Modeling liquid crystal polymeric devices
Gimenez Pinto, Vianney Karina
The main focus of this work is the theoretical and numerical study of materials that combine liquid crystal and polymer. Liquid crystal elastomers are polymeric materials that exhibit both the ordered properties of the liquid crystals and the elastic properties of rubbers. Changing the order of the liquid crystal molecules within the polymer network can induce shape change. These materials are very valuable for applications such as actuators, sensors, artificial muscles, haptic displays, etc. In this work we apply finite element elastodynamics simulations to study the temperature induced shape deformation in nematic elastomers with complex director microstructure. In another topic, we propose a novel numerical method to model the director dynamics and microstructural evolution of three dimensional nematic and cholesteric liquid crystals. Numerical studies presented in this work are in agreement with experimental observations and provide insight into the design of application devices.
Infinite Bar-Joint Frameworks, Crystals and Operator Theory
Owen, J C
2010-01-01
A theory of flexibility and rigidity is developed for general infinite bar-joint frameworks (G,p). Determinations of nondeformability through vanishing flexibility are obtained as well as sufficient conditions for deformability. Forms of infinitesimal flexibility are defined in terms of the operator theory of the associated infinite rigidity matrix R(G,p). The matricial symbol function of an abstract crystal framework is introduced, being the matrix-valued function on the $d$-torus representing R(G,p) as a Hilbert space operator. The symbol function is related to infinitesimal flexibility, deformability and isostaticity. Various generic abstract crystal frameworks which are in Maxwellian equilibrium, such as certain 4-regular planar frameworks, are proven to be square-summably infinitesimally rigid as well as smoothly deformable in infinitely many ways. The symbol function of a three-dimensional crystal framework determines the infinitesimal wave flexes in models for the low energy vibrational modes (RUMs) in...
Controlling flexural waves in semi-infinite platonic crystals
Haslinger, Stewart G; Movchan, Alexander B; Jones, Ian S; Craster, Richard V
2016-01-01
We address the problem of scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener-Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems to exhibit dynami...
Dynamics and ergodicity of the infinite harmonic crystal
van Hemmen, J. L.
1980-10-01
This is a comprehensive, relatively formal study of the a priori infinite harmonic crystal. A phase space is introduced and the equations of motion of a harmonic crystal, which need not be a primitive one, are explicitly solved by several methods. The crystal is taken infinite right at the beginni ng. Exploiting the fact that the dynamics is known we derive the thermal equilibrium state of the infinite system. In so doing we use the classical Kubo-Martin-Schwinger (KMS) condition. The thermal equilibrium state is a, so-called, gaussian measure on the phase space. The traditional procedure of the thermodynamic limit is considered as well. In both cases we exploit the advantages of the technique of Fourier transforms of measures. This technique is elucidated in a separate section, where the many connections with Euclidean quantum field theory are also indicated. Finally we settle the problem of the existence of a crystalline state in its appropriate setting: the infinite system. The system is a “crystal” only if it is three-dimensional. The three essential ingredients of the ergodic analysis are a phase space, a dynamics, and an invariant state, here the thermal equilibrium state. A system is ergodic when the time average of any observable equals its phase average. There are, however, stronger notions of ergodicity which are classified in an “ergodic hierarchy”. When a system is Bernoulli it is at the top of this hierarchy. A finite harmonic system is never ergodic. Here it is shown that, generally speaking, a perfect, infinite harmonic crystal in thermal equilibrium has to be Bernoulli. A detailed discussion of the physical relevance of this result has been included.
George, Janine; Dronskowski, Richard
2017-02-16
Intermolecular bonds play a crucial role in the rational design of crystal structures, dubbed crystal engineering. The relatively new term tetrel bonds (TBs) describes a long-known type of such interactions presently in the focus of quantum chemical cluster calculations. Here, we energetically explore the strengths and cooperativity of these interactions in infinite chains, a possible arrangement of such tetrel bonds in extended crystals, by periodic density functional theory. In the chains, the TBs are amplified due to cooperativity by up to 60%. Moreover, we computationally take apart crystals stabilized by infinite tetrel-bonded chains and assess the importance of the TBs for the crystal stabilization. Tetrel bonds can amount to 70% of the overall interaction energy within some crystals, and they can also be energetically decisive for the taken crystal structure; their individual strengths also compete with the collective packing within the crystal structures.
One Dimensional Polymeric Organic Photonic Crystals for DFB Lasers
Directory of Open Access Journals (Sweden)
F. Scotognella
2008-01-01
Full Text Available We present a very simple method to realize a one-dimensional photonic crystal (1D PC, consisting of a dye-doped polymeric multilayer. Due to the high photonic density of states at the edges of the photonic band-gap (PBG, a surface emitting distributed feedback (DFB laser is obtained with this structure. Furthermore, the incidence angle dependence of the PBG of the polymeric multilayer is reported.
Fiber Drawn 2D Polymeric Photonic Crystal THz Filters
DEFF Research Database (Denmark)
Stecher, Matthias; Jansen, Christian; Ahmadi-Boroujeni, Mehdi
2012-01-01
In this paper, we report on different polymeric 2D photonic crystal filters for THz frequencies which are fabricated by a standard fiber drawing technique. The bandstop filters were simulated and designed by the generalized multipole technique (GMT). The frequency and angle dependent transmission...
Detailing of deformation processes in polymeric crystals
Slutsker, A. I.; Vettegren', V. I.; Kulik, V. B.; Hilarov, V. L.; Polikarpov, Yu. I.; Karov, D. D.
2015-11-01
Structural changes in polymer crystals (polyethylene, polyimide, and others) have been studied using the X-ray diffraction and Raman spectroscopy methods under different influences: tensile loading along the chain molecule axis and heating from 90 to 350 K. An increase in the molecule axial length under loading and a decrease in the molecule axial length upon heating have been identified and measured using X-ray diffraction. A decrease in the skeletal vibration frequency during loading and heating has been identified and measured using Raman spectroscopy, which indicates an increase in the molecule contour length in both cases. A technique for determining the change in the polyethylene molecule contour length in the crystal from the measured change in the skeletal vibration frequency has been justified. The contributions of two components, namely, skeletal (carbon-carbon) bond stretching and the change (an increase during stretching and a decrease during heating) in the angle between skeletal bonds, to the longitudinal deformation of polyethylene crystals, have been quantitatively estimated. It has been shown that the negative thermal expansion (contraction) of the polymer crystal is caused by the dominant contribution of the decrease in the bond angle.
Reversible thermosensitive biodegradable polymeric actuators based on confined crystallization.
Stroganov, Vladislav; Al-Hussein, Mahmoud; Sommer, Jens-Uwe; Janke, Andreas; Zakharchenko, Svetlana; Ionov, Leonid
2015-03-11
We discovered a new and unexpected effect of reversible actuation of ultrathin semicrystalline polymer films. The principle was demonstrated on the example of thin polycaprolactone-gelatin bilayer films. These films are unfolded at room temperature, fold at temperature above polycaprolactone melting point, and unfold again at room temperature. The actuation is based on reversible switching of the structure of the hydrophobic polymer (polycaprolactone) upon melting and crystallization. We hypothesize that the origin of this unexpected behavior is the orientation of polycaprolactone chains parallel to the surface of the film, which is retained even after melting and crystallization of the polymer or the "crystallization memory effect". In this way, the crystallization generates a directed force, which causes bending of the film. We used this effect for the design of new generation of fully biodegradable thermoresponsive polymeric actuators, which are highly desirable for bionano-technological applications such as reversible encapsulation of cells and design of swimmers.
Mathemimetics II. Demonstratio Mirabilis of FLT by infinitely ascending cubical crystal growth
Trell, Erik
2012-09-01
Emulating Nature by observation and ground-up application of its patterns, structures and processes is a classical scientific practice which under the designation of Biomimetics has now been brought to the Nanotechnology scale where even highly complex systems can be realized by continuous or cyclically reiterated assembly of the respective self-similar eigen-elements, modules and algorithms right from their infinitesimal origin. This is actually quite akin to the genuine mathematical art and can find valuable renewed use as here exemplified by the tentatively original Demonstratio Mirabilis of FLT (Fermat's Last Theorem, or, in that case, Triumph) by infinitely ascending sheet-wise cubical crystal growth leading to the binomial `magic triangle' of his close fellow Blaise Pascal.
Effect of crystal packing on the structures of polymeric metallocenes.
Dinnebier, R E; van Smaalen, Sander; Olbrich, F; Carlson, S
2005-02-21
The pressure dependencies of the crystal structures of the polymeric metallocenes lithium cyclopentadienide (LiCp) and potassium cyclopentadienide (KCp) have been determined by synchrotron X-ray powder diffraction. The decrease of the volume of LiCp by 34% up to a pressure of p = 12.2 GPa and of KCp by 23% at p = 5.3 GPa as well as the bulk moduli of K = 7.7 GPa for LiCp and 4.9 GPa for KCp indicate a high compressibility for these compounds. The crystal structures of KCp have been determined up to p = 3.9 GPa. An increase of the bend angle is found from 45 degrees at p = 0 GPa up to 51 degrees at p = 3.9 GPa. This variation is completely explained by a model invoking attractive K+ Cp- interaction and repulsive nonbonded carbon-carbon interactions. It is proposed that the bend angle in the polymeric alkali metal metallocenes is the result of the optimization of the crystal packing.
Characteristics of local photonic state density in an infinite two-dimensional photonic crystal
Institute of Scientific and Technical Information of China (English)
Zhou Yun-Song; Wang Xue-Hua; Gu Ben-Yuan; Wang Fu-He
2005-01-01
The local density of photonic states (LDPS) of an infinite two-dimensional (2D) photonic crystal (PC) composed of rotated square-pillars in a 2D square lattice is calculated in terms of the plane-wave expansion method in a combination with the point group theory. The calculation results show that the LDPS strongly depends on the spatial positions.The variations of the LDPS as functions of the radial coordinate and frequency exhibit "mountain chain" structures with sharp peaks. The LDPS with large value spans a finite area and falls abruptly down to small value at the position corresponding to the interfaces between two different refractive index materials. The larger/lower LDPS occurs inward the lower/larger dielectric-constant medium. This feature can be well interpreted by the continuity of electricdisplacement vector at the interface. In the frequency range of the pseudo-PBG (photonic band gap), the LDPS keeps very low value over the whole Wiger-Seitz cell. It indicates that the spontaneous emission in 2D PCs cannot be prohibited completely, but it can be inhibited intensively when the resonate frequency falls into the pseudo-PBG.
Formation of infinite 2D water layers in a crystal host
Institute of Scientific and Technical Information of China (English)
Cai Hua Zhou; Li Jun Zhou; Long Tang; Yao Yu Wang
2009-01-01
A self-assembled, (H2O)38 cluster stabilized by a mono-nuclear copper(Ⅱ) complex 1 namely {[Cu(phen)2(CO3)].7H2O} is characterized by X-ray diffraction studies. The adjacent (H2O)38 clusters connect together resulting in an infinite 2D water layer structure. The water morphology is stable at room temperature, but upon thermal decomposition, the water loss is irreversible.
Directory of Open Access Journals (Sweden)
E. S. Shapoval
2014-09-01
Full Text Available In situ polymerization method is used for obtaining polymeric composites based on polyamide12 matrix (PA 12, filled with Cr2O3 nanoparticles. The carried out researches result in synthesis method development for polymeric nanocomposites based on PA 12 matrix filled with nano-sized Cr2O3magnetic particles providing uniform embedding of the filler into polymeric matrix without formation of nanoparticles agglomerates. Mechanical tests on samples compression are carried out. It is shown that mechanical properties of polymeric composites (Young’s modulus, durability limit are decreased for 20-30 % as compared with not modified PA 12 synthesized by means of the chosen method. The influence of the filler on crystallization morphology and kinetics of polymeric nanocomposites is determined by electron microscopy and differential scanning calorimetry. The values of crystallization degree, crystallization rate constant for different supercooling intervals and parameters of Avrami equation are obtained. The initial nucleation is shown to be going on according to non-thermal mechanism, and nanoparticles are not the germs of crystallization. It is stated that nanoparticles are embedded into polymeric matrix and uniformly allocated in crystallites. Research results can find their application at creation of electric and magnetic fields, micro-sized mechanical devices, and at development of new materials for 3D printers.
Real-time measurements of crystallization processes in viscoelastic polymeric photonic crystals.
Snoswell, David R E; Finlayson, Chris E; Zhao, Qibin; Baumberg, Jeremy J
2015-11-01
We present a study of the dynamic shear ordering of viscoelastic photonic crystals, based on core-shell polymeric composite particles. Using an adapted shear-cell arrangement, the crystalline ordering of the material under conditions of oscillatory shear is interrogated in real time, through both video imaging and from the optical transmission spectra of the cell. In order to gain a deeper understanding of the macroscopic influences of shear on the crystallization process in this solvent-free system, the development of bulk ordering is studied as a function of the key parameters including duty cycle and shear-strain magnitude. In particular, optimal ordering is observed from a prerandomized sample at shear strains of around 160%, for 1-Hz oscillations. This ordering reaches completion over time scales of order 10 s. These observations suggest significant local strains are needed to drive nanoparticles through energy barriers, and that local creep is needed to break temporal symmetry in such high-viscosity nanoassemblies. Crystal shear-melting effects are also characterized under conditions of constant shear rate. These quantitative experiments aim to stimulate the development of theoretical models which can deal with the strong local particle interactions in this system.
Directory of Open Access Journals (Sweden)
Hiromasa Goto
2010-10-01
Full Text Available We carried out polycondensation of monomers bearing a bulky pyrimidine substituent in a liquid crystal solvent. The resultant polymers formed nematic liquid crystals. The polymers prepared in liquid crystals had higher coplanarity than the polymers prepared in toluene. This can be due to the fact that the ordered medium of the liquid crystal produces an aggregated structure with well-developed π-stacking between the main chains. The present results demonstrated that polymerization of bulky monomers is possible in liquid crystal solvents.
INFLUENCE OF POLYMERIC ADDITIVES ON CRYSTALLIZATION OF CALCIUM SULPHATE DIHYDRATE
Directory of Open Access Journals (Sweden)
Ustinova Yulia Valer’evna
2013-04-01
Full Text Available Currently, functional additives are widely spread in the production of inorganic dry mixtures. However, their impact on the microstructure of products, generated in the process of hardening of inorganic binders, is understudied. In this context, the goal of the work is the study of calcium sulfate dihydrate (CaSO •2H O crystallization. Super plasticizer based on sulfonated melamine-formaldehyde resin, methylcellulose and vinyl acetate, ethylene and vinyl chloride copolymer powder were selected for studies. First, pure calcium sulfate dihydrate crystals were synthesized. Then, synthesized calcium sulfate dihydrate crystals were exposed to the X-ray analysis to determine the nature of influence of polymer additives on the shape and dimensions of crystals. Possible combinations of simple forms of CaSO •2H O were identified by the X-ray analysis and the special software. Electronic microscopy analysis was performed to validate models of calcium sulfate dihydrate crystals. All plasticizers influence the crystallization of calcium sulfate dihydrate. The influence of additives on the shape and dimensions of crystals of calcium sulfate dihydrate can be explained by the fact that molecules of sulfonated melamine-formaldehyde resins, methylcellulose, and copolymers of vinyl acetate, ethylene and vinyl chloride are absorbed by crystal faces. It is proven that the method of X-ray analysis can be used to predict the shape and habitus of crystals.
Energy Technology Data Exchange (ETDEWEB)
Mitchell,C.; Krishnamoorti, R.
2005-01-01
The non-isothermal crystallization behavior of three in situ polymerized, partially tethered poly({var_epsilon}-caprolactone) with functionalized single walled carbon nanotube (SWNT) nanocomposites are examined using differential scanning calorimetry and corroborated using small and wide angle X-ray scattering. While the nanotubes are strong nucleators of the crystals of poly({var_epsilon}-caprolactone) and dramatically accelerate the crystallization of the polymer, they do not alter the unit-cell, the melting temperature and the fractional crystallinity of the polymer crystals.
Nambu, Y.
1967-01-01
The main ingredients of the method of infinite multiplets consist of: 1) the use of wave functions with an infinite number of components for describing an infinite tower of discrete states of an isolated system (such as an atom, a nucleus, or a hadron), 2) the use of group theory, instead of dynamical considerations, in determining the properties of the wave functions.
Nanoporous dipeptide crystals as selective gas sorbents and polymerization nanovessels
Distefano,, E.
2012-01-01
Hydrophobic dipeptide crystals recently emerged as novel “organic zeolites” featuring tailorable pore size. In fact, seven out of nine pairwise combinations of L-isoleucine, L-valine and L-alanine amino acids crystallize according to the same charge-assisted hydrogen bond pattern, generating a family of microporous materials with right-handed 1D channels, having diameters in the sub-nanometer domain (
Polymeric THz 2D Photonic Crystal Filters Fabricated by Fiber Drawing
DEFF Research Database (Denmark)
Stecher, Matthias; Jansen, Christian; Ahmadi-Boroujeni, Mehdi
2012-01-01
In this paper, we report on a new form of polymeric 2D photonic crystal filters for THz frequencies fabricated using a standard fiber drawing technique. The band stop filters were modeled and designed using the generalized multipole technique. The frequency and angle-dependent transmission...
Institute of Scientific and Technical Information of China (English)
LIANG ZHAO-YAN; FANG KUN; XUAN LI; HUANG XI-MIN; DING BAO-QUAN; LU RAN; ZHAO YING-YING
2000-01-01
A new technique to uniformly align liquid crystal molecules is presented.The technique is based on producing an anisotropic surface on the glass substrate coated with photo-polymers by photo-polymerization of linear polarized UVlight.The orientation of liquid crystal molecules is governed by the direction of the polarized vector of UV-light.Using this method,we have studied the photo-polymer PSi-CM aligning LC 6710A molecules.The liquid crystal microscopic texture between crossed polarizers,optical retardation from liquid crystal layers and electro-optical properties of twisted nematic liquid crystal display cell are obtained,which was prepared with one side -photo-alignment and the other siderebbed substrate.
Liquid crystals. Oligomeric and polymeric materials for soft photonic technologies
Coles, M J
2002-01-01
The current pace of today's information technologies might lead the casual observer to believe that this is all new. However the reality is that, as with most things, this is really a long evolution of processes based on tried, tested and re-adapted techniques. This thesis represents 12 years of predominantly technology driven research and covers a whole range of characterising, evaluating and fabricating devices based on liquid crystalline systems. Firstly polymer liquid crystals are discussed with respect to the fabrication of a flexible substrate display based on standard printing techniques and this is shown to have improved display viewing properties over a standard polymer dispersed liquid crystal (PDLC) device. Following on from this work is presented that involves the production of regular grid arrays in isotropic polymers that are used as control structures in nematic liquid crystal systems. This progresses onto a now patented device that allows the production of robust ferroelectric devices based on...
Milling of polymeric photonic crystals by focused ion beam
Energy Technology Data Exchange (ETDEWEB)
Pialat, E. [Unite de Microelectronique et Optoelectronique Polymere (UMOP/CNRS), Pole Limousin des Sciences et Technologies de l' Information et de la Communication (PLSTIC) de l' Universite de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex (France); Trigaud, T. [Unite de Microelectronique et Optoelectronique Polymere (UMOP/CNRS), Pole Limousin des Sciences et Technologies de l' Information et de la Communication (PLSTIC) de l' Universite de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex (France); Bernical, V. [Unite de Microelectronique et Optoelectronique Polymere (UMOP/CNRS), Pole Limousin des Sciences et Technologies de l' Information et de la Communication (PLSTIC) de l' Universite de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex (France); Moliton, J.P. [Unite de Microelectronique et Optoelectronique Polymere (UMOP/CNRS), Pole Limousin des Sciences et Technologies de l' Information et de la Communication (PLSTIC) de l' Universite de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex (France)]. E-mail: jpmlt@unilim.fr
2005-12-15
The achievement of low cost photonic crystals in organic materials is not a trivial challenge even by top-down processes. Firstly the required conditions for the opening of a 2D Photonic Band Gap (PBG) in polymers by implementation of adapted software are shortly presented. The Focused Ion Beam (FIB) technique appears as a suitable process to carry out the patterning of the required sub-micronic dimensions. Then, the optimum experimental procedures leading to the fabrication of 2D photonic crystals in PMMA and CR39 are mainly exposed and discussed.
Tian, Yiwei; Jones, David S; Andrews, Gavin P
2015-04-06
Using phase diagrams derived from Flory-Huggins theory, we defined the thermodynamic state of amorphous felodipine within three different polymeric carriers. Variation in the solubility and miscibility of felodipine within different polymeric materials (using F-H theory) has been identified and used to select the most suitable polymeric carriers for the production of amorphous drug-polymer solid dispersions. With this information, amorphous felodipine solid dispersions were manufactured using three different polymeric materials (HPMCAS-HF, Soluplus, and PVPK15) at predefined drug loadings, and the crystal growth rates of felodipine from these solid dispersions were investigated. Crystallization of amorphous felodipine was studied using Raman spectral imaging and polarized light microscopy. Using this data, we examined the correlation among several characteristics of solid dispersions to the crystal growth rate of felodipine. An exponential relationship was found to exist between drug loading and crystal growth rate. Moreover, crystal growth within all selected amorphous drug-polymer solid dispersion systems were viscosity dependent (η(-ξ)). The exponent, ξ, was estimated to be 1.36 at a temperature of 80 °C. Values of ξ exceeding 1 may indicate strong viscosity dependent crystal growth in the amorphous drug-polymer solid dispersion systems. We argue that the elevated exponent value (ξ > 1) is a result of drug-polymer mixing which leads to a less fragile amorphous drug-polymer solid dispersion system. All systems investigated displayed an upper critical solution temperature, and the solid-liquid boundary was always higher than the spinodal decomposition curve. Furthermore, for PVP-FD amorphous dispersions at drug loadings exceeding 0.6 volume ratio, the mechanism of phase separation within the metastable zone was found to be driven by nucleation and growth rather than liquid-liquid separation.
Lamellar liquid crystal polymerization of sodium oleate/oleic acid/octadiene/water system
Institute of Scientific and Technical Information of China (English)
GUO, Rong; FU, Qing-Hong
2000-01-01
In the lamellar liquid crystallization (LLC) phase of NaOL/OLA/H2O system, the small angle X-ray diffraction measurements show that the oleic acid is solubilized in the oil layer at first and then into the ampliphile layer. The octadiene added is also located partly in the oil layer and partly in the amphiphile layer in the LLC. With the addition of octadiene as cross-linking agent, the LLC phase of NaOL/OLA/H2O system was polymerized under the initiation of AIBN with the protection of pure nitrogen at 60℃. Most of the double bond absorption of the monomers in IR spectra disappeared after polymerization. The polymerization takes place not only in the middle of the amphiphile layer between the double bonds of NaOL or OLA and those of octadiene, but also in the oil layer of LLC between the double bonds of OLA and those of octadiene. Interlayer spacing measurements on the copolymer proved d values decreased by about 1 ～ 2 nm compared with those of the corresponding system before the polymerization,indicating a disruption of the ordered structure by the polymerization. The copolymer still has superior surface activity with the critical micellar concentration (CMC) decreased almost to the half of the value for the system before the polymerization.
INFLUENCE OF POLYMERIC ADDITIVES ON CRYSTALLIZATION OF CALCIUM SULPHATE DIHYDRATE
Ustinova Yulia Valer’evna
2013-01-01
Currently, functional additives are widely spread in the production of inorganic dry mixtures. However, their impact on the microstructure of products, generated in the process of hardening of inorganic binders, is understudied. In this context, the goal of the work is the study of calcium sulfate dihydrate (CaSO •2H O) crystallization. Super plasticizer based on sulfonated melamine-formaldehyde resin, methylcellulose and vinyl acetate, ethylene and vinyl chloride copolymer powder were select...
Matahwa, H.; Ramiah, V.; Sanderson, R. D.
2008-10-01
Crystallization of calcium carbonate was performed in the presence of grafted polysaccharides, polyacrylamide (PAM) and polyacrylic acid (PAA). The grafted polysaccharides gave crystal morphologies that were different from the unmodified polysaccharides but similar to the ones given by homopolymers of the grafted chains. PAM-grafted α-cellulose gave rectangular platelets that aggregated to form 'spherical' crystals on the surface of the fiber, whereas PAA grafted α-cellulose gave spherical crystals on the surface of the fiber. X-ray diffraction (XRD) spectroscopy showed that PAM-grafted α-cellulose, PAM as well as the control (no polymeric additive) gave calcite crystals at both 25 and 80 °C. However, the PAA-grafted α-cellulose and PAA homopolymer gave calcite and vaterite crystals at 25 °C with calcite and aragonite crystals along with traces of vaterite being formed at 80 °C. The fiber surface coverage by these crystals was more on the acrylic- and acrylamide-grafted cellulose than on the ungrafted α-cellulose. The evolution of CaCO 3 polymorphs as well as crystal morphology in PAA-grafted starch was similar to that of PAA-grafted α-cellulose at the two temperatures employed.
Synthesis and crystal structure and nonlinear optical properties of polymeric W (Mo)-Cu-S cluster
Institute of Scientific and Technical Information of China (English)
ZHOU Jian-liang; CHEN Qi-yuan; GU Ying-ying; ZHONG Shi-an
2006-01-01
The polymeric chalcogenide [W2O2S6Cu4(NCMe)4]n (compound 1) was synthesized by the self-assembly reaction of (NH4)2(WOS3) with CuBr in MeCN in the presence of tricyclohexylphosphane (PCy3) under a purified nitrogen atmosphere using standard Schlenk techniques. It gives rise to a novel 1D polymeric compound 1 with solvent MeCN coordinated to the copper atom. This situation is unprecedented in the W(Mo)/Cu/S system. The crystals were characterized by elemental analysis,IR and single-crystal X-ray crystallography. The configuration of the polymeric compound can be viewed as a helical chain which is propagated along the crystallographic c axis. The excited state absorption and refraction of compound 1 in CH3CN solution were studied by using the Z-scan technique with laser pulses of 40 ps pulse-width at a wavelength of 532 nm. The polymeric compound possesses an optical self-focusing performance. The positive nonlinear refraction is attributed to population transitions between singlet states. Compound 1 displays a strong excited-state absorption.
Energy Technology Data Exchange (ETDEWEB)
Weng, Libo; Chien, Liang-Chy [Liquid Crystal Institute, Kent State University, Kent, Ohio 44242 (United States); Liao, Pei-Chun [Liquid Crystal Institute, Kent State University, Kent, Ohio 44242 (United States); AU Optronics Corporation, Hsinchu, 300, Taiwan (China); Lin, Chen-Chun; Ting, Tien-Lun; Hsu, Wen-Hao; Su, Jenn-Jia [AU Optronics Corporation, Hsinchu, 300, Taiwan (China)
2015-09-15
We demonstrate enhanced surface anchoring energy and control of pretilt angle in a nematic liquid crystal cell with vertical alignment and polymerized surfaces (PS-VA). The polymerized surfaces are formed by ultraviolet (UV) irradiation-induced phase separation of a minute amount of a reactive monomer in the vertical-aligned nematic liquid crystal. By introducing a bias voltage during UV curing, surface-localized polymer protrusions with a dimension of 100nm and a field-induced pretilt angle are observed. Experimental evidences and theoretical analyses validate that PS-VA has increased surface anchoring strength by two folds and pretilt angle has been changed from 89° to 86° compared to those of a VA cell. The enabling PS-VA cell technique with excel electro-optical properties such as very good dark state, high optical contrast, and fast rise and decay times may lead to development of a wide range of applications.
Directory of Open Access Journals (Sweden)
Libo Weng
2015-09-01
Full Text Available We demonstrate enhanced surface anchoring energy and control of pretilt angle in a nematic liquid crystal cell with vertical alignment and polymerized surfaces (PS-VA. The polymerized surfaces are formed by ultraviolet (UV irradiation-induced phase separation of a minute amount of a reactive monomer in the vertical-aligned nematic liquid crystal. By introducing a bias voltage during UV curing, surface-localized polymer protrusions with a dimension of 100nm and a field-induced pretilt angle are observed. Experimental evidences and theoretical analyses validate that PS-VA has increased surface anchoring strength by two folds and pretilt angle has been changed from 89° to 86° compared to those of a VA cell. The enabling PS-VA cell technique with excel electro-optical properties such as very good dark state, high optical contrast, and fast rise and decay times may lead to development of a wide range of applications.
Interface nano-confined acoustic waves in polymeric surface phononic crystals
Energy Technology Data Exchange (ETDEWEB)
Travagliati, Marco, E-mail: marco.travagliati@iit.it [Center for Nanotechnology Innovation@NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, 56127 Pisa (Italy); NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza San Silvestro 12, 56127 Pisa (Italy); Nardi, Damiano [JILA and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309 (United States); Giannetti, Claudio; Ferrini, Gabriele; Banfi, Francesco, E-mail: francesco.banfi@unicatt.it [i-LAMP and Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, 25121 Brescia (Italy); Gusev, Vitalyi [LAUM, UMR-CNRS 6613, Université du Maine, av. O. Messiaen, 72085 Le Mans (France); Pingue, Pasqualantonio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza San Silvestro 12, 56127 Pisa (Italy); Piazza, Vincenzo [Center for Nanotechnology Innovation@NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, 56127 Pisa (Italy)
2015-01-12
The impulsive acoustic dynamics of soft polymeric surface phononic crystals is investigated here in the hypersonic frequency range by near-IR time-resolved optical diffraction. The acoustic response is analysed by means of wavelet spectral methods and finite element modeling. An unprecedented class of acoustic modes propagating within the polymer surface phononic crystal and confined within 100 nm of the nano-patterned interface is revealed. The present finding opens the path to an alternative paradigm for characterizing the mechanical properties of soft polymers at interfaces and for sensing schemes exploiting polymers as embedding materials.
Effects of Polymeric Additives on the Crystallization and Release Behavior of Amorphous Ibuprofen
Directory of Open Access Journals (Sweden)
Su Yang Lee
2013-01-01
Full Text Available Some polymeric additives were studied to understand their effects on the amorphous phase of ibuprofen (IBU, used as a poorly water soluble pharmaceutical model compound. The amorphous IBU in bulk, as well as in nanopores (diameter ~24 nm of anodic aluminum oxide, was examined with the addition of poly(acrylic acid, poly(N-vinyl pyrrolidone, or poly(4-vinylphenol. Results of bulk crystallization showed that they were effective in limiting the crystal growth, while the nucleation of the crystalline phase in contact with water was nearly instantaneous in all cases. Poly(N-vinyl pyrrolidone, the most effective additive, was in specific interaction with IBU, as revealed by IR spectroscopy. The addition of the polymers was combined with the nanoscopic confinement to further stabilize the amorphous phase. Still, the IBU with addition of polymeric additives showed sustained release behavior. The current study suggested that the inhibition of the crystal nucleation was probably the most important factor to stabilize the amorphous phase and fully harness its high solubility.
Band Structure of Photonic Crystals Fabricated by Two-Photon Polymerization
Directory of Open Access Journals (Sweden)
Mikhail V. Rybin
2015-01-01
Full Text Available We study theoretically the band-gap structures of several types of three-dimensional photonic crystals with the fcc lattice symmetry: synthetic opals, inverted yablonovite and woodpile. The samples of inverted yablonovite, inverted yablonovite with a glassy superstructure and woodpile are fabricated by two-photon polymerization through a direct laser writing technique, which allows the creation of complex three-dimensional photonic crystals with a resolution better than 100 nm. A material is polymerized along the trace of a moving laser focus, thus enabling the fabrication of any desirable three-dimensional structure by direct “recording” into the volume of a photosensitive material. The correspondence of the structures of the fabricated samples to the expected fcc lattices is confirmed by scanning electron microscopy. We discuss theoretically how the complete photonic band-gap is modified by structural and dielectric parameters. We demonstrate that the photonic properties of opal and yablonovite are opposite: the complete photonic band gap appears in the inverted opal, and direct yablonovite is absent in direct opal and inverted yablonovite.
Quartz crystal microbalance study of the kinetics of surface initiated polymerization
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Surface initiated polymerization (SIP) is a valuable tool in synthesizing functional polymer brushes,yet the kinetic understanding of SIP lags behind the development of its application. We apply quartz crystal microbalance (QCM) to address two issues that are not fully addressed yet play a central role in the rational design of functional polymer brushes,namely quantitative determination of the kinetics and the initiator efficiency (IE) of SIP. SIP are monitored online using QCM. Two quantitative frequencythickness (f-T) relations make the direct determination and comparison of the rate of polymerization possible even for different monomers. Based on the bi-termination model,the kinetics of SIP is simply described by two variables,which are related to two polymerization constants,namely a = 1/(kp,s,app-[M][R·]0) and b = kt,s,app/(kp,s,app[M]). Factors that could alter the kinetics of SIP are studied,including (i) the molecular weight of monomers,(ii) the solvent used,(iii) the initial density of the initiator,(iv) the concentration of monomer,[M],and (v) the catalyst system (ratio among the ingredients,metal,ligands,and additives). The dynamic nature of IE is also described by these two variables,IE = a/(a + bt). Instead of the molecular weight and the polydispersity,we suggest that film thickness,the two kinetic parameters (a and b),and the initial density of the initiator and IE be the parameters that characterize ultrathin polymer brushes. Besides the kinetics study of SIP,the reported method has many other applications,for example,in the fast screening of catalyst system for SIP and other polymerization systems.
Formal aspects of the interaction of particles with infinite and semi-infinite periodic potentials
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Estrada, R.F. (Universidad Complutense de Madrid (Spain). Dept. de Fisica Teorica); Villalon, M.E. (Division de Fisica de Radiaciones, Junta de Energia Nuclear, Madrid-3 (Spain))
1978-01-11
The dynamics and the scattering of quantum particles in infinite and semi-infinite periodic potentials are studied inside a unified and global framework. The particle wave function in the infinite and semi-infinite crystal and the energy for the infinite problem are given by related integral equations (written over a periodicity cell) of the Brillouin-Wigner type. All these equations are controlled mathematically and, in particular, the singular cases of a quasi-momentum crossing a Brillouin zone and an energy crossing the border of a gap, which are treated, respectively, in the infinite and semi-infinite problems.
Structure and Semiconducting Character of a Polymeric Iodoplumbate Coordination Complex
Institute of Scientific and Technical Information of China (English)
SONG De-Sheng; LIU Chang-Chun; CHEN Heng-Jun; SU Dong-Po; FU Zhi-Yong
2011-01-01
A new polymeric iodoplumbate complex [Zn（DMF）6][Pb2I6] 1 has been prepared and characterized by elemental analysis and single-crystal X-ray analysis. Its structure contains infinite iodoplumbate chains constructed by the [PbI5] subunit. EHT crystal orbital calculation and the experimental results show that this material is an unconventional semiconductor and the electrical character is associated with its structural feature.
Energy Technology Data Exchange (ETDEWEB)
Kang, Hyo [Samsung Advanced Institute of Technology, Yongin (Korea, Republic of); Joo, Sangwoo; Kang, Daeseung [Soongsil Univ., Seoul (Korea, Republic of)
2012-04-15
We presented a novel method for the homeotropic alignment of LC by using the irradiation of UV light on the LC/NOA65 mixture cell, in which the photo-initiated-polymerization-induced phase separation lowers the surface energy. When the amount of polymer content is sufficiently small, the gravel and network patterns were formed at the substrates via the vertical phase separation. We found that surface roughness plays an important role in the formation of the homeotropic alignment of LC. We also observed the alignment transition of the cells by varying the mixing ratio of LC/NOA65 or the UV radiation time. Furthermore, the present proposed method has great potential for application in display devices. For decades, studies on the alignment of liquid crystal (LC) molecules have been of significant interest due to their immediate applications for display devices and the intriguing physiochemical properties they exhibit at the surface of mixtures. Usually, homeotropic (or vertical) alignment, in which the long axes of the LC molecules are oriented in a direction perpendicular to the surface, is achieved by using surfactants such as lecithin, silanes or polyimide. Recently homeotropic alignment of liquid crystal molecules was achieved by irradiating photosensitive polymers, by doping nanoparticles into LC, by utilizing nano/micro patterns, or by incorporating self-assembled monolayers (SAMs). However, a clear understanding about the alignment mechanism is still elusive. In this paper, we report a novel method for homeotropic alignment of LC by utilizing the phase separation of LC/polymer mixtures.
Kirtman, Bernard; Springborg, Michael; Rérat, Michel; Ferrero, Mauro; Lacivita, Valentina; Orlando, Roberto; Dovesi, Roberto
2015-01-01
An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.
Boott, Charlotte E.; Gwyther, Jessica; Harniman, Robert L.; Hayward, Dominic W.; Manners, Ian
2017-08-01
The preparation of well-defined nanoparticles based on soft matter, using solution-processing techniques on a commercially viable scale, is a major challenge of widespread importance. Self-assembly of block copolymers in solvents that selectively solvate one of the segments provides a promising route to core-corona nanoparticles (micelles) with a wide range of potential uses. Nevertheless, significant limitations to this approach also exist. For example, the solution processing of block copolymers generally follows a separate synthesis step and is normally performed at high dilution. Moreover, non-spherical micelles—which are promising for many applications—are generally difficult to access, samples are polydisperse and precise dimensional control is not possible. Here we demonstrate the formation of platelet and cylindrical micelles at concentrations up to 25% solids via a one-pot approach—starting from monomers—that combines polymerization-induced and crystallization-driven self-assembly. We also show that performing the procedure in the presence of small seed micelles allows the scalable formation of low dispersity samples of cylindrical micelles of controlled length up to three micrometres.
Institute of Scientific and Technical Information of China (English)
ZHANG Sa-sa; WANG Qing-pu; ZHANG Xing-yu; CHEN Jia-qi; WANG Li
2008-01-01
A three-sidewalls-prism holographic method has been provided for the fabrication of 3-D fcc-type polymeric photonic crystal using negative photoresist.Special fabrication treatment has been introduced to ensure the stability of the fabricated nanostructures.The scanning electronic microscopy (SEM) and the diffraction results testified the good dependability of the fabricared structures.The simulation of the partial band structure is in good agreement with the transmission and reflection spectra obtained by Fouricr transform infrared spectroscopy.
Institute of Scientific and Technical Information of China (English)
A.V.Yakimansky; A.Yu.Menshikova; N.N.Shevchenko; A.G.Bazhenova; S.K.Sazonov; A.I.Vedernikov; S.P.Gromov; V.A.Sazhnikov; M.V.Alfimov
2007-01-01
1 Results Self-assembling of monodisperse polymeric nanoparticles is a perspective method of obtaining photonic crystalline materials for optoelectronics,telecommunication industry and optosensorics.For tuning optical characteristics of photonic crystals it is advisable to functionalize nanoparticles by dyes absorbing or emitting light in the vicinity of the photonic band gap,which position depends on the nanoparticle diameter.To prepare monodisperse nanoparticles with the dye-functionalyzed surface emu...
Simone, E.; Cenzato, M. V.; Nagy, Z. K.
2016-07-01
In the present study, the effect of Hydroxy Propyl Methyl Cellulose (HPMC) on the crystallization of ortho-aminobenzoic acid (OABA) was investigated by seeded and unseeded cooling crystallization experiments. The influence of HPMC on the induction time, crystal shape of Forms I and II of OABA and the polymorphic transformation time was studied. Furthermore, the capability of HPMC to inhibit growth of Form I was evaluated quantitatively and modeled using population balance equations (PBE) solved with the method of moments. The additive was found to strongly inhibit nucleation and growth of Form I as well as to increase the time for the polymorphic transformation from Form II to I. Solvent was also found to influence the shape of Form I crystals at equal concentrations of HPMC. In situ process analytical technology (PAT) tools, including Raman spectroscopy, focused beam reflectance measurement (FBRM) and attenuated total reflectance (ATR) UV-vis spectroscopy were used in combination with off-line techniques, such as optical microscopy, scanning electron microscopy (SEM), Raman spectroscopy, Malvern Mastersizer and differential scanning calorimetry (DSC) to study the crystals produced. The results illustrate how shape, size and stability of the two polymorphs of OABA can be controlled and tailored using a polymeric additive.
Atkinson, D; van Steenwijk, F.J.
The resistance between two arbitrary nodes in an infinite square lattice of:identical resistors is calculated, The method is generalized to infinite triangular and hexagonal lattices in two dimensions, and also to infinite cubic and hypercubic lattices in three and more dimensions. (C) 1999 American
Energy Technology Data Exchange (ETDEWEB)
Mutlu, Selma [Department of Chemical Engineering, Hacettepe University, Beytepe Campus, 06800 Ankara (Turkey)], E-mail: smselma@hacettepe.edu.tr; Coekeliler, Dilek [Plasma Aided Bioengineering and Biotechnology Research Group(PABB), Faculty of Engineering, Hacettepe University, Beytepe Campus, 06800 Ankara (Turkey); Shard, Alex [Department of Engineering Materials, The University of Sheffield, Sir Robert Hadfield Building, Mappin Street, Sheffield, S1 3JD (United Kingdom); Goktas, Hilal [Physics Department, Canakkale Onsekiz Mart University, 17100 Canakkale (Turkey); Ozansoy, Berna [Department of Chemical Engineering, Hacettepe University, Beytepe Campus, 06800 Ankara (Turkey); Mutlu, Mehmet [Plasma Aided Bioengineering and Biotechnology Research Group(PABB), Faculty of Engineering, Hacettepe University, Beytepe Campus, 06800 Ankara (Turkey)
2008-01-30
This paper describes a method for the modification of quartz crystal surfaces to be used as a transducer in biosensors that allow recognition and quantification of certain biomolecules (antibodies, enzymes, proteins, etc). Quartz crystal sensors were modified by a plasma based electron beam generator in order to detect the level of the toxin histamine within biological liquids (blood, serum) and food (wine, cheese, fish etc.). Cysteamine and ethylenediamine were used as precursors in the plasma. After each modification step, the layers on the quartz crystal were characterized by frequency measurements. Modified surfaces were also characterized by contact angle, X-ray photoelectron spectroscopy and atomic force microscopy to determine the physical and chemical characteristics of the surfaces after each modification. Finally, the performance of the sensors were tested by the response to histamine via frequency shifts. The frequency shifts of the sensors prepared by plasma polymerization of ethylenediamine and cysteamine were approximately 3230 Hz and 5630 Hz, respectively, whereas the frequency change of the unmodified crystal surface was around 575 Hz.
