First order phase transitions: equivalence between bimodalities and the Yang-Lee theorem

First order phase transitions in finite systems can be defined through the bimodality of the distribution of the order parameter. This definition is equivalent to the one based on the inverted curvature of the thermodynamic potential. Moreover we show that it is in a one to one correspondence with the Yang Lee theorem in the thermodynamic limit. Bimodality is a necessary and sufficient condition for zeroes of the partition sum in the control intensive variable complex plane to be distributed on a line perpendicular to the real axis with a uniform density, scaling like the number of particles.Comment: 10 pages, no figure

Topology of event distribution as a generalized definition of phase transitions in finite systems

We propose a definition of phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. This generalizes all the definitions based on the curvature anomalies of thermodynamical potentials and provides a natural definition of order parameters. The proposed definition is directly operational from the experimental point of view. It allows to study phase transitions in Gibbs equilibria as well as in other ensembles such as the Tsallis ensemble.Comment: 4 pages, 3 figure

Supply-chain modelling and control under proportional inventory-replenishment policies

A novel state-space model of a multi-node supply chain is presented, controlled via local proportional inventory-replenishment policies. The model is driven by a stochastic sequence representing customer demand. The model is analysed under stationarity conditions and a simple recursive scheme is developed for updating its covariance matrix. This allows us to characterise the ‘bullwhip effect’ (demand amplification) in the chain and to solve an optimisation problem for a three-node model involving the minimisation of inventory subject to a probabilistic constraint on downstream demand. Finally, issues related to estimation schemes based on local historical data are briefly discussed

Non equilibrium effects in fragmentation

We study, using molecular dynamics techniques, how boundary conditions affect the process of fragmentation of finite, highly excited, Lennard-Jones systems. We analyze the behavior of the caloric curves (CC), the associated thermal response functions (TRF) and cluster mass distributions for constrained and unconstrained hot drops. It is shown that the resulting CC's for the constrained case differ from the one in the unconstrained case, mainly in the presence of a ``vapor branch''. This branch is absent in the free expanding case even at high energies . This effect is traced to the role played by the collective expansion motion. On the other hand, we found that the recently proposed characteristic features of a first order phase transition taking place in a finite isolated system, i.e. abnormally large kinetic energy fluctuations and a negative branch in the TRF, are present for the constrained (dilute) as well the unconstrained case. The microscopic origin of this behavior is also analyzed.Comment: 21 pages, 11 figure

A variational approach to strongly damped wave equations

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix--Haase, thus extending several known results and obtaining optimal analyticity angle.Comment: This is an extended version of an article appeared in \emph{Functional Analysis and Evolution Equations -- The G\"unter Lumer Volume}, edited by H. Amann et al., Birkh\"auser, Basel, 2008. In the latest submission to arXiv only some typos have been fixe

Dephasing in sequential tunneling through a double-dot interferometer

We analyze dephasing in a model system where electrons tunnel sequentially through a symmetric interference setup consisting of two single-level quantum dots. Depending on the phase difference between the two tunneling paths, this may result in perfect destructive interference. However, if the dots are coupled to a bath, it may act as a which-way detector, leading to partial suppression of the phase-coherence and the reappearance of a finite tunneling current. In our approach, the tunneling is treated in leading order whereas coupling to the bath is kept to all orders (using P(E) theory). We discuss the influence of different bath spectra on the visibility of the interference pattern, including the distinction between "mere renormalization effects" and "true dephasing".Comment: 18 pages, 8 figures; For a tutorial introduction to dephasing see http://iff.physik.unibas.ch/~florian/dephasing/dephasing.htm

Vitamin D and Risk of Neuroimaging Abnormalities.

