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In this paper we propose new Z-type nonlinear weights of the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme for hyperbolic conservation laws. Instead of employing the classical smoothness indicators for the nonlinear weights, we take the $p$th root of the smoothness indicators and follow the form of Z-type nonlinear weights, leading to fifth order accuracy in smooth regions, even at the critical points, and sharper approximations around the discontinuities. We also prove that the proposed nonlinear weights converge to the linear weights as $p \to \infty$, implying the convergence of the resulting WENO numerical flux to the finite difference numerical flux. Finally, numerical examples are presented by comparing with other WENO schemes, such as WENO-JS, WENO-M and WENO-Z, to demonstrate that the proposed WENO scheme performs better in shock capturing.

In this article, a coupled Two-relaxation-time Lattice Boltzmann-Volume penalization (TRT-LBM-VP) method is presented to simulate flows past obstacles. Two relaxation times are used in the collision operator, of which one is related to the fluid viscosity and the other one is related to the numerical stability and accuracy. The volume penalization method is introduced into the TRT-LBM by an external forcing term. In the procedure of the TRT-LBM-VP, the processes of interpolating velocities on the boundaries points and distributing the force density to the Eulerian points are unneeded. Performing the TRT-LBM-VP on a certain point, only the variables of this point are needed. As a consequence, the TRT-LBM-VP can be conducted parallelly. From the comparison between the result of the cylindrical Couette flow solved by the TRT-LBM-VP and that solved by the Single-relaxation-time LBM-VP (SRT-LBM-VP), the accuracy of the TRT-LBM-VP is higher than that of the SRT-LBM-VP. Flows past a single circular cylinder, a pair of cylinders in tandem and side-by-side arrangements, two counter-rotating cylinders and a NACA-0012 airfoil are chosen as numerical experiments to verify the present method further. Good agreements between the present results and those in the previous literatures are achieved.

In this work, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation using conformable derivative. The Riccati equation method is used to get the analytical solutions to the space-fractional stochastic Kuramoto–Sivashinsky equation. Because this equation has never been examined with space-fractional and multiplicative noise at the same time, we generalize some previous results. Moreover, we display how the multiplicative noise influences on the stability of obtained solutions of the space-fractional stochastic Kuramoto–Sivashinsky equation.

In this paper, we implement the second order Runge – Kutta method for three different population initial value problems. The Runge – Kutta method is a numerical technique used to solve the approximate solution for initial value problems for ordinary differential equations. Runge – Kutta method is implemented to linear population equation, non-linear population equation and non-linear population equation with an oscillation. The method of solving three initial value problems is implemented using Python Programming. Keywords: Differential equation, Runge – Kutta method, Discrete interval, Population equation, Non-linear population equation, Oscillation, Python.

Aiming at the problem that the Ultra-Wide-Band (UWB) positioning accuracy is reduced in the Non-Line-of-Sight (NLOS) environment, a UWB positioning accuracy evaluation mechanism is introduced. This paper analyzes the geometric distribution of UWB equipment theoretically to evaluate the positioning accuracy of the UWB system. Furthermore, it optimizes the geometric distribution of UWB and optimizes the UWB positioning algorithm model to improve the positioning accuracy. A set of UWB positioning accuracy estimation process is proposed. Through theoretical analysis and simulation, a model of the influence of the geometric distribution of base stations on the UWB positioning precision is established. The obtained model provides a reference for setting and adjusting the measurement noise in the Kalman filter for UWB/Inertial Navigation System (INS) integration positioning, which improves the combined positioning accuracy.

Surface appearance of involute gear is the basis to research the dynamic performance of gear transmission system. The Delaunay triangulation method of layered local dynamic is proposed to construct the precise tooth surface of the known tooth surface appearances. The concave and convex region of the real tooth surface was extracted by isosurface subdivision. In order to smooth the surface, the energy method and the improved fractal method with minimum included angle are used to smooth the curve. On the basis of the loaded tooth contact analysis of involute gears, the loaded tooth contact analysis model of digital error tooth surface is constructed. The tooth surface appearances of fuzzy tooth surface were predicted by extracting contact patterns under various working parameters on the experimental platform. Through the analysis on actual examples, it is concluded that the method proposed in this manuscript can accurately predict the tooth surface morphology of fuzzy tooth surface and lay the foundation for the dynamic performance optimization of gear system with fuzzy tooth surface.