Synthesis and Crystal Structure of a Novel Polymeric Complex [WS4Cu4(Py)4(μ-CN)2]∞
Institute of Scientific and Technical Information of China (English)
焦昌梅; 乔善宝; 徐庆峰; 郎建平
2004-01-01
The reaction of [Et4N]2WS4 with 4 equiv of CuCN in pyridine produced a new polymeric complex [WS4Cu4(Py)4(μ-CN)2]∞ 1, whose crystal structure has been characterized by single-crystal X-ray analysis. 1 (C22H2oCu4N6S4W, Mr=934.71) crystallizes in monoclinic, space group P21/n with a ='8.994(2), b=16.038(3), c=12.026(3) A, β= 90.85(1)°, V= 1734.6(6) A3, Z=2, Dc=1.789 g/cm3, F(000)=896,t(MoKa)=59.8 cm-1 and T=193 K. The structure was refined to R=0.064 and Rw=0.080 for 2209 observed reflections (I ＞ 3.0σ(I)). The X-ray analysis shows that the tetrahedral WS4 core is coordinated by four Cu atoms, forming a saddle-like WS4Cu4 unit. These repeating units are further interconnected by four Cu-μ-CN-Cu 2.726(2) and 2.723(2) A, respectively.
Tyborski, T.; Merschjann, C.; Orthmann, S.; Yang, F.; Lux-Steiner, M.-Ch; Schedel-Niedrig, Th
2013-10-01
Based on the arrangement of two-dimensional ‘melon’, we construct a unit cell for polymeric carbon nitride (PCN) synthesized via thermal polycondensation, whose theoretical diffraction powder pattern includes all major features measured in x-ray diffraction. With the help of this unit cell, we describe the process-temperature-induced crystallographic changes in PCN that occur within a temperature interval between 510 and 610 °C. We also discuss further potential modifications of the unit cell for PCN. It is found that both triazine- and heptazine-based g-C3N4 can only account for minor phases within the investigated synthesis products.
On infinitely divisible semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas; Rosiński, Jan
2015-01-01
are strictly representable due to Hida's multiplicity theorem, the classical Stricker's theorem follows from our result. Another consequence is that the question when an infinitely divisible process is a semimartingale can often be reduced to a path property, when a certain associated infinitely divisible...
López, M.; Still, G.J.
2007-01-01
A semi-infinite programming problem is an optimization problem in which finitely many variables appear in infinitely many constraints. This model naturally arises in an abundant number of applications in different fields of mathematics, economics and engineering. The paper, which intends to make a c
Institute of Scientific and Technical Information of China (English)
BAI Yan; PAN Xiao-Jing; DANG Dong-Bin; SHANG Wei-Li; WANG Jing-Ping
2008-01-01
A new one-dimensional polymeric complex [Cd(SCN)2(H2O)]L (L = N,N'-bis(furan-2-ylmethylene)hydrazine) has been synthesized and characterized by IR, UV spectra, TG-DTA technique and single-crystal X-ray diffraction analysis. It crystallizes in triclinic, pace group P1 with a = 5.9268(8), b = 10.8678(15), c = 13.3671(19) A, α = 109.295(2), β = 95.092(2), γ =97.8580(10)°, V - 796.70(19) A3, Z = 2, C12H10CdN4O3S2, Mr = 434.76, μ = 1.648 mm-1, Dc = 1.812 g/cm3, F(000) = 428, R = 0.0308 and wR = 0.0769. The crystal structure reveals that the structure of [Cd(SCN)E(H2O)]n features di-μ-1,3-thiocyante bridges and 1D chains. The octahedrally coordinated Cd atom is surrounded by one oxygen atom from water molecule, three S atoms and two N atoms from five di-μ-1,3 thiocyanato bridges. The Cd atoms are connected by two di-μ-1,3 thiocyanato bridges with the Cd(1)…Cd(1A) separation of 4.239(1) (A) and Cd(1)…Cd(1B) of 5.852(1)(A). In addition, the one-dimensional straight chain structure is further connected by multiform intermolicular N-H…O hydrogen bonds and π…π interactions to form a three-dimensional supramolecular structure.
On Geometric Infinite Divisibility
Sandhya, E.; Pillai, R. N.
2014-01-01
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
Mechanical properties and tuning of three-dimensional polymeric photonic crystals
Juodkazis, Saulius; Mizeikis, Vygantas; Seet, Kock Khuen; Misawa, Hiroaki; Wegst, Ulrike G. K.
2007-12-01
Mechanical properties of photopolymerized photonic crystal (PhC) structures having woodpile and spiral three-dimensional architectures were examined using flat-punch indentation. The structures were found to exhibit a foamlike response with a bend-dominated elastic deformation regime observed at strain levels up to 10%. Numerical simulations of optical properties of these PhC structures demonstrate the possibility of achieving a substantial and reversible spectral tuning of the photonic stop gap wavelength by applying a mechanical load to the PhC.
Synthesis, Crystal Structure and Magnetic Property of the Polymeric Ribbon: [Co(ip)(phen)]n
Institute of Scientific and Technical Information of China (English)
ZHOU You-Fu; SHI Qian; YUAN Da-Qiang; XU Yan-Qing; HONG Mao-Chun
2005-01-01
A metal-organic coordination polymer [Co(ip)(phen)]n (ip = isophthalate, phen = 1,10-phenanthroline) 1 has been hydrothermally synthesized and characterized.Compound 1 crystallizes in P2/c space group with a = 8.37(2), b = 10.41(1), c = 18.36(3) (A), β = 100.41(7)o, C20H12CoN2O4, Mr = 403.25, V = 1573(4) (A)3, Z = 4 and Dc = 1.703 g/cm3.Two Co(II) ions are bridged by μ-carboxylate to form a dinuclear unit, which is extended by ip ligands resulting in a ribbon-like chain.Pairs of phen ligands attach to the dinuclear units on both sides of the chain alternately.Magnetic study reveals that the interaction between the carboxylate-bridged Co(II) ions in 1 is weakly antiferromagnetic.
Institute of Scientific and Technical Information of China (English)
YUAN Fugen; LI Tingting; LI Li; ZHOU Yuan
2012-01-01
Complexes of lanthanide trisborohydrides,formally Ln(BH4)3(THF)n (Ln=La,Ce,Sm,Yb),were synthesized and their catalytic activity for polymerization of ε-caprolactone was studied.All the complexes can catalyze this polymerization.It was found that the catalytic activities decreased in the order of La＞Ce＞Sm＞Yb.The crystal structure of cerium trisborohydride was determined for the first time by single crystal X-ray diffraction analysis.It is an ionic pair complex of [Ce(BH4)2(THF)5][Ce(BH4)4(THF)2].The cationic part involves two η3-BH4 ligands,while the anionic part involves two η3-BH4 groups and two η2-BH4 groups.
Institute of Scientific and Technical Information of China (English)
刘启能
2012-01-01
Set up a resonant cavity model and the analytical formulas of the total reflection tunnel effect frequency of 1D infinite period phononic crystal is deduced by resonance conditions of the resonant cavity. The physical mechanism of the total reflection tunnel effect of 1D infinite period phononic crystal is explained. Using the analytical formulas the change rule of the total reflection runnel effect that response curves of frequency versus order number of band and incident angle and thickness of resonant cavity are studied. Resonance theory results and dispersion method results are compared and their results are the same.%建立了一维无限周期声子晶体的谐振腔模型,利用谐振腔的共振条件推导出金反射隧穿导带频率满足的解析公式,从理论上解释了一维无限周期声子晶体全反射隧穿效应产生的物理机理.利用频率的解析公式对全反射隧穿导带的频率随导带级数、腔厚度以及入射角的变化规律进行了研究,圆满地解释了一维无限周期声子晶体的全反射隧穿效应的变化规律.并且将共振理论的结果与色散法的结果进行比较,其结果完全吻合.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A novel organotin complex [(n-Bu)3Sn(OCOC5H4NO)]n has been synthesized and characterized by elemental analysis, IR and 1H NMR. The crystal structure has been determined by X-ray single-crystal diffraction. The crystal belongs to monoclinic, space group P21/c with a =8.982(2), b = 17.908(4), c = 13.219(3) A, β= 96.981 (4)°, Z = 4, V= 2110.6(8) A3, Dc = 1.347 g/cm3,μ(MoKα) = 12.23 cm-1, F(000) = 880, R = 0.0497 and wR = 0.1263. In the molecular structure of the title complex, the tin atoms are five-coordinated in a distorted trigonal bipyramidal geometry. A one-dimensional linear polymer is formed through an interaction between the O atoms of pyridine-3-carboxylic acid N-oxide and tin atoms of an adjacent molecule.
Wanko, Jeffrey J.
2009-01-01
This article provides a historical context for the debate between Georg Cantor and Leopold Kronecker regarding the cardinality of different infinities and incorporates the short story "Welcome to the Hotel Infinity," which uses the analogy of a hotel with an infinite number of rooms to help explain this concept. Wanko makes use of this history and…
On infinitely divisible semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas; Rosiński, Jan
2015-01-01
processes, including linear fractional processes, mixed moving averages, and supOU processes, as particular cases. The proof of the main theorem relies on series representations of jumps of cadlag infinitely divisible processes given in Basse-O'Connor and Rosinski [2013, Ann. Probab. 41(6)] combined...
Wanko, Jeffrey J.
2009-01-01
This article provides a historical context for the debate between Georg Cantor and Leopold Kronecker regarding the cardinality of different infinities and incorporates the short story "Welcome to the Hotel Infinity," which uses the analogy of a hotel with an infinite number of rooms to help explain this concept. Wanko makes use of this history and…
DEFF Research Database (Denmark)
Srba, Jiří
2002-01-01
This paper provides a comprehensive summary of equivalence checking results for infinite-state systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the web-page http://www.brics.dk/~srba/roadmap....
Meng, Zi-Ming; Zhong, Xiao-Lan; Wang, Chen; Li, Zhi-Yuan
2012-06-01
With the development of micro- or nano-fabrication technologies, great interest has been aroused in exploiting photonic crystal nanobeam structures. In this article the design of high-quality-factor (Q) polymeric photonic crystal nanobeam microcavities suitable for realizing ultrafast all-optical switching is presented based on the three-dimensional finite-difference time-domain method. Adopting the pump-probe technique, the ultrafast dynamic response of the all-optical switching in a nanobeam microcavity with a quality factor of 1000 and modal volume of 1.22 (λ/n)3 is numerically studied and a switching time as fast as 3.6 picoseconds is obtained. Our results indicate the great promise of applying photonic crystal nanobeam microcavities to construct integrated ultrafast tunable photonic devices or circuits incorporating polymer materials with large Kerr nonlinearity and ultrafast response speed.
Energy Technology Data Exchange (ETDEWEB)
Lanciano, Giuseppina [Department of Innovation Engineering, University of Salento, Via per Arnesano, 73100 Lecce (Italy); Greco, Antonio, E-mail: antonio.greco@unile.it [Department of Innovation Engineering, University of Salento, Via per Arnesano, 73100 Lecce (Italy); Maffezzoli, Alfonso [Department of Innovation Engineering, University of Salento, Via per Arnesano, 73100 Lecce (Italy); Mascia, Leno [Department of Materials, Loughborough University, Loughborough, LE 11 3TU (United Kingdom)
2009-09-10
Differential scanning calorimetry was used to study the thermal characteristics and morphological structure of species produced during the ring opening polymerization of cyclic butylene terephthalate (CBT). Thermal programs consisting of a first ramp heating scan and an isothermal step, followed by cooling and a second ramp heating step, were used to study the effects of thermal history, catalyst (butyl chlorotin dihydroxide) at concentrations between 0.1 and 1.3% (w/w), and the presence of a layered silicate nanofiller (montmorillonite at 4.0%, w/w) on the structure of the resulting polymer (poly(butylene terephthalate), pCBT). Wide angle X-ray diffraction was used to monitor the degree of exfoliation of the nanocomposites. It was found that pCBT is formed in the amorphous state, and crystallizes during the heating step or during the isothermal step at temperatures lower than the equilibrium melting temperature of the polymer (T{sub m}{sup 0}). When premixed with the nanofiller, irrespective of whether this was previously intercalated with a tallow surfactant or used in its pristine form, polymerization took place at higher temperatures and most of the crystallization was found to occur during the cooling stage. In those cases where crystallization took place during either the first heating scan, or during a prolonged isothermal step below the T{sub m}{sup 0} of the polymer, the resulting crystals were found to have a higher lamellar thickness, as compared with the same polymer crystallized from the melt during the cooling step from temperatures above the polymer T{sub m}{sup 0}.
Infinite matrices and sequence spaces
Cooke, Richard G
2014-01-01
This clear and correct summation of basic results from a specialized field focuses on the behavior of infinite matrices in general, rather than on properties of special matrices. Three introductory chapters guide students to the manipulation of infinite matrices, covering definitions and preliminary ideas, reciprocals of infinite matrices, and linear equations involving infinite matrices.From the fourth chapter onward, the author treats the application of infinite matrices to the summability of divergent sequences and series from various points of view. Topics include consistency, mutual consi
Institute of Scientific and Technical Information of China (English)
Yu-qin Bai; Jin-bao Guo; Ying Wang; Jie Wei
2013-01-01
A polymerized lyotropic liquid crystal monomer of sodium 3,4,5-tris (11-acryloxyundecyloxy)benzoate was synthesized by a convenient route starting from 3,4,5-trihydroxybenzoic acid via esterification followed by etherification,acylation and finally neutralization.The chemical structure was confirmed by Fourier transform infrared (FT-IR) and 1H nuclear magnetic resonance spectral analysis.The self-organization behavior of the monomer with deionized water in methanol at room temperature was also demonstrated.The assemblies were characterized by polarized optical microscope and X-ray diffraction.The results show that a solution containing 80∶20 of the monomer to water was found to be able to self-organize into Lamellar (La) phase and 92∶8 with inverted hexagonal (HⅡ) phase,which was in accordance with the theoretical calculation of critical packing parameter.It suggests that the concentration of the monomer was the key factor to influence assembly structure.Additionally,the acrylate conversion with different photoinitiators and nanostructure retention after polymerization were investigated.The research shows that the acrylate conversion of the monomer with Darocur2959 could reach up to 78％ when irradiated by 30 mW/cm2 UV light of 365 nm for 30 min characterized by Real-time FT-IR as well as the sol-gel method.Meanwhile,the La and HⅡI phase nanostructures were both retained after polymerization.
Knopp, Konrad
1956-01-01
One of the finest expositors in the field of modern mathematics, Dr. Konrad Knopp here concentrates on a topic that is of particular interest to 20th-century mathematicians and students. He develops the theory of infinite sequences and series from its beginnings to a point where the reader will be in a position to investigate more advanced stages on his own. The foundations of the theory are therefore presented with special care, while the developmental aspects are limited by the scope and purpose of the book. All definitions are clearly stated; all theorems are proved with enough detail to ma
Passman, Donald S
2013-01-01
This groundbreaking monograph in advanced algebra addresses crossed products. Author Donald S. Passman notes that crossed products have advanced from their first occurrence in finite dimensional division algebras and central simple algebras to a closer relationship with the study of infinite group algebras, group-graded rings, and the Galois theory of noncommutative rings. Suitable for advanced undergraduates and graduate students of mathematics, the text examines crossed products and group-graded rings, delta methods and semiprime rings, the symmetric ring of quotients, and prime ideals, bot
Energy Technology Data Exchange (ETDEWEB)
Heinze, D.; Mang, Th. [Aachen University of Applied Sciences, Heinrich-Mussmann-Str. 1, 52428 Jülich (Germany); Popescu, C., E-mail: crisan.popescu@kao.com [KAO Germany GmbH, Pfungstädterstr. 98-100, 64297 Darmstadt (Germany); Weichold, O., E-mail: weichold@ibac.rwth-aachen.de [Institute of Building Materials Research, Schinkelstr. 3, 52062 Aachen (Germany)
2016-08-10
Highlights: • Thermal behaviour of telomerized polyvinyl esters is investigated. • Thermal stability relies mainly on the contribution of side chains. • At equal molecular weights thermal stability is dictated by length of side chain. • Increasing the length of side chains improves also the packing degree of polymer. - Abstract: Four members of a homologous series of chlorinated poly(vinyl ester) oligomers CCl{sub 3}–(CH{sub 2}CH (OCO(CH{sub 2}){sub m}CH{sub 3})){sub n}–Cl with degrees of polymerization of 10 and 20 were prepared by telomerisation using carbon tetrachloride. The number of side chain carbon atoms ranges from 2 (poly(vinyl acetate) to 18 (poly(vinyl stearate)). The effect of the n-alkyl side chain length and of the degree of polymerization on the thermal stability and crystallization behaviour of the synthesized compounds was investigated. All oligomers degrade in two major steps by first losing HCl and side chains with subsequent breakdown of the backbone. The members with short side chains, up to poly(vinyl octanoate), are amorphous and show internal plasticization, whereas those with high number of side chain carbon atoms are semi-crystalline due to side-chain crystallization. A better packing for poly(vinyl stearate) is also noticeable. The glass transition and melting temperatures as well as the onset temperature of decomposition are influenced to a larger extent by the side chain length than by the degree of polymerization. Thermal stability is improved if both the size and number of side chains increase, but only a long side chain causes a significant increase of the resistance to degradation. This results in a stabilization of PVAc so that oligomers from poly(vinyl octanoate) on are stable under atmospheric conditions. Thus, the way to design stable, chlorinated PVEs oligomers is to use a long n-alkyl side chain.
Saroj, A. L.; Chaurasia, S. K.; Kataria, Shalu; Singh, R. K.
2016-06-01
The effect of ionic liquid (IL), 1-butyl-2,3-dimethylimidazolium tetrafluoroborate [BDMIM][BF4], on crystallization behavior of poly(vinyl alcohol) (PVA) has been studied by isothermal and non-isothermal differential scanning calorimetry techniques. The PVA + IL based polymer electrolyte films have been prepared using solution casting technique. To describe the isothermal and non-isothermal crystallization kinetics, several kinetic equations have been employed on PVA + IL based films. There is strong dependence of the peak crystallization temperature (Tc), relative degree of crystallity (Xt), half-time of crystallization (t1/2), crystallization rate constants (Avrami Kt and Tobin AT), and Avrami (n) and Tobin (nT) exponents on the cooling rate and IL loading.
Directory of Open Access Journals (Sweden)
Matthias Rehahn
2013-03-01
Full Text Available In the present study, the synthesis of poly(1,1-dimethylsilacyclobutane (PDMSB by anionic ring opening polymerization (ROP is reinvestigated, leading to narrowly distributed molar masses (polydispersities 1.04–1.15 in the range of 2.3 to 60 kg mol−1. Investigations of thermal behavior for low molar mass PDMSB revealed an untypical multiple peaks melting phenomenon, which at first glance, seems to be of the same origin as low molar mass poly(ethylene oxides. Small angle X-ray scattering (SAXS and X-ray diffraction (XRD measurements are done, proving the fast crystallization and subsequent recrystallization for investigated low molar mass samples. Synthetic attempts are expanded to the surface-initiated anionic ROP of 1,1-dimethylsilacyclobutane (DMSB monomer from the surface of cross-linked polystyrene (PS nanoparticles. Novel polycarbosilanes (PCS/organic core/shell particles are obtained, which are investigated by using transmission electron microscopy (TEM and dynamic light scattering (DLS experiments. First insights into the crystallization behavior of surface-attached PDMSB chains reveal that crystallization seems to be hindered.
Dynamic and Transient Infinite Elements
Zhao, Chongbin
2009-01-01
Intends to provide the theory and the application of dynamic and transient infinite elements for simulating the far fields of infinite domains involved in many of scientific and engineering problems, based on the author's own work over the years. This title is suitable for computational geoscientists, geotechnical engineers, and civil engineers.
Students' Conception of Infinite Series
Martinez-Planell, Rafael; Gonzalez, Ana Carmen; DiCristina, Gladys; Acevedo, Vanessa
2012-01-01
This is a report of a study of students' understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be…
Stochastic and infinite dimensional analysis
Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José
2016-01-01
This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Word learning under infinite uncertainty
Blythe, Richard A; Smith, Kenny
2014-01-01
Language learners learn the meanings of many thousands of words, despite encountering them in complex environments where infinitely many meanings might be inferred by the learner as their true meaning. This problem of infinite referential uncertainty is often attributed to Willard Van Orman Quine. We provide a mathematical formalisation of an ideal cross-situational learner attempting to learn under infinite referential uncertainty, and identify conditions under which this can happen. As Quine's intuitions suggest, learning under infinite uncertainty is possible, provided that learners have some means of ranking candidate word meanings in terms of their plausibility; furthermore, our analysis shows that this ranking could in fact be exceedingly weak, implying that constraints allowing learners to infer the plausibility of candidate word meanings could also be weak.
Gluing an infinite number of instantons
Tsukamoto, Masaki
2007-01-01
This paper is one step toward infinite energy gauge theory and the geometry of infinite dimensional moduli spaces. We generalize a gluing construction in the usual Yang-Mills gauge theory to an ``infinite energy'' situation. We show that we can glue an infinite number of instantons, and that the resulting instantons have infinite energy in general. Moreover we show that they have an infinite dimensional parameter space. Our construction is a generalization of Donaldson's ``alternating method''.
The Infinite Latent Events Model
Wingate, David; Roy, Daniel; Tenenbaum, Joshua
2012-01-01
We present the Infinite Latent Events Model, a nonparametric hierarchical Bayesian distribution over infinite dimensional Dynamic Bayesian Networks with binary state representations and noisy-OR-like transitions. The distribution can be used to learn structure in discrete timeseries data by simultaneously inferring a set of latent events, which events fired at each timestep, and how those events are causally linked. We illustrate the model on a sound factorization task, a network topology identification task, and a video game task.
Walt, David R.; Mandal, Tarun K.; Fleming, Michael S.
2004-04-13
The invention features core-shell microsphere compositions, hollow polymeric microspheres, and methods for making the microspheres. The microspheres are characterized as having a polymeric shell with consistent shell thickness.
2015-01-01
We report a study of the wetting and ordering of thermotropic liquid crystal (LC) droplets that are trapped (or “caged”) within micrometer-sized cationic polymeric microcapsules dispersed in aqueous solutions of surfactants. When they were initially dispersed in water, we observed caged, nearly spherical droplets of E7, a nematic LC mixture, to occupy ∼40% of the interior volume of the polymeric capsules [diameter of 6.7 ± 0.3 μm, formed via covalent layer-by-layer assembly of branched polyethylenimine and poly(2-vinyl-4,4-dimethylazlactone)] and to contact the interior surface of the capsule wall at an angle of ∼157 ± 11°. The internal ordering of LC within the droplets corresponded to the so-called bipolar configuration (distorted by contact with the capsule walls). While the effects of dodecyltrimethylammonium bromide (DTAB) and sodium dodecyl sulfate (SDS) on the internal ordering of “free” LC droplets are similar, we observed the two surfactants to trigger strikingly different wetting and configurational transitions when LC droplets were caged within polymeric capsules. Specifically, upon addition of SDS to the aqueous phase, we observed the contact angles (θ) of caged LC on the interior surface of the capsule to decrease, resulting in a progression of complex droplet shapes, including lenses (θ ≈ 130 ± 10°), hemispheres (θ ≈ 89 ± 5°), and concave hemispheres (θ < 85°). The wetting transitions induced by SDS also resulted in changes in the internal ordering of the LC to yield states topologically equivalent to axial and radial configurations. Although topologically equivalent to free droplets, the contributions that surface anchoring, LC elasticity, and topological defects make to the free energy of caged LC droplets differ from those of free droplets. Overall, these results and others reported herein lead us to conclude that caged LC droplets offer a platform for new designs of LC-droplet-based responsive soft matter that cannot
Directory of Open Access Journals (Sweden)
Ananda S. Amarasekara
2015-05-01
Full Text Available In the title calcium levulinate complex, [Ca(C5H7O32(H2O2]n, the Ca2+ ion lies on a twofold rotation axis and is octacoordinated by two aqua ligands and six O atoms from four symmetry-related carboxylate ligands, giving a distorted square-antiprismatic coordination stereochemistry [Ca—O bond-length range = 2.355 (1–2.599 (1 Å]. The levulinate ligands act both in a bidentate carboxyl O,O′-chelate mode and in a bridging mode through one carboxyl O atom with an inversion-related Ca2+ atom, giving a Ca...Ca separation of 4.0326 (7 Å. A coordination polymeric chain structure is generated, extending along the c-axial direction. The coordinating water molecules act as double donors and participate in intra-chain O—H...O hydrogen bonds with carboxyl O atoms, and in inter-chain O—H...O hydrogen bonds with carbonyl O atoms, thus forming an overall three-dimensional structure.
Chou, Hung-Che; Yan, Tsong-Rong; Chen, Ko-Shao
2009-10-15
This paper utilizes a silver electrode quartz crystal microbalance (QCM) mass sensor to detect the physiology of cells. This study also investigates the plasma surface modification of silver electrode QCMs through deposition of hexamethyldisilazane (HMDSZ) films as a protection film. To improve the cell growth, this paper also performs post-treatments by surface-grafting acrylic acid (AAc), acrylamide (AAm), and oxygen plasma treatment onto the QCM electrodes. Experimental results indicate that plasma deposition is a useful technique to protect the surface of silver electrodes. This technique extends the unpeeling time of silver electrodes from 1 to 7 days. The hydrophilic silver electrode QCM surface modified by AAm exhibited a better storage time effect than other post-treatments.
Kawai, Kotaro; Kuzuwata, Mitsuru; Sasaki, Tomoyuki; Noda, Kohei; Kawatsuki, Nobuhiro; Ono, Hiroshi
2014-12-01
Blazed vector grating liquid crystal (LC) cells, in which the directors of low-molar-mass LCs are antisymmetrically distributed, were fabricated by one-step exposure of an empty glass cell inner-coated with a photocrosslinkable polymer LC (PCLC) to UV light. By adopting a LC cell structure, twisted nematic (TN) and homogeneous (HOMO) alignments were obtained in the blazed vector grating LC cells. Moreover, the diffraction efficiency of the blazed vector grating LC cells was greatly improved by increasing the thickness of the device in comparison with that of a blazed vector grating with a thin film structure obtained in our previous study. In addition, the diffraction efficiency and polarization states of ±1st-order diffracted beams from the resultant blazed vector grating LC cells were controlled by designing a blazed pattern in the alignment films, and these diffraction properties were well explained on the basis of Jones calculus and the elastic continuum theory of nematic LCs.
Baghel, Shrawan; Cathcart, Helen; O'Reilly, Niall J
2016-09-01
Poor water solubility of many drugs has emerged as one of the major challenges in the pharmaceutical world. Polymer-based amorphous solid dispersions have been considered as the major advancement in overcoming limited aqueous solubility and oral absorption issues. The principle drawback of this approach is that they can lack necessary stability and revert to the crystalline form on storage. Significant upfront development is, therefore, required to generate stable amorphous formulations. A thorough understanding of the processes occurring at a molecular level is imperative for the rational design of amorphous solid dispersion products. This review attempts to address the critical molecular and thermodynamic aspects governing the physicochemical properties of such systems. A brief introduction to Biopharmaceutical Classification System, solid dispersions, glass transition, and solubility advantage of amorphous drugs is provided. The objective of this review is to weigh the current understanding of solid dispersion chemistry and to critically review the theoretical, technical, and molecular aspects of solid dispersions (amorphization and crystallization) and potential advantage of polymers (stabilization and solubilization) as inert, hydrophilic, pharmaceutical carrier matrices. In addition, different preformulation tools for the rational selection of polymers, state-of-the-art techniques for preparation and characterization of polymeric amorphous solid dispersions, and drug supersaturation in gastric media are also discussed.
Pasán, Jorge; Sanchiz, Joaquín; Ruiz-Pérez, Catalina; Lloret, Francesc; Julve, Miguel
2005-10-31
Two new phenylmalonate-bridged copper(II) complexes with the formulas [Cu(4,4'-bpy)(Phmal)](n).2nH(2)O (1) and [Cu(2,4'-bpy)(Phmal)(H(2)O)](n)() (2) (Phmal = phenylmalonate dianion, 4,4'-bpy = 4,4'-bipyridine, 2,4'-bpy = 2,4'-bipyridine) have been synthesized and characterized by X-ray diffraction. Complex 1 crystallizes in monoclinic space group P2(1), Z = 4, with unit cell parameters of a = 9.0837(6) Angstroms, b = 9.3514(4) Angstroms, c = 11.0831(8) Angstroms, and beta = 107.807(6) degrees , whereas complex 2 crystallizes in orthorhombic space group C2cb, Z = 8, with unit cell parameters of a = 10.1579(7) Angstroms, b = 10.3640(8) Angstroms, and c = 33.313(4) Angstroms. The structures of 1 and 2 consist of layers of copper(II) ions with bridging bis-monodentate phenylmalonate (1 and 2) and 4,4'-bpy (1) ligands and terminal monodentate 2,4'-bpy (2) groups. Each layer in 1 contains rectangles with dimensions of 11.08 x 4.99 Angstroms(2), the edges being defined by the Phmal and 4,4'-bpy ligands. The intralayer copper-copper separations in 1 through the anti-syn equatorial-apical carboxylate-bridge and the 4,4'-bpy molecule are 4.9922(4) and 11.083(1) Angstroms, respectively. The anti-syn equatorial-equatorial carboxylate bridge links the copper(II) atoms in complex 2 within each layer with a mean copper-copper separation of 5.3709(8) Angstroms. The presence of 2,4'-bpy as a terminal ligand accounts for the large interlayer separation of 15.22 Angstroms. The copper(II) environment presents a static pseudo-Jahn-Teller disorder which has been studied by EPR and low-temperature X-ray diffraction. Magnetic susceptibility measurements of both compounds in the temperature range 2-290 K show the occurrence of weak antiferromagnetic [J = -0.59(1) cm(-1) (1)] and ferromagnetic [J = +0.77(1) cm(-1) (2)] interactions between the copper(II) ions. The conformation of the phenylmalonate-carboxylate bridge and other structural factors, such as the planarity of the exchange
Indian Academy of Sciences (India)
SABITHAKALA THATITURI; BHARGAVI GOVINDUGARI; VENKATA RAMANA REDDY CHITTIREDDY
2017-08-01
A novel water-soluble carboxylate-bridged copper(II) coordination polymer,Cu-BIG was formed by the reaction of Cu(ClO₄)₂ ·6H₂O and tridentate benzimidazole-glycine conjugate ligand, 2-((1H-benzimidazol- 2-yl)methylamino) acetic acid, BIGH and its structure has been determined by IR, UV, powder XRD, VSM, CV, TGA, DTA, EPR and single crystal X-ray diffraction. Crystallographic studies indicate it to be a coordination polymer with P¯ı Space group. The asymmetric unit of complex contains two Cu(II) ions with elongated square pyramid geometry.The axial positions of theCu(II) atoms are occupied by the carbonyl oxygen of the carboxylate group with the bond distances Cu(1)–O(5)axial , 2.28Å, and Cu(2)–O(2)axial , 2.26Å. The two Cu(II) are connected through the carboxylic group present in BIGH, which provides electron mobilisation in the molecule and hence results in the soft ferromagnetic polymer. An in vitro antibacterial activity study of BIGH and Cu-BIG showed moderate activity against Bacillus subtilis. The DNA binding studies showed the interaction of Cu-BIG with CT-DNA.
Decoherence in infinite quantum systems
Energy Technology Data Exchange (ETDEWEB)
Blanchard, Philippe; Hellmich, Mario [Faculty of Physics, University of Bielefeld, Universitaetsstr. 25, 33615 Bielefeld (Germany); Bundesamt fuer Strahlenschutz (Federal Office for Radiation Protection), Willy-Brandt-Strasse 5, 38226 Salzgitter (Germany)
2012-09-01
We review and discuss a notion of decoherence formulated in the algebraic framework of quantum physics. Besides presenting some sufficient conditions for the appearance of decoherence in the case of Markovian time evolutions we provide an overview over possible decoherence scenarios. The framework for decoherence we establish is sufficiently general to accommodate quantum systems with infinitely many degrees of freedom.
Energy Technology Data Exchange (ETDEWEB)
Han, Min-Le [College of Materials & Chemical Engineering, Collaborative Innovation Center for Microgrid of New Energy of Hubei Province, China Three Gorges University, Yichang 443002 (China); Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of the Ministry of Education, College of Chemistry & Materials Science, Northwest University, Xi’an 710069 (China); Wu, Ya-Pan; Zhao, Jun [College of Materials & Chemical Engineering, Collaborative Innovation Center for Microgrid of New Energy of Hubei Province, China Three Gorges University, Yichang 443002 (China); Li, Dong-Sheng, E-mail: lidongsheng1@126.com [College of Materials & Chemical Engineering, Collaborative Innovation Center for Microgrid of New Energy of Hubei Province, China Three Gorges University, Yichang 443002 (China); Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of the Ministry of Education, College of Chemistry & Materials Science, Northwest University, Xi’an 710069 (China); Wang, Yao-Yu [Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of the Ministry of Education, College of Chemistry & Materials Science, Northwest University, Xi’an 710069 (China)
2015-10-15
Two new Co(II) metal-organic frameworks, namely [Co{sub 2}(bpm)(H{sub 2}O){sub 3}(L)]{sub n} (1) and ([Co(bpe)(H{sub 2}O)(H{sub 2}L)]·(bpe){sub 0.5}·(H{sub 2}O)){sub n} (2), (H{sub 4}L=1,1′:2′,1″-terphenyl-3,3″,4′,5′-tetracarboxylic acid, bpm=bis(4-pyridyl)amine, bpe=1,2-bis(4-pyridyl)ethene), have been obtained under hydrothermal conditions. Both complexes 1 and 2 have been characterized by elemental analysis, IR spectra, single-crystal X-ray diffraction, powder X-ray diffraction (PXRD), and thermogravimetric analysis (TGA). Complexes 1 and 2 consist of 1D Co(II) chains bridging by carboxylate groups in syn-anti fashion. 1 shows a novel 3D tri-nodal (4,6,10)-connected net with a (3.4{sup 3}.5{sup 2}){sub 2}(3{sup 2}.4{sup 14}.5{sup 12}.6{sup 12}.7{sup 4}.8)(3{sup 2}.4{sup 2}.5{sup 5}.6{sup 4}.7{sup 2}) topology. While 2 exhibits a 2D sql layer. Magnetic susceptibility measurements indicate that both 1 and 2 show weak antiferromagnetic interactions between the adjacent Co(II) ions in 300–8 K for 1 and 300–16 K for 2, respectively, and then 2 also displays ferromagnetic coupling at lower temperatures. - Graphical abstract: Two Co(II) coordination polymers with similar metal chain bridging by carboxylates in syn-anti fashion have been synthesized. Both 1 and 2 show weak antiferromagnetic interactions in high temperature, and then 2 also displays ferromagnetic coupling at lower temperatures. - Highlights: • Two Co(II) coordination polymers with similar metal chain bridging by carboxylates. • A novel 3D (4,6,10)-connected net and a 2D sql layers. • A antiferromagnetic coupling at high temperature for 1 and 2. • A ferromagnetic coupling at lower temperature for 2.
Ovcharenko, Victor I; Fokin, Sergey V; Kostina, Elvina T; Romanenko, Galina V; Bogomyakov, Artem S; Tretyakov, Eugene V
2012-11-19
The reaction of copper(II) hexafluoroacetylacetonate [Cu(hfac)2] with the stable nitronyl nitroxide 2-(1-ethyl-3-methyl-1H-pyrazol-4-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl (L(a)) resulted in a paired heterospin complex [[Cu(hfac)2]3(μ-O,N-L(a))2][Cu(hfac)2(O-L(a))2]. The crystals of the compound were found to be capable of a reversible single-crystal-to-single-crystal (SC-SC) transformation initiated by the variation of temperature. At room temperature, the molecular structure of [[Cu(hfac)2]3(μ-O,N-L(a))2][Cu(hfac)2(O-L(a))2] is formed by the alternating fragments of the pair complex. Cooling the crystals of the complex below 225 K caused considerable mutual displacements of adjacent molecules, which ended in a transformation of the molecular structure into a polymer chain structure. A reversible topotactic polymerization-depolymerization coordination reaction actually takes place in the solid during repeated cooling-heating cycles: [[Cu(hfac)2]3(μ-O,N-L(a))2][Cu(hfac)2(O-L(a))2] ⇌ Cu(hfac)2(μ-O,N-L(a))]∞. Polymerization during cooling is the result of the anomalously great shortening of intermolecular distances (from 4.403 Å at 295 K to 2.460 Å at 150 K; Δd = 1.943 Å) between the terminal Cu atoms of the trinuclear fragments {[[Cu(hfac)2]3(μ-O,N-L(a))2]} and the noncoordinated N atoms of the pyrazole rings of the mononuclear {[Cu(hfac)2(O-L(a))2]} fragments. When the low-temperature phase was heated above 270 K, the polymer chain structure was destroyed and the compound was again converted to the pair molecular complex. The specifics of the given SC-SC transformation lies in the fact that the process is accompanied by a magnetic anomaly, because the intracrystalline displacements of molecules lead to a considerable change in the mutual orientation of the paramagnetic centers, which, in turn, causes modulation of the exchange interaction between the odd electrons of the Cu(2+) ion and nitroxide. On the temperature curve of
An Infinite Restricted Boltzmann Machine.
Côté, Marc-Alexandre; Larochelle, Hugo
2016-07-01
We present a mathematical construction for the restricted Boltzmann machine (RBM) that does not require specifying the number of hidden units. In fact, the hidden layer size is adaptive and can grow during training. This is obtained by first extending the RBM to be sensitive to the ordering of its hidden units. Then, with a carefully chosen definition of the energy function, we show that the limit of infinitely many hidden units is well defined. As with RBM, approximate maximum likelihood training can be performed, resulting in an algorithm that naturally and adaptively adds trained hidden units during learning. We empirically study the behavior of this infinite RBM, showing that its performance is competitive to that of the RBM, while not requiring the tuning of a hidden layer size.
ADAPTIVE ELLIPSOIDAL ACOUSTIC INFINITE ELEMENT
Institute of Scientific and Technical Information of China (English)
Yang Ruiliang; Wang Hongzhen
2004-01-01
It is shown that the basis of the ellipsoidal acoustic infinite element Burnett method,the multipole expansion,cannot represent real ellipsoidal acoustic field exactly.To solve the problem,a weight of angular direction is added to the multipole expansion.The comparison of the modified method and the prime method shows that the modified method can describe and solve the ellipsoidal acoustic field more accurately than ever.A dilating sphere is used to test the new method further.Unlike other infinite element methods,varied ratio of the ellipsoidal artificial boundary instead of sphere is used.The pressure value of the artificial boundary is utilized as the initial value of the new method.Then the radiating phenomena of the ellipsoidal acoustic field can be researched using the new method.These examples show the feasibility of the adaptive method.
Montenegro, Rivelino V. D.
2003-05-01
The colloidal systems are present everywhere in many varieties such as emulsions (liquid droplets dispersed in liquid), aerosols (liquid dispersed in gas), foam (gas in liquid), etc. Among several new methods for the preparation of colloids, the so-called miniemulsion technique has been shown to be one of the most promising. Miniemulsions are defined as stable emulsions consisting of droplets with a size of 50-500 nm by shearing a system containing oil, water, a surfactant, and a highly water insoluble compound, the so-called hydrophobe 1. In the first part of this work, dynamic crystallization and melting experiments are described which were performed in small, stable and narrowly distributed nanodroplets (confined systems) of miniemulsions. Both regular and inverse systems were examined, characterizing, first, the crystallization of hexadecane, secondly, the crystallization of ice. It was shown for both cases that the temperature of crystallization in such droplets is significantly decreased (or the required undercooling is increased) as compared to the bulk material. This was attributed to a very effective suppression of heterogeneous nucleation. It was also found that the required undercooling depends on the nanodroplet size: with decreasing droplet size the undercooling increases. 2. It is shown that the temperature of crystallization of other n-alkanes in nanodroplets is also significantly decreased as compared to the bulk material due to a very effective suppression of heterogeneous nucleation. A very different behavior was detected between odd and even alkanes. In even alkanes, the confinement in small droplets changes the crystal structure from a triclinic (as seen in bulk) to an orthorhombic structure, which is attributed to finite size effects inside the droplets. An intermediate metastable rotator phase is of less relevance for the miniemulsion droplets than in the bulk. For odd alkanes, only a strong temperature shift compared to the bulk system is
Semi-infinite assignment and transportation games
Sánchez-Soriano, Joaqu´ın; Llorca, Navidad; Tijs, Stef; Timmer, Judith; Goberna, Miguel A.; López, Marco A.
2001-01-01
Games corresponding to semi-infinite transportation and related assignment situations are studied. In a semi-infinite transportation situation, one aims at maximizing the profit from the transportation of a certain good from a finite number of suppliers to an infinite number of demanders. An assignm
Institute of Scientific and Technical Information of China (English)
姚景才; 马勇林; 黄伟; 苟少华
2003-01-01
A new imidazolium compound, C15H17N4(ClO4, was prepared from a flexible bidentate ligand of 1,3-di(imidazol-1-ylmethyl)-5-methylbenzene, and characterized by X-ray analysis. It is of orthorhombic, space group Pnma with a = 8.182(2), b = 12.874(3), c = 15.611(4) （A。）, V = 1644.4(7) （A。）3, Dc = 1.425 g/cm3, Z = 4, Mr = 352.78, μ(MoKα) = 0.944 mm－1, F(000) = 736, S = 1.036, the final R = 0.0521 and wR = 0.1187 for 1128 observed reflections (I > 2σ(I)). An infinite one-dimensional zigzag chain is formed by N-H…N hydrogen bonding interactions between the imidazolium salt cations.
Linguistic variation and change: Middle English infinitive
Directory of Open Access Journals (Sweden)
Frančiška Trobevšek Drobnak
2004-12-01
Full Text Available In Middle English the old inflected infinitive lost its supine function and gradually replaced the uninflected infinitive in all positions, except in the complementation of moal and a limited number of other verbs. According to most linguists, the choice between the to infinitive and the bare infinitive was either lexically or structurally conditioned. The theory of linguistic change as the assertion of weaker or stronger linguistic variants postulates the affinity of stronger variants for more complex, i. e. functionally marked grammaticall environment. The author tests the validity of the theory against the assertion of the English to infinitive at the expanse of the bare infinitive after the Norman Conquest. The results confirm the initial hypothesist that the degree of formal marked ness of the infinitive concurred with the degree of the functional markedness of grammatical pa rameters.
Automated Analysis of Infinite Scenarios
DEFF Research Database (Denmark)
Buchholtz, Mikael
2005-01-01
The security of a network protocol crucially relies on the scenario in which the protocol is deployed. This paper describes syntactic constructs for modelling network scenarios and presents an automated analysis tool, which can guarantee that security properties hold in all of the (infinitely many......) instances of a scenario. The tool is based on control flow analysis of the process calculus LySa and is applied to the Bauer, Berson, and Feiertag protocol where is reveals a previously undocumented problem, which occurs in some scenarios but not in other....
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Indian Academy of Sciences (India)
S Ramakrishnan
2017-04-01
The very idea that large polymer molecules can indeed existwas hotly debated during the early part of the 20th century.As highlighted by Sivaram in his articles on Carothersand Flory, Staudinger’s macromolecular hypothesis was finallyaccepted, and the study of polymers gained momentumbecause of the remarkable efforts of the these two individualswho laid down the foundations concerning the processes thatled to the formation of large polymer molecules, and to thosethat led to an understanding of many of their extraordinaryphysical properties. Condensation polymerizations, as thename suggests, utilizes bond-forming reactions that generatea small molecule condensate, which often needs to be continuouslyremoved to facilitate the formation of the polymer. Inthis article, I shall describe some of the essential principles ofcondensation polymerizations or more appropriately calledstep-growth polymerizations; and I will also describe someinteresting extensions that lead to the formation of polymernetworks and highly branched polymers.
ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS
Institute of Scientific and Technical Information of China (English)
O Hyong-chol; Ro Yong-hwa; Kil Won-gun
2005-01-01
A set of contraction maps of a metric space is called an iterated function systems.Iterated function systems with condensation can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.
Infinite Blueshift of Charged Null Particles
Mann, R. B.; Sajko, W. N.
1994-01-01
We demonstrate that charged null particles can be infinitely blue\\-shifted in a Kerr-Newman spacetime. The surface of infinite blueshift can be outside of the ergosphere in a Kerr-Newman spacetime, and outside of the outer event horizon for a Reissner-Nordstrom spacetime. Implications for extensions of the standard model which incorporate charged neutrinos are discussed.
Variational Infinite Hidden Conditional Random Fields
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja; Ghahramani, Zoubin
2015-01-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An Infinite hidden conditional random field is a hidden conditional random field with a countably infinite number of
Orthogonality preserving infinite dimensional quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Akın, Hasan [Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260 (Turkey); Mukhamedov, Farrukh [Department of Computational & Theoretical Sciences Faculty of Science, International Islamic University Malaysia P.O. Box, 141, 25710, Kuantan Pahang (Malaysia)
2015-09-18
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Understanding the Behaviour of Infinite Ladder Circuits
Ucak, C.; Yegin, K.
2008-01-01
Infinite ladder circuits are often encountered in undergraduate electrical engineering and physics curricula when dealing with series and parallel combination of impedances, as a part of filter design or wave propagation on transmission lines. The input impedance of such infinite ladder circuits is derived by assuming that the input impedance does…
Infinite Charge Algebra of Gravitational Instantons
Hoppe, J; Hoppe, Jens
1994-01-01
Using a formalism of minitwistors, we derive infinitely many conserved charges for the $sl(\\infty )$-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite dimensional algebra through the Poisson bracket which is isomorphic to two dimensional area preserving diffeomorphism with central extentions.
Envisioning the Infinite by Projecting Finite Properties
Ely, Robert
2011-01-01
We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…
Solving Infinite Kolam in Knot Theory
Ishimoto, Yukitaka
2007-01-01
In south India, there are traditional patterns of line-drawings encircling dots, called ``Kolam'', among which one-line drawings or the ``infinite Kolam'' provide very interesting questions in mathematics. For example, we address the following simple question: how many patterns of infinite Kolam can we draw for a given grid pattern of dots? The simplest way is to draw possible patterns of Kolam while judging if it is infinite Kolam. Such a search problem seems to be NP complete. However, it is certainly not. In this paper, we focus on diamond-shaped grid patterns of dots, (1-3-5-3-1) and (1-3-5-7-5-3-1) in particular. By using the knot-theory description of the infinite Kolam, we show how to find the solution, which inevitably gives a sketch of the proof for the statement ``infinite Kolam is not NP complete.'' Its further discussion will be given in the final section.
Infinite sets and double binds.
Arden, M
1984-01-01
There have been many attempts to bring psychoanalytical theory up to date. This paper approaches the problem by discussing the work of Gregory Bateson and Ignacio Matte-Blanco, with particular reference to the use made by these authors of Russell's theory of logical types. Bateson's theory of the double bind and Matte-Blanco's bilogic are both based on concepts of logical typing. It is argued that the two theories can be linked by the idea that neurotic symptoms are based on category errors in thinking. Clinical material is presented from the analysis of a middle-aged woman. The intention is to demonstrate that the process of making interpretations can be thought of as revealing errors in thinking. Changes in the patient's inner world are then seen to be the result of clarifying childhood experiences based on category errors. Matte-Blanco's theory of bilogic and infinite experiences is a re-evaluation of the place of the primary process in mental life. It is suggested that a combination of bilogic and double bind theory provides a possibility of reformulating psychoanalytical theory.
Collaborative Research: Polymeric Multiferroics
Energy Technology Data Exchange (ETDEWEB)
Ren, Shenqiang [Temple Univ., Philadelphia, PA (United States). College of Engineering
2017-04-20
The goal of this project is to investigate room temperature magnetism and magnetoelectric coupling of polymeric multiferroics. A new family of molecular charge-transfer crystals has been emerged as a fascinating opportunity for the development of all-organic electrics and spintronics due to its weak hyperfine interaction and low spin-orbit coupling; nevertheless, direct observations of room temperature magnetic spin ordering have yet to be accomplished in organic charge-transfer solids. Furthermore, room temperature magnetoelectric coupling effect hitherto known multiferroics, is anticipated in organic donor-acceptor complexes because of magnetic field effects on charge-transfer dipoles, yet this is also unexplored. The PI seeks to fundamental understanding of the control of organic crystals to demonstrate and explore room temperature multiferroicity. The experimental results have been verified through the theoretical modeling.
Studies on Epitaxial Polymerization of 1,3-Bis(3-quinolyl)-1,4-butadiyne
Institute of Scientific and Technical Information of China (English)
LI Tie-Sheng; Shuji Okada; Hachiro Nakanishi
2004-01-01
During investigating what causes the low yield of the polymerization product of 1,4-bis (quinolyl)-1, 3-butadiyne(DQ), we found that the DQ crystals formed on the surface of PDQ cauld be polymerized to give blue crystals, in which DQ could be sublimated and crystallized on the surface of PDQ film. According to the experimental results, the reason why the DQ crystals can be polymerized is that the sublimation of DQ changes the molecular orientation of DQ in the crystal. The crystals formed in epitaxial growth on the surface of DQ or PDQ during sublimation of DQ are suitable for 1,4-addition polymerization.
Institute of Scientific and Technical Information of China (English)
MEI Chong-Zhen; WANG Jian-Xu; SHAN Wen-Wen
2011-01-01
The title compound {[Cu（abpy）2]（H3bptc）·（H2O）}n, an ion-pair complex of [Cu（abpy）2]＋ with [（H3bptc）]- （abpy = 3,3＇-dimethyl-2,2＇-bipyridine and H4bptc = 1,1＇-biphenyl-2,2＇,3,3＇-tetracarboxylic acid）, has been synthesized by a hydrothermal reaction, and its structure was deter- mined by X-ray diffraction and characterized by elemental analysis and IR spectrum. The crystal is of triclinic, space group P1 with a = 8.4955（12）, b = 15.164（2）, c = 15.303（2）, α = 105.704（3）, β = 97.374（3）, γ = 96.764（3）o, CuC40H35N4O9, Mr = 779.26, V = 1857.9（4）3, Dc = 1.393 g/cm3, F（000） = 808, μ = 0.649 mm-1, S = 1.026 and Z = 2. The final R = 0.0493 and wR = 0.1034 for 4026 observed reflections with I 2σ（I）. The copper（I） coordination polymer demonstrates a 3-D sandwich-type structure containing 2-D double H3bptc-chain layers intercalated with the [Cu（abpy）2]＋ layers by extensive hydrogen bonding interactions.
Entropy exchange for infinite-dimensional systems
Duan, Zhoubo; Hou, Jinchuan
2017-01-01
In this paper the entropy exchange for channels and states in infinite-dimensional systems are defined and studied. It is shown that, this entropy exchange depends only on the given channel and the state. An explicit expression of the entropy exchange in terms of the state and the channel is proposed. The generalized Klein’s inequality, the subadditivity and the triangle inequality about the entropy including infinite entropy for the infinite-dimensional systems are established, and then, applied to compare the entropy exchange with the entropy change. PMID:28164995
Lyapunov exponents for infinite dimensional dynamical systems
Mhuiris, Nessan Mac Giolla
1987-01-01
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
Khalaji, Aliakbar Dehno; Peyghoun, Seyyed Javad; Akbari, Alireza; Feizi, Nourollah; Dusek, Michal; Eigner, Vaclav
2017-01-01
A new 1D polymeric three coordinated copper(I) complex, [Cu2(μ-(2,6-Cl-ba)2en)(μ-I)2]n, with the bidentate Schiff base ligand N,N‧-bis(2,6-dichlorobenzylidene)ethane-1,2-diamine containing a flexible spacer (dbnd NCH2sbnd CH2sbnd Ndbnd) was synthesized and characterized by elemental analyses, UV-Vis, FT-IR and 1H NMR spectroscopy and thermal analaysis. Its molecular structure was determined by single-crystal X-ray diffraction and shows the (2,6-Cl-ba)2en acts as a bis-monodentate bridging ligand forming the dinuclear [Cu2(μ-(2,6-Cl-ba)2en)] groups. Such dinuclear groups are bridged by two iodine anions [(μ-I)2] to form a 1D polymeric copper(I) complex. The copper(I) ions are coordinated in a distorted trigonal planar geometry by two I atoms and one nitrogen atom of Schiff base ligand (2,6-Cl-ba)2en.
Institute of Scientific and Technical Information of China (English)
蒋晓瑜; 陈文哲
2008-01-01
Three 2D sandwich-like layer heterometallic complexes, formulated as [Ln(idaH)M (ida>2]n·0.5nH2O,(H2ida=iminodiacetic acid, Ln=Nd, M=Co (1); Ln=La, M=Co (2); Ln=La, M=Ni (3)) have been synthesized underhydrothermal reaction condition and characterized by X-ray diffraction single-crystal structure analysis, IRspectroscopy, elemental analysis, TGA analysis, XPS techniques and magnetic analysis. The Ln atoms are ten-coordinated and linked up into chains by carboxylic oxygen atoms, which are engrafted by six-coordinated 3dtransition metal atoms on both sides to give rise to belt-like chains. The belt-like chains are linked up into 2Dnetwork by ida ligands and further extended into 3D open-framework by strong hydrogen-bond interactions.%水热法合成了3个层状异核金属化合物[Ln(idaH)M(ida)2]n·0.5nH2O,(H2ida=亚氨基二乙酸,Ln=Nd,M=Co(1);Ln=La,M=Co(2);Ln=La,M=Ni(3)).进行了晶体结构测定,红外光谱分析、能谱分析与磁性能分析.3个化合物除金属原子不同外具有相同的结构,其晶体都属于单斜晶系,C2/c空间群.单晶结构表明该结构含有由十配位的Ln通过羧基氧连接而成的链,六配位的3d金属(Co、Ni)交替地处在链的两边,形成了带状结构,带状链通过配体连成二维结构,通过氢键形成三维骨架.
Ha, Suk-Woo; Wintermantel, Erich; Maier, Gerhard
Der klinische Einsatz von synthetischen Polymeren begann in den 60-er Jahren in Form von Einwegartikeln, wie beispielsweise Spritzen und Kathetern, vor allem aufgrund der Tatsache, dass Infektionen infolge nicht ausreichender Sterilität der wiederverwendbaren Artikel aus Glas und metallischen Werkstoffen durch den Einsatz von sterilen Einwegartikeln signifikant reduziert werden konnten [1]. Die Einführung der medizinischen Einwegartikel aus Polymeren erfolgte somit nicht nur aus ökonomischen, sondern auch aus hygienischen Gründen. Wegen der steigenden Anzahl synthetischer Polymere und dem zunehmenden Bedarf an ärztlicher Versorgung reicht die Anwendung von Polymeren in der Medizin von preisgünstigen Einwegartikeln, die nur kurzzeitig intrakorporal eingesetzt werden, bis hin zu Implantaten, welche über eine längere Zeit grossen Beanspruchungen im menschlichen Körper ausgesetzt sind. Die steigende Verbreitung von klinisch eingesetzten Polymeren ist auf ihre einfache und preisgünstige Verarbeitbarkeit in eine Vielzahl von Formen und Geometrien sowie auf ihr breites Eigenschaftsspektrum zurückzuführen. Polymere werden daher in fast allen medizinischen Bereichen eingesetzt.
The energy operator for infinite statistics
Stanciu, Sonia
1992-01-01
We construct the energy operator for particles obeying infinite statistics defined by a q-deformation of the Heisenberg algebra. (This paper appeared published in CMP in 1992, but was not archived at the time.)
Astrosociology: Interwiews about an infinite universe
Høg, Erik
2014-01-01
If the universe is infinite now it has always been infinite. This is the opinion of many astronomers today as can be concluded from the following series of interviews, but the opinions differ much more than I had expected. Many astronomers do not have a clear opinion on this matter. Others have a clear opinion, but very different from the majority. Detailed arguments by two experts on general relativity are also included. Observations show that the universe is flat, i.e. the curvature is zero within the small uncertainty of measurements. This implies an infinite universe, though most probably we will never know that for certain. For comparison with the recent interviews, opinions during the past 2300 years since Aristotle about the universe being finite or infinite have been collected from literature, and it appears that the scientists often had quite definite opinions. \\c{opyright} Anita Publications. All rights reserved.
Convergence of Infinite Composition of Entire Functions
Kojima, Shota
2010-01-01
The purpose of the present article is to obtain the condition that the function defined by infinite composition of entire functions becomes an entire function. Moreover, as an example of such functions, we study a function called Poincare function.
PLANE INFINITE ANALYTICAL ELEMENT AND HAMILTONIAN SYSTEM
Institute of Scientific and Technical Information of China (English)
孙雁; 周钢; 刘正兴
2003-01-01
It is not convenient to solve those engineering problems defined in an infinitefield by using FEM. An infinite area can be divided into a regular infinite external area anda finite internal area. The finite internal area was dealt with by the FEM and the regularinfinite external area was settled in a polar coordinate. All governing equations weretransformed into the Hamiltonian system. The methods of variable separation andeigenfunction expansion were used to derive the stiffness matrix of a new infinite analyticalelement. This new element, like a super finite element, can be combined with commonlyused finite elements. The proposed method was verified by numerical case studies. Theresults show that the preparation work is very simple, the infinite analytical element has ahigh precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.
1-d gravity in infinite point distributions
Gabrielli, Andrea; Joyce, Michael; Sicard, Francois
2008-01-01
The dynamics of infinite, asymptotically uniform, distributions of self-gravitating particles in one spatial dimension provides a simple toy model for the analogous three dimensional problem. We focus here on a limitation of such models as treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e. the definition requires explicitly the breaking of statistical translational invariance). The ...
Importance Sampling for the Infinite Sites Model*
Hobolth, Asger; Uyenoyama, Marcy K; Wiuf, Carsten
2008-01-01
Importance sampling or Markov Chain Monte Carlo sampling is required for state-of-the-art statistical analysis of population genetics data. The applicability of these sampling-based inference techniques depends crucially on the proposal distribution. In this paper, we discuss importance sampling for the infinite sites model. The infinite sites assumption is attractive because it constraints the number of possible genealogies, thereby allowing for the analysis of larger data sets. We recall th...
INFINITELY VARIABLE TRANSMISSION USING FOUR BAR MECHANISM
Dr.N. ARUNKUMAR; Santhosh, R.; S. SUNIL SUBRAMANIAM
2014-01-01
Most of the continuously variable transmission systems in automobiles now-a-days are non-positive drives. This means that they cannot be used in heavy vehicles that require very high torque to be transmitted. This new type of infinitely variable transmission is aimed at transmitting high torques by making it a positive drive, thus making continuously variable transmission systems to be suitable for heavy vehicles. Infinitely variable transmission system and continuously variable transmissi...
Infinite Dimensional Differential Games with Hybrid Controls
Indian Academy of Sciences (India)
A J Shaiju; Sheetal Dharmatti
2007-05-01
A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the sense of Elliott–Kalton, we prove the existence of value and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities.
A NOVEL ELLIPSOIDAL ACOUSTIC INFINITE ELEMENT
Institute of Scientific and Technical Information of China (English)
YANG Rui-liang; WANG Hong-zhen
2005-01-01
A novel ellipsoidal acoustic infinite element is proposed. It is based a new pressure representation, which can describe and solve the ellipsoidal acoustic field more exactly. The shape functions of this novel acoustic infinite element are similar .to the Burnett's method, while the weight functions are defined as the product of the complex conjugates of the shaped functions and an additional weighting factor. The code of this method is cheap to generate as for 1-D element because only 1-D integral needs to be numerical. Coupling with the standard finite element, this method provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape. This novel method was deduced in brief and the conclusion was kept in detail. To test the feasibility of this novel method efficiently, in the examples the infinite elements were considered, excluding the finite elements relative. This novel ellipsoidal acoustic infinite element can deduce the analytic solution of an oscillating sphere. The example of a prolate spheroid shows that the novel infinite element is superior to the boundary element and other acoustic infinite elements. Analytical and numerical results of these examples show that this novel method is feasible.
Energy Technology Data Exchange (ETDEWEB)
Silva, M.D.P.; Silva, F.C. [Departamento de Química, CCET, Universidade Federal do Maranhão, 65085-580 São Luís, MA (Brazil); Sinfrônio, F.S.M. [Departamento de Engenharia Elétrica, CCET, Universidade Federal do Maranhão, 65085-580 São Luís, MA (Brazil); Paschoal, A.R. [Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, CE (Brazil); Silva, E.N. [Departamento de Física, CCET, Universidade Federal do Maranhão, 65085-580 São Luís, MA (Brazil); Paschoal, C.W.A., E-mail: paschoal@ufma.br [Departamento de Física, CCET, Universidade Federal do Maranhão, 65085-580 São Luís, MA (Brazil); Department of Materials Science and Engineering, University of California Berkeley, 94720-1760 Berkeley, CA (United States); Department of Physics, University of California Berkeley, 94720-7300 Berkeley, CA (United States)
2014-01-25
Highlights: • We synthesized mixed spinels by polymeric precursor method. • We investigated the structural and vibrational properties of the mixed. • We investigated the synthesis condition effects in these properties. • We proposed a complete phonon description for CuFe{sub 2}O{sub 4} and CoFe{sub 2}O{sub 4} spinels. -- Abstract: In this work Co–Cu mixed spinel Co{sub 1−x}Cu{sub x}Fe{sub 2}O{sub 4} powders were obtained by polymeric precursors method at several annealing temperatures between 700 and 1200 °C. The samples were characterized by means of X-ray powder diffraction, confirming the ideal inverse spinel structure for CoFe{sub 2}O{sub 4} sample and the tetragonal distorted inverse spinel structure for CuFe{sub 2}O{sub 4} sample. Based on FWHM evaluation, we estimated that crystallite sizes varies between 27 and 37 nm for the non-substituted samples. The optical-active modes were determined by infrared and Raman spectroscopies. The phonon spectra showed a local tetragonal distortion for mixed samples.
Kürkçüoğlu, Güneş Süheyla; Sayın, Elvan; Şahin, Onur
2015-12-01
Two cyanide bridged hetero-metallic complexes of general formula, [M(1,2-dmi)2Ni(μ-CN)4]n (1,2-dmi = 1,2-dimethylimidazole and M = Zn(II) or Cd(II)) have been synthesized and characterized by vibrational (FT-IR and Raman) spectroscopy, single crystal X-ray diffraction, thermal analyses and elemental analyses. The crystallographic analyses reveal that the complexes, [Zn(1,2-dmi)2Ni(μ-CN)4] (1) and [Cd(1,2-dmi)2Ni(μ-CN)4] (2), have polymeric 2D networks. In the complexes, four cyanide groups of [Ni(CN)4]2- coordinated to the adjacent M(II) ions and distorted octahedral geometries of complexes are completed by two nitrogen atoms of trans 1,2-dmi ligands. The structures of 1 and 2 are similar and linked via intermolecular hydrogen bonding, C-H⋯Ni interactions to give rise to 3D networks. Vibration assignments are given for all the observed bands and the spectral features also supported to the crystal structures of heteronuclear complexes. The FT-IR and Raman spectra of the complexes are very much consistent with the structural data presented.
Madhu, Sheri; Evans, Hayden A; Doan-Nguyen, Vicky V T; Labram, John G; Wu, Guang; Chabinyc, Michael L; Seshadri, Ram; Wudl, Fred
2016-07-04
We report the preparation and X-ray crystallographic characterization of the first crystalline homoatomic polymer chain, which is part of a semiconducting pyrroloperylene-iodine complex. The crystal structure contains infinite polyiodide I∞ (δ-) . Interestingly, the structure of iodine within the insoluble, blue starch-iodine complex has long remained elusive, but has been speculated as having infinite chains of iodine. Close similarities in the low-wavenumber Raman spectra of the title compound and starch-iodine point to such infinite polyiodide chains in the latter as well. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Shape Derivative of Energy Functional in an Infinite Elastic Strip with a Semi-Infinite Crack
Itou, Hiromichi; TANI, Atusi
2006-01-01
In this paper we study linear elasticity equations in an infinite elastic strip with a semi-infinite crack. We find the derivative of the energy functional as the crack shifts with an angle. Then we obtain the formula given by surface force and the angle.
Infinite Time Cellular Automata: A Real Computation Model
Givors, Fabien; Ollinger, Nicolas
2010-01-01
We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We then show how to simulate the canonical real computation model, BSS machines, with infinite time cellular automata in exactly \\omega steps.
Infinite Random Graphs as Statistical Mechanical Models
DEFF Research Database (Denmark)
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe...... a relation to the so-called uniform infinite tree and results on the Hausdorff and spectral dimension of two-dimensional space-time obtained in B. Durhuus, T. Jonsson, J.F. Wheater, J. Stat. Phys. 139, 859 (2010) are briefly outlined. For the latter we discuss results on the absence of spontaneous...... magnetization and argue that, in the generic case, the values of the Hausdorff and spectral dimension of the underlying infinite trees are not influenced by the coupling to an Ising model in a constant magnetic field (B. Durhuus, G.M. Napolitano, in preparation)...
Ising Model on an Infinite Ladder Lattice
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.
Infinite matrices and their recent applications
Shivakumar, P N; Zhang, Yang
2016-01-01
This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases. Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such ...
Caruso, Francesco; Martínez, Miguel A; Rossi, Miriam; Goldberg, Alexander; Chacón Villalba, M Elizabeth; Aymonino, Pedro J
2009-04-20
Lapachol (2-hydroxy-3-(3-methyl-2-butenyl)-1,4-naphtoquinone) (HLap, C(15)H(14)O(3)) reacts with Mn(2+) producing a novel polymeric complex with formula: [Mn(Lap)(2)](n). Two ligands chelate the metal through their ortho oxygen (O1, O2) moiety while two para oxygens, from other Lap ligands, complete the octahedral coordination sphere. Thus far, all reported Lap metal complexes are mononuclear, lack the metal-trans-quinonic (para) oxygen binding and have Lap as a bidentate ligand. Synthesis, X-ray diffraction, IR, and UV-visible spectroscopic properties, thermogravimetric analysis, and differential thermal analysis of this complex are reported along with a density functional theory study describing electron transfer from the Mn to the Lap ligand at low temperature. X-ray structure determinations at 125, 197, and 300 K describe the progressive trend of a Mn contribution to the Mn-O1 bond length as a function of T. The Mn-O1 bond distance increases with temperature and may be therefore associated with a semiquinonate action at low T by the carbonyl O1 donor (and corresponding to Mn(III)). It transforms to a more classical coordinative bond at room T and stabilizes a Mn(II) species; this is a reversible phenomenon involving Mn(II)-Mn(III) oxidation states.
Ryu, Minjoo; Lee, Young-A.; Jung, Ok-Sang
2017-09-01
A close insight into a systematic solvent-template effect on self-assembly of cadmium(II) chloride with new diallylbis(pyridin-4-yl)silane ligand (L) has been achieved. Each reaction gives rise to the 1: 2 composition of Cd(II): L, but shows significant solvent template effects on the formation of topology. The reaction in MeOH and in MeCN yields 1D loop chain, [CdCl2L2]·4MeOH and [CdCl2L2]·2MeCN, respectively, containing the solvate molecules whereas the same treatment in the relatively bulky solvents such as EtOH, n-PrOH, and i-PrOH yields interpenetrated 2D sheet, [CdCl2L2]. Their packing structures are also strongly depending on the nature of each solvent. Thus, construction and packing of each structure are determined by solvent templates rather than synthetic methodology. Solvate MeOH molecules of [CdCl2L2]·4MeOH crystals in MeCN media are perfectly exchanged to MeCN molecules and the solvate MeCN molecules of [CdCl2L2]·2MeCN crystals in MeOH media are exchanged into MeOH molecules as solvate, indicating that the solvate molecules do not interact significantly with the skeletal structures.
Das, Kinsuk; Konar, Saugata; Jana, Atanu; Barik, Anil Kumar; Roy, Sangita; Kar, Susanta Kumar
2013-03-01
The syntheses, crystal structures and photoluminescence properties of four new Cd(II) complexes are reported using strongly coordinating ligand 3,5-dimethyl-1-(2'-pyridyl) pyrazole (L) in presence of anionic ancillary bridging ligands as nitrite, chloride and dicyanamide. Among the complexes two (1 and 2) are monomeric, 3 is μ2 - chloro bridged dimer and the last one (4) is a mixed alternate chloro - end to end (EE) dicyanamide bridged 1D polymer. All the four complexes have been X-ray crystallographically characterized. The ligand L behaves as a potent bidentate neutral N, N donor. Geometrical diversity of Cd(II) complexes is due to no loss or gain of crystal field stability with the variation of geometry. Consequently the stability of a structure depends on steric requirements. The ligand L shows considerable fluorescence and all four complexes in methanol exhibit interesting photoluminescence properties with different emission intensities. The band maxima and fluorescence efficiency (in methanol) are found to be dependent on the coordination chromophore and structural rigidity induced by the incorporated Cd(II) ion. Among the synthesized complexes 1 exhibits the highest fluorescence intensity in methanol.
A survey of infinite time Turing machines
Hamkins, J.D.
2007-01-01
Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time, thereby providing a natural model of infinitary computability, with robust notions of computability and decidability on the reals, while remaining close to classical concepts of computabilit
SOME RESULTS ON INFINITE DIMENSIONAL NOVIKOV ALGEBRAS
Institute of Scientific and Technical Information of China (English)
赵玉凤; 孟道骥
2003-01-01
This paper gives some sufficient conditions for determining the simplicity of infinite di-mensional Novikov algebras of characteristic 0, and also constructs a class of simple Novikovalgebras by extending the base field. At last, the deformation theory of Novikov algebras isintroduced.
Infinite matrices, wavelet coefficients and frames
Directory of Open Access Journals (Sweden)
N. A. Sheikh
2004-01-01
Full Text Available We study the action of A on f∈L2(ℝ and on its wavelet coefficients, where A=(almjklmjk is a double infinite matrix. We find the frame condition for A-transform of f∈L2(ℝ whose wavelet series expansion is known.
Infinite-dimensional Hamiltonian Lie superalgebras
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.
A Planar Calculus for Infinite Index Subfactors
Penneys, David
2013-05-01
We develop an analog of Jones' planar calculus for II 1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.
Infinite Random Graphs as Statistical Mechanical Models
DEFF Research Database (Denmark)
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe...
Scattering for Infinite Dimensional Port Hamiltonian Systems
Macchelli, Alessandro; Stramigioli, Stefano; Schaft, Arjan van der; Melchiorri, Claudio
2002-01-01
In this paper, an introduction to scattering for infinite dimensional systems within the framework of port Hamiltonian system is presented. The classical results on wave propagation can be extended to generic power propagation phenomena, for example to fluid dynamics or flexible structures. The key-
Crichton ambiguities with infinitely many partial waves
Atkinson, D.; Kok, L.P.; Roo, M. de
1978-01-01
We construct families of spin less two-particle unitary cross sections that possess a nontrivial discrete phase-shift ambiguity, with in general an infinite number of nonvanishing partial waves. A numerical investigation reveals that some of the previously known finite Crichton ambiguities are
Polymerization shrinkage of flowable resin-based restorative materials
Stavridakis, Minos M; Dietschi, Didier; Krejci, Ivo
2005-01-01
This study measured the linear polymerization displacement and polymerization forces induced by polymerization shrinkage of a series of flowable resin-based restorative materials. The materials tested were 22 flowable resin-based restorative materials (Admira Flow, Aelite Flow, Aeliteflow LV, Aria, Crystal Essence, Definite Flow, Dyract Flow, Filtek Flow, FloRestore, Flow-it, Flow-Line, Freedom, Glacier, OmegaFlo, PermaFlo, Photo SC, Revolution 2, Star Flow, Synergy Flow, Tetric Flow, Ultrase...
MESO—STRUCTURED POLYMERIC HYDROGELS
Institute of Scientific and Technical Information of China (English)
Zhen-zhongYang; Jian-huaRong; DanLi
2003-01-01
Meso-structured(opal and inverse opal) polymeric hydrogels of varied morphology and composition were prepared by using two methods:post-modification of the template-synthesized structured polymers and templatepolymerization of functional monomers.A polyacrylic acid based inverse opal hydrogel was chosen to demonstrate its fast pH response by changing color,which is important in designing tunable photonic crystals.Template effects of the hydrogels on controlling structure of the template-synthesized inorganic materials were discussed.The catalytic effect of acid groups in the templates was emphasized for a preferential formation of TiO2 in the region containing acid groups,which allowed duplicating inorganic colloidal crystals from colloidal crystal hydrogels (or macroporous products from macroporous hydrogels) via one step duplication.
MESO-STRUCTURED POLYMERIC HYDROGELS
Institute of Scientific and Technical Information of China (English)
Zhen-zhong Yang; Jian-hua Rong; Dan Li
2003-01-01
Meso-structured (opal and inverse opal) polymeric hydrogels of varied morphology and composition were prepared by using two methods: post-modification of the template-synthesized structured polymers and templatepolymerization of functional monomers. A polyacrylic acid based inverse opal hydrogel was chosen to demonstrate its fast pH response by changing color, which is important in designing tunable photonic crystals. Template effects of the hydrogels on controlling structure of the template-synthesized inorganic materials were discussed. The catalytic effect of acid groups inthe templates was emphasized for a preferential formation of TiO2 in the region containing acid groups, which allowed duplicating inorganic colloidal crystals from colloidal crystal hydrogels (or macroporous products from macroporous hydrogels) via one step duplication.
A Syntactic Study on Bare Infinitive and Infinitival to
Institute of Scientific and Technical Information of China (English)
LIU Jing
2014-01-01
Infinitives which consist of bare infinitive and infinitival to are imperative in linguistic studies. And both of the two kinds of infinitives do not indicate person, tense and number. This research aims to analyze the properties, similarities and differ-ences between bare infinitive and infinitival to from the perspective of syntax. Thus, it enables us to attain a uniform characteriza-tion of the infinitival to and bare infinitive on the syntactic level and help us to understand these two kinds of infinitives better.
Approximate solutions to infinite dimensional LQ problems over infinite time horizon
Institute of Scientific and Technical Information of China (English)
PAN; Liping; ZHANG; Xu; CHEN; Qihong
2006-01-01
This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.
Conducting Polymeric Materials
DEFF Research Database (Denmark)
Hvilsted, Søren
2016-01-01
The overall objective of this collection is to provide the most recent developments within the various areas of conducting polymeric materials. The conductivity of polymeric materials is caused by electrically charged particles, ions, protons and electrons. Materials in which electrons...
Energy Technology Data Exchange (ETDEWEB)
Labeeb, A. [Liquid Crystal Institute, Chemical Physics Interdisciplinary Program, Kent State University, Kent, Ohio 44242 (United States); Microwave Physics and Dielectrics, National Research Center, Dokki 12622 (Egypt); Gleeson, H. F. [School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT (United Kingdom); Hegmann, T., E-mail: thegmann@kent.edu [Liquid Crystal Institute, Chemical Physics Interdisciplinary Program, Kent State University, Kent, Ohio 44242 (United States)
2015-12-07
The smectic C*-alpha (SmC{sub α}*) phase is one of the sub-phases of ferroelectric liquid crystals that has drawn much interest due to its electro-optical properties and ultrafast switching. Generally observed above the ferroelectric SmC* phase in temperature, the SmC{sub α}* commonly shows only very narrow phase temperature range of a few degree Celsius. To broaden the SmC{sub α}* phase, polymer stabilization was investigated for thermal phase stabilization. Two different reactive monomers were tested in three mixtures, and all three broadened the temperature range of the SmC{sub α}* phase from 3 °C to 39 °C. The current reversal method was used to determine the phase existence versus temperature. Moreover, the texture and network structure was studied by polarized optical microscopy and scanning electron microscopy, with the latter revealing the confinement of the smectic layer structure within the porous polymer network.
Smith, J V; Arnold, F P; Parsons, I; Lee, M R
1999-03-30
Catalysis at organophilic silica-rich surfaces of zeolites and feldspars might generate replicating biopolymers from simple chemicals supplied by meteorites, volcanic gases, and other geological sources. Crystal-chemical modeling yielded packings for amino acids neatly encapsulated in 10-ring channels of the molecular sieve silicalite-ZSM-5-(mutinaite). Calculation of binding and activation energies for catalytic assembly into polymers is progressing for a chemical composition with one catalytic Al-OH site per 25 neutral Si tetrahedral sites. Internal channel intersections and external terminations provide special stereochemical features suitable for complex organic species. Polymer migration along nano/micrometer channels of ancient weathered feldspars, plus exploitation of phosphorus and various transition metals in entrapped apatite and other microminerals, might have generated complexes of replicating catalytic biomolecules, leading to primitive cellular organisms. The first cell wall might have been an internal mineral surface, from which the cell developed a protective biological cap emerging into a nutrient-rich "soup." Ultimately, the biological cap might have expanded into a complete cell wall, allowing mobility and colonization of energy-rich challenging environments. Electron microscopy of honeycomb channels inside weathered feldspars of the Shap granite (northwest England) has revealed modern bacteria, perhaps indicative of Archean ones. All known early rocks were metamorphosed too highly during geologic time to permit simple survival of large-pore zeolites, honeycombed feldspar, and encapsulated species. Possible microscopic clues to the proposed mineral adsorbents/catalysts are discussed for planning of systematic study of black cherts from weakly metamorphosed Archaean sediments.
Representations of the infinite symmetric group
Borodin, Alexei
2016-01-01
Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. Complete with detailed proofs, as well as numerous examples and exercises which help to summarize recent developments in the field, this book will enable graduates to enhance their understanding of the topic, while also aiding lecturers and researchers in related areas.
Infinite volume suppression versus quantum fluctuations
Kartavtsev, Alexander
2014-01-01
It is routinely argued that tunneling of the Higgs field along the minimum of the Mexican hat potential is suppressed by the infinite space volume. In the path integral formalism this conclusion is drawn from the analysis of paths on which the field is homogeneous in the whole infinite space. Here we demonstrate that this approach fails to reproduce vacuum properties of even the simplest systems like free real scalar field. On the other hand, adding also the contributions of inhomogeneous field configurations we obtain for the free field the established results. This casts some doubt on the conclusions drawn for the Higgs field using the `homogeneous paths' approach and might call for a careful reanalysis of the mechanism of spontaneous symmetry breaking in quantum field theory.
The Recursion Theorem and Infinite Sequences
Miller, Arnold W
2008-01-01
In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. such that W_{e_n}={e_{n+1}} for every n. Similarly, we prove that there exists an increasing sequence such that W_{e_n}={e_{n+1},e_{n+2},...} for every n. We call a nonempty computably enumerable set A self-constructing if W_e=A for every e in A. We show that every nonempty computable enumerable set which is disjoint from an infinite computable set is one-one equivalent to a self-constructing set
Infinite Chiral Symmetry in Four Dimensions
Beem, Christopher; Liendo, Pedro; Peelaers, Wolfger; Rastelli, Leonardo; van Rees, Balt C
2015-01-01
We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. The meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four-dimensional theory. Infinite chiral symmetry has far-reaching consequences for the spectral data, correlation functions, and central charges of any four-dimensional theory with ${\\mathcal N}=2$ superconformal symmetry.
Infinite Products of Random Isotropically Distributed Matrices
Il'yn, A S; Zybin, K P
2016-01-01
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
Infinite Products of Random Isotropically Distributed Matrices
Il'yn, A. S.; Sirota, V. A.; Zybin, K. P.
2017-01-01
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
Properties of the extremal infinite smooth words
Directory of Open Access Journals (Sweden)
Srecko Brlek
2007-05-01
Full Text Available Smooth words are connected to the Kolakoski sequence. We construct the maximal and the minimal infinite smooth words, with respect to the lexicographical order. The naive algorithm generating them is improved by using a reduction of the De Bruijn graph of their factors. We also study their Lyndon factorizations. Finally, we show that the minimal smooth word over the alphabet {1,3} belongs to the orbit of the Fibonacci word.
ON THE GROWTH OF INFINITE ORDER DIRICHLET SERIES
Institute of Scientific and Technical Information of China (English)
陈特为; 孙道椿
2003-01-01
In this paper, the property of infinite order Dirichlet series in the half-plane areinvestigated. The more exact growth of infinite order Dirichlet series is obtained withoutusing logarithm argument to the type-function for the first time.
Esfandiari, N Melody; Blum, Suzanne A
2011-11-16
A high-sensitivity and high-resolution single-particle fluorescence microscopy technique differentiated between homogeneous and heterogeneous metathesis polymerization catalysis by imaging the location of the early stages of polymerization. By imaging single polymers and single crystals of Grubbs II, polymerization catalysis was revealed to be solely homogeneous rather than heterogeneous or both.
Fidelity of states in infinite dimensional quantum systems
Hou, Jinchuan
2011-01-01
In this paper we discuss the fidelity of states in infinite dimensional systems, give an elementary proof of the infinite dimensional version of Uhlmann's theorem, and then, apply it to generalize several properties of the fidelity from finite dimensional case to infinite dimensional case. Some of them are somewhat different from those for finite dimensional case.
The nominalized infinitive in French: structure and change
Sleeman, P.
2010-01-01
Many European languages have both nominal and verbal nominalized infinitives. They differ, however, in the degree to which the nominalized infinitives possess nominal and verbal properties. In this paper, nominalized infinitives in French are analyzed. It is shown that, whereas Old French was like o
The Great Celestial Numbers - The Infinitely Big and The Infinitely Small
Teodorani, M.
2009-11-01
This book is a travel that brings the reader to penetrate dimensionally the infinitely small and the infinitely large in the Universe, ranging from quarks to galaxies, and to compare these extreme numbers with the numbers that people encounters in normal life here on Earth. Several numerical examples are illustrated all over the text in a sort of scientific orienteering that describes dimensionally the realms of space, time and energy. The last part of the book shows how all spatial and temporal dimensions disappear when the mechanism of quantum entanglement is considered.
Risk Bounds for Infinitely Divisible Distribution
Zhang, Chao
2012-01-01
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation inequalities, we obtain the risk bounds based on the covering number for the ID distribution. Finally, we analyze the asymptotic convergence of the risk bound derived from one of the two deviation inequalities and show that the convergence rate of the bound is faster than the result for the generic i.i.d. empirical process (Mendelson, 2003).
RESONANCE RADIATION OF SUBMERGED INFINITE CYLINDRICAL SHELL
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The resonance sound radiation from submerged infinite elastic cylindrical shell, excited by internal harmonic line force, is investigated. The shell radiation power is presented in terms of resonant modal radiation derived from resonance radiation theory (RRT). The resonance radiation formulae are derived from classical Rayleigh normal mode solution, which are useful for understanding the mechanism of sound radiation from submerged shells. As an example, numerical calculation of a thin steel cylindrical shell is done by using these two methods. It seems that the results of RRT solutions are in good agreement with that of Rayleigh normal mode solutions.
Black di-ring and infinite nonuniqueness
Iguchi, H; Iguchi, Hideo; Mishima, Takashi
2007-01-01
We show that the $S^1$-rotating black rings can be superposed by the solution generating technique. We analyze the black di-ring solution for the simplest case of multiple rings. There exists an equilibrium black di-ring where the conical singularities are cured by the suitable choice of physical parameters. Also there are infinite numbers of black di-rings with the same mass and angular momentum. These di-rings can have two different continuous limits of single black rings. Therefore we can transform the fat black ring to the thin ring with the same mass and angular momentum by way of the di-ring solutions.
Infinite systolic groups are not torsion
Prytuła, Tomasz
2014-01-01
We study k-systolic complexes introduced by T. Januszkiewicz and J. \\'Swi\\k{a}tkowski, which are simply connected simplicial complexes of simplicial nonpositive curvature. Using techniques of filling diagrams we prove that for k > 6 the 1-skeleton of a k-systolic complex is Gromov hyperbolic. We give an elementary proof of so-called Projection Lemma, which implies contractibility of 6-systolic complexes. We also prove that an infinite group acting geometrically on a 6-systolic complex is not ...
Kuramoto model for infinite graphs with kernels
Canale, Eduardo
2015-01-07
In this paper we study the Kuramoto model of weakly coupled oscillators for the case of non trivial network with large number of nodes. We approximate of such configurations by a McKean-Vlasov stochastic differential equation based on infinite graph. We focus on circulant graphs which have enough symmetries to make the computations easier. We then focus on the asymptotic regime where an integro-partial differential equation is derived. Numerical analysis and convergence proofs of the Fokker-Planck-Kolmogorov equation are conducted. Finally, we provide numerical examples that illustrate the convergence of our method.
Approximation of the semi-infinite interval
Directory of Open Access Journals (Sweden)
A. McD. Mercer
1980-01-01
Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.
Dynamics for QCD on an infinite lattice
Grundling, Hendrik
2015-01-01
We prove the existence of the dynamics automorphism group for Hamiltonian QCD on an infinite lattice in R^3, and this is done in a C*-algebraic context. The existence of ground states is also obtained. Starting with the finite lattice model for Hamiltonian QCD developed by Kijowski and Rudolph, we state its field algebra and a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e. algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. On a suitably large C*-algebra acting on this Hilbert space, and containing all the local algebras, we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. We then take as our field algebra the C*-algebra generated by all the orbits of ...
Rigid rod anchored to infinite membrane.
Guo, Kunkun; Qiu, Feng; Zhang, Hongdong; Yang, Yuliang
2005-08-15
We investigate the shape deformation of an infinite membrane anchored by a rigid rod. The density profile of the rod is calculated by the self-consistent-field theory and the shape of the membrane is predicted by the Helfrich membrane elasticity theory [W. Helfrich, Z. Naturforsch. 28c, 693 (1973)]. It is found that the membrane bends away from the rigid rod when the interaction between the rod and the membrane is repulsive or weakly attractive (adsorption). However, the pulled height of the membrane at first increases and then decreases with the increase of the adsorption strength. Compared to a Gaussian chain with the same length, the rigid rod covers much larger area of the membrane, whereas exerts less local entropic pressure on the membrane. An evident gap is found between the membrane and the rigid rod because the membrane's curvature has to be continuous. These behaviors are compared with that of the flexible-polymer-anchored membranes studied by previous Monte Carlo simulations and theoretical analysis. It is straightforward to extend this method to more complicated and real biological systems, such as infinite membrane/multiple chains, protein inclusion, or systems with phase separation.
