Scaling analysis of unsteady natural convection boundary layer for ramp heating

A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasisteady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the start up had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same.

Scaling analysis of unsteady natural convection boundary layer for instantaneous heating

Natural convection thermal boundary layer adjacent to an instantaneous heated inclined flat plate is investigated through a scaling analysis and verified by direct numerical simulations. It is revealed from the analysis that the development of the boundary layer may be characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady state stage. These three stages can be clearly identified from the numerical simulations. Major scales including the flow velocity, flow development time, and the thermal and viscous boundary layer thicknesses are established to quantify the flow development at different stages and over a wide range of flow parameters. Details of the scaling analysis are described in this paper.

Homodimerization controls the fibroblast growth factor 9 subfamily's receptor binding and heparan sulfate-dependent diffusion in the extracellular matrix

Uncontrolled fibroblast growth factor (FGF) signaling can lead to human diseases, necessitating multiple layers of self-regulatory control mechanisms to keep its activity in check. Herein, we demonstrate that FGF9 and FGF20 ligands undergo a reversible homodimerization, occluding their key receptor binding sites. To test the role of dimerization in ligand autoinhibition, we introduced structure-based mutations into the dimer interfaces of FGF9 and FGF20. The mutations weakened the ability of the ligands to dimerize, effectively increasing the concentrations of monomeric ligands capable of binding and activating their cognate FGF receptor in vitro and in living cells. Interestingly, the monomeric ligands exhibit reduced heparin binding, resulting in their increased radii of heparan sulfate-dependent diffusion and biologic action, as evidenced by the wider dilation area of ex vivo lung cultures in response to implanted mutant FGF9-loaded beads. Hence, our data demonstrate that homodimerization autoregulates FGF9 and FGF20's receptor binding and concentration gradients in the extracellular matrix. Our study is the first to implicate ligand dimerization as an autoregulatory mechanism for growth factor bioactivity and sets the stage for engineering modified FGF9 subfamily ligands, with desired activity for use in both basic and translational research.

Scaling analysis of the unsteady natural convection boundary layer adjacent to an inclined plate for Pr > 1 following instantaneous heating

The unsteady natural convection boundary layer adjacent to an instantaneously heated inclined plate is investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer following instantaneous heating may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. Major scaling relations of the velocity and thicknesses and the flow development time of the natural convection boundary layer are obtained using triple-layer integral solutions and verified by direct numerical simulations over a wide range of flow parameters.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.