LOCAL VARIABILITY IN THE ORBIT OF SATURN'S F RING

This work was supported by the Science and Technology Facilities Council (grant number ST/F007566/1)

Algebraic approach to a two-qubit quantum thermal machine

Algebraic methods for solving time dependent Hamiltonians are used to investigate the performance of quantum thermal machines. We investigate the thermodynamic properties of an engine formed by two coupled q-bits, performing an Otto cycle. The thermal interaction occurs with two baths at different temperatures, while work is associated with the interaction with an arbitrary time-dependent magnetic field that varies in intensity and direction. For the coupling, we consider the 1-d isotropic Heisenberg model, which allows us to describe the system by means of the irreducible representation of the $\mathfrak{su}(2)$ Lie algebra within the triplet subspace. We inspect different settings of the temperatures and frequencies of the cycle and investigate the corresponding operation regimes of the engine. Finally, we numerically investigate the engine efficiency under a time varying Rabi frequency, interpolating the abrupt and adiabatic limits.Comment: 11 pages, 5 figures, submitted to Physical Review

Quantum-based solution of time-dependent complex Riccati equations

Using the Wei-Norman theory we obtain a time-dependent complex Riccati equation (TDCRE) as the solution of the time evolution operator (TEO) of quantum systems described by time-dependent (TD) Hamiltonians that are linear combinations of the generators of the $\mathfrak{su}(1,1)$, $\mathfrak{su}(2)$ and $\mathfrak{so}(2,1)$ Lie algebras. Using a recently developed solution for the time evolution of these quantum systems we solve the TDCRE recursively as generalized continued fractions, which are optimal for numerical implementations, and establish the necessary and sufficient conditions for the unitarity of the TEO in the factorized representation. The inherited symmetries of quantum systems can be recognized by a simple inspection of the TDCRE, allowing effective quantum Hamiltonians to be associated with it, as we show for the Bloch-Riccati equation whose Hamiltonian corresponds to that of a generic TD system of the Lie algebra $\mathfrak{su}(2)$. As an application, but also as a consistency test, we compare our solution with the analytic one for the Bloch-Riccati equation considering the Rabi frequency driven by a complex hyperbolic secant pulse generating spin inversion, showing an excellent agreement.Comment: 10 Pages, 1 Figur

Modeling and Real-Time Simulation of a Vascularized Liver Tissue

International audienceIn Europe only, about 100,000 deaths per year are related to cirrhosis or liver cancer. While surgery remains the option that offers the foremost success rate against such pathologies, several limitations still hinder its widespread development. Among the limiting factors is the lack of accurate planning systems, which has been a motivation for several recent works, aiming at better resection planning and training systems, relying on pre-operative imaging, anatomical and biomechanical modelling. While the vascular network in the liver plays a key role in defining the operative strategy, its influence at a biomechanical level has not been taken into account. In the paper we propose a real-time model of vascularized organs such as the liver. The model takes into account separate constitutive laws for the parenchyma and vessels, and defines a coupling mechanism between these two entities. In the evaluation section, we present results of in vitro porcine liver experiments that indicate a significant influence of vascular structures on the mechanical behaviour of tissue. We confirm the val- ues obtained in the experiments by computer simulation using standard FEM. Finally, we show that the conventional modelling approach can be efficiently approximated with the proposed composite model capable of real-time calculations

Interactive Training System for Interventional Electrocardiology Procedures

International audienceRecent progress in cardiac catheterization and devices al-lowed to develop new therapies for severe cardiac diseases like arrhyth-mias and heart failure. The skills required for such interventions are still very challenging to learn, and typically acquired over several years. Vir-tual reality simulators can reduce this burden by allowing to practice such procedures without consequences on patients. In this paper, we propose the first training system dedicated to cardiac electrophysiology, includ-ing pacing and ablation procedures. Our framework involves an efficient GPU-based electrophysiological model. Thanks to an innovative mul-tithreading approach, we reach high computational performances that allow to account for user interactions in real-time. Based on a scenario of cardiac arrhythmia, we demonstrate the ability of the user-guided simulator to navigate inside vessels and cardiac cavities with a catheter and to reproduce an ablation procedure involving: extra-cellular poten-tial measurements, endocardial surface reconstruction, electrophysiology mapping, radio-frequency (RF) ablation, as well as electrical stimulation. This works is a step towards computerized medical learning curriculum

Biomechanical Simulation of Electrode Migration for Deep Brain Stimulation

International audienceDeep Brain Stimulation is a modern surgical technique for treating patients who suffer from affective or motion disorders such as Parkinson's disease. The efficiency of the procedure relies heavily on the accuracy of the placement of a micro-electrode which sends electrical pulses to a specific part of the brain that controls motion and affective symptoms. However, targeting this small anatomical structure is rendered difficult due to a series of brain shifts that take place during and after the procedure. This paper introduces a biomechanical simulation of the intra and postoperative stages of the procedure in order to determine lead deformation and electrode migration due to brain shift. To achieve this goal, we propose a global approach, which accounts for brain deformation but also for the numerous interactions that take place during the procedure (contacts between the brain and the inner part of the skull and falx cerebri, effect of the cerebro-spinal fluid, and biomechanical interactions between the brain and the electrodes and cannula used during the procedure). Preliminary results show a good correlation between our simulations and various results reported in the literature

Have the log-population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century.

We review the classical Gibrat’s process for the population of city sizes. In particular, we are interested in whether the log-population process has stationary and independent (Gibrat’s Law for cities) increments. We have tested these characteristics for the case of the municipalities of Italy and Spain and the places of USA for a time span of more than one century. The results are clear: stationarity and independence are empirically rejected by standard tests. These results open theoretically the way for the observance of other city size distributions other than the lognormal and the double Pareto lognormal, something that in fact has already happened in the literature

Closed-loop separation control over a sharp edge ramp using Genetic Programming

We experimentally perform open and closed-loop control of a separating turbulent boundary layer downstream from a sharp edge ramp. The turbulent boundary layer just above the separation point has a Reynolds number $Re_{\theta}\approx 3\,500$ based on momentum thickness. The goal of the control is to mitigate separation and early re-attachment. The forcing employs a spanwise array of active vortex generators. The flow state is monitored with skin-friction sensors downstream of the actuators. The feedback control law is obtained using model-free genetic programming control (GPC) (Gautier et al. 2015). The resulting flow is assessed using the momentum coefficient, pressure distribution and skin friction over the ramp and stereo PIV. The PIV yields vector field statistics, e.g. shear layer growth, the backflow area and vortex region. GPC is benchmarked against the best periodic forcing. While open-loop control achieves separation reduction by locking-on the shedding mode, GPC gives rise to similar benefits by accelerating the shear layer growth. Moreover, GPC uses less actuation energy.Comment: 24 pages, 24 figures, submitted to Experiments in Fluid