Search results for " Fisica Matematica"

Transition to superfluidity in liquid 4He

2012

In this work the transition from normal liquid helium I to superfluid liquid helium II, controlled by temperature and pressure, is studied in the simplified assumption of absence of viscosity. A macroscopic thermodynamical model is presented, which chooses as new independent fields the heat flux q and a phase field function f. For the heat flux a modification of Cattaneo equation is written, while for the function f a time dependent Ginzburg-Landau equation is proposed.

Phase transition and lambda-line in liquid helium

2013

A hydrodynamical model describing the superfluid phase transition of 4He close to $\lambda$-line is presented. In the work, which generalizes a phase field model of lambda transition previously formulated by the same authors, the independent fields are the density, the temperature, the velocity, the heat flux and a scalar function $f$, linked to the modulus of the wave-function $\psi$, solution of the Ginzburg-Landau equation. In this framework, the heat flux is given by a modified Maxwell-Cattaneo equation. The restrictions on the constitutive quantities are obtained from the entropy principle, using the Liu method of Lagrange multipliers. A maximum theorem is proved that allows the model …

Brain-predicted age difference score is related to specific cognitive functions: A multi-site replication analysis

2021

Abstract Brain-predicted age difference scores are calculated by subtracting chronological age from ‘brain’ age. Positive scores reflect accelerated ageing and are associated with increased mortality risk and poorer physical function. To date, however, the relationship between brain-predicted age difference scores and specific cognitive functions has not been systematically examined. First, applying machine learning to 1,359 T1-weighted MRI scans, we predicted the relationship between chronological age and voxel-wise grey matter data. This model was then applied to MRI data from three independent datasets, significantly predicting chronological age: Dokuz Eylul University (n=175), the Cogni…

A generalized Degn–Harrison reaction–diffusion system: Asymptotic stability and non-existence results

2021

Abstract In this paper we study the Degn–Harrison system with a generalized reaction term. Once proved the global existence and boundedness of a unique solution, we address the asymptotic behavior of the system. The conditions for the global asymptotic stability of the steady state solution are derived using the appropriate techniques based on the eigen-analysis, the Poincare–Bendixson theorem and the direct Lyapunov method. Numerical simulations are also shown to corroborate the asymptotic stability predictions. Moreover, we determine the constraints on the size of the reactor and the diffusion coefficient such that the system does not admit non-constant positive steady state solutions.

A DERIVATION OF THE VLASOV-NAVIER-STOKES MODEL FOR AEROSOL FLOWS FROM KINETIC THEORY

2016

This article proposes a derivation of the Vlasov-Navier-Stokes system for spray/aerosol flows. The distribution function of the dispersed phase is governed by a Vlasov-equation, while the velocity field of the propellant satisfies the Navier-Stokes equations for incompressible fluids. The dynamics of the dispersed phase and of the propellant are coupled through the drag force exerted by the propellant on the dispersed phase. We present a formal derivation of this model from a multiphase Boltzmann system for a binary gaseous mixture, involving the droplets/dust particles in the dispersed phase as one species, and the gas molecules as the other species. Under suitable assumptions on the colli…

Mid-sagittal plane detection for advanced physiological measurements in brain scans

2019

Objective The process of diagnosing many neurodegenerative diseases, such as Parkinson's and progressive supranuclear palsy, involves the study of brain magnetic resonance imaging (MRI) scans in order to identify and locate morphological markers that can highlight the health status of the subject. A fundamental step in the pre-processing and analysis of MRI scans is the identification of the mid-sagittal plane, which corresponds to the mid-brain and allows a coordinate reference system for the whole MRI scan set. Approach To improve the identification of the mid-sagittal plane we have developed an algorithm in Matlab® based on the k-means clustering function. The results have been compared …

Bollettino di Matematica pura ed Applicata Volume III

2010

Turing pattern formation in the Brusselator system with nonlinear diffusion.

2013

In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in 1D and 2D spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supe…

Representable states on quasilocal quasi *-algebras

2011

Continuing a previous analysis originally motivated by physics, we consider representable states on quasi-local quasi *-algebras, starting with examining the possibility for a {\em compatible} family of {\em local} states to give rise to a {\em global} state. Some properties of {\em local modifications} of representable states and some aspects of their asymptotic behavior are also considered.

An operatorial description of desertification

2016

We propose a simple theoretical model for desertification processes based on three actors (soil, seeds, and plants) on a two-dimensional lattice. Each actor is described by a time dependent fermionic operator, and the dynamics is ruled by a self-adjoint Hamilton-like operator. We show that even taking into account only a few parameters, accounting for external actions on the ecosystem or the response to positive feedbacks, the model provides a plausible description of the desertification process, and can be adapted to different ecological landscapes. We first describe the simplified model in one cell. Then, we define the full model on a two-dimensional region, taking into account additional…