Problems of maximal mean resistance on the plane

Plakhov, A.Y.; Gouveia, P.D.F., (2007) 'Problems of maximal mean resistance on the plane', Nonlinearity 20(9) pp.2271-2287 RAE2008

Ab initio calculations of group 4 metallocene reaction mechanisms: atomic layer deposition and bond activation catalysis

Thin film dielectrics based on titanium, zirconium or hafnium oxides are being introduced to increase the permittivity of insulating layers in transistors for micro/nanoelectronics and memory devices. Atomic layer deposition (ALD) is the process of choice for fabricating these films, as it allows for high control of composition and thickness in thin, conformal films which can be deposited on substrates with high aspect-ratio features. The success of this method depends crucially on the chemical properties of the precursor molecules. A successful ALD precursor should be volatile, stable in the gas-phase, but reactive on the substrate and growing surface, leading to inert by-products. In recent years, many different ALD precursors for metal oxides have been developed, but many of them suffer from low thermal stability. Much promise is shown by group 4 metal precursors that contain cyclopentadienyl (Cp = C5H5-xRx) ligands. One of the main advantages of Cp precursors is their thermal stability. In this work ab initio calculations were carried out at the level of density functional theory (DFT) on a range of heteroleptic metallocenes [M(Cp)4-n(L)n], M = Hf/Zr/Ti, L = Me and OMe, in order to find mechanistic reasons for their observed behaviour during ALD. Based on optimized monomer structures, reactivity is analyzed with respect to ligand elimination. The order in which different ligands are eliminated during ALD follows their energetics which was in agreement with experimental measurements. Titanocene-derived precursors, TiCp*(OMe)3, do not yield TiO2 films in atomic layer deposition (ALD) with water, while Ti(OMe)4 does. DFT was used to model the ALD reaction sequence and find the reason for the difference in growth behaviour. Both precursors adsorb initially via hydrogen-bonding. The simulations reveal that the Cp* ligand of TiCp*(OMe)3 lowers the Lewis acidity of the Ti centre and prevents its coordination to surface O (densification) during both of the ALD pulses. Blocking this step hindered further ALD reactions and for that reason no ALD growth is observed from TiCp*(OMe)3 and water. The thermal stability in the gas phase of Ti, Zr and Hf precursors that contain cyclopentadienyl ligands was also considered. The reaction that was found using DFT is an intramolecular α-H transfer that produces an alkylidene complex. The analysis shows that thermal stabilities of complexes of the type MCp2(CH3)2 increase down group 4 (M = Ti, Zr and Hf) due to an increase in the HOMO-LUMO band gap of the reactants, which itself increases with the electrophilicity of the metal. The reverse reaction of α-hydrogen abstraction in ZrCp2Me2 is 1,2-addition reaction of a C-H bond to a Zr=C bond. The same mechanism is investigated to determine if it operates for 1,2 addition of the tBu C-H across Hf=N in a corresponding Hf dimer complex. The aim of this work is to understand orbital interactions, how bonds break and how new bonds form, and in what state hydrogen is transferred during the reaction. Calculations reveal two synchronous and concerted electron transfers within a four-membered cyclic transition state in the plane between the cyclopentadienyl rings, one π(M=X)-to-σ(M-C) involving metal d orbitals and the other σ(C-H)-to-σ(X-H) mediating the transfer of neutral H, where X = C or N. The reaction of the hafnium dimer complex with CO that was studied for the purpose of understanding C-H bond activation has another interesting application, namely the cleavage of an N-N bond and resulting N-C bond formation. Analysis of the orbital plots reveals repulsion between the occupied orbitals on CO and the N-N unit where CO approaches along the N-N axis. The repulsions along the N-N axis are minimized by instead forming an asymmetrical intermediate in which CO first coordinates to one Hf and then to N. This breaks the symmetry of the N-N unit and the resultant mixing of MOs allows σ(NN) to be polarized, localizing electrons on the more distant N. This allowed σ(CO) and π(CO) donation to N and back-donation of π*(Hf2N2) to CO. Improved understanding of the chemistry of metal complexes can be gained from atomic-scale modelling and this provides valuable information for the design of new ALD precursors. The information gained from the model decomposition pathway can be additionally used to understand the chemistry of molecules in the ALD process as well as in catalytic systems.

Spin-state splittings, highest-occupied-molecular-orbital and lowest-unoccupied-molecular-orbital energies, and chemical hardness.

It is known that the exact density functional must give ground-state energies that are piecewise linear as a function of electron number. In this work we prove that this is also true for the lowest-energy excited states of different spin or spatial symmetry. This has three important consequences for chemical applications: the ground state of a molecule must correspond to the state with the maximum highest-occupied-molecular-orbital energy, minimum lowest-unoccupied-molecular-orbital energy, and maximum chemical hardness. The beryllium, carbon, and vanadium atoms, as well as the CH(2) and C(3)H(3) molecules are considered as illustrative examples. Our result also directly and rigorously connects the ionization potential and electron affinity to the stability of spin states.

