Ergonomics of the Operative Field in Paediatric Minimal Access Surgery

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Kinetic Monte Carlo simulation of faceted islands in heteroepitaxy using multi-state lattice model

A solid-on-solid model is generalized to study the formation of Ge pyramid islands bounded by (105) facets on Si(100) substrates in two dimensions. Each atomic column is not only characterized by the local surface height but also by two deformation state variables dictating the local surface tilt and vertical extension. These deformations phenomenologically model surface reconstructions in (105) facets and enable the formation of islands which better resemble faceted pyramids. We demonstrate the model by application to a kinetic limited growth regime. We observe significantly reduced growth rates after faceting and a continuous nucleation of new islands until overcrowding occurs.Comment: 7 pages, 5 figure

Single-Valued Hamiltonian via Legendre-Fenchel Transformation and Time Translation Symmetry

Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and non-determined motion of classical particles, and is physically unacceptable. In this work, we propose a new construction of single-valued Hamiltonian by applying Legendre-Fenchel transformation, which is a mathematically rigorous generalization of conventional Legendre transformation, valid for non-convex Lagrangian systems, but not yet widely known to the physics community. With the new single-valued Hamiltonian, we study spontaneous breaking of time translation symmetry and derive its vacuum state. Applications to theories of cosmology and gravitation are discussed.Comment: Journal Version, 16pp. All results + conclusions un-changed, only minor refinements to clarify the importance of our new LFT method and its physics applications; references adde

Fractional constant elasticity of variance model

This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model is developed. European option pricing formula similar to that of the classical CEV model is obtained and a volatility skew pattern is revealed.Comment: Published at http://dx.doi.org/10.1214/074921706000001012 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Quantum speed limit for noisy dynamics

The laws of quantum physics place a limit on the speed of computation, in particular the evolution time of a system cannot be arbitrarily fast. Bounds on the speed of evolution for unitary dynamics have been long studied. A few bounds on the speed of evolution for noisy dynamics have also been obtained recently, these bounds, however, are in general not tight. In this article we present a new framework for quantum speed limit of noisy dynamics. With this framework we obtain the exact maximal angle that a noisy dynamics can achieve at any given time, this then provides tight bounds on the evolution time for noisy dynamics. The obtained bound reveals that noisy dynamics are generically different from unitary dynamics, in particular we show that the 'orthogonalization' time, which is the minimum time needed to evolve any state to its orthogonal states, is in general not applicable to noisy dynamics.Comment: 6 pages. Comments are welcom