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This paper presents the numerical analysis of a convergent-divergent circular nozzle with the exit Mach number of 1.69 with and without passive control at the exit. The passive control method opted for this analysis was inward and outward ascending triangular protrusion. This paper explores the influence of the passive control geometry and its blockage area concerning the nozzle exit. The nozzle pressure ratio (NPR) used for carrying out the flow analysis were 3, 4.932, and 6. Two different inward and outward protrusions were used with a height of 1.5 mm and 3 mm. From the results, the potential core length of the protrusion 1.5 mm height was not much changed in the both outward and inward cases. But when the height of the protrusion was increased to 3 mm, there was a noticeable core length reduction at all NPR but with different cases. At the NPR of 6, the potential core length of the inward protrusions 3 mm was reduced by 44 % compared to the plain CD nozzle. [ABSTRACT FROM AUTHOR]

In this paper, we suggest joint application of computational probabilistic analysis and the Monte Carlo method for numerical stochastic modeling problems. We use all the capabilities of computational probabilistic analysis while maintaining all the advantages of the Monte Carlo method. Our approach allows us to efficiently implement a computational hybrid scheme. In this way, we reduce the computation time and present the results in the form of distributions. The crucial new points of our method are arithmetic operations on probability density functions and procedures for constructing on the probabilistic extensions. Relying on specific numerical examples of solving systems of linear algebraic equations with random coefficients, we present the advantages of our approach. [ABSTRACT FROM AUTHOR]

The aim of this paper is to derive a novel discrete form of stochastic fractional Grönwall lemma involving a martingale. The proof of the derived inequality is accomplished by a corresponding no randomness form of the discrete fractional Grönwall inequality and an upper bound for discrete-time martingales representing the supremum in terms of the infimum. The release of a martingale term on the right-hand side of the given inequality and the graded L1 difference formula for the time Caputo fractional derivative of order 0 < α < 1 on the left-hand side are the main challenges of the stated and proved main theorem. As an example of application, the constructed theorem is used to derive an a priori estimate for a discrete stochastic fractional model at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, a set of small stoves was designed which is used for alcohol-based fuel combustion. The research object is the atomization process of alcohol-based fuel in the stove. By combining numerical analysis and experiment, this paper investigated the influence of spray pressure on the atomization characteristics of alcohol-based fuel in the stove under the static environment. The results showed that as the increase of spray pressure, the atomization cone angle increased firstly and then decreased slightly and when the spray pressure was 0.8 MPa, the atomization cone angle reached the maximum value of 79.5°; the SMD (Sauter mean diameter) at the same position of the combustion chamber decreased slowly and the spray height increased slowly and both of the SMD and spray height changed slightly when the spray pressure was not less than 0.8 MPa. The experiment verified the correctness of the numerical analysis method, and the coincidence degree between both was more than 92%. This paper also investigated the influence of swirl structure parameters on the atomization characteristics of fuel in the stove under air distribution condition by using numerical analysis method. The results showed that the air central recirculation zone only generated in the stove combustion chamber when the swirl angle was not less than 30°; the minimum SMD and the maximum average velocity of all central recirculation zones sections were obtained when the combustion chamber with 12 swirl plates and 45° swirl angle, and the atomization characteristics of the fuel in this structure were better. Further research showed that when the combustion chamber with 6 swirl plates and 40° swirl angle, the SMD of all the central recirculation zone sections is the smallest and the average velocity was slightly smaller than the maximum value; and after comprehensive analysis, the atomization characteristics of the fuel in the stove with this structure are the best. These above research results will provide reference value for the design and development of alcohol-based fuel special stoves. [ABSTRACT FROM AUTHOR]

In this paper, dispersion decreased profiled tapered fiber is designed whose dispersion characteristics and soliton propagation is investigated numerically using Darboux transformation. The result reveals that solitons pulse gets compression as it propagates along the length of the tapered region. [ABSTRACT FROM AUTHOR]

