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71.
D. Beigie 《Journal of Nonlinear Science》1995,5(1):57-103
Summary We study separatrix crossing in near-integrablek-degree-of-freedom Hamiltonian flows, 2 <k < , whose unperturbed phase portraits contain separatrices inn degrees of freedom, 1 <n <k. Each of the unperturbed separatrices can be recast as a codimension-one separatrix in the 2k-dimensional phase space, and the collection of these separatrices takes on a variety of geometrical possibilities in the reduced representation of a Poincaré section on the energy surface. In general 0 l n of the separatrices will be available to the Poincaré section, and each separatrix may be completely isolated from all other separatrices or intersect transversely with one or more of the other available separatrices. For completely isolated separatrices, transitions across broken separatrices are described for each separatrix by the single-separatrix crossing theory of Wiggins, as modified by Beigie. For intersecting separatrices, a possible violation of a normal hyperbolicity condition complicates the analysis by preventing the use of a persistence and smoothness theory for compact normally hyperbolic invariant manifolds and their local stable and unstable manifolds. For certain classes of multi-degree-of-freedom flows, however, a local persistence and smoothness result is straightforward, and we study the global implications of such a local result. In particular, we find codimension-one partial barriers and turnstile boundaries associated with each partially destroyed separatrix. From the collection of partial barriers and turnstiles follows a rich phase space partitioning and transport formalism to describe the dynamics amongst the various degrees of freedom. A generalization of Wiggins' higher-dimensional Melnikov theory to codimension-one surfaces in the multi-separatrix case allows one to uncover invariant manifold geometry. In the context of this perturbative analysis and detailed numerical computations, we study invariant manifold geometry, phase space partitioning, and phase space transport, with particular attention payed to the role of a vanishing frequency in the limit approaching the intersection of the partially destroyed separatrices. The class of flows under consideration includes flows of basic physical relevance, such as those describing scattering phenomena. The analysis is illustrated in the context of a detailed study of a 3-degree-of-freedom scattering problem. 相似文献
72.
Cécile Huybrechts 《Journal of Algebraic Combinatorics》1996,5(4):329-335
Let be a rank three incidence geometry of points, lines and planes whose planes are linear spaces and whose point residues are dual linear spaces (notice that we do not require anything on the line residues). We assume that the residual linear spaces of belong to a natural class of finite linear spaces, namely those linear spaces whose full automorphism group acts flag-transitively and whose orders are polynomial functions of some prime number. This class consists of six families of linear spaces. In the amalgamation of two such linear spaces imposes an equality on their orders leading, in particular, to a series of diophantine equations, the solutions of which provide a reduction theorem on the possible amalgams of linear spaces that can occur in .We prove that one of the following holds (up to a permutation of the words point and plane):A) the planes of and the dual of the point residues belong to the same family and have the same orders,B) the diagram of is in one of six families,C) the diagram of belongs to a list of seven sporadic cases.Finally, we consider the particular case where the line residues of are generalized digons. 相似文献
73.
《Tetrahedron letters》2003,44(26):4831-4834
A convenient and efficient synthesis of 3,5-di(silylethynyl)phenylacetylene and p-[3,5-di(silylethynyl)phenylethynyl]phenylacetylene has been carried out. These compounds serve to prepare nanometer-sized conjugated 1,4- and 1,3,5-phenylethynyl oligomers, by means of cross-coupling with a convenient haloaryl derivative, catalysed by palladium(II), in excellent yields. The phenylethynyl homologues show fluorescence emission, the wavelength of which is displaced by approximately 20 nm by each phenylethynyl unit increasing the conjugate chain. 相似文献
74.
用ab initio方法研究NaN_3的几何构型、电子结构和热力学、动力学性质 总被引:2,自引:0,他引:2
用abinitioMO方法,在MP2(ful)/6311G水平下,全优化计算了叠氮化钠(NaN3)分子的线状和环状两种稳定构型及其转化过渡态的几何参数、电荷分布、分子总能量和振动频率,并研究了它们的热力学性质及转化速率常数和平衡常数.结果表明,线状比环状构型稍稳定(能量低6.04kJ/mol);两者相互转化的能垒分别为13.15kJ/mol(线型→环状)和7.11kJ/mol(环状→线型).热力学和动力学计算均表明:NaN3通常主要以线型结构存在(占85%以上),且随温度升高而增多(在1000K大于91%). 相似文献
75.
