Fronts, Domain Growth and Dynamical Scaling in a d=1 non-Potential System

We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial dependent terms have been added. As long as the angular velocity is different from zero, there is no known Lyapunov potential for the dynamics of the system. As a consequence the system follows a non-relaxational dynamics and the asymptotic state can not be associated with a final equilibrium state. When the rotation angular velocity is greater than some critical value, the system undergoes the Kuppers-Lortz instability leading to a time dependent chaotic dynamics and there is no coarsening beyond this instability. We have focused on the transient dynamics below this instability, where the dynamics is still non-relaxational. In this regime the dynamics is governed by a non-relaxational motion of fronts separating dynamically equivalent homogeneous states. We classify the families of fronts that occur in the dynamics, and calculate their shape and velocity. We have found that a scaling description of the coarsening process is still valid as in the potential case. The growth law is nearly logarithmic with time for short times and becomes linear after a crossover, whose width is determined by the strength of the non-potential terms.Comment: 15 pages, 10 figure

Thermodynamic work from operational principles

In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines, in an analogous way to the role played, for macroscopic machines, by the energy stored in the idealisation of a lifted weight. Despite of several attempts to resolve this issue by putting forward specific models, these are far from capturing realistically the transitions that a quantum machine is expected to perform. In this work, we adopt a novel strategy by considering arbitrary kinds of systems that one can attach to a quantum thermal machine and seeking for work quantifiers. These are functions that measure the value of a transition and generalise the concept of work beyond the model of a lifted weight. We do so by imposing simple operational axioms that any reasonable work quantifier must fulfil and by deriving from them stringent mathematical condition with a clear physical interpretation. Our approach allows us to derive much of the structure of the theory of thermodynamics without taking as a primitive the definition of work. We can derive, for any work quantifier, a quantitative second law in the sense of bounding the work that can be performed using some non-equilibrium resource by the work that is needed to create it. We also discuss in detail the role of reversibility and correlations in connection with the second law. Furthermore, we recover the usual identification of work with energy in degrees of freedom with vanishing entropy as a particular case of our formalism. Our mathematical results can be formulated abstractly and are general enough to carry over to other resource theories than quantum thermodynamics.Comment: 22 pages, 4 figures, axioms significantly simplified, more comprehensive discussion of relationship to previous approache

A framework for closed-loop supply chains of reusable articles

Reuse practices contribute to the environmental and economical sustainability of production and distribution systems. Surprisingly, reuse closed-loop supply chains (CLSC) have not been widely researched for the moment. In this paper, we explore the scientific literature on reuse and we propose a framework for reusable articles. This conceptual structure includes a typology integrating under the reusable articles term different categories of articles (transportation items, packaging materials, tools) and addresses the management issues that arise in reuse CLSC. We ground our results in a set of case studies developed in real industrial settings, which have also been contrasted with cases available in existing literature.reverse logistics;case studies;closed-loop supply chains;returns managment

The distribution of stars around the Milky Way's central black hole II: Diffuse light from sub-giants and dwarfs

This is the second of three papers that search for the predicted stellar cusp around the Milky Way's central black hole, Sagittarius A*, with new data and methods. We aim to infer the distribution of the faintest stellar population currently accessible through observations around Sagittarius A*. We use adaptive optics assisted high angular resolution images obtained with the NACO instrument at the ESO VLT. Through optimised PSF fitting we remove the light from all detected stars above a given magnitude limit. Subsequently we analyse the remaining, diffuse light density. The analysed diffuse light arises from sub-giant and main-sequence stars with KS ~ 19 - 20 with masses of 1 - 2 Msol . These stars can be old enough to be dynamically relaxed. The observed power-law profile and its slope are consistent with the existence of a relaxed stellar cusp around the Milky Way's central black hole. We find that a Nuker law provides an adequate description of the nuclear cluster's intrinsic shape (assuming spherical symmetry). The 3D power-law slope near Sgr A* is \gamma = 1.23 +- 0.05. At a distance of 0.01 pc from the black hole, we estimate a stellar mass density of 2.3 +- 0.3 x 10^7 Msol pc^-3 and a total enclosed stellar mass of 180 +- 20 Msol. These estimates assume a constant mass-to-light ratio and do not take stellar remnants into account. The fact that no cusp is observed for bright (Ks 16) giant stars at projected distances of roughly 0.1-0.3 pc implies that some mechanism has altered their appearance or distribution.Comment: Accepted for publication A&

The distribution of old stars around the Milky Way's central black hole I: Star counts

(abridged) In this paper we revisit the problem of inferring the innermost structure of the Milky Way's nuclear star cluster via star counts, to clarify whether it displays a core or a cusp around the central black hole. Through image stacking and improved PSF fitting we push the completeness limit about one magnitude deeper than in previous, comparable work. Contrary to previous work, we analyse the stellar density in well-defined magnitude ranges in order to be able to constrain stellar masses and ages. The RC and brighter giant stars display a core-like surface density profile within a projected radius R<0.3 pc of the central black hole, in agreement with previous studies, but show a cusp-like surface density distribution at larger R. The surface density of the fainter stars can be described well by a single power-law at R<2 pc. The cusp-like profile of the faint stars persists even if we take into account the possible contamination of stars in this brightness range by young pre-main sequence stars. The data are inconsistent with a core-profile for the faint stars.Finally, we show that a 3D Nuker law provides a very good description of the cluster structure. We conclude that the observed stellar density at the Galactic Centre, as it can be inferred with current instruments, is consistent with the existence of a stellar cusp around the Milky Way's central black hole, Sgr A*. This cusp is well developed inside the influence radius of about 3 pc of Sgr A* and can be described by a single three-dimensional power-law with an exponent gamma=1.23+-0.05. The apparent lack of RC stars and brighter giants at projected distances of R < 0.3 pc (R<8") of the massive black hole may indicate that some mechanism has altered their distribution or intrinsic luminosity.Comment: Accepted for publication A&

Channel Blockade in a Two-Path Triple-Quantum-Dot System

Electronic transport through a two-path triple-quantum-dot system with two source leads and one drain is studied. By separating the conductance of the two double dot paths, we are able to observe double dot and triple dot physics in transport and study the interaction between the paths. We observe channel blockade as a result of inter-channel Coulomb interaction. The experimental results are understood with the help of a theoretical model which calculates the parameters of the system, the stability regions of each state and the full dynamical transport in the triple dot resonances.Comment: 6 pages, 6 figure

Work and entropy production in generalised Gibbs ensembles

Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble (GGE), reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium.Comment: 22 pages, 4 figures, improvements in presentatio