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The paper aims at constructing two different solutions to an elliptic system u ⋅ ∇ u + ( − Δ ) m u = λ F defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers 2D system. A motivation to consider the above system comes from an examination of unusual properties of the linear operator λ sin ⁡ y ∂ x w + ( − Δ ) m w arising from a linearization of the equation about the dominant part of F . We argue that the skew-symmetric part of the operator provides in some sense a smallness of norms of the linear operator inverse. Our analytical proof is valid for a particular force F and for λ > λ 0 , m > m 0 sufficiently large. The main steps of the proof concern finite dimension approximation of the system and concentrate on analysis of features of large matrices, which resembles standard numerical analysis. Our analytical results are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analytical study of initial–boundary value problems for a system of hyperbolic balance laws derived from a repulsive chemotaxis model with logarithmic sensitivity. In the first part of the paper we show that, subject to the Dirichlet boundary conditions, classical solutions exist globally in time for large initial data. Asymptotically in time, the solutions are shown to converge to their boundary data at an exponential rate as time goes to infinity. Numerical simulations are supplied to corroborate the analytical results. The analytic approach developed herein can be utilized to handle a family of initial and initial–boundary value problems of the model and related models with similar mathematical structure. As a demonstration of the effectiveness of our approach, in the second part of the paper we show that, subject to the Neumann–Dirichlet boundary conditions, classical solutions exist and converge to constant equilibrium states for large initial data and for arbitrary values of the chemical diffusion coefficient. This improves a previous result obtained in [30] where the smallness of the chemical diffusion coefficient was required. [ABSTRACT FROM AUTHOR]

Abstract: In circuit simulation, differential-algebraic equations (DAEs) to be solved numerically are obtained through circuit analysis methods. While the modified nodal analysis (MNA) is the most popular method, the hybrid analysis has been shown to have inherent advantage over MNA in terms of index, which is a measure of the numerical difficulty of DAEs. A recent paper of Iwata, Takamatsu, and Tischendorf (2012) has characterized the network structure that leads to DAEs with tractability index zero and one in the hybrid analysis. As a sequel, this paper gives a necessary condition for the hybrid equations to have tractability index at most two. Moreover, we show that this condition is also sufficient for linear time-invariant circuits if dependent sources satisfy a genericity assumption. Since commonly-used circuits fulfill the condition, it is ensured that the hybrid analysis results in a DAE with tractability index at most two in most cases. By combining our results with the previous one, we obtain criteria for tractability index zero/one/two. [Copyright &y& Elsevier]

Abstract: In Kowar (2012) [25] a diffusion model was developed and analyzed that obeys causality, i.e. the speed of propagation of the concentration is finite. In this article we analyze the respective causal backwards diffusion problem. The motivation for this paper is that because real diffusion obeys causality, a causal diffusion model may contain smaller modeling errors than the noncausal standard model and thus an increase of resolution of inverse and ill-posed problems related to diffusion is possible. We derive an analytic representation of the Green function of causal diffusion in the -domain (wave vector-time domain) that enables us to analyze the properties of the causal backwards diffusion problem. In particular, it is proven that this inverse problem is ill-posed, but not exponentially ill-posed. Furthermore, a theoretical and numerical comparison between the standard diffusion model and the causal diffusion model is performed. The paper is concluded with numerical simulations of the backwards diffusion problem via the Landweber method that confirm our theoretical results. [Copyright &y& Elsevier]

In this paper we introduce a numerical scheme which preserves the behavior of solutions to the Kolmogorov Equation as time tends to infinity. The method presented is based on a self-similar change of variables technique to transform the Kolmogorov Equation into a new form, such that the problem of designing structure preserving schemes, for the original equation, amounts to building a standard scheme for the transformed equation. This transformation also has the added benefit of allowing for an exact operator splitting scheme, whereas in the original form a standard operator splitting was only second-order. Finally, we verify the preservation of long time behavior through numerical simulations. [ABSTRACT FROM AUTHOR]

