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In this paper, we present a mathematical model for the 3D △×n memristor-LC circuit network in the fractional-order sense. First, the impedance of the fractional-order 3D circuit network is derived using matrix transform method and difference equation model. Moreover, we extend the concept of saturation time across the memristor to the circuit network and attempt to explore the relationship between the generalized saturation time and the direct voltage across the network in fractional-order sense. In addition, the effects of the time-varying characteristics of the memristor on the fractional-order 3D circuit network are studied. Also, we propose some issues remaining to be addressed in the near future for the network model. Furthermore, the impedance characteristics are specifically analyzed with theoretical analyses and numerical simulations, where many interesting phenomena are discussed. Finally, sensitivity analysis is provided to carefully investigate the effects of various input parameters on the output response of the fractional-order 3D circuit network. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global asymptotic stability of a class of stochastic bidirectional associative memory neural networks with both multiple discrete and distributed time-varying delays. A new criterion of asymptotic stability is derived in terms of linear matrix inequality, which can be efficiently solved by a standard numerical software. An illustrative numerical example is also given to show the applicability and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper reports the emergence of bi-stability in a third-order memristive Wien-bridge oscillator. By transforming the parallel RC feedback network into a series resistor and capacitor (RC) feedback network in the previous non-ideal voltage-controlled memristor emulator, an improved memristor emulator is proposed and its fingerprints are exhibited. And then through introducing the proposed emulator to replace the parallel resistor in the conventional Wien-bridge oscillator, an improved memristor-based third-order Wien-bridge oscillator is constructed. Based on its mathematical model, the initial condition-dependent dynamical behaviour is revealed by theoretical analyses and numerical simulations and further verified by hardware experiments, from which the emergence of bi-stability in the memristive oscillator is well demonstrated. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a non-standard finite difference (NSFD) scheme that can be used to calculate numerical solutions for an epidemic model with vaccination. Here, the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that when, the discretized model preserves positivity and global dynamics of the continuous model. Numerical simulation illustrates the effectiveness of our results. [ABSTRACT FROM PUBLISHER]

This paper presents a numerical analysis of the migration and transformation mechanism of petroleum hydrocarbons (PHs) pollutants in soil. The mathematical model of the solute migration and plant–microbial remediation for PH polluted soil was established. The model was verified by field experimental data. Then, the software Hydrus-1D was employed to simulate the processes of diffusion, adsorption, desorption, microbial degradation, and plant adsorption of PHs in the soil–water system. The process of plant–microbial remediation for PH-contaminated soil was also simulated. The space-time change of PHs in soil was obtained, and the fate and remediation efficiency of PHs in soil were revealed in different remediation conditions. The results indicated that the Hydrus-1D model can adequately simulate the process of plant–microbial remediation. Plant–microbial remediation appears to be more efficient than the application of bacteria orSuaeda salsa. The majority of PH pollutants are degraded in the upper soil levels. For long-chain petro-alkane-contaminated soil, plant–microbial remediation is a more efficient method. A suitable moisture level in soil is important for improving the bioremediation effect of plant–microbial remediation technology. [ABSTRACT FROM AUTHOR]

This paper presents a new numerical model for simulation of granular materials consisting of 3-D spheres bounded by rigid boundaries. The proposed model is based on Three-Dimensional Discontinuous Deformation Analysis (3-D DDA), a numerical method recently developed for simulation of particles in motion. Stiffness and force matrices due to body forces, point loading, inertia forces, and displacement and directional constraints are derived in detail. Moreover, an efficient model for particle contacts in 3-D is presented. In this model, sphere-sphere and sphere-boundary contacts are simply transformed into the form of point-to-plane contacts. Normal and shear contact forces as well as friction force for both sphere-sphere and sphere-plane contact types are derived by vector analysis and the penalty method. The numerical model developed herein is a simple and efficient method that can be easily coded into a computer program. The validity and capability of the model are demonstrated by numerical results obtained for several illustrative examples. Furthermore, some examples are presented and discussed to illustrate the application of the 3-D DDA to particulate media. [ABSTRACT FROM PUBLISHER]

In this paper, an automotive bumper model was used for low-velocity impact tests. During these tests, the reaction forces at the end of shocks and displacements of the joints were measured. After that, a finite element model was created and the impact test was simulated on the computer using ANSYS. The numerical results obtained from the computer simulation were then compared and correlated to the experimental results. Additionally, an analytical calculation of the impact problem was performed and the analytical solutions were also compared to the experimental and the numerical results to further validate the impact tests and computer simulation. Good agreements were obtained through comparing these results and finally, the impact responses of the bumper system under different tests were obtained and verified through the numerical and analytical analyses. [ABSTRACT FROM AUTHOR]

