Spin distributions in antiferromagnetically coupled Mn2+Cu2+ systems: from the pair to the infinite chain

Probably the most informative description of the ground slate of a magnetic molecular species is provided by the spin density map. Such a map may be experimentally obtained from polarized neutron diffraction (PND) data or theoretically calculated using quantum chemical approaches. Density functional theory (DFT) methods have been proved to be well-adapted for this. Spin distributions in one-dimensional compounds may also be computed using the density matrix renormalization group (DMRG) formalism. These three approaches, PND, DFT, and DMRG, have been utilized to obtain new insights on the ground state of two antiferromagnetically coupled Mn2+Cu2+ compounds, namely [Mn(Me-6-[14]ane-N-4)Cu(oxpn)](CF3SO3)(2) and MnCu(pba)(H2O)(3) . 2H(2)O, with Me-6-[14]ane-N-4 = (+/-)-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane, oxpn = N,N'-bis(3-aminopropyl)oxamido and pba = 1,3-propylenebis(oxamato). Three problems in particular have been investigated: the spin distribution in the mononuclear precursors [Cu(oxpn)] and [Cu(pba)](2-), the spin density maps in the two Mn2+Cu2+ compounds, and the evolution of the spin distributions on the Mn2+ and Cu2+ sites when passing from a pair to a one-dimensional ferrimagnet.

Unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field

The unsteady laminar boundary layer flow of an electrically conducting fluid past a semi-infinite flat plate with an aligned magnetic field has been studied when at time t > 0 the plate is impulsively moved with a constant velocity which is in the same or opposite direction to that of free stream velocity. The effect of the induced magnetic field has been included in the analysis. The non-linear partial differential equations have been solved numerically using an implicit finite-difference method. The effect of the impulsive motion of the surface is found to be more pronounced on the skin friction but its effect on the x-component of the induced magnetic field and heat transfer is small. Velocity defect occurs near the surface when the plate is impulsively moved in the same direction as that of the free stream velocity. The surface shear stress, x-component of the induced magnetic field on the surface and the surface heat transfer decrease with an increasing magnetic field, but they increase with the reciprocal of the magnetic Prandtl number. However, the effect of the reciprocal of the magnetic Prandtl number is more pronounced on the x-component of the induced magnetic field. (C) 1999 Elsevier Science Ltd. All rights reserved.

An inverse problem for the Helmholtz equation involving two semi-infinite fluids

An analytical method is developed for solving an inverse problem for Helmholtz's equation associated with two semi-infinite incompressible fluids of different variable refractive indices, separated by a plane interface. The unknowns of the inverse problem are: (i) the refractive indices of the two fluids, (ii) the ratio of the densities of the two fluids, and (iii) the strength of an acoustic source assumed to be situated at the interface of the two fluids. These are determined from the pressure on the interface produced by the acoustic source. The effect of the surface tension force at the interface is taken into account in this paper. The application of the proposed analytical method to solve the inverse problem is also illustrated with several examples. In particular, exact solutions of two direct problems are first derived using standard classical methods which are then used in our proposed inverse method to recover the unknowns of the corresponding inverse problems. The results are found to be in excellent agreement.

Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents

The unsteady free convection flow over an infinite vertical porous plate, which moves with time-dependent velocity in an ambient fluid, has been studied. The effects of the magnetic field and Hall current are included in the analysis. The buoyancy forces arise due to both the thermal and mass diffusion. The partial differential equations governing the flow have been solved numerically using both the implicit finite difference scheme and the difference-differential method. For the steady case, analytical solutions have also been obtained. The effect of time variation on the skin friction, heat transfer and mass transfer is very significant. Suction increases the skin friction coefficient in the primary flow, and also the Nusselt and Sherwood numbers, but the skin friction coefficient in the secondary flow is reduced. The effect of injection is opposite to that of suction. The buoyancy force, injection and the Hall parameter induce an overshoot in the velocity profiles in the primary flow which changes the velocity gradient from a negative to a positive value, but the magnetic field and suction reduce this velocity overshoot.

