369 research outputs found
Interaction of a vortex ring with the free surface of ideal fluid
The interaction of a small vortex ring with the free surface of a perfect
fluid is considered. In the frame of the point ring approximation the
asymptotic expression for the Fourier-components of radiated surface waves is
obtained in the case when the vortex ring comes from infinity and has both
horizontal and vertical components of the velocity. The non-conservative
corrections to the equations of motion of the ring, due to Cherenkov radiation,
are derived.Comment: LaTeX, 15 pages, 1 eps figur
The microcanonical thermodynamics of finite systems: The microscopic origin of condensation and phase separations; and the conditions for heat flow from lower to higher temperatures
Microcanonical thermodynamics allows the application of statistical mechanics
both to finite and even small systems and also to the largest, self-gravitating
ones. However, one must reconsider the fundamental principles of statistical
mechanics especially its key quantity, entropy. Whereas in conventional
thermostatistics, the homogeneity and extensivity of the system and the
concavity of its entropy are central conditions, these fail for the systems
considered here. For example, at phase separation, the entropy, S(E), is
necessarily convex to make exp[S(E)-E/T] bimodal in E. Particularly, as
inhomogeneities and surface effects cannot be scaled away, one must be careful
with the standard arguments of splitting a system into two subsystems, or
bringing two systems into thermal contact with energy or particle exchange. Not
only the volume part of the entropy must be considered. As will be shown here,
when removing constraints in regions of a negative heat capacity, the system
may even relax under a flow of heat (energy) against a temperature slope. Thus
the Clausius formulation of the second law: ``Heat always flows from hot to
cold'', can be violated. Temperature is not a necessary or fundamental control
parameter of thermostatistics. However, the second law is still satisfied and
the total Boltzmann entropy increases. In the final sections of this paper, the
general microscopic mechanism leading to condensation and to the convexity of
the microcanonical entropy at phase separation is sketched. Also the
microscopic conditions for the existence (or non-existence) of a critical
end-point of the phase-separation are discussed. This is explained for the
liquid-gas and the solid-liquid transition.Comment: 23 pages, 2 figures, Accepted for publication in the Journal of
Chemical Physic
Interplay between bending and stretching in carbon nanoribbons
We investigate the bending properties of carbon nanoribbons by combining
continuum elasticity theory and tight-binding atomistic simulations. First, we
develop a complete analysis of a given bended configuration through continuum
mechanics. Then, we provide by tight-binding calculations the value of the
bending rigidity in good agreement with recent literature. We discuss the
emergence of a stretching field induced by the full atomic-scale relaxation of
the nanoribbon architecture. We further prove that such an in-plane strain
field can be decomposed into a first contribution due to the actual bending of
the sheet and a second one due to edge effects.Comment: 5 pages, 6 figure
Adiabatic invariance with first integrals of motion
The construction of a microthermodynamic formalism for isolated systems based
on the concept of adiabatic invariance is an old but seldom appreciated effort
in the literature, dating back at least to P. Hertz [Ann. Phys. (Leipzig) 33,
225 (1910)]. An apparently independent extension of such formalism for systems
bearing additional first integrals of motion was recently proposed by Hans H.
Rugh [Phys. Rev. E 64, 055101 (2001)], establishing the concept of adiabatic
invariance even in such singular cases. After some remarks in connection with
the formalism pioneered by Hertz, it will be suggested that such an extension
can incidentally explain the success of a dynamical method for computing the
entropy of classical interacting fluids, at least in some potential
applications where the presence of additional first integrals cannot be
ignored.Comment: 2 pages, no figures (REVTeX 4
INDICATION OF META-ANTHRACITE BY MAGNETOTELLURICS IN THE KĆSZEG-RECHNITZ PENNINIC WINDOW : A TEST AREA
One of the Penninic Nappes is the KĆszeg-Rechnitz (K-R) tectonic window at the Eastern end of the Eastern Alps. It has a complicated metamorphic history from the Jurassic time. The organic material of the Penninic Ocean was transformed to electrically conductive meta-anthracite. Its amount in the chalcophyllite is estimated by geochemists to 0.2 per cent.