In the present paper, a new fractional order predator–prey model is considered. The applied fractional operator is a generalized Atangana–Baleanu–Caputo (ABC) derivative, which does not require any restrictions on the initial conditions as in the case of classical ABC fractional derivatives. On the theoretical aspect, we prove the existence, uniqueness, and Ulam–Hyers stability results by using some fixed point theorems and nonlinear analysis techniques. The numerical aspect discusses the approximation solutions for the proposed model by applying the generalized scheme of the Adams–Bashforth technique. At the end, we explain the behavior of the solution to the studied model through graphical representations and numerical simulations. [ABSTRACT FROM AUTHOR]

Micro-propulsion is considered to be the emerging technology for the propulsion of micro and micro aerospace vehicles as it is preferred over mesoscale thruster due to lower overall life-cycle cost and launching costs. Hence this paper investigates the influence of critical parameters like the Nozzle Pressure Ratio (NPR) and Reynolds number (Re) on the operational characteristics of the micronozzle. A conical nozzle with throat diameter 710 µm and exit/throat area ratio ∼2.14 has been designed and is analyzed numerically by using a model based on pressure-based coupled implicit for various NPR, the backpressure with three Res namely, 1000, 1500, and 2000. The performance of this micronozzle has been characterized in terms of thrust, thrust coefficient, and specific impulse for all three Re cases. A subsequent analysis of the subsonic layer reveals that the nozzle is subjected to high viscous losses at low NPRs, which are independent of Re. [ABSTRACT FROM AUTHOR]

In this paper, we present a proof-of-concept for a novel temperature sensing approach that combines the thermal expansion and a compliant mechanism. The objective is first to demonstrate its feasibility at the macroscale, develop and validate an FEM model at the macroscale and then scale down the FEM model to verify the possible implementation of the mechanism at the microscale. The sensing approach relies on a mechanical compliant mechanism that amplifies the thermal expansion of a structure. A testing platform equipped with an IR thermometer, thermocouple, a power supply, and laser distance sensors, is implemented to demonstrate the operability of the proposed sensing mechanism. A numerical model of the sensor is developed using the FE software Ansys. The numerical results show a good agreement with their experimental counterparts at the macro scale. The model is then used to numerically investigate several configurations, namely single, double, triple and quadruple compliant mechanisms. The amplification factor is found the highest when using the double compliant mechanism. A temperature sensitivity of 28.5 μm/°C is achieved for this compliant mechanism. The numerical analysis also demonstrated that the performance obtained at the macro scale, can be conserved for microscale devices. However, buckling of some elements is observed for the microscale system which degrades the performance of the sensor when subjected to relatively large displacements. The microscale FEM model shows the possible prevention of buckling issues by slightly modifying the geometry of the compliant mechanisms. The present study is expected to provide baseline and guidance for the implementation of the sensing approach for MEMS devices. [ABSTRACT FROM AUTHOR]

In this paper, we propose a design of octagonal photonic crystal fiber with relevant parameters such as effective mode index, propagation constant, second-order dispersion and field distribution of fundamental mode (LP01). The measured parameters can be applied for generating supercontinuum, and also this model is used especially for generating vortex modes and OAM modes in space division multiplexing (SDM) applications. Highly negative dispersion is achieved at −800 ps/nm.km at wavelength of 1.1 μm, and second-order dispersion profile leads to study about the nonlinearity as well as broadband spectrum of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced recently. We show that, although the formulation is robust in the incompressible limit for the source problem, its spectrum is strongly dependent on the Lamé parameters and on the underlying mesh. [ABSTRACT FROM AUTHOR]

