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

Binary evolution using the theory of osculating orbits: conservative Algol evolution

Our aim is to calculate the evolution of Algol binaries within the framework of the osculating orbital theory, which considers the perturbing forces acting on the orbit of each star arising from mass exchange via Roche lobe overflow (RLOF). The scheme is compared to results calculated from a `classical' prescription. Using our stellar binary evolution code BINSTAR, we calculate the orbital evolution of Algol binaries undergoing case A and case B mass transfer, by applying the osculating scheme. The velocities of the ejected and accreted material are evaluated by solving the restricted three-body equations of motion, within the ballistic approximation. This allows us to determine the change of linear momentum of each star, and the gravitational force applied by the mass transfer stream. Torques applied on the stellar spins by tides and mass transfer are also considered. Using the osculating formalism gives shorter post-mass transfer orbital periods typically by a factor of 4 compared to the classical scheme, owing to the gravitational force applied onto the stars by the mass transfer stream. Additionally, during the rapid phase of mass exchange, the donor star is spun down on a timescale shorter than the tidal synchronization timescale, leading to sub-synchronous rotation. Consequently, between 15 and 20 per cent of the material leaving the inner-Lagrangian point is accreted back onto the donor (so-called `self-accretion'), further enhancing orbital shrinkage. Self-accretion, and the sink of orbital angular momentum which mass transfer provides, may potentially lead to more contact binaries. Even though Algols are mainly considered, the osculating prescription is applicable to all types of interacting binaries, including those with eccentric orbits.Comment: A&A in press. Minor typos correcte

On the Estimated Variances of Regression Coefficients in Misspecified Error Components Models

In a regression model with an arbitrary number of error components, the covariance matrix of the disturbances has three equivalent representations as linear combinations of matrices. Furthermore, this property is invariant with respect to powers, matrix addition, and matrix multiplication. This result is applied to the derivation and interpretation of the inconsistency of the estimated coefficient variances when the error components structure is improperly restricted. This inconsistency is defined as the difference between the asymptotic variance obtained when the restricted model is correctly specified, and the asymptotic variance obtained when the restricted model is incorrectly specified; when some error components are improperly omitted, and the remaining variance components are consistently estimated, it is always negative. In the case where the time component is improperly omitted from the two-way model, we show that the difference between the true and estimated coefficient variances is of order greater than N-1 in probabilit

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

Dynamics of Vesicles in shear and rotational flows: Modal Dynamics and Phase Diagram

Despite the recent upsurge of theoretical reduced models for vesicle shape dynamics, comparisons with experiments have not been accomplished. We review the implications of some of the recently proposed models for vesicle dynamics, especially the Tumbling-Trembling domain regions of the phase plane and show that they all fail to capture the essential behavior of real vesicles for excess areas, \Delta, greater than 0.4. We emphasize new observations of shape harmonics and the role of thermal fluctuations.Comment: (removed forgotten leftover figure files

Development of a Lumped-Parameter Model for Hermetic Reciprocating Compressor with Thermal-Electrical Coupling

The design of high-efficiency reciprocating compressors requires good understanding of interactions between different phenomena inside the compressor. This paper describes a comprehensive model to predict the performance of reciprocating compressors with thermal-electrical coupling. The simulation of the compression cycle is based on an integral control volume formulation for mass and energy conservation. The thermal model follows steady state thermal energy balances applied to the compressor components by using global thermal conductances. Finally, the equivalent circuit method is employed to simulate a steady-state model of single-phase induction motor. The motor losses are used as heat generation in the energy equation of the thermal model, which in turn provides the motor temperature required to evaluate the windings resistances. Predictions are compared to experimental data under different operating conditions and reasonable agreement is observed

Sea surface temperature of the coastal zones of France

Thermal gradients in French coastal zones for the period of one year were mapped in order to enable a coherent study of certain oceanic features detectable by the variations in the sea surface temperature field and their evolution in time. The phenomena examined were mesoscale thermal features in the English Channel, the Bay of Biscay, and the northwestern Mediterranean; thermal gradients generated by French estuary systems; and diurnal heating in the sea surface layer. The investigation was based on Heat Capacity Mapping Mission imagery

Sea surface temperature of the coastal zones of France

The results of an investigation to map the various thermal gradients in the coastal zones of France are presented. Paricular emphasis is given to the natural phenomena and man made thermal effluents. It is shown that a close correlation exist between wind speed direction and the offshore width of the effluent