Generalized asymptotic expansions for the wavenumbers in infinite flexible in vacuo orthotropic cylindrical shells

Analytical expressions are found for the wavenumbers and resonance frequencies in flexible, orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders n. The Donnell-Mushtari shell theory is used to model the dynamics of the cylindrical shell. Initially, an in vacuo cylindrical isotropic shell is considered and expressions for all the wavenumbers (bending, near-field bending, longitudinal and torsional) are found. Subsequently, defining a suitable orthotropy parameter epsilon, the problem of wave propagation in an orthotropic shell is posed as a perturbation on the corresponding problem for an isotropic shell. Asymptotic expressions for the wavenumbers in the in vacuo orthotropic shell are then obtained by treating epsilon as an expansion parameter. In both cases (isotropy and orthotropy), a frequency-scaling parameter (eta) and Poisson's ratio (nu) are used to find elegant expansions in the different frequency regimes. The asymptotic expansions are compared with numerical solutions in each of the cases and the match is found to be good. The main contribution of this work lies in the extension of the existing literature by developing closed-form expressions for wavenumbers with arbitrary circumferential orders n in the case of both, isotropic and orthotropic shells. Finally, we present natural frequency expressions in finite shells (isotropic and orthotropic) for the axisymmetric mode and compare them with numerical and ANSYS results. Here also, the comparison is found to be good. (C) 2011 Elsevier Ltd. All rights reserved.

Branching Particle Systems and Superprocess

In this paper, we describe a system of particles that perform independent random motions in space and at the end of their lifetimes give birth to a random number of offspring. We show that the system in the large density, small mass, rapid branching or long time scale limit converges to a measure-valued diffusion called the superprocess.

Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell: Comparison between Different Shell Theories

Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo I fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flugge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are, the analytical expressions obtained from the five theories allow one to see how these differences propagate into the asymptotic expansions. Also, they help to quantify the difference between the theories for a wide range of parameter values such as the frequency range, circumferential order, thickness ratio of the shell, etc.

Branching out at C-2 of septanosides. Synthesis of 2-deoxy-2-C-alkyl/aryl septanosides from a bromo-oxepine

This paper deals with the synthesis of 2-deoxy-2-C-alkyl/aryl septanosides. A range of such septanoside derivatives was synthesized by using a common bromo-oxepine intermediate, involving C-C bond forming organometallic reactions. Unsaturated, seven-membered septanoside vinyl bromides or bromo-oxepines, obtained through a ring expansion methodology of the cyclopropane derivatives of oxyglycals, displayed a good reactivity towards several acceptor moieties in C-C bond forming Heck, Suzuki and Sonogashira coupling reactions, thus affording 2-deoxy-2-C-alkyl/aryl septanosides. Whereas Heck and Sonogashira coupling reactions afforded 2-deoxy-2-C-alkenyl and -alkynyl derivatives, respectively, the Suzuki reaction afforded 2-deoxy-2-C-aryl septanosides. Deprotection and reduction of the 2-deoxy-2-alkenyl derivative afforded the corresponding 2-deoxy-2-C-alkyl septanoside free of protecting groups. The present study illustrates the reactivity of bromo-oxepine in the synthesis of hitherto unknown septanosides, branching out at C-2, through C-C bond formation with alkyl and aryl substituents.

Unsteady Rotating Flow Over an Impulsively Rotating Infinite Disk with Axial Magnetic Field and Suction

The unsteady rotating flow of an incompressible laminar viscous electrically conducting fluid over an impulsively rotated infinite disk in the presence of magnetic field and suction is investigated. We have considered the situation where there is a steady state initially (i.e., at t = 0, the fluid is rotating with constant angular velocity over a stationary disk). Then at t > 0, the disk is suddenly rotated with a constant angular velocity either in the same direction or in opposite direction to that of the fluid rotation which causes unsteadiness in the flow field. The effect of the impulsive motion is found to be more pronounced on the tangential shear stress than on the radial shear stress. When the disk and the fluid rotate in the same direction, the tangential shear stress at the surface changes sign in a small time interval immediately after the start of the impulsive motion.

Asymptotic expansions for the coupled wavenumbers in an infinite orthotropic flexible fluid-filled cylindrical shell

Analytical expressions are found for the coupled wavenumbers in flexible, fluid-filled, circular cylindrical orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders. The Donnell-Mushtari shell theory is used to model the shell and the effect of the fluid is introduced through the fluid-loading parameter mu. The orthotropic problem is posed as a perturbation on the corresponding isotropic problem by defining a suitable orthotropy parameter epsilon, which is a measure of the degree of orthotropy. For the first study, an isotropic shell is considered (by setting epsilon = 0) and expansions are found for the coupled wavenumbers using a regular perturbation approach. In the second study, asymptotic expansions are found for the coupled wavenumbers in the limit of small orthotropy (epsilon << 1). For each study, isotropy and orthotropy, expansions are found for small and large values of the fluid-loading parameter mu. All the asymptotic solutions are compared with numerical solutions to the coupled dispersion relation and the match is seen to be good. The differences between the isotropic and orthotropic solutions are discussed. The main contribution of this work lies in extending the existing literature beyond in vacuo studies to the case of fluid-filled shells (isotropic and orthotropic).

