Phase transitions driven by state-dependent poisson noise

Nonlinear systems driven by state-dependent Poisson noise are introduced to model the persistence of climatic anomalies in land-atmosphere interaction caused by the soil-moisture dependence of the frequency of rainfall events. It is found that these systems may give rise to bimodal probability distributions, while the state variable randomly persists around the preferential states because of transient dynamics that are opposite to the long-term behavior. Mean-field analysis and numerical simulations of the spatially distributed systems reveal a symmetry-breaking bifurcation for sufficiently strong spatial diffusive couplings and intermediate noise intensities. In such conditions, the initial development of spatial patterns is followed by a stable configuration, selected on the bases of the initial conditions in correspondence of the remnants of the modes of the uncoupled system.     

Mean velocity profile in a sheared and thermally stratified atmospheric boundary layer

A stability correction function φ(m)(ζ) that accounts for distortions to the logarithmic mean velocity profile (MVP) in the lower atmosphere caused by thermal stratification was proposed by Monin and Obukhov in the 1950s using dimensional analysis. Its universal character was established from many field experiments. However, theories that describe the canonical shape of φ(m)(ζ) are still lacking. A previous link between the spectrum of turbulence and the MVP is expanded here to include the effects of thermal stratification on the turbulent kinetic energy dissipation rate and eddy-size anisotropy. The resulting theory provides a novel explanation for the power-law exponents and coefficients already reported for φ(m)(ζ) from numerous field experiments.     

On the Trajectory Method for the Reconstruction of Differential Equations from Time Series

This work investigates the trajectory method [1] for thereconstruction of ordinary differential equations (ODEs) from timeseries. The potentials of the method are analyzed for dynamical systemsdescribed by second- and third-order ODEs, focusing in particular on therole of the parameters of the method and on the influence of the qualityof the time series in terms of noise, length and sampling frequency.Typical models are investigated, such as the van der Pol, the linearmechanical, the Duffing and the Rössler equations, resulting in arobust and versatile method which is capable of allowing interestingapplications to experimental cases. The method is then applied to themeasured time series of a nonlinear mechanical oscillator, a typicalvelocity oscillation of the bursting phenomenon in near-wall turbulenceand the averaged annual evolution of rainfall, temperature andstreamflow over a hydrological basin.     

Origin of negative temperatures in systems interacting with external fields

The controversial existence of negative temperatures has stirred interesting debates that have reached the foundations of thermodynamics, including questions on the second law, the Carnot efficiency and the statistical definition of entropy. Here we show that for systems interacting with an external field, negative temperatures may arise when the interaction energy with the field is treated as a form of internal energy. We discuss how negative temperatures are avoided when using a thermodynamic formalism that accounts for the intensive and extensive variables associated to the external field. We use the paramagnetic system and a perfect gas in a gravitational field to illustrate these ideas. Considerations about the isothermal and adiabatic work done by the field or the system also shed light on the inconsistency of super-Carnot efficiencies.     

Stokes flow with injection in a plane duct

Summary In this paper flow at low Reynolds number is studied in a plane duct with injection along its boundaries, by determining the Green function for the Stokes equation in the strip: in this way it is possible to calculate the fluid-dynamic field for any distribution of injection. To obtain the bi-harmonic function that governs this problem we write the stream function in terms of two harmonic functions f and g, represent these functions using the relevant Green function and write the integral equations that determine f and g. The solution is obtained by means of the Fourier transform technique. An asymptotic representation of this solution is also given.

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Sommario In questo lavoro si studia il campo fluidodinamico determinato) dall'apporto di fluido in un condotto in cui scorre un fluido a piccoli numeri di Reynolds, determinando la funzione di Green per l'equazione di Stokes nella striscia: in tal modo si può calcolare il campo fluidodinamico per una qualsiasi distribuzione di iniezione. Per determinare la funzione biarmonica con derivata longitudinale infinita in alcuni punti della frontiera che governa questo problema, si scrive l'incognita in termini di funzioni armoniche, si utilizza la funzione di Green per rappresentare tali funzioni ausiliarie e si scrivono le equazioni integrali che le determinano. La soluzione di queste equazioni integrali viene ottenuta mediante la trasformata di Fourier. I risultati vengono presentati sia in forma numerica che con serie asintotiche.

     

Thermo-fluid dynamics of the unsteady channel flow

We present an exact analytical representation of the unsteady thermo-fluid dynamic field arising in a two-dimensional channel with parallel walls for a fluid with constant properties. We assume that the axial pressure gradient is an arbitrary function of time that can be expanded in Taylor series; a particular case is the impulsive motion generated by a sudden jump to a constant value; for large time values the flow reaches the well-known steady Poiseuille solution. As boundary conditions for the dynamic field we consider fixed and moving walls (unsteady Couette flow). The assigned temperature on the walls can be an arbitrary function of time. We also consider the coupling of the energy and momentum equations (i.e. Eckert number different from zero). The solution is obtained by series with simple expressions of the coefficients in terms of the error functions. The fundamental physical parameters, such as shear stress, mass flow and heat flux at the wall are obtained in explicit analytical form and discussed by means of their diagrams.     

Evaluation of the statistical distribution of spheroidal objects from measurements on metallographic cross sections

Summary The paper concerns the quantitative metallographic analysis of dispersed spheroidal objects.The problem of relating the size and shape distribution of the object sections, observed on a metallographic cut surface, to the actual size and shape distributions has been solved exactly.The statistical problems arising from the estimate of the distribution from a finite set of experimental measurements have been studied and an expression for the r.m.s. error of the esimate has been obtained.Finally, numerical applications, performed with the aid of a computer program, are discussed.

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Sommario In questo lavoro si studia la distribuzione spaziale di oggetti di forma sferoidale dispersi in un metallo.L'analisi viene condotta con metodi statistici partendo dalla conoscenza della forma e del numero delle loro sezioni con un piano.Lo studio del problema viene ricondotto a quello di un'equazione integrale di cui si presenta la soluzione esatta.Si presentano inoltre delle espressioni per valutare l'errore quadratico medio.Infine si discutono i risultati numerici ottenuti con un calcolatore.

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List of symbols N spatial density of objects (e.g. cm^–3) - n surface density of objects (e.g. cm^–2) - A larger semiaxis for oblate spheroids or smaller semiaxis for prolate spheroids - B other semiaxis of the spheroid - T B/A - a larger semiaxis of the section ellipse for oblate spheroids or smaller semiaxis of the section ellipse for prolate spheroids - b other semiaxis of the ellipse - t b/a - F spatial weight function - f corresponding surface weight function - F _X derivative with respect to X - F _XY double derivative with respect to X and Y - N _S number of observed cavities - S area of the observed domain - A ₀ smallest value of A - T ₀ smallest value of T - optimal truncation value of the distribution - Gamma function     

Correlation-anti-correlation transition by state-dependent Poisson noise

Noise may induce some degrees of order in many biological and complex systems. We present an example of a noise-dependent transition from correlation to anti-correlation of the states of a bivariate system coupled by state-dependent Poisson noises. By varying the degree of dependence of the rate of jumps on the other variable, the system undergoes different degrees of correlation, from independence to perfect correlation (which in this case coincides with perfect synchronization) in the limit of the deterministic, periodic case.