The paper is theoretically oriented. The main goal is to analyze the sensitivity of aerodynamic characteristics to the properties of the material used for paraglider wing. The paraglider of considerable dimensions is designed without stiffening elements. Thus, the covering material yields adequate pressure distribution between the external and internal parts of the wing. The problem is solved using a geometrical model approximated by the dimensionless coordinates of crucial points and smoothed by spline curves. The finite volume mesh is defined using the Ansys Meshing program. Numerical analysis uses five different covering materials, ranging from the air-impermeable covering to the covering subjected to hydrolytic—mechanical degradation. Optimization of properties of the covering material improves the lift force and the aerodynamic characteristics of the wing. Moreover, numerical modeling is more beneficial and efficient than prototype tests. The obtained pressure distributions and other parameters explain the aerodynamic safety of the paraglider during dynamic conditions of flight. [ABSTRACT FROM AUTHOR]

A gradient discretisation method (GDM) is an abstract setting that designs the unified convergence analysis of several numerical methods for partial differential equations and their corresponding models. In this paper, we study the GDM for anisotropic reaction–diffusion problems, based on a general reaction term, with Neumann boundary condition. With natural regularity assumptions on the exact solution, the framework enables us to provide proof of the existence of weak solutions for the problem, and to obtain a uniform-in-time convergence for the discrete solution and a strong convergence for its discrete gradient. It also allows us to apply non-conforming numerical schemes to the model on a generic grid (the non-conforming ℙ1 finite element scheme and the hybrid mixed mimetic (HMM) methods). Numerical experiments using the HMM method are performed to assess the accuracy of the proposed scheme and to study the growth of glioma tumors in heterogeneous brain environment. The dynamics of their highly diffusive nature is also measured using the fraction anisotropic measure. The validity of the HMM is examined further using four different mesh types. The results indicate that the dynamics of the brain tumor is still captured by the HMM scheme, even in the event of a highly heterogeneous anisotropic case performed on the mesh with extreme distortions. [ABSTRACT FROM AUTHOR]

This is the preface of a special issue dedicated to the memory of Francisco Javier Sayas who passed away on April 2, 2019. The articles reflect Sayas' main research interests in the numerical analysis of partial differential equations, containing contributions on the scattering and propagation of acoustic and electromagnetic waves, and the analysis of discontinuous Galerkin schemes, boundary element methods, and coupled schemes. We discuss the main contributions of Sayas and give an overview of the results covered by this special issue. [ABSTRACT FROM AUTHOR]

The objective of the current study is to investigate the effects of geometric parameters on the fluid flow patterns, diffusion factor, load-split, and off-design performance of the tandem configuration under subsonic, rectilinear, cascade flow. A 2-D computational model using finite volume formulation has been developed and validated against available experimental data. The obtained data is presented in a format involving loss parameter and loading and will help the designer to have sufficient number of combinations within the useful range of application. It is observed that general performance behavior of tandem cascade is similar to a single airfoil data. Load shifting from the front airfoil to the rear airfoil is noted at positive axial overlaps and higher camber ratios. An optimum gap ratio of around 2 is observed for the range of configurations investigated. Contrary to the previous literature, the present study indicates higher loading of the front airfoil for the best overall loading-to-loss ratio of the tandem configuration. [ABSTRACT FROM AUTHOR]

In this paper, we study a finite element discretization of a Level Set Method formulation of free-surface flow. We consider an Euler semi-implicit discretization in time and a Galerkin discretization of the level set function. We regularize the density and viscosity of the flow across the interface, following the Level Set Method. We prove stability in natural norms when the viscosity and density vary from one to the other layer and optimal error estimates for smooth solutions when the layers have the same density. We present some numerical tests for academic flows. [ABSTRACT FROM AUTHOR]

A four-ring microstructure photonic crystal fibre with a descending air hole ring cladding is presented. Numerical analysis of the structure is done using full vectorial finite element method with perfectly matched layer (PML) boundary condition. It is demonstrated that it is possible to achieve at 1.55 µm confinement loss of 2.767 × 10−5 dB/m, birefringence of 0.00346 and a nonlinear co-efficient of 41.77 km−1 W−1. Also, chromatic dispersion realised suggests a tuneable zero dispersion at 0.9–1.1 µm wavelength range. [ABSTRACT FROM AUTHOR]

