Discontinuous Galerkin methods are developed for solving the Vlasov–Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and ...possibly total energy. Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov–Maxwell system. The proposed scheme employs discontinuous Galerkin discretizations for both the Vlasov and the Maxwell equations, resulting in a consistent description of the distribution function and electromagnetic fields. It is proven, up to some boundary effects, that charge is conserved and the total energy can be preserved with suitable choices of the numerical flux for the Maxwell equations and the underlying approximation spaces. Error estimates are established for several flux choices. The scheme is tested on the streaming Weibel instability: the order of accuracy and conservation properties of the proposed method are verified.
A comparative analysis is carried out to study the unsteady flow of a Maxwell fluid in the presence of Newtonian heating near a vertical flat plate. The fractional derivatives presented by Caputo and ...Caputo–Fabrizio are applied to make a physical model for a Maxwell fluid. Exact solutions of the non-dimensional temperature and velocity fields for Caputo and Caputo–Fabrizio time-fractional derivatives are determined via the Laplace transform technique. Numerical solutions of partial differential equations are obtained by employing Tzou’s and Stehfest’s algorithms to compare the results of both models. Exact solutions with integer-order derivative (fractional parameter α = 1) are also obtained for both temperature and velocity distributions as a special case. A graphical illustration is made to discuss the effect of Prandtl number Pr and time t on the temperature field. Similarly, the effects of Maxwell fluid parameter λ and other flow parameters on the velocity field are presented graphically, as well as in tabular form.
The present analysis reports a computational study of Magnetohydrodynamic (MHD) flow behaviour of 2D Maxwell nanofluid across a stretched sheet in appearance of Brownian motion. The substantial term ...thermal radiation and chemical reactions have been employed extensively in the current research. Nanofluids are usually chosen by researchers because of their rheological properties, which are important in determining their appropriateness for convective heat transfer. The present research reveals that the fluid velocity augments for the enhanced values of all the parameters. Heat source, as well as the radiation parameters, ensure that there is enough heat in the fluid, which implies escalation of the thermal boundary layer thickness by accruing radiation parameter. Moreover, streamlines and isotherms have been investigated for the different parametric values. The suggested model is valuable because it has a wide range of applications in domains including medical sciences (treatment of cancer therapeutics), microelectronics, biomedicine, biology, and industrial production processes.
Based on a modified-Darcy–Brinkman–Maxwell model, stability analysis of a horizontal layer of Maxwell fluid in a porous medium heated from below is performed. By solving the eigenvalue problems, the ...critical Rayleigh number, wave number and frequency for overstability are determined. It is found that the critical Rayleigh number for overstability decreases as the relaxation time increases and the elasticity of a Maxwell fluid has a destabilizing effect on the fluid layer in porous media. On the other hand, the critical Rayleigh number for overstability increases by increasing the porous parameter which acts to stabilize the system. In limiting cases, some previous results for viscoelastic fluids in nonporous media are recovered from our results.
This article concerns the following Klein–Gordon–Maxwell system −Δu+u−(2ω+ϕ)ϕu=f(x,u),inR3,Δϕ=(ω+ϕ)u2,inR3,where ω>0 is a constant. When f satisfies a weaker 1-superlinear condition, existence ...results for nontrivial solutions and a sequence of high energy solutions are obtained by the Mountain Pass Theorem and Symmetric Mountain Pass Theorem. Our result completes some recent works concerning research on solutions of this system.
This work is to establish optimal time decay rate of global classical solutions to the two-fluid incompressible Navier–Stokes–Maxwell system with Ohm’s law and the incompressible ...Navier–Stokes–Maxwell system with Ohm’s law in R3. The results show that the optimal time decay rate for the velocity of these two systems achieves the same as that of the incompressible Navier–Stokes equation. In other words, Ohm’s law can offset the negative effects brought by the Maxwell equation on the decay rate of solutions. This is interesting compared to the compressible Navier–Stokes system, whose time decay rate decreases when it is coupled with the self-consistent Maxwell system.
The neutrosophic approach is a potential area to provide a novel framework for dealing with uncertain data. This study aims to introduce the neutrosophic Maxwell distribution (MD̃ ) for dealing with ...imprecise data. The proposed notions are presented in such a manner that the proposed model may be used in a variety of circumstances involving indeterminate, ambiguous, and fuzzy data. The suggested distribution is particularly useful in statistical process control (SPC) for processing uncertain values in data collection. The existing formation of VSQ-chart is incapable of addressing uncertainty on the quality variables being investigated. The notion of neutrosophic VSQ chart (ṼSQ) is developed based on suggested neutrosophic distribution. The parameters of the suggested ṼSQ-chart and other performance indicators, such as neutrosophic power curve (PC̃), neutrosophic characteristic curve (CC̃) and neutrosophic run length (RL̃) are established. The performance of the ṼSQ-chart under uncertain environment is also compared to the performance of the conventional model. The comparative findings depict that the proposed ṼSQ-chart outperforms in consideration of neutrosophic indicators. Finally, the implementation procedure for real data on the COVID-19 incubation period is explored to support the theoretical part of the proposed model.
The subject of this work is the development of an approach describing the transversely isotropic viscoelastic material behaviour of carbon-fibre-reinforced plastics (CFRP) in the frequency domain. To ...identify the composite's macro-scopic transversely isotropic viscoelastic material behaviour, micro-scale numerical studies are performed on statistically representative volume elements (SRVE) under periodic boundary conditions to obtain master curves of five independent components of the homogenised complex stiffness tensor in the frequency domain. These homogenised properties are then depicted by a generalised and by a generalised fractional Maxwell model (GMM, GFMM) building the dataset for parametrising user-defined material models implemented in commercial finite element method (FEM) software. The material models are thus able to capture the material behaviour over multiple orders of magnitude in frequency with a single set of parameters each. Consequently, the conversion of time-dependent data is avoided. A comparison between experimental and numerical results is carried out and further studies on the influence of the fibre volume content are performed. The proposed method is found capable of characterising the viscoelastic behaviour of CFRP in the frequency domain and, thus, presents a viable tool to investigate e.g. the damping characteristics of fibre-reinforced plastics on component level.
The aim of this paper is to review and classify the different methods that have been developed to enable stable long time simulations of the Vlasov–Maxwell equations and the Maxwell equations with ...given sources. These methods can be classified in two types: field correction methods and source correction methods. The field correction methods introduce new unknowns in the equations, for which additional boundary conditions are in some cases non trivial to find. The source correction consists in computing the sources so that they satisfy a discrete continuity equation compatible with a discrete Gauss’ law that needs to be defined in accordance with the discretization of the Maxwell propagation operator.
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