Objective: The paper is focused on developing and analyzing a uniformly convergent numerical scheme for a singularly perturbed reaction-diffusion problem with a negative shift. The solution of such problem exhibits strong boundary layers at the two ends of the domain due to the influence of the perturbation parameter, and the term with negative shift causes interior layer. The rapidly changing behavior of the solution in the layers brings significant difficulties in solving the problem analytically. We have treated the problem by proposing a numerical scheme using the implicit Euler method in the temporal direction and a fitted tension spline method in the spatial direction with uniform meshes.
Result: Stability and uniform error estimates are investigated for the developed numerical scheme. The theoretical finding is demonstrated by numerical examples. It is obtained that the developed numerical scheme is uniformly convergent of order one in time and order two in space.
Voltage-dependent anion channel (VDAC) is the primary conduit for regulated passage of ions and metabolites into and out of a mitochondrion. Calculating the solvation free energy for VDAC is crucial for understanding its stability, function, and interactions within the cellular environment. In this article, numerical schemes for computing the total solvation free energy for VDAC-comprising electrostatic, ideal gas, and excess free energies plus the nonpolar energy-are developed based on a nonuniform size modified Poisson-Boltzmann ion channel (nuSMPBIC) finite element solver along with tetrahedral meshes for VDAC proteins.
Source protection zone delineation has evolved over the past decades from fixed radius or analytical and numerical methods which do not consider uncertainty, to more complex stochastic numerical approaches. In this paper we explore options for delineating a source protection zone, while considering the inherent uncertainty involved in characterizing hydraulic conductivity. We consider a representative pumping well in an unconfined alluvial aquifer under steady-state flow conditions, with the hydraulic conductivity distribution inferred from borehole lithology data in the West Melton area near Christchurch, New Zealand.
In numerical model simulations, data assimilation (DA) on the initial conditions and bias correction (BC) of model outputs have been proven to be promising approaches to improving PM (particulate matter with an aerodynamic equivalent diameter of ≤ 2.5 μm) predictions. This study compared the optimization effects of these two methods and developed a new scheme that combines DA and BC simultaneously.
In this Letter, we have proposed an all-optical scheme for chiral particle separation with a microcylinder-pair system (MCPS) with a micrometer scale channel, applicable in microfluidic environments. By illuminating the MCPS with two counter-incident plane waves of orthogonal polarization, the electromagnetic chirality gradient can be generated. The MCPS can also enhance chirality-dependent lateral optical forces of the coupled fields so that the setup can shift trapping equilibrium positions for opposite-handedness nanoparticles and make the sideways motion observable.
All-dielectric metasurface (ADM) absorbers driven by quasi-bound states in the continuum (BIC) are critical for high-performance optoelectronic devices due to their ability to offer high -factor absorption. However, these all-dielectric metasurfaces usually require the aid of degenerate critical coupling schemes or back-metal reflective layers to achieve high absorption, which often suffers from limitations such as sensitive geometrical parameters, ohmic losses, and low -factors. This work presents an ADM for high- near-perfect light absorption, which consists of double Si nanorods and SiO/TaO multilayers.