An imprecise probability approach based on evidence theory is proposed for squeal instability analysis of uncertain disc brakes in this paper. First, the squeal instability of the finite element (FE) model of a disc brake is investigated and its dominant unstable eigenvalue is detected by running two typical numerical simulations, i.e., complex eigenvalue analysis (CEA) and transient dynamical analysis. Next, the uncertainty mainly caused by contact and friction is taken into account and some key parameters of the brake are described as uncertain parameters. All these uncertain parameters are usually involved with imprecise data such as incomplete information and conflict information. Finally, a squeal instability analysis model considering imprecise uncertainty is established by integrating evidence theory, Taylor expansion, subinterval analysis and surrogate model. In the proposed analysis model, the uncertain parameters with imprecise data are treated as evidence variables, and the belief measure and plausibility measure are employed to evaluate system squeal instability. The effectiveness of the proposed approach is demonstrated by numerical examples and some interesting observations and conclusions are summarized from the analyses and discussions. The proposed approach is generally limited to the squeal problems without too many investigated parameters. It can be considered as a potential method for squeal instability analysis, which will act as the first step to reduce squeal noise of uncertain brakes with imprecise information. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a new method for choosing the parameters of a Two degree-of-freedom (dof) tuned vibration absorber (TVA) with translational and rotational degrees of freedom is described. The dynamic stiffness approach is used to model the device, which is constrained to move in the translational direction and to rotate. The choice of the parameters involves a procedure similar to that proposed by Den Hartog in the optimization of a single dof TVA, in which the invariant (fixed) points of the frequency response function of the TVA and the host structure are used to determine the stiffness of the TVA for a given mass. In this paper the approach is extended and applied to the design of a 2dof TVA, and a numerical procedure is used to determine the optimum amount of damping. The method is simple and easy to implement. A numerical example is presented to compare the performance of the 2dof TVA designed using the method described here with the optimal 2dof TVA. It is shown that the performances of the TVAs are similar, validating the new approach. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce two numerical methods to get an electric source that gives a specified electromagnetic field some time after the source starts emitting. The first one is called the Time Reversal Method (TRM) and originates from acoustics and the second one is called Linear Combination of Configuration Fields (LCCF) and consists in constructing and solving a linear problem in order to find a possible required source. In this paper, we show on 1D and 2D examples that the last method gives lower relative errors when compared with the time reversal method. [Copyright &y& Elsevier]

In this paper, a new advance in the application of Artificial Neural Networks (ANNs) to the automated diagnosis of misfires in Internal Combustion engines(IC engines) is detailed. The automated diagnostic system comprises three stages: fault detection, fault localization and fault severity identification. Particularly, in the severity identification stage, separate Multi-Layer Perceptron networks (MLPs) with saturating linear transfer functions were designed for individual speed conditions, so they could achieve finer classification. In order to obtain sufficient data for the network training, numerical simulation was used to simulate different ranges of misfires in the engine. The simulation models need to be updated and evaluated using experimental data, so a series of experiments were first carried out on the engine test rig to capture the vibration signals for both normal condition and with a range of misfires. Two methods were used for the misfire diagnosis: one is based on the torsional vibration signals of the crankshaft and the other on the angular acceleration signals (rotational motion) of the engine block. Following the signal processing of the experimental and simulation signals, the best features were selected as the inputs to ANN networks. The ANN systems were trained using only the simulated data and tested using real experimental cases, indicating that the simulation model can be used for a wider range of faults for which it can still be considered valid. The final results have shown that the diagnostic system based on simulation can efficiently diagnose misfire, including location and severity. [ABSTRACT FROM AUTHOR]