Based on a black box model of a complex system, and on intervals and probabilities describing the known information about the inputs, we want to estimate the system's reliability. This problem is motivated by a number of problem areas, most specifically in engineering reliability analysis under conditions of poor measurement and high complexity of system models. Using the results of tests performed on the system's computer model, we can estimate the lower and upper bounds of the probability that the system is in a desirable state. This is equivalent to using Monte-Carlo sampling to estimate cumulative belief and plausibility values of functionally propagated finite random intervals. In this paper, we prove that these estimates are correct in the sense that under reasonable assumptions, these estimates converge to the actual probability bounds. [ABSTRACT FROM AUTHOR]

Computer models are increasingly used in the design of crash protection systems, yet the experimental data available for benchmarking these models is limited. The goal of this study was to apportion the contributions of the rib cage, internal viscera and flesh to the mechanical response of the thorax by repeated dynamic loading of human cadavers. Three post-mortem human thoraces in three tissue states (intact, denuded and eviscerated) were subjected to dynamic anterior loading using four loading conditions (distributed, single diagonal belt, double belt and hub). The thoraces were significantly stiffer intact than eviscerated or denuded (paired t test p < 0.05). The distributed (598.7 N/cm) and double belt (529.2 N/cm) intact conditions were the stiffest, followed by the single belt (383.5 N/cm) and then the hub (170.0 N/cm). The degree to which the soft tissues influenced the response depended on the loading. For the hub and distributed conditions, the denuded thoraces retained 60% of the intact stiffness, and the eviscerated thoraces retained 30%. The single and double belt conditions were not as sensitive to tissue state (85% and 55%). The two loading conditions that did not engage the shoulder were highly sensitive to removing the soft tissues, while the two conditions that engaged the shoulder were less sensitive. This is important benchmarking data for computational thoracic models. [ABSTRACT FROM AUTHOR]

I discuss here the definition of computer simulations, and more specifically the views of Humphreys, who considers that an object is simulated when a computer provides a solution to a computational model, which in turn represents the object of interest. I argue that Humphreys's concepts are not able to analyse fully successfully a case of contemporary simulation in physics, which is more complex than the examples considered so far in the philosophical literature. I therefore modify Humphreys's definition of simulation. I allow for several successive layers of computational models, and I discuss the relations that exist between these models, the computer, and the object under study. An aim of my proposal is to clarify the distinction between computational models and numerical methods, and to better understand the representational and the computational functions of models in simulations. [ABSTRACT FROM AUTHOR]

A mathematical model of the well resistivity-sounding problem is investigated. The model leads to an inverse problem of identification of the unknown coefficient (conductivity) in an elliptic equation inR2inside a cylinder. The forward problem is formulated as a mixed BVP in axisymmetric cylindrical coordinates. Measured data along the axis of the well are assumed to be available. Owing to the ill-conditioned nature of the inverse problem, a logarithmic transformation is applied to the unknown coefficient, and the inverse problem is studied as a minimization problem for the residual functional. For the radial electrical-sounding case, an effective numerical method is proposed for interpreting the data of a well sounding. The method is implemented for realistic conductivity distributions, with both noise-free and noisy data. [ABSTRACT FROM AUTHOR]

The buoyancy-induced flow generated by a heat source, such as fire in a long square enclosure with single or multiple horizontal vents, has been of interest in the modeling of enclosure fires and heat removal systems for electronic equipment. This flow is studied using numerical methods. A two-dimensional laminar natural convection flow is investigated with the buoyancy term represented by the Boussinesq approximation. The governing equations are solved in the stream function and vorticity formulation using high accuracy finite difference schemes. The effect of single or multiple horizontal vents of different sizes on the induced flow is studied in detail for different Grashof numbers. The results show a significant change in flow behavior for varying vent width at a fixed Grashof number. A bidirectional flow across the vent occurs due to buoyancy, as previously reported in the literature. The results show that the flow becomes more stable with a decrease in the vent width. The critical Grashof number is identified as beyond which the flow becomes unstable, leading to chaotic flow in the partial enclosure. The main focus is on the time-dependent flow, though steady state flow is also obtained at a longer duration of time in most cases. The implications of these results in the modeling of a fire in an enclosed space with horizontal vents are also discussed. [ABSTRACT FROM AUTHOR]

