRACT FROM AUTHOR]

The concentration distribution of cadmium ion in soil is studied by the phytoavailability model. According to the states of the cadmium complex: fully inert, fully labile and partially labile, we establish three corresponding cadmium uptake sub-models, and derive respective global analytical solutions at steady state. In particular, when the complex is partially labile, we give the steady analytical solution of cadmium ion concentration in cylindrical ge- ometry composed of the analytical solutions of partially labile complex and fully inert complex in planar geometry and fully inert complex in cylindrical geometry, that is, the ration approximation method. In this paper, the global analytical solutions are compared with the results of literature and numerical simulations. Therefore, the double check is realized to ensure the rationality of the analytical method. The global concentration profile of cadmium ions in the whole rhizosphere can be described by the steady state analytical solu- tions: the concentration of cadmium ion increases with the distance from the root surface and finally reaches the initial value; the change rate of cadmium ion concentration is the largest when the complex is fully labile; whatever the state of the complex is, cadmium ions never accumulate on the root surface. Finally, we discuss and compare the effects of moving and fixed right bound- aries of the model on the results. The results show that it is more reasonable to take the fixed right boundary, and plant roots can uptake cadmium ions in a wider range. [ABSTRACT FROM AUTHOR]

In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a result, nonlinear stability for an isolated vortex patch is proved. The proof is based on conservation of energy and vorticity, which is an analogue of the classical Liapunov function method. [ABSTRACT FROM AUTHOR]

This paper deals with a qualitative and computational study of a class of integro-differential model, with a nonlinear growth rate. The model is applied to immunology problems, in particular to the competition between tumors and immune system. Our purpose is to take into account the activity transfer processes between cells. The first part of this paper deals with the modeling, while the second part develops the existence and uniqueness of global solutions to the initial boundary value problem related to the application of the model. Finally, numerical simulations are used to illustrate the results obtained for a dynamic of tumor cells contrasted by the immune system. [ABSTRACT FROM AUTHOR]

Studies of many physical processes lead to the numerical solution of boundary-value problems for macroequations with a small parameter. Classical difference schemes poorly describe the solution of the original differential problem in boundary-layer regions, because they have an approximation viscosity comparable with the mesh size. This paper proposes difference schemes of higher order of approximation, which allow one to adequately simulate the motion of a viscous fluid in a wide range of Reynolds numbers, as well as reduce the time and amount of calculations due to the efficiency of the methods used in numerical simulation. [ABSTRACT FROM AUTHOR]

In the present paper, we consider a nonlinear fractional snap model with respect to a G -Caputo derivative and subject to non-periodic boundary conditions. Some qualitative analysis of the solution, such as existence and uniqueness, are investigated in view of fixed-point theorems. Moreover, the stabilities of Ulam–Hyers and Ulam–Hyers–Rassias criterions are considered and investigated. Some numerical simulations were performed using MATLAB for understanding the theoretical results. All results in this work play an important role in understanding ocean engineering phenomena due to the huge applicability of jerk and snap in seakeeping, ride comfort, and shock response spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we present a regression hybrid method that calculates shape sensitivity coefficients for multiscale crack propagation problems with performance measures that are non-differentiable in numerical implementation. These measures are crack propagation speed (or crack speed) defined at atomistic level obtained by solving coupled atomistic/continuum structures using the bridging scale method (BSM). The major contributions of this paper are: first, by analyzing the characteristics of the performance measures of crack speed in design space, this paper verifies for the first time that these measures are theoretically continuous and differentiable with respect to design variables, and as a result, the sensitivity coefficients exist in theory; second, to overcome the non-differentiability of the performance measures in numerical computation due to the finite size of integration time step, this paper proposes a regression hybrid method that calculates the shape sensitivity coefficients of crack speed through polynomial regression analysis based on the sensitivity of atomic responses, which is calculated through analytical shape design sensitivity analysis (DSA). And finally, the proposed method supports for 3D crack propagation problems with periodic boundary condition in one direction. A nano-beam example is used to demonstrate numerically the feasibility, accuracy, and efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the application of the probabilistic method (PM) for the numerical solution of the Dirichlet generalized harmonic problem in axisymmetric finite homogeneous and isotropic bodies with a right circular cylindrical hole. The term "generalized" indicates that a boundary function has a finite number of first kind discontinuity curves. The suggested algorithm for the numerical solution of boundary problems consists of the following main stages: a) application of the PM, which in turn is based on the computer modeling of the Wiener process; b) finding the intersection point of the trajectory of the simulated Wiener process and the surface of the problem domain; c) development of a code for the numerical implementation and checking the reliability of obtained results; d) finding the probabilistic solution of generalized problems at any fixed points in the considered domains. The algorithm does not require the approximation of a boundary function. The PM is tested on an explicit analytical solution from the literature. To illustrate the effectiveness and simplicity of the proposed method several examples are considered. Numerical results are presented and discussed. [ABSTRACT FROM AUTHOR]

