Statistical Mechanics of Time Independent Non-Dissipative Nonequilibrium States

We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are given by the standard Boltzmann weights. In contrast to previous energy landscape treatments, that have been developed specifically for the glass transition, we do not impose an a priori knowledge of the inter-domain population distribution. Assuming that these domains are robust with respect to small changes in thermodynamic state variables we derive a variety of fluctuation formulae for these systems. We verify our theoretical results using molecular dynamics simulations on a model glass forming system. Non-equilibrium Transient Fluctuation Relations are derived for the fluctuations resulting from a sudden finite change to the system's temperature or pressure and these are shown to be consistent with the simulation results. The necessary and sufficient conditions for these relations to be valid are that the domains are internally populated by Boltzmann statistics and that the domains are robust. The Transient Fluctuation Relations thus provide an independent quantitative justification for the assumptions used in our statistical mechanical treatment of these systems.Comment: 17 pages, 4 figures, minor amendment

Thermodynamics of small superconductors with fixed particle number

The Variation After Projection approach is applied for the first time to the pairing hamiltonian to describe the thermodynamics of small systems with fixed particle number. The minimization of the free energy is made by a direct diagonalization of the entropy. The Variation After Projection applied at finite temperature provides a perfect reproduction of the exact canonical properties of odd or even systems from very low to high temperature.Comment: 4 pages, 3 figure

Landauer-B\"uttiker equation for bosonic carriers

We study the current of Bose particles between two reservoirs connected by a one-dimensional channel. We analyze the problem from first principles by considering a microscopic model of conductivity in the noninteracting limit. Equations for the transient and the stationary current are derived analytically. The asymptotic current has a form similar to the Landauer-B\"uttiker equation for electronic current in mesoscopic devices

On a generalization of Valiron's inequality for k-hypermonogenic functions on upper half-space

We present some results on the asymptotic growth behavior of periodic k-hypermonogenic functions on upper half-space. A generalization of the classical Valiron inequality for this class of functions and some basic properties are discussed

Supply chain integration in New Zealand: benchmark comparisons with the UK automotive sector

Supply chain integration is a promising approach to cross-enterprise process improvement that is still not well understood. This research investigates the level of sophistication (maturity) of supply chain integration in New Zealand from the systems uncertainty perspective. Uncertainty levels of value streams are evaluated using the 'uncertainty circle' concept, thereby enabling benchmark comparisons of value stream performance. A sample of 21 NZ process industry value streams is assessed using a so-called Quick Scan Audit Methodology (QSAM). and the uncertainty results compared with those obtained from 21 value streams in the UK automotive sector. This benchmarking revealed that value streams in New Zealand are weakly integrated and have control mechanisms which are significantly looser than those of the UK sample, even though they face higher uncertainty on the control and demand sides. In contrast, crosscountry differences in supply and process uncertainty are marginal. While providing insights into the general health of New Zealand value streams, the authors acknowledge that the sample is not a comprehensive representation of every NZ value stream

Exotic matter on singular divisors in F-theory

We analyze exotic matter representations that arise on singular seven-brane configurations in F-theory. We develop a general framework for analyzing such representations, and work out explicit descriptions for models with matter in the 2-index and 3-index symmetric representations of SU($N$) and SU(2) respectively, associated with double and triple point singularities in the seven-brane locus. These matter representations are associated with Weierstrass models whose discriminants vanish to high order thanks to nontrivial cancellations possible only in the presence of a non-UFD algebraic structure. This structure can be described using the normalization of the ring of intrinsic local functions on a singular divisor. We consider the connection between geometric constraints on singular curves and corresponding constraints on the low-energy spectrum of 6D theories, identifying some new examples of apparent "swampland" theories that cannot be realized in F-theory but have no apparent low-energy inconsistency.Comment: 71 page

The Lisbon Strategy and the EU's structural productivity problem

The structural nature of the EU's productivity downturn is confirmed by the analysis in this paper, with the bulk of the deterioration emanating from an outdated and inflexible industrial structure which has been slow to adapt to the intensifying pressures of globalisation and rapid technological change. The EU's productivity problems are driven by the combined effect ofan excessive focus on low and medium-technology industries (with declining productivity growth rates and a globalisation-induced contraction in investment levels); an inability to seriously challenge the US's dominance in large areas of the ICT industry, as reflected in the relatively small size of its ICT production sector; and finally, its apparent slowness in reaping the productivity enhancing benefits of ICT in a range of ICT-using industries, although measurement issues severely complicate an assessment of the gains from ICT production and diffusion.lisbon strategy, productivity, growth, labour market, Denis, Mc Morrow, R�ger, Veugelers, structural productivity

Hypervelocity runaways from the Large Magellanic Cloud

We explore the possibility that the observed population of Galactic hypervelocity stars (HVSs) originate as runaway stars from the Large Magellanic Cloud (LMC). Pairing a binary evolution code with an N-body simulation of the interaction of the LMC with the Milky Way, we predict the spatial distribution and kinematics of an LMC runaway population. We find that runaway stars from the LMC can contribute Galactic HVSs at a rate of $3 \times 10^{-6}\;\mathrm{yr}^{-1}$. This is composed of stars at different points of stellar evolution, ranging from the main-sequence to those at the tip of the asymptotic giant branch. We find that the known B-type HVSs have kinematics which are consistent with an LMC origin. There is an additional population of hypervelocity white dwarfs whose progenitors were massive runaway stars. Runaways which are even more massive will themselves go supernova, producing a remnant whose velocity will be modulated by a supernova kick. This latter scenario has some exotic consequences, such as pulsars and supernovae far from star-forming regions, and a small rate of microlensing from compact sources around the halo of the LMC.Comment: MNRAS, in pres