Power Controlled Reverse Channel Training Achieves an Infinite Diversity Order in a TDD-SIMO System with Perfect CSIR

In this letter, we analyze the Diversity Multiplexinggain Tradeoff (DMT) performance of a training-based reciprocal Single Input Multiple Output (SIMO) system. Assuming Channel State Information (CSI) is available at the Receiver (CSIR), we propose a channel-dependent power-controlled Reverse Channel Training (RCT) scheme that enables the transmitter to directly estimate the power control parameter to be used for the forwardlink data transmission. We show that, with an RCT power of (P) over bar (gamma), gamma > 0 and a forward data transmission power of (P) over bar, our proposed scheme achieves an infinite diversity order for 0 <= g(m) < L-c-L-B,L-tau/L-c min(gamma, 1) and r > 2, where g(m) is the multiplexing gain, L-c is the channel coherence time, L-B,L-tau is the RCT duration and r is the number of receive antennas. We also derive an upper bound on the outage probability and show that it goes to zero asymptotically as exp(-(P) over bar (E)), where E (sic) (gamma - g(m)L(c)/L-c-L-B,L-tau), at high (P) over bar. Thus, the proposed scheme achieves a significantly better DMT performance compared to the finite diversity order achieved by channel-agnostic, fixed-power RCT schemes.

Infinite push: a new support vector ranking algorithm that directly optimizes accuracy at the absolute top of the list

Ranking problems have become increasingly important in machine learning and data mining in recent years, with applications ranging from information retrieval and recommender systems to computational biology and drug discovery. In this paper, we describe a new ranking algorithm that directly maximizes the number of relevant objects retrieved at the absolute top of the list. The algorithm is a support vector style algorithm, but due to the different objective, it no longer leads to a quadratic programming problem. Instead, the dual optimization problem involves l1, ∞ constraints; we solve this dual problem using the recent l1, ∞ projection method of Quattoni et al (2009). Our algorithm can be viewed as an l∞-norm extreme of the lp-norm based algorithm of Rudin (2009) (albeit in a support vector setting rather than a boosting setting); thus we refer to the algorithm as the ‘Infinite Push’. Experiments on real-world data sets confirm the algorithm’s focus on accuracy at the absolute top of the list.

Electric current-induced mass flow in very thin infinite metallic films

This paper reports on the mass transport behavior of infinitely extended, continuous, and very thin metallic films under the influence of electric current. Application of direct current of high densities (> 10(8) A/m(2)) results in visible melting of thin film at only one of the electrodes, and the melt then flows towards the other electrode in a circularly symmetric fashion forming a microscale ring pattern. For the two tested thin film systems, namely Cr and Al, of thicknesses ranging from 4 to 20 nm, the above directional flow consistently occurred from cathode to anode and anode to cathode, respectively. Furthermore, application of alternating electric current results in flow of the liquid material from both the electrodes. The dependence of critical flow behavior parameters, such as flow direction, flow velocity, and evolution of the ring diameter, are experimentally determined. Analytical models based on the principles of electromigration in liquid-phase materials are developed to explain the experimental observations.

An infinite family of tight triangulations of manifolds

We give explicit construction of vertex-transitive tight triangulations of d-manifolds for d >= 2. More explicitly, for each d >= 2, we construct two (d(2) + 5d + 5)-vertex neighborly triangulated d-manifolds whose vertex-links are stacked spheres. The only other non-trivial series of such tight triangulated manifolds currently known is the series of non-simply connected triangulated d-manifolds with 2d + 3 vertices constructed by Kuhnel. The manifolds we construct are strongly minimal. For d >= 3, they are also tight neighborly as defined by Lutz, Sulanke and Swartz. Like Kuhnel complexes, our manifolds are orientable in even dimensions and non-orientable in odd dimensions. (c) 2013 Elsevier Inc. All rights reserved.

Model-checking bisimulation-based information flow properties for infinite state sstems

Bisimulation-based information flow properties were introduced by Focardi and Gorrieri [1] as a way of specifying security properties for transition system models. These properties were shown to be decidable for finite-state systems. In this paper, we study the problem of verifying these properties for some well-known classes of infinite state systems. We show that all the properties are undecidable for each of these classes of systems.