Noise-Induced Resonance in Bistable Systems Caused by Delay Feedback

Abstract

The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one-dimensional parametrized stochastic differential equation with point delay; the basic properties of which we check.

With a view to capturing the effective dynamics and, in particular, the resonance-like behavior of the reference model, we construct a simplified or reduced model, the two-state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn can be used to characterize the phenomenon of noise-induced resonance.

Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two-state model and the reference model. The resonance characteristics developed for the reduced model can thus be applied to the original model.     

Stability in Terms of Two Measures for Stochastic Differential Equations with Markovian Switching

Abstract

In this paper, we investigate the stability in terms of two measures for stochastic differential equations with Markovian switching by using the method of Lyapunov functions. Our new theory can not only be used to show a given system to be stochastically stable in the classical sense, but can also be used to deal with some situations where the classical stability theory is not applicable.     

Self-Interacting Markov Chains: Some Asymptotics

Abstract

Guided by the self-interaction mechanisms introduced in Benaim et al. [2 Benaim , M. , Ledoux , M. , and Raimond , O. 2002 . Self-interacting diffusions . Probab. Theory Related Fields 122 : 1 – 41 . [Google Scholar]] and in [5 Del Moral , P. , and Miclo , L. 2006 . Self-interacting Markov chains . Stochastic Anal. Appl. 24 : 615 – 660 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]], we present a more general definition of self-interacting Markov chains (SIMCs) (than in Del Moral and Miclo [5 Del Moral , P. , and Miclo , L. 2006 . Self-interacting Markov chains . Stochastic Anal. Appl. 24 : 615 – 660 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] and Benaim et al. [2 Benaim , M. , Ledoux , M. , and Raimond , O. 2002 . Self-interacting diffusions . Probab. Theory Related Fields 122 : 1 – 41 . [Google Scholar]]). We then establish, for particular self-interaction mechanisms, a stability theorem with error estimation, two central limit theorems, two functional central limit theorems, and the large deviation principle.     

The protection zone for biological population in random environment

A biomathematical model is described by stochastic differential equations with Markovian switching. The long‐time dynamical properties are studied both theoretically and numerically. Results show that both the persistence and extinction have close relationship with environmental noises (white and color noises). These results are of important biological significance for biological conservation. Copyright © 2012 John Wiley & Sons, Ltd.     

Alternative Superalgebras with DCC on Two-Sided Ideals#

We study the structure of alternative superalgebras that satisfy the descending chain condition (DCC) for two-sided ideals. The main results state that the Baer radical in an alternative superalgebra of characteristic ≠ 2, 3 with DCC on two-sided ideals is solvable and every such a semiprime superalgebra (of arbitrary characteristic) is isomorphic to a subdirect sum of an associative superalgebra with this property and a finite direct sum of simple alternative non-associative superalgebras.     

Synthesis and the effect of alkyl chain length on photochromic properties of diarylethene derivatives

A new class of photochromic diarylethenes bearing pyrrole and thiophene units with different length of alkyl chains at 2-position of thiophene rings have been synthesized. Their characteristics, including photochromism and fatigue resistance were investigated systematically, and each diarylethene derivative showed good photochromic properties whether in solution or in PMMA films. The alkyl group moiety was connected directly to the central cyclopentene ring as a heteroaryl unit and availably participated in photoisomerization reaction. And some properties, for example, the conversion ratio in the photostationary state(PSS) and the absorption coefficient of the ring-closed isomers in acetonitrile were significantly affected by the alkyl chain length. The results revealed that substituents of alkyl chain played an important role in the photoisomerization process of diarylethenes.     