In this paper, we consider the Kronrod extension for the Gauss-Radau and Gauss-Lobatto quadrature consisting of any one of the four Chebyshev weights. The main purpose is to effectively estimate the error of these quadrature formulas. This estimate needs a calculation of the maximum of the modulus of the kernel. We compute explicitly the kernel function and determine the locations on the ellipses where a maximum modulus of the kernel is attained. Based on this, we derive effective error bounds of the Kronrod extensions if the integrand is an analytic function inside of a region bounded by a confocal ellipse that contains the interval of integration.

It is a challenging task to produce recipes from images, due to the difficulty in bridging the gap from intuitive, static images to sequential, dynamic recipes. In this paper, we propose a novel recipe generation system for producing effective recipes from images. As medium steps, ingredient generation is introduced to guide recipe generation in our system. With potential information in ingredient lists, ingredient selection and ingredient sequence, the system is taught to generate effective recipes. For information representation, a hierarchical attention mechanism is designed to extract effective features for ingredient production and recipe generation. In order to guarantee the comprehensiveness and logic in recipes, a specific and explicit criterion around ingredients is designed under the framework of reinforcement learning. In ingredient generation, the system is required to generate ingredients with correct sequence in cooking procedures. And in recipe generation, ingredients in recipes are required to be consistent with produced ingredients. In experiments, the proposed method is compared with state-of-the-art methods to evaluate the feasibility. The results indicate that the proposed system achieves a better performance than other methods on both aspects of producing proper ingredients and effective recipes.

In this paper we propose and analyze an hp-version of the composite Gauss-Legendre quadrature rule which includes local subdivision of the integration domain and local variation of the number of quadrature nodes employed on each subinterval. We derive an a priori error estimate that is fully explicit in the local length of each subinterval, in the local number of quadrature nodes employed on each subinterval, and in the local regularity of the integrand. In particular, for integrands with singularities at one or both endpoints, we prove that exponential convergence can be achieved by using geometric partition of the integration domain and linearly increasing of the number of quadrature nodes in successive subintervals. Numerical experiments are provided to illustrate the theoretical results.

In this paper, we propose an angular momentum-based advection technique that can express the turbulent foam effect. The motion of foam particles, which are strongly bound to the motion of the underlying fluid, is viscous, and sometimes clumping problems occur. This problem is a decisive factor that makes it difficult to express realistic foam effects. Since foam particles, which are secondary effects, depend on the motion of the underlying water, in order to exaggerate the foam effects or express more lively foam effects, it is inevitable to tune the motion of the underlying water and then readjust the foam particles. Because of such a cumbersome process, the readjustment of the foam effects requires a change in the motion of the underlying water, and it is not easy to produce such a scene because the water and foam effects must change at the same time. In this paper, we present a method to maintain angular momentum-based force from water particles without tuning the motion of the underlying water. We can restore the lost turbulent flow by additional advection of foam particles based on this force. In addition, our method can be integrated with screen-space projection frameworks, allowing us to fully embrace all the advantages of this approach. In this paper, the turbulence of the foam particles was improved by minimizing the viscous motion of the foam particles without tuning the motion of the underlying water, and as a result, lively foam effects can be expressed.

The aims of this paper is to propose a numerical approach to simulate water flows in a 2D shallow medium. We consider the 2D Shallow water equations following the velocity-denivelation formulation. We solve these equations by a projection technique using a $\mathbb{P}_{N,M}$-type Chebyshev spectral approach which uses the Chebyshev-Gauss-Lobatto collocation points.

High-order bandwidth-optimized weighted essentially non-oscillatory (WENO) schemes with limiters are applied in this study to a wide variety of problems. A comparison of the performance of these schemes with three-point and four-point stencils is shown for one-dimensional and two-dimensional test problems. For the one-dimensional and two-dimensional test cases, these schemes show their advantage over the standard fifth-order and the seventh-order WENO schemes proposed in the literature in capturing the small-scale structures appearing in these flows. Effects of the limiter threshold values are discussed for the bandwidth-optimized WENO schemes. Further, the bandwidth-optimized WENO schemes with limiters are compared with other variants of the WENO scheme found in the literature. Direct numerical simulation of supersonic channel flow is also performed with the bandwidth-optimized WENO scheme (with three-point stencil) with limiter, and the results are found to be in good agreement with the literature. This scheme is then used for performing DNS of shock train in a turbulent channel flow.

