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The paper presents a proposed mechanism, RPCR, for the coupling of two shafts with crossed axes. For the analytical kinematics, the Hartenberg–Denavit methodology cannot be applied due to the planar pair occurrence. To apply the screw theory, the planar pair should be replaced by an assembly of cylindrical pairs, but this is also cumbersome. This work proposes an analytical solution obtained from the structural condition of planar joint based on the formulated expressions with respect to adequately chosen reference frames. A system of trigonometrical equations is obtained, but confusions may occur from classical solving; then, this paper presents the methodology with the correct approach. With the analytical solution for the displacements from the joints found, the conditions required for the constructive parameters of a realistic mechanism are found. The kinematical calculus of the mechanism is presented, and analytical relations are obtained for all relative motions from the pairs of the mechanism. The correctness of the analytical solutions is validated by the results of a numerical simulation. [ABSTRACT FROM AUTHOR]

Simulation tools are important to investigate and predict mobility and the destructive potential of gravitational mass flows (e.g., snow avalanches). AvaFrame – the open avalanche framework – offers well-established computational modeling approaches, tools for data handling and analysis, and ready-to-use modules for evaluation and testing. This paper presents the theoretical background, derivation, and model verification for one of AvaFrame's core modules, the thickness-integrated computational model for avalanches with flow or mixed form of movement, named com1DFA. Particular emphasis within the description of the utilized numerical particle–grid method is given to the computation of spatial gradients and the accurate implementation of driving and resisting forces. The implemented method allows us to provide a time–space criterion connecting the numerical particles, grid, and time discretization. The convergence and robustness of the numerical implementation is checked with respect to the spatiotemporal evolution of the flow variables using tests with a known analytical solution. In addition, we present a new test for verifying the accuracy of the numerical simulation in terms of runout (angle and distance). This test is derived from the total energy balance along the center-of-mass path of the avalanche. This article, particularly in combination with the code availability (open-source code repository) and detailed online documentation provides a description of an extendable framework for modeling and verification of avalanche simulation tools. [ABSTRACT FROM AUTHOR]

Input model bias is the bias found in the output performance measures of a simulation model caused by estimating the input distributions/processes used to drive it. When the simulation response is a nonlinear function of its inputs, as is usually the case when simulating complex systems, input modelling bias is amongst the errors that arise. In this paper, we introduce a method that recalibrates the input parameters of parametric input models to reduce the bias in the simulation output. The proposed method is based on sequential quadratic programming with a closed form analytical solution at each step. An algorithm with guidance on how to practically implement the method is presented. The method is shown to be successful in reducing input modelling bias and the total mean squared error caused by input modelling error. Summary of Contribution: This paper furthers the understanding and treatment of input modelling error in computer simulation. We provide a novel method for reducing input model bias by recalibrating the input parameters used to drive a simulation model. A sequential quadratic programming approach with an explicit solution is provided to recalibrate the input parameters. The method is therefore computationally inexpensive. An algorithm outlining our proposed procedure is provided within the paper. An evaluation of the method shows the method successfully reduces input model bias and may also reduce the mean squared error caused by input modelling in the output of a simulation model. [ABSTRACT FROM AUTHOR]

Compared with non-redundant manipulators, the self-motion of 7-DOF redundant manipulators results in an infinite number of inverse kinematics solutions for a desired end-effector pose. This paper proposes an efficient and accurate analytical solution for inverse kinematics of SSRMS-type redundant manipulators. This solution is applicable to SRS-type manipulators with the same configuration. The proposed method involves introducing an alignment constraint to restrain the self-motion and to decompose the spatial inverse kinematics problem into three independent planar subproblems simultaneously. The resulting geometric equations depend on the part of the joint angles, respectively. These equations are then computed recursively and efficiently using the sequences of (θ 1 , θ 7) , (θ 2 , θ 6) , and (θ 3 , θ 4 , θ 5) , generating up to sixteen sets of solutions for a given desired end-effector pose. Additionally, two complementary methods are proposed for overcoming the possible singular configuration and judging unsolvable poses. Finally, numerical simulations are conducted to investigate the performance of the proposed approach in terms of average calculation time, success rate, average position error, and the ability to plan a trajectory with singular configurations. [ABSTRACT FROM AUTHOR]