Some new approaches to infinite divisibility
Sapatinas, Theofanis; Gupta, Arjun K
2011-01-01
Using an approach based, amongst other things, on Proposition 1 of Kaluza (1928), Goldie (1967) and, using a different approach based especially on zeros of polynomials, Steutel (1967) have proved that each nondegenerate distribution function (d.f.) $F$ (on $\\RR$, the real line), satisfying $F(0-) = 0$ and $F(x) = F(0) + (1-F(0)) G(x)$, $x > 0$, where $G$ is the d.f. corresponding to a mixture of exponential distributions, is infinitely divisible. Indeed, Proposition 1 of Kaluza (1928) implies that any nondegenerate discrete probability distribution ${p_x: x= 0,1, ...}$ that is log-convex or, in particular, completely monotone, is compound geometric, and, hence, infinitely divisible. Steutel (1970), Shanbhag & Sreehari (1977) and Steutel & van Harn (2004, Chapter VI) have given certain extensions or variations of one or more of these results. Following a modified version of the C.R. Rao et al. (2009, Section 4) approach based on the Wiener-Hopf factorization, we establish some further results of signi...
Polymerization Using Phosphazene Bases
Zhao, Junpeng
2015-09-01
In the recent rise of metal-free polymerization techniques, organic phosphazene superbases have shown their remarkable strength as promoter/catalyst for the anionic polymerization of various types of monomers. Generally, the complexation of phosphazene base with the counterion (proton or lithium cation) significantly improves the nucleophilicity of the initiator/chain end resulting in highly enhanced polymerization rates, as compared with conventional metalbased initiating systems. In this chapter, the general features of phosphazenepromoted/catalyzed polymerizations and the applications in macromolecular engineering (synthesis of functionalized polymers, block copolymers, and macromolecular architectures) are discussed with challenges and perspectives being pointed out.
Computational simulation of wave propagation problems in infinite domains
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper deals with the computational simulation of both scalar wave and vector wave propagation problems in infinite domains. Due to its advantages in simulating complicated geometry and complex material properties, the finite element method is used to simulate the near field of a wave propagation problem involving an infinite domain. To avoid wave reflection and refraction at the common boundary between the near field and the far field of an infinite domain, we have to use some special treatments to this boundary. For a wave radiation problem, a wave absorbing boundary can be applied to the common boundary between the near field and the far field of an infinite domain, while for a wave scattering problem, the dynamic infinite element can be used to propagate the incident wave from the near field to the far field of the infinite domain. For the sake of illustrating how these two different approaches are used to simulate the effect of the far field, a mathematical expression for a wave absorbing boundary of high-order accuracy is derived from a two-dimensional scalar wave radiation problem in an infinite domain, while the detailed mathematical formulation of the dynamic infinite element is derived from a two-dimensional vector wave scattering problem in an infinite domain. Finally, the coupled method of finite elements and dynamic infinite elements is used to investigate the effects of topographical conditions on the free field motion along the surface of a canyon.
Organometallic Polymeric Conductors
Youngs, Wiley J.
1997-01-01
over 150 days in air at ambient temperature. The conductivity of the films dropped only half an order of magnitude in that time. Films aged under vacuum at ambient temperature diminished slightly in conductivity in the first day, but did not change thereafter. An experimental design approach will be applied to maximize the efficiency of the laboratory effort. The material properties (initial and long term) will also be monitored and assessed. The experimental results will add to the existing database for electrically conductive polymer materials. Attachments: 1) Synthesis Crystal Structure, and Polymerization of 1,2:5,6:9,10-Tribenzo-3,7,11,13-tetradehydro(14) annulene. 2) Reinvestigation of the Photocyclization of 1,4-Phenylene Bis(phenylmaleic anhydride): Preparation and Structure of (5)Helicene 5,6:9,10-Dianhydride. 3) Preparation and Structure Charecterization of a Platinum Catecholate Complex Containing Two 3-Ethynyltheophone Groups. and 4) Rigid-Rod Polymers Based on Noncoplanar 4,4'-Biphenyldiamines: A Review of Polymer Properties vs Configuration of Diamines.
Semi-infinite programming recent advances
López, Marco
2001-01-01
Semi-infinite programming (SIP) deals with optimization problems in which either the number of decision variables or the number of constraints is finite This book presents the state of the art in SIP in a suggestive way, bringing the powerful SIP tools close to the potential users in different scientific and technological fields The volume is divided into four parts Part I reviews the first decade of SIP (1962-1972) Part II analyses convex and generalised SIP, conic linear programming, and disjunctive programming New numerical methods for linear, convex, and continuously differentiable SIP problems are proposed in Part III Finally, Part IV provides an overview of the applications of SIP to probability, statistics, experimental design, robotics, optimization under uncertainty, production games, and separation problems Audience This book is an indispensable reference and source for advanced students and researchers in applied mathematics and engineering
On infinitely cohomologous to zero observables
de Lima, Amanda
2009-01-01
We show that for a large class of piecewise expanding maps T, the bounded p-variation observables u_0 that admits an infinite sequence of bounded p-variation observables u_i satisfying u_i(x)= u_{i+1}(Tx) -u_{i+1}(x) are constant. The method of the proof consists in to find a suitable Hilbert basis for L^2(hm), where hm is the unique absolutely continuous invariant probability of T. In terms of this basis, the action of the Perron-Frobenious and the Koopan operator on L^2(hm) can be easily understood. This result generalizes earlier results by Bamon, Kiwi, Rivera-Letelier and Urzua in the case T(x)= n x mod 1, n in N-{0,1} and Lipchitizian observables u_0.
Generating functions attached to some infinite matrices
Monsky, Paul
2009-01-01
Let V be an infinite matrix with rows and columns indexed by the positive integers, and entries in a field F. Suppose that v_{i,j} only depends on i-j and is 0 for |i-j| large. Then V^n is defined for all n, and one has a "generating function" G=\\sum a_{1,1}(V^n)z^n. Ira Gessel has shown that G is algebraic over F(z). We extend his result, allowing v_{i,j} for fixed i-j to be eventually periodic in i rather than constant. This result and some variants of it that we prove will have applications to Hilbert-Kunz theory.
Rhim, Won-Kyu; Hyson, Michael T.; Chung, Sang-Kun; Colvin, Michael S.; Chang, Manchium
1989-01-01
Combination of advanced techniques yields uniform particles for biomedical applications. Process combines ink-jet and irradiation/freeze-polymerization techniques to make polymeric microspheres of uniform size in diameters from 100 to 400 micrometer. Microspheres used in chromatography, cell sorting, cell labeling, and manufacture of pharmaceutical materials.
Infinite sequences of $p$-groups with fixed coclass
Eick, Bettina
2010-01-01
Eick & Leedham-Green sketched a construction for infinite sequences of finite $p$-groups with fixed coclass. These infinite sequences have turned out to be very useful in the theory of finite $p$-groups. We exhibit a detailed description for the construction of the finite sequences and we determine presentations for the infinite sequences for the primes and coclasses $(2,1)$, $(2,2)$ and $(3,1)$.
Dimension free and infinite variance tail estimates on Poisson space
Breton, J. C.; Houdré, C.; Privault, N.
2004-01-01
Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic Wiener functionals, including L\\'evy's stochastic area and the square norm of Brownian paths. In the infinite vari...
Dynamics for QCD on an Infinite Lattice
Grundling, Hendrik; Rudolph, Gerd
2017-02-01
We prove the existence of the dynamics automorphism group for Hamiltonian QCD on an infinite lattice in R^3, and this is done in a C*-algebraic context. The existence of ground states is also obtained. Starting with the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph (cf. J Math Phys 43:1796-1808 [15], J Math Phys 46:032303 [16]), we state its field algebra and a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e., kinematics algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. On a suitably large C*-algebra acting on this Hilbert space, and containing all the local algebras, we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. We then take as our field algebra the C*-algebra generated by all the orbits of the local algebras w.r.t. the global time evolution. Thus the time evolution creates the field algebra. The time evolution is strongly continuous on this choice of field algebra, though not on the original larger C*-algebra. We define the gauge transformations, explain how to enforce the Gauss law constraint, show that the dynamics automorphism group descends to the algebra of physical observables and prove that gauge invariant ground states exist.
Applied bioactive polymeric materials
Carraher, Charles; Foster, Van
1988-01-01
The biological and biomedical applications of polymeric materials have increased greatly in the past few years. This book will detail some, but not all, of these recent developments. There would not be enough space in this book to cover, even lightly, all of the major advances that have occurred. Some earlier books and summaries are available by two of this book's Editors (Gebelein & Carraher) and these should be consul ted for additional information. The books are: "Bioactive Polymeric Systems" (Plenum, 1985); "Polymeric Materials In Medication" (Plenum, 1985); "Biological Acti vi ties of Polymers" (American Chemical Society, 1982). Of these three, "Bioacti ve Polymeric Systems" should be the most useful to a person who is new to this field because it only contains review articles written at an introductory level. The present book primarily consists of recent research results and applications, with only a few review or summary articles. Bioactive polymeric materials have existed from the creation of life...
Infinite-Dimensional Linear Dynamical Systems with Chaoticity
Fu Xin Chu; Fu, Xin-Chu; Duan, Jinqiao
1998-01-01
The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fréchet space. The other is about the chaoticity of a translation map in the space of real continuous functions. The chaos is shown in the senses of both Li-Yorke and Wiggins. Treating dimensions as freedoms, the two results imply that in the case of an infinite number of freedoms, a system may exhibit complexity even when the action is linear. Finally, the authors discuss physical applications of infinite-dimensional linear chaotic dynamical systems.
Semantic coherence in English accusative-with-bare-infinitive constructions
DEFF Research Database (Denmark)
Jensen, Kim Ebensgaard
2013-01-01
Drawing on usage-based cognitively oriented construction grammar, this paper investigates the patterns of coattraction of items that appear in the two VP positions (the VP in the matrix clause, and the VP in the infinitive subordinate clause) in the English accusative-with-bare-infinitive constru......Drawing on usage-based cognitively oriented construction grammar, this paper investigates the patterns of coattraction of items that appear in the two VP positions (the VP in the matrix clause, and the VP in the infinitive subordinate clause) in the English accusative...... relations of English accusatives-with-bare-infinitives through the relations of semantic coherence between the two VPs....
Conduction heat transfer in semi-infinite and infinite regions with discrete heat sources
Energy Technology Data Exchange (ETDEWEB)
Venkataraman, Nellore S.; Castillo, Omar E. Meza [Puerto Rico Univ., Dept. of Mechanical Engineering, Mayaguez (Puerto Rico)
2006-01-15
The steady state temperature distribution in semi-infinite slabs and infinite quadrants due to two- and three-dimensional discrete heating sources shaped in the form of thin electric current carrying wires has been determined. The temperature field is obtained using Green's function integral techniques. The solutions obtained here are compared with numerical solutions obtained from a commercial software package. It is shown that for the cases considered here we get closed form solutions or solutions in the form of simple numerically calculable integrals which are far superior to numerical methods in terms of elegance and labor involved for parametric studies. The behavior of the non-dimensional temperature with the various relevant parameters is discussed. (Author)
Pang, Yu; Liu, Yu-Shan; Liu, Jin-Xi; Feng, Wen-Jie
2016-04-01
In this paper, SH bulk/surface waves propagating in the corresponding infinite/semi-infinite piezoelectric (PE)/piezomagnetic (PM) and PM/PE periodically layered composites are investigated by two methods, the stiffness matrix method and the transfer matrix method. For a semi-infinite PE/PM or PM/PE medium, the free surface is parallel to the layer interface. Both PE and PM materials are assumed to be transversely isotropic solids. Dispersion equations are derived by the stiffness/transfer matrix methods, respectively. The effects of electric-magnetic (ME) boundary conditions at the free surface and the layer thickness ratios on dispersion curves are considered in detail. Numerical examples show that the results calculated by the two methods are the same. The dispersion curves of SH surface waves are below the bulk bands or inside the frequency gaps. The ratio of the layer thickness has an important effect not only on the bulk bands but also on the dispersion curves of SH surface waves. Electric and magnetic boundary conditions, respectively, determine the dispersion curves of SH surface waves for the PE/PM and PM/PE semi-infinite structures. The band structures of SH bulk waves are consistent for the PE/PM and PM/PE structures, however, the dispersive behaviors of SH surface waves are indeed different for the two composites. The realization of the above-mentioned characteristics of SH waves will make it possible to design PE/PM acoustic wave devices with periodical structures and achieve the better performance.
Optical Properties of the Self-Assembling Polymeric Colloidal Systems
Directory of Open Access Journals (Sweden)
Alexandra Mocanu
2013-01-01
Full Text Available In the last decade, optical materials have gained much interest due to the high number of possible applications involving path or intensity control and filtering of light. The continuous emerging technology in the field of electrooptical devices or medical applications allowed the development of new innovative cost effective processes to obtain optical materials suited for future applications such as hybrid/polymeric solar cells, lasers, polymeric optical fibers, and chemo- and biosensing devices. Considering the above, the aim of this review is to present recent studies in the field of photonic crystals involving the use of polymeric materials.
The core and related solution concepts for infinite assignment games
Llorca, Natividad; Sanchez-Soriano, Joaquin; Tijs, Stef; Timmer, Judith B.
2004-01-01
Assignment problems where both sets of agents that have to be matched are countably infinite, the so-called infinite assignment problems, are studied as well as the related cooperative assignment games. Further, several solution concepts for these assignment games are studied. The first one is the
On the geometry and arithmetic of infinite translation surfaces
Valdez, Ferrán
2011-01-01
We prove by constructing explicit examples that most of the classical results for number fields associated to flat surfaces fail in the realm of infinite type translation surfaces. We also investigate the relations among this fields and give a characterization for infinite type Origamis.
Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
Directory of Open Access Journals (Sweden)
Luigi Accardi
2009-05-01
Full Text Available The present paper reviews some intriguing connections which link together a new renormalization technique, the theory of *-representations of infinite dimensional *-Lie algebras, quantum probability, white noise and stochastic calculus and the theory of classical and quantum infinitely divisible processes.
Solving semi-infinite optimization problems with interior point techniques
Stein, Oliver; Still, Georg
2003-01-01
We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads
A copositive formulation for the stability number of infinite graphs
Dobre, Cristian; Dür, Mirjam; Frerick, Leonhard; Vallentin, Frank
2016-01-01
In the last decade, copositive formulations have been proposed for a variety of combinatorial optimization problems, for example the stability number (independence number). In this paper, we generalize this approach to infinite graphs and show that the stability number of an infinite graph is the
STABILITY OF GENERALIZED JACKSON NETWORKS WITH INFINITE SUPPLY OF WORK
Institute of Scientific and Technical Information of China (English)
Yongjiang GUO
2008-01-01
A general Jackson network (GJN) with infinite supply of work is considered. By fluid limit model, the author finds that the Markov process describing the dynamics of the GJN with infinite supply of work is positive Harris recurrent if the corresponding fluid model is stable. Furthermore, the author proves that the fluid model is stable if the usual traffic condition holds.
Infinite-dimensional dynamical systems in mechanics and physics
Temam, Roger
1997-01-01
In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology This second edition has been updated and extended
Generalized semi-infinite programming: Theory and methods
Still, G.
1999-01-01
Generalized semi-infinite optimization problems (GSIP) are considered. The difference between GSIP and standard semi-infinite problems (SIP) is illustrated by examples. By applying the `Reduction Ansatz', optimality conditions for GSIP are derived. Numerical methods for solving GSIP are considered i
Solving semi-infinite optimization problems with interior point techniques
Stein, Oliver; Still, Georg J.
2003-01-01
We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads
A copositive formulation for the stability number of infinite graphs
Dobre, Cristian; Dür, Mirjam; Frerick, Leonhard; Vallentin, Frank
2016-01-01
In the last decade, copositive formulations have been proposed for a variety of combinatorial optimization problems, for example the stability number (independence number). In this paper, we generalize this approach to infinite graphs and show that the stability number of an infinite graph is the
An infinite-dimensional weak KAM theory via random variables
Gomes, Diogo A.
2016-08-31
We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables\\' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.
Semantic coherence in English accusative-with-bare-infinitive constructions
DEFF Research Database (Denmark)
Jensen, Kim Ebensgaard
2013-01-01
Drawing on usage-based cognitively oriented construction grammar, this paper investigates the patterns of coattraction of items that appear in the two VP positions (the VP in the matrix clause, and the VP in the infinitive subordinate clause) in the English accusative-with-bare-infinitive constru......Drawing on usage-based cognitively oriented construction grammar, this paper investigates the patterns of coattraction of items that appear in the two VP positions (the VP in the matrix clause, and the VP in the infinitive subordinate clause) in the English accusative......-with-bare-infinitive construction. The main methodological framework is that of covarying collexeme analysis, which, through statistical corpus analysis, allows for the analyst to address the semantics of a construction. Using this method on data from the BNC, the ultimate purpose of the paper is to address the underlying semantic...... relations of English accusatives-with-bare-infinitives through the relations of semantic coherence between the two VPs....
Nonanalyticities of entropy functions of finite and infinite systems.
Casetti, Lapo; Kastner, Michael
2006-09-08
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems. The relation between finite and infinite system nonanalyticities is illustrated by means of a simple classical spinlike model which is exactly solvable for both finite and infinite system sizes, showing a phase transition in the latter case. The microcanonical entropy is found to have exactly one nonanalytic point in the interior of its domain. For all finite system sizes, this point is located at the same fixed energy value epsilon(c)(finite), jumping discontinuously to a different value epsilon(c)(infinite) in the thermodynamic limit. Remarkably, epsilon(c)(finite) equals the average potential energy of the infinite system at the phase transition point. The result indicates that care is required when trying to infer infinite system properties from finite system nonanalyticities.
Coupled Cluster studies of infinite nuclear matter
Baardsen, G; Hagen, G; Hjorth-Jensen, M
2013-01-01
The aim of this work is to develop the relevant formalism for performing Coupled Cluster calculations in nuclear matter and neutron star matter, including thereby important correlations to infinite order in the interaction and testing modern nuclear forces based on chiral effective field theory. Our formalism includes the exact treatment of the so-called Pauli operator in a partial wave expansion of the equation of state. Nuclear and neutron matter calculations are done using a coupled particle-particle and hole-hole ladder approximation. The coupled ladder equations are derived as an approximation of CC theory, leaving out particle-hole and non-linear diagrams from the CC doubles amplitude equation. This study is a first step toward CC calculations for nuclear and neutron matter. We present results for both symmetric nuclear matter and pure neutron matter employing state-of-the-art nucleon-nucleon interactions based on chiral effective field theory. We employ also the newly optimized chiral interaction [A. E...
Many-body localization in infinite chains
Enss, T.; Andraschko, F.; Sirker, J.
2017-01-01
We investigate the phase transition between an ergodic and a many-body localized phase in infinite anisotropic spin-1 /2 Heisenberg chains with binary disorder. Starting from the Néel state, we analyze the decay of antiferromagnetic order ms(t ) and the growth of entanglement entropy Sent(t ) during unitary time evolution. Near the phase transition we find that ms(t ) decays exponentially to its asymptotic value ms(∞ ) ≠0 in the localized phase while the data are consistent with a power-law decay at long times in the ergodic phase. In the localized phase, ms(∞ ) shows an exponential sensitivity on disorder with a critical exponent ν ˜0.9 . The entanglement entropy in the ergodic phase grows subballistically, Sent(t ) ˜tα , α ≤1 , with α varying continuously as a function of disorder. Exact diagonalizations for small systems, on the other hand, do not show a clear scaling with system size and attempts to determine the phase boundary from these data seem to overestimate the extent of the ergodic phase.
Ordered groups and infinite permutation groups
1996-01-01
The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that t...
Polymeric bicontinuous microemulsions
DEFF Research Database (Denmark)
Bates, F.S.; Maurer, W.W.; Lipic, P.M.
1997-01-01
High molecular weight block copolymers can be viewed as macromolecular surfactants when blended with thermodynamically incompatible homopolymers. This Letter describes the formation of polymeric bicontinuous microemulsions in nurtures containing a model diblock copolymer and two homopolymers...
Peinemann, Klaus-Viktor
2015-01-22
The present application offers a solution to the current problems associated with recovery and recycling of precious metals from scrap material, discard articles, and other items comprising one or more precious metals. The solution is premised on a microporous chelating polymeric membrane. Embodiments include, but are not limited to, microporous chelating polymeric membranes, device comprising the membranes, and methods of using and making the same.
Structural stability of infinite- layer CaCuO2 under high pressure
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
In situ high-pressure energy dispersive X-ray diffraction measurements on polycrystalline powder CaCuO2 with an infinite layer structure (IL CaCuO2) have been performed by using diamond anvil cell (DAC) instrument with synchrotron radiation. The results suggest that the crystal structure of IL CaCuO2 is stable under pressure up to 30 GPa at room temperature. According to Birch-Murn- aghan equation of state, assuming pressure derivative the bulk modulus B0=181 ± 9 GPa is obtained.
Elcoro, Luis; Etxebarria, Jesus
2011-01-01
The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used…
From infinite ergodic theory to number theory (and possibly back)
Energy Technology Data Exchange (ETDEWEB)
Isola, Stefano, E-mail: stefano.isola@unicam.it [Dipartimento di Matematica e Informatica, Universita di Camerino, via Madonna delle Carceri, I-62032 Camerino (Italy)
2011-07-15
Highlights: > Systems preserving an infinite measure need new indicators such as the wandering rate. > Coping wild behaviour of the ergodic sums with very good sets and universal sequences. > Applications to Farey map and slow convergents in continued fractions theory. - Abstract: Some basic facts of infinite ergodic theory are reviewed in a form suitable to be applied to interval maps with number theoretic significance such as the Farey map. This is an enlarged version of the lecture notes accompanying a short course on Infinite Ergodic Theory at the First meeting of the (mostly) young italian hyperbolicians (Corinaldo, Italy, June 8-12, 2009).
About the Infinite Repetition of Histories in Space
Directory of Open Access Journals (Sweden)
Manuel Alfonseca
2014-08-01
Full Text Available This paper analyzes two different proposals, one by Ellis and Brundrit, based on classical relativistic cosmology, the other by Garriga and Vilenkin, based on the DH interpretation of quantum mechanics, both concluding that, in an infinite universe, planets and beings must be repeated an infinite number of times. We point to possible shortcomings in these arguments. We conclude that the idea of an infinite repetition of histories in space cannot be considered strictly speaking a consequence of current physics and cosmology. Such ideas should be seen rather as examples of «ironic science» in the terminology of John Horgan.
The Infinite Sum of Reciprocal of the Fibonacci Numbers
Institute of Scientific and Technical Information of China (English)
Guo Jie ZHANG
2011-01-01
In this paper,we consider infinite sums of the reciprocals of the Fibonacci numbers.Then applying the floor function to the reciprocals of this sums,we obtain a new identity involving the Fibonacci numbers.
A NEW ONE-DIMENSIONAL CHAOTIC MAP WITH INFINITE COLLAPSES
Institute of Scientific and Technical Information of China (English)
Qiu Yuehong; He Chen; Zhu Hongwen
2002-01-01
This letter presents a new one-dimensional chaotic map with infinite collapses. Theoretical analyses show that the map has complicated dynamical behavior and ideal distribution.The map can be applied in chaotic spreading spectrum communication and chaotic cipher.
Infinite ensemble of support vector machines for prediction of ...
African Journals Online (AJOL)
user
Many researchers have demonstrated the use of artificial neural networks (ANNs) to ..... Following section discusses the effect of infinite ensemble approach ..... major problem with artificial intelligence-based modeling approaches is their ...
Wigner's infinite spin representations and inert matter
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [CBPF, Rio de Janeiro (Brazil); Institut fuer Theoretische Physik FU-Berlin, Berlin (Germany)
2017-06-15
Positive energy ray representations of the Poincare group are naturally subdivided into three classes according to their mass and spin content: m > 0, m = 0 finite helicity and m = 0 infinite spin. For a long time the localization properties of the massless infinite spin class remained unknown, until it became clear that such matter does not permit compact spacetime localization and its generating covariant fields are localized on semi-infinite space-like strings. Using a new perturbation theory for higher spin fields we present arguments which support the idea that infinite spin matter cannot interact with normal matter and we formulate conditions under which this also could happen for finite spin s > 1 fields. This raises the question of a possible connection between inert matter and dark matter. (orig.)
Some Infinite Summation Formulae Involving Kampe de Feriet Function
Directory of Open Access Journals (Sweden)
V. L. Deshpande
1971-04-01
Full Text Available Two infinite summation formulae for Kampe de Feriet function have been established and results are generalised by applying operational technique and method of finite mathematical induction. Various special cases are also obtained of which few are known.
Global infinite energy solutions for the cubic wave equation
Burq, N.; L. Thomann; Tzvetkov, N.
2012-01-01
International audience; We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.
An existence theorem for Volterra integrodifferential equations with infinite delay
Directory of Open Access Journals (Sweden)
Ferenc Izsak
2003-01-01
Full Text Available Using Schauder's fixed point theorem, we prove an existence theorem for Volterra integrodifferential equations with infinite delay. As an appplication, we consider an $n$ species Lotka-Volterra competitive system.
Plasma polymerization by Softplasma
DEFF Research Database (Denmark)
Jiang, J.; Wu, Zhenning; Benter, Maike
2008-01-01
In the late 19th century, the first depositions - known today as plasma polymers, were reported. In the last century, more and more research has been put into plasma polymers. Many different deposition systems have been developed. [1, 2] Shi F. F. broadly classified them into internal electrode......, external electrode, and electrodeless microwave or high frequency reactors. [3] Softplasma™ is an internal electrode plasma setup powered by low frequenc~ gower supply. It was developed in late 90s for surface treatment of silicone rubber. [ ]- 5] It is a low pressure, low electron density, 3D homogenous...... plasma. In this study, we are presenting the surface modification"pf polymers by plasma polymerization using Softplasma™. Softplasma™ can be used for two major types of polymerization: polymerization of vinyl monomers, where plasma acts as initiator; chemical vapour deposition, where plasma acts...
About the Infinite Repetition of Histories in Space
Gil, Francisco José Soler
2013-01-01
This paper analyzes two different proposals, one by Ellis and Brundrit, based on classical relativistic cosmology, the other by Garriga and Vilenkin, based on the DH interpretation of quantum mechanics, both of which conclude that, in an infinite universe, planets and living beings must be repeated an infinite number of times. We show that those scenarios cannot be considered a consequence of current physics and cosmology, and their conclusions are little more than literary fantasy.
Trading Off Generations: Infinitely-Lived Agent Versus OLG
2010-01-01
The prevailing literature discusses intergenerational trade-offs predominantly in infinitely-lived agent models despite the finite lifetime of individuals. We discuss these trade-offs in a continuous time OLG framework and relate the results to the infinitely-lived agent setting. We identify three shortcomings of the latter: First, underlying normative assumptions about social preferences cannot be deduced unambiguously. Second, the distribution among generations living at the same time canno...
Measurement of rectangular surface mobility of an infinite plate
Institute of Scientific and Technical Information of China (English)
DAI Jue
2001-01-01
A measuring method of surface mobility for an infinite plate subject to a uniform conphase velocity excitation is investigated. In the measurement, a finite plate is employed to simulate an infinite plate and a rigid cone is used to make a uniform conphase velocity excitation. A method to deduct the affect of additional mass is derived: The results of the measurement agree with that calculated theoretically.
Polyharmonic functions of infinite order on annular regions
Kounchev, Ognyan; Render, Hermann
2013-01-01
Polyharmonic functions $f$ of infinite order and type $\\tau$ on annular regions are systematically studied. The first main result states that the Fourier-Laplace coefficients $f_{k,l}(r)$ of a polyharmonic function $f$ of infinite order and type $0$ can be extended to analytic functions on the complex plane cut along the negative semiaxis. The second main result gives a constructive procedure via Fourier-Laplace series for the analytic extension of a polyharmonic function on annular ...
Aspects of infinite dimensional ℓ-super Galilean conformal algebra
Aizawa, N.; Segar, J.
2016-12-01
In this work, we construct an infinite dimensional ℓ-super Galilean conformal algebra, which is a generalization of the ℓ = 1 algebra found in the literature. We give a classification of central extensions, the vector field representation, the coadjoint representation, and the operator product expansion of the infinite dimensional ℓ-super Galilean conformal algebra, keeping possible applications in physics and mathematics in mind.
Transport for Stochastic System with Infinite Locally Coupled Oscillators
Institute of Scientific and Technical Information of China (English)
ZHAO Ying-Kui; LI Jing-Hui; ZHAO Xian-Geng
2003-01-01
We consider the transport of particles for spatially periodic system with infinite locally coupled oscillatorsdriven by additive and multiplicative noises. A formula of the probability current derived by us shows that the couplingamong the infinite oscillators is an ingredient for transport. This coupling of the oscillators can induce transport ofparticles in the absence of the correlation of the additive and multiplicative noises, even without the multiplicative noise.
A notion of graph likelihood and an infinite monkey theorem
Banerji, Christopher R S; Severini, Simone
2013-01-01
We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.
A notion of graph likelihood and an infinite monkey theorem
Banerji, Christopher R. S.; Mansour, Toufik; Severini, Simone
2014-01-01
We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.
Periodic Solutions of Multispecies Mutualism System with Infinite Delays
Directory of Open Access Journals (Sweden)
Wenbo Zhao
2014-01-01
Full Text Available We studied the delayed periodic mutualism system with Gilpin-Ayala effect. Some new and interesting sufficient conditions are obtained to guarantee the existence of periodic solution for the multispecies mutualism system with infinite delays. Our method is based on Mawhin's coincidence degree. To the best knowledge of the authors, there is no paper considering the existence of periodic solutions for n-species mutualism system with infinite delays.
Numerical computations and mathematical modelling with infinite and infinitesimal numbers
Sergeyev, Yaroslav D.
2012-01-01
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers \\textit{numerically}. This can be done on a new kind of a computer - the Infinity Computer - able to work with all these types of numbers. The new computatio...
The Decidability Frontier for Probabilistic Automata on Infinite Words
Chatterjee, Krishnendu; Tracol, Mathieu
2011-01-01
We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, B\\"uchi, coB\\"uchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs for probabilistic finite automata and present a complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words.
A unified approach to infinite-dimensional integration
Albeverio, S.; Mazzucchi, S.
2016-04-01
An approach to infinite-dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite-dimensional construction of integrals as linear functionals, as much as possible independent of the underlying topological and measure theoretical structure. Various applications are given, including, next to Feynman path integrals, Schrödinger and diffusion equations, as well as higher order hyperbolic and parabolic equations.
Acoustic Radiation from Transducer in Semi-infinite Fluid Medium
2016-06-07
IIIII v 841087 121CilN ACOUSTIC RADIATION F~ TRANSDUCER IN SFMI-INFINITE FLUID MEDIUM Date: June 19, 1984 Prepared by: Jay ant S. Patel...1. REPORT DATE 19 JUN 1984 2. REPORT TYPE Technical Memo 3. DATES COVERED 19-06-1984 to 19-06-1984 4. TITLE AND SUBTITLE Acoustic Radiation ...Technical Menorandum TM No. 841087 ACOUSTIC RADIATION FROM TRANSOOCER IN SEMI-INFINITE FliJID MEDIUM Date: June 19, 1984 Prepared by: Jayant s. Patel
POLYMERIC SURFACTANT STRUCTURE
Institute of Scientific and Technical Information of China (English)
P.M. Saville; J.W. White
2001-01-01
Polymeric surfactants are amongst the most widespread of all polymers. In nature, proteins and polysaccharides cause self organization as a result of this surfactancy; in industry, polymeric surfactants play key roles in the food, explosives and surface coatings sectors. The generation of useful nano- and micro-structures in films and emulsions as a result of polymer amphiphilicity and the application of mechanical stress is discussed. The use of X-ray and neutron small angle scattering and reflectivity to measure these structures and their dynamic properties will be described. New results on linear and dendritic polymer surfactants are presented.
Morgado, Jorge; Aquino-Olivos, Marco Antonio; Martínez-Hernández, Ranulfo; Corea, Mónica; Grolier, Jean Pierre E; del Río, José Manuel
2008-06-01
This work examines the binding in aqueous solution, through the experimental determination of specific volumes and specific adiabatic compressibility coefficients, of decyltrimethylammonium bromide to lysozyme and to non-charged polymeric particles (which have been specially synthesized by emulsion polymerization). A method was developed to calculate the specific partial properties at infinite dilution and it was shown that a Gibbs-Duhem type equation holds at this limit for two solutes. With this equation, it is possible to relate the behavior of the partial properties along different binding types at a constant temperature. It was found that the first binding type, specific with high affinity, is related to a significant reduction of surfactant compressibility. The second binding type is accompanied by the unfolding of the protein and the third one is qualitatively identical to the binding of the surfactant to non-charged polymeric particles.
Polymerized and functionalized triglycerides
Plant oils are useful sustainable raw materials for the development of new chemical products. As part of our research emphasis in sustainability and green polymer chemistry, we have explored a new method for polymerizing epoxidized triglycerides with the use of fluorosulfonic acid. Depending on the ...
1981-02-01
Skydrol 500B is a fire resistant hydraulic fluid available from Monsanto and which is primarily tricresyl phosphate. In most cases, the above table...Makromol. Chem. 1979, 82 149.- 23. Ger. Offen 2,804,609; (8/9/79). Bayer AG. 24. Odian, G. "Principles of Polymerization; "McGraw-Hill Book Co.: New York
Synthesis of PPy-like Nanocrystallines by Oriented Plasma Polymerization at Atmospheric Pressure
Institute of Scientific and Technical Information of China (English)
FANG Xin-sheng; GUO Ying; XU Jin-zhou; ZHANG Jing
2006-01-01
Polymeric polypyrrole-like (PPy-like) nanocrystallines were fast synthesized through oriented plasma polymerization at atmospheric pressure and room temperature. The effects of discharge power on the nanocrystalline morphology were investigated. Larger power tends to produce longer nanocrystallines. 3 mm long nanowires were produced at the largest power in our experiment. TEM image and the sharp electronic diffraction spots in SAD suggest that the nanoparticles have a single crystal phase. The chemical structure of the nanocrystalline has been studied through FTIR, EDX etc. This novel polymerization method could have great applications in fabricating functional polymeric nanocrystallines.
On the impedance of infinite LC ladder networks
Klimo, Paul
2017-01-01
The subject of electrical impedance is on the syllabi of most undergraduate courses in physics and electrical engineering. For example, Richard Feynman in his famous undergraduate text Lectures on Physics shows how to calculate the impedance of an infinite LC ladder. However, the formula he obtains has no useful physical interpretation if considered in the steady state frequency domain. In fact the value of this impedance becomes infinite unless one assumes that the energy flow along the infinite LC ladder is spatially uniform and in one direction only. This ad-hoc assumption, which renders the solution non-causal, is entirely unnecessary if the problem is considered in the time domain. It is important for students to appreciate that the concept of impedance works well only in dissipative circuits where the effects of transients are largely short lived. The purpose of this paper is to show that the same problem treated in the time domain by the Laplace transform method provides a qualitatively different and more satisfying explanation. We show that the current response of an infinite LC ladder, which is in the zero state before a causal harmonic driving voltage is applied, contains a significant non-harmonic component. This component, which is present in addition to the forced harmonic waveform, decays only very slowly and extracts an infinite amount of energy from the source.
Representations of Canonical Commutation Relations Describing Infinite Coherent States
Joye, Alain; Merkli, Marco
2016-10-01
We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is mathematically and physically natural to consider their phases to be random and identically distributed. The infinite volume states give rise to Hilbert space representations of the canonical commutation relations which we construct concretely. In the case of random phases, the representations are random as well and can be expressed with the help of Itô stochastic integrals. We analyze the dynamics of the infinite state alone and the open system dynamics of small systems coupled to it. We show that under the free field dynamics, initial phase distributions are driven to the uniform distribution. We demonstrate that coherences in small quantum systems, interacting with the infinite coherent state, exhibit Gaussian time decay. The decoherence is qualitatively faster than the one caused by infinite thermal states, which is known to be exponentially rapid only. This emphasizes the classical character of coherent states.
Simplicities and Automorphisms of a Sp ecial Infinite Dimensional Lie Algebra
Institute of Scientific and Technical Information of China (English)
YU De-min; LI Ai-hua
2013-01-01
In this paper, a special infinite dimensional Lie algebra is studied. The infinite dimensional Lie algebra appears in the fields of conformal theory, mathematical physics, statistic mechanics and Hamilton operator. The infinite dimensional Lie algebras is pop-ularized Virasoro-like Lie algebra. Isomorphisms, homomorphisms, ideals of the infinite dimensional Lie algebra are studied.
Kroonblawd, Matthew P.; Mathew, Nithin; Jiang, Shan; Sewell, Thomas D.
2016-10-01
A Generalized Crystal-Cutting Method (GCCM) is developed that automates construction of three-dimensionally periodic simulation cells containing arbitrarily oriented single crystals and thin films, two-dimensionally (2D) infinite crystal-crystal homophase and heterophase interfaces, and nanostructures with intrinsic N-fold interfaces. The GCCM is based on a simple mathematical formalism that facilitates easy definition of constraints on cut crystal geometries. The method preserves the translational symmetry of all Bravais lattices and thus can be applied to any crystal described by such a lattice including complicated, low-symmetry molecular crystals. Implementations are presented with carefully articulated combinations of loop searches and constraints that drastically reduce computational complexity compared to simple loop searches. Orthorhombic representations of monoclinic and triclinic crystals found using the GCCM overcome some limitations in standard distributions of popular molecular dynamics software packages. Stability of grain boundaries in β-HMX was investigated using molecular dynamics and molecular statics simulations with 2D infinite crystal-crystal homophase interfaces created using the GCCM. The order of stabilities for the four grain boundaries studied is predicted to correlate with the relative prominence of particular crystal faces in lab-grown β-HMX crystals. We demonstrate how nanostructures can be constructed through simple constraints applied in the GCCM framework. Example GCCM constructions are shown that are relevant to some current problems in materials science, including shock sensitivity of explosives, layered electronic devices, and pharmaceuticals.
Permittivity and permeability of semi-infinite metamaterial
Porvatkina, O. V.; Tishchenko, A. A.; Strikhanov, M. N.
2016-08-01
In our work we investigate dielectric and magnetic properties of semi-infinite metamaterial consisting of particles of different possible nature: atoms, molecules, nanoparticles, etc. It is important that these particles would have magnetic properties. Polarization of a near-surface layer is known to differ from its bulk value for non-magnetic materials; for magnetic materials, including metamaterials, the situation should be similar, which is the subject of our research. We obtain analogues of the Clausius-Mossotti relation both for permittivity and permeability taking into account the local field effects in the longwave approximation for semi-infinite metamaterial. These relations describe the connection between macroscopic characteristics of the semi-infinite metamaterial (permittivity and permeability) and characteristics of constituent particles (dielectric polarizability and magnetic polarizability), which is a bright example of multi-scale approach - method very popular today in physical and computer simulating.
OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.
Ott, William; Rivas, Mauricio A; West, James
2015-12-01
Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ (N) using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C(1) maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).
Numerical computations and mathematical modelling with infinite and infinitesimal numbers
Sergeyev, Yaroslav D
2012-01-01
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers \\textit{numerically}. This can be done on a new kind of a computer - the Infinity Computer - able to work with all these types of numbers. The new computational tools both give possibilities to execute computations of a new type and open new horizons for creating new mathematical models where a computational usage of infinite and/or infinitesimal numbers can be useful. A number of numerical examples showing the potential of the new approach and dealing with divergent series, limits, probability theory, linear algebra, and calculation of volumes of objects consisting of parts of different dimensions are given.
Dallas, Panagiotis; Georgakilas, Vasilios
2015-10-01
In the recent advances in the field of conductive polymers, the fibrillar or needle shaped nanostructures of polyaniline and polypyrrole have attracted significant attention due to the potential advantages of organic conductors that exhibit low-dimensionality, uniform size distribution, high crystallinity and improved physical properties compared to their bulk or spherically shaped counterparts. Carrying the polymerization reaction in a restricted two dimensional space, instead of the three dimensional space of the one phase solution is an efficient method for the synthesis of polymeric nanostructures with narrow size distribution and small diameter. Ultra-thin nanowires and nanofibers, single crystal nanoneedles, nanocomposites with noble metals or carbon nanotubes and layered materials can be efficiently synthesized with high yield and display superior performance in sensors and energy storage applications. In this critical review we will focus not only on the interfacial polymerization methods that leads to polymeric nanostructures and composites and their properties, but also on the mechanism and the physico-chemical processes that govern the diffusion and reactivity of molecules and nanomaterials at an interface. Recent advances for the synthesis of conductive polymer composites with an interfacial method for energy storage applications and future perspectives are presented.
Preparation of polyvinylpyrrodione microspheres by dispersion polymerization
Institute of Scientific and Technical Information of China (English)
Linfeng ZHAI; Tiejun SHI; Hualin WANG
2009-01-01
The preparation of polyvinylpyrrolidone (PVP) microspheres in ethyl acetate by dispersion polymerization with N-vinylpyrrolidone (NVP) as initial monomer, poly(N-vinylpyrrolidone-co-vinyl acetate) (P (NVP-co-VAc)) as dispersant, and 2, 2'-azobisisobutyr-onitrile(AIBN) as initiator is reported. The influences of monomer concentration, dispersant concentration and initiator concentration on the size of PVP microspheres as well as the monomer conversion were studied. The structure and properties of PVP microspheres were analyzed. The results show that the prepared PVP micro-spheres have a mean diameter of 3-4 μm. With an increase in NVP concentration, the size and the molecular weight of the PVP microspheres as well as the monomer conversion all increase. With increasing P(NVP-co-VAc) concentra-tions, the PVP molecular weight and monomer conversion both increase while the size of the microspheres becomes smaller. As the concentration of AIBN increases, the microsphere size and monomer conversion increase whereas the PVP molecular weight decreases. The PVP prepared by dispersion polymerization has a crystal structure, and its molecular weight is lower compared to that prepared by solution polymerization.
Robust Consumption-Investment Problem on Infinite Horizon
Energy Technology Data Exchange (ETDEWEB)
Zawisza, Dariusz, E-mail: dariusz.zawisza@im.uj.edu.pl [Jagiellonian University in Krakow, Institute of Mathematics, Faculty of Mathematics and Computer Science (Poland)
2015-12-15
In our paper we consider an infinite horizon consumption-investment problem under a model misspecification in a general stochastic factor model. We formulate the problem as a stochastic game and finally characterize the saddle point and the value function of that game using an ODE of semilinear type, for which we provide a proof of an existence and uniqueness theorem for its solution. Such equation is interested on its own right, since it generalizes many other equations arising in various infinite horizon optimization problems.
Surface optical Bloch oscillations in semi-infinite waveguide arrays.
Chremmos, I D; Efremidis, N K
2012-06-01
We predict that surface optical Bloch oscillations can exist in semi-infinite waveguide arrays with a linear index variation, if the array parameters close to the boundary are appropriately perturbed. The perturbation is such that the surface states obtain the Wannier-Stark ladder eigenvalues of the unperturbed infinite array. The number of waveguides, whose parameters need to be controlled, decreases with increasing ratio of index gradient over coupling. The configuration can find applications as a "matched" termination of waveguide arrays to eliminate the distortion of Bloch oscillations due to reflection on the boundaries.
