Satisfiability Modulo Transcendental Functions via Incremental Linearization

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear functions. Suitable numerical techniques are used to ensure that the abstractions of the transcendental functions are sound even in presence of irrationals. Our experimental evaluation on benchmarks from verification and mathematics demonstrates the potential of our approach, showing that it compares favorably with delta-satisfiability /interval propagation and methods based on theorem proving

Ready Access to the Echinopine s Skeleton via Gold(I) – Catalyzed Alkoxycyclization s of Enynes

The [3,5,5,7] tetracyclic skeleton of echinopines has been stereoselectively accessed through a gold(I)-catalyzed alkoxycyclization of cyclopropyl-tethered 1,6-enynes. The key bicycle[4.2.1]nonane core of the enyne precursors was readily assembled by means of a Co-catalyzed [6+2] cycloaddition. Furthermore, the attempted alkoxycyclization of 1,5-enyne substrates revealed an uncovered cyclopropyl rearrangement that gives rise to [3,6,5,7] tetracyclic structures

Strategies for the Synthesis of Higher Acenes

The outstanding performance of pentacene-based molecules in molecular electronics, as well as the predicted en- hanced semiconducting properties of extended acenes, have stimulated the development of new synthetic methods and functionalization strategies for the preparation of stable and soluble acenes larger than tetracene with the aim of obtaining improved functional materials

Interface kinetics of rapid solidification of binary alloys by atomistic simulations: Application to Ti-Ni alloys

Using molecular dynamics and Monte Carlo simulations we investigate the non-equilibrium interfacial kinetics during rapid solidification of Ti-Ni alloys. According to the existing theories, the kinetic coefficient is related, via an analytical expression, to the equilibrium and non-equilibrium solute concentration profiles across the crystal-melt interface, the interface temperature and velocity, and the drag coefficient. The kinetic coefficient was obtained by deriving these properties from specifically designed atomistic simulations and then fitting using the analytical expression. The results show that the kinetic coefficient is only weakly anisotropic and increases with increasing temperature. The velocity-dependent partition coefficient, as described by two solute trapping models, the continuous growth and the local non-equilibrium models, were fitted to the molecular dynamics simulation results. In addition, molecular dynamics and semi-grand canonical Monte Carlo simulations suggest that complete solute trapping might occur only under certain conditions. This can be explained by the fact that the maximum achievable effective free energy driving force for solidification, which defines the complete solute trapping, is limited by the chemical potential and free energy profiles for the Ti-Ni alloy. The investigations, using molecular dynamics simulations, of the dependence of crystal-melt interface width on solidification velocity show, at high velocities, similar trend to that predicted by the hyperbolic phase field model which is suitable for studies of rapid solidification of alloys

Quantitative prediction of rapid solidification by integrated atomistic and phase-field modeling

Systematic integration of atomistic simulations with phase-field modeling is presented for quantitative predictions of cellular growth and solute trapping during solidification of alloys for solidification velocities relevant to additive manufacturing. For parametrization of the phase-field model, molecular dynamics simulations are utilized as an alternative to complex experiments to obtain the anisotropic crystal-melt interface free energy, kinetic coefficient, and diffusive interface velocity. The accuracy of this integrated model is tested for rapid solidification of Ti-3.4at.%Ni alloy. The predicted solute trapping of the proposed phase-field model is comparable with the continuous growth model for solidification velocities of additive manufacturing. The predicted primary dendritic arm spacing is weakly dependent on the diffuse interface width enabling simulations in larger length scales. The concentration profile and partition coefficient obtained from both two-and three-dimensional phase-field simulations are comparable to the results of Kurz-Fisher\u27s analytical and continuous growth models, respectively. Unlike other computational models for rapid solidification, the proposed model enables predictions completely based on computations without fitting to experiments

Combined molecular dynamics and phase field simulation investigations of crystal-melt interfacial properties and dendritic solidification of highly undercooled titanium

