1,462 research outputs found
On the apparent failure of the topological theory of phase transitions
The topological theory of phase transitions has its strong point in two
theorems proving that, for a wide class of physical systems, phase transitions
necessarily stem from topological changes of some submanifolds of configuration
space. It has been recently argued that the lattice -model
provides a counterexample that falsifies this theory. It is here shown that
this is not the case: the phase transition of this model stems from an
asymptotic () change of topology of the energy level sets, in spite
of the absence of critical points of the potential in correspondence of the
transition energy.Comment: 5 pages, 4 figure
Numerical solution of three-dimensional rectangular submerged jets with the evidence of the undisturbed region of flow
The evolution of turbulent rectangular submerged free jets has been
investigated numerically with a two-dimensional (2D) approach by the
present authors and, by using the large eddy simulations (LES) at several
Reynolds numbers. The average numerical results confirmed the presence of
the undisturbed region of flow (URF) located between the slot exit and the
beginning of the potential core region (PCR) previously observed
experimentally at the University of Rome “Tor Vergata” by Gori and
coworkers. The 2D study of the present authors carried out under the
conditions previously investigated in the literature, showed that the URF has
a self-similar behavior, and proposed a new law for the evolution of the
momentum. The present paper extends the LES to three-dimensional (3D)
rectangular submerged free jets, in the range from Re =5,000 to
Re =40,000, showing that the self-similar behavior of URF is also present
in the 3D numerical simulations, as well as in the PCR and in the fully
developed region (FDR)
Collective behavior of oscillating electric dipoles
The present work reports about the dynamics of a collection of randomly
distributed, and randomly oriented, oscillators in 3D space, coupled by an
interaction potential falling as , where r stands for the inter-particle
distance. This model schematically represents a collection of identical
biomolecules, coherently vibrating at some common frequency, coupled with a
potential stemming from the electrodynamic interaction between
oscillating dipoles. The oscillating dipole moment of each molecule being a
direct consequence of its coherent (collective) vibration. By changing the
average distance among the molecules, neat and substantial changes in the power
spectrum of the time variation of a collective observable are found. As the
average intermolecular distance can be varied by changing the concentration of
the solvated molecules, and as the collective variable investigated is
proportional to the projection of the total dipole moment of the model
biomolecules on a coordinate plane, we have found a prospective experimental
strategy of spectroscopic kind to check whether the mentioned intermolecular
electrodynamic interactions can be strong enough to be detectable, and thus to
be of possible relevance to biology.Comment: 20 pages, 4 figure
A 2d-Numerical Study on Slot Jet Applied to a Wind Turbine as a Circulation Control Technique
The file attached to this record is the author's final peer reviewed version.A study on the feasibility of the Circulation Control
(CC) technique for wind turbines is proposed. The
CC was born in aeronautic field to improve the lift
force on the wings, allowing the short take-off and
landing of aircraft. It consists in blowing air at a
relatively high speed over a rounded trailing edge.
The thin jet of air remains attached to the convex
curved surface, imposing a certain curvature to the
outer streamlines, and, hence, increasing the lift force
of the airfoil. Aim of this study is to numerically
investigate the advantages on a wind turbine, based
on the S809 airfoil, taking into account the energy related
considerations, as the cost of the jet
production. The paper, after a thorough evaluation of
the increase of the generated power, finds that this
technique could be promising in the energy harvesting
aim
On the origin of Phase Transitions in the absence of Symmetry-Breaking
In this paper we investigate the Hamiltonian dynamics of a lattice gauge
model in three spatial dimension. Our model Hamiltonian is defined on the basis
of a continuum version of a duality transformation of a three dimensional Ising
model. The system so obtained undergoes a thermodynamic phase transition in the
absence of symmetry-breaking. Besides the well known use of quantities like the
Wilson loop we show how else the phase transition in such a kind of models can
be detected. It is found that the first order phase transition undergone by
this model is characterised according to an Ehrenfest-like classification of
phase transitions applied to the configurational entropy. On the basis of the
topological theory of phase transitions, it is discussed why the seemingly
divergent behaviour of the third derivative of configurational entropy can be
considered as the "shadow" of some suitable topological transition of certain
submanifolds of configuration space.Comment: 31 pages, 9 figure
Geometrical aspects in the analysis of microcanonical phase-transitions
In the present work, we discuss how the functional form of thermodynamic
observables can be deduced from the geometric properties of subsets of phase
space. The geometric quantities taken into account are mainly extrinsic
curvatures of the energy level sets of the Hamiltonian of a system under
investigation. In particular, it turns out that peculiar behaviours of
thermodynamic observables at a phase transition point are rooted in more
fundamental changes of the geometry of the energy level sets in phase space.
More specifically, we discuss how microcanonical and geometrical descriptions
of phase-transitions are shaped in the special case of models with
either nearest-neighbours and mean-field interactions
The Berezinskii Kosterlitz Thouless phase transition is of second-order in the microcanonical ensemble
A paradigmatic example of a phase transition taking place in the absence of
symmetry-breaking is provided by the Berezinkii-Kosterlitz-Thouless (BKT)
transition in the two-dimensional XY model. In the framework of canonical
ensemble, this phase transition is defined as an infinite-order one. To the
contrary, by tackling the transitional behavior of the two dimensional XY model
in the microcanonical ensemble, we show that the BKT phase transition is of
second order. This provides a new example of statistical ensemble inequivalence
that could apply to a broad class of systems undergoing BKT phase transitions
Persistent Homology analysis of Phase Transitions
Persistent homology analysis, a recently developed computational method in
algebraic topology, is applied to the study of the phase transitions undergone
by the so-called XY-mean field model and by the phi^4 lattice model,
respectively. For both models the relationship between phase transitions and
the topological properties of certain submanifolds of configuration space are
exactly known. It turns out that these a-priori known facts are clearly
retrieved by persistent homology analysis of dynamically sampled submanifolds
of configuration space.Comment: 10 pages; 10 figure
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