Mathematical modeling and simulation in an individual cancer cell associated with invadopodia formation

The degradation of the extracellular matrix (ECM) is driven by actin-rich membrane protrusions called invadopodia, which leading to the cancer cell invasion across the surrounding tissue barriers. Signaling pathways through ligand and membrane associated receptor bindation are vital point in order to enhance the actin polymerization activities that push the membrane of migrating cells. The results presented by Saitou et. al, [36] are contradict to this fact since actins are not only pushed, but also diffused beyond the cell membrane into the ECM region. Hence, in this study, we considered mathematical modeling for an individual cancer cell. We investigated one-dimensional Stefan-like problem of the signal process, (CM-I-B) and treated the cell membrane as a free boundary surface to separate any activity happen in intra- and extracellular regions. An approximation problem, (CM-I-C) is introduced by transforming the Stefan-like problem into an initial-boundary value problem for the signal equation with penalty term. The velocity concerning the movement of the free boundary is then calculated by the integration of the penalty term. The auxiliary problem is solved numerically using finite-difference scheme, (CM-I-C0) for the above integrated penalty method, [21]. Two convergences of CM-I-C and CM-I-C0 into CM- I-B are investigated by taking E and ox goes to 0, respectively. Our results showed a good agreement with the other known fixed domain method for the free boundary positions and the signal distributions

Unsteady MHD squeezing flow of Casson fluid over horizontal channel in presence of chemical reaction

The fluid flow with chemical reaction is one of well-known research areas in the field of computational fluid dynamic. It has been acknowledged by many researchers due to its industrial applications in the modelling of flow on a nuclear reactor. Motivated by the implementation of the flow in the industry problems, the aim of this study is to explore the impacts of chemical reaction on magnetohydrodynamic (MHD) squeeze flow of Casson fluid over a permeable medium in the slip condition with viscous dissipation. The flow is induced due to compress of two plates. Transformation of the partial differential equations (PDEs) to ordinary differential equations (ODEs) is performed by imposing similarity variables. The numerical procedure of Keller-box is used to solve the dimensionless equations. Comparison of the numerical results with former studies to validate the current solutions is conducted. It is shown to be in proper agreement. The results show that the velocity and wall shear stress enhance as both plates moving nearer. Moreover, increase in Hartmann and Casson parameters reducing the velocity, temperature and concentration. The temperature and the rate of thermal transfer boosts with the existence of viscous dissipation. Furthermore, the mass transfer rate is discovered boosts in destructive chemical reaction and adverse outcome is noted in constructive chemical reaction

THE EXISTENCE AND UNIQUENESS OF THE MILD SOLUTION TO A NONLINEAR CAUCHY PROBLEM ASSOCIATED WITH A NONLOCAL REACTION-DIFFUSION SYSTEM

We study the existence and uniqueness of a mild solution to a nonlinear Cauchy problem associated with a nonlocal reaction diffusion system by employing the properties of analytic semigroup operator generated by the linear part of the problem which is sectorial and then applying Banach Fixed Point Theorem to the problem. We show that the problem has a unique mild solution under a Lipschitz condition on the nonlinear part of the problem. An example as an application of the result obtained is also given

G-jitter fully developed heat transfer by mixed convection flow of nanofluid in a vertical channel

In this study, the effect of g-jitter fully developed heat transfer by mixed convection flow of nanofluid in a vertical channel is investigated. The nanoparticles of aluminum oxide and copper with water as a base fluid are used in this study. The equations corresponding to this study are solved analytically to find the exact solutions. The results of velocity and temperature profiles with the influence of physical parameters such as mixed convection, oscillation, temperature ratio and volume fraction of the nanoparticles are plotted and analyze in details. The behavior of steady state flow is also investigated. Results shown that as mixed convection, oscillation, and temperature ratio increased, the velocity profiles increased. The conductivity and viscosity of the nanofluid are also increased due to the increase of the volume fraction of nanoparticles in the water base fluid

Unsteady free convection flow near the stagnation point of a three-dimensional body

This study deals with the study of unsteady free convection in the stagnation point region of a three-dimensional body placed in an ambient fluid under the assumption of a step change in the surface temperature of the body. The non-linear coupled partial differential equations governing the free convection flow are solved numerically using an implicit finite-difference method for different values of the governing parameters entering these equations. Results for the flow and heat characteristics show that the transition from the initial unsteady-state flow to the final steady-state flow takes place smoothly

Free convection boundary layer flow of a viscoelastic fluid in the presence of heat generation

The present paper considers the steady free convection boundary layer flow of a viscoelastics fluid with constant temperature in the presence of heat generation. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing boundary layer equations are first transformed into non-dimensional form by using special dimensionless group. Computations are performed numerically by using Keller-box method by augmenting an extra boundary condition at infinity and the results are displayed graphically to illustrate the influence of viscoelastic K, heat generation γ, and Prandtl Number, Pr parameters on the velocity and temperature profiles. The results of the surface shear stress in terms of the local skin friction and the surface rate of heat transfer in terms of the local Nusselt number for a selection of the heat generation parameter γ (=0.0, 0.2, 0.5, 0.8, 1.0) are obtained and presented in both tabular and graphical formats. Without effect of the internal heat generation inside the fluid domain for which we take γ = 0.0, the present numerical results show an excellent agreement with previous publication

Mathematical modelling of unsteady free convection boundary layer flow over a three-dimensional stagnation point

The three-dimensional axisymmetric stagnation point flow have applications in many manufacturing processes in industry such as the boundary layer along material handling conveyers, the aerodynamic extrusion of plastic sheet, and the cooling of an infinite metallic plate in cooling bath. In this thesis, mathematical models to study the heat and mass transfer of an unsteady three-dimensional body near the stagnation point are developed. Problems considered involve the flow in viscous fluid and micropolar fluid. In addition, the effect of heat generation is also considered for viscous fluid problem. The governing equations which consist of coupled nonlinear partial differential equations are solved numerically through an implicit finite difference scheme known as the Keller-box method. The results presented include the velocity, temperature and microrotation profiles as well as the fluid flow and heat transfer characteristics for various parametric physical conditions such as the absorption parameter, Q and the material or micropolar parameter, K. The results obtained show that the effect of heat generation, Q gives rises to the skin friction and heat transfer coefficients. However, the skin friction and heat transfer coefficients are decreased when the material parameter, K is increased