Charged stellar model with three layers

We establish new charged stellar models from the Einstein-Maxwell field equations for relativistic superdense objects outfitted with three layers. The core layer is described by a linear equation of state (EoS) describing quark matter, while the intermediate layer is described by a Bose-Einstein condensate EoS for Bose-Einstein condensate matter and the envelope layers satisfying a quadratic EoS for the neutron fluid. We have specified a new choice of the electric field and one of the metric potentials. It is interesting to note that the choice of electric field in this model can be set to vanish and we can regain earlier neutral models. Plots generated depict that the matter variables, gravitational potentials and other physical conditions are consistent with astrophysical studies. The interior layers and exterior boundary are also matched.

Unsymmetrical Growth Synthesis of Nontraditional Dendrimers

Developing highly complex molecules is of great significance in science and technology. Here we present an unprecedented type of dendrimer assembled from linear ABB-type monomer. The construction of this nontraditional ramified architecture was facilely achieved through one simple convergent strategy established on the iridium-catalyzed cycloaddition of organic azides with internal 1-thioalkynes (IrAAC). By virtue of the unsymmetrically growing fashion in this process, diverse functional groups could be conveniently distributed on both of its exterior and interior layers. Syntheses of two dendrons from the cooperation of one linear alkyne motif with different azides were presented to demonstrate the efficiency and fidelity of this protocol. Post-modifications on their core or periphery were further conducted, resulting in diverse newly functionalized dendrimers with up to ~16.0 kDa molecular weight. The identity and purity of these unsymmetrical dendritic macromolecules were well confirmed by 1H NMR, MS and SEC analysis.

Boundary separated and clustered layer positive solutions for an elliptic Neumann problem with large exponent

Given a smooth bounded domain [Formula: see text] in [Formula: see text] with [Formula: see text], we study the existence and the profile of positive solutions for the following elliptic Neumann problem: [Formula: see text] where [Formula: see text] is a large exponent and [Formula: see text] denotes the outer unit normal vector to the boundary [Formula: see text]. For suitable domains [Formula: see text], by a constructive way we prove that, for any non-negative integers [Formula: see text], [Formula: see text] with [Formula: see text], if [Formula: see text] is large enough, such a problem has a family of positive solutions with [Formula: see text] boundary layers and [Formula: see text] interior layers which concentrate along [Formula: see text] distinct [Formula: see text]-dimensional minimal submanifolds of [Formula: see text], or collapse to the same [Formula: see text]-dimensional minimal submanifold of [Formula: see text] as [Formula: see text].

Special adaptive grids and Runge - Richardson correction in problems with layers

При решении задач с пограничными и внутренними слоями на адаптивных сетках весьма желательно пользоваться разностными схемами, которые имеют достаточно хорошую точность и сходятся равномерно по малому параметру при стремлении шагов сетки к нулю. Однако эти требования оказываются противоречивыми: схемы высокой точности не сходятся равномерно, а равномерно сходящиеся схемы имеют обычно лишь первый порядок точности. Тем не менее существует уникальная возможность разрешить это противоречие, повышая порядок точности путем применения экстраполяционных поправок Рунге-Ричардсона, представляющих собой линейные комбинации разностных решений на вложенных сетках. В данной работе на примере нескольких употребительных разностных схем изучается эффективность такого подхода к расчетам, полученным на адаптивных сетках, явно задаваемых специальными координатными преобразованиями. Исследуются две схемы противопотокового типа с диагональным преобладанием, равномерно сходящиеся, в сравнении с аналогом схемы с центральной разностью, не имеющей диагонального преобладания и не сходящейся равномерно. Кроме простых поправок применяются также двукратные поправки, еще более повышающие порядок точности результирующих решений It is highly desirable using difference schemes with high accuracy and uniform convergence in a small parameter as the grid steps tend to zero for solving the problems with both boundary and interior layers. However, these requirements turn out to be contradictory: highly-accurate schemes may not converge uniformly, and uniformly converging schemes usually have only the first order of accuracy. Nevertheless, there is a unique opportunity to resolve this contradiction by increasing the order of accuracy by applying the Richardson-Runge extrapolation corrections, which are linear combinations of difference solutions on nested grids. In this paper, using the example of several common difference schemes, we study the efficiency of such approach for calculations obtained on adaptive grids that are explicitly specified by special coordinate transformations. Two diagonal-dominated upstream-type uniformly converging schemes are investigated. They are compared with an analogue of the scheme with central difference that does not have a diagonal dominance and does not converge uniformly. In addition to simple corrections, double corrections are also used, which further increase the order of accuracy of the resulting solutions

A Special Multigrid Strategy on Non-Uniform Grids for Solving 3D Convection–Diffusion Problems with Boundary/Interior Layers

Boundary or interior layer problems of high-dimensional convection–diffusion equations have distinct asymmetry. Consequently, computational grid distributions and linear algebraic systems arising from finite difference schemes for them are also asymmetric. Numerical solutions for these kinds of problems are more complicated than those symmetric problems. In this paper, we extended our previous work on the partial semi-coarsening multigrid method combined with the high-order compact (HOC) difference scheme for solving the two-dimensional (2D) convection–diffusion problems on non-uniform grids to the three-dimensional (3D) cases. The main merit of the present method is that the multigrid method on non-uniform grids can be performed with a different number of grids in different coordinate axes, which is more efficient than the multigrid method on non-uniform grids with the same number of grids in different coordinate axes. Numerical experiments are carried out to validate the accuracy and efficiency of the present method. It is shown that, without losing the high precision, the present method is very effective to reduce computing cost by cutting down the number of grids in the direction(s) which does/do not contain boundary or interior layer(s).