The effects of kinetic and capillary anisotropies on crystal morphology and growth rate during solidification of titanium are studied using atomistically-informed phase field simulations. Molecular dynamics (MD) is employed to calculate the anisotropic kinetic coefficient and crystal-melt interface free energy using the free solidification and capillary methods. The phase field simulation results for solidification velocity and interface temperature are in quantitative good agreement with experimental and analytical data for undercoolings below 150 K. As the role of interface kinetic effects increases with undercooling the use of a modified phase field model allowed the extension of its quantitative prediction capability to higher undercoolings. In addition, the effect of MD calculated kinetic and capillary anisotropy parameters on dendrite shape and tip and solidification velocity was investigated

A combined molecular dynamics/Monte Carlo simulation of Cu thin film growth on TiN substrates: Illustration of growth mechanisms and comparison with experiments

Using a sequential molecular dynamics (MD)/time-stamped force-bias Monte Carlo (tfMC) algorithm to simulate the deposition of Cu species onto a TiN(001) substrate at 600 K, it is shown for the first time that at the very early stage of growth, BCC-Cu grows pseudomorphically on the TiN(001) substrate as a very thin continuous film with the BCC-Cu[001]//TiN[001] growth direction. By increasing the thickness of the Cu thin film, however, the film transforms through the Nishiyama-Wasserman mechanism from BCC into predominantly FCC-Cu with abundant nanotwins, which is the same type of structure obtained in the experiment conducted here via a dc magnetron sputter deposition technique to grow Cu on TiN(001) at 105 °C. In agreement with the experimental observations in the literature, the devised MD/tfMC is employed further to reveal that on the N-terminated TiN(111), Cu shows a very poor wettability, and FCC-Cu(111) grows vertically in the form of tall 3D islands. On Ti-terminated TiN(111) surface, however, FCC-Cu(111) initially grows in the form of 2D islands with high wettability. With additional Cu deposition, a triangular misfit dislocation network is generated at the Cu(111)//Ti-terminated TiN(111) interface with subsequent formation of a two-layer nanotwin with its twinning plane parallel to the surface substrate

The Rise and Fall of "Respectable" Spanish Liberalism, 1808-1923: An Explanatory Framework

The article focuses on the reasons behind both the consolidation of what I have termed “respectable” liberalism between the 1830s and the 1840s and its subsequent decline and fall between 1900 and 1923. In understanding both processes I study the links established between “respectable” liberals and propertied elites, the monarchy, and the Church. In the first phase these links served to consolidate the liberal polity. However, they also meant that many tenets of liberal ideology were compromised. Free elections were undermined by the operation of caciquismo, monarchs established a powerful position, and despite the Church hierarchy working with liberalism, the doctrine espoused by much of the Church was still shaped by the Counter-Reformation. Hence, “respectable” liberalism failed to achieve a popular social base. And the liberal order was increasingly denigrated as part of the corrupt “oligarchy” that ruled Spain. Worse still, between 1916 and 1923 the Church, monarch, and the propertied elite increasingly abandoned the liberal Monarchist Restoration. Hence when General Primo de Rivera launched his coup the rug was pulled from under the liberals’ feet and there was no one to cushion the fall

All-photochemical rotation of molecular motors with a phosphorus stereoelement

Unidirectional molecular rotation based on alternating photochemical and thermal isomerizations of overcrowded alkenes is well established, but rotary cycles based purely on photochemical isomerizations are rare. Herein we report three new second-generation molecular motors featuring a phosphorus center in the lower half, which engenders a unique element of axial chirality. These motors exhibit unusual behavior, in that all four diastereomeric states can interconvert solely photochemically. Kinetic analysis and modeling reveal that the behavior of the new motors is consistent with all-photochemical unidirectional rotation. Furthermore, X-ray crystal structures of all four diastereomeric states of two of these new motors were obtained, which constitute the first achievements of crystallographic characterization of the full 360° rotational cycle of overcrowded-alkene-based molecular motors. Finally, the axial phosphorus stereoelement in the phosphine motor can be thermally inverted, and this epimerization enables a “shortcut” of the traditional rotational cycle of these compounds