Search

Continental arcs in active continental margins (especially deep-seated arc magmatism, anatexis, and metamorphism) can be extremely significant in evaluating continent building processes. In this contribution, a Paleozoic continental arc section is constructed based on coeval granulite-facies metamorphism, anatexis, and magmatism on the northern margin of the Qilian Block, which record two significant episodes of continental crust growth. The deeper layer of the lower crust mainly consists of medium-high pressure mafic and felsic granulites, with apparent peak pressure-temperature conditions of 11-13 kbar and 800-950 °C, corresponding to crustal depths of ~35-45 km. The high-pressure mafic granulite and local garnet-cumulate represent mafic residues via dehydration melting involving breakdown of amphibole with anatectic garnet growth. Zircon U-Pb geochronology indicates that these high-grade metamorphic rocks experienced peak granulite-facies metamorphism at ca. 450 Ma. In the upper layer of the lower crust, the most abundant rocks are preexisting garnet-bearing metasedimentary rocks, orthogneiss, and local garnet amphibolite, which experienced medium-pressure amphibolite-facies to granulite-facies metamorphism at depths of 20-30 km at ca. 450 Ma. These metasedimentary rocks and orthogneiss have also experienced partial melting involving mica and rare amphibole at 457-453 Ma. The shallow to mid-crust is primarily composed of diorite-granodiorite batholiths and volcanic cover with multiple origin, which were intruded during 500-450 Ma, recording long-term crustal growth and differentiation episode. As a whole, two episodes of continental crust growth were depicted in the continental arc section on the northern margin of the Qilian Block, including: (a) the first episode is documented in a lithological assemblage composing of coeval mafic-intermediate intrusive and volcanic rocks derived from partial melting of modified lithospheric mantle and subducted oceanic crust during southward subduction of the North Qilian Ocean at 500-480 Ma; (b) the second episode is recorded in mafic rocks derived from partial melting of modified lithospheric mantle during transition from oceanic subduction to initial collision at 460-450 Ma. [ABSTRACT FROM AUTHOR]

The fractional (3+1)-dimensional nonlinear Schrödinger equation with cubic–quintic–septic nonlinearities plays a significant role in the study of ultra-short pulses in highly nonlinear optical phenomena. The main purpose of this work is to determine the solution of (3+1)-dimensional nonlinear Schrödinger equation containing cubic–quintic–septic nonlinearities with conformal temporal operator. The solution of the considered problem is investigated using an adaptation of the residual power series method for the conformal fractional derivative. To illustrate the authenticity of the residual power series method to solve the nonlinear conformable Schrödinger equation with cubic–quintic–septic nonlinearities, three test applications are considered subject to different initial conditions. The variations of wave solutions of the applications corresponding to changes in the conformal derivative are depicted through graphical illustrations. The numerical comparisons confirm the accuracy of the presented results for the conformal (3+1)-dimensional nonlinear Schrödinger equation. The obtained results indicate the accuracy, suitability and competency of the residual power series method to examine other nonlinear conformable fractional differential equations arising in optics and other areas of physics.

Heat transfer analysis of partially heated non-Newtonian liquid suspensions in closed enclosures rooted with the porous medium attracts the attention of researchers due to its abundant applications in thermal engineering. The problem appears at the solution exploration stage of the non-linear differential system constructed against heated liquid suspension equipped in a partially heated porous cavity. Therefore, the present numerical study is devoted to reporting the untapped characteristics of the non-Newtonian liquid suspension in a partially heated square enclosure rooted with diamond obstruction. The flow in a porous medium is induced by in-taking free convection. To encounter liquid suspension heat transfer aspects we have incorporated the energy equation. The enclosures lower wall is evenly heated, while the upper wall is held adiabatic. We used the finite element approach to solve the partial differential equations that resulted from the modeling. To bring hybrid meshing of the porous domain, both rectangular and triangular elements are selected. The free convection and porous media result in the Rayleigh number and Darcy number. We execute both contour and line graph studies to report the variation in Casson fluid stream function, Casson fluid temperature, pressure, dimensionless vertical velocity, horizontal velocity, and Nusselt number. It is concluded that installing Diamond-shaped obstruction in a porous medium result in heat transfer enhancement within a closed square cavity. The current theoretical research is intended to assist in the analysis of non-Newtonian fluid flow fields in heated porous enclosures.

Analytical solutions of the fractional wave equation via Caputo-Fabrizio fractional derivative are presented in this paper. For this analysis, three cases are considered, the classical, the damped and the damped with a source term defined by fractional wave equations. We show that these solutions are special cases of the time fractional equations with exponential law. Illustrative examples are presented.

A mosquito born viral disease (Dengue) becoming endemic around the globe which including cause of severe illness and death in various Asian and Latin American countries. It needs proper management by researchers and medicine professionals. The current research work is a step towards the prevention/reduction of such deadly disease in the society. More precisely, this work addressing various mathematical proofs interconnected to the existence and stability along with numerical findings by using mathematical modeling techniques. Further, the existence results have been established for the proposed model under the Atangana-Baleanu derivative in Caputo sense (ABC) with fractional order. In continuation, we find the deterministic stability for the proposed model. Lastly, the new version of numerical approximation’s framework for the approximation of ABC fractional derivative is used to carried out the numerical simulation for the obtained results.

Installing obstructions in the path of the flowing stream in a Convergent-Divergent channel results in complex Reynolds Navier-Stokes (NS)-equations and an exact solution in this direction is not feasible. The current work is a notable attempt in this direction, reporting the evaluation of hydrodynamic forces faced by case-wise installation of infinite cylinders as obstacles to a continuous fluid stream. To be more specific, Newtonian fluid is initiated from inlet with bound of parabolic profile. The outlet of CD channel is carried with Neumann condition. The optimized path of installation of obstacle includes: (i) Two circular shaped cylinders are installed in left and right vicinity of CD throat (ii) Circular cylinder in right vicinity of CD throat is optimized with square cylinder (iii) Circular cylinder in left vicinity of CD throat is optimized with square cylinder. The flow field is mathematically modelled in terms of steady Reynolds NS-equations. The comparative solution is reported by using finite element method along rectangular and triangular elements as a hybrid meshing scheme. The obtained outcomes are shared by means of contour and line graphs. Optimized values of hydrodynamic forces subject to installed obstacles in convergent-divergent channel are reported by doing line integration around the outer surfaces of obstructions. It is observed that in each case, the obstructions in left vicinity of CD throat admits inciting values of drag coefficient as compared to obstruction rooted in right vicinity of CD throat.

This paper is dedicated to construct a viscosity extragradient algorithm for finding fixed points in a CAT(0) space. The mappings we consider are nonexpansive. Strong convergence of the algorithm is obtained. The results established in this work extend and improve some recent discovers in the literature.