Langevin PDF simulation of particle deposition in a turbulent pipe flow

The paper deals with the description of particle deposition on walls from a turbulent flow over a large range of particle diameter, using a Langevin PDF model. The first aim of the work is to test how the present Langevin model is able to describe this phenomenon and to outline the physical as- pects which play a major role in particle deposition. The general features and characteristics of the present stochastic model are first recalled. Then, results obtained with the standard form of the model are presented along with an analysis which has been carried out to check the sensitivity of the predictions on different mean fluid quantities. These results show that the physical repre- sentation of the near-wall physics has to be improved and that, in particular, one possible route is to introduce specific features related to the near-wall coherent structures. In the following, we propose a simple phenomenological model that introduces some of the effects due to the presence of turbulent coherent structures on particles in a thin layer close to the wall. The results obtained with this phenomenological model are in good agreement with experimental evidence and this suggests to pursue in that direction, towards the development of more general and rigorous stochastic models that provide a link between a geometrical description of turbulent flow and a statistical one.Comment: 40 pages, 8 figure

The second law of quantum thermodynamics as an equality

We investigate the connection between recent results in quantum thermodynamics and fluctuation relations by adopting a fully quantum mechanical description of thermodynamics. By including a work system whose energy is allowed to fluctuate, we derive a set of equalities which all thermodynamical transitions have to satisfy. This extends the condition for maps to be Gibbs-preserving to the case of fluctuating work, providing a more general characterisation of maps commonly used in the information theoretic approach to thermodynamics. For final states, block diagonal in the energy basis, this set of equalities are necessary and sufficient conditions for a thermodynamical state transition to be possible. The conditions serves as a parent equation which can be used to derive a number of results. These include writing the second law of thermodynamics as an equality featuring a fine-grained notion of the free energy. It also yields a generalisation of the Jarzynski fluctuation theorem which holds for arbitrary initial states, and under the most general manipulations allowed by the laws of quantum mechanics. Furthermore, we show that each of these relations can be seen as the quasi-classical limit of three fully quantum identities. This allows us to consider the free energy as an operator, and allows one to obtain more general and fully quantum fluctuation relations from the information theoretic approach to quantum thermodynamics.Comment: 11+3 pages. V4: Updated to match published version. Discussion of thermo-majorization and implementing arbitary unitaries added. V3: Added funding information. V2: Expanded discussion on relation to fluctuation theorem

Risk measurement with the equivalent utility principles.

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable at- tention in the financial mathematics literature. Mathematically, a risk measure is a mapping from a class of random variables defined on some measurable space to the (extended) real line. Economically, a risk measure should capture the preferences of the decision-maker. In incomplete financial markets, prices are no more unique but depend on the agents' attitudes towards risk. This paper complements the study initiated in Denuit, Dhaene & Van Wouwe (1999) and considers several theories for decision under uncertainty: the classical expected utility paradigm, Yaari's dual approach, maximin expected utility theory, Choquet expected utility theory and Quiggin rank-dependent utility theory. Building on the actuarial equivalent utility pricing principle, broad classes of risk measures are generated, of which most classical risk measures appear to be particular cases. This approach shows that most risk measures studied recently in the financial literature disregard the utility concept (i.e. correspond to linear utilities), causing some deficiencies. Some alternatives proposed in the literature are discussed, based on exponential utilities.Actuarial; Coherence; Decision; Expected; Market; Markets; Measurement; Preference; Premium; Prices; Pricing; Principles; Random variables; Research; Risk; Risk measure; Risk measurement; Space; Studies; Theory; Uncertainty; Utilities; Variables;