Cooperative Jahn-Teller phase transition of icosahedral molecular units

Non-linear molecules undergo distortions when the orbital degeneracy of the highest occupied level is lifted by the Jahn–Teller effect. If such molecules or clusters of atoms are coupled to one another, the system may experience a cooperative Jahn–Teller effect (CJTE). In this paper, we describe a model of how the CJTE leads to the crystallization of the disordered phase. The model Hamiltonian is based on a normal mode decomposition of the clusters in order to maintain the symmetry labels. We take account of the electron-strain and the electron-phonon couplings and, by displacing the coordinates of the oscillators, obtain a term that explicitly couples the Jahn–Teller centers, enabling us to perform a mean-field analysis. The calculation of the free energy then becomes straightforward, and obtaining phase diagrams in various regimes follows from the minimization of this free energy. The results show that the character of the phase transition may change from strong to weak first order and even to second-order, depending on the coupling to the vibrational modes. Taken together, these results may serve as a paradigm for crystallization near the transition temperature, where the atoms tend to form clusters of icosahedral symmetry

User's guide to Monte Carlo methods for evaluating path integrals

We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings

Free-energy coarse-grained potential for C60

We propose a new deformable free energy method for generating a free-energy coarse-graining potential for C60. Potentials generated from this approach exhibit a strong temperature dependence and produce excellent agreement with benchmark fully atomistic molecular dynamics simulations. Parameter sets for analytical fits to this potential are provided at four different temperatures

Self-ordered nanostructures on patterned substrates: experiment and theory of metalorganic vapor-phase epitaxy of V-groove quantum wires and pyramidal quantum dots

The formation of nanostructures during metalorganic vapor-phase epitaxy on patterned (001)/(111)B GaAs substrates is reviewed. The focus of this review is on the seminal experiments that revealed the key kinetic processes during nanostructure formation and the theory and modelling that explained the phenomenology in successively greater detail. Experiments have demonstrated that V-groove quantum wires and pyramidal quantum dots result from self-limiting concentration profiles that develop at the bottom of V-grooves and inverted pyramids, respectively. In the 1950s, long before the practical importance of patterned substrates became evident, the mechanisms of capillarity during the equilibration of non-planar surfaces were identified and characterized. This was followed, from the late 1980s, by the identification of growth rate anisotropies (i.e. differential growth rates of crystallographic facets) and precursor decomposition anisotropies, with parallel developments in the fabrication of V-groove quantum wires and pyramidal quantum dots. The modelling of these growth processes began at the scale of facets and culminated in systems of coupled reaction–diffusion equations, one for each crystallographic facet that defines the pattern, which takes account of the decomposition and surface diffusion kinetics of the group-III precursors and the subsequent surface diffusion and incorporation of the group-III atoms released by these precursors. Solutions of the equations with optimized parameters produced concentration profiles that provided a quantitative interpretation of the time-, temperature-, and alloy-concentration-dependence of the self-ordering process seen in experiments

Pressure statistics from the path integral for Darcy flow through random porous media

The path integral for classical statistical dynamics is used to determine the properties of one-dimensional Darcy flow through a porous medium with a correlated stochastic permeability for several spatial correlation lengths. Pressure statistics are obtained from the numerical evaluation of the path integral by using the Markov chain Monte Carlo method. Comparisons between these pressure distributions and those calculated from the classic finite-volume method for the corresponding stochastic differential equation show excellent agreement for Dirichlet and Neumann boundary conditions. The evaluation of the variance of the pressure based on a continuum description of the medium provides an estimate of the effects of discretization. Log-normal and Gaussian fits to the pressure distributions as a function of position within the porous medium are discussed in relation to the spatial extent of the correlations of the permeability fluctuations

Growth of epitaxial graphene: Theory and experiment

A detailed review of the literature for the last 5-10 years on epitaxial growth of graphene is presented. Both experimental and theoretical aspects related to growth on transition metals and on silicon carbide are thoroughly reviewed. Thermodynamic and kinetic aspects of growth on all these materials, where possible, are discussed. To make this text useful for a wider audience, a range of important experimental techniques that have been used over the last decade to grow (e.g. CVD, TPG and segregation) and characterize (STM, LEEM, etc.) graphene are reviewed, and a critical survey of most important theoretical techniques is given. Finally, we critically discuss various unsolved problems related to growth and its mechanism which we believe require proper attention in future research

Scaling of the surface vasculature on the human placenta

The networks of veins and arteries on the chorionic plate of the human placenta are analyzed in terms of Voronoi cells derived from these networks. Two groups of placentas from the United States are studied: a population cohort with no prescreening, and a cohort from newborns with an elevated risk of developing autistic spectrum disorder. Scaled distributions of the Voronoi cell areas in the two cohorts collapse onto a single distribution, indicating common mechanisms for the formation of the complete vasculatures, but which have different levels of activity in the two cohorts