This work builds an isobaric steady-state fluid analytical-physical model of the plasma conduction region in a conical target. The hydrodynamic instability in the double-cone ignition scheme[] for inertial confinement fusion (ICF) proposed by Zhang is studied with the built model. With this idealized model, the relevant parameters, such as density, temperature, and length of the plasma in the conduction region of the conical target under long-pulse conditions are given. The solution of the proposed analytical model dovetails with the trend of the numerical simulation. The model and results in this paper are beneficial for discussing how to attenuate Rayleighâ€"Taylor instability in ICF processes with conical and spherical targets. [ABSTRACT FROM AUTHOR]

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension 1 < d < 2. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in t1/d where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model. [ABSTRACT FROM AUTHOR]

Simulation of the failure process of non-intact rock containing initial cracks, voids, and other discontinuities is a research hotspot in rock mechanics and geotechnical engineering. The damage smear method has attracted wide attention due to its ability to realistically depict the complete failure processes of rock from the microscopic to the macroscopic scale. However, when portraying pre-existed discontinuities, the damage smear method suffers from major difficulties such as mesh dependency and stress singularity. To overcome the limitations of current methodology, this paper proposes a novel non-break modeling strategy inspired by the extended finite element method for dealing with embedded discontinuities, in which the discontinuity of the physical fields across crack faces or the void boundary, as well as the stress singularity at the crack tip, can be characterized by introducing appropriate enrichment functions, and the penalty method is used to impose frictional contact constraints. Applications of the combined method of the improved modeling strategy and damage smear analysis to laboratory-scale and engineering-scale numerical examples show a satisfactory approximation with the analytical solution or experimental observations, indicating that the current modeling strategy can further improve computational accuracy while retaining the advantages of the damage smear method. [ABSTRACT FROM AUTHOR]

Finite element method is an important method to solve mathematical problems in engineering. Many mathematical equations are difficult to solve, but it becomes very simple after using the finite element method. In this paper, the finite element method is applied to the calculation of gravity anomaly. First, the variational equation of gravity anomaly calculation is established, and then the gravity anomaly value ten times the distance away from the anomaly body is used as the boundary condition. By comparing the gravity anomaly obtained by solving the stiffness matrix with the analytical solution, it can be found that the method in this paper has high accuracy. Finally, the model of Jinchuan copper nickel deposit is used for calculation, and the calculated gravity anomaly field is inverted with Growth3D. It can be found that the inversion result is very close to the model, which verifies the effectiveness of the algorithm in this paper. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical solution for bond-slip behavior of SRC interface based on experiment, numerical simulation, and theoretical derivation. Push-out tests of five specimens were firstly carried out, based on which, the simplified bond-slip model was proposed. The specimen was fabricated using the Q345H-shape steel (400 mm × 200 mm×13 mm × 8 mm) and C50 concrete (350 mm × 600 mm) with a bonding length of 500 mm. A FE model was established based on the bond-slip model to analyze the nonlinear bonding stress that are difficult to obtain from the experiment. The research shows that although the bonding stress in the elastic stage is not uniformly distributed, it is basically uniformly distributed when the ultimate bearing capacity is reached. It proves that assuming the average interfacial bonding stress under ultimate load to replace the maximum bonding stress is reasonable, which is crucial for designer to estimate interface bearing capacity and maximum bonding stress. Moreover, five different stages were obtained by the FE model analysis and the theoretical equations of bonding stress nonlinear distribution were obtained based on the boundary condition of each stage. The theoretical solution clearly showed the relationship between interface nonlinear stress distribution and influencing parameters including the bond area, elasticity modulus of material, section area of specimen, bond-slip constitutive model, and the external load. Based on the theoretical model, the influences of different parameters can be directly obtained without conducting further experiments and establishing different FE models. • The simplified bond-slip model was proposed and nonlinear distributiion of interfacial bonding stress was analyzed. • Assuming the average interfacial bonding stress under ultimate load to replace the maximum bonding stress is reasonable. • Corresponding analytical formulas for the interfacial stress in five different stages were established, respectively. • The theoretical solution showed the quantitative relationship between interface nonlinear stress and influencing parameters. [ABSTRACT FROM AUTHOR]

The work in this paper concerns the study of different approximations for one-dimensional one-phase Stefan-like problems with a space-dependent latent heat. It is considered two different problems, which differ from each other in their boundary condition imposed at the fixed face: Dirichlet and Robin conditions. The approximate solutions are obtained by applying the heat balance integral method (HBIM), the modified HBIM and the refined integral method (RIM). Taking advantage of the exact analytical solutions, we compare and test the accuracy of the approximate solutions. The analysis is carried out using the dimensionless generalised Stefan number (Ste) and Biot number (Bi). It is also studied the case when Bi goes to infinity in the problem with a convective condition, recovering the approximate solutions when a temperature condition is imposed at the fixed face. Some numerical simulations are provided in order to assert which of the approximate integral methods turns out to be optimal. Moreover, we pose an approximate technique based on minimising the least-squares error, obtaining also approximate solutions for the classical Stefan problem. [ABSTRACT FROM AUTHOR]

