This study addresses the entropy generation in a magnetohydrodynamic flow of a Maxwell nanofluid over an infinite horizontal surface. The flow is then induced by the non-linear surface stretching. ...Furthermore, thermal radiation and viscous dissipation are also included in the present study as external sources. Similarity solutions are obtained by transformation of governing partial differential equations (PDEs) to ordinary differential equations (ODEs) using similarity variables. Keller box method is then adopted to find the approximate solutions of reduced ordinary differential equations. Two different classes of nanofluids, Copper-water (Cu − H2O) and Titanium-water (TiO2 − H2O) are considered for our analysis. Significant results of various parameters in flow, heat, Skin friction (Cf), Nusselt number (Nux), and entropy analysis are elaborated graphically. The remarkable finding of this work is that the thermal conductivity in Maxwell phenomena gradually increases as compared to the conventional fluid. The entropy of the system exaggerates with the incorporation of nanoparticle volume fraction ϕ, Reynolds number Re, Biot number Bi, Eckert number Ec, Brinkan number Bi and thermal radiation Nr. The sticking feature of the present study is that Cu-water based nanofluid is detected as a superior thermal conductor instead of TiO2-water based nanofluid.
This study reports an incompressible electrically conducting Casson–Maxwell fluid flow confined across two uniformly stretchable disks. Buongiorno nanofluid model is implemented in the fluid flow. ...Cattaneo–Christov theory of double-diffusion is characterized through the heat and mass equations. Velocity, thermal and concentration slip conditions are executed at the lower stretchable disk. The flow model is dimensionalized through the similarity functions and then numerical solution is attained by RKF-45 scheme combined with shooting technique. The results of physical parameters are discussed by plotting the effects of such parameters on velocity, thermal and concentration fields. The results revealed that the Maxwell liquid is highly effected by Lorentz force than the Casson liquid. Thermal gradient of Maxwell liquid is highly influenced by stretching ratio parameter when compared to Casson fluid. Increase in Casson parameter and Deborah number declines the velocity gradient. Rise in the values of Brownian motion parameter declines the concentration gradient. Finally, the upsurge in thermal relaxation time parameter enhances the thermal gradient quickly in absence of thermal slip parameter.
This work investigates the classical and quantum duality between the SIM(1)-Maxwell-Chern-Simons (MCS) model and its self-dual counterpart. Initially, we focus on free-field cases to establish ...equivalence through two distinct approaches: comparing the equations of motion and utilizing the master Lagrangian method. In both instances, the classical correspondence between the self-dual and MCS dual fields undergoes modifications due to very special relativity (VSR). Specifically, the duality is established when the associated VSR-mass parameters are identical, and the dual field is introduced through a non-local VSR correction. Furthermore, we analyze the duality when the self-dual model is minimally coupled to fermions. As a result, we demonstrate that Thirring-like interactions, corrected for non-local VSR contributions, are included in the MCS model. Additionally, we establish the quantum equivalence of the models by performing a functional integration of the fields and comparing the resulting effective Lagrangians.
Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of the Klein–Gordon–Maxwell system{−ε2Δgu+au=up−1+ω2(qv−1)2uin M,−Δgv+(1+q2u2)v=qu2in M and ...Schrödinger–Maxwell system{−ε2Δgu+u+ωuv=up−1in M,−Δgv+v=qu2in M when p∈(4,6). We prove that the number of one peak solutions depends on the topological properties of the manifold M, by means of the Lusternik Schnirelmann category.
