Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It ...is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the corresponding discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.
Linear stability analysis of Maxwell fluid in the Bénard problem for a double-diffusive mixture in a porous medium is studied based on the Darcy–Maxwell model. The critical Rayleigh number and the ...corresponding wave number for the exchange of stability are obtained. On the other hand, the effect of the relaxation time of Maxwell fluid on the critical Rayleigh number is discussed. In limiting cases, some results published previously are recovered from our results.
The stress relaxation behavior of barium titanate (BTO)‐elastomer (Ecoflex) composites, as used in large strain sensors, is studied using the generalized Maxwell‐Wiechert model. In this article, we ...examine the stress relaxation behavior of ceramic polymer composites by conducting stress relaxation tests on samples prepared with varying the particle loading by 0, 10, 20, 30, and 40 wt% of 100 and 200 nm BTO ceramic particles embedded in a Ecoflex silicone‐based hyperelastic elastomer. The influence of BTO on the Maxwell‐Wiechert model parameters was studied through the stress relaxation results. While a pristine Ecoflex silicone elastomer is predominantly a hyperelastic material, the addition of BTO made the composite behave as a visco‐hyperelastic material. However, this behavior was shown to have a negligible effect on the electrical sensing performance of the large strain sensor.
Magnetic cavities are sudden depressions of magnetic field strength widely observed in the space plasma environments, which are often accompanied by plasma density and pressure enhancement. To ...describe these cavities, self‐consistent kinetic models have been proposed as equilibrium solutions to the Vlasov‐Maxwell equations. However, observations from the Magnetospheric Multi‐Scale (MMS) constellation have shown the existence of helical magnetic cavities characterized by the presence of azimuthal magnetic field, which could not be reconstructed by the aforementioned models. Here, we take into account another invariant of motion, the canonical axial momentum, to construct the particle distributions and accordingly modify the equilibrium model. The reconstructed magnetic cavity shows excellent agreement with the MMS1 observations not only in the electromagnetic field and plasma moment profiles but also in electron pitch‐angle distributions. With the same set of parameters, the model also predicts signatures of the neighboring MMS3 spacecraft, matching its observations satisfactorily.
Plain Language Summary
Magnetic cavities, also referred to as magnetic holes, are ubiquitous in the space plasma environment characterized by depressed magnetic field strength and enhanced plasma pressure. These structures are usually believed to result from plasma instabilities, although recent observations and simulations have suggested their quasi‐stationary nature. Kinetic models of magnetic cavities have been also proposed, which show excellent agreement with spacecraft observations to indicate the formation of quasi‐equilibrium cavities during the turbulent evolution of space plasmas. These models, however, apply only to magnetic cavities with straight field lines, and therefore cannot describe the helical magnetic cavities recently discovered by NASA's Magnetospheric Multi‐Scale (MMS) constellation. In this paper, we propose a revised model by incorporating the canonical axial momentum as an additional invariant of particle motion into the particle distributions, to resolve the self‐consistent profiles of the electromagnetic field and particle distributions within the magnetic cavity. This revision accommodates the field‐aligned current to support the helical field lines, which shows remarkable agreement with the observations from the MMS constellation.
Key Points
Spacecraft observations of magnetic cavities are sometimes accompanied by azimuthal magnetic field indicating the helical structure
Kinetic, equilibrium model of helical magnetic cavities is developed based on four invariants of particle motion
The model reproduces the MMS observations of helical magnetic cavities in both electromagnetic field and particle distributions
The traditional laminar plane wall jet is studied when the medium is filled with nanoparticles of Ag, Cu, CuO, Al2O3 and TiO2. It is aimed to understand the effects of several nanofluids on the heat ...and flow behaviors of the wall jet. Momentum and thermal integral flux relations are obtained initially. Later on, some important shape factors are defined designing the momentum boundary layer, shear layer as well as the thermal boundary layer when the wall is subjected to either adiabatic or isothermal wall constraints. By means of these parameters, the flow field is shown to be decelerated and as a consequence the shear stress on the wall is enhanced. Without solving the energy equation, the thermal layer shape factor enables one to fully seize the cooling effect of considered nanofluids for both adiabatic and isothermal wall cases. As a result, the heat transfer rate is found to be greatly enhanced by the presence of nanoparticles. Same conclusions are reached by two different popular nanofluid models made use in the recent nanofluid researches.
•The momentum layer shape factor indicates decay regarding the velocity field.•The shape factor explains why the nanofluid Ag most enhances the skin friction.•An explicit correlation between the skin friction and the rate of heat transfer.•Without solving the energy equation, the rate of heat transfer is enhanced.•The Maxwell–Garnett model and the Patel model lead to the same conclusions.