Numerical simulation of laser drilling is rapidly gaining interest in academia and industry since this process remains one of the most important and widely-used technologies in modern manufacturing. Meshfree methods such as Smoothed Particle Hydrodynamics (SPH) have proven to be successful as a numerical tool for the computation of the heat transfer and material removal associated with a laser drilling problem. Nonetheless, the vast majority of recent developments incorporate an inconsistent SPH kernel into their thermal simulations. In this paper, several enhanced schemes are implemented to address this problem by solving the heat transfer more accurately. These meshfree schemes can provide a second-order accurate discretization of the Laplace operator and abolish the inconsistency issue of the standard SPH kernels. An efficient approach is additionally suggested to handle the associated boundary conditions, which relies on the idea of the color function and particle label. The implementation is initially validated by a 3D benchmark study and then applied for the first time to a laser drilling problem. [ABSTRACT FROM AUTHOR]

Analysis of the slipstream development around the high-speed trains in tunnels would provide references for assessing the transient gust loads on trackside workers and trackside furniture in tunnels. This paper focuses on the computational analysis of the slipstream caused by high-speed trains passing through double-track tunnels with a cross-sectional area of 100 m2. Three-dimensional unsteady compressible Reynolds-averaged Navier-Stokes equations and a realizable k-ε turbulence model were used to describe the airflow characteristics around a high-speed train in the tunnel. The moving boundary problem was treated using the sliding mesh technology. Three cases were simulated in this paper, including two tunnel lengths and two different configurations of the train. The train speed in these three cases was 250 km/h. The accuracy of the numerical method was validated by the experimental data from full-scale tests, and reasonable consistency was obtained. The results show that the flow field around the high-speed trains can be divided into three distinct regions: the region in front of the train nose, the annular region and the wake region. The slipstream development along the two sides of train is not in balance and offsets to the narrow side in the double-track tunnels. Due to the piston effect, the slipstream has a larger peak value in the tunnel than in open air. The tunnel length, train length and length ratio affect the slipstream velocities; in particular, the velocities increase with longer trains. Moreover, the propagation of pressure waves also induces the slipstream fluctuations: substantial velocity fluctuations mainly occur in front of the train, and weaken with the decrease in amplitude of the pressure wave. [ABSTRACT FROM AUTHOR]

In this paper, the principles of finite-element modeling for the electroacoustic simulation of bulk-acoustic-wave devices will be summarized. We will outline the model setup including governing equations and boundary conditions, as well as its efficient computer implementation. Particular emphasis will be given to tailoring the model dimension to the specific requirements of the desired investigation. As 3-D simulations still require a major effort, it will be illustrated that various aspects of device physics and design can already be addressed by fast and efficient 2-D simulations. Multiple theoretical and experimental evidence will be presented to demonstrate the validity of the modeling concepts. Based on various examples, it will be sketched how to benefit from numerical simulations for understanding fundamental effects, designing devices for actual products, and exploring novel technologies. [ABSTRACT FROM AUTHOR]

