Dynamics of Relative Phases: Generalised Multibreathers

For small Hamiltonian perturbation of a Hamiltonian systemof arbitrary number of degrees of freedom with anormally non-degenerate submanifold of periodic orbits we construct a nearbysubmanifold and an `effective Hamiltonian' on it such that the differencebetween the two Hamiltonian vector fields is small. The effective Hamiltonianis independent of one coordinate, the `overall phase', and hence thecorresponding action is preserved. Unlike standard averaging approaches,critical points of our effective Hamiltonian subject to given actioncorrespond to exact periodic solutions. We prove there has to be at least acertain number of these critical points given by global topological principles.The linearisation of the effective Hamiltonian about critical points is provedto give the linearised dynamics for the full system to leading order in theperturbation. Hence in the case of distinct eigenvalues which move at non-zerospeed with ,the linear stability type of the periodic orbit can be read offfrom the effective Hamiltonian. Our principal application is to networks ofoscillators or rotors where many such submanifolds of periodic orbits occurat the uncoupled limit – simply excite a number N 2 of the units inrational frequency ratio and put the others on equilibria, subject to anon-resonance condition. The resulting exact periodic solutions for weakcoupling are known as multibreathers. We call the approximate solutions givenby the effective Hamiltonian dynamics, `generalised multibreathers'. Theycorrespond to solutions which look periodic on a short time scale but therelative phases of the excited units may evolve slowly. Extensions aresketched to travelling breathers and energy exchange between degrees offreedom.     

Three-dimensional viscoelastic simulation of coextrusion process: comparison with experimental data

 Three-dimensional numerical simulation of viscoelastic coextrusion process has been performed and numerical results were compared with the experimental data of Karagiannis et al. (1990). By varying the magnitude of the second normal stress difference and its ratio of Fluid I and Fluid II, we were able to control the interface profile and the degree of encapsulation along the downstream direction. By increasing the parameter α (α_Fluid I=α_Fluid II) from 0.1 to 0.4 in the Giesekus model and increasing the α ratio (α_Fluid Iα_Fluid II) between Fluid I and Fluid II from 2.0 to 4.0 in the permissible range of realistic polymeric systems, the interface profile and the degree of encapsulation along the downstream direction were fitted with the experimental results. There was little difference between the numerical results and the experimental data in the interface profile and the degree of encapsulation along the downstream direction when the α ratio was set to 3.0 (0.3:0.1). Fluid I with larger magnitude of the second normal stress difference protrudes into Fluid II with smaller magnitude of the second normal stress difference around the symmetric plane, while Fluid II wraps around Fluid I near the side walls. As the ξ ₁ ratio (ξ _{1 ,Fluid I}ξ _{1 ,Fluid II}) increases from 1.0 to 3.0 for the two-mode Phan-Thien and Tanner model, it was found that the curvature of the interface profile increased, and the difference between the numerical results and the experimental data in the interface profile and the degree of encapsulation along the downstream direction was almost negligible when the ξ ₁ ratio was set to 3.0 (0.54:0.18). Although the parameters of viscoelastic models were fitted by using the shear viscosity data only, quantitative agreements between the numerical results and the experimental coextrusion data were quite satisfactory. Received: 24 April 2001 Accepted: 5 June 2001     

Strain hardening behavior of polymer blends with fibril morphology

We investigate the rheological behavior of the polymer blends with fibril morphology, with special focus on the effect of fibril morphology on the extensional properties under uniaxial extension. We add a small amount of the dispersed phase to the matrix, and control the blend morphology by changing the viscosity ratio. When the fibril morphology is maintained, the blend shows not only a significant increase of the extensional viscosity but the strain hardening behavior. The extensional viscosity increases depending on the aspect ratio of the fibers, while the strain hardening behavior originates from the restricted stretching of deformable fibers, which has been confirmed theoretically by introducing the concept of rigidity of the fiber. It suggests a way to induce the strain hardening behavior by introducing deformable fibrils into the matrix, that is, by the design of polymer blends with a small amount of dispersed phase such that the fibril structure is maintained.     

A Family of Molecular Sieves Containing Framework‐Bound Organic Structure‐Directing Agents

Organic structure‐directing agents (OSDAs), such as quaternary ammonium cations and amines, used in the synthesis of zeolites and related crystalline microporous oxides usually end up entrapped inside the void spaces of the crystallized inorganic host lattice. But none of them is known to form direct chemical bonds to the framework of these industrially important catalysts and adsorbents. We demonstrate that ECR‐40, currently regarded as a typical silicoaluminophosphate molecular sieve, constitutes instead a new family of inorganic‐organic hybrid networks in which the OSDAs are covalently bonded to the inorganic framework. ECR‐40 crystallization begins with the formation of an Al–OSDA complex in the liquid phase in which the Al is octahedrally coordinated. This unit is incorporated in the crystallizing ECR‐40. Subsequent removal of framework‐bound OSDAs generates Al‐O‐Al linkages in a fully tetrahedrally coordinated framework.     

Interfacial Engineering of CdO–CdSe 3D Microarchitectures with in situ Photopolymerized PEDOT for an Enhanced Photovoltaic Performance

In the present work, porous 3D CdO‐microstructured electrode obtained by pyrolysis of 3D CdCO₃ microstructures is self‐sensitized with CdSe using an ion exchange reaction. After sensitization, an interfacial treatment of the CdO–CdSe interface is performed by depositing a thin film of PEDOT using a photoinduce polymerization route. The microstructured electrode before and after interfacial treatment is characterized using field‐emission scanning microscope, energy dispersive X‐ray analyzer, contact angle measurement, UV–Visible absorption spectrophotometer and X‐ray photoelectron spectrometer. After constructing a liquid junction solar cell with a Pt counter electrode, the photovoltaic performance and interfacial charge transfer kinetics across the CdO–CdSe interface before and after PEDOT treatment are investigated. The results exhibit an improved interfacial charge‐transfer resistance after the PEDOT treatment, which leads to enhance the short‐circuit current by 15.81% and the power conversion efficiency by 19.82%.     

