Complex Obtuse Random Walks and their Continuous-Time Limits

We study a particular class of complex-valued random variables and their associated random walks: the complex obtuse random variables. They are the generalization to the complex case of the real-valued obtuse random variables which were introduced in \cite{A-E} in order to understand the structure of normal martingales in \RR^n.The extension to the complex case is mainly motivated by considerations from Quantum Statistical Mechanics, in particular for the seek of a characterization of those quantum baths acting as classical noises. The extension of obtuse random variables to the complex case is far from obvious and hides very interesting algebraical structures. We show that complex obtuse random variables are characterized by a 3-tensor which admits certain symmetries which we show to be the exact 3-tensor analogue of the normal character for 2-tensors (i.e. matrices), that is, a necessary and sufficient condition for being diagonalizable in some orthonormal basis. We discuss the passage to the continuous-time limit for these random walks and show that they converge in distribution to normal martingales in \CC^N. We show that the 3-tensor associated to these normal martingales encodes their behavior, in particular the diagonalization directions of the 3-tensor indicate the directions of the space where the martingale behaves like a diffusion and those where it behaves like a Poisson process. We finally prove the convergence, in the continuous-time limit, of the corresponding multiplication operators on the canonical Fock space, with an explicit expression in terms of the associated 3-tensor again

Entanglement of Bipartite Quantum Systems driven by Repeated Interactions

We consider a non-interacting bipartite quantum system $\mathcal H_S^A\otimes\mathcal H_S^B$ undergoing repeated quantum interactions with an environment modeled by a chain of independant quantum systems interacting one after the other with the bipartite system. The interactions are made so that the pieces of environment interact first with $\mathcal H_S^A$ and then with $\mathcal H_S^B$. Even though the bipartite systems are not interacting, the interactions with the environment create an entanglement. We show that, in the limit of short interaction times, the environment creates an effective interaction Hamiltonian between the two systems. This interaction Hamiltonian is explicitly computed and we show that it keeps track of the order of the successive interactions with $\mathcal H_S^A$ and $\mathcal H_S^B$. Particular physical models are studied, where the evolution of the entanglement can be explicitly computed. We also show the property of return of equilibrium and thermalization for a family of examples

High-throughput in-situ characterization and modelling of precipitation kinetics in compositionally graded alloys

The development of new engineering alloy chemistries is a time consuming and iterative process. A necessary step is characterization of the nano/microstructure to provide a link between the processing and properties of each alloy chemistry considered. One approach to accelerate the identification of optimal chemistries is to use samples containing a gradient in composition, ie. combinatorial samples, and to investigate many different chemistries at the same time. However, for engineering alloys, the final properties depend not only on chemistry but also on the path of microstructure development which necessitates characterization of microstructure evolution for each chemistry. In this contribution we demonstrate an approach that allows for the in-situ, nanoscale characterization of the precipitate structures in alloys, as a function of aging time, in combinatorial samples containing a composition gradient. The approach uses small angle x-ray scattering (SAXS) at a synchrotron beamline. The Cu-Co system is used for the proof-of-concept and the combinatorial samples prepared contain a gradient in Co from 0% to 2%. These samples are aged at temperatures between 450{\textdegree}C and 550{\textdegree}C and the precipitate structures (precipitate size, volume fraction and number density) all along the composition gradient are simultaneously monitored as a function of time. This large dataset is used to test the applicability and robustness of a conventional class model for precipitation that considers concurrent nucleation, growth and coarsening and the ability of the model to describe such a large dataset.Comment: Published in Acta Materiali

A NTU-Based Model to Estimate Suction Superheating In Scroll Compressors

Suction superheating plays a major role in determining the efficiency degradation of hermetic scroll compressors. Current models to predict superheating are usually experimentally calibrated and therefore can only be applied to existing compressors. This paper presents a thermal model to estimate suction superheating in scroll compressors, based on the NTU method for heat exchangers design. The model considers an isothermal surface exchanging heat with the gas in the suction path and in the discharge plenum. Compared to other models, the new approach described herein has the advantage of not requiring any experimental input data. The thermal model is coupled to a thermodynamic model and applied to evaluate the performance of a scroll compressor. The model was capable to predict the suction gas temperature in good agreement with experimental data, making it particularly useful for compressor design

A Neural Network to Predict the Temperature Distribution in Hermetic Refrigeration Compressors

The understanding of heat transfer interactions in refrigeration compressors is of fundamental importance to characterize their overall performance. Certain temperatures, such as those of the motor, oil, shell, and at suction and discharge chambers, have strong influence on the compressor electrical consumption and reliability. Experimental and numerical approaches have been successfully employed to characterize the thermal profile of compressors under different operating conditions. This paper presents a multi-layered feed-forward neural network developed to predict the main temperatures of a hermetic reciprocating compressor. Such a model can be used for different compressor layouts without major modifications, being a fast method for estimating temperatures without the solution of the compression cycle. Predictions of the neural network were compared with experimental data and numerical results from comprehensive thermodynamic simulations, and good agreement was observed in a wide range of evaporating and condensing temperatures. The neural network was found to predict the temperature distribution with sufficient accuracy for compressor analysis and development

A Combined Experimental-Numerical Procedure to Estimate Leakage Gap of Compressor Valves