The improper infinite derivatives of Takagi's nowhere-differentiable function
Allaart, Pieter C
2010-01-01
Let T be Takagi's continuous but nowhere-differentiable function. Using a representation in terms of Rademacher series due to N. Kono, we give a complete characterization of those points where T has a left-sided, right-sided, or two-sided infinite derivative. This characterization is illustrated by several examples. A consequence of the main result is that the sets of points where T'(x) is infinite have Hausdorff dimension one. As a byproduct of the method of proof, some exact results concerning the modulus of continuity of T are also obtained.
Using classical probability to guarantee properties of infinite quantum sequences
Gutmann, S
1995-01-01
We consider the product of infinitely many copies of a spin-1\\over 2 system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of \\sigma^x measurements has any specified property. In many cases, product states are eigenstates of the projections, and therefore the result of measuring the property is determined. Thus we obtain a nonprobabilistic quantum analogue to the law of large numbers, the randomness property, and all other familiar almost-sure theorems of classical probability.
Infinite System of Differential Equations in Some Spaces
Directory of Open Access Journals (Sweden)
M. Mursaleen
2012-01-01
Full Text Available The first measure of noncompactness was defined by Kuratowski in 1930 and later the Hausdorff measure of noncompactness was introduced in 1957 by Goldenštein et al. These measures of noncompactness have various applications in several areas of analysis, for example, in operator theory, fixed point theory, and in differential and integral equations. In particular, the Hausdorff measure of noncompactness has been extensively used in the characterizations of compact operators between the infinite-dimensional Banach spaces. In this paper, we present a brief survey on the applications of measures of noncompactness to the theory of infinite system of differential equations in some spaces and .
Polymerization of chloro-p-xylylenes, quantum-chemical study.
Czaplewski, Cezary; Smalara, Krzysztof; Giełdoń, Artur; Bobrowski, Maciej
2017-02-01
The p-xylylene monomers of parylene N, C and D have similar high polymerization reactivity. For effective copolymerization processes this fact is basically a drawback and for instance the copolymerization with styrene doesn't go at all (Corley et al. J Pol Sc 13(68):137-156, [15]). Substitution of terminal hydrogen atoms by chlorine atoms reduces reactivity dramatically. 7,7,8,8-tetrachloro-p-xylylene and 2,5,7,7,8,8-hexachloro-p-xylylene can be isolated as yellow crystals. These crystals can be kept without any change in temperature below 0 (∘)C, but they polymerize slowly at room temperature. Perchloro-p-xylylene is stable even at elevated temperatures and does not polymerize under any conditions. Both 7,7,8,8-tetrachloro-p-xylylene and 2,5,7,7,8,8-hexachloro-p-xylylene copolymerize with various vinyl monomers, such as styrene and others. In this work the polymerization reactions of different chloro-derivatives of p-xylylene were modeled by means of the DFT method with hybrid correlation functionals (B3LYP and PBE0) and, for comparison, by means of the Hartree Fock methods. We inquired both initiation as well as elongation polymeric reactions for each of the reactants. We survied their reactivity analytically examining energetics and configurations in Szwarc-like process. The quantitative influence of chlorine atoms on the reactivity in polymerization steps, their location in the reactants' structure (aromatic and/or aliphatic) as well as their number, were reviewed. The polymerizations of p-xylylenes with chlorine atoms as terminal aliphatic substituents yet revealed one more access path for parylenes' in situ functionalization.
Sergienko, V. S.; Martsinko, E. E.; Seifullina, I. I.; Churakov, A. V.; Chebanenko, E. A.
2016-03-01
The synthesis and X-ray diffraction study of compound {[Ag2Ge(H Cit)2(H2O)2] • 2H2O} n , where H4 Cit is the citric acid, are performed. In the polymeric structure, the H Cit 3- ligand fulfils the tetradentate chelate-μ4-bridging (3Ag, Ge) function (tridentate with respect to Ge and Ag atoms). The Ge atom is octahedrally coordinated by six O atoms of two H Cit 3-ligands. The coordination polyhedron of the Ag atom is an irregular five-vertex polyhedron [four O atoms of four H Cit 3- ligands and the O(H2O) atom]. An extended system of O-H···O hydrogen bonds connects complex molecules into a supramolecular 3D-framework.
Mixing in polymeric microfluidic devices.
Energy Technology Data Exchange (ETDEWEB)
Schunk, Peter Randall; Sun, Amy Cha-Tien; Davis, Robert H. (University of Colorado at Boulder, Boulder, CO); Brotherton, Christopher M. (University of Colorado at Boulder, Boulder, CO)
2006-04-01
This SAND report describes progress made during a Sandia National Laboratories sponsored graduate fellowship. The fellowship was funded through an LDRD proposal. The goal of this project is development and characterization of mixing strategies for polymeric microfluidic devices. The mixing strategies under investigation include electroosmotic flow focusing, hydrodynamic focusing, physical constrictions and porous polymer monoliths. For electroosmotic flow focusing, simulations were performed to determine the effect of electroosmotic flow in a microchannel with heterogeneous surface potential. The heterogeneous surface potential caused recirculations to form within the microchannel. These recirculations could then be used to restrict two mixing streams and reduce the characteristic diffusion length. Maximum mixing occurred when the ratio of the mixing region surface potential to the average channel surface potential was made large in magnitude and negative in sign, and when the ratio of the characteristic convection time to the characteristic diffusion time was minimized. Based on these results, experiments were performed to evaluate the manipulation of surface potential using living-radical photopolymerization. The material chosen to manipulate typically exhibits a negative surface potential. Using living-radical surface grafting, a positive surface potential was produced using 2-(Dimethylamino)ethyl methacrylate and a neutral surface was produced using a poly(ethylene glycol) surface graft. Simulations investigating hydrodynamic focusing were also performed. For this technique, mixing is enhanced by using a tertiary fluid stream to constrict the two mixing streams and reduce the characteristic diffusion length. Maximum mixing occurred when the ratio of the tertiary flow stream flow-rate to the mixing streams flow-rate was maximized. Also, like the electroosmotic focusing mixer, mixing was also maximized when the ratio of the characteristic convection time to the
Energy Technology Data Exchange (ETDEWEB)
Qualey, D.L.; Welty, J.R. [Oregon State Univ., Corvallis, OR (United States). Dept. of Mechanical Engineering; Drost, M.K. [Pacific Northwest Lab., Richland, WA (United States)
1997-02-07
A two-dimensional Monte Carlo method has been applied to a classic radiant energy exchange problem that models the interior of an industrial furnace. The configuration involves a source as an infinite radiating plane and the heat sink as parallel rows of infinitely long tubes. Hottel used a graphical technique to solve this furnace model for the two-tube-row configuration. This work extends Hottel`s results by increasing the number of rows in the original equilateral triangular array and then generalizing the results to isosceles triangular arrangements.
LQR control for scalar finite and infinite platoons
Curtain, R.F.; Iftime, O.V.; Zwart, H.J.; El Jai, A.; Afifi, L.; Zerrik, E.
2009-01-01
In this paper we compare the behaviour of the LQR solution for a finite platoon model with its infinite version. We give examples where these are similar and some where they are quite different. For the scalar case we obtain sufficient conditions for the LQR solutions to be similar by relating the T
A KAM theorem for infinite--dimensional discrete systems
Perfetti, P
2003-01-01
Infinite--dimesional, discrete hamiltonian systems of the type kinetic energy + potential energy over ${\\Bbb R}^{{\\Bbb Z}}\\times {\\Bbb T}^{{\\Bbb Z}}$ are studied. The existence of many quasi--periodic motions with a maximal set of nonzero frequencies is shown
How Fragile Is Consolidated Knowledge? Ben's Comparisons of Infinite Sets
Tsamir, Pessia; Dreyfus, Tommy
2005-01-01
This article builds on two previous ones in which we presented the processes of construction and consolidation of one student's knowledge structures about comparisons of infinite sets, according to a recently proposed theory of abstraction. In the present article, we show that under slight variations of context, knowledge structures that have…
Infinitely Many Symmetries of Konopelchenko-Dubrovsky Equation
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lou. These symmetries constitute an infinite-dimensional generalized w∞ algebra.
Generalized (,,-Pairs for Uncertain Linear Infinite-Dimensional Systems
Directory of Open Access Journals (Sweden)
Naohisa Otsuka
2009-01-01
Full Text Available We introduce the concept of generalized (,,-pairs which is related to generalized (,-invariant subspaces and generalized (,-invariant subspaces for infinite-dimensional systems. As an application the parameter-insensitive disturbance-rejection problem with dynamic compensator is formulated and its solvability conditions are presented. Further, an illustrative example is also examined.
The Limits of Some Infinite Families of Complex Contracting Mappings
Pagon, Dušan
2008-11-01
Self-similarity is strongly presented in modern mathematics and physics. We study a broad class of planar fractals—strongly self-similar sets of points in complex plane, obtained from a unit interval as geometric limits of certain infinite families of contracting mappings. Different 1-1 correspondences between the constructed set and the initial unit interval are established.
The peeling process of infinite Boltzmann planar maps
DEFF Research Database (Denmark)
Budd, Timothy George
2016-01-01
criterion has a very simple interpretation. The finite random planar maps under consideration were recently proved to possess a well-defined local limit known as the infinite Boltzmann planar map (IBPM). Inspired by recent work of Curien and Le Gall, we show that the peeling process on the IBPM can...
Reparametrization of the Relativistic Infinitely Extended Charged Particle Action
Saadat, Hassan; Pourhassan, Behnam
2016-09-01
In this letter, relativistic infinitely extended particles formulated. Correct form of action with possibility of reparametrization obtained and effect of electric field considered. It may be one of the first step to re-introduce theory of every things given by Nakano and Hessaby many years ago.
Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay
Directory of Open Access Journals (Sweden)
Li Fang
2011-01-01
Full Text Available We study the existence and uniqueness of mild solution of a class of nonlinear nonautonomous fractional integrodifferential equations with infinite delay in a Banach space . The existence of mild solution is obtained by using the theory of the measure of noncompactness and Sadovskii's fixed point theorem. An application of the abstract results is also given.
Linear measure functional differential equations with infinite delay
Monteiro, G.; Slavík, A.
2014-01-01
We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.
Periodic Solutions for Functional Differential Inclusions With Infinite Delay
Institute of Scientific and Technical Information of China (English)
李勇; 周钦德; 吕显瑞
1994-01-01
By means of asymptotic fixed point theory,it is established that every dissipative functional differential inclusion (probably with infinite delay) has a periodic solution.This provides a theoretical basis for the applications of Liapunov’s second method to multivalued systems.As a result,a positive answer to Hutson’s open problem is given for more general multivalued systems.
Infinite conditional random fields for human behavior analysis
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja
2013-01-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models that have been shown to successfully learn the hidden structure of a given classification problem (provided an appropriate validation of the number of hidden states). In this brief, we present the infinite HCRF (iHCRF
The infinite volume limit of Ford's alpha model
Stefansson, Sigurdur Orn
2009-01-01
We prove the existence of a limit of the finite volume probability measures generated by tree growth rules in Ford's alpha model of phylogenetic trees. The limiting measure is shown to be concentrated on the set of trees consisting of exactly one infinite spine with finite, identically and independently distributed outgrowths.
Semigroups on Frechet Spaces and Equations with Infinite Delays
Indian Academy of Sciences (India)
T Sengadir
2007-02-01
In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.
Convergence of generic infinite products of affine operators
Directory of Open Access Journals (Sweden)
S. Reich
1999-01-01
Full Text Available We establish several results concerning the asymptotic behavior of random infinite products of generic sequences of affine uniformly continuous operators on bounded closed convex subsets of a Banach space. In addition to weak ergodic theorems we also obtain convergence to a unique common fixed point and more generally, to an affine retraction.
Joining primeness and disjointness from infinitely divisible systems
Lemanczyk, Mariusz; Roy, Emmanuel
2009-01-01
We show that ergodic dynamical systems generated by infinitely divisible stationary processes are disjoint in the sense of Furstenberg with distally simple systems and systems whose maximal spectral type is singular with respect to the convolution of any two continuous measures.
THE STRICT BOUNDED REAL LEMMA IN INFINITE DIMENSIONS
CURTAIN, RF
1993-01-01
The strict bounded real lemma is generalized to an infinite-dimensional setting. This relates the existence of a stabilizing solution to a Riccati equation to an H(infinity)-norm bound and to the existence of a solution to a Riccati inequality.
Functional DNA: Teaching Infinite Series through Genetic Analogy
Kowalski, R. Travis
2011-01-01
This article presents an extended analogy that connects infinite sequences and series to the science of genetics, by identifying power series as "DNA for a function." This analogy allows standard topics such as convergence tests or Taylor approximations to be recast in a "forensic" light as mathematical analogs of genetic concepts such as DNA…
Local distinguishability of quantum states in infinite dimensional systems
Ogata, Y
2005-01-01
We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and classical communications, even for infinite dimensional systems. An estimate of the local discrimination probability is also given for some family of more than two pure states.
Finding Sums for an Infinite Class of Alternating Series
Chen, Zhibo; Wei, Sheng; Xiao, Xuerong
2012-01-01
Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…
Parabolic vortex equations and instantons of infinite energy
Biquard, Olivier; García-Prada, Oscar
1997-02-01
We study the vortex equations on parabolic bundles over a Riemann surface and prove a Hitchin-Kobayashi-type correspondence relating the existence of solutions to a certain stability condition. This is achieved by translating our problem into a four-dimensional one, via dimensional reduction arguments. In return we obtain examples of instantons of infinite energy.
Coherent States for Supersymmetric Partners of the Infinite Well
Hussin, V.; Morales-Salgado, V. S.
2017-05-01
We define linear and quadratic coherent states for the supersymmetric partners of the quantum infinite well through formal series expansions of the energy eigenfunctions of the systems and we study the appropriateness of this definitions as coherent states by means of their properties. In particular, we examine the localization in position and time evolution, minimum uncertainty relations and the behavior of the Wigner function.
ADAPTIVE COMPENSATORS FOR PERTURBED POSITIVE REAL INFINITE-DIMENSIONAL SYSTEMS
Curtain, Ruth F.; Demetriou, Michael A.; Ito, Kazufumi
2003-01-01
The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinite-dimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain.
Infinite S-expansion with ideal subtraction and some applications
Peñafiel, D. M.; Ravera, L.
2017-08-01
According to the literature, the S-expansion procedure involving a finite semigroup is valid no matter what the structure of the original Lie (super)algebra is; however, when something about the structure of the starting (super)algebra is known and when certain particular conditions are met, the S-expansion method (with its features of resonance and reduction) is able not only to lead to several kinds of expanded (super)algebras but also to reproduce the effects of the standard as well as the generalized Inönü-Wigner contraction. In the present paper, we propose a new prescription for S-expansion, involving an infinite abelian semigroup S(∞ ) and the subtraction of an infinite ideal subalgebra. We show that the subtraction of the infinite ideal subalgebra corresponds to a reduction. Our approach is a generalization of the finite S-expansion procedure presented in the literature, and it offers an alternative view of the generalized Inönü-Wigner contraction. We then show how to write the invariant tensors of the target (super)algebras in terms of those of the starting ones in the infinite S-expansion context presented in this work. We also give some interesting examples of application on algebras and superalgebras.
Infinite Face Centered Cubic Network of Identical Resistors
Asad, J H
2012-01-01
The equivalent resistance between the origin and any other lattice site, in an infinite Face Centered Cubic network consisting from identical resistors, has been expressed rationally in terms of the known value and . The asymptotic behavior is investigated, and some calculated values for the equivalent resistance are presented.
Comparing Structural Brain Connectivity by the Infinite Relational Model
DEFF Research Database (Denmark)
Ambrosen, Karen Marie Sandø; Herlau, Tue; Dyrby, Tim;
2013-01-01
The growing focus in neuroimaging on analyzing brain connectivity calls for powerful and reliable statistical modeling tools. We examine the Infinite Relational Model (IRM) as a tool to identify and compare structure in brain connectivity graphs by contrasting its performance on graphs from...... modeling tool for the identification of structure and quantification of similarity in graphs of brain connectivity in general....
The matrix type of purely infinite simple Leavitt path algebras
Abrams, Gene
2009-01-01
Let $R$ denote the purely infinite simple unital Leavitt path algebra $L(E)$. We completely determine the pairs of positive integers $(c,d)$ for which there is an isomorphism of matrix rings $M_c(R)\\cong M_d(R)$, in terms of the order of $[1_R]$ in the Grothendieck group $K_0(R)$.
Model reduction for controller design for infinite-dimensional systems
Opmeer, Mark Robertus
2006-01-01
The main aim of this thesis is, as the title suggests, the presentation of results on model reduction for controller design for infinite-dimensional systems. The obtained results are presented for both discrete-time systems and continuous-time systems. They are perfect generalizations of the corresp
Plasmonic waves of a semi-infinite random nanocomposite
Energy Technology Data Exchange (ETDEWEB)
Moradi, Afshin [Department of Basic Sciences, Kermanshah University of Technology, Kermanshah, Iran and Department of Nano Science, Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran (Iran, Islamic Republic of)
2013-10-15
The dispersion curves of the plasmonic waves of a semi-infinite random metal-dielectric nanocomposite, consisting of bulk metal embedded with dielectric inclusions, are presented. Two branches of p-polarized surface plasmon-polariton modes are found to exist. The possibility of experimentally observing the surface waves by attenuated total reflection is demonstrated.
Existence Results for Functional Differential Inclusions with Infinite Delay
Institute of Scientific and Technical Information of China (English)
Shi Huang HONG
2006-01-01
The aim of the present paper is to investigate the existence of solutions to functional differential inclusions with infinite delay in Banach spaces. A relevant set of phase space axioms is proposed. The main tools used in this paper are certain fixed point theorems based on the set-contraction theory.
Infinite Runs in Weighted Timed Automata with Energy Constraints
DEFF Research Database (Denmark)
Bouyer, Patricia; Fahrenberg, Uli; Larsen, Kim Guldstrand
2008-01-01
and locations, corresponding to the production and consumption of some resource (e.g. energy). We ask the question whether there exists an infinite path for which the accumulated weight for any finite prefix satisfies certain constraints (e.g. remains between 0 and some given upper-bound). We also consider...
Living olefin polymerization processes
Schrock, Richard R.; Baumann, Robert
1999-01-01
Processes for the living polymerization of olefin monomers with terminal carbon-carbon double bonds are disclosed. The processes employ initiators that include a metal atom and a ligand having two group 15 atoms and a group 16 atom or three group 15 atoms. The ligand is bonded to the metal atom through two anionic or covalent bonds and a dative bond. The initiators are particularly stable under reaction conditions in the absence of olefin monomer. The processes provide polymers having low polydispersities, especially block copolymers having low polydispersities. It is an additional advantage of these processes that, during block copolymer synthesis, a relatively small amount of homopolymer is formed.
Phosphazene-promoted anionic polymerization
Zhao, Junpeng
2014-01-01
In the recent surge of metal-free polymerization techniques, phosphazene bases have shown their remarkable potential as organic promoters/catalysts for the anionic polymerization of various types of monomers. By complexation with the counterion (e.g. proton or lithium cation), phosphazene base significantly improve the nucleophilicity of the initiator/chain-end resulting in rapid and usually controlled anionic/quasi-anionic polymerization. In this review, we will introduce the general mechanism, i.e. in situ activation (of initiating sites) and polymerization, and summarize the applications of such a mechanism on macromolecular engineering toward functionalized polymers, block copolymers and complex macromolecular architectures.
One-dimensional gravity in infinite point distributions.
Gabrielli, A; Joyce, M; Sicard, F
2009-10-01
The dynamics of infinite asymptotically uniform distributions of purely self-gravitating particles in one spatial dimension provides a simple and interesting toy model for the analogous three dimensional problem treated in cosmology. In this paper we focus on a limitation of such models as they have been treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e., the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by "Jeans swindle" for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling of the Jeans swindle in three dimensions, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show explicitly that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N -body simulations. For identical particles the dynamics of the simplest toy model (without expansion) is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss and compare with previous results in the literature and present new results for the specific case of this simplest (static) model starting from "shuffled lattice" initial conditions. These show qualitative properties of the evolution (notably its "self-similarity") like those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.
Finite-Repetition threshold for infinite ternary words
Directory of Open Access Journals (Sweden)
Golnaz Badkobeh
2011-08-01
Full Text Available The exponent of a word is the ratio of its length over its smallest period. The repetitive threshold r(a of an a-letter alphabet is the smallest rational number for which there exists an infinite word whose finite factors have exponent at most r(a. This notion was introduced in 1972 by Dejean who gave the exact values of r(a for every alphabet size a as it has been eventually proved in 2009. The finite-repetition threshold for an a-letter alphabet refines the above notion. It is the smallest rational number FRt(a for which there exists an infinite word whose finite factors have exponent at most FRt(a and that contains a finite number of factors with exponent r(a. It is known from Shallit (2008 that FRt(2=7/3. With each finite-repetition threshold is associated the smallest number of r(a-exponent factors that can be found in the corresponding infinite word. It has been proved by Badkobeh and Crochemore (2010 that this number is 12 for infinite binary words whose maximal exponent is 7/3. We show that FRt(3=r(3=7/4 and that the bound is achieved with an infinite word containing only two 7/4-exponent words, the smallest number. Based on deep experiments we conjecture that FRt(4=r(4=7/5. The question remains open for alphabets with more than four letters. Keywords: combinatorics on words, repetition, repeat, word powers, word exponent, repetition threshold, pattern avoidability, word morphisms.
Extremely correlated Fermi liquids in the limit of infinite dimensions
Energy Technology Data Exchange (ETDEWEB)
Perepelitsky, Edward, E-mail: eperepel@ucsc.edu; Sriram Shastry, B.
2013-11-15
We study the infinite spatial dimensionality limit (d→∞) of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory (Shastry 2011, 2013) [17,18] for the t–J model at J=0. We directly analyze the Schwinger equations of motion for the Gutzwiller projected (i.e. U=∞) electron Green’s function G. From simplifications arising in this limit d→∞, we are able to make several exact statements about the theory. The ECFL Green’s function is shown to have a momentum independent Dyson (Mori) self energy. For practical calculations we introduce a partial projection parameter λ, and obtain the complete set of ECFL integral equations to O(λ{sup 2}). In a related publication (Zitko et al. 2013) [23], these equations are compared in detail with the dynamical mean field theory for the large U Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional t–J model (with J=0) can be mapped to the infinite-U Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green’s function g and the caparison factor μ. Additionally, the optical conductivity is shown to be obtainable from G with negligibly small vertex corrections. These results are shown to hold to each order in λ. -- Highlights: •Infinite-dimensional t–J model (J=0) studied within new ECFL theory. •Mapping to the infinite U Anderson model with self consistent hybridization. •Single particle Green’s function determined by two local self energies. •Partial projection through control variable λ. •Expansion carried out to O(λ{sup 2}) explicitly.
Quasi bound states in the continuum with few unit cells of photonic crystal slab
DEFF Research Database (Denmark)
Taghizadeh, Alireza; Chung, Il-Sug
2017-01-01
Bound states in the continuum (BICs) in photonic crystal slabs represent the resonances with an infinite quality (Q)-factor, occurring above the light line for an infinitely periodic structure. We show that a set of BICs can turn into quasi-BICs with a very high Q-factor even for two or three unit...
Gratings in polymeric waveguides
Mishakov, G.; Sokolov, V.; Kocabas, A.; Aydinli, A.
2007-04-01
Laser-induced formation of polymer Bragg grating filters for Dense Wavelength Division Multiplexing (DWDM) applications is discussed. Acrylate monomers halogenated with both fluorine and chlorine, which possess absorption losses less than 0.25 dB/cm and wide choice of refractive indices (from 1.3 to 1.5) in the 1.5 μm telecom wavelength region were used. The monomers are highly intermixable thus permitting to adjust the refractive index of the composition within +/-0.0001. Moreover they are photocurable under UV exposure and exhibit high contrast in polymerization. These properties make halogenated acrylates very promising for fabricating polymeric waveguides and photonic circuits. Single-mode polymer waveguides were fabricated on silicon wafers using resistless contact lithography. Submicron index gratings have been written in polymer waveguides using holographic exposure with He-Cd laser beam (325 nm) through a phase mask. Both uniform and apodized gratings have been fabricated. The gratings are stable and are not erased by uniform UV exposure. The waveguide gratings possess narrowband reflection spectra in the 1.5 μm wavelength region of 0.4 nm width, nearly rectangular shape of the stopband and reflectivity R > 99%. The fabricated Bragg grating filters can be used for multiplexing/demultiplexing optical signals in high-speed DWDM optical fiber networks.
Weak-coupling approach to the semi-infinite Hubbard model: Non-locality of the self-energy
Potthoff, M.; Nolting, W.
1997-01-01
The Hubbard model on a semi-infinite three-dimensional lattice is considered to investigate electron-correlation effects at single-crystal surfaces. The standard second-order perturbation theory in the interaction U is used to calculate the electronic self-energy and the quasi-particle density of states (QDOS) in the bulk as well as in the vicinity of the surface. Within a real-space representation we fully account for the non-locality of the self-energy and examine the quality of the local a...
Positive operator semigroups from finite to infinite dimensions
Bátkai, András; Rhandi, Abdelaziz
2017-01-01
This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate t...
Constructing Restricted Patterson Measures for Geometrically Infinite Kleinian Groups
Institute of Scientific and Technical Information of China (English)
Kurt FALK; Bernd O. STRATMANN
2006-01-01
In this paper, we study exhaustions, referred to as ρ-restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infinite case, where we obtain that the limit set of each of these Kleinian groups contains an infinite family of closed subsets, referred to as ρ-restricted limit sets, such that there in this family. Generalizing concepts which are well known in the geometrically finite case, we then introduce the notion of ρ-restricted Patterson measure, and show that these measures are non-atomic,δρ-harmonic, δρ-subconformal on special sets and δρ-conformal on very special sets. Furthermore, we obtain the results that each ρ-restriction of our Kleinian group is of δρ-divergence type and that the Hausdorff dimension of the ρ-restricted limit set is equal to δρ.
Structure of the spectrum of infinite dimensional Hamiltonian operators
Institute of Scientific and Technical Information of China (English)
Alatancang
2008-01-01
This paper deals with the structure of the spectrum of infinite dimensional Hamiltonian operators.It is shown that the spectrum,the union of the point spectrum and residual spectrum,and the continuous spectrum are all symmetric with respect to the imaginary axis of the complex plane. Moreover,it is proved that the residual spectrum does not contain any pair of points symmetric with respect to the imaginary axis;and a complete characterization of the residual spectrum in terms of the point spectrum is then given.As applications of these structure results,we obtain several necessary and sufficient conditions for the residual spectrum of a class of infinite dimensional Hamiltonian operators to be empty.
Abstraction and Learning for Infinite-State Compositional Verification
Directory of Open Access Journals (Sweden)
Dimitra Giannakopoulou
2013-09-01
Full Text Available Despite many advances that enable the application of model checking techniques to the verification of large systems, the state-explosion problem remains the main challenge for scalability. Compositional verification addresses this challenge by decomposing the verification of a large system into the verification of its components. Recent techniques use learning-based approaches to automate compositional verification based on the assume-guarantee style reasoning. However, these techniques are only applicable to finite-state systems. In this work, we propose a new framework that interleaves abstraction and learning to perform automated compositional verification of infinite-state systems. We also discuss the role of learning and abstraction in the related context of interface generation for infinite-state components.
Dynamical Crossing of an Infinitely Degenerate Critical Point
Bachmann, Sven; Fraas, Martin; Graf, Gian Michele
2017-05-01
We study the evolution of a driven harmonic oscillator with a time-dependent frequency $\\omega_t \\propto |t|$. At time $t=0$ the Hamiltonian undergoes a point of infinite spectral degeneracy. If the system is initialized in the instantaneous vacuum in the distant past then the asymptotic future state is a squeezed state whose parameters are explicitly determined. We show that the squeezing is independent on the sweeping rate. This manifests the failure of the adiabatic approximation at points where infinitely many eigenvalues collide. We extend our analysis to the situation where the gap at $t=0$ remains finite. We also discuss the natural geometry of the manifold of squeezed states. We show that it is realized by the Poincar\\'e disk model viewed as a K\\"ahler manifold.
Regularisable and minimal orbits for group actions in infinite dimensions
Arnaudon, M
1995-01-01
We introduce a class of regularisable infinite dimensional principal fibre bundles which includes fibre bundles arising in gauge field theories like Yang-Mills and string theory and which generalise finite dimensional Riemannian principal fibre bundles induced by an isometric action. We show that the orbits of regularisable bundles have well defined, both heat-kernel and zeta function regularised volumes. We introduce two notions of minimality (which extend the finite dimensional one) for these orbits, using both heat-kernel and zeta function regularisation methods and show they coincide. For each of these notions, we give an infinite dimensional version of Hsiang's theorem which extends the finite dimensional case, interpreting minimal orbits as orbits with extremal (regularised) volume.
Quantum spin systems on infinite lattices a concise introduction
Naaijkens, Pieter
2017-01-01
This course-based primer offers readers a concise introduction to the description of quantum mechanical systems with infinitely many degrees of freedom – and quantum spin systems in particular – using the operator algebraic approach. Here, the observables are modeled using elements of some operator algebra, usually a C*-algebra. This text introduces readers to the framework and the necessary mathematical tools without assuming much mathematical background, making it more accessible than advanced monographs. The book also highlights the usefulness of the so-called thermodynamic limit of quantum spin systems, which is the limit of infinite system size. For example, this makes it possible to clearly distinguish between local and global properties, without having to keep track of the system size. Together with Lieb-Robinson bounds, which play a similar role in quantum spin systems to that of the speed of light in relativistic theories, this approach allows ideas from relativistic field theories to be implemen...
Energy Dynamics of an Infinitely Large Offshore Wind Farm
DEFF Research Database (Denmark)
Frandsen, Sten Tronæs; Barthelmie, R.J.; Pryor, S.C.
, particularly in the near-term, can be expected in the higher resource, moderate water depths of the North Sea rather than the Mediterranean. There should therefore be significant interest in understanding the energy dynamics of the infinitely large wind farm – how wakes behave and whether the extraction...... of energy by wind turbines over a large area has a significant and lasting impact on the atmospheric boundary layer. Here we focus on developing understanding of the infinite wind farm through a combination of theoretical considerations, data analysis and modeling. Initial evaluation of power losses due...... to wakes in the large Danish offshore wind farms at Horns Rev and Nysted indicated that losses were larger than expected. Temporary solutions have been found to account for this in wind farm models including use of an ‘added roughness’ block around the offshore wind farm. In the long-term however physical...
Polygons in restricted geometries subjected to infinite forces
Beaton, N. R.; Eng, J. W.; Soteros, C. E.
2016-10-01
We consider self-avoiding polygons in a restricted geometry, namely an infinite L × M tube in {{{Z}}}3. These polygons are subjected to a force f, parallel to the infinite axis of the tube. When f\\gt 0 the force stretches the polygons, while when f\\lt 0 the force is compressive. We obtain and prove the asymptotic form of the free energy in both limits f\\to +/- ∞ . We conjecture that the f\\to -∞ asymptote is the same as the limiting free energy of ‘Hamiltonian’ polygons, polygons which visit every vertex in a L× M× N box. We investigate such polygons, and in particular use a transfer-matrix methodology to establish that the conjecture is true for some small tube sizes. Dedicated to Anthony J Guttmann on the occasion of his 70th birthday.
Accelerated Gibbs Sampling for Infinite Sparse Factor Analysis
Energy Technology Data Exchange (ETDEWEB)
Andrzejewski, D M
2011-09-12
The Indian Buffet Process (IBP) gives a probabilistic model of sparse binary matrices with an unbounded number of columns. This construct can be used, for example, to model a fixed numer of observed data points (rows) associated with an unknown number of latent features (columns). Markov Chain Monte Carlo (MCMC) methods are often used for IBP inference, and in this technical note, we provide a detailed review of the derivations of collapsed and accelerated Gibbs samplers for the linear-Gaussian infinite latent feature model. We also discuss and explain update equations for hyperparameter resampling in a 'full Bayesian' treatment and present a novel slice sampler capable of extending the accelerated Gibbs sampler to the case of infinite sparse factor analysis by allowing the use of real-valued latent features.
Potential theory of infinite dimensional L\\'evy processes
Beznea, Lucian; Röckner, Michael
2010-01-01
We study the potential theory of a large class of infinite dimensional L\\'evy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e. excessive functions with compact level sets. Then many techniques from classical potential theory carry over to this infinite dimensional setting. Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as e.g. formulated by R. Carmona in 1980. In particular, we prove the analog of the known result, that the Cameron-Martin space is polar, in the L\\'evy case and apply the technique of controlled convergence to solve the Dirichlet problem with general (not necessarily continuous) boundary data.
Defocusing of null rays in infinite derivative gravity
Conroy, Aindriú; Koshelev, Alexey S.; Mazumdar, Anupam
2017-01-01
Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing condition for null congruences without assuming any ansatz-dependent background solution. The two important criteria are: (1) an additional scalar degree of freedom, besides the massless graviton must be introduced into the spacetime; and (2) an infinite derivative theory of gravity is required in order to avoid tachyons or ghosts in the graviton propagator. In this regard, our analysis strengthens earlier arguments for constructing non-singular bouncing cosmologies within an infinite derivative theory of gravity, without assuming any ansatz to solve the full equations of motion.
Conformal field theories with infinitely many conservation laws
Energy Technology Data Exchange (ETDEWEB)
Todorov, Ivan [Institut des Hautes Etudes Scientifiques F-91440, Bures-sur-Yvette (France)
2013-02-15
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th
Effects of some polymeric additives on the cocrystallization of caffeine
Chung, Jihae; Kim, Il Won
2011-11-01
Effects of polymeric additives on the model cocrystallization were examined. The model cocrystal was made from caffeine and oxalic acid, and poly(ethylene glycol) (PEG), poly( L-lactide) (PLLA), poly(ɛ-caprolactone) (PCL), and poly(acrylic acid) (PAA) were the additives. The cocrystals were formed as millimeter-sized crystals without additives, and they became microcrystals with PLLA and PCL, and nanocrystals with PAA. XRD and IR revealed that the cocrystal structure was unchanged despite the strong effects of the additives on the crystal morphology, although some decrease in crystallinity was observed with PAA as confirmed by DSC. The DSC study also showed that the cocrystal melted and recrystallized to form α-caffeine upon heating. The present study verified that the polymeric additives can be utilized to modulate the size and morphology of the cocrystals without interfering the intermolecular interactions essential to the integrity of the cocrystal structures.
Newton's law in braneworlds with an infinite extra dimension
Ito, M
2002-01-01
We study the behavior of the four$-$dimensional Newton's law in warped braneworlds. The setup considered here is a $(3+n)$-brane embedded in $(5+n)$ dimensions, where $n$ extra dimensions are compactified and a dimension is infinite. We show that the wave function of gravity is described in terms of the Bessel functions of $(2+n/2)$-order and that estimate the correction to Newton's law. In particular, the Newton's law for $n=1$ can be exactly obtained.
Borel Hierarchies in Infinite Products of Polish Spaces
Indian Academy of Sciences (India)
Rana Barua; Ashok Maitra
2007-05-01
Let be a product of countably infinite number of copies of an uncountable Polish space . Let $_(\\overline{}_)$ be the class of Borel sets of additive class for the product of copies of the discrete topology on (the Polish topology on ), and let $\\mathcal{B}=\\cup_{ < _1}\\overline{}_$. We prove in the Lévy-Solovay model that $$\\overline{}_ = _ \\cap\\mathcal{B}$$ for 1 ≤ < 1.
EXACT ANALYSIS OF WAVE PROPAGATION IN AN INFINITE RECTANGULAR BEAM
Institute of Scientific and Technical Information of China (English)
孙卫明; 杨光松; 李东旭
2004-01-01
The Fourier series method was extended for the exact analysis of wave propagation in an infinite rectangular beam. Initially, by solving the three-dimensional elastodynamic equations a general analytic solution was derived for wave motion within the beam. And then for the beam with stress-free boundaries, the propagation characteristics of elastic waves were presented. This accurate wave propagation model lays a solid foundation of simultaneous control of coupled waves in the beam.
Directed structure at infinity for infinite-dimensional systems
Laakkonen, Petteri; Pohjolainen, Seppo
2011-04-01
In this article the structure at infinity of infinite-dimensional linear time invariant systems with finite-dimensional input and output spaces is discussed. It is shown that a diagonal form describing behaviour near infinity can be found. This diagonal form is a generalisation of the Smith-McMillan form at infinity for rational matrices. It is then used to simplify certain solvability conditions of a regulation problem. Examples on time-delay and distributed parameter systems are given.
(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)
Institute of Scientific and Technical Information of China (English)
Pankaj Mathur
2006-01-01
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).
A plug with infinite order and some exotic 4-manifolds
Tange, Motoo
2012-01-01
Every exotic pair in 4-dimension is obtained each other by twisting a {\\it cork} or {\\it plug} which are codimension 0 submanifolds embedded in the 4-manifolds. The twist was an involution on the boundary of the submanifold. We define cork (or plug) with order $p\\in {\\Bbb N}\\cup \\{\\infty\\}$ and show there exists a plug with infinite order. Furthermore we show twisting $(P,\\varphi^2)$ gives to enlargements of $P$ compact exotic manifolds with boundary.
Constructing entanglement witnesses for infinite-dimensional systems
Hou, Jinchuan
2010-01-01
It is shown that, every entangled state in an infinite-dimensional composite system has an entanglement witness of simpler form $\\alpha I+T$ with $\\alpha$ a nonnegative number and $T$ a finite rank self-adjoint operator. We also provide two method of constructing entanglement witness and apply them to obtain some entangled states that cannot be detected by the PPT criterion and the realignment criterion.
Optimal Layout of Transshipment Facilities on An Infinite Homogeneous Plane
Xie, Weijun; Ouyang, Yanfeng
2014-01-01
This paper studies optimal spatial layout of transshipment facilities and the corresponding service regions on an infinite homogeneous plane $\\mathbb{R}^2$ that minimize the total cost for facility set-up, outbound delivery and inbound replenishment transportation. The problem has strong implications in the context of freight logistics and transit system design. This paper first focuses on a Euclidean plane and presents a new proof for the known Gersho's conjecture, which states that the opti...
Identifying interacting pairs of sites in infinite range Ising models
Galves, Antonio; Takahashi, Daniel Yasumasa
2010-01-01
We consider Ising models (pairwise interaction Gibbs probability measures) in $\\Z^d$ with an infinite range potential. We address the problem of identifying pairs of interacting sites from a finite sample of independent realisations of the Ising model. The sample contains only the values assigned by the Ising model to a finite set of sites in $\\Z^d$. Our main result is an upperbound for the probability with our estimator to misidentify the pairs of interacting sites in this finite set.
Noncommutative Independence in the Infinite Braid and Symmetric Group
Gohm, Rolf
2011-01-01
This is an introductory paper about our recent merge of a noncommutative de Finetti type result with representations of the infinite braid and symmetric group which allows to derive factorization properties from symmetries. We explain some of the main ideas of this approach and work out a constructive procedure to use in applications. Finally we illustrate the method by applying it to the theory of group characters.
Analysis of Multiple Cracks in an Infinite Functionally Graded Plate
Shbeeb, N. I.; Binienda, W. K.; Kreider, K. L.
1999-01-01
A general methodology was constructed to develop the fundamental solution for a crack embedded in an infinite non-homogeneous material in which the shear modulus varies exponentially with the y coordinate. The fundamental solution was used to generate a solution to fully interactive multiple crack problems for stress intensity factors and strain energy release rates. Parametric studies were conducted for two crack configurations. The model displayed sensitivity to crack distance, relative angular orientation, and to the coefficient of nonhomogeneity.
Private algebras in quantum information and infinite-dimensional complementarity
Energy Technology Data Exchange (ETDEWEB)
Crann, Jason, E-mail: jason-crann@carleton.ca [School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6 (Canada); Laboratoire de Mathématiques Paul Painlevé–UMR CNRS 8524, UFR de Mathématiques, Université Lille 1–Sciences et Technologies, 59655 Villeneuve d’Ascq Cédex (France); Kribs, David W., E-mail: dkribs@uoguelph.ca [Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Levene, Rupert H., E-mail: rupert.levene@ucd.ie [School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4 (Ireland); Todorov, Ivan G., E-mail: i.todorov@qub.ac.uk [Pure Mathematics Research Centre, Queen’s University Belfast, Belfast BT7 1NN (United Kingdom)
2016-01-15
We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem.
Infinite Horizon Discrete Time Control Problems for Bounded Processes
Directory of Open Access Journals (Sweden)
Hayek Naïla
2008-01-01
Full Text Available We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
Explicit solution for an infinite dimensional generalized inverse eigenvalue problem
Directory of Open Access Journals (Sweden)
Kazem Ghanbari
2001-01-01
Full Text Available We study a generalized inverse eigenvalue problem (GIEP, Ax=λBx, in which A is a semi-infinite Jacobi matrix with positive off-diagonal entries ci>0, and B= diag (b0,b1,…, where bi≠0 for i=0,1,…. We give an explicit solution by establishing an appropriate spectral function with respect to a given set of spectral data.
Infinite Body Centered Cubic Network of Identical Resistors
Asad, J H
2013-01-01
We express the equivalent resistance between the origin and any other lattice site in an infinite Body Centered Cubic (BCC) network consisting of identical resistors each of resistance R rationally in terms of known values and . The equivalent resistance is then calculated. Finally, for large separation between the origin and the lattice site two asymptotic formulas for the resistance are presented and some numerical results with analysis are given.
Criteria for resolving the cosmological singularity in Infinite Derivative Gravity
Conroy, Aindriú; Mazumdar, Anupam
2016-01-01
Einstein's General theory of relativity permits space-time singularities, where null congruences \\emph{focus} in the presence of matter, which satisfies an appropriate energy condition. In this paper, we argue that such a singularity may be avoided if two important criteria are satisfied: (1) An additional scalar degree of freedom, besides the massless graviton, must be introduced to the spacetime; and (2) An infinite-derivative extension is required in order to avoid tachyons or ghosts from the graviton propagator.
Infinite-genus surfaces and the universal Grassmannian
Davis, Simon
1995-01-01
Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus, verifying the inclusion of these surfaces in the Grassmannian. In particular, a subset of the class of $O_{HD}$ surfaces can be identified with a subset of the Grassmannian. The concept of flux through the ideal boundary is used to study the connection bet...
Temperature distribution of an infinite slab under point heat source
Directory of Open Access Journals (Sweden)
Wu Zhao-Chun
2014-01-01
Full Text Available The temperature field in an infinite slab under an instantaneous or continuous point heat source is studied numerically. The numerical results reveal the temperature distribution and its change regularity, which are significant for the temperature control encountered in many practical manufacturing processes, such as the laser treatment processes on the surface of films, welding and cutting, and even the design of measuring devices for thermal properties of material.