In a recent work, we developed a method [H. Takahashi et al., J. Chem. Phys. 143, 084104 (2015)] referred to as exchange-core function (ECF) approach, to compute exchange repulsion Eex between solute and solvent in the framework of the quantum mechanical (QM)/molecular mechanical (MM) method. The ECF, represented with a Slater function, plays an essential role in determining Eex on the basis of the overlap model. In the work of Takahashi et al. [J. Chem. Phys. 143, 084104 (2015)], it was demonstrated that our approach is successful in computing the hydrogen bond energies of minimal QM/MM systems including a cationic QM solute. We provide in this paper the extension of the ECF approach to the free energy calculation in condensed phase QM/MM systems by combining the ECF and the QM/MM-ER approach [H. Takahashi et al., J. Chem. Phys. 121, 3989 (2004)]. By virtue of the theory of solutions in energy representation, the free energy contribution δμex from the exchange repulsion was naturally formulated. We found that the ECF approach in combination with QM/MM-ER gives a substantial improvement on the calculation of the hydration free energy of a hydronium ion. This can be attributed to the fact that the ECF reasonably realizes the contraction of the electron density of the cation due to the deficit of an electron. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the impact of bending a multi-wire endoscope in the context of subwavelength imaging and near-field transport. To this end, we study the reflection and transmission by a "bent" wire medium in different configurations and demonstrate that the structure can be quite robust to the effect of bending provided the total length of the bent wires satisfies the Fabry-Pérot condition. The study is carried out relying on an analytical homogenization theory and using two additional boundary conditions obtained with physical arguments. It is proven that a structure formed by two connected sets of tilted metallic wires can allow for the near field transport with a deeply subwavelength resolution. To illustrate the applications and potentials of the results, the performance of bent multi-wire endoscopes is characterized using full wave numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we present the formulation and a method for solving the problem of freezing living biological tissue with a flat circular cryoapplicator. The model is a two-dimensional boundary-value problem of Stefan type with nonlinear heat sources of a special type that provide the actually observed spatial localization of the temperature field. Some results of computer simulation are presented. [ABSTRACT FROM AUTHOR]

In this paper, we present a method of computer calculation of Green functions in the form of generalized power series for third-order linear differential equations admitting regular singularities. For specific boundary-value problems, we construct Green functions by using the software proposed. [ABSTRACT FROM AUTHOR]

Many problems of modern laser physics are governed by equations or sets of equations in an unbounded domain. For solving these problems using the computer simulation, it is necessary to introduce the bounded domain, which size should be extended significantly to avoid the spurious wave reflection from the domain boundaries. Alternatively, the artificial (non‐reflective or transparent) boundary conditions should be stated. This approach is also effective for enhancing computation performance at the numerical solution of the nonlinear partial differential equations (PDEs). In the current paper, we investigate the laser pulse propagation in a semiconductor, governed by the Schrödinger equation, under the appearance of spatio‐temporal contrast structures of semiconductor characteristics. Their evolution is described by a set of PDEs. The optical pulse is partly reflected from the boundaries of these structures. Consequently, even a little reflection of the optical pulse from the artificial boundaries can essentially distort the numerical solution. Thus, these artificial boundary conditions must possess a high quality to minimize their reflection coefficients. With this aim, we propose the method for constructing adaptive artificial boundary conditions and discuss their advantages. [ABSTRACT FROM AUTHOR]

The immersed boundary method (IBM) is a well-suited tool for the direct numerical simulation of flows with dense particle suspensions, which feature strong and complex flow-particle and particle-particle interactions. With the aim to model such flows, this paper proposes to extend the Regularised Discrete Momentum Forcing (RDMF-) IBM of Abdol Azis et al. (2018) to immersed boundaries (IBs) whose motion is coupled to the flow. A modification to the direct-forcing formulation, resulting in an offset of the imposed no-slip boundary from a moving immersed boundary, is proposed. This offset is exploited in an iterative strong flow-particle coupling scheme, where the boundary forces are applied at the location of the IB known from the previous time level, while correctly enforcing the no-slip condition at the new location of the IB. This avoids having to reconstruct the interpolation and spreading stencils for every linear iteration of the flow-particle coupling, therefore reducing the computational load of the method. A technique to ensure the stable modelling of flows involving light particles is also presented and is shown to stably cope with a wide range of particle-fluid density ratios. The framework is validated by comparing the results of the simulation of a single sedimenting sphere with published experimental results. Simulations of the fluidisation of heavy rigid particles, as well as of the ascent of closely packed light particles, are also presented. Use of the radius retraction procedure, to compensate for the diffuse representation of the smooth-interface IBM, is demonstrated to consistently yield significant improvements for moving IB cases with low to intermediate Reynolds numbers. The present framework shows good stability properties for a wide range of flow regimes with concentrated particle suspensions. [ABSTRACT FROM AUTHOR]