Leakage through valves can significantly reduce the volumetric and isentropic efficiencies of compressors. Despite its importance for compressor design, the dimensional characterization of leakage gaps is not a trivial task. In this paper, we present a combined experimental-numerical method to estimate leakage gap of compressor valves. Measurements of leakage were carried out via the constant volume method, which is widely employed in the analysis of gas flow through microchannels. Additionally, numerical predictions were obtained with a one-dimensional flow model, taking into account viscous friction, slip at the walls, and gas compressibility. The leakage gap in the simulation model is adjusted so that predictions match the experimental results of leakage for different pressure differences. The procedure is applied for the analysis of three valve designs of refrigeration compressors

An Experimental-Numerical Procedure to Characterize Compressor Performance under Cycling Operating Conditions of Refrigerators

The design of reciprocating compressors is commonly based on steady-state operating conditions. However, most household refrigerators operate under transient and periodic regimes, characterized by alternate periods in which the compressor is either operating (on) or not operating (off). The result is a decoupled design approach since stabilized conditions not necessarily represent the actual operating conditions of refrigerators. This paper presents a strategy in which a virtual refrigeration system is developed and coupled to an experimental facility in order to test compressors under on-off conditions typical of household refrigerators. The virtual refrigeration system simulates the dynamic behavior of a household refrigerator, except for the compressor, and provides the instantaneous operating condition to the compressor in the test bench. The developed procedure was used to emulate a refrigerator operating at ambient temperature of 32 °C and freezer cut-off temperature of -16 °C. The results were in good agreement with the experimental data, with the system energy consumption and the compressor run time predicted with a maximum deviation of 1.3%. The experimental facility is particularly useful to evaluate the effect that changes in the compressor design may have on the refrigerator energy consumption

Differential Hox expression in murine embryonic stem cell models of normal and malignant hematopoiesis

The Hox family are master transcriptional regulators of developmental processes, including hematopoiesis. The Hox regulators, caudal homeobox factors (Cdx1-4), and Meis1, along with several individual Hox proteins, are implicated in stem cell expansion during embryonic development, with gene dosage playing a significant role in the overall function of the integrated Hox network. To investigate the role of this network in normal and aberrant, early hematopoiesis, we employed an in vitro embryonic stem cell differentiation system, which recapitulates mouse developmental hematopoiesis. Expression profiles of Hox, Pbx1, and Meis1 genes were quantified at distinct stages during the hematopoietic differentiation process and compared with the effects of expressing the leukemic oncogene Tel/PDGFR;2. During normal differentiation the Hoxa cluster, Pbx1 and Meis1 predominated, with a marked reduction in the majority of Hox genes (27/39) and Meis1 occurring during hematopoietic commitment. Only the posterior Hoxa cluster genes (a9, a10, a11, and a13) maintained or increased expression at the hematopoietic colony stage. Cdx4, Meis1, and a subset of Hox genes, including a7 and a9, were differentially expressed after short-term oncogenic (Tel/PDGFR;2) induction. Whereas Hoxa4-10, b1, b2, b4, and b9 were upregulated during oncogenic driven myelomonocytic differentiation. Heterodimers between Hoxa7/Hoxa9, Meis1, and Pbx have previously been implicated in regulating target genes involved in hematopoietic stem cell (HSC) expansion and leukemic progression. These results provide direct evidence that transcriptional flux through the Hox network occurs at very early stages during hematopoietic differentiation and validates embryonic stem cell models for gaining insights into the genetic regulation of normal and malignant hematopoiesis

Hydrological budget of Lake Chad : assessment of lake-groundwater interaction by coupling Bayesian approach and chemical budget

International audienceEstimation of lake-groundwater interactions is a crucial step to constrain water balance of lacustrine and aquifersystems. Located in the Sahel, the Lake Chad is at the center of an endorheic basin of 2,5.106 km2. One of themost remarkable features of this terminal lake is that, despite the semi-arid context and high evaporation rates of thearea, its waters are fresh. It is proposed in the literature that the solutes are evacuated in the underlying quaternaryaquifer bearing witness to the importance of surface water and groundwater exchanges for the chemical regulationof the lake. The water balance of this system is still not fully understood. The respective roles of evaporation versusinfiltration into the quaternary aquifer are particularly under constrained.To assess lake-groundwater flows, we used the previous conceptual hydrological model of the lake Chad proposedby Bader et al. (Hydrological Sciences Journal, 2011). This model involves six parameters including infiltrationrate. A probabilistic inversion of parameters, based on an exploration of the parameters space through a Metropolisalgorithm (a Monte Carlo Markov Chain method), allows the construction of an a posteriori Probability DensityFunction of each parameter yielding to the best fits between observed lake levels and simulated. Then, a chemicalbudget of a conservative element, such as chloride, is introduced in the water balance model using the optimalparameters resulting from the Bayesian inverse approach.The model simulates lake level and chloride concentration variations of lake Chad from 1956 up to 2008. Simulated lake levels are in overall agreement with the observations, with a Nash-Sutcliffe efficiency coefficient above0.94 for all sets of parameters retained. The infiltration value, obtained by such probabilistic inversion approach,accounts for 120±20 mm/yr, representing 5% of the total outputs of the lake. However, simulated chloride concentrations are overestimated in comparison to the scarce measurements available over that period. As an example,the mean chloride concentration measured in the southern pool on a basis of our synthesis of existing chemicaldata since the 1970’s is approximately three time lower than the computed mean concentration. This may be dueto either the non-representativeness of our chemical dataset or overestimation of the evaporation rate that is fixedto 2000 mm/yr in our model.This study tackles the quantification of the lake water flows to the quaternary aquifer system and the associateduncertainties from a probabilistic point of view. This is an essential step to improve predictions of groundwaterresources in the Lake Chad Basin under climate change