A Magneto-Mechanically Coupled Phase-Field Model at Large Deformation

The aggregate magneto-mechanical behavior of magneto-rheological elastomers (MREs) stems from the magnetic properties of the ferromagnetic inclusion and the mechanical properties of the matrix material. We propose a large deformation micro-magnetic theory, to predict the behavior and interaction of ferromagnetic particles inside an elastomeric matrix. A rate-type variational principle, with the magnetization as the order parameter is proposed. A large deformation Landau-Lifshitz-Gilbert equation for the time evolution of the magnetization, is obtained directly from the proposed variational principle. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of magnetorheological elastomer to vibration absorber

Traditional dynamic vibration absorber (DVA) is widely used in industries as a vibration absorption equipment. However, it is only effective at narrow working frequency range. This shortcoming has limited its stability and application. This paper develops an adaptive tuned vibration absorber (ATVA) based on unique characteristics of magnetorheological elastomers (MREs), whose modulus can be controlled by an applied magnetic field. This ATVA works in shear mode and consists of dynamic mass, static mass and smart spring elements with MREs. Based on the double pole model of MR effects, the shift-frequency capability of the ATVA has been theoretically and experimentally evaluated. The experimental results demonstrated that the natural frequency of the ATVA can be tuned from 27.5 Hz to 40 Hz. To study its vibration absorption capacity, a beam structure with two ends supported has been employed. To analyze the vibration absorption capacity, a dynamic model of coupling beam and absorber has been established. Both the calculation and experimental results show that the absorption capacity of the developed ATVA is better than the traditional TVA and can achieve as high as 25 dB which was justified by the experiment.     

A note on various supersymmetric extensions of the standard model of high-energy particles and E-Infinity theory

By imposing various auxiliary conditions connected to supersymmetry, colours and chirality, three minimally extended versions of the standard model are proposed.Based on these tentative models, it is possible to predict that few new particles are very likely to be found experimentally in the near future and that these particles will be closely related to the Higgs mechanism.     

预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型北大核心CSCD

基于广义自洽法,同时采用Gurtin-Murdoch界面模型和界面相模型研究了纳米纤维复合材料的有效弹性性能,获得了两种模型下有效体积模量的封闭解析解和计算有效面内剪切模量数值解的全部公式.基于界面模型的解答,讨论了有效体积模量和有效面内剪切模量的界面效应.证明了界面模型的解答可由界面相模型的解答退化得到,其中有效体积模量可以实现解析退化,有效面内剪切模量则可以数值退化.以含纳米孔洞的金属铝为例,比较了两种模型计算结果的差异.结果表明,当纳米孔洞半径较小时,两个模型的结果存在很大差异,而当半径较大时两个模型的结果差别不大.     

A Finite Deformation Microsphere Model for Magneto-Visco-Elastic Response in Magnetorheological Elastomers

In this work we present a novel approach to the modeling of magnetorheological elastomers (MREs) for finite deformations. Keeping in mind the composite nature at the microscale, we employ the microsphere model as an effective tool to capture the constitutive response of the material. The microsphere model has been successfully applied to the modelling of rubber-like materials. Here, we extend this approach by taking into account the effect of the magnetic dipole-dipole interactions on the orientation of the polymer chains. Thus, the presented microsphere model is directly motivated by considering the underlying phenomena at the microscale level. Finally the material model is embedded in a finite element framework and the results of a boundary value problems is presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional mathematical modelling of magnetic bead interactions within a magnetic separation system

Magnetic separation relates to the ability to separate particles based on their magnetic mobilities. This is often limited by the formation of bead agglomerates. Bead agglomerates are formed as a result of attractive magnetic induced interactions among magnetic beads suspended in fluid. A three-dimensional model of the interactions among three equal sized super-paramagnetic beads suspended in a static fluid within a uniform magnetic field is presented here. The beads’ trajectories were recorded on video while the relative axial displacement of the bead was obtained using the recorded off-focus images. A good agreement was obtained by comparing the beads’ simulated trajectories with the video data. Therefore, the model is able to predict the behaviour of magnetic beads in immunoassays as well as magnetic separation system.     

Modeling treatment of cancer using virotherapy with generalized logistic growth of tumor cells

Abstract

Virotherapy is an effective strategy in cancer treatment. It eliminates tumor cells without harming the healthy cells. In this article, a deterministic mathematical model to understand the dynamics of tumor cells in response to virotherapy is formulated and analyzed by incorporating cytotoxic T lymphocytes (CTLs). The basic reproduction number and the immune response reproduction number are computed and different equilibria of the proposed model are found. The local stability of different equilibria is discussed in detail. Further, the proposed model is extended to stochastic model. Numerical simulation is performed for both deterministic and stochastic models. It is observed that when both the reproduction numbers are greater than one, which corresponds to existence of unique nontrivial equilibrium point, dynamics of deterministic and stochastic models are almost same. The deterministic model shows a very complex dynamics when one or both the reproduction numbers are below one. The system exhibits both backward bifurcation and Hopf-bifurcation for suitable sets of parameters and in this situation it is not easy to predict the dynamics of cancer cells and virus particles. The existence of backward bifurcation demonstrates the fact that partial success of virotherapy can be achieved even if the immune response reproduction number is less than one.     

