A numerical study on nonlinear DPL model for analyzing heat transfer in tissue during thermal therapy

In the present paper, therapeutic treatment of infected tumorous cells has been studied through mathematical modeling and simulation of heat transfer in tissues by using a nonlinear dual-phase lag bioheat transfer model with Dirichlet boundary condition. The components of volumetric heat source in this model such as blood perfusion and metabolism are assumed experimentally validated temperature-dependent function, which gives more accurate temperature distribution in tissues through this model. We have used the finite difference and RK (4, 5) techniques of numerical methods to solve the proposed problem and obtained the exact solution in a particular case. After comparison, we got a good agreement between them. We have used dimensionless quantities throughout this paper. The effect of relaxation and thermalization time with respect to dimensionless temperature distribution has been analyzed in the treatment process.     

Nonsimilar solution of a boundary layer flow of a Reiner–Philippoff fluid with nonlinear thermal convection

The thermodynamics modeling of a Reiner–Philippoff-type fluid is essential because it is a complex fluid with three distinct probable modifications. This fluid model can be modified to describe a shear-thinning, Newtonian, or shear-thickening fluid under varied viscoelastic conditions. This study constructs a mathematical model that describes a boundary layer flow of a Reiner–Philippoff fluid with nonlinear radiative heat flux and temperature- and concentration-induced buoyancy force. The dynamical model follows the usual conservation laws and is reduced through a nonsimilar group of transformations. The resulting equations are solved using a spectral-based local linearization method, and the accuracy of the numerical results is validated through the grid dependence and convergence tests. Detailed analyses of the effects of specific thermophysical parameters are presented through tables and graphs. The study reveals, among other results, that the buoyancy force, solute and thermal expansion coefficients, and thermal radiation increase the overall wall drag, heat, and mass fluxes. Furthermore, the study shows that amplifying the space and temperature-dependent heat source parameters allows fluid particles to lose their cohesive force and, consequently, maximize flow and heat transfer.     

Structural,electrical, and linear/nonlinear optical characteristics of thermally evaporated molybdenum oxide thin films

Homogeneous thin films of Molybdenum oxide (MoO₃) were grown on quartz and glass substrates using the thermal evaporation method. XRD results showed that the MoO₃ powder has a polycrystalline structure with an orthorhombic crystal system whereas the MoO₃ thin films have amorphous nature. SEM images showed that the MoO₃ thin films have a nearly uniform surfaces with worm-like shape grains. The film thickness influences on the linear and nonlinear optical characteristics of MoO₃ thin films that were examined using spectrophotometric measurements and from which, the linear optical constants of the MoO₃ thin films were estimated. The electronic transition type was determined as a direct allowed one. The values of the optical band gap were obtained to be in the range of 3.88–3.72 eV. The dispersion parameters, third-order nonlinear optical susceptibility, and the nonlinear refractive index of the MoO₃ thin films were determined and interpreted in the light of the single oscillator model. The temperature dependence of the DC electrical conductivity and the corresponding conduction mechanism for the MoO₃ films were investigated at temperatures ranging from 303 to 463 K.     

梯度铝蜂窝夹芯板的力学行为

梯度分层铝合金蜂窝板是一种有效的吸能结构,本工作在梯度铝蜂窝结构的基础上根据梯度率的概念,通过改变蜂窝芯层的胞壁长度,设计了4种质量相同、梯度率不同的铝蜂窝夹芯结构。通过准静态压缩实验,并结合非线性有限元模拟准静态及冲击态下梯度铝蜂窝夹芯结构的变形情况及其力学性能,分析对比了相同质量下梯度铝蜂窝夹芯结构在准静态下的变形模式以及冲击载荷下分层均质蜂窝结构和不同梯度率的分层梯度蜂窝结构的动态响应和能量吸收特性。结果表明:在准静态压缩过程中,铝蜂窝梯度夹芯板的变形具有明显的局部化特征,蜂窝芯的变形为低密度优先变形直至密实,层级之间的密实化应变差随芯层密度的增大而逐渐减小;在高速冲击下,梯度蜂窝板并非严格按照准静态过程中逐级变形直至密实,而是在锤头冲击惯性及芯层密度的相互作用下整体发生的线弹性变形、弹性屈曲、塑性坍塌及密实化;另外,在本工作所设计的梯度率中,当梯度率为γ₁=0.0276时,梯度蜂窝夹芯板的吸能性达到最好,相较于同等质量下的均质蜂窝夹芯板,能量吸收提高了10.63%。     

Delay compensated control of the Stefan problem and robustness to delay mismatch

This paper presents a control design for the one‐phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid‐solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first‐order hyperbolic partial differential equation (PDE), resulting in a cascaded transport‐diffusion PDE system defined on a time‐varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.     

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

Polynomial filtering for nonlinear stochastic systems with state‐ and disturbance‐dependent noises

This article is concerned with the polynomial filtering problem for a class of nonlinear stochastic systems governed by the Itô differential equation. The system under investigation involves polynomial nonlinearities, unknown‐but‐bounded disturbances, and state‐ and disturbance‐dependent noises ((x,d)‐dependent noises for short). By expanding the polynomial nonlinear functions in Taylor series around the state estimate, a new polynomial filter design method is developed with hope to reduce the conservatism of the existing results. In virtue of stochastic analysis and inequality technique, sufficient conditions in terms of parameter‐dependent linear matrix inequalities (PDLMIs) are derived to guarantee that the estimation error system is input‐to‐state stable in probability. Moreover, the desired polynomial matrix can be obtained by solving the PDLMIs via the sum‐of‐squares approach. The effectiveness and applicability of the proposed method are illustrated by two numerical examples with one concerning the permanent magnet synchronous motor.     

Stochastic stabilization and destabilization of nonlinear and time‐varying hybrid systems by noise

The aim of this article is to design a suitable strength function g(t,x,r(t)) such that the Wiener noise g(t,x(t),r(t))dw(t) either stabilizes or destabilizes a given nonlinear and time‐varying hybrid system . To this end, the basic properties, including the existence and uniqueness of the local and global solutions and the nonzero property of solutions of the nonlinear and time‐varying hybrid stochastic systems, are first investigated as the theoretical basis of the article. Second, two theorems and the corresponding corollaries on the stability and instability of the hybrid stochastic systems are established. Third, the design method for the noise strength g(t,x,r(t)) is then proposed based on the established theorems. We also point out that the Markov jump r(t) may have a stabilizing (respectively, destabilizing) effect when we design the noise strength g(t,x,r(t)) so that the introduced noise g(t,x(t),r(t))dw(t) stabilizes (respectively, destabilizes) the corresponding hybrid system. Finally, we illustrate our method using two examples. Compared with the existing literature, our method is suitable for a wider class of nonlinear and time‐varying systems with weaker conditions than quasi‐linear systems.     

H∞ control for uncertain one‐sided Lipschitz nonlinear systems in finite frequency domain

The current article discusses the H_∞ disturbance attenuation control design problem for one‐sided Lipschitz systems in finite frequency domain. Models containing norm‐bounded parameter uncertainties, disturbances, and input nonlinearities are considered. By contrast to existing full frequency methods, the H_∞ controller is computed depending on the frequency ranges of disturbances. The finite frequency disturbance attenuation index is initially defined. Thanks to Finsler's lemma, sufficient and less conservative analysis conditions are also derived for the closed‐loop system. Then, synthesis conditions in the low, middle, and high frequency ranges as well as the whole frequency range, are formulated in terms of linear matrix inequalities. At last, to prove the effectiveness and the superiority of the proposed approach, a physical example is used and a comparative study is done.