Abstract This paper conducts numerical studies of optical solitons with Lakshmanan–Porsezian–Daniel model having spatio-temporal dispersion. A newly proposed version of the well-known Adomian's decomposition method is applied to secure numerical simulations of the recently reported analytical soliton solutions. The focus of this paper stays with bright soliton solutions to the model. [ABSTRACT FROM AUTHOR]

Abstract This paper presents results from a series of numerical modeling tests conducted with the objective of developing a computational framework for studying rock burst events. A commercially available distinct element code with its explicit time-stepping scheme is adopted for modeling the initial quasi-static and the subsequent dynamic response of rock burst in compression and shear. Ground reaction curves are introduced to discuss criteria for stability of a failure through stress analyses. Energy balance equations are analyzed for assessing the rock burst intensity by estimating radiated seismic energy once conditions of instability emerge. Two methods are discussed for estimating radiated seismic energy: tracking of the energy conversion during failure; recording the kinetic energy that is damped by mechanical damping schemes. Modeling approach and methodologies for studying compressive-type rock burst are developed and calibrated against available analytical solutions with respect to radiated seismic energy and excavation convergence. Factors participating in the intensity of rock burst in compression are examined by modeling a rectangular tabular excavation supported by a single pillar with ductile, semi-brittle, and brittle failure responses under different compressive loading. A shear-type rock burst along a strike-slip fault model is simulated and modeling approach is calibrated by checking the resulting slip distribution, radiated seismic energy, and seismic moment against analytical solutions. Factors contributing to the occurrence and intensity of shear-type rock burst are explored by simulating different slip scenarios under different loading conditions. With presented analyses, this paper provides a computational framework calibrated for studying rock burst events and, as a reference for treatment of more complex cases, shows how Young's modulus of the rock, failure stress drop, rock brittleness, and slip-weakening behaviors of faults govern the rock burst occurrence and intensity. [ABSTRACT FROM AUTHOR]

This paper proposes analytical solutions to optimal underactuated spacecraft formation reconfiguration in elliptic orbits, without either the radial or in-track thrust. For either underactuated case, the dynamical model of underactuated formation reconfiguration was developed, based on which the system controllability and reconfiguration feasibility then were analyzed. By using the indirect optimization method, a detailed optimization procedure was designed, and the optimal trajectory of formation reconfiguration was derived analytically for the underactuated cases. A fully actuated optimal reconfiguration scheme was introduced to make comparisons. Numerical simulations indicated that the proposed optimal underactuated reconfiguration schemes can manage formation reconfiguration with a control cost similar to that of the fully actuated scheme, even in the absence of radial or in-track thrust. Numerical comparisons with existing nonoptimal reconfiguration schemes further verified that the proposed optimal schemes can perform underactuated formation reconfiguration in an energy-optimal way. [ABSTRACT FROM AUTHOR]

P-wave conversion to slow diffusion (Biot) modes at mesoscopic (small-scale) inhomogeneities in porous media is believed to be the most important attenuation mechanisms at seismic frequencies. This study considers three periodic thin layers saturated with gas, oil, and water, respectively, a realistic scenario in hydrocarbon reservoirs, and perform finite-element numerical simulations to obtain the wave velocities and quality factors along the direction perpendicular to layering. The results are validated by comparison to the Norris-Cavallini analytical solution, constituting a cross-check for both theory and numerical simulations. The approach is not restricted to partial saturation but also applies to relevant properties in reservoir geophysics, such as porosity and permeability heterogeneities. This paper considers two cases, namely, the same rock skeleton and different fluids, and the same fluid and different dry-rock properties. Unlike the two-layer case (two fluids), the results show two relaxation peaks and the agreement between numerical and analytical solutions is excellent. [ABSTRACT FROM AUTHOR]

