Extinction and Non-extinction of Solutions to a Fast Diffusion p-Laplace Equation with Logarithmic Non-linearity

This paper deals with a class of fast diffusion p-Laplace equation with logarithmic non-linearity in a bounded smooth domain with homogeneous Dirichlet boundary condition. By using energy estimates and some ordinary differential inequalities, we study the conditions on extinction and non-extinction of global solutions. The results of this paper extend and complete the previous studies on this equation.

     

On the Stability of a Degenerate Wave Equation Under Fractional Feedbacks Acting on the Degenerate Boundary

Journal of Dynamical and Control Systems - In this work, we are concerned with the study of stabilization of one-dimensional weakly degenerate wave equation utt ? (xγux)x = 0 with x...     

Analysis of pressure and heat distribution in a dilating or contracting filter chamber with two outlets using multivariate spectral quasilinearization method

The development of efficient filters is an essential part of industrial machinery design, specifically to increase the lifespan of a machine. In the filter chamber design considered in this study, the magnetic material is placed along the horizontal surface of the filter chamber. The inside of the filter chamber is layered with a porous material to restrict the outflow of unwanted particles. This study aims to investigate the flow, pressure, and heat distribution in a dilating or contracting filter chamber with two outlets driven by injection through a permeable surface. The proposed model of the fluid dynamics within the filter chamber follows the conservation equations in the form of partial differential equations. The model equations are further reduced to a steady case through Lie's symmetry group of transformation. They are then solved using a multivariate spectral-based quasilinearization method on the Chebyshev–Gauss–Lobatto nodes. Insights and analyses of the thermophysical parameters that drive optimal outflow during the filtration process are provided through the graphs of the numerical solutions of the differential equations. We find, among other results, that expansion of the filter chamber leads to an overall decrease in internal pressure and an increase in heat distribution inside the filter chamber. The results also show that shrinking the filter chamber increases the internal momentum inside the filter, which leads to more outflow of filtrates.     

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.     

Influence of radiation and viscous dissipation on MHD heat transfer Casson nanofluid flow along a nonlinear stretching surface with chemical reaction

The present article investigates the influence of Joule heating and chemical reaction on magneto Casson nanofluid phenomena in the occurrence of thermal radiation through a porous inclined stretching sheet. Consideration is extended to heat absorption/generation and viscous dissipation. The governing partial differential equations were transformed into nonlinear ordinary differential equations and numerically solved using the Implicit Finite Difference technique. The article analyses the effect of various physical flow parameters on velocity, heat, and mass transfer distributions. For the various involved parameters, the graphical and numerical outcomes are established. The analysis reveals that the enhancement of the radiation parameter increases the temperature and the chemical reaction parameter decreases the concentration profile. The empirical data presented were compared with previously published findings.     

Hall current effects on MHD flow of chemically reacting fluid through a porous medium with heat source

We considered the magnetohydrodynamic (MHD) free convective flow of an incompressible electrically conducting viscous fluid past an infinite vertical permeable porous plate with a uniform transverse magnetic field, heat source and chemical reaction in a rotating frame taking Hall current effects into account. The momentum equations for the fluid flow during absorbent medium are controlled by the Brinkman model. Through the undisturbed state, both the plate and fluid are in a rigid body rotation by the uniform angular velocity perpendicular to an infinite vertical plate. The perpendicular surface is subject to the homogeneous invariable suction at a right angle to it and the heat on the surface varies about a non-zero unvarying average whereas the warmth of complimentary flow is invariable. The systematic solutions of the velocity, temperature, and concentration distributions are acquired systematically by utilizing the perturbation method. The velocity expressions consist of steady-state and fluctuating situations. It is revealed that the steady part of the velocity field has a three-layer characteristic while the oscillatory part of the fluid field exhibits a multi-layer characteristic. The influence of various governing flow parameters on the velocity, temperature, and concentration are analyzed graphically. We also discuss computational results for the skin friction, Nusselt number, and Sherwood number in the tabular forms.     