This paper is focused on the numerical simulation of the interaction of an ultrasound wave with a bubble. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects. As the volume oscillation of the bubble occurs in a low Mach number regime, a specific care must be paid to the effectiveness of the numerical method which is chosen to solve the compressible Euler equations. Three different numerical solvers, an explicit HLLC (Harten–Lax–van Leer-Contact) solver [48] , a preconditioning explicit HLLC solver [14] and the compressible projection method [21,53,55] , are described and assessed with a one dimensional spherical benchmark. From this preliminary test, we can conclude that the compressible projection method outclasses the other two, whether the spatial accuracy or the time step stability are considered. Multidimensional numerical simulations are next performed. As a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities, a specific velocity/pressure time splitting is proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided, since both the accuracy and the stability of the overall algorithm are enhanced if this new time splitting is used. Finally, the numerical simulation of the interaction of a moving and deformable bubble with a plane wave is presented in order to bring out the ability of the new method in a more complex situation. [ABSTRACT FROM AUTHOR]

This study uses the Rayleigh–Ritz method to derive a dynamic model for the free vibration analysis of a circular cylindrical shell. In particular, explicit expressions for the mass and stiffness matrices are obtained to easily implement a computer simulation under different shell theories and boundary conditions. The dynamic model is constructed according to the Donnell–Mushtari theory, which is fully discussed herein, and then, dynamic models are constructed by using Sanders theory, Love–Timoshenko theory, Reissner theory, Flügge theory, and Vlasov theory. This paper also discusses the use of eigenfunctions of a uniform beam as admissible functions that produce compact expressions for the mass and stiffness matrices. The numerical results indicate that the Donnell–Mushtari theory is not sufficiently accurate to calculate the natural frequencies and that there is no discernible difference between the other shell theories considered in this study. [ABSTRACT FROM AUTHOR]

Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM). [ABSTRACT FROM AUTHOR]

This paper deals with the comparison of Eulerian methods to take into account the capillary contribution in the vicinity of a fluid–fluid interface. Eulerian methods are well-known to produce additional vorticity close to the interface that leads to non-physical spurious currents. Numerical equilibrium between pressure gradient and capillary force for the static bubble test case within a VOF framework has been reached in [35] with the height-function technique [14,35] . However, once the bubble is translated in a uniform flow, spurious currents are maintained by slight errors induced by translation schemes. In this work, two main points are investigated: the ability of Volume of Fluid and Level Set methods to accurately calculate the curvature, and the magnitude of spurious currents due to errors in the calculation of the curvature after advection in both translating and rotating flows. The spurious currents source term is expressed from the vorticity equation and used to discuss and compare the methods. Simulations of gas–liquid Taylor flow at low capillary number show that the flow structure and the bubble velocity can be significantly affected by spurious currents. [ABSTRACT FROM AUTHOR]

The paper investigates elastic waves guided by thick-walled, hollow cylindrical structures. Theoretical, numerical and experimental investigations are presented to facilitate understanding of various wave propagation phenomena in thick-walled cylinders for potential damage detection applications. Semi-analytical analysis of dispersion characteristics is performed, revealing a repetitive pattern of coupled pairs of higher-order longitudinal modes. This behaviour is found to be analogue to terrace-like structures formed by interlacing high-frequency symmetric and antisymmetric plate mode curves. A hyperbolic behaviour of curves and modeshape transitions is observed due to mode coupling. The work presented demonstrates analytically how solutions for a thick-walled hollow cylinder correspond to the Lamb wave theory. The relevant pseudo-symmetry relations for mode displacement patterns are obtained using asymptotic approximations of Bessel functions. Theoretical solutions of dispersion characteristics are compared with numerical simulations that are based on the local interaction simulation approach. The results are validated experimentally using laser vibrometry. [ABSTRACT FROM AUTHOR]

Mechanical structures often consist of active and passive parts, the former containing the sources, the latter the transfer paths and the targets. The active and passive parts are connected to each other by means of links. In this paper, an innovative theoretical model has been developed to achieve the mathematical decoupling of such structures without disassembling the substructures, when the links connecting the structures are resilient enough. This procedure is required to identify components causing a specific Noise, Vibration and Harsh-ness (NVH) problem. The links are regarded as a parallel connection of springs and dampers, ignoring some physical properties. However, the new procedure will provide a powerful construction in which different link models can be investigated. Therefore, this procedure will be called the Link-Preserving, Decoupling Method (LPD method). The absence of a time-consuming physical decoupling procedure distinguishes the LPD method from all known methods such as the classical TPA method. The LPD method is validated by two numerical simulations using linear and nonlinear lumped parameter models and by an experimental case study. [ABSTRACT FROM AUTHOR]

