14,923 research outputs found
Minimum Dissipation Principle in Nonlinear Transport
We extend Onsager's minimum dissipation principle to stationary states that
are only subject to local equilibrium constraints, even when the transport
coefficients depend on the thermodynamic forces. Crucial to this generalization
is a decomposition of the thermodynamic forces into those that are held fixed
by the boundary conditions, and the subspace which is orthogonal with respect
to the metric defined by the transport coefficients. We are then able to apply
Onsager and Machlup's proof to the second set of forces. As an example we
consider two-dimensional nonlinear diffusion coupled to two reservoirs at
different temperatures. Our extension differs from that of Bertini et al. in
that we assume microscopic irreversibility and we allow a nonlinear dependence
of the fluxes on the forces.Comment: 20 pages, 1 figur
Cumulant expansions for atmospheric flows
The equations governing atmospheric flows are nonlinear. Consequently, the
hierarchy of cumulant equations is not closed. But because atmospheric flows
are inhomogeneous and anisotropic, the nonlinearity may manifest itself only
weakly through interactions of mean fields with disturbances such as thermals
or eddies. In such situations, truncations of the hierarchy of cumulant
equations hold promise as a closure strategy.
We review how truncations at second order can be used to model and elucidate
the dynamics of atmospheric flows. Two examples are considered. First, we study
the growth of a dry convective boundary layer, which is heated from below,
leading to turbulent upward energy transport and growth of the boundary layer.
We demonstrate that a quasilinear truncation of the equations of motion, in
which interactions of disturbances among each other are neglected but
interactions with mean fields are taken into account, can capture the growth of
the convective boundary layer even if it does not capture important turbulent
transport terms. Second, we study the evolution of two-dimensional large-scale
waves representing waves in Earth's upper atmosphere. We demonstrate that a
cumulant expansion truncated at second order (CE2) can capture the evolution of
such waves and their nonlinear interaction with the mean flow in some
circumstances, for example, when the wave amplitude is small enough or the
planetary rotation rate is large enough. However, CE2 fails to capture the flow
evolution when nonlinear eddy--eddy interactions in surf zones become
important. Higher-order closures can capture these missing interactions.
The results point to new ways in which the dynamics of turbulent boundary
layers may be represented in climate models, and they illustrate different
classes of nonlinear processes that can control wave dissipation and momentum
fluxes in the troposphere.Comment: 43 pages, 10 figures, accepted for publication in the New Journal of
Physic
Thermal conduction in classical low-dimensional lattices
Deriving macroscopic phenomenological laws of irreversible thermodynamics
from simple microscopic models is one of the tasks of non-equilibrium
statistical mechanics. We consider stationary energy transport in crystals with
reference to simple mathematical models consisting of coupled oscillators on a
lattice. The role of lattice dimensionality on the breakdown of the Fourier's
law is discussed and some universal quantitative aspects are emphasized: the
divergence of the finite-size thermal conductivity is characterized by
universal laws in one and two dimensions. Equilibrium and non-equilibrium
molecular dynamics methods are presented along with a critical survey of
previous numerical results. Analytical results for the non-equilibrium dynamics
can be obtained in the harmonic chain where the role of disorder and
localization can be also understood. The traditional kinetic approach, based on
the Boltzmann-Peierls equation is also briefly sketched with reference to
one-dimensional chains. Simple toy models can be defined in which the
conductivity is finite. Anomalous transport in integrable nonlinear systems is
briefly discussed. Finally, possible future research themes are outlined.Comment: 90 pages, revised versio
Broken space-time symmetries and mechanisms of rectification of ac fields by nonlinear (non)adiabatic response
We consider low-dimensional dynamical systems exposed to a heat bath and to
additional ac fields. The presence of these ac fields may lead to a breaking of
certain spatial or temporal symmetries which in turn cause nonzero averages of
relevant observables. Nonlinear (non)adiabatic response is employed to explain
the effect. We consider a case of a particle in a periodic potential as an
example and discuss the relevant symmetry breakings and the mechanisms of
rectification of the current in such a system.Comment: 11 pages, 10 figure
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