Influence of Convective and Radiative Cooling on Heat Transfer for a Thin Wire with Temperature-Dependent Thermal Conductivity

In this study, a numerical prediction of temperature profiles in a thin wire exposed to convective, radiative and temperature-dependent thermal conductivity is carried out using a finite-difference linearization approach. The procedure involves a numerical solution of a one-dimensional nonlinear unsteady heat transfer equation with specified boundary and initial conditions. The resulting system of nonlinear equations is solved with the Newton-Raphson’s technique. However unlike the traditional approach involving an initial discretization in space then in time, a different numerical paradigm involving an Euler scheme temporal discretization is applied followed by a spatial discretization. Appropriate numerical technique involving partial derivatives are devised to handle a squared gradient nonlinear term which plays a key role in the formulation of the Jacobian matrix. Tests on the numerical results obtained herein confirm the validity of the formulation.

Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces

The purpose of this paper is to prove some fixed point results dealing with a system of nonlinear equations defined in an angelic Hausdorff locally convex space ( X , { | ⋅ | p } p ∈ Λ ) (X,\{\lvert\,{\cdot}\,\rvert_{p}\}_{p\in\Lambda}) having the 𝜏-Krein–Šmulian property, where 𝜏 is a weaker Hausdorff locally convex topology of 𝑋. The method applied in our study is connected with a family Φ Λ τ \Phi_{\Lambda}^{\tau} -MNC of measures of weak noncompactness and with the concept of 𝜏-sequential continuity. As a special case, we discuss the existence of solutions for a 2 × 2 2\times 2 block operator matrix with nonlinear inputs. Furthermore, we give an illustrative example for a system of nonlinear integral equations in the space C ⁢ ( R + ) × C ⁢ ( R + ) C(\mathbb{R}^{+})\times C(\mathbb{R}^{+}) to verify the effectiveness and applicability of our main result.

Evolution equation for interaction of opposite directed waves with arbitrary polarization in 1D-metamaterial

In this paper, a theoretical study of wave propagation in 1D metamaterial is presented. A system of evolution equations for electromagnetic waves with both polarizations account is derived by means of projection operators method for general nonlinearity and dispersion. It describes interaction of opposite directed waves with a given polarization. The particular case of Kerr nonlinearity and Drude dispersion is considered. In such approximation, it results in the corresponding system of nonlinear equations that generalizes the Schäfer–Wayne one. Traveling wave solution for the system of equation of interaction of orthogonal-polarized waves is also obtained. Dependence of wavelength on amplitude is written and plotted.

Motion control of the two joint planar robotic manipulators through accelerated Dai–Liao method for solving system of nonlinear equations

PurposeThe purpose of this research is to propose a new choice of nonnegative parameter t in Dai–Liao conjugate gradient method.Design/methodology/approachConjugate gradient algorithms are used to solve both constrained monotone and general systems of nonlinear equations. This is made possible by combining the conjugate gradient method with the Newton method approach via acceleration parameter in order to present a derivative-free method.FindingsA conjugate gradient method is presented by proposing a new Dai–Liao nonnegative parameter. Furthermore the proposed method is successfully applied to handle the application in motion control of the two joint planar robotic manipulators.Originality/valueThe proposed algorithm is a new approach that will not either submitted or publish somewhere.

Discrete Fracture Model for Hydro-Mechanical Coupling in Fractured Reservoirs

The process of coupled flow and mechanics occurs in various environmental and energy applications, including conventional and unconventional fractured reservoirs. This work establishes a new formulation for modeling hydro-mechanical coupling in fractured reservoirs. The discrete-fracture model (DFM), in which the porous matrix and fractures are represented explicitly in the form of unstructured grid, has been widely used to describe fluid flow in fractured formations. In this work, we extend the DFM approach for modeling coupled flow-mechanics process, in which flow problems are solved using the multipoint flux approximation (MPFA) method, and mechanics problems are solved using the multipoint stress approximation (MPSA) method. The coupled flow-mechanics problems share the same computational grid to avoid projection issues and allow for convenient exchange between them. We model the fracture mechanical behavior as a two-surface contact problem. The resulting coupled system of nonlinear equations is solved in a fully-implicit manner. The accuracy and generality of the numerical implementation are accessed using cases with analytical solutions, which shows an excellent match. We then apply the methodology to more complex cases to demonstrate its general applicability. We also investigate the geomechanical influence on fracture permeability change using 2D rock fractures. This work introduces a novel formulation for modeling the coupled flow-mechanics process in fractured reservoirs, and can be readily implemented in reservoir characterization workflow.

Development of the Approximating Functions Method for Problems in a Planar Waveguide with Constant Polarization

Article introduces an extension of the approximating functions method, a particular case of the finite element method (FEM) with interpolating functions in the form of Lagrange polynomials of a special form, to solve electrodynamics problems in a planar waveguide with constant polarization in the spatial-temporal domain using the Volterra integral equation method. The main goal of the article is to expand the area of ​​applicability of this method to three-dimensional problems in a planar waveguide with constant polarization, as well as to obtain general interpolation expressions in analytical form, which will be used to construct a system of nonlinear equations for solving specific problems.

Typical curve with G1 constraints for curve completion

This paper presents a novel algorithm for planar G1 interpolation using typical curves with monotonic curvature. The G1 interpolation problem is converted into a system of nonlinear equations and sufficient conditions are provided to check whether there is a solution. The proposed algorithm was applied to a curve completion task. The main advantages of the proposed method are its simple construction, compatibility with NURBS, and monotonic curvature.

On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

In this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations simultaneously. Further we extend this family of root estimating methods for solving a system of nonlinear equations. Convergence analysis shows that the order of convergence is 3 in case of the single root finding method as well as for the system of nonlinear equations and is 5 for simultaneous determination of all distinct and multiple roots of a nonlinear equation. The computational cost, basin of attraction, efficiency, log of residual and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in literature.

DETERMINATION OF MODEL PARAMETERS OF ROCKET STABILIZATION SYSTEM IN FLIGHT

The dynamic characteristics of the system that includes the controlled object and the regulator largely depend on the choice of the control law, which is determined based on the nominal values of the parameters of the mathematical model of the stabilization process and its priority indicator. Due to the deviation of the missile parameters and, accordingly, the model from the nominal values, the designers set the safety factors based on the most unfavorable conditions, which negatively affects the overall performance, in particular, the relative weight of the payload. Therefore, there is a need to develop algorithms for adjustment that is identification model parameters during the flight using the signals of measuring devices and the capabilities of on-board computers. This will increase the efficiency of methods of choosing the control law based on such indicators as stabilization accuracy, stability margin and power requirements of the actuator. The aim of the article is to develop methods for refining the parameters of the rocket stabilization system in the yawing plane, which are based on the use of current data of measuring devices of the part of coordinates of the state vector, and verify the effectiveness of refinement in terms of the above indicators. A linear stationary model of a system for stabilizing the perturbed motion of a rocket taking into account the inertia of the actuator in the form of ordinary fifth-order differential equations is adopted. Two approaches are proposed to approximate the model parameters to their actual values. In the first in the model parameter space there is a minimum of the integral of the distance between the points of the trajectory according to the signals of the measuring devices and the trajectory obtained by modeling the perturbation compensation process. In the second, the actual values of the parameters are the result of solving a system of nonlinear equations, which includes data from measuring devices and the corresponding data obtained by simulation. On the example of space rocket parameters it is shown that the choice of the control law based on the actual coefficients of the model leads to a significant reduction of deviations from the set value of the system stability margin, stabilization error and power of the actuator.