In this paper, we exploit an idea of nonlinear modal series method to investigate the effects of modal interaction in the one-cycle controlled (OCC) double-input SEPIC DC–DC converter. Based on the proposed nonlinear averaged model, the analytical approximate solutions are obtained to characterize the dynamic response characteristic of the transient behaviors in the double-input SEPIC converters. The fundamental modal analysis is utilized to identify the dominant oscillation modes and discover the relationship between parameters, fundamental modes and state variables. Furthermore, the second-order interaction indices are proposed to uncover the underlying mechanism of nonlinear interaction behaviors. In particular, the correlation between parameters and modal interaction are derived to optimize the transient process of the double-input SEPIC converters. Finally, numerical simulations are performed to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper develops an improved disk discontinuous deformation analysis (DDDA) model to simulate mixing particles in rotary drums. The original DDDA is improved by developing a disk-movable line segment contact model to motivate the constant movements of the disks during the mixing operation. The analytical solution of the movement of a single disk in a rotary drum is achieved by building a force analysis model, and the improved DDDA is validated by comparing this analytical solution with the proposed numerical simulation. Then, the improved DDDA is utilized to simulate mixing 8805 disks in a rotary drum, during which the influences of rotational speed and layouts of stirring blades are studies. Model performance shows that, the improved DDDA is a feasible tool to simulate the particle mixing process in rotary drums, which may optimize schemes for mixing particles and designing mixing equipment in industry. Unlabelled Image • An improved DDDA model for simulating mixing particles in rotary drums is developed. • A disk-movable line segment contact model is developed. • The analytical solution of the movement of a single disk in rotary drum is achieved. • The validity of the improved DDDA is demonstrated. • The ability of the improved DDDA in simulating mixing disks in rotary drums is verified. [ABSTRACT FROM AUTHOR]

In this paper, we derive analytical solutions of the Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation via symbol calculation approach. Applying the exp − φ z -expansion method, we achieve the trigonometric, exponential, hyperbolic, and rational function solutions for the CDGSK equation. By choosing the appropriate parameters, we give some computer simulation to the analytical solutions of the CDGSK equation. [ABSTRACT FROM AUTHOR]

The present paper deals with the numerical solution of space–time-fractional reaction–diffusion problems used to model some complex phenomena that are governed by dynamic of anomalous diffusion. The time- and space-fractional reaction–diffusion equation is modeled by replacing the first-order derivative in time and the second-order derivative in space, respectively, with the Caputo and Riesz operators. We propose an adaptable numerical scheme for the approximation of the derivatives. Accuracy of the method is justified by reporting both the maximum error and relative error in 2D with analytical solutions given. The effectiveness and applicability of the proposed methods are tested on two of practical problems that are of current and recurring interests in one and two dimensions to cover pitfalls that may arise. [ABSTRACT FROM AUTHOR]

The distribution width of piezoelectric charges induced by strain in a junction is one of important parameters for piezotronic devices. Capacitance-voltage characteristics based on piezotronic MIS structure can be used to estimate the distribution width of piezoelectric charges, which can be applied to piezotronic and piezo-phototronic devices. Third generation semiconductors for piezotronics and piezo-phototronics, such as ZnO and GaN, have both piezoelectric and semiconducting properties. Piezotronic devices normally exhibit high strain sensitivity because strain-induced piezoelectric charges control or tune the carrier transport at junctions, contacts and interfaces. The distribution width of piezoelectric charges in a junction is one of important parameters. Capacitance-voltage (C-V) characteristics can be used to estimate the distribution width of strain-induced piezoelectric charges. Piezotronic metal–insulator-semiconductor (MIS) has been modelled by analytical solutions and numerical simulations in this paper, which can serve as guidance for C-V measurements and experimental designs of piezotronic devices. [ABSTRACT FROM AUTHOR]

• Robust algorithms with weighted L1-norm minimization for 1-bit CS are presented. • Analytical solution is derived for the resulting problem. • Representative ways are introduced to calculate the weights. • It is shown that the weights can be either positive or negative. In recent years, one-bit compressive sensing (1-bit CS) has been attracting much attentions owing to its advantages of low system complexity and outstanding environmental robustness. Nevertheless, how to recover the signal from 1-bit measurements still needs deeper investigation. Inspired by the excellent performance of weighted ℓ 1 -norm minimization in conventional CS techniques, this paper presents robust algorithms with weighted ℓ 1 -norm minimization for 1-bit CS. Specifically, it is first shown that the analytical solution for Passive model can be straightforwardly extended to the weighted case, and the weights are not necessarily positive. On this basis, two representative ways are introduced to calculate the weights. Under the weighted ℓ 1 -norm minimization framework, the proposed weighted ℓ 1 -norm algorithms can be easily implemented. Numerical simulations show that the recovery fidelity can be effectively improved with the weighted ℓ 1 -norm minimization techniques. [ABSTRACT FROM AUTHOR]