The environment of the fully mechanized working face in coal mines is harsh and the dust concentration is high. When ultra wide band (UWB) is used for positioning, it is easy to be interfered by dust. UWB ranging will have certain errors, so the positioning precision cannot meet the requirements of intelligent coal mines. To order to solve this problem, the principle of UWB ranging is analyzed, and it is pointed out that the main factors affecting the precision of UWB ranging are multipath effect and non-line-of-sight propagation. The generation of multipath effect and non-line-of-sight propagation is closely related to dust concentration, and the influence of dust concentration on the precision of UWB ranging in coal mines is explored through experiments. The experimental results show that the UWB ranging error increases as the dust concentration increases, and the growth rate of UWB ranging error accelerates.

ConspectusMolecular chirality has been of scientific interest since 1848 when Pasteur demonstrated its direct connection to the rotation of light by solutions of chiral compounds. In the 1960s the ...

Many physical problems in the real world are frequently modeled by ordinary differential equations (ODEs). Real-life problems are usually non-linear, numerical methods are therefore needed to approximate their solution. We consider different numerical methods viz., Explicit (Forward) and Implicit (Backward) Euler method, Classical second-order Runge-Kutta (RK2) method (Heun’s method or Improved Euler method), Third-order Runge-Kutta (RK3) method, Fourth-order Runge-Kutta (RK4) method, and Butcher fifth-order Runge-Kutta (BRK5) method which are popular classical iteration methods of approximating solutions of ODEs. Moreover, an intuitive explanation of those methods is also be presented, comparing among them and also with exact solutions with necessary visualizations. Finally, we analyze the error and accuracy of these methods with the help of suitable mathematical programming software.

In simulation of heat conduction with temperature-independent physical properties and boundary conditions (BCs), Galerkin residual analysis and variational analysis yield equivalent finite element method (FEM), the conventional FEM. However, if the properties and BCs are temperature-dependent, it is discovered that their derivatives further induce nonlinearity of FEM which consequently generates divergence between the two analyses. A general FEM, extension of variational analysis, is derived as general form of conventional FEM modeling nonlinear heat conduction. Numerical examples demonstrate that the general FEM produces results with considerably higher accuracy and stability and also possesses higher performances on conforming with both two analyses. Since general FEM degenerates to conventional FEM if derivatives are of small-amplitude or zero and its direct implementation to the entire domain is costive, general FEM is alternatively utilized as local refinement of governing equation only to points with significant derivatives. The strategy of local refinement is optimized to enhance efficiency.

In this article, we discuss the Chebyshev Polynomial and its characteristics. The second order difference equation and the process obtaining the explicit solution of the Chebyshev polynomial have been given for each real number. The symmetry and orthogonality of the Chebyshev polynomial has also been demonstrated using the explicit solutions obtained. Furthermore, we have also given how to approx the polynomial function using the Chebyshev polynomials.

The main purpose of this paper is to present a methodology for precisely calculating the tooth thickness of cylindrical worm gear, which is expounded detailedly with the worm gear in the toroidal surface enveloping cylindrical worm pair as an example. This method can compute the tooth thickness in any cross section of cylindrical worm gear, and it is universal for cylindrical worm gears. In an objective cross section, the tooth profile equations of both flanks of a typical cylindrical worm gear tooth are derived. A given radial dimension intersects with both flanks of the tooth profile, and the coordinates of intersection points are obtained by solving the corresponding nonlinear equations. Then, the distance between the two intersection points is tooth thickness. By utilizing the acquired key points, the tooth profile of cylindrical worm gear in its cross section is drawn by interpolation method. Based on the theory brought forward, the tooth thickness characteristics of cylindrical worm gear are analyzed. The change rule of the top thickness of cylindrical worm gear along the tooth width is discovered, and the change curve is plotted. The rule obtained is consistent with the experimental results, and thus the correctness of the current work is verified.

In order to obtain a new structure of beam flexure hinge with good performance, the flexure hinge based on the X-lattice structure is researched in this paper. The truss model in the finite element method is used to model the 6-DOF compliance of the flexure hinge based on the X-lattice structure. The influence of structural parameters on the compliance and compliance ratio of flexure hinges is analyzed based on this model, and the performance is compared with the traditional beam flexure hinge of the same size. In order to design a flexure hinge based on the X-lattice structure with good comprehensive performance, this paper proposes an intelligent structure optimization method based on a genetic algorithm. The feasibility of the optimization algorithm is verified by an example.

Over a century has passed since Einstein formulated general relativity, a remarkable theory of gravitation about which he grappled for about a decade following his theory of special relativity. The...