This paper discusses an inverse source problem for time-dependent linear Maxwell's equations. We propose a numerical procedure to compute a current density source that gives a specified electromagnetic field. The efficiency of our method is shown by numerical tests, first in 1D and then we move on to a 3D example with antennas. In that case, we show potential applications for fault detection. [ABSTRACT FROM AUTHOR]

The paper focuses on a theoretical description and numerical evaluation of active and reactive components of sound intensity in enclosed spaces. As the study was dedicated to low-frequency room responses, a modal expansion of the sound pressure was used. Numerical simulations have shown that the presence of energy vortices whose size and distribution depend on the character of the room response is a distinctive feature of the active intensity field. When several modes with frequencies close to a source frequency are excited, the vortices within the room are positioned irregularly. However, if the response is determined by one or two dominant modes, a regular distribution of vortices in the room can be observed. The irrotational component of the active intensity was found using the Helmholtz decomposition theorem. As was evidenced by numerical simulations, the suppression of the vortical flow of sound energy in the nearfield permits obtaining a clear image of the sound source. [ABSTRACT FROM AUTHOR]

A numerical scheme is developed for two- and three-dimensional time-dependent diffusion equations in numerical simulations involving mixed cells. The focus of the development is on the formulations for both transient and steady states, the property for large time steps, second-order accuracy in both space and time, the correct treatment of the discontinuity in material properties, and the handling of mixed cells. For a mixed cell, interfaces between materials are reconstructed within the cell so that each of resulting sub-cells contains only one material and the material properties of each sub-cell are known. Diffusion equations are solved on the resulting polyhedral mesh even if the original mesh is structured. The discontinuity of material properties between different materials is correctly treated based on governing physics principles. The treatment is exact for arbitrarily strong discontinuity. The formulae for effective diffusion coefficients across interfaces between materials are derived for general polyhedral meshes. The scheme is general in two and three dimensions. Since the scheme to be developed in this paper is intended for multi-physics code with adaptive mesh refinement (AMR), we present the scheme on mesh generated from AMR. The correctness and features of the scheme are demonstrated for transient problems and steady states in one-, two-, and three-dimensional simulations for heat conduction and radiation heat transfer. The test problems involve dramatically different materials. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a non-autonomous delayed Nicholsonʼs blowflies model. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions. This answers an open problem proposed by Berezansky et al. (2010) [2]. We also provide numerical simulations to support the theoretical result. [Copyright &y& Elsevier]

Abstract: In this paper, a novel algorithm for incompressible flows of two-phase granular mixtures is proposed. The algorithm constitutes a generalization of projection-type methods to multi-phase flows and employs a predictor–corrector time-marching scheme. For the computation of the phasial pressures, a Poisson equation and a second-order elliptic PDE with variable coefficients are solved at both the prediction and the correction stage. Further, the algorithm is combined with a regularization scheme for the numerical treatment of material interfaces which are a common characteristic of the flows of interest. The efficiency and robustness of the proposed algorithm are illustrated via numerical simulations of unsteady two-dimensional shear flows for a reference mixture of beach sand and water. [Copyright &y& Elsevier]

Abstract: The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The present study focuses only on solving the reactive system by the fractional step method using the Strang splitting. Studies shows that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general. [Copyright &y& Elsevier]

Abstract: A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the density and velocity orientation. Short-range repulsion is included through a singular pressure which becomes infinite at the jamming density. The singular limit of infinite pressure stiffness leads to phase transitions from compressible to incompressible dynamics. The paper proposes an Asymptotic-Preserving scheme which takes care of the singular pressure while preventing the breakdown of the Courant–Friedrichs–Lewy (CFL) stability condition near congestion. It relies on a relaxation approximation of the system and an elliptic formulation of the pressure equation. Numerical simulations of impinging clusters show the efficiency of the scheme to treat congestions. A two-fluid variant of the model provides a model of path formation in crowds. [Copyright &y& Elsevier]

