Scaling asymptotics for quantized Hamiltonian flows

In recent years, the near diagonal asymptotics of the equivariant components of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map

Local trace formulae and scaling asymptotics in Toeplitz quantization

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hamiltonian flow of the symbol, reminiscent of the scaling asymptotics of the equivariant components of the Szeg\"o kernel along the diagonal

Bioaccumulation modelling and sensitivity analysis for discovering key players in contaminated food webs: the case study of PCBs in the Adriatic Sea

Modelling bioaccumulation processes at the food web level is the main step to analyse the effects of pollutants at the global ecosystem level. A crucial question is understanding which species play a key role in the trophic transfer of contaminants to disclose the contribution of feeding linkages and the importance of trophic dependencies in bioaccumulation dynamics. In this work we present a computational framework to model the bioaccumulation of organic chemicals in aquatic food webs, and to discover key species in polluted ecosystems. As a result, we reconstruct the first PCBs bioaccumulation model of the Adriatic food web, estimated after an extensive review of published concentration data. We define a novel index aimed to identify the key species in contaminated networks, Sensitivity Centrality, and based on sensitivity analysis. The index is computed from a dynamic ODE model parametrised from the estimated PCBs bioaccumulation model and compared with a set of established trophic indices of centrality. Results evidence the occurrence of PCBs biomagnification in the Adriatic food web, and highlight the dependence of bioaccumulation on trophic dynamics and external factors like fishing activity. We demonstrate the effectiveness of the introduced Sensitivity Centrality in identifying the set of species with the highest impact on the total contaminant flows and on the efficiency of contaminant transport within the food web

Nonlinear behaviour of self-excited microcantilevers in viscous fluids

Microcantilevers are increasingly being used to create sensitive sensors for rheology and mass sensing at the micro- and nano-scale. When operating in viscous liquids, the low quality factor of such resonant structures, translating to poor signal-to-noise ratio, is often manipulated by exploiting feedback strategies. However, the presence of feedback introduces poorly-understood dynamical behaviours that may severely degrade the sensor performance and reliability. In this paper, the dynamical behaviour of self-excited microcantilevers vibrating in viscous fluids is characterized experimentally and two complementary modelling approaches are proposed to explain and predict the behaviour of the closed-loop system. In particular, the delay introduced in the feedback loop is shown to cause surprising non-linear phenomena consisting of shifts and sudden-jumps of the oscillation frequency. The proposed dynamical models also suggest strategies for controlling such undesired phenomena

Semiclassical almost isometry

Let M be a complex projective manifold, and L an Hermitian ample line bundle on it. A fundamental theorem of Gang Tian, reproved and strengthened by Zelditch, implies that the Khaeler form of L can be recovered from the asymptotics of the projective embeddings associated to large tensor powers of L. More precisely, with the natural choice of metrics the projective embeddings associated to the full linear series |kL| are asymptotically symplectic, in the appropriate rescaled sense. In this article, we ask whether and how this result extends to the semiclassical setting. Specifically, we relate the Weinstein symplectic structure on a given isodrastic leaf of half-weighted Bohr-Sommerfeld Lagrangian submanifolds of M to the asymptotics of the the pull-back of the Fubini-Study form under the semiclassical projective maps constructed by Borthwick, Paul and Uribe.Comment: exposition improve

Self-driven soft imaging in liquid by means of photothermal excitation

The use of a laser to induce oscillations of an atomic force microscopy cantilever provides a way to excite the dynamics of the system in a very controlled manner. This excitation scheme has been used to obtain reliable self-sustained oscillations, in air and in liquid environments, and to implement an additional control loop leading to a soft, low-interaction, working mode. The dynamics of the oscillating cantilever has been characterized, both theoretically and experimentally, and the effectiveness of the approach has been verified on a test sample. © 2011 American Institute of Physics.Peer Reviewe

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure