Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise

We prove that every Markov solution to the three dimensional Navier-Stokes equation with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast. Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term which ensures equality in the balance.Comment: 32 page

Strong uniqueness for stochastic evolution equations with unbounded measurable drift term

We consider stochastic evolution equations in Hilbert spaces with merely measurable and locally bounded drift term $B$ and cylindrical Wiener noise. We prove pathwise (hence strong) uniqueness in the class of global solutions. This paper extends our previous paper (Da Prato, Flandoli, Priola and M. Rockner, Annals of Prob., published online in 2012) which generalized Veretennikov's fundamental result to infinite dimensions assuming boundedness of the drift term. As in our previous paper pathwise uniqueness holds for a large class, but not for every initial condition. We also include an application of our result to prove existence of strong solutions when the drift $B$ is only measurable, locally bounded and grows more than linearly.Comment: The paper will be published in Journal of Theoretical Probability. arXiv admin note: text overlap with arXiv:1109.036

Seasonal changes in population of the Amphipod Gammarus aequicauda (Martynov, 1931)

Monthly collections were made for one year (March 2001 to February 2002) in Mar Piccolo of Taranto (Ionian sea, Italy), in order to establish the seasonal fluctuations of a population of Gammarus aequicauda (Crustacea, Amphipoda). Variations in the population structure, sex ratio and fecundity were studied. The population comprised all stages of the life cycle all year round, thus showing continuous reproduction. Size differences between males and females occurred throughout the year with males being larger than females. The recruitment of juveniles into the population occurred particularly in autumn-winter. Females consistently predominated in numbers over males during winter months. Female cephalic length was positively correlated with eggs number

Dimension-independent Harnack inequalities for subordinated semigroups

Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the Bakry-Emery curvature condition, the subordinate semigroup with power $\alpha$ satisfies a dimension-free Harnack inequality provided $\alpha \in(1/2, 1)$, and it satisfies the log-Harnack inequality for all $\alpha \in (0,1).$ Some infinite-dimensional examples are also presented

The Symplectic Penrose Kite

The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.Comment: 24 pages, 7 figures, minor changes in last version, to appear in Comm. Math. Phys

Reliability of digital mems sensors: Metrological characterization of accelerometersand microphones

The reliability of digital MEMS accelerometer and microphone sensors is investigated, on the basis of suitable calibration procedures developed at INRiM, in order to provide the metrological traceability and the proper sensitivity in the digital domain. Nowadays, digital sensing systems, based on MEMS technology, are largely used in a wide range of advanced industrial, environmental, energy and medical applications. The possibility to have many accurate, low-power consuming and low-cost sensors present undoubted advantages, in terms of costs reduction and energy saving, while maintaining high quality in the control processes, monitoring or measurements and being flexible in providing enhanced data collection, automation and operation. Nevertheless, at present, digital MEMS sensors are not always reliable to quantify with adequate accuracy the measured physical phenomena, due to the lack of metrological traceability and sensitivity parameters for digital sensors

Continuity equation in LlogL for the 2D Euler equations under the enstrophy measure

The 2D Euler equations with random initial condition has been investigates by Albeverio and Cruzeiro (Commun Math Phys 129:431–444, 1990) and other authors. Here we prove existence of solutions for the associated continuity equation in Hilbert spaces, in a quite general class with LlogL densities with respect to the enstrophy measure

Statistical properties of stochastic 2D Navier-Stokes equations from linear models

A new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence has been proposed and tested through numerical simulations. This is achieved by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. In this paper, we investigate this conjecture for the 2D Navier-Stokes equations driven by an additive noise. In order to check this conjecture, we analyze the coupled system Navier-Stokes/linear advection system in the unknowns $(u,w)$. We introduce a parameter $\lambda$ which gives a system $(u^\lambda,w^\lambda)$; this system is studied for any $\lambda$ proving its well posedness and the uniqueness of its invariant measure $\mu^\lambda$. The key point is that for any $\lambda \neq 0$ the fields $u^\lambda$ and $w^\lambda$ have the same scaling exponents, by assuming universality of the scaling exponents to the force. In order to prove the same for the original fields $u$ and $w$, we investigate the limit as $\lambda \to 0$, proving that $\mu^\lambda$ weakly converges to $\mu^0$, where $\mu^0$ is the only invariant measure for the joint system for $(u,w)$ when $\lambda=0$.Comment: 23 pages; improved versio

Self-calibration of the 1 MN deadweight force standard machine at INRiM

open4noThe INRiM 1 MN deadweight force standard machine (DFSM) was installed in 1995. It adopts a binary sequence of ten weights whose combinations generate forces up to 1 MN. The advantage of this system lies in the self-calibration of its weights. The procedure is based on the comparison between two forces generated by a single weight and by a group of smaller weights, nominally equal. After 25 years, a verification of the DFSM was performed. Results are within the declared CMC limits, i.e. a relative expanded uncertainty of 2 × 10-5.openPrato, A.; Mazzoleni, F.; Facello, A.; Germak, A.Prato, A.; Mazzoleni, F.; Facello, A.; Germak, A