Abstract: This paper presents the derivation and partial analysis of a general producer–consumer model. The model is stoichiometric in that it includes the growth constraints imposed by species-specific biomass carbon to nutrient ratios. The model unifies the approaches of other studies in recent years, and is calibrated from an extensive review of the algae–Daphnia literature. Numerical simulations and bifurcation analysis are used to examine the impact of energy enrichment under nutrient and stoichiometric constraints. Our results suggest that the variety of system responses previously cited for related models can be attributed to the size of the total system nutrient pool, which is here assumed fixed. New, more complicated bifurcation sequences, such as multiple homoclinic bifurcations, are demonstrated as well. The mechanistic basis of the model permits us to show the robustness of the system’s dynamics subject to alternate approaches to modeling producer and consumer biomass production. [Copyright &y& Elsevier]

Abstract: Bolted flange joints are widely used in engineering structures; however, the dynamic behavior of this connection is complex in nature. In this paper, a simplified nonlinear dynamic model with bi-linear springs is proposed and validated for pipe structures with bolted flange joints. First, static mechanical properties of the bolted flange joint are investigated. The analytical solution reveals that the axial stiffness of the bolted flange joint is different in tension and compression. Then, nonlinear springs with different stiffness in tension and compression are employed to represent the bolted flange joint. A special type of dynamic behavior, coupling vibration in the transverse and longitudinal directions, is observed in analytical derivation. Finally, relevant physical experiments and numerical simulations are performed. The physical experiments confirm the existence of the coupling vibration behavior. The relationship of longitudinal and transverse vibration frequencies is discussed. The numerical solutions reveal that the simplified nonlinear dynamic model better fits the physical response than conventional reduced linear beam model. [Copyright &y& Elsevier]

Abstract: Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell’s equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart–Thomas–Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l 2 norm achieved for the lowest-order Raviart–Thomas–Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the efficient time-splitting Fourier pseudospectral method to solve the generalized Gross–Pitaevskii (GP) equations, which model the dynamics of spin F =2 Bose–Einstein condensates at extremely low temperature. Using the time-splitting technique, we split the generalized GP equations into one linear part and two nonlinear parts: the linear part is solved with the Fourier pseudospectral method; one of nonlinear parts is solved analytically while the other one is reformulated into a matrix formulation and solved by diagonalization. We show that the method keeps well the conservation laws related to generalized GP equations in 1D and 2D. We also show that the method is of second-order in time and spectrally accurate in space through a one-dimensional numerical test. We apply the method to investigate the dynamics of spin F =2 Bose–Einstein condensates confined in a uniform/nonuniform magnetic field. [Copyright &y& Elsevier]

Abstract: In this paper the closed form expressions for the transverse vibrations of a homogenous isotropic, thermoelastic thin beam with voids, based on Euler–Bernoulli theory have been derived. The effects of voids, relaxation times, thermomechanical coupling, surface conditions and beam dimensions on energy dissipation induced by thermoelastic damping in (micro-electromechanical systems) MEMS/(nano-electromechanical systems) NEMS resonators are investigated for beams under clamped and simply supported conditions. Analytical expressions for deflection, temperature change, frequency shifts and thermoelastic damping in the beam have been derived. Some numerical results with the help of MATLAB programming software in case of magnesium like material have also been presented. The computer simulated results in respect of damping factor and frequency shift have been presented graphically. [Copyright &y& Elsevier]

