We consider patterns formed by active transport of auxin in a tissue, where the accumulation of transporters is activated by local fluxes of auxin. We characterize the steady states for which auxin is homogeneous in the tissue. Under a condition of regularity of the dependence of transporters to the flux, we can prove that one of these steady states, with zero flux everywhere, is always locally...

theory Constant flux (CF) states describe the steady state response of a photonic medium with an arbitrary, possibly frequency dependent index of refraction n(x, ω) to a harmonically oscillating source. CF states were initially introduced to describe steady state oscillations of complex lasers. Here we describe their application to various phenomena in photonics and quantum optics.

We employ numerical simulations to explore the development of flow-induced self-excited oscillations in three-dimensional collapsible tubes which are subject to boundary conditions (flow rate prescribed at the outflow boundary) that encourage the development of high-frequency oscillations via an instability mechanism originally proposed by Jensen & Heil (J. Fluid Mech., vol. 481, 2003, p. 235)....

We report numerical and experimental results indicating successful stabilization of unstable steady states and periodic orbits in an electrochemical system. Applying a continuous delayed-feedback technique not only periodic and chaotic oscillations are suppressed via stabilization of steady-state solutions but also the chaotic dynamics can be converted to periodic behavior. In all cases the fee...

The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of gro...

We present some new criteria for the oscillation of even order dynamic equation[Formula: see text]on time scale T, where α is the ratio of positive odd integers a and q is a real valued positive rd-continuous functions defined on T.

A mathematical model was used to investigate the filter properties of the thick ascending limb (TAL), that is, the response of TAL luminal NaCl concentration to oscillations in tubular fluid flow. For the special case of no transtubular NaCl backleak and for spatially homogeneous transport parameters, the model predicts that NaCl concentration in intratubular fluid at each location along the TA...

Abstract The three-dimensional traction problem for steady elastic oscillations equations is studied. Representability of its solution by means a double layer potential considered instead the more usual simple potential.