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Synthesis of high surface-area colloidal assemblies of calixarene-phosphine-capped nanoporous gold with a remarkably high surface-to-volume ratio is reported.
Abstract This paper is the first part of a two part work that aims to introduce a new family of piecewise‐linear differential equations that exhibit chaotic behaviour in numerical simulations and to provide a rigorous mathematical proof of its chaotic nature. The new family presented here has the same eigenvalue distribution as the well‐known Lorenz equations in its chaotic regime but has a different symmetry. It is a derivative of the recently investigated double‐scroll family of piecewise‐linear differential equations. 1 It differs, however, from the double‐scroll family in that its members have all real eigenvalues at the origin. In particular, since the associated eigenspace E s (0) is similar to that of an overdamped linear circuit, we will henceforth refer to this family as the overdamped double‐scroll family . We establish Chua's circuit 2 as a member of this family under appropriate conditions. Preliminary numerical simulations exhibit some interesting phenomena such as period‐doubling, periodic windows between chaotic behaviour, and strange attractors of differing geometric structure. Our approach in the rigorous analysis will be that employed for the double‐scroll family in Reference 1. We derive a linearly equivalent class of piecewise‐linear differential equations which includes the family simulated numerically as a special case. the necessary and sufficient condition for two piecewise‐linear vector fields belonging to this new overdamped double‐scroll family to be linearly equivalent is that their respective eigenvalues at respective equilibrium points be scalar multiples of each other. If the scalars are all identity, then we have linear conjugacy of the vector fields. an explicit normal form equation, in the sense of global bifurcation, is presented that is parametrized by its own eigenvalues. We find that linearly equivalent vector fields associated with the overdamped double‐scroll family exhibit the same global behaviour even though their equivalence is based on the local concept of normalized eigenvalues. In addition, the piecewise‐linear differential equations associated with these equivalent vector fields can be quite different from each other.
This paper presents an explicit topological formulation of the Lagrangian and the Hamiltonian equations for a large class of nonlinear networks. In particular, formulations are given for networks containing both linear and nonlinear controlled sources. Classically, the Lagrangian and Hamiltonian equations are derived from variational techniques; in this paper topological techniques are used for the formulation.
We describe a xed point approach for the following stochastic optimization problem: given a multicast tree and probability distributions of user utilities, compute prices to oer the users in order to maximize the expected pro t of the service provider. We show that any optimum pricing is a xed point of an eciently computable map. In the language of classical numerical analysis, we show that the non-linear Jacobi and Gauss-Seidel methods of coordinate descent are applicable to this problem. We provide proof of convergence to the optimum prices for special cases of utility distributions and tree edge costs.
ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSynthesis and characterization of the neutral lanthanide silyl complexes (.eta.5-C5Me5)2LnSiH(SiMe3)2 (Ln = Nd, Sm)Nora S. Radu, T. Don Tilley, and Arnold L. RheingoldCite this: J. Am. Chem. Soc. 1992, 114, 21, 8293–8295Publication Date (Print):October 1, 1992Publication History Published online1 May 2002Published inissue 1 October 1992https://pubs.acs.org/doi/10.1021/ja00047a052https://doi.org/10.1021/ja00047a052research-articleACS PublicationsRequest reuse permissionsArticle Views321Altmetric-Citations73LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-AlertscloseSupporting Info (1)»Supporting Information Supporting Information Get e-Alerts
In this paper, the case when the potential distribution inside a corrosion cavity obeys Ohm's law is considered. Mathematically, the potential drop in the crevice is described by a Poisson-type equation with a non linear source term. It is shown that, in the general case, this problem has more than one solution, indicating that the potential and current distributions in the crevice depend not only on the metal potential, solution conductivity, and geometry of the crevice, but also on the history of crevice initiation. The absence of a unique solution of the charge transfer equation can explain the fact that both passive and active crevices with approximately equal geometrical parameters are often observed simultaneously on the same metal surface. It is further shown that, in the general case, it is impossible to neglect the potential drop in the external environment when quantitatively describing crevice corrosion.
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view Abstract Citations (89) References (67) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Mass of the Probable Black Hole in the X-Ray Nova GRO J0422+32 Filippenko, Alexei V. ; Matheson, Thomas ; Ho, Luis C. Abstract A series of 21 moderate-resolution (∼2.4 Å) spectra of the now quiescent Galactic X-ray nova GRO J0422+32, obtained in 1994 November and 1995 January with the W. M. Keck 10 m telescope, is used to derive the physical parameters of the binary system. The Hα emission-line profile exhibits large variations in consecutive half-hour exposures taken in 1994 November, but smaller variations in 1995 January. Cross-correlation of the 6000-6500 Å spectral region with that of late-type dwarf stars yields reliable absorption-line radial velocities for the secondary star. The orbital period is found to be 0d.21159±0d.00057, with a semiamplitude of 380.6±6.5 km s-1; the implied mass function is 1.21±0.06 Msun. Inspection of the averaged spectrum of GRO J0422+32 in the rest frame of the secondary star suggests that the secondary is an M2 V star, but the accretion disk contributes 30%-60% of the light at ∼6300 Å. Fits to the wings of the strong, double-peaked Hα emission line yield approximate radial velocities for the compact primary; the velocity curve has a semi-amplitude of 41.6±3.2 km s-1, but with a phase offset by 253° (rather than 180°) from that of the secondary star. The offset, which is similar to that of several other X-ray novae and many dwarf novae, may be indicative of geometric distortions or additional emission components on the accretion disk; hence, the observed semi-amplitude does not necessarily reflect the true motion of the compact primary. Under the assumption that it does, however, we find q = 0.1093±0.0086, the mass ratio of the secondary to the primary. If the secondary star is a normal M2 dwarf (M = 0.39±0.02 M0), as suggested by its spectrum and (independently) by the requirement that it fill its Roche lobe, the mass of the primary is 3.57±0.34 Msun, somewhat higher than the theoretical upper limit (∼3.2 Msun) for a slowly rotating neutron star with an extremely stiff equation of state, and considerably above the measured masses of neutron stars. We conclude that the compact object is probably a black hole, as suggested by its hard X-ray spectrum during outburst. The derived inclination angle of the system (48±3° ) is consistent with the apparent absence of eclipses of the accretion disk. Publication: The Astrophysical Journal Pub Date: December 1995 DOI: 10.1086/176609 Bibcode: 1995ApJ...455..614F Keywords: STARS: BINARIES: CLOSE; BLACK HOLE PHYSICS; X-RAYS: STARS; STARS: INDIVIDUAL ALPHANUMERIC: GRO J0422+32; STARS: NOVAE; CATACLYSMIC VARIABLES full text sources ADS | data products SIMBAD (7)