Components in gear pumps usually involve complex geometrical arrangements in order to achieve the desired performance. The use of lumped parametric models is considered the most accurate and effective method for investigation of the associated design issues. In this study, the numerical modelling approach based on the lumped parameters and control volume concepts is reviewed, especially for gear teeth within the meshing zone. To apply the approach to the entire gear pump, control volume concepts are generalized to all gear pockets and flow orifices with some reasonable assumptions. The assumptions include instantaneous angular positions, orifice transitions and imagined control volumes with internal flows. The fluid dynamics and pump performance, which even have the measurement difficulties, can be estimated to investigate and optimize the design parameters of gears by the model. A simulation example and its experimental results of a gear machine are presented to validate the proposed approach in this article. [ABSTRACT FROM AUTHOR]

This article presents numerical simulation of underwater explosions using a one-dimensional 'wedge' model of ANSYS-AUTODYN explicit software for nonlinear dynamics, provided by ANSYS Century Dynamics, Inc. (Canonsburg, PA, USA). Through numerical analysis of a typical underwater TNT explosion problems, the effects of the quadratic and linear viscosity on the key phenomenon of this complicated energetic physical process are conducted. The results show that appropriate values exist for these two viscosities to model the process in given mesh sizes. Based on these preliminary simulations, values of quadratic and linear viscosity, 1 and 0.034, 1 and 0.068 are determined for the ranges of scaled distance from 3 to 10 and 1.5 to 3, respectively. Effects of charge depth, charge mass, and mesh density on the shock wave and bubble pulse parameters are performed for four different explosives, 2,4,5-trinitrotoluene (TNT), H-6, pentolite, and pentaerythritol tetranitrate (PETN). All of the results are compared with empirical equations and show that the ANSYS-AUTODYN software can be used to model and capture the major features of underwater explosion phenomena at acceptable accuracy and timesaving. [ABSTRACT FROM AUTHOR]

The simulation of the delamination process in composite structures is quite complex and requires advanced FE modelling techniques. These techniques are difficult to implement when the modelled structures are industrial-size like helicopter blades and sine-wave crash absorber beams. In order to simplify the damage modelling in complex structure, the development of a solid hexahedron element for composite delamination analysis has been carried out. The 8-node solid is derived from a 20-node hexahedron element and it can be transformed into 2 physically independent 4-node shell elements. This separation into two shells which corresponds to the propagation of delamination process was controlled by a delamination beam criterion. This element simplifies present models and decreases the calculation time that is accepted only for 1D propagation of delamination. In this study a new way of modelling delamination growth is proposed. A delamination criterion based on the Ritz method and plate theory is used to govern the delamination propagation. Experimental tests are carried out on composite structures such as square composite panels in mode I. The crack propagates with an angle of 45 degrees relative to the panel's edge. This test is modelled using the new element. The numerical simulation correlates well with the experimental results. [ABSTRACT FROM AUTHOR]

Manoeuvrability is of great importance for large tankers in the marine industry. Manoeuvring, involving yaw rates and drift velocities, which are not small compared with the forward speed, demands a mathematical model of considerable complexity. A great deal of effort has been devoted to the construction of non-linear mathematical models describing the manoeuvrability of large tankers in deep and confined waters. This study is concerned with the effect of the rudder on the turning dynamics of a specific model for ESSO's 190,000-deadweight-ton (dwt) tankers, whose manoeuvrability performance has been investigated in 1972 using full-scale trial results. The turning or heading response of the tanker depends on the turning moment generated by the rudder, which in turn depends on the flow of water over the surface of the rudder. Unfortunately, the classical model used for representing the flow velocity at the rudder causes the rudder to react too quickly and to a greater magnitude (increased turning moment) than is physically possible for an oil tanker of the size considered. As a result, any control system designed using this “fast” model benefits from the improved speed of reaction and increased turning moment produced by the rudder. Consequently, the controller performance derived from simulation results will be significantly reduced when applied to a real tanker. To compensate for this increase, a new rudder model has recently been proposed in the literature. In this study, a comprehensive validation study of this new model is carried out using the original experimental data presented in 1972. This study provides strong evidence to alert readers interested in marine applications that the standard model used for decades in the literature on ship dynamics is not representative of the motions of a real tanker. The proposed model, on the other hand, is superior over the classical model and provides an accurate description of the physical system. [ABSTRACT FROM AUTHOR]

Quality and reliability design practitioners have utilized Taguchi's methodology of matrix experimentation to generate computer simulation data for characterizing performance variation of product designs. However, the sampling strategy employed renders computer implementation of matrix experimentation cumbersome and statistically invalid. Weaknesses of this approach also include sample size limitation and overestimation of performance variation. An alternative approach that combines Monte Carlo simulation with the strategies of independent sampling across runs and correlated sampling between runs is presented. An application case study shows that the proposed approach constitutes an improvement on the matrix approach with respect to statistical validity and estimation accuracy. [ABSTRACT FROM AUTHOR]