Reproduction by individuals is typically recorded as count data (e.g., number of fledglings from a nest or inflorescences on a plant) and commonly modeled using Poisson or negative binomial ...distributions, which assume that variance is greater than or equal to the mean. However, distributions of reproductive effort are often underdispersed (i.e., variance < mean). When used in hypothesis tests, models that ignore underdispersion will be overly conservative and may fail to detect significant patterns. Here we show that generalized Poisson (GP) and Conway-Maxwell-Poisson (CMP) distributions are better choices for modeling reproductive effort because they can handle both overdispersion and underdispersion; we provide examples of how ecologists can use GP and CMP distributions in generalized linear models (GLMs) and generalized linear mixed models (GLMMs) to quantify patterns in reproduction. Using a new R package, glmmTMB, we construct GLMMs to investigate how rainfall and population density influence the number of fledglings in the warbler Oreothlypis celata and how flowering rate of Heliconia acuminata differs between fragmented and continuous forest. We also demonstrate how to deal with zero-inflation, which occurs when there are more zeros than expected in the distribution, e.g., due to complete reproductive failure by some individuals.
A positive preserving scheme is proposed for Vlasov‐Bhatnagar‐Gross‐Krook (BGK)‐Maxwell model to simulate the laser‐plasma‐interaction with relativistic effect. The Strang‐splitting method is adopted ...and the Vlasov‐BGK equation is divided into two parts, the kinetic part and acceleration part. Asymptotic gas‐kinetic scheme is designed for the kinetic part and the solver for p direction is analytically accurate along the characteristic. Maxwell equations are solved by characteristic line method. The scheme is proved positive preserving. Stimulated Raman Scattering and Relativistic Modulational Instability are used to verify the validity of scheme.
The minimum value of different time for f(x,p) with nonpositive preserving scheme (A) and positive preserving scheme (B) in FRS Time evolution of energy in FRS of positive preserving reconstruction: (C) electrostatic energy and (D) kinetic energy
We investigate the onset of a non-equilibrium phase transition in a one-dimensional ring, constituted by two urns connected by two strands, called active and passive channels. A set of N particles ...move inside the ring with constant individual speeds; collisions against the channel entries produce reflections with certain probabilities, that differ between active and passive channels. The microscopic dynamics differs from a classical 1D billiard owing to the presence of an interaction mechanism acting inside the active channel, which potentially reverses velocities of its particles. We outline a general theory for the feedback-controlled system which describes quantitatively the phase diagram of the model, based on a mixing property, that is analytically predicted and numerically verified. The probability distributions we define and evolve in time are 1D projections of uniform distributions on d-dimensional spherical surfaces, with d≥1 and d=∞. Consequently results that apply to higher dimensional systems are recovered.
The study of shadow is quite prominent nowadays because of the ongoing Event Horizon Telescope1 observations. We construct the shadow images of charged wormholes in Einstein–Maxwell–dilaton (EMD) ...theory. The spacetime metric of the charged wormholes contains three charges: magnetic charge P, electric charge Q, and dilaton charge Σ. We evaluate the photon geodesics around the charged wormholes. We also calculate the effective potential and discuss its behavior with angular momentum L and different values of charges P, Q, and Σ. A study of the shadow of charged wormholes reveals that the shadow has an effect of the charges P and Q. The radius of the shadow increases with the magnetic charge P as well as the electric charge Q. We also find that the dilaton charge does not affect the shadow of the charged wormholes.
•Mixed convective flow of Maxwell nanomaterial containing motile gyrotactic microorganisms is addressed.•Magnetohydrodynamics (MHD) and stratifications are present.•Computations are made to obtain ...the solution expressions.
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The ultimate purpose of present article is to investigate the heat, mass and motile microorganisms transfer rates in the convective stretched flow of Maxwell fluid consisting of nanoparticles and gyrotactic microorganisms. Magneto nanofluid in presence of mixed convection and stratification is considered. Concept of microorganisms is utilized just to stabilize the suspended nanoparticles through bioconvection which has been induced by combined effects of buoyancy forces and magnetic field. Further interesting aspects of Brownian motion, thermophoresis and stratification are examined. Convergent series solutions for the obtained nonlinear differential systems are derived. Impacts of different emerging parameters on velocity, temperature, concentration and motile microorganisms density are addressed through graphs. Numerical values for the local Nusselt, Sherwood and density number of motile microorganisms are computed and analyzed. It is observed that thermal, concentration and motile density stratification parameters result in the reduction of temperature, concentration and motile microorganisms density distributions, respectively.
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