Taking this conducting structure as a test area pilot deep magnetotelluric (MT) soundings have been carried out and we determined
- the structure of the conductivity anomaly due to 0.2 per cent meta anthracite in the K-R window and its surroundings
- the different kinds of MT distortions as lateral (side) effect of the conductor appearing in the crust and mantle
- the most probable depth of the conductive asthenosphere at the border of the Pannonian Basin (having extreme shallow asthenosphere). The obtained ~140 km depth is in correlation with value of the asthenospheric map based mainly on seismic data
Thermodynamics of adiabatic feedback control
We study adaptive control of classical ergodic Hamiltonian systems, where the
controlling parameter varies slowly in time and is influenced by system's state
(feedback). An effective adiabatic description is obtained for slow variables
of the system. A general limit on the feedback induced negative entropy
production is uncovered. It relates the quickest negentropy production to
fluctuations of the control Hamiltonian. The method deals efficiently with the
entropy-information trade off.Comment: 6 pages, 1 figur
Does the Boltzmann principle need a dynamical correction?
In an attempt to derive thermodynamics from classical mechanics, an
approximate expression for the equilibrium temperature of a finite system has
been derived [M. Bianucci, R. Mannella, B. J. West, and P. Grigolini, Phys.
Rev. E 51, 3002 (1995)] which differs from the one that follows from the
Boltzmann principle S = k log (Omega(E)) via the thermodynamic relation 1/T=
dS/dE by additional terms of "dynamical" character, which are argued to correct
and generalize the Boltzmann principle for small systems (here Omega(E) is the
area of the constant-energy surface). In the present work, the underlying
definition of temperature in the Fokker-Planck formalism of Bianucci et al. is
investigated and shown to coincide with an approximate form of the
equipartition temperature. Its exact form, however, is strictly related to the
"volume" entropy S = k log (Phi(E)) via the thermodynamic relation above for
systems of any number of degrees of freedom (Phi(E) is the phase space volume
enclosed by the constant-energy surface). This observation explains and
clarifies the numerical results of Bianucci et al. and shows that a dynamical
correction for either the temperature or the entropy is unnecessary, at least
within the class of systems considered by those authors. Explicit analytical
and numerical results for a particle coupled to a small chain (N~10) of quartic
oscillators are also provided to further illustrate these facts.Comment: REVTeX 4, 10 pages, 2 figures. Accepted to J. Stat. Phy
Minimal Work Principle and its Limits for Classical Systems
The minimal work principle asserts that work done on a thermally isolated
equilibrium system, is minimal for the slowest (adiabatic) realization of a
given process. This principle, one of the formulations of the second law, is
operationally well-defined for any finite (few particle) Hamiltonian system.
Within classical Hamiltonian mechanics, we show that the principle is valid for
a system of which the observable of work is an ergodic function. For
non-ergodic systems the principle may or may not hold, depending on additional
conditions. Examples displaying the limits of the principle are presented and
their direct experimental realizations are discussed.Comment: 4 + epsilon pages, 1 figure, revte
Topological character of hydrodynamic screening in suspensions of hard spheres: an example of universal phenomenon
Although in the case of polymer solutions the existence of hydrodynamic
screening is considered as established, use of the same methods for suspensions
of hard spheres so far have failed to produce similar results. In this work we
reconsider this problem. Using superposition of topological, combinatorial and
London-style qualitative arguments, we prove the existence of screening in
suspensions. We show that the nature of hydrodynamic screening in suspensions
is analogous to that known for the Meissner effect in superconductors. The
extent of screening depends on volume fraction of hard spheres. The zero volume
fraction limit corresponds to the normal state. The case of finite volume
fractions-to the mixed state typical for superconductors of the second kind.
Such a state is becoming fully "superconducting" at some critical volume
fraction for which the (zero frequency) relative viscosity diverges. Our
analytical results describing this divergence are in accord with known scaling
results obtained by Brady and Bicerano et al which are well supported by
experimental data. We provide theoretical explanation of the divergence of
relative viscosity in terms of a topological-type transition which
mathematically can be made isomorphic to the more familiar Bose-Einstein
condensation transition. Because of this, the methods developed in this work
are not limited to suspensions only. In concluding section we mention other
applications of the developed formalism ranging from turbulence and
magnetohydrodynamics to high temperature superconductors, QCD, string models,
etc.Comment: 49 page
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