Negligibility of haptotaxis effect in a chemotaxis–haptotaxis model

In this work, we rigorously study chemotaxis effect versus haptotaxis effect on boundedness, blow-up and asymptotical behavior of solutions for a chemotaxis-haptotaxis model in 2D settings. It is well-known that the corresponding Keller–Segel chemotaxis-only model possesses a striking feature of critical mass blowup phenomenon, namely, subcritical mass ensures boundedness, whereas, supercritical mass induces the existence of blow-ups. Herein, we show that this critical mass blow-up phenomenon stays almost the same in the full chemotaxis-haptotaxis model and that any global-in-time haptotaxis solution component vanishes exponentially and the other two solution components converge exponentially to that of chemotaxis-only model in a global sense for suitably large chemo-sensitivity and in the usual sense for suitably small chemo-sensitivity. Therefore, haptotaixs is neither good nor bad than chemotaxis, showing negligibility of haptotaxis effect in the underlying chemotaxis-haptotaxis model.

Wertschöpfungsnetzwerk und Produktion integrieren/Integrating supply network and manufacturing: An adaptive, closed-loop-based approach

Von der Integration von Wertschöpfungsnetzwerk und Produktion versprechen sich produzierende Unternehmen eine schnellere Reaktion auf Ereignisse und signifikante Kosteneinsparungen. Der Beitrag zeigt einen adaptiven Regelkreis als technischen Lösungsbaustein für solch eine vertiefte Integration.   By integrating supply network and manufacturing, companies expect a faster response to events and significant cost savings. This article shows an adaptive control loop as a technical solution component for such a deep integration.

Existence of Positive Solutions to Singular Boundary Value Problems Involving φ-Laplacian

This paper is concerned with the existence of positive solutions to singular Dirichlet boundary value problems involving φ -Laplacian. For non-negative nonlinearity f = f ( t , s ) satisfying f ( t , 0 ) ¬ ≡ 0 , the existence of an unbounded solution component is shown. By investigating the shape of the component depending on the behavior of f at ∞ , the existence, nonexistence and multiplicity of positive solutions are studied.

Generating the Isocurve Representation for Configuration Space of Mechanisms

This paper proposes an approach for generating a set of isocurves as a representation for configuration space (CS) of a mechanism. An isocurve here is a curve in CS with some parameters fixed. Compared with conventional methods like box approximations, sampling points, and boundary tessellations, the isocurve-based representation has some advantages in space parameterization and data management. This approach directly formulates the joint loop equations in the form of kinematic matrices, which does not need any extra conversions and solves the equations with an isocurve-tracing method applying ODE solvers. Since the isocurves are connected in certain orders with the guide isocurves in a lower-dimensional space, tracing all the isocurves only needs one initial solution point for an isolated solution component. In addition, the proposed approach includes an interference-handling step, which trims off the collision portions of the isocurves by checking their feasibility according to the previously defined half-space constraints, and a measure for identifying the forward direction at singular points where the first-order derivatives vanish. The approach is implemented through programming and the results for a few examples show its effectiveness.

Strategies for Defect-Free and Deep Wet Etching of Pyrex 7740

In this paper, two aspects in the wet glass etching, the pre-annealing of the glass and the mask process, are taken into consideration to achieve the deep and defect-free wet etching of Pyrex glass. Compared with the conventional strategies, i.e.,HFsolution component and mask kinds, our experiment results prove the pre-annealing is another key role to obtain theoretical isotropy character in wet etching. Besides, the high temperature pre-annealing dramatically improves the structure profiles and reduces the notching defects. Additionally, a novel multilayer mask process is proposed. With 1.5μmPR/ 100nmAu/ 100 nmAu/ 20 nmCrmask and > 450 °C pre-annealing, > 150 μm deep and non-pin-holes Pyrex glass structures are achieved and the roughness of etched surface is lower than 1 nm.

On the Exact Traveling Wave Solutions of (2 + 1)-Dimensional Higher Order Broer–Kaup Equation

In this paper, we study the dynamical behavior and exact parametric representations of all traveling wave solutions for (2 + 1)-dimensional higher order Broer–Kaup equation. By using the method of dynamical systems, under different parametric conditions, for the solution component U, exact monotonic and nonmonotonic kink wave solutions, two-peak wave solutions, periodic wave solutions, as well as unbounded traveling wave solutions are obtained. Exact wave profiles of traveling wave solutions for all solution components U, V, W, P are shown.