Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

Equivalence of weak formulations of the steady water waves equations

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.

Study of the nonlinear optical properties of a crosslinkable chromophore for use in guest host polymer films

A guest/host material system in which the guest molecule is a functionalized, optically nonlinear, chromophore is described. A verification of the crosslinking process, an assessment of the nonlinear properties of the chromophore, using Solvatochromic methods, and an investigation of the electric field induced molecular orientation using second-harmonic generation are included.

A comparison of photoinduced poling and thermal poling of azo‐dye‐doped polymer films for second order nonlinear optical applications

Photoinduced poling (PIP) is a new technique which allows the room‐temperature preparation of guest/host polymer films exhibiting significant polar order for nonlinear optical applications. We report a comparison of this novel technique with the conventional electrode poling procedure performed at the glass transition temperature of the polymer using disperse red 1/poly(methylmethacrylate) films. In particular, in situ second harmonic generation measurements show that levels of polar order achieved using these two techniques are similar. In contrast, the stability of the polar order is reduced by up to 20 times in terms of the decay time constant in films prepared using PIP although the stability is very dependent upon the temperature at which the poling was performed.

Gravity well visibility in haptic interfaces for motion-impaired

Haptic computer interfaces provide users with feedback through the sense of touch, thereby allowing users to feel a graphical user interface. Force feedback gravity wells, i.e. attractive basins that can pull the cursor toward a target, are one type of haptic effect that have been shown to provide improvements in "point and click" tasks. For motion-impaired users, gravity wells could improve times by as much as 50%. It has been reported that the presentation of information to multiple sensory modalities, e.g. haptics and vision, can provide performance benefits. However, previous studies investigating the use of force feedback gravity wells have generally not provided visual representations of the haptic effect. Where force fields extend beyond clickable targets, the addition of visual cues may affect performance. This paper investigates how the performance of motion-impaired computer users is affected by having visual representations of force feedback gravity wells presented on-screen. Results indicate that the visual representation does not affect times and errors in a "point and click" task involving multiple targets.

Stable Nonlinear Receding Horizon Regulator Using RBF Neural Network Models

The general stability theory of nonlinear receding horizon controllers has attracted much attention over the last fifteen years, and many algorithms have been proposed to ensure closed-loop stability. On the other hand many reports exist regarding the use of artificial neural network models in nonlinear receding horizon control. However, little attention has been given to the stability issue of these specific controllers. This paper addresses this problem and proposes to cast the nonlinear receding horizon control based on neural network models within the framework of an existing stabilising algorithm.

Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Closed loop design for a simple nonlinear aircraft model using eigenstructure assignment

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled flight. The aim of this work is to construct a robust closed-loop control that optimally extends the stable and decoupled flight envelope. For the study of these systems nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and investigate control effects on dynamic behavior. In this work linear feedback control designs calculated by eigenstructure assignment methods are investigated for a simple aircraft model at a fixed flight condition. Bifurcation analysis in conjunction with linear control design methods is shown to aid control law design for the nonlinear system.