In this paper,we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary *** is shown that there exist global weak solutions of the micropolar equations...
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In this paper,we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary *** is shown that there exist global weak solutions of the micropolar equations in a general bounded smooth *** particular,we establish the uniform estimate of the strong solutions for when the boundary is ***,we obtain the rate of convergence of viscosity solutions to the inviscid solutions as the viscosities tend to zero(i.e.,(ε,χ,γ,κ)→0).
In this paper,we study a posteriori error estimates of the L1 scheme for time discretizations of time fractional parabolic differential equations,whose solutions have generally the initial *** derive optimal order a p...
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In this paper,we study a posteriori error estimates of the L1 scheme for time discretizations of time fractional parabolic differential equations,whose solutions have generally the initial *** derive optimal order a posteriori error estimates,the quadratic reconstruction for the L1 method and the necessary fractional integral reconstruction for the first-step integration are *** using these continuous,piecewise time reconstructions,the upper and lower error bounds depending only on the discretization parameters and the data of the problems are *** numerical experiments for the one-dimensional linear fractional parabolic equations with smooth or nonsmooth exact solution are used to verify and complement our theoretical results,with the convergence ofαorder for the nonsmooth case on a uniform *** recover the optimal convergence order 2-αon a nonuniform mesh,we further develop a time adaptive algorithm by means of barrier function recently *** numerical implementations are performed on nonsmooth case again and verify that the true error and a posteriori error can achieve the optimal convergence order in adaptive mesh.
For fractional Volterra integro-differential equations(FVIDEs)with weakly singular kernels,this paper proposes a generalized Jacobi spectral Galerkin *** basis functions for the provided method are selected generalize...
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For fractional Volterra integro-differential equations(FVIDEs)with weakly singular kernels,this paper proposes a generalized Jacobi spectral Galerkin *** basis functions for the provided method are selected generalized Jacobi functions(GJFs),which can be utilized as natural basis functions of spectral methods for weakly singular FVIDEs when appropriately *** developed method's spectral rate of convergence is determined using the L^(∞)-norm and the weighted L^(2)-*** results indicate the usefulness of the proposed method.
In view of the fact that impulsive differential equations have the discreteness due to the impulse phenomenon, this article proposes a single hidden layer neural networkmethod-based extreme learning machine and a phys...
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In view of the fact that impulsive differential equations have the discreteness due to the impulse phenomenon, this article proposes a single hidden layer neural networkmethod-based extreme learning machine and a physics-informed neural network method combined with learning rate attenuation strategy to solve linear impulsive differential equations and nonlinear impulsive differential equations, respectively. For the linear impulsive differential equations, first, the interval is segmented according to the impulse points, and a single hidden layer neural network model is constructed, the weight parameters of the hidden layer are randomly set, the optimal output parameters, and solution of the first segment are obtained by the extreme learning machine algorithm, then we calculate the initial value of the second segment according to the jumping equation and the remaining segments are solved in turn in the same way. Although the single hidden layer neural network method proposed can solve linear equations with high accuracy, it is not suitable for solving nonlinear equations. Therefore, we propose the physics-informed neural network combined with a learning rate attenuation strategy to solve the nonlinear impulsive differential equations, then the Adam algorithm and L-BFGS algorithm are combined to find the optimal approximate solution of each segment. Numerical examples show that the single hidden layer neural network method with Legendre polynomials as the activation function and the physics-informed neural network method combined with learning rate attenuation strategy can solve linear and nonlinear impulsive differential equations with higher accuracy. Impact Statement-It is difficult to obtain the analytical solutions of impulsive differential equations because of the existence of impulse points, and the current numerical methods are complicated and demanding. In recent years, artificial neural network methods have been widely used due to its simplicity and efficie
In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solv...
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In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the *** particular,when the fractional order is no longer varying,the conclusions obtained are consistent with the relevant conclusions in the existing ***,the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.
A novel arbitrary high-order energy-stable fully discrete schemes are proposed for the nonlinear Benjamin-Bona-Mahony-Burgers equation based on linearized Crank-Nicolson scheme in time and the virtual element discreti...
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In this paper,we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's *** propose two a posteriori error estimators,one is the recovery-type estimator,and the othe...
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In this paper,we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's *** propose two a posteriori error estimators,one is the recovery-type estimator,and the other is the residual-type *** first propose the curl-recovery method for the staggered discontinuous Galerkin method(SDGM),and based on the super-convergence result of the postprocessed solution,an asymptotically exact error estimator is *** residual-type a posteriori error estimator is also proposed,and it's reliability and effectiveness are proved for variable coefficients time-harmonic Maxwell's *** efficiency and robustness of the proposed estimators is demonstrated by the numerical experiments.
Locomotor intent classification has become a research hotspot due to its importance to the development of assistive robotics and wearable *** work have achieved impressive performance in classifying steady locomotion ...
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Locomotor intent classification has become a research hotspot due to its importance to the development of assistive robotics and wearable *** work have achieved impressive performance in classifying steady locomotion ***,it remains challenging for these methods to attain high accuracy when facing transitions between steady locomotion *** to the similarities between the information of the transitions and their adjacent steady ***,most of these methods rely solely on data and overlook the objective laws between physical activities,resulting in lower accuracy,particularly when encountering complex locomotion modes such as *** address the existing deficiencies,we propose the locomotion rule embedding long short-term memory(LSTM)network with Attention(LREAL)for human locomotor intent classification,with a particular focus on transitions,using data from fewer sensors(two inertial measurement units and four goniometers).The LREAL network consists of two levels:One responsible for distinguishing between steady states and transitions,and the other for the accurate identification of locomotor *** classifier in these levels is composed of multiple-LSTM layers and an attention *** introduce real-world motion rules and apply constraints to the network,a prior knowledge was added to the network via a rule-modulating *** method was tested on the ENABL3S dataset,which contains continuous locomotion date for seven steady and twelve transitions *** results showed that the LREAL network could recognize locomotor intents with an average accuracy of 99.03%and 96.52%for the steady and transitions states,*** is worth noting that the LREAL network accuracy for transition-state recognition improved by 0.18%compared to other state-of-the-art network,while using data from fewer sensors.
*** this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodi...
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*** this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodinger equation into an equivalent system and to transform the energy into a quadratic *** use the standard continuous finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time *** mass and energy conservation laws are shown for the semi-discrete finite element scheme,and also preserved for the full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta *** examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations.
Creep rupture of the reduced activation ferritic/martensitic(RAFM)steel and 316L steel dissimilar joint by friction stir welding was *** creep rupture time of the dissimilar joint was 1941 h at 600℃/100 MPa and 120 h...
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Creep rupture of the reduced activation ferritic/martensitic(RAFM)steel and 316L steel dissimilar joint by friction stir welding was *** creep rupture time of the dissimilar joint was 1941 h at 600℃/100 MPa and 120 h at 650℃/100 *** creep fracture occurred in heat affect zone(HAZ)of RAFM steel side where coarse Laves phase was *** formation and coarsening of the Laves phase particles in HAZ of RAFM steel side were the main reasons that caused the creep fracture of the dissimilar *** Laves phase particles nucleated adjacent to the large M_(23)C_(6) particles at the grain boundaries where W element segregated and grew fast during creep *** large Laves phase would deteriorate the pinning effect of M_(23)C_(6) carbides and weaken the solid solution strengthening ***,the size of the Laves phase in HAZ of RAFM steel side was bigger than that in stir zone of RAFM steel *** reasons explain the creep fracture in HAZ of RAFM steel side of dissimilar joint.
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