On Robust Control Designs for Infinite Dimensional Systems
1986-09-01
Series. and Products. Academic Press, Orlando. Florida. 1980. 72. Fraleigh . J.B.. A First Course in Abstract Algebra. Addison-Wesley. Reading...Often in current control design practice for infinite dimensional systems, a reduced-order model (e.g. [57]. [58]. [59]) is first generated to...next subsection. In Section 2.4 we shall discuss some consequences of this theorem. 2.2.3 Kaiman Inequality for LQHD Systems - Derivation First
Finite and Infinite Arithmetic Progressions Related to Beta-Expansion
Directory of Open Access Journals (Sweden)
Bing Li
2014-01-01
Full Text Available Let 1<β<2 and ε(x,β be the β-expansion of x∈[0,1. Denote by Aβ(x the set of positions where the digit 1 appears in ε(x,β. We consider the sets of points x such that Aβ(x contains arbitrarily long arithmetic progressions and includes infinite arithmetic progressions, respectively. Their sizes are investigated from the topological, metric, and dimensional viewpoints.
Infinite Horizon Discrete Time Control Problems for Bounded Processes
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
3-tuples have at most 7 prime factors infinitely often
Maynard, James
2012-01-01
Let $L_1$, $L_2$ $L_3$ be integer linear functions with no fixed prime divisor. We show there are infinitely many $n$ for which the product $L_1(n)L_2(n)L_3(n)$ has at most 7 prime factors, improving a result of Porter. We do this by means of a weighted sieve based upon the Diamond-Halberstam-Richert multidimensional sieve.
Verifying the Simulation Hypothesis via Infinite Nested Universe Simulacrum Loops
Sharma, Vikrant
2017-01-01
The simulation hypothesis proposes that local reality exists as a simulacrum within a hypothetical computer's dimension. More specifically, Bostrom's trilemma proposes that the number of simulations an advanced 'posthuman' civilization could produce makes the proposition very likely. In this paper a hypothetical method to verify the simulation hypothesis is discussed using infinite regression applied to a new type of infinite loop. Assign dimension n to any computer in our present reality, where dimension signifies the hierarchical level in nested simulations our reality exists in. A computer simulating known reality would be dimension (n-1), and likewise a computer simulating an artificial reality, such as a video game, would be dimension (n +1). In this method, among others, four key assumptions are made about the nature of the original computer dimension n. Summations show that regressing such a reality infinitely will create convergence, implying that the verification of whether local reality is a grand simulation is feasible to detect with adequate compute capability. The action of reaching said convergence point halts the simulation of local reality. Sensitivities to the four assumptions and implications are discussed.
Infinite slope stability under steady unsaturated seepage conditions
Lu, N.; Godt, J.
2008-01-01
[1] We present a generalized framework for the stability of infinite slopes under steady unsaturated seepage conditions. The analytical framework allows the water table to be located at any depth below the ground surface and variation of soil suction and moisture content above the water table under steady infiltration conditions. The framework also explicitly considers the effect of weathering and porosity increase near the ground surface on changes in the friction angle of the soil. The factor of safety is conceptualized as a function of the depth within the vadose zone and can be reduced to the classical analytical solution for subaerial infinite slopes in the saturated zone. Slope stability analyses with hypothetical sandy and silty soils are conducted to illustrate the effectiveness of the framework. These analyses indicate that for hillslopes of both sandy and silty soils, failure can occur above the water table under steady infiltration conditions, which is consistent with some field observations that cannot be predicted by the classical infinite slope theory. A case study of shallow slope failures of sandy colluvium on steep coastal hillslopes near Seattle, Washington, is presented to examine the predictive utility of the proposed framework. Copyright 2008 by the American Geophysical Union.
Single file diffusion into a semi-infinite tube
Farrell, Spencer G.; Brown, Aidan I.; Rutenberg, Andrew D.
2015-12-01
We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.
The Short Infinitive in Slovene: A Corpus-based Approach
Directory of Open Access Journals (Sweden)
Sara Može
2013-05-01
Full Text Available The article presents the results of an in-depth, corpus-based study on the use of the short and long infinitive in Slovene. After a few introductory remarks followed by a brief theoretical overview of the topic, a categorised list of problematic infinitive structures based upon a previously performed analysis of Šolar, a corpus of student texts, is provided. Šolar’s data gave insight into the whole range of linguistic problems associated with the use of two forms and allowed for the subject of the study, i.e. ‘full verb + infinitival complement’ structures, to be precisely defined. The following section describes the method used to compile a shortlist of high-frequency full verbs co-occurring with infinitival complements from the half-million-word, morphosyntactically and syntactically annotated training corpus that was created within the Communication in Slovene project. Finally, the co-relation between genre, mode and the use of the two forms is examined in detail; based on a quantitative analysis of data extracted from corpora of written (FidaPLUS and spoken language (GOS for each full verb on the shortlist, new findings on the actual use of the short and long infinitive in both written and spoken texts are presented.
Infinite variance in fermion quantum Monte Carlo calculations.
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
Entanglement and Nonlocality in Infinite 1D Systems
Wang, Zizhu; Singh, Sukhwinder; Navascués, Miguel
2017-06-01
We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori, since, as we show, there exist instances of local separable states (classical boxes) which admit only entangled (nonclassical) TI extensions. We provide a simple characterization of the set of local states of multiseparable TI spin chains and construct a family of linear witnesses which can detect entanglement in infinite TI states from the nearest-neighbor reduced density matrix. Similarly, we prove that the set of classical TI boxes forms a polytope and devise a general procedure to generate all Bell inequalities which characterize it. Using an algorithm based on matrix product states, we show how some of them can be violated by distant parties conducting identical measurements on an infinite TI quantum state. All our results can be easily adapted to detect entanglement and nonlocality in large (finite, not TI) 1D condensed matter systems.
Single file diffusion into a semi-infinite tube.
Farrell, Spencer G; Brown, Aidan I; Rutenberg, Andrew D
2015-11-23
We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.
Infinite variance in fermion quantum Monte Carlo calculations
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
A NEW POLYMERIC FLAME RETARDANT ADDITIVE FOR NYLON
Institute of Scientific and Technical Information of China (English)
M. SRINIVASAN; R. VASANTHAKUMARI; P. T. UTHIAH
1993-01-01
The present paper deals with the use of a new polymeric flame retardant material, polyphenylene sulphide (PPS) for plastics. Incorporation of 15 - 20% PPS into nylon-6 has provided UL V- 0 rating for the system and there is enhancement in tensile and flexural properties. The results obtained on the thermal, crystallization and flow characteristics of the nylon-PPS system uptoa loading of 40% PPS are also discussed.
Osorio Iregui, Juan; Troyer, Matthias; Corboz, Philippe
2017-09-01
In spite of their intrinsic one-dimensional nature, matrix product states have been systematically used to obtain remarkably accurate results for two-dimensional systems. Motivated by basic entropic arguments favoring projected entangled-pair states as the method of choice, we assess the relative performance of infinite matrix product states and infinite projected entangled-pair states on cylindrical geometries. By considering the Heisenberg and half-filled Hubbard models on the square lattice as our benchmark cases, we evaluate their variational energies as a function of both bond dimension and cylinder width. In both examples, we find crossovers at moderate cylinder widths, i.e., for the largest bond dimensions considered, we find an improvement on the variational energies for the Heisenberg model by using projected entangled-pair states at a width of about eleven sites, whereas for the half-filled Hubbard model, this crossover occurs at about seven sites.
Modality, Infinitives, and Finite Bare Verbs in Dutch and English Child Language
Blom, Elma
2007-01-01
This article focuses on the meaning of nonfinite clauses ("root infinitives") in Dutch and English child language. I present experimental and naturalistic data confirming the claim that Dutch root infinitives are more often modal than English root infinitives. This cross-linguistic difference is significantly smaller than previously assumed,…
High temperature structural, polymeric foams from high internal emulsion polymerization
Energy Technology Data Exchange (ETDEWEB)
Hoisington, M.A.; Duke, J.R.; Apen, P.G.
1996-02-01
In 1982, a high internal phase emulsion (HIPE) polymerization process to manufacture microcellular, polymeric foam systems was patented by Unilever. This patent discloses a polymerization process that occurs in a water-in-oil emulsion in which the water represents at least 76% of the emulsion by volume. The oil phase consists of vinyl monomers such as styrene and acrylates that are crosslinked by divinyl monomers during polymerization. After polymerization and drying to remove the water phase, the result is a crosslinked polymer foam with an open cell microstructure that is homogeneous throughout in terms of morphology, density, and mechanical properties. Since 1982, numerous patents have examined various HIPE polymerized foam processing techniques and applications that include absorbents for body fluids, cleaning materials, and ion exchange systems. All the published HIPE polymerized foams have concentrated on materials for low temperature applications. Copolymerization of styrene with maleic anhydride and N-substituted maleimides to produce heat resistant thermoplastics has been studied extensively. These investigations have shown that styrene will free radically copolymerize with N-substituted maleimides to create an alternating thermoplastic copolymer with a Tg of approximately 200{degrees}C. However, there are many difficulties in attempting the maleimide styrene copolymerization in a HIPE such as lower polymerization temperatures, maleimide solubility difficulties in both styrene and water, and difficulty obtaining a stable HIPE with a styrene/maleimide oil phase. This work describes the preparation of copolymer foams from N-ethylmaleimide and Bis(3-ethyl-5-methyl-4-maleimide-phenyl)methane with styrene based monomers and crosslinking agents.
A new applied approach for executing computations with infinite and infinitesimal quantities
Sergeyev, Yaroslav D
2012-01-01
A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle `The part is less than the whole' introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework. The new methodology has allowed us to introduce the Infinity Computer working with such numbers (its simulator has already been realized). Examples dealing with divergent series, infinite sets, and limits are given.
Dipole and slot elements and arrays on semi-infinite substrates
Kominami, M.; Pozar, D. M.; Schaubert, D. H.
1985-01-01
The printed dipole or slot antenna on a semi-infinite substrate and infinite phased arrays of these elements are investigated. The solution is based on the moment method in the Fourier transform domain. The generalized impedance or admittance matrix can be expressed in rapidly converging infinite-integral or infinite-summation forms, allowing the accurate determination of the current distributions. Using the present formulation, the input impedance, resonant length, and radiation pattern for the isolated antennas, and the reflection coefficient for infinite phased arrays, are calculated.
Electroactivity in Polymeric Materials
2012-01-01
Electroactivity in Polymeric Materials provides an in-depth view of the theory of electroactivity and explores exactly how and why various electroactive phenomena occur. The book explains the theory behind electroactive bending (including ion-polymer-metal-composites –IPMCs), dielectric elastomers, electroactive contraction, and electroactive contraction-expansion cycles. The book also balances theory with applications – how electroactivity can be used – drawing inspiration from the manmade mechanical world and the natural world around us. This book captures: A complete introduction to electroactive materials including examples and recent developments The theory and applications of numerous topics like electroactive bending of dielectric elastomers and electroactive contraction and expansion New topics, such as biomimetic applications and energy harvesting This is a must-read within the electroactive community, particularly for professionals and graduate students who are interested in the ...
Kinetics of silica polymerization
Energy Technology Data Exchange (ETDEWEB)
Weres, O.; Yee, A.; Tsao, L.
1980-05-01
The polymerization of silicic acid in geothermal brine-like aqueous solutions to produce amorphous silica in colloidal form has been studied experimentally and theoretically. A large amount of high quality experimental data has been generated over the temperature rang 23 to 100{sup 0}C. Wide ranges of dissolved silica concentration, pH, and sodium chloride concentration were covered. The catalytic effects of fluoride and the reaction inhibiting effects of aluminum and boron were studied also. Two basic processes have been separately studied: the formation of new colloidal particles by the homogeneous nucleation process and the deposition of dissolved silica on pre-existing colloidal particles. A rigorous theory of the formation of colloidal particles of amorphous silica by homogeneous nucleation was developed. This theory employs the Lothe-Pound formalism, and is embodied in the computer code SILNUC which quantitatively models the homogeneous nucleation and growth of colloidal silica particles in more than enough detail for practical application. The theory and code were extensively used in planning the experimental work and analyzing the data produced. The code is now complete and running in its final form. It is capable of reproducing most of the experimental results to within experimental error. It is also capable of extrapolation to experimentally inaccessible conditions, i.e., high temperatures, rapidly varying temperature and pH, etc.
Polymerization of anionic wormlike micelles.
Zhu, Zhiyuan; González, Yamaira I; Xu, Hangxun; Kaler, Eric W; Liu, Shiyong
2006-01-31
Polymerizable anionic wormlike micelles are obtained upon mixing the hydrotropic salt p-toluidine hydrochloride (PTHC) with the reactive anionic surfactant sodium 4-(8-methacryloyloxyoctyl)oxybenzene sulfonate (MOBS). Polymerization captures the cross-sectional radius of the micelles (approximately 2 nm), induces micellar growth, and leads to the formation of a stable single-phase dispersion of wormlike micellar polymers. The unpolymerized and polymerized micelles were characterized using static and dynamic laser light scattering, small-angle neutron scattering, 1H NMR, and stopped-flow light scattering. Stopped-flow light scattering was also used to measure the average lifetime of the unpolymerized wormlike micelles. A comparison of the average lifetime of unpolymerized wormlike micelles with the surfactant monomer propagation rate was used to elucidate the mechanism of polymerization. There is a significant correlation between the ratio of the average lifetime to the monomer propagation rate and the average aggregation number of the polymerized wormlike micelles.
Surface glycosylation of polymeric membranes
Institute of Scientific and Technical Information of China (English)
DAI ZhengWei; WAN LingShu; XU ZhiKang
2008-01-01
Surface glycosylation of polymeric membranes has been inspired by the structure of natural biomembranes. It refers to that glycosyl groups are introduced onto the membrane surface by various strategies, which combine the separation function of the membrane with the biological function of the saccharides in one system. In this review, progress in the surface glycosylation of polymeric membranes is highlighted in two aspects, i.e. the glycosylation methods and the potential applications of the surface-glycosylated membranes.
Geometric MCMC for infinite-dimensional inverse problems
Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.
2017-04-01
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.
Interference Energy Spectrum of the Infinite Square Well
Directory of Open Access Journals (Sweden)
Mordecai Waegell
2016-04-01
Full Text Available Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the interference energy spectrum of the state. This name is appropriate because the same splitting procedure applied at the stationary nodes of any eigenstate does not change the measurable energy of the state. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations. An analytic derivation is given for the interference spectrum of a given wavefunction Ψ ( x , t with N known zeros located at points s i = ( x i , t i . Numerical simulations were used to verify that a barrier can be rapidly raised at a zero of the wavefunction without significantly affecting it. The interpretation of this result with respect to the conservation of energy and the energy-time uncertainty relation is discussed, and the idea of alternate energy eigenbases is fleshed out. The question of whether or not a preferred discrete energy spectrum is an inherent feature of a particle’s quantum state is examined.
Random matrix models of stochastic integral type for free infinitely divisible distributions
Molina, J Armando Domínguez
2010-01-01
The Bercovici-Pata bijection maps the set of classical infinitely divisible distributions to the set of free infinitely divisible distributions. The purpose of this work is to study random matrix models for free infinitely divisible distributions under this bijection. First, we find a specific form of the polar decomposition for the L\\'{e}vy measures of the random matrix models considered in Benaych-Georges who introduced the models through their measures. Second, random matrix models for free infinitely divisible distributions are built consisting of infinitely divisible matrix stochastic integrals whenever their corresponding classical infinitely divisible distributions admit stochastic integral representations. These random matrix models are realizations of random matrices given by stochastic integrals with respect to matrix-valued L\\'{e}vy processes. Examples of these random matrix models for several classes of free infinitely divisible distributions are given. In particular, it is shown that any free sel...
Development of Polymeric Coatings for Antifouling Applications
Toumayan, Edward Philip
Fouling, or the deposition of unwanted material onto a surface, is a serious problem that can impair the function of submerged structures, such as marine-going vessels and underwater equipment. Water filtration membranes are particularly susceptible to fouling due to their microstructure and high water pressure operating conditions. For this reason, there has been considerable interest in developing fouling-resistant, or "antifouling" coatings for membranes, specifically coatings that mitigate fouling propensity while maintain high water flux. Polymer coatings have garnered significant interest in antifouling literature, due to their synthetic versatility and variety, and their promising resistance to a wide range of foulants. However, antifouling research has yet to establish a consistent framework for polymer coating synthesis and fouling evaluation, making it difficult or impossible to compare previously established methodologies. To this end, this work establishes a standardized methodology for synthesizing and evaluating polymer antifouling coatings. Specifically, antifouling coatings are synthesized using a grafting-from polymerization and fouling propensity is evaluated by quartz crystal microbalance with dissipation (QCM-D). Using this framework, a number of different surface functionalization strategies are compared, including grafting-to and grafting-from polymerization. A number of different surface functionalization strategies, including grafting-to and grafting-from, were investigated and the fouling performance of these films was evaluated. Primarily, sulfobetaine methacrylate, and poly(ethylene oxide) methacrylate monomers were investigated, among others. Grafting-to, while advantageous from a characterization standpoint, was ultimately limited to low grafting densities, which did not afford a significant improvement in fouling resistance. However, the higher grafting densities achievable by grafting-from did indicate improved fouling resistance. A
Institute of Scientific and Technical Information of China (English)
周彩虹; 郭纯; 刘建青; 洪小迪; 柳明; 宁保安; 高志贤
2013-01-01
目的 制备聚甲基丙烯酸(PMAA)反蛋白石光子晶体,观察其在不同环境因素刺激下的反应特性,并初步尝试将己烯雌酚(DES)印迹的PMAA光子晶体应用于检测小分子DES,为此类传感器检测小分子提供新的技术.方法 制备DES印迹的PMAA反蛋白石光子晶体.首先采用垂直沉积法制备二氧化硅蛋白石光子晶体模板,通过向模板中灌入预聚合液聚合形成薄膜,再除去二氧化硅模板和目标分子,得到印迹的反蛋白石光子晶体.在光纤光谱仪下观察pH等环境因素对光子晶体反射峰信号的影响.在体积比1∶1的甲醇和水中检测DES.结果 环境因素溶剂乙醇、离子强度、温度对光子晶体的反射峰信号影响较大,pH对其基本没有影响；印迹光子晶体对DES有明显的吸附反应,检测范围为1～500 ng/ml.结论 制备的DES分子印迹反蛋白石光子晶体对环境因素刺激反应灵敏,并且能够检测微量的DES.%Objective To prepare polymerized methyl acrylic acid ( PMAA) photonic crystal, and to observe its characteristic response to different environmental factors, as well as to try to apply it to detecting diethyl-stilbestrol (DES) ,so as to provide a new method for this kind of sensor to detect small molecules. Methods A colloidal crystal template was prepared from monodisperse SiO2 nanospheres by vertical deposition method first. Then the precursors were infused into the void spaces of the SiO2 templates and aggregated at 60 ℃ for 4 h. The template and the imprinted DES were removed,and then molecularly imprinted photonic polymers were prepared. The effects of pH, concentration of ethanol, temperature, and ionic strength on this photonic crystal property were observed using a fiber-optic spectrometer. Finally, DES in the aqueous solution of ethanol ( 1 : 1) was detected. Results The environmental factors such as ethanol solvent,ionic strength, and temperature markedly affected the reflection peak signal
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
Superconducting spin-triplet-MRAM with infinite magnetoresistance ratio
Energy Technology Data Exchange (ETDEWEB)
Lenk, Daniel; Ullrich, Aladin; Obermeier, Guenter; Mueller, Claus; Krug von Nidda, Hans-Albrecht; Horn, Siegfried; Tidecks, Reinhard [Institut fuer Physik, Universitaet Augsburg, D-86159 Augsburg (Germany); Morari, Roman [Institut fuer Physik, Universitaet Augsburg, D-86159 Augsburg (Germany); D. Ghitsu Institute of Electronic Engineering and Nanotechnologies ASM, Academiei Str. 3/3, MD2028 Kishinev (Moldova, Republic of); Solid State Physics Department, Kazan Federal University, 420008 Kazan (Russian Federation); Zdravkov, Vladimir I. [Institut fuer Physik, Universitaet Augsburg, D-86159 Augsburg (Germany); D. Ghitsu Institute of Electronic Engineering and Nanotechnologies ASM, Academiei Str. 3/3, MD2028 Kishinev (Moldova, Republic of); Institute of Applied Physics and Interdisciplinary Nanoscience Center, Universitaet Hamburg, Jungiusstrasse 9A, D-20355 Hamburg (Germany); Sidorenko, Anatoli S. [D. Ghitsu Institute of Electronic Engineering and Nanotechnologies ASM, Academiei Str. 3/3, MD2028 Kishinev (Moldova, Republic of); Tagirov, Lenar R. [Institut fuer Physik, Universitaet Augsburg, D-86159 Augsburg (Germany); Solid State Physics Department, Kazan Federal University, 420008 Kazan (Russian Federation)
2016-07-01
We fabricated a nanolayered hybrid superconductor-ferromagnet spin-valve structure, i.e. the superconducting transition temperature of this structure depends on its magnetic history. The observed spin-valve effect is based on the generation of the long range odd in frequency triplet component, arising from a non-collinear relative orientation of the constituent ferromagnetic layers. We investigated the effect both as a function of the sweep amplitude of the magnetic field, determining the magnetic history, and the applied transport current. Moreover, we demonstrate the possibility of switching the system from the normal o the superconducting state by applying field pulses, yielding an infinite magnetoresistance ratio.
Stable limits for sums of dependent infinite variance random variables
DEFF Research Database (Denmark)
Bartkiewicz, Katarzyna; Jakubowski, Adam; Mikosch, Thomas;
2011-01-01
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most...... of these results are qualitative in the sense that the parameters of the limit distribution are expressed in terms of some limiting point process. In this paper we will be able to determine the parameters of the limiting stable distribution in terms of some tail characteristics of the underlying stationary...
Approximate Controllability of Fractional Neutral Stochastic System with Infinite Delay
Sakthivel, R.; Ganesh, R.; Suganya, S.
2012-12-01
The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.
Infinitely dimensional control Markov branching chains in random environments
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
First of all we introduce the concepts of infinitely dimensional control Markov branching chains in random environments (β-MBCRE) and prove the existence of such chains, then we introduce the concepts of conditional generating functionals and random Markov transition functions of such chains and investigate their branching property. Base on these concepts we calculate the moments of the β-MBCRE and obtain the main results of this paper such as extinction probabilities, polarization and proliferation rate. Finally we discuss the classification ofβ-MBCRE according to the different standards.
Infinite invariant densities due to intermittency in a nonlinear oscillator
Meyer, Philipp; Kantz, Holger
2017-08-01
Dynamical intermittency is known to generate anomalous statistical behavior of dynamical systems, a prominent example being the Pomeau-Manneville map. We present a nonlinear oscillator, i.e., a physical model in continuous time, whose properties in terms of weak ergodity breaking and aging have a one-to-one correspondence to the properties of the Pomeau-Manneville map. So for both systems in a wide range of parameters no physical invariant density exists. We show how this regime can be characterized quantitatively using the techniques of infinite invariant densities and the Thaler-Dynkin limit theorem. We see how expectation values exhibit aging in terms of scaling in time.
Extending Hoare Logic with an Infinite While—Rule
Institute of Scientific and Technical Information of China (English)
邵志清
1992-01-01
In the paper we generalize the while-rule in Hoare calculus to an infinite one and then present a sufficient condition much weaker than the expressiveness for Cook'2 relative completeness theorem with respect to our new axiomatic system.Using the extended Hoare calculus we can derive true Hoare formulas which contain while statements free of loop invariants.It is also pointed out that the weak condition is a first order property and therefore provides a possible approach to the characterization of relative completeness which is also a first order property.
Harmonic Functions and Potentials on Finite or Infinite Networks
Anandam, Victor
2011-01-01
Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws. The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established. The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifications from Bauer, Constantinescu and Cornea. A network is a graph with edge-w
Heat and Mass Transfer in a Semi Infinite Porous
Directory of Open Access Journals (Sweden)
H. N. Narang
1967-07-01
Full Text Available Unsteady axially symmetric transfer of heat and mass in a semi-infinite porous circular cylinder initially at a constant temperature and mass transfer potential has been considered. The circular boundary of the porous cylinder is maintained at temperature and mass transfer potential which are functions of both axial co-ordinate and time, whereas the plane end is impervious to heat and mass transfer. Both the axial and radial components of heat and diffusive mass transfer have been taken into account. A particular case when the temperature and mass transfer potential are unit step functions has been discussed in detail and some results have been exhibited graphically.
Finite de Finetti theorem for infinite-dimensional systems.
D'Cruz, Christian; Osborne, Tobias J; Schack, Rüdiger
2007-04-20
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state |Psi/Psi| chosen from a family of subsets {Cn} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family {Cn}.
A Finite de Finetti Theorem for Infinite-Dimensional Systems
D'Cruz, C; Schack, R; Cruz, Christian D'; Osborne, Tobias J.; Schack, Ruediger
2006-01-01
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state from a family of subspaces {S_n} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give two simple equivalent characterizations of the family {S_n}.
Infinite volume of noncommutative black hole wrapped by finite surface
Zhang, Baocheng; You, Li
2017-02-01
The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein-Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.
Scan blindness in infinite phased arrays of printed dipoles
Pozar, D. M.; Schaubert, D. H.
1984-01-01
A comprehensive study of infinite phased arrays of printed dipole antennas is presented, with emphasis on the scan blindness phenomenon. A rigorous and efficient moment method procedure is used to calculate the array impedance versus scan angle. Data are presented for the input reflection coefficient for various element spacings and substrate parameters. A simple theory, based on coupling from Floquet modes to surface wave modes on the substrate, is shown to predict the occurrence of scan blindness. Measurements from a waveguide simulator of a blindness condition confirm the theory.
A New Infinite Class of Sasaki-Einstein Manifolds
Gauntlett, J P; Sparks, J F; Waldram, D; Gauntlett, Jerome P.; Martelli, Dario; Sparks, James F.; Waldram, Daniel
2004-01-01
We show that for every positive curvature Kahler-Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki-Einstein manifolds X_{2n+3} in dimension 2n+3. When n=1 we recover a recently discovered family of supersymmetric AdS_5 x X_5 solutions of type IIB string theory, while when n=2 we obtain new supersymmetric AdS_4 x X_7 solutions of D=11 supergravity. Both are expected to provide new supergravity duals of superconformal field theories.
Asymmetric de Finetti Theorem for Infinite-dimensional Quantum Systems
Niu, Murphy Yuezhen
2016-01-01
The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires the original state to obey permutation symmetry conditioned on successful experimental verification on k of N subsystems. We generalize the de Finetti theorem to include asymmetric bounds on the variance of canonical observables and biased basis selection during the verification step. Our result thereby enables application of infinite-dimensional de Finetti theorem to situations where two conjugate measurements obey different statistics, such as the security analysis of quantum key distribution protocols based on squeezed state against coherent attack.
Optimal Control of Gas Pipelines via Infinite-Dimensional Analysis
Durgut, Ismail; Leblebiciolu, Kemal
1996-05-01
A general optimal control approach employing the principles of calculus of variations has been developed to determine the best operating strategies for keeping the outlet pressure of gas transmission pipelines around a predetermined value while achieving reasonable energy consumption. The method exploits analytical tools of optimal control theory. A set of partial differential equations characterizing the dynamics of gas flow through a pipeline is directly used. The necessary conditions to minimize the specific performance index come from the infinite-dimensional model. The optimization scheme has been tested on a pipeline subject to stepwise change in demand.
Coarsely Invariant Hilbert Spaces over Infinite Connected Graphs
Institute of Scientific and Technical Information of China (English)
WANG Qin
2002-01-01
We study in this paper a Hilbert space HV associated with the coarse geometry of an infinite connected graph X(V, E) with vertex set V and edge set E. We show that X(V,E) is uniformly expanding if and only ifl2(V)can be continuously included in HV as a closed subspace,and that the inner product structure of HV is topologically invariant under uniform coarsening of the graph. We also discuss the functorial properties of these Hilbert spaces.
Examples of infinite direct sums of spectral triples
Falk, Kevin
2017-02-01
We study two ways of summing an infinite family of noncommutative spectral triples. First, we propose a definition of the integration of spectral triples and give an example using algebras of Toeplitz operators acting on weighted Bergman spaces over the unit ball of Cn. Secondly, we construct a spectral triple associated to a general polygonal self-similar set in C using algebras of Toeplitz operators on Hardy spaces. In this case, we show that we can recover the Hausdorff dimension of the fractal set.
Optimality Conditions for Nondifferentiable Multiobjective Semi-Infinite Programming Problems
Directory of Open Access Journals (Sweden)
D. Barilla
2016-01-01
Full Text Available We have considered a multiobjective semi-infinite programming problem with a feasible set defined by inequality constraints. First we studied a Fritz-John type necessary condition. Then, we introduced two constraint qualifications and derive the weak and strong Karush-Kuhn-Tucker (KKT in brief types necessary conditions for an efficient solution of the considered problem. Finally an extension of a Caristi-Ferrara-Stefanescu result for the (Φ,ρ-invexity is proved, and some sufficient conditions are presented under this weak assumption. All results are given in terms of Clark subdifferential.
Fabricating colloidal crystals and construction of ordered nanostructures
Directory of Open Access Journals (Sweden)
Sun Zhiqiang
2006-01-01
Full Text Available AbstractColloidal crystals of polymeric or inorganic microspheres are of extensive interest due to their potential applications in such as sensing, optics, photonic bandgap and surface patterning. The article highlights a set of approaches developed in our group, which are efficient to prepare colloidal crystals with ordered voids, patterned colloidal crystals on non-planar surfaces, heterogeneous colloidal crystals of different building blocks, colloidal crystals composed of non-spherical polyhedrons, and colloidal crystals of non-close-packed colloidal microspheres in particular. The use of these colloidal crystals as templates for different microstructures range from nanoscale to micron-scale is also summarized.
AQUEOUS STABLE FREE RADICAL POLYMERIZATION PROCESSES
Institute of Scientific and Technical Information of China (English)
Andrea R. Szkurhan; Michael K. Georges
2004-01-01
An overview of aqueous polymerizations, which include emulsion, miniemulsion and suspension polymerizations,under stable free radical polymerization (SFRP) conditions is presented. The success of miniemulsion and suspension SFRP polymerizations is contrasted with the difficulties associated with obtaining a stable emulsion polymerization. A recently developed unique microprecipitation technique is referenced as a means of making submicron sized particles that can be used to achieve a stable emulsion SFRP process.
Polymeric strontium ranelate nonahydrate
Directory of Open Access Journals (Sweden)
Kenny Stahl
2011-04-01
Full Text Available The title compound, poly[[μ-aqua-tetraaqua{μ-5-[bis(carboxylatomethylamino]-3-carboxylatomethyl-4-cyanothiophene-2-carboxylato}distrontium(II] tetrahydrate], [Sr2(C12H6N2O8S(H2O5]·3.79H2O, crystallizes with nine- and eight-coordinated Sr2+ cations. They are bound to seven of the eight ranelate O atoms and five of the water molecules. The SrO8 and SrO9 polyhedra are interconnected by edge-sharing, forming hollow layers parallel to (011. The layers are, in turn, interconnected by ranelate anions, forming a metal–organic framework (MOF structure with channels along the a axis. The four water molecules not coordinated to strontium are located in these channels and hydrogen bonded to each other and to the ranelates. Part of the water H atoms are disordered. The compound dehydrates very easily and 0.210 (4 water molecules out of nine were lost during crystal mounting causing additional disorder in the water structure.
Polymeric materials for neovascularization
DeVolder, Ross John
Revascularization therapies have emerged as a promising strategy to treat various acute and chronic wounds, cardiovascular diseases, and tissue defects. It is common to either administer proangiogenic growth factors, such as vascular endothelial growth factor (VEGF), or transplant cells that endogenously express multiple proangiogenic factors. Additionally, these strategies utilize a wide variety of polymeric systems, including hydrogels and biodegradable plastics, to deliver proangiogenic factors in a sophisticated manner to maintain a sustained proangiogenic environment. Despite some impressive results in rebuilding vascular networks, it is still a challenging task to engineer mature and functional neovessels in target tissues, because of the increasing complexities involved with neovascularization applications. To resolve these challenges, this work aims to design a wide variety of proangiogenic biomaterial systems with tunable properties used for neovascularization therapies. This thesis describes the design of several biomaterial systems used for the delivery of proangiogenic factors in neovascularization therapies, including: an electrospun/electrosprayed biodegradable plastic patch used for directional blood vessel growth (Chapter 2), an alginate-g-pyrrole hydrogel system that biochemically stimulates cellular endogenous proangiogenic factor expression (Chapter 3), an enzyme-catalyzed alginate-g-pyrrole hydrogel system for VEGF delivery (Chapter 4), an enzyme-activated alginate-g-pyrrole hydrogel system with systematically controllable electrical and mechanical properties (Chapter 5), and an alginate-g-pyrrole hydrogel that enables the decoupled control of electrical conductivity and mechanical rigidity and is use to electrically stimulate cellular endogenous proangiogenic factor expression (Chapter 6). Overall, the biomaterial systems developed in this thesis will be broadly useful for improving the quality of a wide array of molecular and cellular based
Spectra of Semi-Infinite Quantum Graph Tubes
Shipman, Stephen P.; Tillay, Jeremy
2016-10-01
The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half of the tube. The eigenfunctions associated to the spectrum of the half-tube involve all Floquet modes of the full tube. This requires solving the complex dispersion relation {D(λ,k_1,k_2)=0} with {(k_1,k_2)in({C}/2π{Z})^2} subject to the constraint {a k_1 + b k_2 ≡ 0} (mod {2π}), where a and b are integers. The number of Floquet modes for a given {λin{R}} is {2max{ a, b }}. Rightward and leftward modes are determined according to an indefinite energy flux form. The spectrum may contain eigenvalues that depend on the boundary conditions, and some eigenvalues may be embedded in the continuous spectrum.
Nuclear Matter Phase Transition in Infinite and Finite Systems
Terranova, S.; Bonasera, A.
2005-04-01
A new "semiclassical" model of the nuclear matter, composed of u, d colored quarks, is proposed. The approach, named Constrained Molecular Dynamics (CoMD) is based on the molecular dynamics simulation of the quarks, which interact through the Richardson's potential, and on a constraint due to Pauli blocking. With a suitable choice of the quark masses, some possible Equation of State (EOS) of the nuclear matter, at temperature equal to zero and finite baryon density, are obtained. These equations of state, not only present some known properties of the nuclear matter, as the Quark-Gluon Plasma (QGP) phase transition, but also shown the existence of a new state, the Exotic Color Clustering (ECC) state, in which cluster of quarks with the same color are formed. Some new quantities, "indicators" of the phase transition, are introduced: three order parameters, Mc2, Mc3, Mc4 defined trough the Gell-Mann matrices λα, and the lifetime of the J/Ψ particle. The behavior of the J/Ψ particle is studied also in the "finite" systems, obtained by expanding the corresponding "infinite" systems. It seems that the dynamics and the finite size effects do not wash completely the phase transition occurred in infinite systems, and the J/Ψ particle is still a good signature.
Fermat Reals - Nilpotent Infinitesimals and Infinite Dimensional Spaces
Giordano, Paolo
2009-01-01
F.: Good morning Hermann, I would like to talk with you about infinitesimals. G.: Tell me Pierre. F.: I'm fed up of all these slanders about my attitude to be non rigorous, so I've started to study nonstandard analysis (NSA) and synthetic differential geometry (SDG). G.: Yes, I've read something ... F.: Ok, no problem about their rigour. But, when I've seen that the sine of an infinite in NSA is infinitely near to a real number I was astonished: what is the intuitive meaning of this number, if any? Then, I've seen that to work in SDG I must learn to work in intuitionistic logic ... You know, I love margins of books, and I don't want to loose too much time, I have many things to do ... G.: In SDG they also say that every infinitesimal is at the same time positive and negative, what is the meaning of all these? And why does the square of a first order infinitesimal equal zero, whereas the product of two first order infinitesimals is not necessarily zero? And do you know that from any single infinitesimal in NSA...
Conformal field theories with infinitely many conservation laws
Todorov, Ivan
2013-02-01
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Unitary positive energy representations of scalar bilocal fields," Commun. Math. Phys. 271, 223-246 (2007), 10.1007/s00220-006-0182-2; e-print arXiv:math-ph/0604069v3; B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Infinite dimensional Lie algebras in 4D conformal quantum field theory," J. Phys. A Math Theor. 41, 194002 (2008), 10.1088/1751-8113/41/19/194002; e-print arXiv:0711.0627v2 [hep-th
Regular conditional distributions of max infinitely divisible processes
Dombry, Clément
2011-01-01
This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $\\{\\eta(t)\\}_{t\\in T}$ given observations $\\{\\eta(t_i)=y_i,\\ 1\\leq i\\leq k\\}$. Our starting point is the point process representation of max-infinitely divisible processes by Gin\\'e, Hahn and Vatan (1990). We carefully analyze the structure of the underlying point process, introduce the notions of extremal function, sub-extremal function and hitting scenario associated to the constraints and derive the associated distributions. This allows us to explicit the conditional distribution as a mixture over all hitting scenarios compatible with the conditioning constraints. This formula extends a recent related result by Wang and Stoev (2011) dealing with the case of spectrally discrete max-stable random fields. We believe this work offers new tools and perspective for prediction in extreme value theory togethe...
To infinity and beyond a cultural history of the infinite
Maor, Eli
1987-01-01
The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. . . - David Hilbert (1862-1943) Infinity is a fathomless gulf, There is a story attributed to David Hilbert, the preeminent mathe into which all things matician whose quotation appears above. A man walked into a vanish. hotel late one night and asked for a room. "Sorry, we don't have o Marcus Aurelius (121- 180), Roman Emperor any more vacancies," replied the owner, "but let's see, perhaps and philosopher I can find you a room after alL" Leaving his desk, the owner reluctantly awakened his guests and asked them to change their rooms: the occupant of room #1 would move to room #2, the occupant of room #2 would move to room #3, and so on until each occupant had moved one room over. To the utter astonish ment of our latecomer, room #1 suddenly became vacated, and he happily moved in and...
Bensoussan, A.; Delfour, M. C.; Mitter, S. K.
1976-01-01
Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.
Institute of Scientific and Technical Information of China (English)
CHEN Hui; WANG Wen-Guo; MA Cheng-Bing; CHEN Chang-Neng; LIU Qiu-Tian; LIAO Dai-Zheng; LI Li-Cun
2007-01-01
A new two-dimensional polymeric manganese compound [Mn(PhCOO)2(4,4'-bipyridine)]n 1 has been prepared and structurally characterized by X-ray diffraction. The complex crystallizes in space group Pbcn with a = 18.7158(2), b = 11.6919(3), c = 9.4799(2)(A), V = 2074.42(7)(A)3, Z = 4, Mr = 453.34, Dc = 1.452 g/cm3, μ = 0.670 mm-1 and F(000) = 932. The final refinement gave R = 0.0458 and wR = 0.1439 for 1358 observed reflections with Ⅰ＞ 2σ(Ⅰ). The complex consists of repeating units of Mn(PhCOO)2(4,4'-bipyridine). Each Mn center is sixcoordinated by four carboxylate O atoms of four benzoate anions and two pyridyl N atoms from bipy ligands to furnish a slightly distorted octahedral geometry. The two adjacent Mn atoms are connected by a pair of μ1,3-carboxylate groups to form infinite chains, which are further interlinked by bipy to complete a 2D grid network. The magnetic property of the polymeric complex has also been investigated.
Stereospecific olefin polymerization catalysts
Bercaw, John E.; Herzog, Timothy A.
1998-01-01
A metallocene catalyst system for the polymerization of .alpha.-olefins to yield stereospecific polymers including syndiotactic, and isotactic polymers. The catalyst system includes a metal and a ligand of the formula ##STR1## wherein: R.sup.1, R.sup.2, and R.sup.3 are independently selected from the group consisting of hydrogen, C.sub.1 to C.sub.10 alkyl, 5 to 7 membered cycloalkyl, which in turn may have from 1 to 3 C.sub.1 to C.sub.10 alkyls as a substituent, C.sub.6 to C.sub.15 aryl or arylalkyl in which two adjacent radicals may together stand for cyclic groups having 4 to 15 carbon atoms which in turn may be substituted, or Si(R.sup.8).sub.3 where R.sup.8 is selected from the group consisting of C.sub.1 to C.sub.10 alkyl, C.sub.6 to C.sub.15 aryl or C.sub.3 to C.sub.10 cycloalkyl; R.sup.4 and R.sup.6 are substituents both having van der Waals radii larger than the van der Waals radii of groups R.sup.1 and R.sup.3 ; R.sup.5 is a substituent having a van der Waals radius less than about the van der Waals radius of a methyl group; E.sup.1, E.sup.2 are independently selected from the group consisting of Si(R.sup.9).sub.2, Si(R.sup.9).sub.2 --Si(R.sup.9).sub.2, Ge(R.sup.9).sub.2, Sn(R.sup.9).sub.2, C(R.sup.9).sub.2, C(R.sup.9).sub.2 --C(R.sup.9).sub.2, where R.sup.9 is C.sub.1 to C.sub.10 alkyl, C.sub.6 to C.sub.15 aryl or C.sub.3 to C.sub.10 cycloalkyl; and the ligand may have C.sub.S or C.sub.1 -symmetry. Preferred metals are selected from the group consisting of group III, group IV, group V or lanthanide group elements. The catalysts are used to prepare stereoregular polymers including polypropylene from .alpha.-olefin monomers.
Mechanically controlled radical polymerization initiated by ultrasound
Mohapatra, Hemakesh; Kleiman, Maya; Esser-Kahn, Aaron Palmer
2017-02-01
In polymer chemistry, mechanical energy degrades polymeric chains. In contrast, in nature, mechanical energy is often used to create new polymers. This mechanically stimulated growth is a key component of the robustness of biological materials. A synthetic system in which mechanical force initiates polymerization will provide similar robustness in polymeric materials. Here we show a polymerization of acrylate monomers initiated and controlled by mechanical energy provided by ultrasonic agitation. The activator for an atom-transfer radical polymerization is generated using piezochemical reduction of a Cu(II) precursor complex, which thus converts a mechanical activation of piezoelectric particles to the synthesis of a new material. This polymerization reaction has some characteristics of controlled radical polymerization, such as narrow molecular-weight distribution and linear dependence of the polymeric chain length on the time of mechanical activation. This new method of controlled radical polymerization complements the existing methods to synthesize commercially useful well-defined polymers.
