Cooperative Jahn-Teller distortion, phase transitions, and weak ferromagnetism in the KCrF3 perovskite

At ambient conditions, the ternary fluoride with formula KCrF3 adopts a perovskite-type structure and incorporates the Jahn-Teller active Cr2+ (d4) whose electronic configuration and magnetic response are analogous to those of Mn3+ (d4) and Cu2+ (d9). These ingredients make it an attractive system to study owing to the striking similarities with LaMnO3 and the expected strong interplay between spin, orbital, and structural ordering phenomena. Indeed, probing the properties of KCrF3 as a function of temperature (5 < T < 300 K) has revealed a structurally and magnetically far richer phase diagram than hitherto supposed. We found that KCrF3 exhibits large cooperative Jahn-Teller distortions which are driven by orbital ordering, a series of temperature induced complex structural transitions, and weak ferromagnetism which is reminiscent of what is observed in LaMnO3.     

Solvent-dependent changes in the ene reaction of RTAD with alkenes: the cyclopropyl group as a mechanistic probe

[reaction: see text] The vinylcyclopropyl moiety was used as an efficient probe to test mechanistic possibilities of the triazolinedione-alkene ene reaction. In non-hydroxylic solvents, this reaction afforded only the ene adducts via a closed three-membered aziridinium imide (AI) intermediate, whereas in hydroxylic solvents a dipolar intermediate is favored and trapped by the cyclopropyl moiety to form the corresponding cyclopropyl-rearranged solvent-trapped adducts.     

MIP-based decomposition strategies for large-scale scheduling problems in multiproduct multistage batch plants: A benchmark scheduling problem of the pharmaceutical industry

An efficient systematic iterative solution strategy for solving real-world scheduling problems in multiproduct multistage batch plants is presented. Since the proposed method has its core a mathematical model, two alternative MIP scheduling formulations are suggested. The MIP-based solution strategy consists of a constructive step, wherein a feasible and initial solution is rapidly generated by following an iterative insertion procedure, and an improvement step, wherein the initial solution is systematically enhanced by implementing iteratively several rescheduling techniques, based on the mathematical model. A salient feature of our approach is that the scheduler can maintain the number of decisions at a reasonable level thus reducing appropriately the search space. A fact that usually results in manageable model sizes that often guarantees a more stable and predictable optimization model behavior. The proposed strategy performance is tested on several complicated problem instances of a multiproduct multistage pharmaceuticals scheduling problem. On average, high quality solutions are reported with relatively low computational effort. Authors encourage other researchers to adopt the large-scale pharmaceutical scheduling problem to test on it their solution techniques, and use it as a challenging comparison reference.     

Uptake of n-hexane, 1-butene, and toluene by Au/Pt bimetallic surfaces: a tool for selective sensing of hydrocarbons under high-vacuum conditions

The dissociative adsorption and decomposition on a range of metal surfaces of an alkane, an alkene, and an aromatic, all representative of species present in an important technological application, has been studied under conditions relevant to selective gas sensing based on solid electrolyte potentiometry. At 870 K, pure polycrystalline Pt surfaces do not discriminate between n-hexane, toluene, and 1-butene: graphitic carbon accumulation occurs at almost the same rate. However, by varying the composition of polycrystalline bimetallic Pt/Au surfaces, good discrimination between these species can be achieved. Thus at a nominal surface composition of approximately 75% Au (XPS), good selectivity toward 1-butene and toluene uptake is achieved, with essentially no response to n-hexane. At approximately 80% Au the system is selective to 1-butene alone. Particular merits of these systems include good high-temperature stability and good tunability of their chemical selectivity. This makes possible the development of array devices in which the elements have overlapping but different selectivity profiles.     

Linearly implicit methods for nonlinear evolution equations

Summary.  We construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear evolution equations and extend thus recent results concerning the discretization of nonlinear parabolic equations. The resulting schemes are linearly implicit and include as particular cases implicit–explicit multistep schemes as well as the combination of implicit Runge–Kutta schemes and extrapolation. We establish optimal order error estimates. The abstract results are applied to a third–order evolution equation arising in the modelling of flow in a fluidized bed. We discretize this equation in space by a Petrov–Galerkin method. The resulting fully discrete schemes require solving some linear systems to advance in time with coefficient matrices the same for all time levels. Received October 22, 2001 / Revised version received April 22, 2002 / Published online December 13, 2002 Mathematics Subject Classification (1991): Primary 65M60, 65M12; Secondary 65L06 Correspondence to: G. Akrivis     

Bimetallic Pd/Sn-based Nanoparticles and their Catalytic Properties in the Semihydrogenation of Diphenylacetylene

Multimetallic nanoparticles often enhance the catalytic performance of their monometallic counterparts by increasing reaction rates, catalyst selectivity, and/or stability. A prerequisite for understanding structure- and composition-associated properties, however, is the careful design of multimetallic nanoparticles with various structures and compositions. Here, bimetallic Pd/Sn-based nanoparticles are prepared with a tunable composition and structure exploiting ionic liquids (ILs) as reaction medium (i. e., methyltrioctylammonium bis(trifluoromethylsulfonyl)imide). The nanoparticles are obtained in a one-pot synthetic procedure by reducing the metal salt precursors with triethylborohydride in the IL. The results show that the reaction parameters, in particular the nature and ratio of the Pd²⁺/Sn²⁺ precursors as well as the reaction temperature, influence NP formation and composition. X-ray diffraction with Rietveld analysis and transmission electron microscopy are employed to determine NP size and phase composition. Under optimized reaction conditions Pd₂Sn or PdSn nanocrystals are formed as single-phase products after introducing an additional annealing step at 200 °C. Nanocrystals with intermetallic composition reveal enhanced catalytic properties in the semihydrogenation of diphenylacetylene which was used as a model reaction.     

Cubic structures and ideal class groups

We establish a generalization of Breen's theory of cubic structures on line bundles over group schemes. We study such “n-cubic structures” inductively using multiextensions. As a result we obtain information on the set of isomorphism classes of line bundles with n-cubic structures over finite multiplicative group schemes over Spec(Z) by relating this set to certain corresponding eigenspaces of ideal class groups of cyclotomic fields.     

Torus Knot Polynomials and Susy Wilson Loops

We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of (n, m) torus knots, and present a number of equivalent expressions, all related by Heine’s transformations. Using this result, the \({ (m, n) \leftrightarrow (n, m)}\) symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang–Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang–Mills theory, which is known to give averages of Wilson loops in \({\mathcal{N}}\) = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones–Rosso representation in terms of q-harmonic oscillators.