基于二噻吩并吡咯π桥的窄带隙非富勒烯受体材料在有机太阳能电池中的应用

以不同烷基取代的二噻吩并吡咯(DTP)为π桥,连接吲哒省并二噻吩(IDT)中间单元和氰基茚酮(IC)或二氟代氰基茚酮(2F-IC)末端基团,设计并合成了6个窄带隙的非富勒烯受体材料。 其中,IDTDTP-C₂C₂-H和IDTDTP-C₂C₂-F中的DTP单元以1-乙基丙基为侧链,IDTDTP-C₆C₆-H和IDTDTP-C₆C₆-F中的DTP单元以1-己基庚基为侧链,IDTDTP-C₁₂-H和IDTDTP-C₁₂-F中的DTP单元以十二烷基为侧链。 6个分子均具有较窄的光学带隙(1.37~1.44 eV)。 相比于以IC为末端基团的分子(IDTDTP-C₂C₂-H、IDTDTP-C₆C₆-H和IDTDTP-C₁₂-H),由于氟原子的拉电子效应,以2F-IC为末端基团的分子(IDTDTP-C₂C₂-F、IDTDTP-C₆C₆-F和IDTDTP-C₁₂-F)具有红移的吸收光谱,以及更低的最高分子占有轨道能级(HOMO)和最低分子空轨道(LUMO)能级。 以宽带隙聚合物聚[2,6-(4,8-双(5-(2-乙基己基))噻吩-2-基)-苯并[1,2-b:4,5-b']二噻吩-alt-5,5-(1',3'-二-2-噻吩)-5',7'-双(2-乙基己基)-苯并[1',2'-c:4',5'-c']二噻吩-4,8-二酮](PBDB-T)为给体材料,制备了有机太阳能电池器件。 PBDB-T:IDTDTP-C₆C₆-F共混薄膜具有较高且更平衡的空穴/电子迁移率,以及良好的形貌,基于PBDB-T:IDTDTP-C₆C₆-F的有机太阳能电池获得了6.94%的能量转换效率,开路电压为0.86 V,短路电流密度为13.56 mA/cm²,填充因子为59.5%。     

两个包含联苯类三羧酸配体的钴(Ⅱ)和镍(Ⅱ)配位聚合物的合成、晶体结构及磁性质

采用水热方法,用2种联苯类三羧酸配体:联苯-2,4,4′-三羧酸(H3btc)、5-(3,4-二羧基苯基)吡啶甲酸(H_3dppa)和4,4′-联吡啶(4,4′-bipy)分别与CoCl_2·6H_2O和NiCl_2·6H_2O反应,合成了具有一维双螺旋链结构的配合物[Co(μ_2-H_2btc)2(4,4′-bipy)_2]_n(1)以及二维层状配位聚合物{[Ni_3(μ4-dppa)_2(H_2O)_6]·2H_2O}n(2),并对其结构和磁性质进行了研究。结构分析结果表明2个配合物都属于三斜晶系,P1空间群。配合物1具有一维双螺旋链结构,而且这些链通过O-H…O/N氢键作用进一步形成了三维超分子框架。而配合物2具有基于一维链单元的二维层状结构。4,4′-联吡啶在配合物1和2中分别起配位作用和模板作用。研究表明,配合物1中相邻钴离子间存在铁磁相互作用。     

Effects of chain extender and uniaxial stretching on the properties of PLA/PPC/mica composites

Poly(lactic acid) (PLA)/poly(propylene carbonate) (PPC)/mica composites with different amount of chain extender (CE) were melt compounded and then processed via two routes (compression molding and uniaxial stretching) into sheets and films. The tensile, thermal, and oxygen barrier properties of all the samples were investigated. Tensile test showed that the tensile strength and elongation at break of all films were much higher than that of all sheets, especially for PLA/PPC/mica with 0.9‐wt% CE composite (CM₃(CE)_0.9) film. The crystallinity of all films increased significantly after uniaxial stretching of sheet samples. The Fourier transform infrared spectroscopy (FTIR) results proved the chemical reactions occurred between PLA/PPC and CE. Scanning electron microscope (SEM) analysis revealed that compatibility and interfacial adhesion of all samples were improved after adding mica and CE, and they were further enhanced after uniaxial stretching. The addition of CE was not favorable to improve the oxygen barrier performance of PLA/PPC/mica sheet samples. However, the oxygen barrier performance of film samples was significantly improved after uniaxial stretching. In particular, the CM₃(CE)_0.9 film had the lowest oxygen permeability coefficient (1.4 × 10^?15 cm³·cm/(cm²·s·Pa)), and this was the best oxygen barrier properties reported in the literature for PLA‐based composites, which was comparable with PA film. This study demonstrated the high efficiency of uniaxial stretching on improvement of properties of composites, which would promote the application of biodegradable polymers in oxygen sensitive food packaging.