Energy Technology Data Exchange (ETDEWEB)
Chono, S.; Iemoto, Y. (Fukui Univ. (Japan). Faculty of Engineering); Taniguchi, A.; Tsuji, T. (Fukui Univ., Fukui (Japan). Graduate School)
1992-11-25
Liquid crystal is an anisotropic fluid having both fluidity possessed by liquid and optical anisotropy inherent in crystals. Heretofore, Doi theory, which was established in 1981, is the only theory that can describe the rheology behavior of polymeric liquid crystal. Conventionally, there have been studies carried out based on the Doi theory for clarifying the rheology characteristics of polymeric liquid crystal, but there have been very few in which the Doi theory is applied to the flow in a tube. In this paper, the simple shearing flows of polymeric liquid crystal are first described by employing the Doi theory, and then the results of analysis of flows between parallel plates are stated. The main results obtained are as follows. The orientation of polymeric liquid crystal is determined by relative magnitudes of the terms of average field potential and of velocity gradient. In the flows between parallel plates, the propotion of increase of flow rate increases with the pressure gradient, and polymeric liquid crystal possesses a shear-thinning viscosity like normal polymeric fluid. 14 refs., 7 figs.
Even, J.; Bertault, M.; Girard, A.; Délugeard, Y.
1996-12-01
DNP is a symmetrical disubstituted polymerizable diacetylene RCCCCR where R is CH 2O(NO 2) 2. The monomer crystal of DNP undergoes a ferroelectric phase transition at low temperature; it disappears in fully polymerized DNP crystal because polymerization changes the diacetylene backbone conformation. We show that hydrostatic isotropic pressure also stabilizes the ferroelectric phase in the DNP monomer crystal by enhancing van der Waals interactions between side groups.
DEFF Research Database (Denmark)
Christensen, Claus H.; Schmidt, I.; Carlsson, A.;
2005-01-01
A major factor governing the performance of catalytically active particles supported on a zeolite carrier is the degree of dispersion. It is shown that the introduction of noncrystallographic mesopores into zeolite single crystals (silicalite-1, ZSM-5) may increase the degree of particle dispersion...... of the zeolite particles, particularly after thermal treatment. When using mesoporous zeolites, the particles were evenly distributed throughout the mesopore system of the zeolitic support, even after calcination, leading to nanocrystals within mesoporous zeolite single crystals....
Supramolecular Polymeric Materials Containing Cyclodextrins.
Nakahata, Masaki; Takashima, Yoshinori; Harada, Akira
2017-01-01
Smart design of polymeric materials may lead to intelligent materials exhibiting unique functional properties. Looking at nature, living systems use specific and reversible intermolecular interactions in realizing complex functions. Hence reversible bonds based on selective molecular recognition can impart artificial materials with unique functional properties. This review mainly focuses on supramolecular polymeric materials based on cyclodextrin-based host-guest interactions. Polymeric materials using molecular recognition at polymer main chain, side chain, and termini are described. Polymers carrying host and guest residues exhibit unique properties such as: 1) formation of macroscopic self-assembly of polymer gels carrying host and guest residues; 2) stimuli-responsive self-healing properties due to the reversible nature of host-guest interactions; and 3) macroscopic motion of artificial muscle cross-linked by host-guest interaction controlled by external stimuli. An overview of recent developments in this new frontier between materials science and life science is given.
InfTucker: t-Process based Infinite Tensor Decomposition
Xu, Zenglin; Yuan,; Qi,
2011-01-01
Tensor decomposition is a powerful tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---conduct multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g. missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose a tensor-variate latent $t$ process model, InfTucker, for robust multiway data analysis: it conducts robust Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, it handles both continuous and binary data in a probabilistic framework. Unlike previous nonparametric Bayesian models on matrices and tensors, our latent $t$-process model focuses on multiway analysis and uses nonlinear covariance functions. To efficiently learn InfTucker from data, we develop a novel variational inference technique on tensors. Compared with classical implementation,...
Fat Branes in Infinite-Volume Extra Space
Middleton, C E; Middleton, Chad; Siopsis, George
2002-01-01
We study branes residing in infinite volume space and of finite extent in the transverse directions. We calculate the graviton propagator in the harmonic gauge both inside and outiside the brane and discuss its dependence on the thickness of the brane. Our treatment includes the full tensor structure of the propagator. In five dimensions, we show that the van Dam-Veltman-Zakharov (vDVZ) discontinuity can be avoided by an appropriate choice of gauge. This new gauge is written explicitly in terms of the metric field without evoking the field equations. It has a singular limit as the transverse size of the brane shrinks to zero, so no such simple representation is possible in that limit.
Spectral theory of infinite-area hyperbolic surfaces
Borthwick, David
2016-01-01
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constan...
Casimir Energy of a Semi-Circular Infinite Cylinder
Nesterenko, V V; Scarpetta, G
2001-01-01
The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of the cylinder and by considering only a half of this configuration. All the surfaces, including the cutting plane, are assumed to be perfectly conducting. The zeta functions for scalar massless fields obeying the Dirichlet and Neumann boundary conditions on the semi-circular cylinder are constructed exactly. The sum of these zeta functions gives the zeta function for electromagnetic field in question. The relevant plane problem is considered also. In all the cases the final expressions for the corresponding Casimir energies contain the pole contributions. This implies that further renormalization is needed in order for the finite physical values for vacuum energy to be obtained for given boundary conditions.
Casimir energy of a semi-circular infinite cylinder
Nesterenko, V. V.; Lambiase, G.; Scarpetta, G.
2001-05-01
The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of the cylinder and by considering only half of this configuration. All the surfaces, including the cutting plane, are assumed to be perfectly conducting. The zeta functions for scalar massless fields obeying the Dirichlet and Neumann boundary conditions on the semi-circular cylinder are constructed exactly. The sum of these zeta functions gives the zeta function for the electromagnetic field in question. The relevant plane problem is considered also. In all the cases the final expressions for the corresponding Casimir energies contain the pole contributions which are the consequence of the edges or corners in the boundaries. This implies that further renormalization is needed in order for the finite physical values for vacuum energy to be obtained for given boundary conditions.
Dynamics of Bubbles Rising in Finite and Infinite Media
Energy Technology Data Exchange (ETDEWEB)
C.C. Maneri; P.F. Vassallo
2000-10-27
The dynamic behavior of single bubbles rising in quiescent liquid Suva (R134a) in a duct has been examined through the use of a high speed video system. Size, shape and velocity measurements obtained with the video system reveal a wide variety of characteristics for the bubbles as they rise in both finite and infinite media. This data, coupled with previously published data for other working fluids, has been used to assess and extend a rise velocity model given by Fan and Tsuchiya. As a result of this assessment, a new rise velocity model has been developed which maintains the physically consistent characteristics of the surface tension in the distorted bubbly regime. In addition, the model is unique in that it covers the entire range of bubble sizes contained in the spherical, distorted and planar slug regimes.
The concept of free will as an infinite metatheoretic recursion
Hashim, Hanaan
2015-01-01
It is argued that the concept of free will, like the concept of truth in formal languages, requires a separation between an object level and a meta-level for being consistently defined. The Jamesian two-stage model, which deconstructs free will into the causally open "free" stage with its closure in the "will" stage, is implicitly a move in this direction. However, to avoid the dilemma of determinism, free will additionally requires an infinite regress of causal meta-stages, making free choice a hypertask. We use this model to define free will of the rationalist-compatibilist type. This is shown to provide a natural three-way distinction between quantum indeterminism, freedom and free will, applicable respectively to artificial intelligence (AI), animal agents and human agents. We propose that the causal hierarchy in our model corresponds to a hierarchy of Turing uncomputability. Possible neurobiological and behavioral tests to demonstrate free will experimentally are suggested. Ramifications of the model for...
Broadband computation of the scattering coefficients of infinite arbitrary cylinders.
Blanchard, Cédric; Guizal, Brahim; Felbacq, Didier
2012-07-01
We employ a time-domain method to compute the near field on a contour enclosing infinitely long cylinders of arbitrary cross section and constitution. We therefore recover the cylindrical Hankel coefficients of the expansion of the field outside the circumscribed circle of the structure. The recovered coefficients enable the wideband analysis of complex systems, e.g., the determination of the radar cross section becomes straightforward. The prescription for constructing such a numerical tool is provided in great detail. The method is validated by computing the scattering coefficients for a homogeneous circular cylinder illuminated by a plane wave, a problem for which an analytical solution exists. Finally, some radiation properties of an optical antenna are examined by employing the proposed technique.
The peeling process of infinite Boltzmann planar maps
Budd, Timothy
2015-01-01
We start by studying a peeling process on finite random planar maps with faces of arbitrary degrees determined by a general weight sequence, which satisfies an admissibility criterion. The corresponding perimeter process is identified as a biased random walk, in terms of which the admissibility criterion has a very simple interpretation. The finite random planar maps under consideration were recently proved to possess a well-defined local limit known as the infinite Boltzmann planar map (IBPM). Inspired by recent work of Curien and Le Gall, we show that the peeling process on the IBPM can be obtained from the peeling process of finite random maps by conditioning the perimeter process to stay positive. The simplicity of the resulting description of the peeling process allows us to obtain the scaling limit of the associated perimeter and volume process for arbitrary regular critical weight sequences.
Defect energy of infinite-component vector spin glasses.
Lee, L W; Young, A P
2005-09-01
We compute numerically the zero-temperature defect energy DeltaE of the vector spin glass in the limit of an infinite number of spin components m , for a range of dimensions 2< or d < or =5 . Fitting to DeltaE approximately L(theta) , where L is the system size, we obtain: theta similar to-1.54 (d=2) , theta similar to-1.04 (d=3) , theta similar to -0.67 (d=4) , and theta similar to -0.37 (d=5) . These results show that the lower critical dimension dl (the dimension where theta changes sign) is significantly higher for m=infinity than for finite m (where 2< dl <3 ).
Doubly infinite separation of quantum information and communication
Liu, Zi-Wen; Perry, Christopher; Zhu, Yechao; Koh, Dax Enshan; Aaronson, Scott
2016-01-01
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the exclusion game [C. Perry et al., Phys. Rev. Lett. 115, 030504 (2015), 10.1103/PhysRevLett.115.030504] for which there exist instances where the quantum information complexity tends to zero as the size of the input n increases. By showing that the quantum communication complexity of these games scales at least logarithmically in n , we obtain our result. We further show that the established lower bounds and gaps still hold even if we allow a small probability of error. However in this case, the n -qubit quantum message of the zero-error strategy can be compressed polynomially.
Model and Controller Order Reduction for Infinite Dimensional Systems
Directory of Open Access Journals (Sweden)
Fatmawati
2010-05-01
Full Text Available This paper presents a reduced order model problem using reciprocal transformation and balanced truncation followed by low order controller design of infinite dimensional systems. The class of systems considered is that of an exponentially stable state linear systems (A, B, C, where operator A has a bounded inverse, and the operator B and C are of finite-rank and bounded. We can connect the system (A, B, C with its reciprocal system via the solutions of the Lyapunov equations. The realization of the reciprocal system is reduced by balanced truncation. This result is further translated using reciprocal transformation as the reduced-order model for the systems (A, B, C. Then the low order controller is designed based on the reduced order model. The numerical examples are studied using simulations of Euler-Bernoulli beam to show the closed-loop performance.
ANALYSIS ON THE COHESIVE STRESS AT HALF INFINITE CRACK TIP
Institute of Scientific and Technical Information of China (English)
王利民; 徐世烺
2003-01-01
The nonlinear fracture behavior of quasi-brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip. Based on fracture character of quasi-brittle materials, a mechanical analysis model of half infinite crack with cohesive stress is presented. A pair of integral equations is established according to the superposition principle of crack opening displacement in solids, and the fictitious adhesive stress is unknown function. The properties of integral equations are analyzed, and the series function expression of cohesive stress is certified. By means of the data of actual crack opening displacement, two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation. They are the integral transformation method for continuous displacement of actual crack opening, and the least square method for the discrete data of crack opening displacement. The calculation examples of two approaches and associated discussions are given.
An Infinite Dimensional Symmetry Algebra in String Theory
Evans, Mark; Nanopoulos, Dimitri V.; Evans, Mark; Giannakis, Ioannis
1994-01-01
Symmetry transformations of the space-time fields of string theory are generated by certain similarity transformations of the stress-tensor of the associated conformal field theories. This observation is complicated by the fact that, as we explain, many of the operators we habitually use in string theory (such as vertices and currents) have ill-defined commutators. However, we identify an infinite-dimensional subalgebra whose commutators are not singular, and explicitly calculate its structure constants. This constitutes a subalgebra of the gauge symmetry of string theory, although it may act on auxiliary as well as propagating fields. We term this object a {\\it weighted tensor algebra}, and, while it appears to be a distant cousin of the $W$-algebras, it has not, to our knowledge, appeared in the literature before.
Strong mixing properties of max-infinitely divisible random fields
Dombry, Clément
2012-01-01
Let $\\eta=(\\eta(t))_{t\\in T}$ be a sample continuous max-infinitely random field on a locally compact metric space $T$. For a closed subset $S\\in T$, we note $\\eta_{S}$ the restriction of $\\eta$ to $S$. We consider $\\beta(S_1,S_2)$ the absolute regularity coefficient between $\\eta_{S_1}$ and $\\eta_{S_2}$, where $S_1,S_2$ are two disjoint closed subsets of $T$. Our main result is a simple upper bound for $\\beta(S_1,S_2)$ involving the exponent measure $\\mu$ of $\\eta$: we prove that $\\beta(S_1,S_2)\\leq 2\\int \\bbP[\\eta\
Recurrent kernel machines: computing with infinite echo state networks.
Hermans, Michiel; Schrauwen, Benjamin
2012-01-01
Echo state networks (ESNs) are large, random recurrent neural networks with a single trained linear readout layer. Despite the untrained nature of the recurrent weights, they are capable of performing universal computations on temporal input data, which makes them interesting for both theoretical research and practical applications. The key to their success lies in the fact that the network computes a broad set of nonlinear, spatiotemporal mappings of the input data, on which linear regression or classification can easily be performed. One could consider the reservoir as a spatiotemporal kernel, in which the mapping to a high-dimensional space is computed explicitly. In this letter, we build on this idea and extend the concept of ESNs to infinite-sized recurrent neural networks, which can be considered recursive kernels that subsequently can be used to create recursive support vector machines. We present the theoretical framework, provide several practical examples of recursive kernels, and apply them to typical temporal tasks.
Variational optimization with infinite projected entangled-pair states
Corboz, Philippe
2016-07-01
We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states, a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state of a local Hamiltonian. The method is based on a systematic summation of Hamiltonian contributions using the corner-transfer-matrix method. Benchmark results for challenging problems are presented, including the two-dimensional Heisenberg model, the Shastry-Sutherland model, and the t -J model, which show that the variational scheme yields considerably more accurate results than the previously best imaginary-time evolution algorithm, with a similar computational cost and with a faster convergence towards the ground state.
Infinite dilution conductimetry of plasma and urine: correlation with osmolality.
Genain, C; Tellier, P; Syrota, A; Pocidalo, J J; Hans, M
1978-08-15
The infinite dilution conductivity (IDC) of plasma and urine allows a measurement of the electrolyte content in small samples (5 to 15 microliter). The method was compared to the corrected osmolality (II'p) measured by the freezing-point depression. A linear correlation existed between II'p and the IDC: for plasma: II'p = 13.10 sigma o,p + 37.00 (n = 46 and r = 0.9949) for urine: II'u = 12.75 sigma o,u + 16.56 (n = 85 and r = 0.9504). The measurement of the IDC does not depend on protein concentration and can be used instead of the osmometer methods to determine the total plasma and urine electrolyte content.
On q-deformed infinite-dimensional n-algebra
Directory of Open Access Journals (Sweden)
Lu Ding
2016-03-01
Full Text Available The q-deformation of the infinite-dimensional n-algebras is investigated. Based on the structure of the q-deformed Virasoro–Witt algebra, we derive a nontrivial q-deformed Virasoro–Witt n-algebra which is nothing but a sh-n-Lie algebra. Furthermore in terms of the pseud-differential operators, we construct the (cosine n-algebra and the q-deformed SDiff(T2 n-algebra. We find that they are the sh-n-Lie algebras for the n even case. In terms of the magnetic translation operators, an explicit physical realization of the (cosine n-algebra is given.
Surface glycosylation of polymeric membranes
Institute of Scientific and Technical Information of China (English)
2008-01-01
Surface glycosylation of polymeric membranes has been inspired by the structure of natural biomem-branes. It refers to that glycosyl groups are introduced onto the membrane surface by various strate-gies, which combine the separation function of the membrane with the biological function of the sac-charides in one system. In this review, progress in the surface glycosylation of polymeric membranes is highlighted in two aspects, i.e. the glycosylation methods and the potential applications of the sur-face-glycosylated membranes.
On-demand photoinitiated polymerization
Boydston, Andrew J; Grubbs, Robert H; Daeffler, Chris; Momcilovic, Nebojsa
2013-12-10
Compositions and methods for adjustable lenses are provided. In some embodiments, the lenses contain a lens matrix material, a masking compound, and a prepolymer. The lens matrix material provides structure to the lens. The masking compound is capable of blocking polymerization or crosslinking of the prepolymer, until photoisomerization of the compound is triggered, and the compound is converted from a first isomer to a second isomer having a different absorption profile. The prepolymer is a composition that can undergo a polymerization or crosslinking reaction upon photoinitiation to alter one or more of the properties of the lenses.
Infinitely many solutions of p-Laplacian equations with limit subcritical growth
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We discussed a class of p-Laplacian boundary problems on a bounded smooth domain, the nonlinearity is odd symmetric and limit subcritical growing at infinite. A sequence of critical values of the variational functional was constructed after the generalized Palais-Smale condition was verified.We obtain that the problem possesses infinitely many solutions and corresponding energy levels of the functional pass to positive infinite.The result is a generalization of a similar problem in the case of subcritical.
Surface Initiated Polymerizations via e-ATRP in Pure Water
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Seyed Schwan Hosseiny
2013-10-01
Full Text Available Here we describe the combined process of surface modification with electrochemical atom transfer radical polymerization (e-ATRP initiated from the surface of a modified gold-electrode in a pure aqueous solution without any additional supporting electrolyte. This approach allows for a very controlled growth of the polymer chains leading towards a steady increase in film thickness. Electrochemical quartz crystal microbalance displayed a highly regular increase in surface confined mass only after the addition of the pre-copper catalyst which is reduced in situ and transformed into the catalyst. Even after isolation and washing of the modified electrode surface, reinitiation was achieved with retention of the controlled electrochemical ATRP reaction. This reinitiation after isolation proves the livingness of the polymerization. This approach has interesting potential for smart thin film materials and offers also the possibility of post-modification via additional electrochemical induced reactions.
Construction and optical properties of infinite Cd and finite Cu molecules stairs
Zhao, Qiang; Mao, Wutao; Shen, Zhi; Wang, Qinghong; Zhou, Qian
2017-02-01
Two coordination complexes, namely [(hpdq)(pta)Cd]n (1) and [(pptp)(pta)Cu2Cl] (2) have been synthesized by solvothermal method based on two polypyridyl ligands, 2,3,6,7,10,11-hexakis- (2-pyridyl)dipyrazino[2,3-f:2‧,3‧-h]quinoxaline) (hpdq), 4‧-(4- (3H-pyrrol-3-yl)phenyl)- 2,2‧:6‧,2″- terpyridine (pptp) and auxiliary ligand p-phthalic acid (pta), respectively. Single crystal x-ray diffraction analyses reveal that complexes 1 and 2 assembled based on distinct asymmetric unit comprising one and two respective polypyridyl ligands but one Cd(II) and two Cu(I)ions, respectively. Among them, The asymmetric units in 1 was extended to one dimensional chain via the link of auxiliary ligand pta, just like infinite layers of stairs that connected by cadmium ions as the node. While that in 2 to Zero dimensional tetranuclear structure via the link of auxiliary ligand pta, just like finite four layers of stairs that Copper ion as the node connection. Furthermore, solid fluorescence spectra properties of two complexes were also investigated, and the result shows the fluorescence intensity of complex 1 is stronger than that of the hpdq ligand, but the fluorescence intensity of complex 2 is weaker than that of the pptp ligand. CCDC number of 1and 2 are 1483301 and 1483302.
Freudenmann, Dominic; Feldmann, Claus
2014-10-07
[BMIm]4[AgMo10Cl35] is prepared by reaction of MoCl5 and elemental silver in the ionic liquid [BMIm][AlCl4] ([BMIm(+)]: 1-butyl-4-methylimidazolium). Surprisingly, elemental silver is oxidized under these conditions. The title compound contains a new wheel-shaped [Mo10Cl35](5-) chlorido molybdenum(iii) species with five pairs of Mo-Mo bonds. The Mo-Mo distances are found to be 263 pm on average. The [Mo10Cl35](5-) wheels exhibit a maximum opening of 558 pm in diameter. They are interlinked via Ag(+) to form infinite [AgMo10Cl35](4-) chains. The title compound is characterized by single crystal structure analysis, EDX, FT-IR and UV-Vis spectroscopy. The wheel-type structure and Ag(+) linkage to infinite chains are a new aspect of halogenido metalates and low-valence molybdenum compounds.
Mixed dimensional infinite soliton trains for nonlinear Schr\\"odinger equations
Lin, LiRen; Tsai, Tai-Peng
2015-01-01
In this note we construct mixed dimensional infinite soliton trains, which are solutions of nonlinear Schr\\"odinger equations whose asymptotic profiles at time infinity consist of infinitely many solitons of multiple dimensions. For example infinite line-point soliton trains in 2D space, and infinite plane-line-point soliton trains in 3D space. This note extends the works of Le Coz, Li and Tsai [5, 6], where single dimensional trains are considered. In our approach, spatial $L^\\infty$ bounds ...
Twinning of Polymer Crystals Suppressed by Entropy
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Nikos Ch. Karayiannis
2014-09-01
Full Text Available We propose an entropic argument as partial explanation of the observed scarcity of twinned structures in crystalline samples of synthetic organic polymeric materials. Polymeric molecules possess a much larger number of conformational degrees of freedom than low molecular weight substances. The preferred conformations of polymer chains in the bulk of a single crystal are often incompatible with the conformations imposed by the symmetry of a growth twin, both at the composition surfaces and in the twin axis. We calculate the differences in conformational entropy between chains in single crystals and chains in twinned crystals, and find that the reduction in chain conformational entropy in the twin is sufficient to make the single crystal the stable thermodynamic phase. The formation of cyclic twins in molecular dynamics simulations of chains of hard spheres must thus be attributed to kinetic factors. In more realistic polymers this entropic contribution to the free energy can be canceled or dominated by nonbonded and torsional energetics.
DEFF Research Database (Denmark)
Andersen, T.E.; Kingshott, Peter; Benter, M.
with a surface less prone to the adsorption of biological matter. In the current study two different hydrophilic nanoscale coatings were produced by low energy plasma polymerization [3] and investigated· f()rl()w ... pr()tein adsorption and bacterial attachment properties. Methods were setup to enable...... and Methods: Coatings: Plasma polymerized poly(vinyl pyrrolidone) (PP-PVP), poly(2-methoxyethyl methacrylate) (PPPMEA) or an inorganic oxide (10) coating were applied onto medical grade silicon rubber sheets (Silopren LSR 2050, Momentive Performance Materials Inc.). Plasma polymerization chamber......-coated crystals were then treated with one of the plasma polymerized coatings. Adsorption of fibrinogen, human serum albumin or immunoglobulin G was measured using a QCM-D instrument [5] (model E4, Q-Sense AB, Vastra Frolunda, Sweden) using a solution of 50llg/1 protein in PBS buffer. Results and Discussion: Our...
Functionalization and Polymerization on the CNT Surfaces
Albuerne, Julio
2013-07-01
In this review we focus on the current status of using carbon nanotube (CNT) as a filler for polymer nanocomposites. Starting with the historical background of CNT, its distinct properties and the surface functionalization of the nanotube, the three different surface polymerization techniques, namely grafting "from", "to" and "through/in between" were discussed. Wider focus has been given on "grafting from" surface initiated polymerizations, including atom transfer radical polymerization (ATRP), reversible addition fragmentation chain-transfer (RAFT) Polymerization, nitroxide mediated polymerization (NMP), ring opening polymerization (ROP) and other miscellaneous polymerization methods. The grafting "to" and "through / in between" also discussed and compared with grafting from polymerization. The merits and shortcomings of all three grafting methods were discussed and the bottleneck issue in grafting from method has been highlighted. Furthermore the current and potential future industrial applications were deliberated. Finally the toxicity issue of CNTs in the final product has been reviewed with the limited available literature knowledge. © 2013 Bentham Science Publishers.
Instabilities in liquid crystals
Barclay, G J
1998-01-01
and we examine the differences which occur for differing dielectric anisotropies. Finally, in Chapter 7 we study how a sample of smectic C liquid crystal behaves when it is subjected to a uniform shear flow within the smectic plane. We find travelling wave solutions for the behaviour of the c-director and adapt these solutions to incorporate the effects of an applied field. This thesis contains theoretical work dealing with the effects of magnetic and electric fields on samples of nematic, smectic A and smectic C liquid crystals. Some background material along with the continuum theory is introduced in Chapter 2. In Chapter 3 we consider the effect on the director within an infinite sample of nematic liquid crystal which is subjected to crossed electric and magnetic fields. In particular we examine the stability of the travelling waves which describe the director motion by considering the behaviour of the stable perturbations as time increases. The work of Chapter 4 examines a bounded sample of smectic A liqu...
The absorption of polymeric composites
Řídký, R.; Popovič, M.; Rolc, S.; Drdlová, M.; Krátký, J.
2016-06-01
An absorption capacity of soft, viscoelastic materials at high strain rates is important for wide range of practical applications. Nowadays there are many variants of numerical models suitable for this kind of analysis. The main difficulty is in selection of the most realistic numerical model and a correct setup of many unknown material constants. Cooperation between theoretical simulations and real testing is next crucial point in the investigation process. Standard open source material database offer material properties valid for strain rates less than 250 s-1. There are experiments suitable for analysis of material properties with strain rates close to 2000 s-1. The high strain-rate characteristics of a specific porous blast energy absorbing material measured by modified Split Hopkinson Pressure Bar apparatus is presented in this study. Testing these low impedance materials using a metallic split Hopkinson pressure bar setup results in poor signal to noise ratios due to impedance mismatching. These difficulties are overcome by using polymeric Hopkinson bars. Conventional Hopkinson bar analysis cannot be used on the polymeric bars due to the viscoelastic nature of the bar material. One of the possible solution leads to complex and frequency depended Young modulus of testing bars material. This testing technique was applied to materials composed of porous glass/ceramic filler and polymeric binder, with density of 125 - 300 kg/m3 and particle size in range of 50 µm - 2 mm. The achieved material model was verified in practical application of sandwich structure includes polymeric composites under a blast test.
The Viscosity of Polymeric Fluids.
Perrin, J. E.; Martin, G. C.
1983-01-01
To illustrate the behavior of polymeric fluids and in what respects they differ from Newtonian liquids, an experiment was developed to account for the shear-rate dependence of non-Newtonian fluids. Background information, procedures, and results are provided for the experiment. Useful in transport processes, fluid mechanics, or physical chemistry…
Biodegradable polymeric prodrugs of naltrexone
Bennet, D.B.; Li, X.; Adams, N.W.; Kim, S.W.; Hoes, C.J.T.; Feijen, J.
1991-01-01
The development of a biodegradable polymeric drug delivery system for the narcotic antagonist naltrexone may improve patient compliance in the treatment of opiate addiction. Random copolymers consisting of the ¿-amino acids N5-(3-hydroxypropyl--glutamine and -leucine were synthesized with equimolar
Buckling of polymerized monomolecular films
Bourdieu, L.; Daillant, J.; Chatenay, D.; Braslau, A.; Colson, D.
1994-03-01
The buckling of a two-dimensional polymer network at the air-water interface has been evidenced by grazing incidence x-ray scattering. A comprehensive description of the inhomogeneous octadecyltrichlorosilane polymerized film was obtained by atomic force microscopy and x-ray scattering measurements. The buckling occurs with a characteristic wavelength ~=10 μm.
Novel polymeric materials from triglycerides
Triglycerides are good platforms for new polymeric products that can substitute for petroleum-based materials. As part of our research emphasis in sustainability and green polymer chemistry, we have explored a number of reactions in efforts to produce a wide range of value-added products. In this ...
Ramachandran, V.; Halfpenny, PJ; Roberts, KJ
2017-01-01
The fundamentals of crystal science notably crystallography, crystal chemistry, crystal defects, crystal morphology and the surface chemistry of crystals are introduced with particular emphasis on organic crystals.
Polymeric amines and biomedical uses thereof
Broekhuis, Antonius; Zhang, Youchum; Picchioni, Francesco; Roks, Antonius
2010-01-01
The invention relates to the field of polymers and biomedical applications thereof. In particular, it relates to the use of polymeric amines derived from alternating polyketones.Provided is the use of a polymeric amine for modulating or supporting cellular behavior, said polymeric amine being an alt
THE POLYMERIZATION OF AROMATIC AND HETEROCYCLIC DINITRILES
Institute of Scientific and Technical Information of China (English)
HUANG Zhitang
1988-01-01
This review is a concise survey about the works in our laboratory on the polymerization of aromatic and heterocyclic dinitriles, including the polymerization kinetics and mechanism, synthesis of heterocyclic dinitriles, the structure of polymers, and the correlation between the structures of dinitriles and polymerization rates and thermal performances of polymers.
Glycine Polymerization on Oxide Minerals
Kitadai, Norio; Oonishi, Hiroyuki; Umemoto, Koichiro; Usui, Tomohiro; Fukushi, Keisuke; Nakashima, Satoru
2016-07-01
It has long been suggested that mineral surfaces played an important role in peptide bond formation on the primitive Earth. However, it remains unclear which mineral species was key to the prebiotic processes. This is because great discrepancies exist among the reported catalytic efficiencies of minerals for amino acid polymerizations, owing to mutually different experimental conditions. This study examined polymerization of glycine (Gly) on nine oxide minerals (amorphous silica, quartz, α-alumina and γ-alumina, anatase, rutile, hematite, magnetite, and forsterite) using identical preparation, heating, and analytical procedures. Results showed that a rutile surface is the most effective site for Gly polymerization in terms of both amounts and lengths of Gly polymers synthesized. The catalytic efficiency decreased as rutile > anatase > γ-alumina > forsterite > α- alumina > magnetite > hematite > quartz > amorphous silica. Based on reported molecular-level information for adsorption of Gly on these minerals, polymerization activation was inferred to have arisen from deprotonation of the NH3 + group of adsorbed Gly to the nucleophilic NH2 group, and from withdrawal of electron density from the carboxyl carbon to the surface metal ions. The orientation of adsorbed Gly on minerals is also a factor influencing the Gly reactivity. The examination of Gly-mineral interactions under identical experimental conditions has enabled the direct comparison of various minerals' catalytic efficiencies and has made discussion of polymerization mechanisms and their relative influences possible Further systematic investigations using the approach reported herein (which are expected to be fruitful) combined with future microscopic surface analyses will elucidate the role of minerals in the process of abiotic peptide bond formation.
Tan, Yueming; Deng, Wenfang; Li, Yunyong; Huang, Zhao; Meng, Yue; Xie, Qingji; Ma, Ming; Yao, Shouzhuo
2010-04-22
We report here on the facile preparation of polymer-enzyme-multiwalled carbon nanotubes (MWCNTs) cast films accompanying in situ laccase (Lac)-catalyzed polymerization for electrochemical biosensing and biofuel cell applications. Lac-catalyzed polymerization of dopamine (DA) as a new substrate was examined in detail by UV-vis spectroscopy, cyclic voltammetry, quartz crystal microbalance, and scanning electron microscopy. Casting the aqueous mixture of DA, Lac and MWCNTs on a glassy carbon electrode (GCE) yielded a robust polydopamine (PDA)-Lac-MWCNTs/GCE that can sense hydroquinone with 643 microA mM(-1) cm(-2) sensitivity and 20-nM detection limit (S/N = 3). The DA substrate yielded the best biosensing performance, as compared with aniline, o-phenylenediamine, or o-aminophenol as the substrate for similar Lac-catalyzed polymerization. Casting the aqueous mixture of DA, glucose oxidase (GOx), Lac, and MWCNTs on a Pt electrode yielded a robust PDA-GOx-Lac-MWCNTs/Pt electrode that exhibits glucose-detection sensitivity of 68.6 microA mM(-1) cm(-2). In addition, 2,2'-azinobis (3-ethylbenzothiazoline-6-sulfonate) diammonium salt (ABTS) was also coimmobilized to yield a PDA-Lac-MWCNTs-ABTS/GCE that can effectively catalyze the reduction of O(2), and it was successfully used as the biocathode of a membraneless glucose/O(2) biofuel cell (BFC) in pH 5.0 Britton-Robinson buffer. The proposed biomacromolecule-immobilization platform based on enzyme-catalyzed polymerization may be useful for preparing many other multifunctional polymeric bionanocomposites for wide applications.
Crystal structure of dimethylammonium hydrogen oxalate hemi(oxalic acid
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Waly Diallo
2015-05-01
Full Text Available Single crystals of the title salt, Me2NH2+·HC2O4−·0.5H2C2O4, were isolated as a side product from the reaction involving Me2NH, H2C2O4 and Sn(n-Bu3Cl in a 1:2 ratio in methanol or by the reaction of the (Me2NH22C2O4 salt and Sn(CH33Cl in a 2:1 ratio in ethanol. The asymmetric unit comprises a dimethylammonium cation (Me2NH2+, an hydrogenoxalate anion (HC2O4−, and half a molecule of oxalic acid (H2C2O4 situated about an inversion center. From a supramolecular point of view, the three components interact together via hydrogen bonding. The Me2NH2+ cations and the HC2O4− anions are in close proximity through bifurcated N—H...(O,O hydrogen bonds, while the HC2O4− anions are organized into infinite chains via O—H...O hydrogen bonds, propagating along the a-axis direction. In addition, the oxalic acid (H2C2O4 molecules play the role of connectors between these chains. Both the carbonyl and hydroxyl groups of each diacid are involved in four intermolecular interactions with two Me2NH2+ and two HC2O4− ions of four distinct polymeric chains, via two N—H...O and two O—H...O hydrogen bonds, respectively. The resulting molecular assembly can be viewed as a two-dimensional bilayer-like arrangement lying parallel to (010, and reinforced by a C—H...O hydrogen bond.
Density of conformon states in a disordered polymeric crystal
Klinskikh, A. F.
1999-03-01
Following Volkenstein's idea the density of conformon states (rho) (E) is investigated. Using the path-integral method in conditions of the strong conformational disorder the numerical account (rho) (E) is carried out. The results of account (rho) (E) under the new formula are discussed.
Two-Photon Polymerization of Defects in Photonic Crystals
2006-01-01
Garcia -Santamaria, H. Miguez, M. Ibisate, F. Meseguer, C. Lopez , Langmuir 2002, 18, 1942. 7. P. Jiang, J. F. Bertone, K. S. Hwang, V. L. Colvin, Chem...Leonard, C. Lopez , F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, H. M. van Driel, Nature 2000, 405, 437. 17. F. Garcia -Santamaria...and Robert Shimmin. It has also been a pleasure working with Christy (Ying-Chieh) Chen, Vinayak Ramanan, Erik Nelson, Wendy Chan, and the rest of
Boffa, Vittorio; Perrone, Daniele G.; MAGNACCA, Giuliana; Montoneri, Enzo
2014-01-01
An inexpensive polymeric biosurfactant isolated from urban bio-wastes is shown to be a useful chemical aid in the synthesis of nanostructured materials with tunable pore size and surface hydrophilicity. Photocatalytic active TiO2 powders were prepared by sol–gel reaction in the presence of variable amounts of a waste-derived polymeric biosurfactant. The products were characterized for morphology, crystal structures and surface hydrophilicity. The porosity data indicate that an increase of the...
Directory of Open Access Journals (Sweden)
Yi-Mei Xu
2017-03-01
Full Text Available The nickel(II catalyst has manifested higher catalytic activity compared to that of other late transition metal catalysts for norbornene polymerization. Therefore, several structurally similar trans-nickel(II compounds of N,O-chelate bidentate ligands were synthesized and characterized. Both the electronic effect and the steric hindrance influence polymerization. The molecular structures of 2, 4 and 5 were further confirmed by single-crystal X-ray diffraction.
WORTH property, Garc\\'{i}a-Falset coefficient and Opial property of infinite sums
Hardtke, Jan-David
2014-01-01
We prove some results concerning the WORTH property and the Garc\\'{i}a-Falset coefficient of absolute sums of infinitely many Banach spaces. The Opial property/uniform Opial property of infinite $\\ell^p$-sums is also studied and some properties analogous to the Opial property/uniform Opial property for Lebesgue-Bochner spaces $L^p(\\mu,X)$ are discussed.
Maxwell-Higgs self-dual solitons on an infinite cylinder
Casana, Rodolfo; Sourrouille, Lucas
2015-07-01
We have studied the Maxwell-Higgs model on the surface of an infinite cylinder. In particular, we show that this model supports self-dual topological soliton solutions on the infinite tube. Finally, the Bogomol’nyi-type equations are studied from theoretical and numerical point of view.
Institute of Scientific and Technical Information of China (English)
Yi Lin CAO; Huan Ying LI
2003-01-01
In this paper, we calculated 37 structural descriptors of 174 organic compounds. The154 molecules were used to derive quantitative structure-infinite dilution activity coefficientrelationship by genetic programming, the other 20 compounds were used to test the model. Theresult showed that molecular partition property and three-dimensional structural descriptors havesignificant influence on the infinite dilution activity coefficients.
DISCRETE-TIME STOCHASTIC EQUILIBRIUM WITH INFINITE HORIZON INCOMPLETE ASSET MARKETS
Institute of Scientific and Technical Information of China (English)
ZhangShunming
2001-01-01
Abstract. This paper examines the existence of general equilibrium in a discrete time economywith the infinite horizon incomplete markets. There is a single good at each node in the eventtree. The existence of general equilibrium for the infinite horizon economy is proved by takinglimit of equilibria in truncated economies in which trade stops at a sequence of dates.
A nonlinear discrete integrable coupling system and its infinite conservation laws
Institute of Scientific and Technical Information of China (English)
Yu Fa-Jun
2012-01-01
We construct a nonlinear integrable coupling of discrete soliton hierarchy,and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy.As an explicit application of the method proposed in the paper,the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.
Optimal value functions of generalized semi-infinite min-max programming on a noncompact set
Institute of Scientific and Technical Information of China (English)
WANG; Changyu; YANG; Xiaoqi; YANG; Xinmin
2005-01-01
In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subdifferential characterizations of optimal value functions are given. Using these properties,we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.
analysis of pressure variation of fluid in an infinite acting reservoir
African Journals Online (AJOL)
user
2017-01-01
Jan 1, 2017 ... radial diffusivity equation for a reservoir acting as if it was infinite in size ... differential equation there is an infinite number of a possible ..... the main course of many researchers. It will be .... First edition, Elsevier Science. 2001.
Finite Dimensional Compensators for Infinite Dimensional Systems with Unbounded Control Action.
1984-05-01
from infinite dimensional linear systems theory that A + GC . V(A) + X generates an exponentially stable semigroup on X (see (5) or [161). It is also...Matheatica Aplicada e Computacional, 2 (1983). 15] R.F. CURTAIN/A.J. PRITCHARD Infinite Dimensional Linear Systems Theory LNCIS 8, Springer-Verlag
Oostveen, JC; Curtain, RF
1997-01-01
We solve the problem of robust stabilization with respect to normalized coprime factor perturbations for a new class of infinite-dimensional systems with finite-rank, colocated actuators and sensors and possibly infinitely many unstable eigenvalues on the imaginary axis. Such systems are often used
Gharibi, Wajeb
2011-01-01
In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in general, and based on this method, we propose an algorithm for the mixed linear and nonlinear infinite-norm minimization cases with numerical results.
Infinite Matrix Products and the Representation of the Matrix Gamma Function
Directory of Open Access Journals (Sweden)
J.-C. Cortés
2015-01-01
Full Text Available We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.
Monreal, Marisa J; Seaman, Lani A; Goff, George S; Michalczyk, Ryszard; Morris, David E; Scott, Brian L; Kiplinger, Jaqueline L
2016-03-07
Two organometallic 1D infinite coordination polymers and two organometallic monometallic complexes of thorium diazide have been synthesized and characterized. Steric control of these self-assembled arrays, which are dense in thorium and nitrogen, has also been demonstrated: infinite chains can be circumvented by using steric bulk either at the metallocene or with a donor ligand in the wedge.
Infinite-Dimensional Feedback Systems : The Circle Criterion and Input-to-State Stability
Jayawardhana, Bayu; Logemann, Hartmut; Ryan, Eugene P.
2008-01-01
An input-to-state stability theory, which subsumes results of circle criterion type, is developed in the context of a class of infinite-dimensional systems. The generic system is of Lur’e type: a feedback interconnection of a well-posed infinite-dimensional linear system and a nonlinearity. The
DEFF Research Database (Denmark)
2005-01-01
The aim of the workshop is, to provide a forum for researchers interested in the development of mathematical techniques for the analysis and verification of systems with infinitely many states. Topics: Techniques for modeling and analysis of infinite-state systems; Equivalence-checking and model-...
WORTH property, Garc\\'{i}a-Falset coefficient and Opial property of infinite sums
Hardtke, Jan-David
2014-01-01
We prove some results concerning the WORTH property and the Garc\\'{i}a-Falset coefficient of absolute sums of infinitely many Banach spaces. The Opial property/uniform Opial property of infinite $\\ell^p$-sums is also studied and some properties analogous to the Opial property/uniform Opial property for Lebesgue-Bochner spaces $L^p(\\mu,X)$ are discussed.
Electromagnetic field interacting with a semi-infinite plasma.
Apostol, M; Vaman, G
2009-07-01
Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma by using a general, unifying procedure based on the equation of motion of the polarization and the electromagnetic potentials. Known results are reproduced in a much more direct manner, and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The propagation of an electromagnetic wave in this plasma is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved, and the reflected and refracted fields are computed, as well as the reflection coefficient. Generalized Fresnel relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon-polariton modes are identified. As is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).
A Nekhoroshev theorem for some infinite-dimensional systems
Perfetti, P
2005-01-01
We study the persistence for long times of the solutions of some infinite--dimensional discrete hamiltonian systems with {\\it formal hamiltonian} $\\sum_{i=1}^\\infty h(A_i) + V(\\vp),$ $(A,\\vp)\\in {\\Bbb R}^{\\Bbb N}\\times {\\Bbb T}^{\\Bbb N}.$ $V(\\vp)$ is not needed small and the problem is perturbative being the kinetic energy unbounded. All the initial data $(A_i(0), \\vp_i(0)),$ $i\\in {\\Bbb N}$ in the phase--space ${\\Bbb R}^{\\Bbb N} \\times {\\Bbb T}^{\\Bbb N},$ give rise to solutions with $\\mod A_i(t) - A_i(0).$ close to zero for exponentially--long times provided that $A_i(0)$ is large enough for $\\mod i.$ large. We need $\\o \\partial h,\\partial A_i,{\\scriptstyle (A_i(0))}$ unbounded for $i\\to+\\infty$ making $\\vp_i$ a {\\it fast variable}; the greater is $i,$ the faster is the angle $\\vp_i$ (avoiding the resonances). The estimates are obtained in the spirit of the averaging theory reminding the analytic part of Nekhoroshev--theorem.