MoS2 Nanosheets Supported on 3D Graphene Aerogel as a Highly Efficient Catalyst for Hydrogen Evolution

The development of efficient catalysts for electrochemical hydrogen evolution is essential for energy conversion technologies. Molybdenum disulfide (MoS₂) has emerged as a promising electrocatalyst for hydrogen evolution reaction, and its performance greatly depends on its exposed edge sites and conductivity. Layered MoS₂ nanosheets supported on a 3D graphene aerogel network (GA‐MoS₂) exhibit significant catalytic activity in hydrogen evolution. The GA‐MoS₂ composite displays a unique 3D architecture with large active surface areas, leading to high catalytic performance with low overpotential, high current density, and good stability.     

Aggregation of ranked votes considering different relative gaps between rank positions

This paper considers ranked voting systems to determine the rank order of candidates who compete for a limited number of positions. We show that the preferential voting problems based on the data envelopment analysis (DEA) (Wang et al, 2007) can be solved using the extreme points of constraints on rank position importance incorporated in the formulation. This is basically due to the fact that the so-called inverse positive property of the constraints makes it possible to easily find their extreme points. Further, we emphasize that this finding is not restricted to Wang et al’s two linear models, but is also applicable to other DEA-based preferential voting problems, which include the constraints accounting for different relative gaps between rank positions.     

Large amplitude oscillatory shear behavior of PEO-PPO-PEO triblock copolymer solutions

Rheological properties of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer solution in both linear and nonlinear regions have been investigated. PEO-PPO-PEO triblock copolymer solution shows a dramatic change in mechanical properties as temperature changes. PEO-PPO-PEO triblock copolymer undergoes a transition from sol to gel with increase of temperature. During this transition the copolymer solution passes through three different stages, namely sol, soft gel, and hard gel. In our previous research (Hyun et al. in J Non-Newtonian Fluid Mech 55:51–65, 2002), large amplitude oscillatory shear (LAOS) behavior was found to be very sensitive to the generated microstructures. In this study, we investigated the relationship between the LAOS type and the microdomain structure. Newtonian behavior is observed in sol region, while there appear two kinds of LAOS types in the soft gel region. One is type I (G′, G′′ decreasing) and the other is a combination of type I and type IV (G′, G′′ increasing followed by decreasing). Type III (G′ decreasing, G′′ increasing followed by decreasing) is observed in the hard gel region. We compared the shape of stress curves, Lissajous pattern, and Fourier transform (FT) rheology of hard gel and soft gel under LAOS, and tried to relate the complex LAOS behavior with the microstructural change. From these investigations, it was found that the LAOS behavior and the stress pattern at large strain are closely related to the microdomain structure of PEO-PPO-PEO triblock copolymer, and provide a lot of useful information on the microstructures induced by large deformation.     

Chlorin e6 Derivative Radachlorin Mainly Accumulates in Mitochondria,Lysosome and Endoplasmic Reticulum and Shows High Affinity toward Tumors in Nude Mice in Photodynamic Therapy

The efficacy of photodynamic therapy (PDT) depends upon the amount of photosensitizer accumulated in the malignant tissues. Radachlorin is a popular photosensitizer used in photodynamic therapy to treat various types of cancer. In this study, we have studied the main organelles responsible for the accumulation of radachlorin in human anaplastic thyroid cancer in vitro and in vivo. The optimal time window for uptake and clearance of radachlorin also was studied. Confocal microscopic images confirmed that the radachlorin is mainly acquired by mitochondria and partially by lysosome and endoplasmic reticulum. Studies also showed that the maximum amount of radachlorin was accumulated within 3–6 h after the treatment. Radachlorin also showed a higher affinity toward malignant tumors compared to the other organs in mice xenograft model. Uptake of radachlorin reached an optimum amount within 6 h and most of the radachlorins were also cleared from the body in next 48 h. Therefore, detailed information regarding exact accumulation sites and a time window in which maximum amount of drug is accumulated and cleared were obtained by this study. Hence, not only the efficacy of the treatment can be increased but the phototoxicity after the treatment also can be controlled.     

Polyatomic anion versus acetonitrile in coordinating ability: structural properties of AgX-bearing 1,4-bis(2-isonicotinoyloxyethyl)piperazine (X??=?NO3?, CF3SO3?, ClO4?, BF4?, and PF6?)

Type studies on competitive polyatomic anion versus acetonitrile coordination in the self-assembly of a series of [Ag₂(X) _m (bip)(NCCH₃) _n ](X)_2−m (X⁻ = NO₃ ⁻, CF₃SO₃ ⁻, ClO₄ ⁻, BF₄ ⁻, and PF₆ ⁻; m = 0, 2; n = 0, 2, 4; bip = 1,4-bis(2-isonicotinoyloxyethyl)piperazine) were carried out. Each bip spacer acts as an N₄ tetradentate ligand and is linked to four silver(I) centers through two pyridine and two piperazine moieties, producing a double strand consisting of two 20-membered ring units. The coordinating environment around the silver(I) center is subtly determined by the competition of the polyatomic anions with acetonitrile, that is, by the Ag···NCCH₃ versus Ag···X interactions. The coordinating ability of acetonitrile is inversely proportional to the order of the coordination ability of the Hoffmeister series of polyatomic anions, NO₃ ⁻ ≫ CF₃SO₃ ⁻ > ClO₄ ⁻ > BF₄ ⁻ ≫ PF₆ ⁻.