• Linear and nonlinear positive position feedback controllers are investigated. • Closed-form expressions of the optimal parameters of the controllers are obtained. • The nonlinear controller outperforms its linear counterpart for a Duffing oscillator. • The analytical study is validated experimentally. This paper investigates the potential of using a nonlinear positive position feedback controller for vibration mitigation of a Duffing oscillator. The proposed controller is designed based on the principle of similarity which states that anti-vibration devices should be governed by the same equations as those of the host structure. Closed-form expressions for the H ∞ optimal control parameters that minimise the maximal response of the structure are firstly derived for the linear positive position feedback controller and then extended to the nonlinear counterpart. The harmonic balance method is employed to approximate the analytical solutions. Both numerical simulations and experimental validations are performed to demonstrate the proposed control strategy. [ABSTRACT FROM AUTHOR]

The aim of the paper is to present selected examples of queueing theory applications to problems in the military and defence domain, to mark the 110th anniversary of queueing theory. The intention was to find and present more works from domestic authors published in a longer period in order to promote the theory in the domestic military and defence circles thus motivating future research related to waiting lines phenomena. In dealing with military queueing phenomena, researchers are usually faced with some specific requirements which involve a multidisciplinary approach. In the queueing theory community, it is recognized that solutions to queueing problems could be reached in three ways: by analytical, numerical and simulation methods. Not all queueing problems are solvable by analytics or by numerical mathematics and, for such problems in particular, simulation methodology is a resolving tool. [ABSTRACT FROM AUTHOR]

• General propagation lattice Boltzmann model for vc-cKdVB equation is derived. • Chapman–Enskog analysis is given to recover vc-cKdVB equation from our model. • Effects of the free parameters induced in our model are discussed in detail. • Numerical results agree well with analytical solutions. • Our model could be more stable and more accurate than the standard model. In this paper, a general propagation lattice Boltzmann model for a variable-coefficient compound Korteweg-de Vries-Burgers (vc-cKdVB) equation is investigated through selecting equilibrium distribution function and adding a compensation function, which can provide some more realistic models than their constant-coefficient counterparts in fluids or plasmas. Chapman–Enskog analysis shows that the vc-gKdVB equation can be recovered correctly from the present model. Numerical simulations in different situations of this equation are conducted, including the propagation and interaction of the bell-type, kink-type and periodic-depression solitons and the evolution of the shock-wave solutions. It is found that the numerical results match well with the analytical solutions, which demonstrates that the current lattice Boltzmann model is a satisfactory and efficient algorithm. In addition, it is also shown the present model could be more stable and more accurate than the standard lattice Bhatnagar–Gross–Krook model through adjusting the two free parameters introduced into the propagation step. [ABSTRACT FROM AUTHOR]

In this paper, the impact of non-Darcy seepage on the steady seepage field in front of a grouted subsea tunnel face is analysed. Analytical solutions are proposed by combining the three-dimensional (3D) seepage continuity equation, which is expressed in spherical coordinates, with the Hansbo seepage model. These solutions, which are also suitable for calculating the hydraulic head distribution in front of the tunnel face without a grouted zone, are verified by a series of numerical simulations. Comparisons show that this study enabled the augmentation of the classical analytical model. Finally, the influence of relevant parameters, including the nonlinear parameters in the Hansbo seepage model, the relative permeability (i.e., k r / k g), and the grouted zone thickness, are investigated. The results show that the exponential parameter m and critical hydraulic gradient i 1 in the Hansbo seepage model have a more significant impact on the water inflow than the water pressure on the grouted zone. Based on the non-Darcy seepage model, the water inflow is lower and the water pressure on the grouted zone is larger than that obtained by Darcy's model. [ABSTRACT FROM AUTHOR]

The stress state in backfilled mine stopes is an important issue to assess the behavior of the interaction between the backfill and the surroundings or barricades. Most previous arching analyses have considered only the vertical backfilled stopes in both 3D and 2D conditions, and the 3D stress distribution that results from the arching effect in inclined mine stopes remains unclear. In this paper, based on the limit equilibrium theory, a 3D stress solution that is applicable to vertical and inclined backfilled stopes is proposed to further examine the arching effect. The solution is validated against an available centrifuge model by changing the inclination of the model. The proposed analytical solution is consistent with the numerical simulations, and it is suggested that neglecting the wall inclination causes one to underestimate the arching phenomenon. In other words, the vertical stresses at the bottom of the stope can decrease when the wall inclination is considered. Hence, when the stope is assumed in plain strain conditions, both the vertical and horizontal stresses exerted on the barricades are overestimated. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a general propagation lattice Boltzmann model for variable-coefficient non-isospectral Korteweg–de Vries (vc-nKdV) equation, which can describe the interfacial waves in a two layer liquid and Alfvén waves in a collisionless plasma, is proposed by selecting appropriate equilibrium distribution function and adding the compensate function. The Chapman–Enskog analysis shows that the vc-nKdV equation can be recovered correctly from the present model. Numerical simulation for the non-propagating one soliton of this equation in different situations is conducted as validation. It is found that the numerical results match well with the analytical solutions, which demonstrates that the current general propagation lattice Boltzmann model is a satisfactory and efficient method, and could be more stable and accurate than the standard lattice Bhatnagar–Gross–Krook model. [ABSTRACT FROM AUTHOR]

