In current communication, the thin-film flow of Casson hybrid nanofluid consists copper and alumina nanoparticles that dissolved in carboxymethyl cellulose (CMC) plus water over an unsteady stretching porous sheet is elucidated. Using suitable similarity variables, resultant partial governing equations are turned into a set nonlinear ordinary differential equations. The Keller box approach then...

Chemotaxis plays a crucial role in a variety of processes in biology and ecology. In many instances, processes involving chemical attraction take place in fluids. One of the most studied PDE models of chemotaxis is given by Keller-Segel equation, which describes a population density of bacteria or mold which attract chemically to substance they secrete. Solution of Keller-Segel equation can exh...

We investigate nonnegativity of exact and numerical solutions to a generalized Keller– Segel model. This model includes the so-called ‘‘minimal’’ Keller–Segel model, but can cover more general chemistry. We use maximum principles and invariant sets to prove that all components of the solution of the generalized model are nonnegative. We then derive numerical methods, using finite element techni...

We introduce stochastic models of chemotaxis generalizing the deterministic KellerSegel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean’s approach, we derive the exact kinetic equation satisfied by the density distribution of cells. In the mean field limit where statistical correlations between cell...

231 words) We report results of a series of experiments on decision-making in the presence of irreducibly imprecise probabilities. Subjects faced decisions among actions where the payoffs depend on the probability of drawing balls from an urn whose composition was not fully known. Consistent with the vagueness avoidance hypothesis, Decision Makers (DMs) displayed systematic preferences for risk...

Abstract: A simplified Keller–Segel model is studied by means of Lie symmetry based approaches. It is shown that a (1 + 2)-dimensional Keller–Segel type system, together with the correctly-specified boundary and/or initial conditions, is invariant with respect to infinite-dimensional Lie algebras. A Lie symmetry classification of the Cauchy problem depending on the initial profile form is prese...

In his seminal “Clio and the Economics of Qwerty”, Paul David indicates Thorstein Veblen’s famous discussion British system coal rail haulage as an intellectual antecedent to idea lock in. This note documents how Albert G. Keller, a Yale sociologist contemporary Veblen, had presented similar argument in connection establishment brick tax England its effects on size bricks. Like Keller used this...