246 research outputs found
Comparison of three-dimensional and two-dimensional statistical mechanics of shear layers for flow between two parallel plates
It is shown that the averaged velocity profiles predicted by statistical
mechanics of point vortices and statistical mechanics of vortex lines are
practically indistinguishable for a shear flow between two parallel walls
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
Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium
The paper deals with the problem of existence of a convergent "strong" normal
form in the neighbourhood of an equilibrium, for a finite dimensional system of
differential equations with analytic and time-dependent non-linear term. The
problem can be solved either under some non-resonance hypotheses on the
spectrum of the linear part or if the non-linear term is assumed to be (slowly)
decaying in time. This paper "completes" a pioneering work of Pustil'nikov in
which, despite under weaker non-resonance hypotheses, the nonlinearity is
required to be asymptotically autonomous. The result is obtained as a
consequence of the existence of a strong normal form for a suitable class of
real-analytic Hamiltonians with non-autonomous perturbations.Comment: 10 page
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
On a new definition of quantum entropy
It is proved here that, as a consequence of the unitary quantum evolution,
the expectation value of a properly defined quantum entropy operator (as
opposed to the non-evolving von Neumann entropy) can only increase during non
adiabatic transformations and remains constant during adiabatic ones. Thus
Clausius formulation of the second law is established as a theorem in quantum
mechanics, in a way that is equivalent to the previously established
formulation in terms of minimal work principle [A. E. Allahverdyan and T. M.
Nieuwenhuizen, Phys. Rev. E 71, 046107 (2005)]. The corresponding Quantum
Mechanical Principle of Entropy Increase is then illustrated with an exactly
solvable example, namely the driven harmonic oscillator. Attention is paid to
both microcanonical and canonical initial condition. The results are compared
to their classical counterparts.Comment: 4 pages, 3 figure
Derivation of Boltzmann Principle
We present a derivation of Boltzmann principle
based on classical mechanical models of thermodynamics. The argument is based
on the heat theorem and can be traced back to the second half of the nineteenth
century with the works of Helmholtz and Boltzmann. Despite its simplicity, this
argument has remained almost unknown. We present it in a modern, self-contained
and accessible form. The approach constitutes an important link between
classical mechanics and statistical mechanics
Relation between Stochastic Resonance and Synchronization of Passages in a Double-Well System
We calculate, numerically, the residence times (and their distribution) of a
Brownian particle in a two-well system under the action of a periodic,
saw-tooth type, external field. We define hysteresis in the system. The
hysteresis loop area is shown to be a good measure of synchronization of
passages from one well to the other. We establish connection between this
stochastic synchronization and stochastic resonance in the system.Comment: To appear in PRE May 1997, figures available on reques
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
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
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