Abstract: Several important applications use nonlinear feedback methods for synthetically inducing self-excited oscillations in mechanical systems. The van der Pol and saturation function type feedback methods are widely used. The effects of time-delay on the self-excited oscillation of single and two degrees-of-freedom systems under nonlinear feedback have been studied in this paper. It is shown that a single degree-of-freedom oscillator with the van der Pol type nonlinear feedback can produce unbounded response in presence of time-delay. In general, an uncontrolled time-delay in the feedback changes the state of oscillations in an uncertain manner. Therefore, a bounded saturation type feedback with controllable time-delay is proposed for inducing self-excited oscillations. The feedback signal is essentially an infinite weighted sum of a nonlinear function of the state variables of the system measured at equal intervals in the past. More recent is the measurement, higher is the weight. Thus, the feedback signal uses a large amount of information about the past history of the dynamics. Such a control signal can be realized in practice by a recursive means. The control law allows three parameters to be varied namely, the time-delay, feedback and recursive gains. Multiple time scale analysis is used to plot amplitude vs. time-delay curves. Time-delay can be controlled to vary the amplitude of oscillation as well as to switch the oscillation from one mode to the other in a two degrees-of-freedom system. It is shown that a higher recursive gain can exercise a better and a more robust control on the amplitude of oscillation of the system. Analytical results are compared with the results of numerical simulations. [Copyright &y& Elsevier]

Abstract: In the present paper, an Eulerian scheme combined with the hybrid particle level set method for numerical simulation of spall fracture due to high-velocity impact is proposed. An axisymmetric framework is established, based on an improved CE/SE scheme, to solve the high-velocity impact problems with large deformations, high strain rates and spall fractures. The hybrid particle level set method is adopted for tracking material interfaces and describing the formation and propagation of a crack. A novel representation of crack by level set is proposed. Numerical simulations are carried out and compared to the corresponding experimental results. The numerical results are in good agreement with the experimental data. The edge effects are reproduced and the decrease of scab thickness with increase in impact velocity is observed owing to the numerical analysis. It is proved that our computational technique is feasible and reliable for analyzing the spall fracture. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the solution of the Riemann Problem for the one-dimensional, free-surface Shallow Water Equations over a bed step is analyzed both from a theoretical and a numerical point of view. Particular attention has been paid to the wave that is generated at the location of the bed discontinuity. Starting from the classical Shallow Water Equations, considering the bed level as an additional variable, and adding to the system an equation imposing its time invariance, we show that this wave is a contact wave, across which one of the Riemann invariants, namely the energy, is not constant. This is due to the fact that the relevant problem is nonconservative. We demonstrate that, in this type of system, Riemann Invariants do not generally hold in contact waves. Furthermore, we show that in this case the equations that link the flow variables across the contact wave are the Generalized Rankine–Hugoniot relations and we obtain these for the specific problem. From the numerical point of view, we present an accurate and efficient solver for the step Riemann Problem to be used in a finite-volume Godunov-type framework. Through a two-step predictor–corrector procedure, the solver is able to provide solutions with any desired accuracy. The predictor step uses a well-balanced Generalized Roe solver while the corrector step solves the exact nonlinear system of equations that consitutes the problem by means of an iterative procedure that starts from the predictor solution. In order to show the effectiveness and the accuracy of the proposed approach, we consider several step Riemann Problems and compare the exact solutions with the numerical results obtained by using a standard Roe approach far from the step and the novel two-step algorithm for the fluxes over the step, achieving good results. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a predator–prey model with modified Leslie–Gower and Holling-type II schemes with stochastic perturbation. We show there is a unique positive solution to the system with positive initial value, and mainly investigate the long time behavior of the system. Condition for the system to be extinct is given and persistent condition is established. At last, numerical simulations are carried out to support our results. [Copyright &y& Elsevier]