Highlights • The analytic solution of the bond stress-slip relationship is presented. • The effect of the loading rate and stirrups are also considered. • The predicted bond strength displays strong correspondence with the experimental results. • The presented bond stress-slip relationship can be used to simulate the bond performance. Abstract This paper presents a three stage bond stress-slip relationship between rebar and concrete under static and dynamic loads, with coordinate values at key points determined by an analytic solution. Based on the elastic mechanic solutions of a thick-walled cylinder under uniform pressure, radial stress and radial slip at the end of the elastic stage is proposed. When concrete cracks, the fictitious crack model of fracture mechanics is used to consider the softening behavior of concrete under tension. The radial stress and radial slip at the partial cracked stage and full cracked stage is presented, and the bond stress is deduced from the radial stress based on the equilibrium of forces. By assuming the rebar between adjacent ribs is a circular truncated cone, the relationship between slip and radial strain is established. Meanwhile, as an additional external constraint in the thick-walled cylinder model, the restraint of stirrups is taken into account. For the dynamic effect, the dynamic tensile strength and elastic modulus of concrete is introduced to consider the effect of the loading rate. The bond strength calculated by the presented model is compared with the experimental results, and the errors are generally within 15%. The presented bond stress-slip relationship is then used to simulate pull-out test specimens, including the effect of stirrups and loading rates by ABAQUS software. The comparison between simulated and experimental results shows that the proposed bond stress-slip relationship can successfully predict the bond stress-slip between rebar and concrete. [ABSTRACT FROM AUTHOR]

This paper presents measurements of the mechanical response of assemblages formed by spheroid particles. Sets of such particles in the form of thin, cylindrical samples were subjected to uniaxial confined compression. The particles were flattened and elongated, with aspect ratios ranging from 0.5 to 2.5. All particles were fabricated using a 3D printer and each had the same volume. Because the particles had well-defined shapes, it was possible to experimentally observe how the mechanical response of the anisotropic and highly constrained samples depended on the elongation of the particles. In particular, we showed how the sample density, lateral pressure ratio, and work done to compact a sample of elongated or flattened particles changed with change in particle aspect ratio. Furthermore, we found that the evolution of packing density in subsequent loading–unloading cycles followed a stretched exponential law regardless of particle aspect ratio. [ABSTRACT FROM AUTHOR]

In this paper, a new explicit, local collision response analysis algorithm is proposed. Its computational cost at each time step is guaranteed to be O(n) in all cases leading to a solution which is faster than most of the previous approaches if the same number of nodes are used. The main contributions of this paper include: (1) forward Lagrange multiplier method is used in virtual simulation for arbitrary collision and for avoiding the undesired penalty coefficient and the singularity problem of the conventional Lagrange multiplier method when explicit time integration is used; (2) local finite element method, a new variation of the conventional finite element method, is introduced to reduce the computational cost to O(n). In the local finite element method, all calculations are performed at the element level (i.e. locally in terms of each finite element) such that no global matrix factorization, inversion, and assembly are required leading to a fast solution. In addition, primitive 4-node tetrahedron elements and the Gauss–Seidel iteration for enforcing the Coulomb friction law at contact surfaces are naturally incorporated into the algorithm in favor of computational efficiency. The experimental results indicate that the proposed approach is capable of capturing all the key features during complex oblique collision of deformable objects at a reasonably fast speed and also matches closely with the well-known analytical solution in solid mechanics. [ABSTRACT FROM PUBLISHER]