In the present work, a three-dimensional numerical analysis of multi-hole film cooling on an adiabatic flat plate with combined backward and forward injection holes is carried out at varying velocity ratios from 0.5 to 2.5. The effect of three different multi-hole arrangements, square-diamond, long-diamond, and super-long-diamond with constant perforated percentage (3.27%), on film cooling performance is studied. Combining backward and forward injection holes help in achieving higher velocity boundary layer thickness in the multi-hole arrangement. It is observed that super-long-diamond arrangement provides the highest film cooling effectiveness than square-diamond and long-diamond arrangements and favours early development of coolant film layer. [ABSTRACT FROM AUTHOR]

The current work is devoted to investigating the disease dynamics and numerical modeling for the delay diffusion infectious rabies model. To this end, a non-linear diffusive rabies model with delay count is considered. Parameters involved in the model are also described. Equilibrium points of the model are determined and their role in studying the disease dynamics is identified. The basic reproduction number is also studied. Before going towards the numerical technique, the definite existence of the solution is ensured with the help of the Schauder fixed point theorem. A standard result for the uniqueness of the solution is also established. Mapping properties and relative compactness of the operator are studied. The proposed finite difference method is introduced by applying the rules defined by R.E. Mickens. Stability analysis of the proposed method is done by implementing the Von–Neumann method. Taylor's expansion approach is enforced to examine the consistency of the said method. All the important facts of the proposed numerical device are investigated by presenting the appropriate numerical test example and computer simulations. The effect of τ on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted. [ABSTRACT FROM AUTHOR]

We construct a symmetric interior penalty method for an elliptic distributed optimal control problem with pointwise state constraints on general polygonal domains. The resulting discrete problems are quadratic programs with simple box constraints that can be solved efficiently by a primal-dual active set algorithm. Both theoretical analysis and corroborating numerical results are presented. [ABSTRACT FROM AUTHOR]

Air Insulated substations (AIS) experience over-voltages like lightning, switching and temporary over-voltages. The voltage distribution across air insulated surge arrester (AISA) is highly non-uniform and its non-uniformity increases with increase of rated voltage. To achieve non-uniformity voltage factor within permissible limits, special grading shields like window based shields are proposed. In the present study, 420 / 800 kV surge arrester models with composite insulator housing have been considered to analyze voltage distribution across the metal-oxide (MO) blocks. The electrostatic field and voltage distribution analyses are carried out on AISA by considering various shield designs using numerical techniques. Instead of single grading shield, multiple voltage grading-cum-electric field controlled shields are adopted to achieve uniform electric field and optimized non-uniformity voltage factors in the order of ±8 % irrespective of rated voltage of surge arrester. An electrical model is also developed using PSPICE software to calculate voltage distribution across MO blocks. The validity of the network model developed through PSPICE is validated by comparing with the results obtained from numerical analysis. Different configurations of grading shields are proposed and effect of various parameters like rated voltage i.e. 420/800 kV, height of shield, diameter of shield and type of shield like high voltage, floating, LT shield etc. on non-uniformity voltage factor and electric field distribution of surge arrester are analyzed. [ABSTRACT FROM AUTHOR]

The purpose of this article is to formulate a simplified nonlinear fractional mathematical model to illustrate the dynamics of the new coronavirus (COVID-19). Based on the infectious characteristics of COVID-19, the population is divided into five compartments: susceptible S(t), asymptomatic infection I(t), unreported symptomatic infection U(t), reported symptomatic infections W(T) and recovered R(t), collectively referred to as (SIUWR). The existence, uniqueness, boundedness, and non-negativeness of the proposed model solution are established. In addition, the basic reproduction number R0 is calculated. All possible equilibrium points of the model are examined and their local and global stability under specific conditions is discussed. The disease-free equilibrium point is locally asymptotically stable for R0leq1 and unstable for R0 > 1. In addition, the endemic equilibrium point is locally asymptotically stable with respect to R0 > 1. Perform numerical simulations using the Adams–Bashforth–Moulton-type fractional predictor–corrector PECE method to validate the analysis results and understand the effect of parameter variation on the spread of COVID-19. For numerical simulations, the behavior of the approximate solution is displayed in the form of graphs of various fractional orders. Finally, a brief conclusion about simulation on how to model transmission dynamics in social work. [ABSTRACT FROM AUTHOR]