Dufour and Soret influence on MHD boundary layer flow of a Maxwell fluid over a stretching sheet with nanoparticles

An analysis has been carried out to examine the heat and mass transfer properties of a two-dimensional incompressible electrically conducting Maxwell fluid over a stretching sheet in the existence of Soret, Dufour, and nanoparticles. In many practical scenarios, such as the polymer extrusion process, the problem presented here is crucial. The flow is examined in terms of the impacts of magnetohydrodynamics and elasticity. Brownian motion and thermophoresis are incorporated into the transport equations. Using adequate similarity variables, the governing partial differential equations and related boundary conditions are non-dimensionalized. The fourth–fifth-order Runge–Kutta–Fehlberg procedure is utilized to solve the consequent transformed ordinary differential equations. The effects of various embedded thermo-physical parameters on the fluid velocity, temperature, concentration, Nusselt number, and Sherwood number have been determined and discussed quantitatively. A comparison of a special case of our results with the one previously reported in the literature shows a very good agreement. An increase in the values of Du and Sr leads to an increase in the temperature and concentration distribution. Nusselt number estimates decrease as Nb estimations increase. Furthermore, this study leads to the study of different flows of electrically conducting fluid over a stretching sheet problem that includes the two-dimensional nonlinear boundary equations.     

子集模拟中马尔可夫链蒙特卡洛抽样算法比较

文章着重研究子集模拟中马尔可夫链蒙特卡洛(MCMC)抽样算法的抽样效率与计算精度。首先，阐述可靠度子集模拟的基本原理与中间状态样本生成的各种MCMC抽样算法，在稳态马尔可夫链构造基础上提出延迟拒绝MMH(Modified Metropolis Hasting)算法，通过在MMH算法上增加备选样本的延迟拒绝步提高MMH算法的抽样效率；阐述基于随机游走与基于扩散方程MCMC方法中建议分布的差异，进一步对备选样本接受率为1的preconditioned Crank-Nicolson(pCN)算法和条件抽样(Conditional sampling, CS)算法开展研究，证明两种算法的等价性；推导有效样本量的计算方法，提出采用有效样本量与总样本量的比值定义MCMC方法的抽样效率。通过复杂目标分布的样本生成研究不同MCMC抽样算法建议分布及其参数对备选样本接受率与抽样效率的影响，最后通过计算实例研究子集模拟过程采用不同MCMC抽样算法得到失效概率的相对误差及其变异性，揭示不同MCMC抽样算法对失效概率计算精度的影响。研究表明：不同MCMC抽样算法生成备选样本的接受率及其自相关性受建议分布及其参数影响较大，对于复杂的目标分布，pCN算法和CS算法的抽样效率较高，延迟拒绝MMH算法次之；采用CS算法和延迟拒绝MMH算法进行子集模拟得到的失效概率精度较高且变异性较低；增加子集模拟中间状态样本量可以提高失效概率计算精度并降低其变异性。     

新型防屈曲高强钢腹板可更换钢连梁抗震性能研究

文章率先提出一种新型防屈曲高强钢腹板可更换钢连梁(简称“新型钢连梁”)：腹板采用高强钢，可提高钢连梁的屈服抗剪强度，连梁变形减小，从而减小可更换结构整体变形，便于更换；加劲肋紧贴腹板(但不焊接)提供约束，仅与上下翼缘焊接，可减少60%以上的焊接量。其次，设计并开展了11个试件的拟静力试验，研究了加劲肋间距(规范限值dmax、0.85dmax)、腹板厚度(6mm、8mm)、腹板钢材强度(Q460、Q550)和构造形式(加劲肋与腹板贴紧或焊接)等参数对新型钢连梁抗震性能的影响。试验结果表明：试件均发生剪切破坏；满足加劲肋间距限值的新型钢连梁，滞回曲线饱满，峰值时腹板未发生鼓曲且极限转角均超过0.1rad，大于规范限值0.08rad，表现出良好的耗能和变形能力；缩小加劲肋间距、增加腹板厚度或提高腹板钢材强度，新型钢连梁刚度及承载力提高；新型钢连梁峰值承载力较传统构造试件低约5%。最后，基于试验结果建立了有限元模型并开展了分析，研究结果表明：对腹板采用Q460、Q550高强钢材的新型钢连梁，峰值承载力计算时超强系数建议取1.43(长度比为0.5～1.0)或1.39(长度比为1.0～1.6)、1.25，以期为实际工程设计提供依据。