The mononuclear vanadium(Ⅴ) complex with 2-hydroxyl-1-naphthaldehyde isoncotinoyl hydrazone was synthesized and characterized by single-crystal X-ray diffraction.The crystal is of monoclinic,space group P2 1/n with a = 10.3153(15),b = 7.4024(11 ),c = 24.413(4) (A),β= 101.911(2)°,V= 1824.0(5) (A)3,Z = 4,Mr = 427.28,Dc = 1.556 g/cm3,F(000) = 880,μ(MoKα) =0.591,the final R = 0.0372 and wR = 0.0926.The vanadium(Ⅴ) atom adopts a distorted square-pyramidal geometry coordinated by the tridentate ligand and two oxygen atoms.The hydrogen bonds and strong π…π stacking interactions link the complex molecules into a 3-D network structure. 相似文献
76.
New equations are derived and implemented for efficient and accurate computation of solvation energy derivatives for the conductor-like polarizable continuum model (C-PCM) and the isotropic integral equation formalism polarizable continuum model (IEF-PCM). Two new molecular surface tessellation procedures GEPOL-RT and GEPOL-AS that generate near continuous potential energy surfaces are proposed for PCM geometry optimization. The combined use of these new techniques leads to efficient and convergent geometry optimizations with the PCMs. 相似文献
77.
78.
Schlegel HB 《Journal of computational chemistry》2003,24(12):1514-1527
Potential energy surfaces form a central concept in the application of electronic structure methods to the study of molecular structures, properties, and reactivities. Recent advances in tools for exploring potential energy surfaces are surveyed. Methods for geometry optimization of equilibrium structures, searching for transition states, following reaction paths and ab initio molecular dynamics are discussed. For geometry optimization, topics include methods for large molecules, QM/MM calculations, and simultaneous optimization of the wave function and the geometry. Path optimization methods and dynamics based techniques for transition state searching and reaction path following are outlined. Developments in the calculation of ab initio classical trajectories in the Born-Oppenheimer and Car-Parrinello approaches are described. 相似文献
79.
A variational method for solving the time-independent single-particle Dirac equation in the Coulomb field of two nuclei is
described. A minimax variational principle and basis functions that have the proper analytic behavior, i.e. behave like r
γ,γ non-integer, in the neighborhood of a nucleus, are used. A momentum space integration scheme for computing the necessary
two-center integrals is described. Results are given for a standard test problem on two nuclei with Z=90 with an internuclear separation of 2.0/Z. The results confirm those of a previous calculation [F.A. Parpia and A.K. Mohanty, Chem Phys Lett 238: 209 (1995)].
Received: 13 May 1998 / Accepted: 22 June 1998 / Published online: 28 August 1998 相似文献
80.
Mauricio Alcolea Palafox Nerea Iza Manuel Gil Jos Luís Núez 《International journal of quantum chemistry》2002,89(1):25-47
A quantum chemical study of several complex monocyclic 4‐benzoyl‐4‐phenyl‐β‐lactam derivatives was carried out using cyclobutane, azetidine, 2‐azetidinone, 1‐methyl‐2‐azetidinone, and 3‐methyl‐2‐azetidinone as model compounds. The optimum geometry was obtained for the different conformations. The planarity of the ring was discussed in terms of the influence of the substituents on the amide resonance. To better analyze the amide resonance and the activity of the β‐lactam ring, a vibrational study was also carried out. To examine the influence of solvent polarity on the carbonyl bands, the Fourier transform–infrared (FT‐IR) spectra of the β‐lactam monocyclic derivatives were recorded in CCl4, C6H6, and CHCl3 solutions. The normal vibrations of the β‐lactam ring in the model compounds were characterized and used in the analysis of the β‐ring of more complex derivatives. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 相似文献