In this paper, the authors study the forward and inverse problems for a fractional boundary value problem with Dirichlet boundary conditions. The existence and uniqueness of solutions for the forward problem is first proved. Then an inverse source problem is considered. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of sign changing periodic solutions for the Chafee-Infante equation , subject to homogeneous Dirichlet boundary condition. If , where is the m-th eigenvalue of the one-dimensional Laplacian, then there exists a periodic solution, whose zero number is less than or equal to . Specially, if is independent of t, there exists sign changing stationary solutions. Furthermore, numerical simulations verify our result. In some sense, we generalize the result of Bartsch, Polácik and Quittner [Theorem 1.8] 1 to the case of Chafee-Infante equation. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to propose a hybrid optimization approach with high level of solving precision and efficiency for endo-atmospheric ascent trajectory planning of launch vehicles.Design/methodology/approach Based on the indirect method of optimal control problems, the optimal endo-atmospheric ascent problem with path constraints and final condition constraints is transformed into a Hamiltonian two point boundary value problem (TPBVP). An advanced Gauss pseudo-spectral method is applied to change the Hamiltonian TPBVP into a system of nonlinear algebraic equations, which is solved by a modified Newton method. To guarantee the convergence of the solution, analytical initial guess technology and homotopy technology are also introduced. At last, simulation tests are made.Findings The hybrid approach for optimal endo-atmospheric ascent trajectory planning has both fast convergence rate and high solution precision. The simulation results indicate that not only the proposed method is feasible but also it is better than the indirect method, which is a most popular approach for solving the optimal endo-atmospheric ascent problem. Given the same degree of solution accuracy, the new method consumes quite less time on the CPU than that of the indirect method.Practical implications The new optimization approach has high level of both solution accuracy and efficiency. It can be used in rapid trajectory designing, on-line trajectory planning and closed-loop guidance of launch vehicles. Also, the proposed Gauss pseudo-spectral method in this paper is a new and efficient method for solving general TPBVPs.Originality/value The paper provides a new hybrid optimization method for rapid endo-atmospheric ascent trajectory planning of launch vehicles. [ABSTRACT FROM AUTHOR]

In this paper, we present a gate capacitance model for the aligned carbon nanotube (CNT) array-based FETs with arbitrary distribution of separations between CNTs. By using conformal mapping, the boundary conditions of a capacitor formed by a CNT and a finite planar gate electrode are transformed into a symmetrical circular geometry that simplifies the formulation of the capacitance. The derived model shows improved accuracy compared with the existing models in most of the practical situations, including closely packed CNTs with strong electric field screening, nonuniform CNT spacing, endpoint capacitance with finite gate electrode termination, and substrate material with a different dielectric constant from the gate dielectric. The model has been extensively verified by numerical simulation. To demonstrate the usefulness of the model, it has been applied to predict the gate capacitance of a CNTFET with an experimentally measured CNT spacing distribution. [ABSTRACT FROM PUBLISHER]