This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for interface problems in nonlinear elasticity. It concerns 푝-Laplacian-type Hencky materials with an unbounded stress-strain relation, as they arise in the modelling of ice sheets, non-Newtonian fluids or porous media. We propose a functional analytic framework for the numerical analysis and obtain a priori and a posteriori error estimates for Galerkin approximations to the resulting boundary/domain variational inequality. [ABSTRACT FROM AUTHOR]

This document is a corrigendum to an article published in the Journal of Numerical Mathematics. It addresses an error in the proof of Lemma 3.2 and provides a solution. The error is due to a constant not being independent of Δt, causing the equation to become unstable. The document suggests replacing a term in equations (3.8)–(3.11) and proposes testing equation (2.21a) with a specific value. The text concludes by presenting a formula that incorporates various terms and constants. This technical and mathematical information may be useful for researchers studying this topic. The authors express gratitude for the identification and correction of errors. [Extracted from the article]

We study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis – construction of a local Fortin operator – is infeasible for the convection-reaction problem. We then develop a line of argument based on a direct proof of discrete stability; we find that employing a polynomial enrichment for the test space does not suffice for this purpose, motivating the introduction of a (two-element) subgrid mesh. The argument combines mathematical analysis with numerical experiments. [ABSTRACT FROM AUTHOR]

A diffuse interface model for tumour growth in the presence of a nutrient consumed by the tumour is considered. The system of equations consists of a Cahn–Hilliard equation with source terms for the tumour cells and a reaction–diffusion equation for the nutrient. We introduce a fully-discrete finite element approximation of the model and prove stability bounds for the discrete scheme. Moreover, we show that discrete solutions exist and depend continuously on the initial and boundary data. We then pass to the limit in the discretization parameters and prove convergence to a global-in-time weak solution to the model. Under additional assumptions, this weak solution is unique. Finally, we present some numerical results including numerical error investigation in one spatial dimension and some long time simulations in two and three spatial dimensions. [ABSTRACT FROM AUTHOR]

Integrated planar lenses are critical components for analog optical information processing that enable a wide range of applications including beam steering. Conventional planar lenses require gradient index control which makes their on-chip realization challenging. Here, we introduce a new approach for beam steering by designing an array of coupled waveguides with segmented tails that allow for simultaneously achieving planar lensing and off-chip radiation. The proposed arrayed waveguide lens is built on engineering the evanescent coupling between adjacent channels to realize a photonic lattice with an equi-distant ladder of propagation constants that emulates the continuous parabolic index profile. Through coupled-mode analysis and full-wave numerical simulations, we show that selective excitation of waveguide channels enables beam steering with large field-of-views of ∼60°. The proposed arrayed waveguide lens can serve as a compact component in integrated photonic circuits for applications in imaging, sensing, and metrology. [ABSTRACT FROM AUTHOR]

We present the design and a closed-form error analysis of accuracy-configurable multipliers via segmented carry chains. To address this problem, we model the approximate partial-product accumulations as a sequential process. According to a given splitting point of the carry chains, the technique herein discussed allows varying the quality of the accumulations and, consequently, the overall product. Due to these shorter critical paths, such kinds of approximate multipliers can trade-off accuracy for an increased performance whilst exploiting the inherent area savings of sequential over combinatorial approaches. We implemented multiple architectures targeting FPGAs and ASICs with different bit-widths and accuracy configurations to 1) estimate resources, power consumption, and delay, as well as to 2) evaluate those error metrics that belong to the so-called #P-complete class. [ABSTRACT FROM AUTHOR]