Heat Transfer in Nanomaterial Suspension (CuO and Al2O3) Using KKL Model

Novel nonlinear power-law flux models were utilized to model the heat transport phe-nomenon in nano-micropolar fluid over a flexible surface. The nonlinear conservation laws (mass, momentum, energy, mass transport and angular momentum) and KKL cor-relations for nanomaterial under novel flux model were solved numerically. Computed results were used to study the shear-thinning and shear-thickening nature of nano pol-ymer suspension by considering n-diffusion theory. Normalized velocity, temperature and micro-rotation profiles were investigated under the variation of physical parame-ters. Shear stresses at the wall for nanoparticles (CuO and Al2O3) were recorded and dis-played in the table. Error analyses for different physical parameters were prepared for various parameters to validate the obtained results.

Biological networks with singular Jacobians: their origins and adaptation criteria

ABSTRACTThis work is focused on Ordinary Differential Equations(ODE)-based models of biochemical systems that possess a singular Jacobian manifesting in non-hyperbolic equilibria. We show that there are several classes of systems that exhibit this behavior: a)systems with monomial-type interaction terms and b)systems with linear or nonlinear conservation laws. While models derived from mass-action principles often present with linear conservation laws stemming from the underlying biologic rationale, nonlinear conservation laws are more subtle and harder to detect. Nevertheless, in both situations the corresponding ODE system will contain non-hyperbolic equilibria. While having a potentially more complex dynamics and falling outside of the scope of existing theoretical frameworks, this class of systems can still exhibit adapting behavior associated with certain nodes and inputs. We derive a generalized adaptation condition that extends to singular systems and is compatible with both single-input/single-output and multiple-input/multiple-output settings. The approach explored herein, based on the notion of Moore-Penrose pseudoinverse, is tested on several synthetic systems that are shown to exhibit homeostatic behavior but are not covered by existing methods. These results highlight the role of the network structure and modeling assumptions when understanding system response to input and can be helpful in discovering intrinsic relationships between the nodes.