基于表面起皱法的梯度图案的可控制备

报道了基于非刻蚀法的表面起皱机制来实现高分子薄膜表面的周期性梯度图案的简单可控制备.即对于处于机械拉伸状态的聚二甲基硅氧烷(PDMS)弹性基底,在其底部垫入"积木",而后对其进行紫外-臭氧(UVO)和氧等离子体(OP)的联合表面处理."积木"的加入引起了表面处理后表面硅氧层(SiOx)梯度厚度的形成,进而当释放拉伸应变后,诱导产生了梯度皱纹图案.结果表明:当UVO与OP联用处理时,不仅实现了较小拉伸应变下梯度皱纹形貌的制备,而且扩大了UVO单独使用时梯度皱纹周期的变化范围.通过OP与UVO的处理顺序和处理时间等因素的简单调节,进一步实现了不同梯度皱纹微结构的精细构筑.     

Fabrication of extreme wettability patterns with water-film protection for organic liquids

Selective fabrication of superhydrophilic (S-philic) region on a superhydrophobic (S-phobic) surface requires complex technology and high cost, which has limited applications of extreme wettability patterns. In this paper, a twice-chemical-etching approach without special modification is used to prepare the extreme wettability patterns. Superhydrophobicity and superhydrophilicity can be successfully achieved after twice chemical etching for 20 seconds. The obtained patterns can maintain their extreme wettability for at least 30 days. Functional platforms with single-S-philic and multi-S-philic regions are fabricated to manipulate water and various organic liquids with water-film protection in an air environment.     

Individual behavior and macro social properties. An agent-based model

The paper aims at presenting an agent-based modeling exercise to illustrate how small differences in the cognitive properties of agents can generate very different macro social properties. We argue that it is not necessary to assume highly complicated cognitive architectures to introduce cognitive properties that matter for computational social science purposes. Our model is based on different simulation settings characterized by a gradual sophistication of behavior of agents, from simple heuristics to macro-micro feedback and other second-order properties. Agents are localized in a spatial interaction context. They have an individual task but are influenced by a collective coordination problem. The simulation results show that agents can generate efficiency at a macro level particularly when socio-cognitive sophistication of their behavior increases.

Singular and nonsingular first-order initial value problems

Under barrier strip type arguments we investigate the existence of global solutions to the initial value problem x^′=f(t,x,x^′), x(0)=A, where the scalar function f(t,x,p) may be singular at x=A.     

Existence and stability of spatially localized patterns

Spatially localized patterns have been observed in numerous physical contexts, and their bifurcation diagrams often exhibit similar snaking behavior: symmetric solution branches, connected by bifurcating asymmetric solution branches, wind back and forth in an appropriate parameter. Previous papers have addressed existence of such solutions; here we address their stability, taking the necessary first step of unifying existence and uniqueness proofs for symmetric and asymmetric solutions. We then show that, under appropriate assumptions, temporal eigenvalues of the front and back underlying a localized solution are added with multiplicity in the right half plane. In a companion paper, we analyze the behavior of eigenvalues at $\lambda =0$ and inside the essential spectrum. Our results show that localized snaking solutions are stable if, and only if, the underlying fronts and backs are stable: unlike localized non-oscillatory solutions, no interaction eigenvalues are present. We use the planar Swift–Hohenberg system to illustrate our results.     

Multiple and sign‐changing solutions for the multivalued p ‐Laplacian equation

We consider a class of elliptic inclusions under Dirichlet boundary conditions involving multifunctions of Clarke's generalized gradient. Under conditions given in terms of the first eigenvalue as well as the Fu?ik spectrum of the p ‐Laplacian we prove the existence of a positive, a negative and a sign‐changing solution. Our approach is based on variational methods for nonsmooth functionals (nonsmooth critical point theory, second deformation lemma), and comparison principles for multivalued elliptic problems. In particular, the existence of extremal constant‐sign solutions plays a key role in the proof of sign‐changing solutions (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spike patterns in a reaction–diffusion ODE model with Turing instability

We explore a mechanism of pattern formation arising in processes described by a system of a single reaction–diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions between cellular processes and diffusing growth factors. We focus on the model of early carcinogenesis proposed by Marciniak‐Czochra and Kimmel, which is an example of a wider class of pattern formation models with an autocatalytic non‐diffusing component. We present a numerical study showing emergence of periodic and irregular spike patterns because of diffusion‐driven instability. To control the accuracy of simulations, we develop a numerical code on the basis of the finite‐element method and adaptive mesh grid. Simulations, supplemented by numerical analysis, indicate a novel pattern formation phenomenon on the basis of the emergence of nonstationary structures tending asymptotically to a sum of Dirac deltas. Copyright © 2013 John Wiley & Sons, Ltd.     

The Ginzburg-Landau manifold is an attractor

Summary The Ginzburg-Landau modulation equation arises in many domains of science as a (formal) approximate equation describing the evolution of patterns through instabilities and bifurcations. Recently, for a large class of evolution PDE's in one space variable, the validity of the approximation has rigorously been established, in the following sense: Consider initial conditions of which the Fourier-transforms are scaled according to the so-calledclustered mode-distribution. Then the corresponding solutions of the “full” problem and the G-L equation remain close to each other on compact intervals of the intrinsic Ginzburg-Landau time-variable. In this paper the following complementary result is established. Consider small, but arbitrary initial conditions. The Fourier-transforms of the solutions of the “full” problem settle to clustered mode-distribution on time-scales which are rapid as compared to the time-scale of evolution of the Ginzburg-Landau equation.     

Bifurcations and spatiotemporal patterns in a ratio‐dependent diffusive Holling‐Tanner system with time delay

In this paper, we concentrate on the spatiotemporal patterns of a delayed reaction‐diffusion Holling‐Tanner model with Neumann boundary conditions. In particular, the time delay that is incorporated in the negative feedback of the predator density is considered as one of the principal factors to affect the dynamic behavior. Firstly, a global Turing bifurcation theorem for τ = 0 and a local Turing bifurcation theorem for τ > 0 are given. Then, further considering the degenerated situation, we derive the existence of Bogdanov‐Takens bifurcation and Turing‐Hopf bifurcation. The normal form method is used to study the explicit dynamics near the Turing‐Hopf singularity. It is shown that a pair of stable nonconstant steady states (stripe patterns) and a pair of stable spatially inhomogeneous periodic solutions (spot patterns) could be bifurcated from a positive equilibrium. Moreover, the Turing‐Turing‐Hopf–type spatiotemporal patterns, that is, a subharmonic phenomenon with two spatial wave numbers and one temporal frequency, are also found and explained theoretically. Our results imply that the interaction of Turing and Hopf instabilities can be considered as the simplest mechanism for the appearance of complex spatiotemporal dynamics.     

Dynamics and pattern formations in diffusive predator‐prey models with two prey‐taxis

A reaction‐diffusion two‐predator‐one‐prey system with prey‐taxis describes the spatial interaction and random movement of predator and prey species, as well as the spatial movement of predators pursuing preys. The global existence and boundedness of solutions of the system in bounded domains of arbitrary spatial dimension and any small prey‐taxis sensitivity coefficient are investigated by the semigroup theory. The spatial pattern formation induced by the prey‐taxis is characterized by the Turing type linear instability of homogeneous state; it is shown that prey‐taxis can both compress and prompt the spatial patterns produced through diffusion‐induced instability in two‐predator‐one‐prey systems.