Search results for " Matematica"

Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

2016

Abstract We investigate the evolution equation for the average vortex length per unit volume L of superfluid turbulence in inhomogeneous flows. Inhomogeneities in line density L andincounterflowvelocity V may contribute to vortex diffusion, vortex formation and vortex destruction. We explore two different families of contributions: those arising from asecondorder expansionofthe Vinenequationitself, andthose whichare notrelated to the original Vinen equation but must be stated by adding to it second-order terms obtained from dimensional analysis or other physical arguments.

Estimates for Sums of Eigenvalues of the Free Plate via the Fourier Transform

2017

Using the Fourier transform, we obtain upper bounds for sums of eigenvalues of the free plate.

Weyl Type Theorems for Left and Right Polaroid Operators

2010

A bounded operator defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. In this paper we consider the two related notions of left and right polaroid, and explore them together with the condition of being a-polaroid. Moreover, the equivalences of Weyl type theorems and generalized Weyl type theorems are investigated for left and a-polaroid operators. As a consequence, we obtain a general framework which allows us to derive in a unified way many recent results, concerning Weyl type theorems (generalized or not) for important classes of operators.

Conjunction, Disjunction and Iterated Conditioning of Conditional Events

2013

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the…

Refrigeration of an array of cylindrical nanosystems by superfluid helium counterflow

2017

Abstract Motivated by the challenge of computer refrigeration, we study the limits set by the transition to quantum turbulence on the cooling of an array of heat-producing cylindrical nanosystems by means of superfluid-helium counterflow. The effective thermal conductivity in laminar counterflow superfluid helium is obtained in channels with rectangular cross section, through arrays of mutually parallel cylinders and in the combined situation of arrays of orthogonal cylinders inside the rectangular channel. The maximum cooling capacity is analyzed on the condition that turbulence is avoided and that the highest temperature does not exceed the lambda temperature.

On the propagation of a perturbation in an anharmonic system

2007

We give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution.

Fusion Burning in Magnetically Confined Toroidal Plasmas

The thermonuclear instability in a toroidal fusion burning plasma [1] is shown to manifest itself as a driving factor of modes that are radially localized around closed field lines on rational magnetic surfaces. The radial profile of the electron temperature perturbations can be of two parities: even and odd. In the first case the effective longitudinal thermal conductivity can be reduced by the effects of modes involving magnetic reconnection that have a radial transverse reconnected field with a odd (radial) profile. In the second case magnetic reconnection is shown to have a stronger effect and is characterized by reconnected transverse fields that have an even radial profile. A class of…

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2022

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

Applications of Topological *-Algebras of Unbounded Operators

1998

In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the time evolution of two interacting models of matter and bosons. We show that for all these systems it is possible to build up a common framework where the thermodynamical limit of the algebraic dynamics can be conveniently studied and obtained.

Some classes of topological quasi *-algebras

2001

The completion $\overline{A}[\tau]$ of a locally convex *-algebra $A [ \tau ]$ with not jointly continuous multiplication is a *-vector space with partial multiplication $xy$ defined only for $x$ or $y \in A_{0}$, and it is called a topological quasi *-algebra. In this paper two classes of topological quasi *-algebras called strict CQ$^*$-algebras and HCQ$^*$-algebras are studied. Roughly speaking, a strict CQ$^*$-algebra (resp. HCQ$^*$-algebra) is a Banach (resp. Hilbert) quasi *-algebra containing a C$^*$-algebra endowed with another involution $\sharp$ and C$^*$-norm $\| \|_{\sharp}$. HCQ$^*$-algebras are closely related to left Hilbert algebras. We shall show that a Hilbert space is a H…