球形涂层粒子增强复合材料的有效模量

本文通过四相球模型和复合材料的等效介质理论,研究了球形涂层粒子增强复合材料的有效模量性质,得到了这种增强复合材料的有效体积模量和有效剪切模量的理论预测公式。这些结果在特殊情况下,可退化到三相球模型确定的球形粒子增强复合材料的有效模量公式。     

低密度和高密度水化硅酸钙的纳米压痕数值模拟

水化硅酸钙(C-S-H)是决定以硅酸盐水泥为主要组分的水泥基材料性能的关键组分,水化硅酸钙(C-S-H)是存在于水化产物中连续的固体物质,占水化水泥浆体体积的50%～60%,是水泥浆体中决定硬化水泥浆体物理结构和性能的主要成分,同时水化硅酸钙(C-S-H)也是混凝土结构宏观尺度的凝聚性和耐久性的重要影响因素．模型的建立对于预测水泥的体积性能如收缩、蠕变、渗透率和裂缝等方面越来越重要．通过将水化硅酸钙(C-S-H)分为低密度和高密度两种数值模型,并且将水化硅酸钙(C-S-H)视为在纳米尺度上具有实际微观粒子性能的离散颗粒的集合,运用分子动力学方法,通过控制水化硅酸钙(C-S-H)的紧密堆积体积分数和保持颗粒级别的其他材料属性不变来进行纳米压痕实验模拟,进而验证了压痕模量和硬度符合纳米压痕实验数据的规律．     

A numerical scheme for the Maxwell equations in the quasi-static regime with a non-local source

In this paper we study a non-linear evolution equation, based on quasi-static electromagnetic fields, with a non-local field-dependent source. This model occurs in transformer driven active magnetic shielding. We present a numerical scheme for both time and space discretization and prove convergence of this scheme. We also derive the corresponding error estimates.     

Imperfect interface effect for nano-composites accounting for fiber section shape under antiplane shear

This paper investigates the elastic responses of fibrous nano-composites with imperfectly bonded interface under longitudinal shear. The proposed imperfect interface model is the shear lag (or the spring layer) model; the presented nano interfacial stress model is the Gurtin–Murdoch surface/interface model; and the three-phase confocal elliptical cylinder model is the geometry model accounting for the fiber section shape. By virtue of the complex variable method, a generalized self-consistent method is employed to derive the closed from solution of the effective antiplane shear modulus of the fibrous nano-composites with imperfect interface. Five existing solutions can be regarded as the limit form the present analytic expression. The influences of the interface elastic constant, the interfacial imperfection parameter, the size of the elliptic section fiber, the fiber section aspect ratio, the fiber volume fraction and the fiber elastic property on the effective antiplane shear modulus of the nano-composites are discussed. Particularly, numerical results demonstrate that the interfacial elastic imperfection will always cause a significant reduction in the effective antiplane shear modulus; and the fiber interface stress effect on the effective modulus of the fibrous nano-composites will weaken with the interfacial imperfection increases.     

A novel hybrid decomposition-ensemble model based on VMD and HGWO for container throughput forecasting

This paper built a hybrid decomposition-ensemble model named VMD-ARIMA-HGWO-SVR for the purpose of improving the stability and accuracy of container throughput prediction. The latest variational mode decomposition (VMD) algorithm is employed to decompose the original series into several modes (components), then ARIMA models are built to forecast the low-frequency components, and the high-frequency components are predicted by SVR models which are optimized with a recently proposed swarm intelligence algorithm called hybridizing grey wolf optimization (HGWO), following this, the prediction results of all modes are ensembled as the final forecasting result. The error analysis and model comparison results show that the VMD is more effective than other decomposition methods such as CEEMD and WD, moreover, adopting ARIMA models for prediction of low-frequency components can yield better results than predicting all components by SVR models. Based on the results of empirical study, the proposed model has good prediction performance on container throughput data, which can be used in practical work to provide reference for the operation and management of ports to improve the overall efficiency and reduce the operation costs.     

Hydrodynamic interaction in suspended sediment distribution of open channel turbulent flow

In the present study, a theoretical model is proposed to predict the vertical distribution of suspended sediment in open channel turbulent flow. We derive our mathematical model based on the six prominent hydrodynamic mechanisms, which are upward sediment flux due to the turbulent diffusion, downward gravitational settling of the sediment, hindered settling phenomenon, secondary current, fluid induced lift force on the suspended particles and the gradient of Reynolds normal stress of the suspended sediment. The importance of the hydrodynamics is described by the changes of suspended sediment concentration profile in terms of the particle-flow interaction caused by those mechanisms. We also address the significance of the co-existence of those mechanisms for estimating the suspended sediment concentration profile. The present model agrees satisfactorily with a wide spectrum of experimental data in available literature. Unlike the previous researchers, we select a broad range of previously published models of vertical sediment concentration distribution for comparison analysis, and the proposed model shows better prediction accuracy which is confirmed by error analysis.     