In the color gradient lattice Boltzmann model (CG-LBM), a fictitious-density wetting boundary condition has been widely used because of its ease of implementation. However, as we show, this may lead to inaccurate results in some cases. In this paper, a new scheme for the wetting boundary condition is proposed which can handle complicated 3D geometries. The validity of our method for static problems is demonstrated by comparing the simulated results to analytical solutions in 2D and 3D geometries with curved boundaries. Then, capillary rise simulations are performed to study dynamic problems where the three-phase contact line moves. The results are compared to experimental results in the literature (Heshmati and Piri, 2014). If a constant contact angle is assumed, the simulations agree with the analytical solution based on the Lucas–Washburn equation. However, to match the experiments, we need to implement a dynamic contact angle that varies with the flow rate. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the implementation of optimal homotopy asymptotic method to handle the approximate analytical solutions of fractional order partial differential equations. Fractional differential equations have great importance regarding distinct fields of science and engineering. Approximate solutions of space fractional order diffusion model and its various special cases are handled using the innovative proposed method. The space fractional derivatives are described in the Caputo sense. The results obtained by the proposed method are compared with various methods. The proposed method demonstrates excellent accuracy and strength over various methods. [ABSTRACT FROM AUTHOR]

This paper introduces a new iterative scheme for solving the discrete Smoluchowski equation and explores the numerical convergence properties of the method for a range of kernels admitting analytical solutions, in addition to some more physically realistic kernels typically used in kinetics applications. The solver is extended to spatially dependent problems with non-uniform velocities and its performance investigated in detail. [ABSTRACT FROM AUTHOR]

The need for multiple transmit chains poses a major challenge in optical orthogonal frequency division multiplexing (OFDM) system utilising grouped light emitting diodes (LEDs) for the purpose of peak-to-average power ratio (PAPR) reduction. Thus, recent study propose the use of pilot-assisted (PA) electrical PAPR reduction technique to further reduce PAPR and limit the number of transmit chains in the system. This paper presents the application of order statistics to derive the analytical solutions of PAPR distributions in the PA optical OFDM system utilising grouped LEDs. It is shown that the results obtained via analysis are in good agreement with that of computer simulations. [ABSTRACT FROM AUTHOR]

This paper proposes a Bayesian statistics-based analytical solution and a Markov Chain Monte Carlo (MCMC) method-based numerical solution to estimate the credible interval for fraction nonconforming. Both solutions provide a more accurate, reliable, and interpretable estimation of sampling uncertainty and can be used to improve the functionality of automated, nonconforming quality management systems. To reveal how the inherent mathematical mechanism functions for an analytical solution, a step-by-step proof with a calculation example is provided. For the numerical solution, a specialized Metropolis-Hastings algorithm and an illustrative simulation example are provided to elaborate the stochastic processes of the method. An industrial case study, from a pipe fabrication company in Alberta, Canada, is presented to demonstrate the feasibility and applicability of the proposed credible interval estimation methods. Results of the case study indicate that both solutions can accurately and reliably serve the nonconforming quality inference purpose. This research can be implemented as a decision-making tool for credible interval estimation and will provide valuable support for understanding and improving quality performance of automated, nonconforming quality control processes. [ABSTRACT FROM AUTHOR]

Although there are extensive investigations on fiber reinforced polymer (FRP)-strengthened concrete structures, reliable numerical simulation is still one of the major challenges in the analysis of such structures. This paper has successfully developed a rational FRP-to-concrete model based on the 3D rigid body spring model (RBSM). This is the first work to study the bond problem by involving FRP in the 3D RBSM. All the parameters in the developed model are proposed with clear and precise physical meanings and straightforward calculation methods. The simulation results are in good agreement with both the results of tested specimens and analytical solutions. Based on the proposed model, parametric studies are conducted to study the effects of the adhesive-concrete interfacial strength and width factor. From the simulation results, the relationship between the adhesive-concrete interfacial strength and failure mode is revealed. It is also found from the simulation results that the width factor has an upper limit, which is ignored by all the existing models. When the concrete width (b c) is greater than a certain value (e.g., FRP width (b F) + 30 mm in this work), the bond increase due to the width factor is insignificant. [ABSTRACT FROM AUTHOR]

This paper presents a non-hydrostatic model to simulate the generation and propagation of ship waves in the presence of a uniform current. A moving pressure field method is incorporated into the model to represent the movement of a ship hull. Numerical results of ship waves in the presence of a following or an opposing uniform current are compared with those of ship waves without current. The calculated cusp-line angles in the presence of a following or opposing uniform current agree well with analytical solutions. The effects of a following uniform current and an opposing uniform current on the characteristic wave parameters are presented and discussed. The response of the maximum water level elevation to the ship draft is also presented in the presence of a following or an opposing uniform current and is compared with that for ship waves without current. It is found that the maximum water level elevation lateral to the ship hull can be increased by the presence of a following uniform current for a certain range of Froude numbers F r ′ = U s / g h , where U s is the ship speed and h is the water depth. If the uniform current is neglected, the response of the maximum water level elevation to the ship draft in the presence of a following or an opposing current can be underestimated. The present study indicates that the effect of a uniform current should be considered in the analysis of ship waves. • Ship waves in the presence of a uniform current are studied by a non-hydrostatic model. • Effects of a following current on characteristic wave parameters are investigated. • Effects of an opposing current on characteristic wave parameters are investigated. • The response of the maximum water level elevation to the ship draft is discussed. [ABSTRACT FROM AUTHOR]