In order to develop a computationally efficient implementation of the maximally permissive deadlock avoidance policy (DAP) for complex resource allocation systems (RAS), a recent approach focuses on the identification of a set of critical states of the underlying RAS state-space, referred to as minimal boundary unsafe states. The availability of this information enables an expedient one-step-lookahead scheme that prevents the RAS from reaching outside its safe region. The work presented in this paper seeks to develop a symbolic approach, based on binary decision diagrams (BDDs), for efficiently retrieving the (minimal) boundary unsafe states from the underlying RAS state-space. The presented results clearly demonstrate that symbolic computation enables the deployment of the maximally permissive DAP for complex RAS with very large structure and state-spaces with limited time and memory requirements. Furthermore, the involved computational costs are substantially reduced through the pertinent exploitation of the special structure that exists in the considered problem. [ABSTRACT FROM PUBLISHER]

Many congestion charging projects charge traffic only within part of a day with predetermined congestion tolls. Demand peaks have been witnessed just around the time when the charge jumps up or down. Such peaks may not be desirable, in particular (a) when the resulting peaks are much higher than available capacities; (b) traffic speeding up to get into the charging zone causes more incidents just before the toll rises up to a higher level; or (c) traffic slowing down or parking on the roadside decreases road traffic throughput just before the toll falls sharply. We term these types of demand peaks 'boundary effects' of congestion charging. This paper investigates these effects in a bottleneck scenario and aims to design charging schemes that reduce undesired demand peaks. For this purpose, we observe and analyse the boundary effects utilising a bottleneck model under three types of toll profiles that are indicative of real charging schemes. The first type maintains a constant toll across the charging period, the second type allows the toll to increase from zero to a given maximum level and then decrease back to zero and the third type allows the toll to rise from zero to a given maximum level, remain at this level for a fixed period and then fall down to zero. This investigation shows that all three types of toll profiles can produce greater boundary peak demands than the bottleneck capacity. A significant contribution of this work is that instead of designing an optimal traffic congestion pricing scheme we analyse how existing sub-optimal congestion pricing schemes could be improved and suggest how observed problems may be overcome. Hence, we propose a set of extra requirements to supplement existing principles or requirements for design and implementation of congestion charging, which aim to reduce the adverse consequences of boundary effects. Concluding remarks are made on implications of this investigation for the improvement of existing congestion charging projects and for future research. [ABSTRACT FROM AUTHOR]

The main parameters characterizing the process of deformation of solids are displacements, strain and stress tensors. From the point of view of the strength and reliability of the structure and its elements, researchers and engineers are mainly interested in the distribution of stresses in the objects under study. Unfortunately, all boundary value problems are formulated and solved in solid mechanics mainly with respect to displacements, or an additional stress functions. And the required stresses are calculated from known displacements or stress functions. In this case, the accuracy of stress calculation is strongly affected by the error of numerical differentiation, as well as the approximation order of the boundary conditions. The formulation of boundary value problems directly with respect to stresses or strains allows to increase the accuracy of stress calculation by bypassing the process of numerical differentiation. Therefore, the present work is devoted to the formulation and numerical solution of boundary value problems directly with respect to stresses and strains. Using the well-known Beltrami-Miechell equation, and considering the equilibrium equation as ah additional boundary condition, a boundary value problem (BVP) is formulated directly with respect to stresses. In a similar way, using the strain compatibility condition, the Beltrami-Mitchell type equations for strains are written. The finite difference equations for two-dimensional BVP are constructed and written in convenient a form for the use of iterative method. A number of problems on the equilibrium of a rectangular plate under the action of various loads applied on opposite sides are numerically solved. The reliability of the results is ensured by comparing the numerical results of the 2D elasticity problems in stresses and strains, and with the exact solution, as well as with the known solutions of the plate tension problem under parabolic and uniformly distributed loads. [ABSTRACT FROM AUTHOR]

In the present paper, we analyze a coupled system of nonlinear three point boundary value problems (BVPs) consisting of a coupled system of higher order hybrid sequential differential equations formulated by fractional operators. We study several new conditions in the direction of existence theory for solutions of the given hybrid system under the weaker hypotheses based on the method of measure of non-compactness in degree theory. The required conditions confirming the uniqueness and stability are derived in relation to the coupled system of hybrid sequential BVPs. Lastly, we extend our hybrid sequential system to a real mathematical model of typhoid treatment with four compartments and by deriving numerical schemes for this generalized hybrid sequential system, we analyze the variations of different fractional orders and their impact on dynamical behaviors of the mentioned hybrid system of typhoid model. [ABSTRACT FROM AUTHOR]