Simulated fractal permeability for porous membranes

Fractal permeability model for bi-dispersed porous media is developed based on the fractal characteristics of pores in the membrane. The fractal permeability model is found to be a function of the tortuosity fractal dimension, pore area fractal dimension, sizes of particles and clusters, micro-porosity inside clusters, and the effective porosity of a medium. The pore area fractal dimension and the tortuosity fractal dimension of the porous membranes are determined by the box counting method. To verify the validity of the model, the predicted permeability were compared with the experimental data utilizing H₂ gas permeating through porous Pd-alumina, silicalite-1 and B-ZSM-5, and O₂ across perovskite-alumina membranes form the past effort.     

Stokes flow of an assemblage of porous particles: stress jump condition

The present article investigates the overall bed permeability of an assemblage of porous particles. For the bed of porous particles, the fluid-particle system is represented as an assemblage of uniform porous spheres fixed in space. Each sphere, with a surrounding envelope of fluid, is uncoupled from the system and considered separately. This model is popularly known as cell model. Stokes equations are employed inside the fluid envelope and Brinkman equations are used inside the porous region. The stress jump boundary condition is used at the porous-liquid interface together with the continuity of normal stress and continuity of velocity components. On the surface of the fluid envelope, three different possible boundary conditions are tested. The obtained expression for the drag force is used to estimate the overall bed permeability of the assemblage of porous particles and the behavior of overall bed permeability is analyzed with various parameters like modified Darcy number (Da*), stress jump coefficient (??), volume fraction (??), and effective viscosity.     

Asymptotic solutions for electromagnetic waves in a nonlinear optical cylinder

Interactions between electromagnetic waves and a cylinder with field-dependent permeability is considered. Asymptotic solutions which represent the solutions to modifications of the nonlinear Schrödinger equation are found, in particular, soliton solutions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 1, pp. 84–91, January, 1996.     

Micropolar fluid flow through the membrane composed of impermeable cylindrical particles coated by porous layer under the effect of magnetic field

In the present work, the magnetohydrodynamic flow of a micropolar fluid through the membrane composed of impermeable cylindrical particles coated by porous layer is considered. The flow of a fluid is taken parallel to an axis of cylinder and a uniform magnetic field is applied in transverse direction of the flow. The problem is solved by using the cell model technique for the flow through assemblage of cylindrical particles. The solution of the problem has been obtained by using no-slip condition, continuity of velocity and stresses at interfaces along with Happle's no-couple stress condition as the boundary conditions. The expressions for the linear velocity, micro-rotational velocity, flow rate and hydrodynamic permeability of the membrane are achieved in this work. The obtained solution for velocities is used to plot the graph against various transport parameters such as, Hartmann number, coupling parameter, porosity, scaling parameter etc. The effect of these transport parameters on the flow velocity, micro-rotational velocity, and the hydrodynamic permeability of the membrane have been presented and discussed in this work.     

Response of fly ash-reinforced functionally graded rubber composites subjected to mechanical loading

A novel approach to estimate the Young’s modulus of a functionally graded rubber composite (FGRC) from the damping ratio is demonstrated with the examples of unreinforced and fly ash-reinforced materials. FGRC coupons were prepared using the conventional casting technique. The occurrence of gradation in the specimens was attributed to the variable density of particles present in the fly ash, settling at different depths. The technique of free vibrations was used for experimentation. The damping response of the FGRC specimens was studied. The results obtained from the experiments showed that, with growing filler weight fraction, the Young’s modulus of the composite increased. The empirical model developed to predict the magnitude of the modulus turned out to be in good agreement with experimental data.     

Effect of dust particles on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium

The problem of the effect of dust particles on the thermal convection in micropolar ferromagnetic fluid saturating a porous medium subject to a transverse uniform magnetic field has been investigated theoretically. Linear stability analysis and normal mode analysis methods are used to find an exact solution for a flat micropolar ferromagnetic fluid layer contained between two free boundaries. In case of stationary convection, the effect of various parameters like medium permeability, dust particles, non-buoyancy magnetization, coupling parameter, spin-diffusion parameter and micropolar heat conduction parameter are analyzed. For sufficiently large values of magnetic parameter M₁, the critical magnetic thermal Rayleigh number for the onset of instability is determined numerically and results are depicted graphically. It is also observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and dust particles.     

Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability

Scattering of electromagnetic (EM) waves by many small impedance particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a→0, where a is the characteristic size of a particle and the number M(a) of the particles tends to infinity at a suitable rate. The proposed theory allows one to create a medium with a desirable spatially inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability μ(x) of the limiting medium. The computational results confirm a possibility to create the media with various distributions of μ(x).