In the past years there was a huge interest in experimental and theoretical studies in the area of few-optical-cycle pulses and in the broader fast growing field of the so-called extreme nonlinear ...optics. This review concentrates on theoretical studies performed in the past decade concerning the description of few optical cycle solitons beyond the slowly varying envelope approximation (SVEA). Here we systematically use the powerful reductive expansion method (alias multiscale analysis) in order to derive simple integrable and nonintegrable evolution models describing both nonlinear wave propagation and interaction of ultrashort (femtosecond) pulses. To this aim we perform the multiple scale analysis on the Maxwell–Bloch equations and the corresponding Schrödinger–von Neumann equation for the density matrix of two-level atoms. We analyze in detail both long-wave and short-wave propagation models. The propagation of ultrashort few-optical-cycle solitons in quadratic and cubic nonlinear media are adequately described by generic integrable and nonintegrable nonlinear evolution equations such as the Korteweg–de Vries equation, the modified Korteweg–de Vries equation, the complex modified Korteweg–de Vries equation, the sine–Gordon equation, the cubic generalized Kadomtsev–Petviashvili equation, and the two-dimensional sine–Gordon equation. Moreover, we consider the propagation of few-cycle optical solitons in both (1+1)- and (2+1)-dimensional physical settings. A generalized modified Korteweg–de Vries equation is introduced in order to describe robust few-optical-cycle dissipative solitons. We investigate in detail the existence and robustness of both linearly polarized and circularly polarized few-cycle solitons, that is, we also take into account the effect of the vectorial nature of the electric field. Some of these results concerning the systematic use of the reductive expansion method beyond the SVEA can be relatively easily extended to few-cycle solitons in the general case of multilevel atoms. Prospects of the studies overviewed in this work are given in the conclusions.
The Vlasov–Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extremely expensive from a ...computational point of view. In this paper, we exploit the low-rank structure in the solution of the Vlasov equation. More specifically, we consider the Vlasov–Maxwell system and propose a dynamic low-rank integrator. The key idea is to approximate the dynamics of the system by constraining it to a low-rank manifold. This is accomplished by a projection onto the tangent space. There, the dynamics is represented by the low-rank factors, which are determined by solving lower-dimensional partial differential equations. The proposed scheme performs well in numerical experiments and succeeds in capturing the main features of the plasma dynamics. We demonstrate this good behavior for a range of test problems. The coupling of the Vlasov equation with the Maxwell system, however, introduces additional challenges. In particular, the divergence of the electric field resulting from Maxwell's equations is not consistent with the charge density computed from the Vlasov equation. We propose a correction based on Lagrange multipliers which enforces Gauss' law up to machine precision.
► Sorption study of ZIF-8. ► Generally good adhesion between 6FDA-DAM and bare ZIF-8 particles. ► Enhanced C3H6/C3H8 separation performance of ZIF-8/6FDA-DAM mixed matrix membrane. ► Comparison of ...experimental results with the Maxwell model simulation results.
We report significantly enhanced propylene/propane (C
3H
6/C
3H
8) selectivity in mixed matrix membranes fabricated using 6FDA-DAM polyimide and a zeolitic imidazolate framework (ZIF-8). Equilibrium isotherms and sorption kinetics of C
3H
6 and C
3H
8 at 35
°C were studied on a 200
nm commercially available ZIF-8 sample produced by BASF. Mixed matrix dense films were formed with 6FDA-DAM and 200
nm BASF ZIF-8 particles. SEM imaging showed generally good adhesion between the ZIF-8 and 6FDA-DAM without the need for surface-treating ZIF-8. Pure gas permeation showed significantly enhanced mixed matrix ZIF-8/6FDA-DAM membrane C
3H
6/C
3H
8 separation performance over the pure 6FDA-DAM membrane performance. A C
3H
6 permeability of 56.2
Barrer and C
3H
6/C
3H
8 ideal selectivity of 31.0 was found in ZIF-8/6FDA-DAM mixed matrix membrane with 48.0
wt% ZIF-8 loading, which are 258% and 150% higher than the pure 6FDA-DAM membrane, respectively for permeability and selectivity. Permeation properties of C
3H
6 and C
3H
8 in ZIF-8 were back-calculated by the Maxwell model for composite permeability using pure gas permeation data, leading to a C
3H
6 permeability of 277
Barrer and C
3H
6/C
3H
8 selectivity of 122. Mixed gas permeation also verified that selectivity enhancements were achievable in mixed gas environment by ZIF-8.
This paper deals with the low Mach number limit of the full compressible Navier–Stokes–Maxwell system. It is justified rigorously that, for the well-prepared initial data, the solutions of the full ...compressible Navier–Stokes–Maxwell system converge to that of the incompressible Navier–Stokes–Maxwell system as the Mach number tends to zero.
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