−− The transformation group theoretic approach is applied to the system of equations governing the unsteady boundary layer flow of a micropolar fluid near the rear stagnation point of a plane surface in a porous media. The application of a two-parameter group reduces the number of independent variables by two, and consequently the system of governing partial differential equations with boundary...

Techniques that have become common in aerodynamics codes have recently begun to be implemented in space-physic codes, which solve the governing equations for a compressible plasma. These techniques include high-resolution upwind schemes, block-based solution-adaptive grids and domain decomposition for parallelization. While some of these techniques carry over relatively straightforwardly from a...

Dynamical systems see widespread use in natural sciences like physics, biology, and chemistry, as well engineering disciplines such circuit analysis, computational fluid dynamics, control. For simple systems, the differential equations governing dynamics can be derived by applying fundamental physical laws. However, for more complex this approach becomes exceedingly difficult. Data-driven model...

S U M M A R Y To approximate seismic wave propagation in double porosity media, the 2.5-D governing equations of poroelastic waves are developed and numerically solved. The equations are obtained by taking a Fourier transform in the strike or medium-invariant direction over all of the field quantities in the 3-D governing equations. The new memory variables from the Zener model are suggested as...

The brain is a prototype of a hierarchical system, as Fig. 1 shows. More precisely, it is hierarchical dynamical system. To specify a dynamical system, characteristic state variables and evolution equations governing the change of state should be defined. At the molecular level, the dynamic laws can be identified with chemical kinetics, at the channel level with biophysically detailed equations...

We present a novel application of the successive linearisation method to the classical Van der Pol and Duffing oscillator equations. By recasting the governing equations as nonlinear eigenvalue problems we obtain accurate values of the frequency and amplitude. We demonstrate that the proposed method can be used to obtain the limit cycle and bifurcation diagrams of the governing equations. Compa...

The longitudinal analysis of patient response time course following doses therapeutics is currently performed using Pharmacokinetic/Pharmacodynamic (PK/PD) methodologies, which requires significant human experience and expertise in the modeling dynamical systems. By utilizing recent advancements deep learning, we show that governing differential equations can be learnt directly from data. In pa...

Summary The unsteady reflection of dam-break flow along a horizontal channel by remote barrier is modelled using the nonlinear shallow water equations. interaction generates an upstream moving bore that connects collapsing reservoir fluid to rapidly deepening layer adjacent barrier. These motions are modified when released into containing pre-wetted layer, because oncoming itself headed alters ...

In this research various nonlinear fluid models have been introduced and the balloon movement in the porous arteries, including third-order non-Newtonian fluid, is described under the influence of the magnetic field. In order to solve the nonlinear equations governing the desired artery, an analytical method of approximation collocation and least squares are proposed. The effect of various para...