We study the Kuramoto-Sivashinsky equation (KSE) in scalar form on the two-dimensional torus with and without advection by an incompressible vector field. We prove local existence of mild solutions for arbitrary data in L2. We then study the issue of global existence. We prove global existence for the KSE in the presence of advection for arbitrary data, provided the advecting velocity field v satisfies certain conditions that ensure the dissipation time of the associated hyperdiffusion-advection equation is sufficiently small. In the absence of advection, global existence can be shown only if the linearized operator does not admit any growing mode and for sufficiently small initial data.

A method for constructing a Chebyshev approximation of the multivariable functions by exponential, logarithmic and power expressions is proposed. It consists in reducing the problem of the Chebyshev approximation by a nonlinear expression to the construction of an intermediate Chebyshev approximation by a generalized polynomial. The intermediate Chebyshev approximation by a generalized polynomial is calculated for the values of a certain functional transformation of the function we are approximating. The construction of the Chebyshev approximation of the multivariable functions by a polynomial is realized by an iterative scheme based on the method of least squares with a variable weight function.

Forward-backward sweep method (FBSM) is an indirect numerical method used for solving optimal control problems, in which the differential equation arising from this method is solved by the Pontryagin’s maximum principle. In this paper, a set of hybrid methods based on explicit 6th-order RungeKutta method is presented for the FBSM solution of optimal control problems. Order of truncation error, stability region, and numerical results of the new hybrid methods were compared with those of the 6th-order Runge Kutta method. Numerical results show that new hybrid methods are more accurate than the 6th-order Runge–Kutta method and that their stability regions are also wider than that of the 6th-order Runge–Kutta method.

We discuss features of the calculation of a Fraunhofer integral by traditional quadrature numerical integration methods and a special collocation Levin method when calculating the diffraction of a plane electromagnetic wave by a rectangular aperture. For the quadrature numerical integration methods, a criterion for the assessment of the integration step is derived depending on the screen size and required calculation accuracy. Advantages of the use of the special collocation Levin method in comparison with the traditional quadrature numerical integration methods are shown.

We show that a master integrand basis exists for all planar, two-loop amplitudes in massless four-dimensional theories which is fully stratified by rigidity -- with each integrand being either pure and strictly polylogarithmic or (pure and) strictly elliptic-polylogarithmic, with each of the later involving a single elliptic curve. Such integrands can be said to have definite rigidity., 45 pages; 72 (tikz) figures; ancillary files include explicit details for examples discussed

We consider a space–time fractional parabolic problem. Combining a sinc quadrature-based method for discretizing the Riesz–Dunford integral with $hp$-FEM in space yields an exponentially convergent scheme for the initial boundary value problem with homogeneous right-hand side. For the inhomogeneous problem, an $hp$-quadrature scheme is implemented. We rigorously prove exponential convergence with focus on small times $t$, proving robustness with respect to startup singularities due to data incompatibilities.

The paper presents the method of analysis and a comparison of the effectiveness of modified and conventional syntactic foams. The method employs the two-phase superposition approach recently developed for composite materials consisting of several concentric phases. Conventional syntactic foams consisting of spherical voids surrounded by thin glass shells embedded in the matrix are compared to modified foams with cylindrical or spheroidal voids. Modified syntactic foams analyzed in the paper include foams with cylindrical voids aligned along the applied stress or perpendicular to the stress and foams with randomly oriented cylindrical voids. It is demonstrated that while conventional syntactic foams with spherical voids absorb more energy than their modified counterparts, the stiffness of such foams is compromised due to the presence of voids to a larger degree than in modified foams. Accordingly, modified syntactic foams may appear a better compromise if a high energy absorption has to be combined with a prescribed large stiffness of the material.

Under tooth profile wear condition, with running time increasing, the tooth chord length of the gear tooth is thinner and the tooth profile is not involute profile any more, which results in the changes in amplitude and fluctuation of time-varying meshing stiffness. In this work, in order to reveal the influence of tooth profile wear on time-varying meshing stiffness, an analytical model for calculating the time-varying meshing stiffness under tooth wear condition is built and incorporated with a “translational-rotational” dynamic model of compound planetary gear set. Poincare section, the phase trajectory and bifurcation diagram are employed for analysis of periodic and chaotic motion. The results indicate that, tooth wear accumulation result in the reduction in the amplitude of meshing stiffness at the meshing region of double-pair teeth, but makes no difference in meshing stiffness for the meshing region of single-pair teeth. In order to avoid the system being in Chaos motions, under large tooth wear condition, the input speed should be avoided away from 3700 r/min-6725 r/min, so as to keep the system in a stable periodic motion state.

