A Unified Dissertation on Bearing Rigidity Theory

This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original contributions are twofold. The first one consists in the definition of a general framework for the statement of the principal definitions and results that are then particularized by evaluating the most studied metric spaces, providing a complete overview of the existing literature about the bearing rigidity theory. The second one rests on the determination of a necessary and sufficient condition guaranteeing the rigidity properties of a given multi-element system, independently of its metric space

Laboratory simulations of local winds in the atmospheric boundary layer via image analysis

In the atmospheric boundary layer, under high pressure conditions and negligible geostrophic winds, problems associated with pollution are the most critical. In this situation local winds play a major role in the evaluation of the atmospheric dynamics at small scales and in dispersion processes. These winds originate as a result of nonuniform heating of the soil, either when it is homogeneous or in discontinuous terrain in the presence of sea and/or slopes. Depending on the source of the thermal gradient, local winds are classified into convective boundary layer, sea and land breezes, urban heat islands, and slope currents. Local winds have been analyzed by (i) simple analytical models; (ii) numerical models; (iii) field measurements; (iv) laboratory measurements through which it is impossible to completely create the necessary similarities, but the parameters that determine the phenomenon can be controlled and each single wind can be separately analyzed. The present paper presents a summary of laboratory simulations of local winds neglecting synoptic winds and the effects of Coriolis force. Image analysis techniques appear suitable to fully describe both the individual phenomenon and the superposition of more than one local wind. Results do agree with other laboratory studies and numerical experiments

Three-dimensional structure of the flow inside the left ventricle of the human heart

The laboratory models of the human heart left ventricle developed in the last decades gave a valuable contribution to the comprehension of the role of the fluid dynamics in the cardiac function and to support the interpretation of the data obtained in vivo. Nevertheless, some questions are still open and new ones stem from the continuous improvements in the diagnostic imaging techniques. Many of these unresolved issues are related to the three-dimensional structure of the left-ventricular flow during the cardiac cycle. In this paper we investigated in detail this aspect using a laboratory model. The ventricle was simulated by a flexible sack varying its volume in time according to a physiologically shaped law. Velocities measured during several cycles on series of parallel planes, taken from two orthogonal points of view, were combined together in order to reconstruct the phase averaged, three-dimensional velocity field. During the diastole, three main steps are recognized in the evolution of the vortical structures: i) straight propagation in the direction of the long axis of a vortex-ring originated from the mitral orifice; ii) asymmetric development of the vortex-ring on an inclined plane; iii) single vortex formation. The analysis of three-dimensional data gives the experimental evidence of the reorganization of the flow in a single vortex persisting until the end of the diastole. This flow pattern seems to optimize the cardiac function since it directs velocity towards the aortic valve just before the systole and minimizes the fraction of blood residing within the ventricle for more cycles

Newton-Raphson Consensus for Distributed Convex Optimization

We address the problem of distributed uncon- strained convex optimization under separability assumptions, i.e., the framework where each agent of a network is endowed with a local private multidimensional convex cost, is subject to communication constraints, and wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proved, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton- Raphson direction by means of suitable average consensus ratios. We show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers. Finally, we propose some alternative strategies which trade-off communication and computational requirements with convergence speed.Comment: 18 pages, preprint with proof

Towards time-varying proximal dynamics in Multi-Agent Network Games

Distributed decision making in multi-agent networks has recently attracted significant research attention thanks to its wide applicability, e.g. in the management and optimization of computer networks, power systems, robotic teams, sensor networks and consumer markets. Distributed decision-making problems can be modeled as inter-dependent optimization problems, i.e., multi-agent game-equilibrium seeking problems, where noncooperative agents seek an equilibrium by communicating over a network. To achieve a network equilibrium, the agents may decide to update their decision variables via proximal dynamics, driven by the decision variables of the neighboring agents. In this paper, we provide an operator-theoretic characterization of convergence with a time-invariant communication network. For the time-varying case, we consider adjacency matrices that may switch subject to a dwell time. We illustrate our investigations using a distributed robotic exploration example.Comment: 6 pages, 3 figure

Entrainment in two coalescing axisymmetric turbulent plumes

AbstractA model of the total volume flux and entrainment occurring in two coalescing axisymmetric turbulent plumes is developed and compared with laboratory experiments. The dynamical evolution of the two plumes is divided into three regions. In region 1, where the plumes are separate, the entrainment in each plume is unaffected by the other plume, although the two plumes are drawn together due to the entrainment of ambient fluid between them. In region 2 the two plumes touch each other but are not yet merged. In this region the total entrainment is a function of both the dynamics of the touching plumes and the reduced surface area through which entrainment occurs. In region 3 the two plumes are merged and the entrainment is equivalent to that in a single plume. We find that the total volume flux after the two plumes touch and before they merge increases linearly with distance from the sources, and can be expressed as a function of the known total volume fluxes at the touching and merging heights. Finally, we define an ‘effective’ entrainment constant, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\alpha _{eff}$, as the value of $\alpha$ needed to obtain the same total volume flux in two independent plumes as that occurring in two coalescing plumes. The definition of $\alpha _{eff}$ allows us to find a single expression for the development of the total volume flux in the three different dynamical regions. This single expression will simplify the representation of coalescing plumes in more complex models, such as in large-scale geophysical convection, in which plume dynamics are not resolved. Experiments show that the model provides an accurate measure of the total volume flux in the two coalescing plumes as they evolve through the three regions.The authors gratefully acknowledge the National Science Foundation (Grant OCE- 0824636) and the Office of Naval Research (Grant N00014-09-1-0844) for their support of the 2013 WHOI Geophysical Fluid Dynamics Summer School where this project was initiated. Support to CC was given by the National Science Foundation project OCE- 1130008. CC wishes to thank Jason Hyatt for improving the clarity of this manuscript.This is the author accepted manuscript. The final version is available from CUP at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9300855&fileId=S0022112014003899

What moves international stock and bond markets?

We study the relation between international mutual fund flows and the different return components of aggregate equity and bond markets. First, we decompose international equity and bond market returns into changes in expectations of future real cash payments, interest rates, exchange rates, and discount rates. News about future cash flows, rather than discount rates, is the main driver of international stock returns. This evidence is in contrast with the typical results reported only for the US. Inflation news instead is the main driver of international bond returns. Next, we turn to the interaction between these return components and international portfolio flows. We find evidence consistent with price pressure, short-term trend chasing, and short-run overreaction in the equity market. We also find that international bond flows to emerging markets are more sensitive to interest rate shocks than equity flow

On the estimation of atmospheric turbulence layers for AO systems

In current and next generation of ground telescopes, Adaptive Optics (AO) are employed to overcome the detrimental effects induced by the presence of atmospheric turbulence, that strongly affects the quality of data transmission and therefore limits the actual resolution of the overall system. The analysis as well as the prediction of the turbulent phase affecting the light wavefront is therefore of paramount impor- tance to guarantee the effective performance of the AO solution. In this work, a layered model of turbulence is proposed, based on the definition of a Markov-Random-Field whose parameters are determined according to the turbulence statistics. The problem of turbulence estimation is formalized within the stochastic framework and conditions for the identifiability of the turbulence structure (numbers of layers, energies and velocities) are stated. Finally, an algorithm to allow the layer detection and characterization from measurements is designed. Numerical simulations are used to assess the proposed procedure and validate the results, confirming the validity of the approach and the accuracy of the detection