Recurrence for persistent random walks in two dimensions

We discuss the question of recurrence for persistent, or Newtonian, random walks in Z^2, i.e., random walks whose transition probabilities depend both on the walker's position and incoming direction. We use results by Toth and Schmidt-Conze to prove recurrence for a large class of such processes, including all "invertible" walks in elliptic random environments. Furthermore, rewriting our Newtonian walks as ordinary random walks in a suitable graph, we gain a better idea of the geometric features of the problem, and obtain further examples of recurrence.Comment: 20 pages, 7 figure

Jump and pull-in dynamics of an electrically actuated bistable MEMS device

This study analyzes a theoretical bistable MEMS device, which exhibits a considerable versatility of behavior. After exploring the coexistence of attractors, we focus on each rest position, and investigate the final outcome, when the electrodynamic voltage is suddenly applied. Our aim is to describe the parameter range where each attractor may practically be observed under realistic conditions, when an electric load is suddenly applied. Since disturbances are inevitably encountered in experiments and practice, a dynamical integrity analysis is performed in order to take them into account. We build the integrity charts, which examine the practical vulnerability of each attractor. A small integrity enhances the sensitivity of the system to disturbances, leading in practice either to jump or to dynamic pull-in. Accordingly, the parameter range where the device, subjected to a suddenly applied load, can operate in safe conditions with a certain attractor is smaller, and sometimes considerably smaller, than in the theoretical predictions. While we refer to a particular case-study, the approach is very general

Theoretical Prediction of Experimental Jump and Pull-In Dynamics in a MEMS Sensor

The present research study deals with an electrically actuated MEMS device. An experimental investigation is performed, via frequency sweeps in a neighbourhood of the first natural frequency. Resonant behavior is explored, with special attention devoted to jump and pull-in dynamics. A theoretical single degree-of-freedom spring-mass model is derived. Classical numerical simulations are observed to properly predict the main nonlinear features. Nevertheless, some discrepancies arise, which are particularly visible in the resonant branch. They mainly concern the practical range of existence of each attractor and the final outcome after its disappearance. These differences are likely due to disturbances, which are unavoidable in practice, but have not been included in the model. To take disturbances into account, in addition to the classical local investigations, we consider the global dynamics and explore the robustness of the obtained results by performing a dynamical integrity analysis. Our aim is that of developing an applicable confident estimate of the system response. Integrity profiles and integrity charts are built to detect the parameter range where reliability is practically strong and where it becomes weak. Integrity curves exactly follow the experimental data. They inform about the practical range of actuality. We discuss the combined use of integrity charts in the engineering design. Although we refer to a particular case-study, the approach is very general

A map from 1d Quantum Field Theory to Quantum Chaos on a 2d Torus

Dynamics of a class of quantum field models on 1d lattice in Heisenberg picture is mapped into a class of `quantum chaotic' one-body systems on configurational 2d torus (or 2d lattice) in Schr\" odinger picture. Continuum field limit of the former corresponds to quasi-classical limit of the latter.Comment: 4 pages in REVTeX, 1 eps-figure include

Microsurgical neurovascular anastomosis: The example of superficial temporal artery to middle cerebral artery bypass. Technical principles

AbstractThe superficial temporal artery to the middle cerebral artery (STA-MCA) bypass is a good example of cerebrovascular anastomosis. In this article, we describe the different stages of the procedure: patient installation, superficial temporal artery harvesting, recipient artery exposure, microsurgical anastomosis, and closure of the craniotomy. When meticulously performed, with the observance of important details at each stage, this technique offers a high rate of technical success (patency>90%) with a very low morbi-mortality (respectively 3% and 1%). Some anesthetic parameters have to be considered to insure perioperative technical and clinical success. STA-MCA bypass is a very useful technique for the management of complex or giant aneurysms where surgical treatment sometimes requires the sacrifice and revascularization of a main arterial trunk. It is also a valuable option for the treatment of chronic and symptomatic hemispheric hypoperfusion (Moyamoya disease, carotid or middle cerebral artery occlusion)

Selective organic functionalization of polycrystalline silicon-germanium for bioMEMS applications

AbstractWe selectively immobilized organofunctional silanes on top of polycrystalline silicon-germanium (poly-SiGe) layers, as a first step towards the fabrication of poly-SiGe-based bioMEMS (biomedical MicroElectroMechanicalSystems) by means of standard UV photolithography. 3-aminopropyl-dimethyl-ethoxysilane (APDMES) and 3-aminopropyl-triethoxysilane (APTES) molecules were immobilized onto resist-patterned poly-SiGe surfaces. The protocols for surface hydroxylation and silane immobilization were designed to be CMOS-compatible and to avoid damage to photoresist. Silanized surfaces were investigated both by means of fluorescence microscopy, and by FEG-SEM observation after labeling with 30 nm-diameter gold nanoparticles (NPs). We report the silanization protocols, together with the results indicating successful organic functionalization of the samples

Pointwise convergence of Birkhoff averages for global observables

It is well-known that a strict analogue of the Birkhoff Ergodic Theorem in infinite ergodic theory is trivial; it states that for any infinite-measure-preserving ergodic system the Birkhoff average of every integrable function is almost everywhere zero. Nor does a different rescaling of the Birkhoff sum that leads to a non-degenerate pointwise limit exist. In this paper we give a version of Birkhoff's theorem for conservative, ergodic, infinite-measure-preserving dynamical systems where instead of integrable functions we use certain elements of $L^\infty$, which we generically call global observables. Our main theorem applies to general systems but requires an hypothesis of "approximate partial averaging" on the observables. The idea behind the result, however, applies to more general situations, as we show with an example. Finally, by means of counterexamples and numerical simulations, we discuss the question of finding the optimal class of observables for which a Birkhoff theorem holds for infinite-measure-preserving systems.Comment: Final version. 33 pages, 10 figure

Vascular anomalies of the celiac trunk and implications in treatment of HCC with TACE. Description of a case and review of the literature

Knowledge of the vascular anatomy of the upper abdomen is important in the daily practice of surgeons specialized in the hepatobiliary and pancreatic area, and for general surgeons and radiologists, mainly those involved in interventional radiology. Since anatomical variants of the celiac axis and hepatic arteries are common, an accurate description of vascularization is required before procedures to avoid iatrogenic vascular changes. We reported a case of a young male patient with HBV related cirrhosis, who came to our institution for the treatment of 2 HCC nodules. The preprocedural contrast-enhanced CT examination showed combined variations of celiac trunk, hepatic arteries, gastroduodenal artery, and right inferior phrenic artery. The careful pre- and intraprocedural evaluation of vascularization allowed us to perform transarterial chemoembolization of the 2 nodules without complications. The incidence and developmental and clinical significance of this variation is discussed with a detailed review of the literature. Knowledge of such a case has important clinical significance in abdominal operations or invasive arterial procedures

Typical support and Sanov large deviations of correlated states

Discrete stationary classical processes as well as quantum lattice states are asymptotically confined to their respective typical support, the exponential growth rate of which is given by the (maximal ergodic) entropy. In the iid case the distinguishability of typical supports can be asymptotically specified by means of the relative entropy, according to Sanov's theorem. We give an extension to the correlated case, referring to the newly introduced class of HP-states.Comment: 29 pages, no figures, references adde

Fluctuations of Quantum Currents and Unravelings of Master Equations

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system.Comment: 18 pages, v1-->v2, Replaced the former Appendix B by a (thematically) different one. Mainly changes in the introductory Section 2+ added reference