Dynamical aspects of inextensible chains

In the present work the dynamics of a continuous inextensible chain is studied. The chain is regarded as a system of small particles subjected to constraints on their reciprocal distances. It is proposed a treatment of systems of this kind based on a set Langevin equations in which the noise is characterized by a non-gaussian probability distribution. The method is explained in the case of a freely hinged chain. In particular, the generating functional of the correlation functions of the relevant degrees of freedom which describe the conformations of this chain is derived. It is shown that in the continuous limit this generating functional coincides with a model of an inextensible chain previously discussed by one of the authors of this work. Next, the approach developed here is applied to a inextensible chain, called the freely jointed bar chain, in which the basic units are small extended objects. The generating functional of the freely jointed bar chain is constructed. It is shown that it differs profoundly from that of the freely hinged chain. Despite the differences, it is verified that in the continuous limit both generating functionals coincide as it is expected.Comment: 15 pages, LaTeX 2e + various packages, 3 figures. The title has been changed and three references have been added. A large part of the manuscript has been rewritten to improve readability. Chapter 4 has been added. It contains the construction of the generating functional without the shish-kebab approximation and a new derivation of the continuous limit of the freely jointed bar chai

Plug-and-Play Fault Detection and control-reconfiguration for a class of nonlinear large-scale constrained systems

This paper deals with a novel Plug-and-Play (PnP) architecture for the control and monitoring of Large-Scale Systems (LSSs). The proposed approach integrates a distributed Model Predictive Control (MPC) strategy with a distributed Fault Detection (FD) architecture and methodology in a PnP framework. The basic concept is to use the FD scheme as an autonomous decision support system: once a fault is detected, the faulty subsystem can be unplugged to avoid the propagation of the fault in the interconnected LSS. Analogously, once the issue has been solved, the disconnected subsystem can be re-plugged-in. PnP design of local controllers and detectors allow these operations to be performed safely, i.e. without spoiling stability and constraint satisfaction for the whole LSS. The PnP distributed MPC is derived for a class of nonlinear LSSs and an integrated PnP distributed FD architecture is proposed. Simulation results in two paradigmatic examples show the effectiveness and the potential of the general methodology

Two brains in action: joint-action coding in the primate frontal cortex

Daily life often requires the coordination of our actions with those of another partner. After sixty years (1968-2018) of behavioral neurophysiology of motor control, the neural mechanisms which allow such coordination in primates are unknown. We studied this issue by recording cell activity simultaneously from dorsal premotor cortex (PMd) of two male interacting monkeys trained to coordinate their hand forces to achieve a common goal. We found a population of 'joint-action cells' that discharged preferentially when monkeys cooperated in the task. This modulation was predictive in nature, since in most cells neural activity led in time the changes of the "own" and of the "other" behavior. These neurons encoded the joint-performance more accurately than 'canonical action-related cells', activated by the action per se, regardless of the individual vs. interactive context. A decoding of joint-action was obtained by combining the two brains activities, using cells with directional properties distinguished from those associated to the 'solo' behaviors. Action observation-related activity studied when one monkey observed the consequences of the partner's behavior, i.e. the cursor's motion on the screen, did not sharpen the accuracy of 'joint-action cells' representation, suggesting that it plays no major role in encoding joint-action. When monkeys performed with a non-interactive partner, such as a computer, 'joint-action cells' representation of the "other" (non-cooperative) behavior was significantly degraded. These findings provide evidence of how premotor neurons integrate the time-varying representation of the self-action with that of a co-actor, thus offering a neural substrate for successful visuo-motor coordination between individuals.SIGNIFICANT STATEMENTThe neural bases of inter-subject motor coordination were studied by recording cell activity simultaneously from the frontal cortex of two interacting monkeys, trained to coordinate their hand forces to achieve a common goal. We found a new class of cells, preferentially active when the monkeys cooperated, rather than when the same action was performed individually. These 'joint-action neurons' offered a neural representation of joint-behaviors by far more accurate than that provided by the canonical action-related cells, modulated by the action per se regardless of the individual/interactive context. A neural representation of joint-performance was obtained by combining the activity recorded from the two brains. Our findings offer the first evidence concerning neural mechanisms subtending interactive visuo-motor coordination between co-acting agents

Bosonic Field Propagators on Algebraic Curves

In this paper we investigate massless scalar field theory on non-degenerate algebraic curves. The propagator is written in terms of the parameters appearing in the polynomial defining the curve. This provides an alternative to the language of theta functions. The main result is a derivation of the third kind differential normalized in such a way that its periods around the homology cycles are purely imaginary. All the physical correlation functions of the scalar fields can be expressed in terms of this object. This paper contains a detailed analysis of the techniques necessary to study field theories on algebraic curves. A simple expression of the scalar field propagator is found in a particular case in which the algebraic curves have $Z_n$ internal symmetry and one of the fields is located at a branch point.Comment: 26 pages, TeX + harvma

On the asymmetric zero-range in the rarefaction fan

We consider the one-dimensional asymmetric zero-range process starting from a step decreasing profile. In the hydrodynamic limit this initial condition leads to the rarefaction fan of the associated hydrodynamic equation. Under this initial condition and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps we derive the Law of Large Numbers for the position of a second class particle under the initial configuration in which all the positive sites are empty, all the negative sites are occupied with infinitely many first class particles and with a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle, this particle chooses randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation through some sort of renormalization function. By coupling the zero-range with the exclusion process we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic

Electron Transport and Hot Phonons in Carbon Nanotubes

We demonstrate the key role of phonon occupation in limiting the high-field ballistic transport in metallic carbon nanotubes. In particular, we provide a simple analytic formula for the electron transport scattering length, that we validate by accurate first principles calculations on (6,6) and (11,11) nanotubes. The comparison of our results with the scattering lengths fitted from experimental I-V curves indicates the presence of a non-equilibrium optical phonon heating induced by electron transport. We predict an effective temperature for optical phonons of thousands Kelvin.Comment: 4 pages, 1 figur

Water waves overtopping over barriers

A numerical and experimental analysis of the wave overtopping over emerged and submerged structures, is presented. An original model is used in order to simulate three-dimensional free surface flows. The model is based on the numerical solution of the motion equations expressed in an integral form in time-dependent curvilinear coordinates. A non-intrusive and continuous-in-space image analysis technique, which is able to properly identify the free surface even in very shallow waters or breaking waves, is adopted for the experimental tests. Numerical and experimental results are compared, for several wave and water depth conditions