In this paper, we consider sums of finite products of the second and third type Chebyshev polynomials, those of the second and fourth type Chebyshev polynomials and those of the third and fourth type Chebyshev polynomials, and represent each of them as linear combinations of Chebyshev polynomials of all types. Here the coefficients involve some terminating hypergeometric functions $ {}_{2}F_{1} $. This problem can be viewed as a generalization of the classical linearization problems and is done by explicit computations.

The error of approximation of a function using Poly-Sinc approximation was shown to have a convergence rate of exponential order over a global partition. However, it was assumed that the function values at the interpolation points were known. In this paper, we extend our work on poly-Sinc-based discontinuous Galerkin approximation, in which the function values at the interpolation points are replaced by unknown coefficients and solved by the discontinuous Galerkin method. To deal with functions having a singularity at an endpoint, we use Sinc partitions in our discontinuous Galerkin approximation. For such functions, we show that, by using a weighted L 2 norm over a Sinc partition in which the weight function is the reciprocal of the asymptotic density of Sinc points in that partition and computing the l 2 norm over all Sinc partitions constituting the global partition except the partition containing the singularity, the error of approximation between the exact solution of the ordinary differential equation and its poly-Sinc-based discontinuous Galerkin approximation has a convergence rate of exponential order similar to the one over the global partition. The numerical results are in agreement with our theoretical derivations of the approximation error. We compare our poly-Sinc-based discontinuous Galerkin method with the poly-Sinc collocation method. Our method shows better performance in the L 2 norm.

Since the classical WENO schemes [27] might suffer from slight post-shock oscillations (which are responsible for the numerical residual to hang at a truncation error level) and the new high-order multi-resolution WENO schemes [59] are successful to solve for steady-state problems, we apply these high-order finite volume multi-resolution WENO techniques to serve as limiters for high-order Runge-Kutta discontinuous Galerkin (RKDG) methods in simulating steady-state problems. Firstly, a new troubled cell indicator is designed to precisely detect the cells which would need further limiting procedures. Then the high-order multi-resolution WENO limiting procedures are adopted on a sequence of hierarchical L 2 projection polynomials of the DG solution within the troubled cell itself. By doing so, these RKDG methods with multi-resolution WENO limiters could gradually degrade from the optimal high-order accuracy to the first-order accuracy near strong discontinuities, suppress the slight post-shock oscillations, and push the numerical residual to settle down to machine zero in steady-state simulations. These new multi-resolution WENO limiters are very simple to construct and can be easily implemented to arbitrary high-order accuracy for solving steady-state problems in multi-dimensions.

The fluid motion characteristics have an important influence on the evolution of the backflow vortex near the pipe wall. The instantaneous velocity and instantaneous temperature of the outlet flow ...

An algorithm based on a class of the Chebyshev polynomials family called the fifth-kind Chebyshev polynomials (FCPs) is introduced to solve the multi-term variable-order time-fractional diffusion-w...

The Sinc-Galerkin and Sinc-Collocation methods are presented to solve linear Schrodinger equation and obtain the electronic spectrum of linear Schrodinger equations. Some properties of the Sinc methods required for our subsequent development are given and utilized. In sequel, Sinc-Galerkin method is compared with Sinc-Collocation method. Numerical examples are included to demonstrate the validity and applicability of the presented techniques. We prove that the present methods are easy to implement and yields accurate results. Our main result is also that the Sinc-Collocation method fails for some potentials, but the Sinc-Galerkin method is successful.

This study carries the novel applications of the Sinc collocation method to investigate the numerical computing paradigm of Schrodinger wave equation and Transport equation as a great level of accuracy and precision. A global collocation-based Sinc function is embedded with a cardinal expansion to discretize initially time derivatives by finite difference method and secondly spatial derivatives are approximated with $$\theta $$ -weighted scheme. Sinc collocation method (SCM) is found to be a more robust approach in order to avoid singularities in proposed problems and for yielding accurate numerical results. The governing PDEs are transformed with the help of Sinc function into algebraic system of equations, and further, these algebraic equations are solved with the help of computational iteration scheme to obtain the numerical results. The scheme provides a reliable and excellent procedure for adaptation of finding unknown in Sinc function for these problems. An extensive stability analysis is done to validate the convergence, accuracy and exactness of the proposed scheme.