Vitamin D deficiency has been linked with an increased risk of incident all-cause dementia and Alzheimer's disease. The aim of the current study was to explore the potential mechanisms underlying these associations by determining whether low vitamin D concentrations are associated with the development of incident cerebrovascular and neurodegenerative neuroimaging abnormalities. The population consisted of 1,658 participants aged ≥65 years from the US-based Cardiovascular Health Study who were free from prevalent cardiovascular disease, stroke and dementia at baseline in 1992-93. Serum 25-hydroxyvitamin D (25(OH)D) concentrations were determined by liquid chromatography-tandem mass spectrometry from blood samples collected at baseline. The first MRI scan was conducted between 1991-1994 and the second MRI scan was conducted between 1997-1999. Change in white matter grade, ventricular grade and presence of infarcts between MRI scan one and two were used to define neuroimaging abnormalities. During a mean follow-up of 5.0 years, serum 25(OH)D status was not significantly associated with the development of any neuroimaging abnormalities. Using logistic regression models, the multivariate adjusted odds ratios (95% confidence interval) for worsening white matter grade in participants who were severely 25(OH)D deficient (<25 nmol/L) and deficient (≥25-50 nmol/L) were 0.76 (0.35-1.66) and 1.09 (0.76-1.55) compared to participants with sufficient concentrations (≥50 nmol/L). The multivariate adjusted odds ratios for ventricular grade in participants who were severely 25(OH)D deficient and deficient were 0.49 (0.20-1.19) and 1.12 (0.79-1.59) compared to those sufficient. The multivariate adjusted odds ratios for incident infarcts in participants who were severely 25(OH)D deficient and deficient were 1.95 (0.84-4.54) and 0.73 (0.47-1.95) compared to those sufficient. Overall, serum vitamin D concentrations could not be shown to be associated with the development of cerebrovascular or neurodegenerative neuroimaging abnormalities in Cardiovascular Health Study participants.The Cardiovascular Health Study was supported by contracts HHSN268201200036C, HHSN268200800007C, N01 HC55222, N01HC85079, N01HC85080, N01HC85081, N01HC85082, N01HC85083, N01HC85086, and grant HL080295 from the National Heart, Lung, and Blood Institute (NHLBI), with additional contribution from the National Institute of Neurological Disorders and Stroke (NINDS). Additional support was provided by AG023629, AG20098, AG15928 and HL084443 from the National Institute on Aging (NIA). A full list of principal CHS investigators and institutions can be found at chs-nhlbi.org. Additional support was also provided by NIRG-11-200737 from the Alzheimer’s Association, the Mary Kinross Charitable Trust, the James Tudor Foundation, the Halpin Trust, the Age Related Diseases and Health Trust, and the Norman Family Charitable Trust (to D.J.L.). This research was supported by the National Institute for Health Research (NIHR) Collaboration for Leadership in Applied Health Research and Care South West Peninsula at the Royal Devon and Exeter NHS Foundation Trust. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health. The National Institutes of Health was involved in the original design and conduct of the Cardiovascular Health Study and in the data collection methods

Resolving the dusty circumstellar environment of the A[e] supergiant HD 62623 with the VLTI/MIDI

B[e] stars are hot stars surrounded by circumstellar gas and dust responsible for the presence of emission lines and IR-excess in their spectra. How dust can be formed in this highly illuminated and diluted environment remains an open issue. HD 62623 is one of the very few A-type supergiants showing the B[e] phenomenon. We obtained nine calibrated visibility measurements using the VLTI/MIDI instrument in SCI-PHOT mode and PRISM spectral dispersion mode with projected baselines ranging from 13 to 71 m and with various position angles. We used geometrical models and physical modeling with a radiative transfer code to analyze these data. The dusty circumstellar environment of HD 62623 is partially resolved by the VLTI/MIDI even with the shortest baselines. The environment is flattened and can be separated into two components: a compact one whose extension grows from 17 mas at 8 microns to 30 mas at 9.6 microns and stays almost constant up to 13 microns, and a more extended one that is over-resolved even with the shortest baselines. Using the radiative transfer code MC3D, we managed to model HD 62623's circumstellar environment as a dusty disk with an inner radius of 3.85+-0.6 AU, an inclination angle of 60+-10 deg, and a mass of 2x10^-7Mo. It is the first time that the dusty disk inner rim of a supergiant star exhibiting the B[e] phenomenon is significantly constrained. The inner gaseous envelope likely contributes up to 20% to the total N band flux and acts like a reprocessing disk. Finally, the hypothesis of a stellar wind deceleration by the companion's gravitational effects remains the most probable case since the bi-stability mechanism does not seem to be efficient for this star.Comment: 13 pages, 11 figures. A&A accepted pape