Abstract: The assessment of Diffusion-Weighted MRI (DW-MRI) fibre-tracking algorithms has been limited by the lack of an appropriate ‘gold standard’. Practical limitations of alternative methods and physical models have meant that numerical simulations have become the method of choice in practice. However, previous numerical phantoms have consisted of separate fibres embedded in homogeneous backgrounds, which do not capture the true nature of white matter. In this paper we describe a method that is able to randomly generate numerical structures consisting of densely packed bundles of fibres, which are much more representative of human white matter, and simulate the DW-MR images that would arise from them under many imaging conditions. User-defined parameters may be adjusted to produce structures with a range of complexities that spans the levels we would expect to find in vivo. These structures are shown to contain many different features that occur in human white matter and which could confound fibre-tracking algorithms, such as tract kissing and crossing. Furthermore, combinations of such features can be sampled by the random generation of many different structures with consistent levels of complexity. The proposed software provides means for quantitative assessment via direct comparison between tracking results and the exact location of the generated fibres. This should greatly improve our understanding of algorithm performance and therefore prove an important tool for fibre tracking development. [Copyright &y& Elsevier]

Abstract: Recently the author has shown that there are only finitely many p-groups with trivial Schur multiplicator of a given coclass if p is an odd prime. This paper introduces an algorithm to compute these finitely many p-groups for any given prime and coclass. As an application, we classify these groups for coclass 1, give a conjectural description for them for coclass 2 and determine them for coclass 3 and and coclass 4 and . Based on the experimental evidence, we conjecture that the order of a p-group with trivial Schur multiplicator and coclass r is bounded by a function which is independent of the prime p. [Copyright &y& Elsevier]

Structural health monitoring is nowadays a problem of major concern, as recent catastrophic failures of in-operation civil structures with important human losses and high costs demonstrate. A global assessment method with sufficient sensitivity and reliable enough to detect incipient damage in order to prevent unexpected failures is necessary. Pursuing this goal, in this paper some new developments of the detection and relative damage quantification indicator, concerning the detection, localization and also the relative severity of damage are presented. This method, based on the use of the frequency domain assurance criterion and of the response vector assurance criterion, seems to be an effective damage indicator. To illustrate the procedure, the authors present some numerical simulations, as well as some experimental examples taken on two beams. [Copyright &y& Elsevier]

In this paper, signal processing algorithms for damage localisation purposes in plate-like structures were proposed. Algorithms use elastic wave propagation phenomenon for damage detection and localisation. As a result of application to signals registered from the structure, special maps are created that indicate damage location. In this work the algorithms were introduced, described and experimentally implemented. Also one example coming from numerical simulation was included. The proposed methods were successfully tested on aluminium alloy specimen and carbon–epoxy specimen. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to study and identify suitable outflow boundary conditions for the numerical simulation of viscous supersonic/hypersonic flow over blunt bodies, governed by the compressible Navier–Stokes equations, with an emphasis motivated primarily by the use of spectral methods without any filtering. The subsonic/supersonic composition of the outflow boundary requires a dual boundary treatment for well-posedness. All compatibility relations, modified to undertake the hyperbolic/parabolic behaviour of the governing equations, are used for the supersonic part of the outflow. Regarding the unknown downstream information in the subsonic region, different subsonic outflow conditions in the sense of the viscous blunt-body problem are examined. A verification procedure is conducted to make out the distinctive effect of each outflow condition on the solution. Detailed comparisons are performed to examine the accuracy and performance of the outflow conditions considered for two model geometries of different surface curvature variations. Numerical simulations indicate a noticeable influence of pressure from subsonic portion to supersonic portion of the boundary layer. It is demonstrated that two approaches for imposing subsonic outflow conditions namely (1) extrapolating all flow variables and (2) extrapolation of pressure along with using proper compatibility relations are more suitable than the others for accurate numerical simulation of viscous high-speed flows over blunt bodies using spectral collocation methods. [Copyright &y& Elsevier]