In this paper, the Chebyshev collocation numerical method is developed for solving generalized thermoelasticity problems of the isotropic homogeneous two dimensional media. The coupled thermoelasti...

This paper considers some integrals where the integrand comprises the log gamma function or the digamma function multiplied by exponential or trigonometric functions.

Summary of GEANT4 processes for application in muon scattering tomography

In discontinuous Galerkin spectral element methods (DGSEM), the two most common approaches to numerically integrate the terms of the weak form are either using Gauss-Legendre or Gauss-Lobatto quadratures. The former yields more accurate results but at a higher computational cost, so that a priori it is not clear whether one approach is more efficient that the other. In this paper, it is shown (theoretically for a particular case and numerically for the general case) that using Gauss-Lobatto quadrature for the convection matrix actually introduces a negligible error. In contrast, using Gauss-Lobatto quadratures for the evaluation of the jump term in the element faces introduces a sizeable error. This leads to the proposal of a new DG approach, where the convection matrix is evaluated using Gauss-Lobatto quadratures, whereas the face mass matrices are integrated using Gauss-Legendre quadratures. For elements with constant Jacobian and constant coefficients, a formal proof shows that no numerical integration error is actually introduced in the evaluation of the residual, even though both the mass and the convection matrices are not computed exactly with Gauss-Lobatto quadratures. For elements with non-constant Jacobian and/or non-constant coefficients, the impact of numerical integration error on the overall error is evaluated through a series of numerical tests, showing that this is also negligible. In addition, the computational cost associated to the matrix-vector products required to evaluate the residual is evaluated precisely for the different cases considered. The proposed approach is particularly attractive in the most general case, since the use of Gauss-Lobatto quadratures significantly speeds-up the evaluation of the residual.

This study presents a novel observer-based fuzzy control for chaotic systems (CSs). A class of CSs with unmeasurable states, unknown input constraints and unknown dynamics is taken to account. A ge...

Discusses practical solutions versus theoretical solutions for a radial cavity excited at its midpoint.

Since wind energy covers an important part of the increasing electricity demands, accurate wind speed and direction forecasts are essential for the optimal operation of both the wind farms and the ...

In this paper, based on the two-step Ulm–Chebyshev iterative procedure and the Cayley transform, we propose a two-step Ulm–Chebyshev-like Cayley transform method for inverse eigenvalue problems. Un...

A modified Trapezoidal Broyden’s method for nonlinear equations is presented. We design and implement an alternative approximation to Jacobian matrix of Trapezoidal Broyden’s method. This method improve the efficiency by reducing the number of iterations required by the Broyden’s method, and solve the problem that the approximate matrix almost singular or singular at some points. The local convergence properties of the new method is presented. Numerical results illustrate that the proposedmethod is efficient and robust.

In this paper, we present a framework to construct general stochastic Runge–Kutta Lawson schemes. We prove that the schemes inherit the consistency and convergence properties of the underlying Runge–Kutta scheme, and confirm this in some numerical experiments. We also investigate the stability properties of the methods and show for some examples, that the new schemes have improved stability properties compared to the underlying schemes.

In this paper, the properties of Chebyshev polynomials and the Gauss–Legendre quadrature rule are employed to construct a new operational matrix of distributed-order fractional derivative. This ope...

A new collocation integrator with Lobatto spacings is proposed for numerical solving mixed systems of firstand second-order differential equations for dynamic problems. The general theory of collocation integrators is outlined from which the basic formulas of the new integrator are derived.

International audience; In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin (ADER-DG) method. To obtain this desired result, we equip the space part of the method with entropy correction terms that balance the entropy production in space, inspired by the work of Abgrall. Whereas for the time-discretization we apply the relaxation approach introduced by Ketcheson that allows to modify the timestep to preserve the entropy to machineprecision. Up to our knowledge, it is the first time that a provable fully discrete entropy preserving ADER-DG scheme is constructed. We verify our theoretical results with various numerical simulations.

We demonstrate InGaN/GaN quantum dot light-emitting diodes on silicon substrates with a planar buffer layer formed by coalescing GaN nanowires. The GaN buffer layer and the light-emitting diode het...

Multifunctional motion sensors have broad applications in the field of the internet of things (IoT). An octopus-shaped self-powered motion sensor is proposed to monitor the acceleration, motion dir...