Philosophy in sport made science in earnest; being an attempt to illustrate the first principles of natural philosophy by the aid of popular toys and sports.

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An introduction to the elements of algebra, designed for the use of those who are acquainted only with the first principles of arithmetic.

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"Unto this last": four essays on the first principles of political economy.

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The first principles of evolution,

"Literature": p. 321-328.

First principles.

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5,6-Dihydroxyindole-2-carboxylic acid: a first principles density functional study

We report first principles density functional calculations for 5,6-dihydroxyindole-2-carboxylic acid (DHICA) and several oxidised forms. DHICA and 5,6-dihydroxyindole (DHI) are believed to be the basic building blocks of the eumelanins. Our results show that carboxylation has a significant effect on the physical properties of the molecules. In particular, the relative stabilities and the highest occupied molecular orbital-lowest unoccupied molecular orbital gaps (calculated with the DeltaSCF method) of the various redox forms are strongly affected. We predict that, in contrast to DHI, the density of unpaired electrons, and hence the ESR signal, in DHICA is negligibly small. (C) 2004 Elsevier B.V. All rights reserved.

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

First-principles investigation of the alloy scattering potential in dilute Si1-xCx

A first-principles method is applied to find the intra and intervalley n-type carrier scattering rates for substitutional carbon in silicon. The method builds on a previously developed first-principles approach with the introduction of an interpolation technique to determine the intravalley scattering rates. Intravalley scattering is found to be the dominant alloy scattering process in Si1-xCx, followed by g-type intervalley scattering. Mobility calculations show that alloy scattering due to substitutional C alone cannot account for the experimentally observed degradation of the mobility. We show that the incorporation of additional charged impurity scattering due to electrically active interstitial C complexes models this residual resistivity well.

First principles calculation of electron-phonon and alloy scattering in strained SiGe

First-principles electronic structure methods are used to predict the mobility of n-type carrier scattering in strained SiGe. We consider the effects of strain on the electron-phonon deformation potentials and the alloy scattering parameters. We calculate the electron-phonon matrix elements and fit them up to second order in strain. We find, as expected, that the main effect of strain on mobility comes from the breaking of the degeneracy of the six Δ and L valleys, and the choice of transport direction. The non-linear effects on the electron-phonon coupling of the Δ valley due to shear strain are found to reduce the mobility of Si-like SiGe by 50% per % strain. We find increases in mobility between 2 and 11 times that of unstrained SiGe for certain fixed Ge compositions, which should enhance the thermoelectric figure of merit in the same order, and could be important for piezoresistive applications.

First-principles calculation of carrier-phonon scattering in n-type Si1−xGex alloys

First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley n-type carrier scattering in Si1-xGex alloys. Scattering parameters for all relevant Delta and L intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon (x approximate to 0) or almost pure germanium (x approximate to 1), where acoustic phonon scattering is predominant. The n-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys..

First-principles calculation of P-type alloy scattering in Si1-xGex

The p-type carrier scattering rate due to alloy disorder in Si1-xGex alloys is obtained from first principles. The required alloy scattering matrix elements are calculated from the energy splitting of the valence bands, which arise when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Alloy scattering within the valence bands is found to be characterized by a single scattering parameter. The hole mobility is calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation. The results are in good agreement with experiments on bulk, unstrained alloys..

First-principles calculation of alloy scattering in GexSi1-x

First-principles electronic structure methods are used to find the rates of intravalley and intervalley n-type carrier scattering due to alloy disorder in Si1-xGex alloys. The required alloy scattering matrix elements are calculated from the energy splitting of nearly degenerate Bloch states which arises when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Scattering parameters for all relevant Delta and L intravalley and intervalley alloy scattering are calculated. Atomic relaxation is found to have a substantial effect on the scattering parameters. f-type intervalley scattering between Delta valleys is found to be comparable to other scattering channels. The n-type carrier mobility, calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys.

A first principles analysis of the effect of hydrogen concentration in hydrogenated amorphous silicon on the formation of strained Si-Si bonds and the optical and mobility gaps

In this paper, we use a model of hydrogenated amorphous silicon generated from molecular dynamics with density functional theory calculations to examine how the atomic geometry and the optical and mobility gaps are influenced by mild hydrogen oversaturation. The optical and mobility gaps show a volcano curve as the hydrogen content varies from undersaturation to mild oversaturation, with largest gaps obtained at the saturation hydrogen concentration. At the same time, mid-gap states associated with dangling bonds and strained Si-Si bonds disappear at saturation but reappear at mild oversaturation, which is consistent with the evolution of optical gap. The distribution of Si-Si bond distances provides the key to the change in electronic properties. In the undersaturation regime, the new electronic states in the gap arise from the presence of dangling bonds and strained Si-Si bonds, which are longer than the equilibrium Si-Si distance. Increasing hydrogen concentration up to saturation reduces the strained bonds and removes dangling bonds. In the case of mild oversaturation, the mid-gap states arise exclusively from an increase in the density of strained Si-Si bonds. Analysis of our structure shows that the extra hydrogen atoms form a bridge between neighbouring silicon atoms, thus increasing the Si-Si distance and increasing disorder in the sample.