The paper presents numerical simulation of polycrystalline titanium deformation in terms of the crystal plasticity theory. Based on the experimental data, a three-dimensional polycrystalline model is generated by a method of step-by-step packing. Constitutive relations for the deformation behavior of grains are based on the crystal plasticity theory with regard to the crystalline structure and dislocation glide in hexagonal closepacked crystal lattices. The boundary value problem of elastoplastic deformation is solved numerically using the finite element method. The proposed model is tested by elastoplastic deformation of titanium single crystals having different orientation. The proposed model is used to study the influence of the crystallographic orientation on localized plastic deformation in polycrystals. [ABSTRACT FROM AUTHOR]

In this paper we investigate the application of the localized method of fundamental solutions (LMFS) for solving three-dimensional inhomogeneous elliptic boundary value problems. A direct Chebyshev collocation scheme (CCS) is employed for the approximation of the particular solutions of the given inhomogeneous problem. The Gauss–Lobatto collocation points are used in the CCS to ensure the pseudo-spectral convergence of the method. The resulting homogeneous equations are then calculated by using the LMFS. In the framework of the LMFS, the computational domain is divided into a set of overlapping local subdomains where the traditional MFS formulation and the moving least square method are applied. The proposed CCS-LMFS produces sparse and banded stiffness matrix which makes the method possible to perform large-scale simulations on a desktop computer. Numerical examples involving Poisson, Helmholtz as well as modified-Helmholtz equations (with up to 1,000,000 unknowns) are presented to illustrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In the present study, numerical simulations of two-dimensional steady-state incompressible Newtonian fluid flow in one-sided square and two-sided deep lid driven cavities under the aspect ratio K = 1, 4, 6 are reported. For the one-sided lid driven cavity, the upper wall is moved to the right with up to 5000 Reynolds numbers under a grid size of up to 501 × 501. This lends support to previous findings in the literature with Ghia et al.’s results. Three cases are used in this article for the two-sided deep lid driven square cavity specifically. In these cases, the top and lower walls are moved to the right, while the left and right walls remain fixed up to at high Reynolds numbers (5000) under the grid size of up to 201×201. All possible flow solutions are studied in the present article, and flow bifurcation diagrams are constructed as velocity profiles and streamline contours for the same Reynolds number using a finite volume SIMPLE technique. The work done in this paper includes flow properties such as the location of primary and secondary vortices, velocity components, and numerical values for benchmarking purposes, and it is in excellent agreement with previous findings in the literature. A PARAM Shavak, high-performance computing (HPC) computer, was used to execute the calculations. [ABSTRACT FROM AUTHOR]

An analytical solution is presented for line source excitation of a cylinder with perfect electromagnetic conductor (PEMC) core which is coated with multilayer anisotropic materials. Exact solution is presented using analytical relations for scattering from cylindrical structures. For multilayer structures, we have to calculate the inverse of a matrix which is sparse, thus, we use recursive relations to calculate the fields. A recursive relation for solving the problem with PEMC boundary condition is presented. Finally, some examples are given using this method and the results are compared and validated with the simulation results and other works. The advantage of analytical relation proposed in this paper is much less run time compared to numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, using the Nagel-Schreckenberg model, we numerically investigate the probability of entering/circulating car accidents to occur at single-lane roundabout under the expanded open boundary. The roundabout consists of N on-ramps (respectively, off-ramps). The boundary is controlled by the injecting rates and the extracting rate . The simulation results show that, depending on the injecting rates, the car accidents are more likely to happen when the capacity of the rotary is set to its maximum. Moreover, we found that the large values of rotary size L and the probability of preferential are reliable to improve safety and reduce accidents. However, the usage of indicator, the increase of and/or N provokes an increase of car accident probability. [ABSTRACT FROM AUTHOR]