Abstract: This paper takes a fresh look at the geometric conservation law (GCL) from the perspective of the finite element method (FEM) for incompressible flows. The GCL arises naturally in the context of Arbitrary Lagrangian Eulerian (ALE) formulations for solving problems on deforming domains. GCL compliance is traditionally interpreted as a consistency criterion for applying an unsteady flow solution algorithm to simulate exactly a uniform flow on a deforming domain. We introduce an additional requirement: the time integrator must maintain its fixed mesh accuracy when applied to deforming meshes. A review of the literature shows that while many authors use an ALE FEM, few of them discuss the GCL issues. We show how a fixed mesh unsteady FEM using high order time integrator (up to fifth order in time) can be transposed to solve problems on deforming meshes and preserve its fixed mesh high order temporal accuracy. An appropriate construction of the divergence of the mesh velocity guarantees GCL compliance while a separate construction of the mesh velocity itself allows the time-integrator to deliver its fixed mesh high order temporal accuracy on deforming domains. Analytical error analysis of problems with closed form solutions provides insight on the behavior of the time integrators. It also explains why high order temporal accuracy is achieved with a conservative formulation of the incompressible Navier–Stokes equations, while only first order time accuracy is observed with the non-conservative formulation and all time-integrators investigated here. We present thorough time-step and grid refinement studies for simple problems with closed form solutions and for a manufactured solution with a non-trivial flow on a deforming mesh. In all cases studied, the proposed reconstructions of the mesh velocity and its divergence for the conservative formulation lead to optimal time accuracy on deforming grids. [Copyright &y& Elsevier]

Abstract: Computer simulation studies of the stability and transport properties of trapped non-neutral plasmas require the numerical realization of a three-dimensional plasma distribution. This paper presents a new numerical method for obtaining, without an explicit model for physical collisions in the code, a low noise three-dimensional computational equilibrium distribution. This requires both the loading of particles into an idealized distribution and the relaxation from that distribution toward an approximate numerical equilibrium. The equilibrium can then be modified through a slow change of system parameters, to generate other equilibria. In the present, work we apply this method to a UC Berkeley experiment on electron confinement in magnetic geometries appropriate for the ALPHA anti-hydrogen experiment, using the three-dimensional particle-in-cell code WARP. WARP’s guiding center mover and its option to switch between different solvers during a simulation are highly valuable because they speed up the simulations; they enable the practical use of the new technique for generating numerical equilibrium states of trapped non-neutral plasmas. [Copyright &y& Elsevier]

Abstract: In model checking, the state-explosion problem occurs when one checks a nonflat system, i.e., a system implicitly described as a synchronized product of elementary subsystems. In this paper, we investigate the complexity of a wide variety of model-checking problems for nonflat systems under the light of parameterized complexity, taking the number of synchronized components as a parameter. We provide precise complexity measures (in the parameterized sense) for most of the problems we investigate, and evidence that the results are robust. [Copyright &y& Elsevier]

• The piezo-metastructure is shunted with a one-way electrical transmission line. • Local-resonance bandgaps are maintained in opposite directions. • Nonreciprocal wave attenuation behaviors exist in the bandgap. • The presented nonreciprocal system is linear, adaptive and easily implemented. • Theoretical and experimental results verify nonreciprocity of the system. In contrary to elastic media, it is easy to attain one-way coupling feature among electrical elements, which enables unidirectional transmission of electrical wave. In this paper, we explore and exploit the interaction of a piezoelectric beam with a one-way electrical transmission line to facilitate nonreciprocal transmission of elastic wave in the linear fashion. Theoretical dispersion analysis and numerical simulations are performed to reveal transmission behaviors of elastic wave in the presented piezoelectric metastructure. It is uncovered that, when the one-way electrical coupling feature is introduced, local-resonance bandgaps are maintained in opposite directions of the piezoelectric metastructure. However, the bandgap attenuation capability in one direction is increased compared to conventional local-resonance metastructures, in which no electrical coupling exists between cells, while that in the other direction is decreased. Therefore, nonreciprocal transmission of elastic wave emerges in this system due to the distinct bandgap attenuation capability in opposite directions. It is also revealed that this sort of nonreciprocal wave attenuation capability is adaptive with the one-way electrical coupling coefficient and the resistance of electrical cells. An experimental set-up of the piezoelectric metastructure is built and experimental results verify the nonreciprocity property and its adaptiveness. Overall, the presented piezoelectric metastructure provides a linear and concise approach to realize adaptive nonreciprocal transmission of elastic wave. [ABSTRACT FROM AUTHOR]