Noise-induced transitions for random versions of Verhulst model

According to the Verhulst model the rate of increase/decrease of a biological population with size x(t) at time t is equal to the sum of $\rho x\left(t\right)$ and $-x{(t)}^2$, where $\rho \in \mathbb{R}$ is a constant. The constant ρ is positive and negative for favorable and hostile environments, respectively. The limitation of resources is quantified by the term $-x{(t)}^2$. We examine random versions of the Verhulst model obtained by replacing ρ with $(\rho +\mathrm{white}\mathrm{noise})$. Gaussian (GWN) and Poisson (PWN) white noise processes are considered. The state X(t) of the random Verhulst model satisfies stochastic differential equations driven by Gaussian and Poisson white noises. Our objective is to identify noise-induced transitions, that is, noise levels at which the stationary density of X(t) exhibits qualitative changes. It is shown that noise levels causing transitions under Poisson white noise approach those under Gaussian white noise as the frequency of Poisson jumps increases indefinitely while their size approaches zero.     

Numerical analysis of conjugate natural and mixed convection heat transfer of nanofluids in a square cavity using the two-phase method

In the present study, the problem of conjugate natural and mixed convection of nanofluid in a square cavity containing several pairs of hot and cold cylinders is visualized using non-homogenous two-phase Buongiorno's model. Such configuration is considered as a model of heat exchangers in order to prevent the fluids contained in the pipelines from freezing or condensing. Water-based nanofluids with Cu, Al₂O₃, and TiO₂ nanoparticles at different diameters ($25\text{nm}?d_p?145\text{nm}$) are chosen for investigation. The governing equations together with the specified boundary conditions are solved numerically using the finite volume method based on the SIMPLE algorithm over a wide range of Rayleigh number (${10}^4?\mathit{Ra}?{10}^7$), Richardson number (${10}^{-2}?\mathit{Ri}?{10}^2$) and nanoparticle volume fractions ($0?\phi ?5\%$). Furthermore, the effects of three types of influential factors such as: orientation of conductive wall, thermal conductivity ratio ($0.2?K_r?25$) and conductive obstacles on the fluid flow and heat transfer rate are also investigated. It is found that the heat transfer rate is significantly enhanced by incrementing Rayleigh number and thermal conductivity ratio. It is also observed that at all Rayleigh numbers, the total Nusselt number rises and then reduces with increasing the nanoparticle volume fractions so that there is an optimal volume fraction of the nanoparticles where the heat transfer rate within the enclosure has a maximum value. Finally, the results reveal that by increasing the thermal conductivity of the nanoparticles and Rayleigh number, distribution of solid particles becomes uniform.     

Microstructure,texture evolution and mechanical properties of cold rolled Ti-32.5Nb-6.8Zr-2.7Sn biomedical beta titanium alloy

Ti-32.5 Nb-6.8 Zr-2.7 Sn(TNZS,wt%) alloy was produced by using vacuum arc melting method,followed by solution treatment and cold rolling with the area reductions of 50% and 90%.The effects of cold rolling on the microstructure,texture evolution and mechanical properties of the experimental alloy were investigated by optical microscopy,X-ray diffraction,transmission electron microscopy and universal material testing machine.The results showed that the grains of the alloy were elongated along rolling direction and stress-induced α' martensite was not detected in the deformed samples.The plastic deformation mechanisms of the alloy were related to {112} 111 type deformation twinning and dislocation slipping.Meanwhile,the transition from γ-fiber texture to α-fiber texture took place during cold rolling and a dominant {001} 110_(α-fiber) texture was obtained after 90% cold deformation.With the increase of cold deformation degree,the strength increased owing to the increase of microstrain,dislocation density and grain refinement,and the elastic modulus decreased owing to the increase of dislocation density as well as an enhanced intensity of {001} 110_(α-fiber)texture and a weakened intensity of {111} 112_(γ-fiber)texture.The 90% cold rolled alloy exhibited a great potential to become a new candidate for biomedical applications,since it possesses low elastic modulus(47.1 GPa),moderate strength(883 MPa) and high elastic admissible strain(1.87%),which are superior than those of Ti-6 Al-4 V alloy.     

Axisymmetric multiquadrics

This paper reviews the previous axisymmetric global interpolation functions used in the context of the dual reciprocity boundary element method and dual reciprocity method of fundamental solutions connected to axisymmetric Laplace operator. It complements our axisymmetric thin plate splines [1] with the axisymmetric form of the Hardy's multiquadrics ${(r^2+r_0^2)}^{m/2}$; m=±1. This new functions can be used in the improved Golberg–Chen–Karur [2] type of approximations. The basic equations are accompanied by a set of related expressions that permit straightforward use of the developed global interpolation functions in a broad spectrum of dual reciprocity boundary element method and method of fundamental solutions, and meshless direct collocation like discrete approximate procedures.