Traditionally, indirect methods for trajectory optimization start with the non-intuitive guesses of the initial costates, but it is difficult to generate the initial guesses for the low-thrust many-revolution problems. In this paper, a new indirect method with analytical initialization of the costates has been developed for obtaining the minimum-time low-thrust geocentric rendezvous trajectories. The initial guesses of the rendezvous state and costates are initialized by starting with an analytical solution and taking some reduced optimal control problems as transitions. The reduced problems are considered with different independent variables and final conditions, in which the solutions are all equivalent, and one of these problems is easier to solve. In addition, the paper embeds the reduced problem into a switched system, which allows analytical costates evaluation, such that it can be solved efficiently in combination with the orbital averaging technique. The application of the proposed method to the geocentric rendezvous mission from the geostationary transfer orbit to the geostationary orbit is presented. Numerical simulations have shown that the favorable estimations provided by the proposed reduced problem enable a rapid convergence for the many-revolution rendezvous problem. [ABSTRACT FROM AUTHOR]

We study theoretically the generation of a continuous-wave signal by two weakly coupled delay-line oscillators. In such oscillators, the cavity length is longer than the wavelength of the signal. We show by using an analytical solution and comprehensive numerical simulations that in delay-line oscillators, the dynamics of the amplitude response cannot be neglected even when the coupling between the oscillators is weak. Therefore, weakly coupled delay-line oscillators cannot be accurately modeled by using coupled phase-oscillator models. In particular, we show that synchronization between the oscillators can be obtained in cases that are not allowed by coupled phase-oscillator models. We study the stability of the continuous-wave solutions. In delay-line oscillators, several cavity modes can potentially oscillate. To ensure stability, the bandwidth of the delay-line oscillator should be limited. We show that the weakly coupled delay-line oscillator model that is described in this paper can be used to accurately model the synchronization between two weakly coupled optoelectronic oscillators. A very good quantitative agreement is obtained between a comprehensive numerical model to study optoelectronic oscillators and the model results given in this paper. [ABSTRACT FROM AUTHOR]

The egress literature abounds with studies and models of emergency pedestrian evacuation behavior. Each model tries to incorporate more details and features of the crowd movement dynamics to improve its accuracy. This paper combines a relatively simple pedestrian motion model with a position dependent Voter model to study the effects of opinion sharing on crowd evacuation characteristics. Effect of the presence of leaders on the final outcome of the evacuation is studied in detail. An analytical solution for a simplified version of the egress dynamics with opinion exchange is presented, followed by a set of numerical simulations. Interesting findings about the effect of the strength of interaction between individuals, number and distribution of leaders and initial bias of the evacuees on the final distribution of evacuees over available exits, mean number of steps to evacuate, etc. are presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with the estimation of amplitude and phase of an analog multi-harmonic signal based on a series of differential values of the signal. To this end, assuming the signal fundamental frequency is known before hand (i.e., estimated in an independent stage), a complexity-reduced scheme is proposed here, based on the matrix method classically used to estimate the Fourier coefficients. The reduction in complexity is achieved owing to completely new analytical and summarized expressions that enable a quick estimation at a low numerical error. It is applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise root mean square (rms) measurements (for power and energy) of a periodic signal based on the presented signal reconstruction. The paper investigates the errors related to the signal parameter estimation, and there is a computer simulation that demonstrates the accuracy of these algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we have developed an efficient wavelet based approximation method to biofilm model under steady state arising in enzyme kinetics. Chebyshev wavelet based approximation method is successfully introduced in solving nonlinear steady state biofilm reaction model. To the best of our knowledge, until now there is no rigorous wavelet based solution has been addressed for the proposed model. Analytical solutions for substrate concentration have been derived for all values of the parameters δ and SL. The power of the manageable method is confirmed. Some numerical examples are presented to demonstrate the validity and applicability of the wavelet method. Moreover the use of Chebyshev wavelets is found to be simple, efficient, flexible, convenient, small computation costs and computationally attractive. [ABSTRACT FROM AUTHOR]