Smooth normal forms of folded resonance saddles and nodes and complete classification of generic linear second order PDE's on the plane The smooth normal forms of generic implicit differential equations of first-order near its resonance folded singular point of type saddle or node are given. These...
1. Introduction One of the most basic PDEs is the Burgers equation for u(ξ, τ ) ∈ R ∂ξ u = −θ ∂τ [u(1 − u)], θ∈ R+. (1) As is standard in PDE theory, the Eq. (1) may be solved by the method of characteristics. This may produce several solutions, ...
The present proposed higher-order PDE's is transformed to the non-linear system of ODE's. For the solution of the proposed high non-linear model HAM method is employed. As the hybrid nanofluid are highlighted on the second-grade fluid flow over a horizontal porous flat plate. During the ...
Influence of embedded parameters on velocity distribution is seen in Fig. 1, Fig. 2, Fig. 3, Fig. 4, Fig. 5. Fig. 1 is drawn to witness the impact of first order slip parameter γ1 on f′(η). Here we have seen that motion of the fluid reduces for greater γ1=0,0.9,1.8,2.7...
Some readers are bound to want to take the techniques we’ve introduced here and try them on the problem of forecasting the future price of securities on the stock market (or currency exchange rates, and so on). However, markets have very different statistical characteristics than natural phenom...
Aerodynamic characteristicsDifferential equationsSecond order rigid flapping response statistics of lifting rotor blades are obtained by efficient algorithms developed in this paper. These statistics make it possible to analyze the effect of a finite load correlation length on the blade response. For the ...
The system of the governing nonlinear PDE is solved by using the perturbation method to second-order in dimensionless wavenumber. The analytic solution has been obtained in the form of a stream function from which the axial pressure gradient has been derived. The flow is investigated in a wave ...
A typical characteristic of eukaryotic cells compared to prokaryotes is represented by the spatial heterogeneity of the different structural and functional components: for example, most of the genetic material is surrounded by a highly specific membrane
Since asymmetric cell division plays an essential role in survival forC. crescentus, understanding how the asymmetry is regulated provides insight into the life cycle of many bacteria with similar characteristics. Many proteins, genes, and other molecules involved in the asymmetric pattern have been re...
Thereby a one-dimensional PDE is obtained for the free surface dynamics of second-grade fluid with varying fluid properties. In the derivation of the asymptotic model, the fluid parameters are assumed to depend on temperature-function linearly. The linear and non-linear steady stretching speed is ...