Resonant and Secular Orbital Interations

In stable solar systems, planets remain in nearly elliptical orbits around their stars. Over longer timescales, however, their orbital shapes and sizes change due to mutual gravitational perturbations. Orbits of satellites around a planet vary for the same reason. Because of their interactions, the orbits of planets and satellites today are different from what they were earlier. In order to determine their original orbits, which are critical constraints on formation theories, it is crucial to understand how orbits evolve over the age of the Solar System. Depending on their timescale, we classify orbital interactions as either short-term (orbital resonances) or long-term (secular evolution). My work involves examples of both interaction types. Resonant history of the small Neptunian satellites In satellite systems, tidal migration brings satellite orbits in and out of resonances. During a resonance passage, satellite orbits change dramatically in a very short period of time. We investigate the resonant history of the six small Neptunian moons. In this unique system, the exotic orbit of the large captured Triton (with a circular, retrograde, and highly tilted orbit) influences the resonances among the small satellites very strongly. We derive an analytical framework which can be applied to Neptune's satellites and to similar systems. Our numerical simulations explain the current orbital tilts of the small satellites as well as constrain key physical parameters of both Neptune and its moons. Secular orbital interactions during eccentricity damping Long-term periodic changes of orbital shape and orientation occur when two or more planets orbit the same star. The variations of orbital elements are superpositions of the same number of fundamental modes as the number of planets in the system. We investigate how this effect interacts with other perturbations imposed by external disturbances, such as the tides and relativistic effects. Through analytical studies of a system consisting of two planets, we find that an external perturbation exerted on one planet affects the other indirectly. We formulate a general theory for how both orbits evolve in response to an arbitrary externally-imposed slow change in eccentricity.

New SB2 orbital elements for accurate masses with Gaia: HD 9312, HD 9313 and HD 183255

info:eu-repo/semantics/published

Trembling the plane of immanence: media arts philosophy and the re-vision of art (or what’s acoustics got to do with the visual?)

Invited lecture at the Royal Academy of Art.

Leaving on a jet plane of immanence

This is about politics and protest, or rather about a politics of protest, and of rebellion. But it is also about creativity and the way in which theory and practice combine within the context of the ‘productive/creative’ process. In this case the combination is explicit and can be traced along a clear trajectory. The following will set out the way in which the accompanying piece of music – a cover of the 1969 protest song Leaving on a Jet Plane by Peter, Paul & Mary - came into being. In doing so it will make reference to a number of theoretical ideas/concepts that fed into the productive process and/or appeared relevant postproduction. It will draw on various aspects of thought from Heidegger (Standing reserve, Enframing and Authenticity), Camus (The Rebel), Foucault (Luminosity), and Deleuze (Immanence, Difference and Repetition and The Fold). [From the Author].

Application of regularization methods to damage detection in large scale plane frame structures using incomplete noisy modal data

This paper presents an approach for detecting local damage in large scale frame structures by utilizing regularization methods for ill-posed problems. A direct relationship between the change in stiffness caused by local damage and the measured modal data for the damaged structure is developed, based on the perturbation method for structural dynamic systems. Thus, the measured incomplete modal data can be directly adopted in damage identification without requiring model reduction techniques, and common regularization methods could be effectively employed to solve the developed equations. Damage indicators are appropriately chosen to reflect both the location and severity of local damage in individual components of frame structures such as in brace members and at beam-column joints. The Truncated Singular Value Decomposition solution incorporating the Generalized Cross Validation method is introduced to evaluate the damage indicators for the cases when realistic errors exist in modal data measurements. Results for a 16-story building model structure show that structural damage can be correctly identified at detailed level using only limited information on the measured noisy modal data for the damaged structure.

Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

Transfer ionization process p+He -> H-0+He2++e(-) with the ejected electron detected in the plane perpendicular to the incident beam direction

A joint experimental and theoretical study of the transfer ionization process p+He→ H-0+He2++e(-) is presented for 630-keV proton impact energy, where the electron is detected in a plane perpendicular to the proton beam direction. With this choice of kinematics we find the triple-differential cross section to be particularly sensitive to angular correlation in the helium target. There is a good agreement between the experimental data and theoretical calculations.

Plane wave and Coulomb asymptotics

A simple plane wave solution of the Schrodinger-Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J. Leech et al., Phys. Rev. Lett. 88. 257901 (2002)). The problem is resolved via non- uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.

Far-Field Optical Microscopy with a Nanometer-Scale Resolution Based on the In-Plane Image Magnification by Surface Plasmon Polaritons

A new far-field optical microscopy capable of reaching nanometer-scale resolution is developed using the in-plane image magnification by surface plasmon polaritons. This approach is based on the optical properties of a metal-dielectric interface that may provide extremely large values of the effective refractive index neff up to 103 as seen by surface polaritons, and thus the diffraction limited resolution can reach nanometer-scale values of lambda/2neff. The experimental realization of the microscope has demonstrated the optical resolution better than 60 nm at 515 nm illumination wavelength.