The Wideband Slope of Interference Channels: The Infinite Bandwidth Case
Shen, Minqi
2010-01-01
It is well known that minimum received energy per bit in the interference channel is $-1.59dB$ as if there were no interference. Thus, the best way to mitigate interference is to operate the interference channel in the low power regime, that is in the limit of infinite bandwidth. However, when the bandwidth is large, but finite, minimum received energy per bit alone does not characterize performance. Verdu introduced the wideband slope $\\mathcal{S}_{0}$ to characterize the performance in this regime. We show that a wideband slope of ${\\mathcal{S}_{0}}/{\\mathcal{S}_{0,{no interference}}}=1/2$ is achievable. This result is similar to recent results on degrees of freedom in the high SNR regime, and we use a type of interference alignment using delays to obtain the result. We also show that in many cases the wideband slope is upper bounded by ${\\mathcal{S}_{0}}/{\\mathcal{S}_{0,{no interference}}}\\leq 1/2}$ for large number of users $K$.
Infinite N phase transitions in continuum Wilson loop operators
Narayanan, R
2006-01-01
We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Lambda-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N-universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators...
A Conformal Truncation Framework for Infinite-Volume Dynamics
Katz, Emanuel; Walters, Matthew T
2016-01-01
We present a new framework for studying conformal field theories deformed by one or more relevant operators. The original CFT is described in infinite volume using a basis of states with definite momentum, $P$, and conformal Casimir, $\\mathcal{C}$. The relevant deformation is then considered using lightcone quantization, with the resulting Hamiltonian expressed in terms of this CFT basis. Truncating to states with $\\mathcal{C} \\leq \\mathcal{C}_{\\max}$, one can numerically find the resulting spectrum, as well as other dynamical quantities, such as spectral densities of operators. This method requires the introduction of an appropriate regulator, which can be chosen to preserve the conformal structure of the basis. We check this framework in three dimensions for various perturbative deformations of a free scalar CFT, and for the case of a free $O(N)$ CFT deformed by a mass term and a non-perturbative quartic interaction at large-$N$. In all cases, the truncation scheme correctly reproduces known analytic result...
Complexity Classification in Infinite-Domain Constraint Satisfaction
Bodirsky, Manuel
2012-01-01
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values to the variables. Depending on the type of constraints that we allow in the input, a CSP might be tractable, or computationally hard. In recent years, general criteria have been discovered that imply that a CSP is polynomial-time tractable, or that it is NP-hard. Finite-domain CSPs have become a major common research focus of graph theory, artificial intelligence, and finite model theory. It turned out that the key questions for complexity classification of CSPs are closely linked to central questions in universal algebra. This thesis studies CSPs where the variables can take values from an infinite domain. This generalization enhances dramatically the range of computational problems that can be modeled as a CSP. Many problems from areas that have so far seen no interactio...
The Concept of Free Will as an Infinite Metatheoretic Recursion
Directory of Open Access Journals (Sweden)
Hashim Hanaan
2015-07-01
Full Text Available It is argued that the concept of free will, like the concept of truth in formal languages, requires a separation between an object level and a meta-level for being consistently defined. The Jamesian two stage model, which deconstructs free will into the causally open “free” stage with its closure in the “will” stage, is implicitly a move in this direction. However, to avoid the dilemma of determinism, free will additionally requires an infinite regress of causal meta-stages, making free choice a hypertask. We use this model to define free will of the rationalist-compatibilist type. This is shown to provide a natural three-way distinction between quantum indeterminism, freedom and free will, applicable respectively to artificial intelligence (AI, animal agents and human agents. We propose that the causal hierarchy in our model corresponds to a hierarchy of Turing uncomputability. Possible neurobiological and behavioral tests to demonstrate free will experimentally are suggested. Ramifications of the model for physics, evolutionary biology, neuroscience, neuropathological medicine and moral philosophy are briefly outlined.
Axisymmetric free vibrations of infinite micropolar thermoelastic plate
Institute of Scientific and Technical Information of China (English)
Rajneesh Kumar; Geeta Partap
2007-01-01
The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation.The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.
On the infinite fern of Galois representations of unitary type
Chenevier, Gaetan
2009-01-01
Let E be a CM number field, F its maximal totally real subfield, c the generator of Gal(E/F), p an odd prime totally split in E, and S a finite set of places of E containing the places above p. Let r : G_{E,S} --> GL_3(F_p^bar) be a modular, absolutely irreducible, Galois representation of type U(3), i.e. such that r^* = r^c, and let X(r) be the rigid analytic generic fiber of its universal G_{E,S}-deformation of type U(3). We show that each irreducible component of the Zariski-closure of the modular points in X(r) has dimension at least 6[F:Q]. We study an analogue of the infinite fern of Gouvea-Mazur in this context and deal with the Hilbert modular case as well. As important steps, we prove that any first order deformation of a generic enough crystalline representation of Gal(Q_p^bar/Q_p) (of any dimension) is a linear combination of trianguline deformations, and that unitary eigenvarieties (of any rank) are etale over the weight space at the non-critical classical points. As another application, we obtain...
Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents
Athanassoulis, Agissilaos
2016-08-30
Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.
Second law analysis of an infinitely segmented magnetohydrodynamic generator
Arash, Ardeshir; Saidi, Mohammad Hassan; Najafi, Mohammad
2017-03-01
The performance of an infinitely segmented magnetohydrodynamic generator is analyzed using the second law of thermodynamics entropy generation criterion. The exact analytical solution of the velocity and temperature fields are provided by applying the modified Hartmann flow model, taking into account the occurrence of the Hall effect in the considered generator. Contributions of heat transfer, fluid friction, and ohmic dissipation to the destruction of useful available work are found, and the nature of irreversibilities in the considered generator is determined. In addition, the electrical isotropic efficiency scheme is used to evaluate the generator performance. Finally, the implication of the Hall parameter, Hartmann number, and load factor for the entropy generation and the generator performance are studied and the optimal operating conditions are determined. The results show that the heat transfer has the smallest contribution to the entropy generation compared to that of the friction and ohmic dissipation. The application of the Hall effect on the system showed an appreciable augmentation of entropy generation rate which is along with what the logic implies. A parametric study is conducted and its results provide the generated entropy and also efficiency diagrams which show the influence of the Hall effect on the considered generator.
Infinite Variance in Fermion Quantum Monte Carlo Calculations
Shi, Hao
2015-01-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, lattice QCD calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied upon to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple sub-areas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations turn out to have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calc...
Infinitely extended Kac table of solvable critical dense polymers
Pearce, Paul A; Villani, Simon P
2012-01-01
Solvable critical dense polymers is a Yang-Baxter integrable model of polymers on the square lattice. It is the first member LM(1,2) of the family of logarithmic minimal models LM(p,p'). The associated logarithmic conformal field theory admits an infinite family of Kac representations labelled by the Kac labels r,s=1,2,.... In this paper, we explicitly construct the conjugate boundary conditions on the strip. The boundary operators are labelled by the Kac fusion labels (r,s)=(r,1) x (1,s) and involve a boundary field xi. Tuning the field xi appropriately, we solve exactly for the transfer matrix eigenvalues on arbitrary finite-width strips and obtain the conformal spectra using the Euler-Maclaurin formula. The key to the solution is an inversion identity satisfied by the commuting double-row transfer matrices. The transfer matrix eigenvalues are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. This yields selection rules for the physically relevant sol...
Zhang, Lei; Ling, Yun; Peng, Feng; Du, Miao
2007-03-01
Four novel fluconazole-bridged Zn(II) complexes, [Zn(HFlu)Cl 2(DMF)] 2 ( 1), {[Zn(HFlu) 2(H 2O) 2](NO 3) 2·2DMF} n ( 2), {[Zn(HFlu) 2(H 2O) 2](NO 3) 2} n ( 3) and {[Zn(HFlu)(SCN) 2]·H 2O} n ( 4) [HFlu = 2-(2,4-difluorophenyl)-1,3-bis(1,2,4-triazol-1-yl)-propan-2-ol], have been synthesized and structurally characterized by X-ray diffraction method. The structure of dimeric complex 1 consists of 20-membered macrometallacyclic ring-like structure, in which the Zn(II) ion is in a five-coordinated distorted trigonal bipyramidal geometry with the Zn⋯Zn distance of 10.265(3) Å across the cis HFlu ligand. Complex 2 shows infinite 1-D macrocyclic double chain structure with the central Zn(II) ions being six-coordinated by four HFlu ligands and two apical water molecules and with the intrachain Zn⋯Zn distance of 10.722(3) Å across the trans HFlu ligand. The crystal structure of complex 3 is analogous to that of complex 2 with the intrachain Zn⋯Zn distance of 10.654(2) Å. The structure of complex 4 consists of infinite 1-D coordination polymeric chain with the tetrahedral coordination geometry of Zn(II) ion and with the intrachain Zn⋯Zn distance of 11.173(2) Å across the cis HFlu ligand. Complexes 1- 4 show the similar fluorescence emission to the free HFlu ligand at ambient temperature and the thermal stabilities of the complexes have also been investigated.
Energy Technology Data Exchange (ETDEWEB)
Ceyhan, Goekhan [Chemistry Department, K.Maras Suetcue Imam University, 46100 K.Maras (Turkey); Tuemer, Mehmet, E-mail: mtumer@ksu.edu.tr [Chemistry Department, K.Maras Suetcue Imam University, 46100 K.Maras (Turkey); Koese, Muhammet; McKee, Vickie [Chemistry Department, Loughborough University, LE11 3TU Leicestershire (United Kingdom)
2012-03-15
In this paper, we obtained a novel poly(vanillinato potassium) complex (PVP) as a single crystal and characterized by analytical and spectroscopic methods. A single crystal of the PVP was obtained from the acetone solution. X-ray structural data show that crystals contain polymeric K{sup +} complex of vanillin. Each potassium ion in the polymeric structure is identical and seven-coordinate, bonded to two methoxy, two phenoxy and three aldehyde oxygen atoms from four vaniline molecules. Two aldehyde oxygen atoms are bridging between potassium ions. It crystallizes in the monoclinic system, space group P2{sub 1}/c, with lattice parameters a=9.6215(10) A, b=17.4139(19) A, c=9.6119(10) A, {beta}=100.457(2) Degree-Sign and Z=4. Thermal properties of the PVP were investigated by TGA, DTA and DSC methods. The electrochemical properties of the complex were studied in different solvents and at various scan rates. The luminescence properties of the complex in different solvents and at different pH values have been investigated. The results show that the complex exhibits more efficient luminescence property in CH{sub 3}CN and n-butanol. - Highlights: Black-Right-Pointing-Pointer Novel polymeric potassium complex was prepared and fully characterized. Black-Right-Pointing-Pointer X-ray crystal structure of complex was reported. Black-Right-Pointing-Pointer Electrochemical properties of compound were investigated. Black-Right-Pointing-Pointer Thermal and DSC measurements of complex were examined.
SCATTERING FROM RAMIFIED POLYMERIC SYSTEMS
Directory of Open Access Journals (Sweden)
M.Benhamou
2004-01-01
Full Text Available Here, of great interest to us is a quantitative study of the scattering properties from ramified polymeric systems of arbitrary topology. We consider three types of systems, namely ramified polymers in solution, ramified polymer blends, or ternary mixtures made of two ramified polymers of different chemical nature immersed in a good solvent. To achieve the goal of the study, use is made of the Random Phase Approximation. First we determine the exact expression of the form factor of an ideal ramified polymer of any topology, from which we extract the exact expression of its gyration radius. Using the classical Zimm's formulae and the exact form factor, we determine all scattering properties of these three types of ramified polymeric systems. The main conclusion is that ramification of the chains induces drastic changes of the scattering properties.
Magnetic properties of polymerized diphenyloctatetrayne
Energy Technology Data Exchange (ETDEWEB)
Beristain, Miriam F.; Jimenez-Solomon, Maria F.; Ortega, Alejandra; Escudero, Roberto [Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-360, Ciudad Universitaria, Mexico DF 04510 (Mexico); Munoz, Eduardo [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-364, Ciudad Universitaria, Mexico DF 01000 (Mexico); Maekawa, Yasunari; Koshikawa, Hiroshi [High Performance Polymer Group, Quantum Beam Science Directorate, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292 (Japan); Ogawa, Takeshi, E-mail: ogawa@unam.mx [Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-360, Ciudad Universitaria, Mexico DF 04510 (Mexico)
2012-10-15
A new type of metal-free ferromagnetic carbon material was obtained by thermal polymerization and electron beam irradiation of diphenyloctatetrayne (DPOT). The isothermal magnetic measurements showed hysteresis loops indicating weak but intrinsic ferromagnetism with Curie temperatures of around 600 K. Electron spin resonance spectroscopy showed that the material contained stable free radicals in the range of 10{sup 17}-10{sup 20} radicals g{sup -1} depending on the polymerization process. The ferromagnetism should be due to high radical concentration although no correlation was observed between them. It was shown that an amorphous ferromagnetic carbon could be obtained from a simple crystalline solid by heating at moderate temperatures. Highlights: Black-Right-Pointing-Pointer Diphenyloctatetrayne as a precursor for carbon with high radical concentration. Black-Right-Pointing-Pointer The carbon material consists of sp{sup 2} configuration. Black-Right-Pointing-Pointer A weak intrinsic metal-free ferromagnetism was observed for the carbon products.
Energy Technology Data Exchange (ETDEWEB)
Qian, Denghui, E-mail: qdhsd318@163.com; Shi, Zhiyu, E-mail: zyshi@nuaa.edu.cn
2017-05-03
This paper couples the plane wave expansion (PWE) and finite element (FE) methods to calculate the band structures of the semi-infinite beam-like phononic crystals (PCs) with the infinite periodicity in z-direction and finiteness in x–y plane. Explicit matrix formulations are developed for the calculation of band structures. In order to illustrate the applicability and accuracy of the proposed coupled plane wave expansion and finite element (PWE/FE) method to beam-like PCs, several examples are displayed. At first, PWE/FE method is applied to calculate the band structures of the Pb/rubber beam-like PCs with circular and rectangular cross sections, respectively. Then, it is used to calculate the band structures of steel/epoxy and steel/aluminum beam-like PCs with the same geometric parameters. Last, the band structure of the three-component beam-like PC is also calculated by the proposed method. Moreover, all the results calculated by PWE/FE method are compared with those calculated by finite element (FE) method, and the corresponding results are in good agreement. - Highlights: • The concept of the semi-infinite beam-like phononic crystals (PCs) is proposed. • The PWE/FE method is proposed and formulized to calculate the band structures of the semi-infinite beam-like PCs. • The strong applicability and high accuracy of PWE/FE method are verified.
Polymeric Microspheres for Medical Applications
Directory of Open Access Journals (Sweden)
Ketie Saralidze
2010-06-01
Full Text Available Synthetic polymeric microspheres find application in a wide range of medical applications. Among other applications, microspheres are being used as bulking agents, embolic- or drug-delivery particles. The exact composition of the spheres varies with the application and therefore a large array of materials has been used to produce microspheres. In this review, the relation between microsphere synthesis and application is discussed for a number of microspheres that are used for different treatment strategies.
Partitioning of Laponite Clay Platelets in Pickering Emulsion Polymerization.
Brunier, Barthélémy; Sheibat-Othman, Nida; Chevalier, Yves; Bourgeat-Lami, Elodie
2016-01-12
Partitioning of laponite disklike clay platelets between polymer particles and bulk aqueous phase was investigated in Pickering surfactant-free emulsion polymerization of styrene. Adsorption of laponite clay platelets plays an important role in the stabilization of this system, influencing the particle size and the number of particles, and, hence, the reaction rate. Adsorption isotherms show that, while the laponite clay platelets are almost fully exfoliated in water, they form multilayers on the surface of the polymer particles by the end of polymerization, as confirmed by transmission electron microscopy (TEM). This observation is supported by quartz crystal microbalance, conductivity, and TEM measurements, which reveal interactions between the clay and polystyrene, as a function of the ionic strength. The strong adsorption of clay platelets leaves a low residual concentration in the aqueous phase that cannot cause further nucleation of polymer particles, as demonstrated during seeded emulsion polymerization experiments in the presence of a high excess of clay. A Brunauer-Emmett-Teller (BET)-type model for laponite adsorption on polystyrene particles matches the adsorption isotherms.
Infinite Coordination Polymer Nano- and Micro-Particles
2015-06-12
potential applications is in part due to the fact that these structures , consisting of repeating ligands interconnected by metallic nodes, can be made...Figure 5: Representations of the crystal structure of NU-135. (a) Detail of pores, viewed along the ab plane. Lilac spheres indicate the...based linkers exhibit not only bending in the alkyne regions, but also twisting at the cobalt metal center. These structural considerations behave in
Ultrasound-Mediated Polymeric Micelle Drug Delivery.
Xia, Hesheng; Zhao, Yue; Tong, Rui
2016-01-01
The synthesis of multi-functional nanocarriers and the design of new stimuli-responsive means are equally important for drug delivery. Ultrasound can be used as a remote, non-invasive and controllable trigger for the stimuli-responsive release of nanocarriers. Polymeric micelles are one kind of potential drug nanocarrier. By combining ultrasound and polymeric micelles, a new modality (i.e., ultrasound-mediated polymeric micelle drug delivery) has been developed and has recently received increasing attention. A major challenge remaining in developing ultrasound-responsive polymeric micelles is the improvement of the sensitivity or responsiveness of polymeric micelles to ultrasound. This chapter reviews the recent advance in this field. In order to understand the interaction mechanism between ultrasound stimulus and polymeric micelles, ultrasound effects, such as thermal effect, cavitation effect, ultrasound sonochemistry (including ultrasonic degradation, ultrasound-initiated polymerization, ultrasonic in-situ polymerization and ultrasound site-specific degradation), as well as basic micellar knowledge are introduced. Ultrasound-mediated polymeric micelle drug delivery has been classified into two main streams based on the different interaction mechanism between ultrasound and polymeric micelles; one is based on the ultrasound-induced physical disruption of the micelle and reversible release of payload. The other is based on micellar ultrasound mechanochemical disruption and irreversible release of payload.
First Evidence of Near-Infrared Photonic Bandgap in Polymeric Rod-Connected Diamond Structure
Chen, Lifeng; Zheng, Xu; Lin, Jia-De; Oulton, Ruth; Lopez-Garcia, Martin; Ho, Ying-Lung D; Rarity, John G
2015-01-01
We present the simulation, fabrication, and optical characterization of low-index polymeric rod-connected diamond (RCD) structures. Such complex three-dimensional photonic crystal structures are created via direct laser writing by two-photon polymerization. To our knowledge, this is the first measurement at near-infrared wavelengths, showing partial photonic bandgaps. We characterize structures in transmission and reflection using angular resolved Fourier image spectroscopy to visualize the band structure. Comparison of the numerical simulations of such structures with the experimentally measured data show good agreement for both P- and S-polarizations.
Photochemical stability of nonlinear optical chromophores in polymeric and crystalline materials.
Rezzonico, Daniele; Kwon, Seong-Ji; Figi, Harry; Kwon, O-Pil; Jazbinsek, Mojca; Günter, Peter
2008-03-28
We compare the photochemical stability of the nonlinear optical chromophore configurationally locked polyene 2-{3-[2-(4-dimethylaminophenyl)vinyl]-5,5-dimethylcyclohex-2-enylidene} malononitrile (DAT2) embedded in a polymeric matrix and in a single-crystalline configuration. The results show that, under resonant light excitations, the polymeric compound degrades through an indirect process, while the DAT2 crystal follows a slow direct process. We show that chromophores in a crystalline environment exhibit three orders of magnitude better photostability as compared to guest-host polymer composites.
Studies in reactive extrusion processing of biodegradable polymeric materials
Balakrishnan, Sunder
Various reaction chemistries such as Polymerization, Polymer cross-linking and Reactive grafting were investigated in twin-screw extruders. Poly (1,4-dioxan-2-one) (PPDX) was manufactured in melt by the continuous polymerization of 1,4-dioxan-2-one (PDX) monomer in a twin-screw extruder using Aluminum tri-sec butoxide (ATSB) initiator. Good and accurate control over molecular weight was obtained by controlling the ratio of monomer to initiator. A screw configuration consisting of only conveying elements was used for the polymerization. The polymerization reaction was characterized by a monomer-polymer dynamic equilibrium, above the melting temperature of the polymer, limiting the equilibrium conversion to 78-percent. Near complete (˜100-percent) conversion was obtained on co-polymerizing PDX monomer with a few mol-percent (around 8-percent) Caprolactone (CL) monomer in a twin-screw extruder using ATSB initiator. The co-polymers exhibited improved thermal stability with reduction in glass transition temperature. The extruder was modeled as an Axial Dispersed Plug Flow Reactor for the polymerization of CL monomer using Residence Time Distribution (RTD) Analysis. The model provided a good fit to the experimental RTD and conversion data. Aliphatic and aliphatic-aromatic co-polyesters, namely Polycaprolactone (PCL) and Poly butylenes (adipate-co-terephthalate) (Ecoflex) were cross-linked in a twin-screw extruder using radical initiator to form micro-gel reinforced biodegradable polyesters. Cross-linked Ecoflex was further extrusion blended with talc to form blends suitable to be blown into films. A screw configuration consisting of conveying and kneading elements was found to be effective in dispersion of the talc particles (5--10 microns) in the polyester matrix. While the rates of crystallization increased for the talc filled polyester blends, overall crystallinity reduced. Mechanical, tear and puncture properties of films made using the talc filled polyester blends
Polymeric architectures of bismuth citrate based on dimeric building blocks
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Four bismuth complexes, (H2En)[Bi2(cit)2(H2O)4/3]·(H2O)x (1), (H2En)3[Bi2(cit)2Cl4]·(H2O)x (2), (HPy)2[Bi2(cit)2(H2O)8/5]·(H2O)x (3) and (H2En)[Bi2(cit)2](H2O)x (4) [cit = citrate4-; En = ethylenediamine; Py = pyridine] have been synthesized and crystallized. The crystal structures reveal that the basic building blocks in all of these complexes are bismuth citrate dimeric units which combine to form polymeric architectures. The embedded protonated ethylenediamine and pyridine moieties in the polymeric frameworks have been identified by X-ray crystallography and solid-state cross polarization/magic angle spinning (CP/MAS) 13C NMR. Based on the framework of complex 1, a structural model of a clinically used antiulcer drug, ranitidine bismuth citrate (RBC) was generated. The behavior of the protonated amine-bismuth citrate complexes in acidic aqueous solution has been studied by electrospray ionization-mass spectrometry (ESI-MS).
Mercuric iodide semiconductor detectors encapsulated in polymeric resin
Energy Technology Data Exchange (ETDEWEB)
Martins, Joao F. Trencher; Santos, Robinson A. dos; Ferraz, Caue de M.; Oliveira, Adriano S.; Velo, Alexandre F.; Mesquita, Carlos H. de; Hamada, Margarida M., E-mail: mmhamada@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil); Disch, Christian; Fiederle, Michael [Albert-Ludwigs Universität Freiburg - UniFreibrug, Freiburg Materials Research Center - FMF, Freiburg (Germany)
2015-07-01
The development of new semiconductor radiation detectors always finds many setback factors, such as: high concentration of impurities in the start materials, poor long term stability, the surface oxidation and other difficulties discussed extensively in the literature, that limit their use. In this work was studied, the application of a coating resin on HgI2 detectors, in order to protect the semiconductor crystal reactions from atmospheric gases and to isolate electrically the surface of the crystals. Four polymeric resins were analyzed: Resin 1: 50% - 100%Heptane, 10% - 25% methylcyclohexane, <1% cyclohexane; Resin 2: 25% - 50% ethanol, 25% - 50% acetone, <2,5% ethylacetate; Resin 3: 50% - 100% methylacetate, 5% - 10% n-butylacetate; Resin 4: 50% - 100% ethyl-2-cyanacrylat. The influence of the polymeric resin type used on the spectroscopic performance of the HgI{sub 2} semiconductor detector is, clearly, demonstrated. The better result was found for the detector encapsulated with Resin 3. An increase of up to 26 times at the stability time was observed for the detectors encapsulated compared to that non-encapsulated detector. (author)
Xia, Hesheng; Wang, Qi; Liao, Yongqin; Xu, Xi; Baxter, Steven M; Slone, Robert V; Wu, Shuguang; Swift, Graham; Westmoreland, David G
2002-07-01
The factors affecting the induction period and polymerization rate in ultrasonically initiated emulsion polymerization of n-butyl acrylate (BA) were investigated. The induction period takes only an instant in ultrasonically initiated emulsion polymerization of BA without any added initiator by enhancing the N2 flow rate. Increasing temperature, power output and SDS concentration, decreasing the monomer concentration results in further decreasing induction period and enhanced polymerization rate. Under optimized reaction conditions the conversion of BA reaches 92% in 11 min. The polymerization rate can be controlled by varying reaction parameters. The apparatus of ultrasonically initiated semi-continuous and continuous emulsion polymerization were set up and the feasibility was first studied. Based on the experimental results, a free radical polymerization mechanism for ultrasonically initiated emulsion polymerization was proposed, including the sources of the radicals, the process of radical formation, the locus of polymerization and the polymerization process. Compared with conventional emulsion polymerization, where the radicals come from thermal decomposition of a chemical initiator, ultrasonically initiated emulsion polymerization has attractive features such as no need for a chemical initiator, lower reaction temperature, faster polymerization rate, and higher molecular weight of the polymer prepared.
Institute of Scientific and Technical Information of China (English)
WANG Chun-ling; HUANG Yi; JIA Ji-hong
2007-01-01
The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load. And an integral representations for the displacements of the semi-infinite elastic foundation was presented. The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semiinfinite elastic foundation. Some computational results and the analysis on the influence of parameters were presented.
Purely infinite simple reduced C*-algebras of one-relator separated graphs
Ara, Pere
2012-01-01
Given a separated graph $(E,C)$, there are two different C*-algebras associated to it, the full graph C*-algebra $C^*(E,C)$, and the reduced one $C^*_{\\text{red}} (E,C)$. For a large class of separated graphs $(E,C)$, we prove that $C^*_{\\text{red}} (E,C)$ either is purely infinite simple or admits a faithful tracial state. The main tool we use to show pure infiniteness of reduced graph C*-algebras is a generalization to the amalgamated case of a result on purely infinite simple free products due to Dykema.
Institute of Scientific and Technical Information of China (English)
G.J. Zalmai; Qing-hong Zhang
2007-01-01
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of parametric duality results under various generalized (η, p)-invexity assumptions for a semi-infinite minmax fractional programming problem.
Diagonalization of infinite transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model
Kojima, Takeo
2010-01-01
We study infinitely many commuting operators $T_B(z)$, which we call infinite transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model. We diagonalize infinite transfer matrix $T_B(z)$ by using free field realizations of the vertex operators of the elliptic quantum group $U_{q,p}(A_{N-1}^{(1)})$.
Nanoporous Polymeric Grating-Based Biosensors
Gao, Tieyu
2012-05-02
We demonstrate the utilization of an interferometrically created nanoporous polymeric gratings as a platform for biosensing applications. Aminopropyltriethoxysilane (APTES)-functionalized nanoporous polymeric gratings was fabricated by combining holographic interference patterning and APTES-functionalization of pre-polymer syrup. The successful detection of multiple biomolecules indicates that the biofunctionalized nanoporous polymeric gratings can act as biosensing platforms which are label-free, inexpensive, and applicable as high-throughput assays. Copyright © 2010 by ASME.
PHOTOSENSITIVITY OF CERIC ION INITIATED ACRYLAMIDE POLYMERIZATION
Institute of Scientific and Technical Information of China (English)
DONG Jianhua; QIU Kunyuan; FENG Xinde
1992-01-01
Polymerization of acrylamide initiated by ceric ammonium nitrate alone has been studied in aqueous medium. The effects of UV light irradiation on the initial rates of polymerization, the activation energy and on the polymer molecular weights have been investigated. Compared with that in the dark, the rate of polymerization under UV light was accelerated to eleven times higher, and the overall activation energy was lowered markedly.
Order and Chaos in Some Deterministic Infinite Trigonometric Products
Albert, Leif; Kiessling, Michael K.-H.
2017-08-01
It is shown that the deterministic infinite trigonometric products \\prod _{n\\in N}[ 1- p +p cos ( style n^{-s}_{_{}}t) ] =: {{ Cl }_{p;s}^{}}(t) with parameters p\\in (0,1] & s>1/2, and variable t\\in R, are inverse Fourier transforms of the probability distributions for certain random series Ω p^ζ (s) taking values in the real ω line; i.e. the {{ Cl }_{p;s}^{}}(t) are characteristic functions of the Ω p^ζ (s). The special case p=1=s yields the familiar random harmonic series, while in general Ω p^ζ (s) is a "random Riemann-ζ function," a notion which will be explained and illustrated—and connected to the Riemann hypothesis. It will be shown that Ω p^ζ (s) is a very regular random variable, having a probability density function (PDF) on the ω line which is a Schwartz function. More precisely, an elementary proof is given that there exists some K_{p;s}^{}>0, and a function F_{p;s}^{}(|t|) bounded by |F_{p;s}^{}(|t|)|!≤ \\exp \\big (K_{p;s}^{} |t|^{1/(s+1)}), and C_{p;s}^{} =-1/s\\int _0^∞ ln |{1-p+p cos ξ }|1/ξ ^{1+1/s}{d}ξ , such that \\forall t\\in R:\\quad {{ Cl }_{p;s}^{}}(t) = \\exp \\bigl ({- C_{p;s}^{} |t|^{1/s}\\bigr )F_{p;s}^{}(|t|)}; the regularity of Ω p^ζ (s) follows. Incidentally, this theorem confirms a surmise by Benoit Cloitre, that ln {{ Cl }_{{{1}/{3}};2}^{}}(t) ˜ -C√{t} ( t→ ∞) for some C>0. Graphical evidence suggests that {{ Cl }_{{{1}/{3}};2}^{}}(t) is an empirically unpredictable (chaotic) function of t. This is reflected in the rich structure of the pertinent PDF (the Fourier transform of {{ Cl }_{{{1}/{3}};2}^{}}), and illustrated by random sampling of the Riemann-ζ walks, whose branching rules allow the build-up of fractal-like structures.
Directional Growth of Polymeric Nanowires
Thapa, Prem; Flanders, Bret
2009-03-01
This work establishes an innovative electrochemical approach to the template free growth of conducting polypyrrole and polythiophene wires. These polymeric wires exhibit a knobby structure, but persistent growth in a given direction up to 30 μm in length. A long-range component of the applied voltage signal defines the growth-path. Moreover, the presence of this component enables the growth of amorphous nanowires with wire-like geometries. Such wires are employed in a non-invasive methodology for attaining strong mechanical attachments to live cells. This capability is of potential use in the electro-mechanical probing of cell physiological processes.
Marketing NASA Langley Polymeric Materials
Flynn, Diane M.
1995-01-01
A marketing tool was created to expand the knowledge of LaRC developed polymeric materials, in order to facilitate the technology transfer process and increase technology commercialization awareness among a non-technical audience. The created brochure features four materials, LaRC-CP, LaRC-RP46, LaRC-SI, and LaRC-IA, and highlights their competitive strengths in potential commercial applications. Excellent opportunities exist in the $40 million per year microelectronics market and the $6 billion adhesives market. It is hoped that the created brochure will generate inquiries regarding the use of the above materials in markets such as these.
Charge transport in polymeric transistors
Directory of Open Access Journals (Sweden)
Alberto Salleo
2007-03-01
Full Text Available Polymeric semiconductors have attracted much attention because of their possible use as active materials in printed electronics. Thin-film transistors (TFTs are a convenient tool for studying charge-transport physics in conjugated polymers. Two families of materials are reviewed here: fluorene copolymers and polythiophenes. Because charge transport is highly anisotropic in molecular conductors, the electrical properties of conjugated polymers are strongly dependent on microstructure. Molecular weight, polydispersity, and regioregularity all affect morphology and charge-transport in these materials. Charge transport models based on microstructure are instrumental in identifying the electrical bottlenecks in these materials.
High Vacuum Techniques for Anionic Polymerization
Ratkanthwar, Kedar
2015-09-01
Anionic polymerization high vacuum techniques (HVTs) are the most suitable for the preparation of polymer samples with well-defined complex macromolecular architectures. Though HVTs require glassblowing skill for designing and making polymerization reactor, it is the best way to avoid any termination of living polymers during the number of steps for the synthesis of polymers with complex structure. In this chapter, we describe the different polymerization reactors and HVTs for the purification of monomers, solvents, and other reagents for anionic polymerization as well as few model reactions for the synthesis of polymers with simple to complex structure.
The correlation length in thin film and semi-infinite medium
Korneta, W.; Pytel, Z.
1983-03-01
Correlation lengths in directions parallel and perpendicular to a surface of a thin ferromagnetic film and a semi-infinite ferromagnet are calculated. Their dependences both on temperature and distance to a surface are discussed.
Green's function formalism in semi-infinite composites: an investigation of local field distribution
Li, Chen; Gu, Ying; Dai, Bing; Gong, Qi-Huang
2004-11-01
In the resonant composites, the formerly developed Green's function formalism (GFF) can be used to compute the local field distribution near resonance. In this paper, we extend the GFF in the infinite network to the semi-infinite networks by the method of image. Using the formalism, we investigate the local field distribution near resonance for the impurity clusters with admittance epsilon0 embedded in one semi-infinite network with epsilon1. With varying the admittance epsilon2 of another semi-infinite network, we find that the local fields in the boundary experience great changes, especially at epsilon2 = -epsilon1. The existence of the boundary enhances the localization of the fields within and around the metallic clusters. Therefore, the intensity of local field is influenced by the arrangement of impurity metallic bonds and its distance from the boundary.
Green's function formalism in semi-infinite composites:an investigation of local field distribution
Institute of Scientific and Technical Information of China (English)
Li Chen; Gu Ying; Dai Bing; Gong Qi-Huang
2004-01-01
In the resonant composites, the formerly developed Green's function formalism (GFF) can be used to compute the local field distribution near resonance. In this paper, we extend the GFF in the infinite network to the semi-infinite networks by the method of image. Using the formalism, we investigate the local field distribution near resonance for the impurity clusters with admittance ∈0 embedded in one semi-infinite network with ∈1. With varying the admittance ∈2 of another semi-infinite network, we find that the local fields in the boundary experience great changes, especially at ∈2= -∈1. The existence of the boundary enhances the localization of the fields within and around the metallic clusters.Therefore, the intensity of local field is influenced by the arrangement of impurity metallic bonds and its distance from the boundary.
Liang, Xiao; Wang, Linshan; Wang, Yangfan; Wang, Ruili
2016-09-01
In this paper, we focus on the long time behavior of the mild solution to delayed reaction-diffusion Hopfield neural networks (DRDHNNs) driven by infinite dimensional Wiener processes. We analyze the existence, uniqueness, and stability of this system under the local Lipschitz function by constructing an appropriate Lyapunov-Krasovskii function and utilizing the semigroup theory. Some easy-to-test criteria affecting the well-posedness and stability of the networks, such as infinite dimensional noise and diffusion effect, are obtained. The criteria can be used as theoretic guidance to stabilize DRDHNNs in practical applications when infinite dimensional noise is taken into consideration. Meanwhile, considering the fact that the standard Brownian motion is a special case of infinite dimensional Wiener process, we undertake an analysis of the local Lipschitz condition, which has a wider range than the global Lipschitz condition. Two samples are given to examine the availability of the results in this paper. Simulations are also given using the MATLAB.
Existence of infinitely many periodic solutions for second-order nonautonomous Hamiltonian systems
Directory of Open Access Journals (Sweden)
Wen Guan
2015-04-01
Full Text Available By using minimax methods and critical point theory, we obtain infinitely many periodic solutions for a second-order nonautonomous Hamiltonian systems, when the gradient of potential energy does not exceed linear growth.
Diffraction of a Shear Plane Wave in Elastic Medium with Piecewise Homogeneous Infinite Inclusion
Directory of Open Access Journals (Sweden)
Voskanyan A. R.
2007-06-01
Full Text Available Diffraction of shear plane wave incident from infinity at arbitrary angle on infinite inclusion is considered. The infinite inclusion consists of two semi-infinite parts made of different materials. The problem’s solution is presented in the form of sum of its even and odd problems. The case of long waves is considered and these problems (the even and odd ones are modelled in a corresponding way after which each of them is reduced to the solution of Wiener-Hopf functional equation. Asymptotic formulas are obtained for displacement’s amplitude and contacts stresses in the far field. The behaviors of contact stresses in the neighborhood of the bonding line of the semi-infinite parts of the inclusion are also obtained.
ASYMPTOTIC SIMILARITY OF INFINITE-DIMENSIONAL LINEAR SYSTEMS AND APPLICATIONS TO STABILITY
Institute of Scientific and Technical Information of China (English)
WU Jingbo
2000-01-01
In this note a generalization of the concept of similarity called asymptotic similarity for infinite-dimensional linear systems is introduced. We show that this asymptotic similarity preserves the spectrum and the exponential growth bound.
High-energy scatterings in infinite-derivative field theory and ghost-free gravity
Talaganis, Spyridon; Mazumdar, Anupam
2016-07-01
In this paper, we will consider scattering diagrams in the context of infinite-derivative theories. First, we examine a finite-order, higher-derivative scalar field theory and find that we cannot eliminate the growth of scattering diagrams for large external momenta. Then, we employ an infinite-derivative scalar toy model and obtain that the external momentum dependence of scattering diagrams is convergent as the external momenta become very large. In order to eliminate the external momentum growth, one has to dress the bare vertices of the scattering diagrams by considering renormalised propagator and vertex loop corrections to the bare vertices. Finally, we investigate scattering diagrams in the context of a scalar toy model which is inspired by a ghost-free and singularity-free infinite-derivative theory of gravity, where we conclude that infinite derivatives can eliminate the external momentum growth of scattering diagrams and make the scattering diagrams convergent in the ultraviolet.
Stochastic optimal control in infinite dimension dynamic programming and HJB equations
Fabbri, Giorgio; Święch, Andrzej
2017-01-01
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...
Surface charge of polyoxometalates modulates polymerization of the scrapie prion protein.
Wille, Holger; Shanmugam, Maheswaran; Murugesu, Muralee; Ollesch, Julian; Stubbs, Gerald; Long, Jeffrey R; Safar, Jiri G; Prusiner, Stanley B
2009-03-10
Prions are composed solely of an alternatively folded isoform of the prion protein (PrP), designated PrP(Sc). N-terminally truncated PrP(Sc), denoted PrP 27-30, retains infectivity and polymerizes into rods with the ultrastructural and tinctorial properties of amyloid. We report here that some polyoxometalates (POMs) favor polymerization of PrP 27-30 into prion rods, whereas other POMs promote assembly of the protein into 2D crystals. Antibodies reacting with epitopes in denatured PrP 27-30 also bound to 2D crystals treated with 3 M urea. These same antibodies did not bind to either native PrP(Sc) or untreated 2D crystals. By using small, spherical POMs with Keggin-type structures, the central heteroatom was found to determine whether prion rods or 2D crystals were preferentially formed. An example of a Keggin-type POM with a phosphorous heteroatom is the phosphotungstate anion (PTA). Both PTA and a Keggin-type POM with a silicon heteratom have low-charge densities and favor formation of prion rods. In contrast, POMs with boron or hydrogen heteroatoms exhibiting higher negative charges encouraged 2D crystal formation. The 2D crystals of PrP 27-30 produced by selective precipitation with POMs were larger and more well ordered than those obtained by sucrose gradient centrifugation. Our findings argue that the negative charge of Keggin-type POMs determines the quaternary structure adopted by PrP 27-30. The mechanism by which POMs function in competing prion polymerization pathways--one favoring 2D crystals and the other, amyloid fibrils--remains to be established.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A series of St/BA/MAA emulsion polymerizations was carried out. By using PCS (photon correlation spectroscopy), the particle size distribution(PSD) of the whole St/BA/MAA emulsion polymerization process was gotten easily and quickly. The effect of polymerization condition on PSD in St/BA/MAA emulsion process was discussed.
Twin screw extruders as polymerization reactors for a free radical homo polymerization
Ganzeveld, K.J.; Janssen, L.P.B.M.
1993-01-01
The bulk polymerization of n-butylmethacrylate was investigated in a counter-rotating twin screw extruder. It appeared that the gel effect, occurring with bulk polymerizations, affected the polymerization progress very strongly. Due to this effect the conversion of the reaction is independent of the
Weak crystallization theory of metallic alloys
Martin, Ivar; Gopalakrishnan, Sarang; Demler, Eugene A.
2016-06-01
Crystallization is one of the most familiar, but hardest to analyze, phase transitions. The principal reason is that crystallization typically occurs via a strongly first-order phase transition, and thus rigorous treatment would require comparing energies of an infinite number of possible crystalline states with the energy of liquid. A great simplification occurs when crystallization transition happens to be weakly first order. In this case, weak crystallization theory, based on unbiased Ginzburg-Landau expansion, can be applied. Even beyond its strict range of validity, it has been a useful qualitative tool for understanding crystallization. In its standard form, however, weak crystallization theory cannot explain the existence of a majority of observed crystalline and quasicrystalline states. Here we extend the weak crystallization theory to the case of metallic alloys. We identify a singular effect of itinerant electrons on the form of weak crystallization free energy. It is geometric in nature, generating strong dependence of free energy on the angles between ordering wave vectors of ionic density. That leads to stabilization of fcc, rhombohedral, and icosahedral quasicrystalline (iQC) phases, which are absent in the generic theory with only local interactions. As an application, we find the condition for stability of iQC that is consistent with the Hume-Rothery rules known empirically for the majority of stable iQC; namely, the length of the primary Bragg-peak wave vector is approximately equal to the diameter of the Fermi sphere.
Noise Prevents Infinite Stretching of the Passive Field in a Stochastic Vector Advection Equation
Flandoli, Franco; Maurelli, Mario; Neklyudov, Mikhail
2014-09-01
A linear stochastic vector advection equation is considered; the equation may model a passive magnetic field in a random fluid. When the driving velocity field is rough but deterministic, in particular just Hölder continuous and bounded, one can construct examples of infinite stretching of the passive field, arising from smooth initial conditions. The purpose of the paper is to prove that infinite stretching is prevented if the driving velocity field contains in addition a white noise component.
Recurrence and invariant measure of Markov chains in double-infinite random environments
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The concepts of π-irreduciblity, recurrence and transience are introduced into the research field of Markov chains in random environments.That a π-irreducible chain must be either recurrent or transient is proved, a criterion is shown for recurrent Markov chains in double-infinite random environments, the existence of invariant measure of π-irreducible chains in double-infinite environments is discussed,and then Orey's open-questions are partially answered.