432 research outputs found
Entropy production selects nonequilibrium states in multistable systems
Far-from-equilibrium thermodynamics underpins the emergence of life, but how
has been a long-outstanding puzzle. Best candidate theories based on the
maximum entropy production principle could not be unequivocally proven, in part
due to complicated physics, unintuitive stochastic thermodynamics, and the
existence of alternative theories such as the minimum entropy production
principle. Here, we use a simple, analytically solvable, one-dimensional
bistable chemical system to demonstrate the validity of the maximum entropy
production principle. To generalize to multistable stochastic system, we use
the stochastic least-action principle to derive the entropy production and its
role in the stability of nonequilibrium steady states. This shows that in a
multistable system, all else being equal, the steady state with the highest
entropy production is favored, with a number of implications for the evolution
of biological, physical, and geological systems.Comment: 15 pages, 4 figure
Towards Realistic Progenitors of Core-Collapse Supernovae
Two-dimensional (2D) hydrodynamical simulations of progenitor evolution of a
23 solar mass star, close to core collapse (about 1 hour, in 1D), with
simultaneously active C, Ne, O, and Si burning shells, are presented and
contrasted to existing 1D models (which are forced to be quasi-static).
Pronounced asymmetries, and strong dynamical interactions between shells are
seen in 2D. Although instigated by turbulence, the dynamic behavior proceeds to
sufficiently large amplitudes that it couples to the nuclear burning. Dramatic
growth of low order modes is seen, as well as large deviations from spherical
symmetry in the burning shells. The vigorous dynamics is more violent than that
seen in earlier burning stages in the 3D simulations of a single cell in the
oxygen burning shell, or in 2D simulations not including an active Si shell.
Linear perturbative analysis does not capture the chaotic behavior of
turbulence (e.g., strange attractors such as that discovered by Lorenz), and
therefore badly underestimates the vigor of the instability. The limitations of
1D and 2D models are discussed in detail. The 2D models, although flawed
geometrically, represent a more realistic treatment of the relevant dynamics
than existing 1D models, and present a dramatically different view of the
stages of evolution prior to collapse. Implications for interpretation of
SN1987A, abundances in young supernova remnants, pre-collapse outbursts,
progenitor structure, neutron star kicks, and fallback are outlined. While 2D
simulations provide new qualitative insight, fully 3D simulations are needed
for a quantitative understanding of this stage of stellar evolution. The
necessary properties of such simulations are delineated.Comment: 26 pages, 1 table, 4 figure
Order out of Randomness : Self-Organization Processes in Astrophysics
Self-organization is a property of dissipative nonlinear processes that are
governed by an internal driver and a positive feedback mechanism, which creates
regular geometric and/or temporal patterns and decreases the entropy, in
contrast to random processes. Here we investigate for the first time a
comprehensive number of 16 self-organization processes that operate in
planetary physics, solar physics, stellar physics, galactic physics, and
cosmology. Self-organizing systems create spontaneous {\sl order out of chaos},
during the evolution from an initially disordered system to an ordered
stationary system, via quasi-periodic limit-cycle dynamics, harmonic mechanical
resonances, or gyromagnetic resonances. The internal driver can be gravity,
rotation, thermal pressure, or acceleration of nonthermal particles, while the
positive feedback mechanism is often an instability, such as the
magneto-rotational instability, the Rayleigh-B\'enard convection instability,
turbulence, vortex attraction, magnetic reconnection, plasma condensation, or
loss-cone instability. Physical models of astrophysical self-organization
processes involve hydrodynamic, MHD, and N-body formulations of Lotka-Volterra
equation systems.Comment: 61 pages, 38 Figure
Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence
The theoretical motivations to perform experimental tests of the stationary
state fluctuation relation are reviewed. The difficulties involved in such
tests, evidenced by numerical simulations, are also discussed.Comment: 36 pages, 4 figures. Extended version of a presentation to the
discussion "Is it possible to experimentally verify the fluctuation
theorem?", IHP, Paris, December 1, 2006. Comments are very welcom
Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations
We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors
Competition between transport phenomena in a Reaction-Diffusion-Convection system
This doctoral dissertation consists of three main parts.
In part one, a general overview of the basic concepts of nonlinear science, nonlinear analysis and non-equilibrium thermodynamics is presented. Kinetics of chemical oscillations and the well known Belousov-Zhabotinsky reaction are also illustrated.
In part two, a Reaction-Diffusion-Convection (RDC) model is introduced as a convenient framework for studying instability scenarios by which chemical oscillators are driven to chaos, along with its translation to an opportune code for numerical simulations.
In part three, we report the methods and the data obtained. We observe that distinct bifurcation points are found in the oscillating patterns as Diu-sion coecients (di) or Grashof numbers (Gri) vary. Singularly there emerge peculiar bifurcation paths, inscribed in a general scenario of the RTN type, in which quasi{periodicity transmutes into a period-doubling sequence to chemical chaos. The opposite influence exhibited by the two parameters in these transitions clearly indicate that diusion of active species and natural convection are in `competition` for the stability of ordered dynamics. Moreover, a mirrored behavior between chemical oscillations and spatio-temporal dynamics is observed, suggesting that the emergence of the two observables are a manifestation of the same phenomenon. The interplay between chemical and transport phenomena instabilities is at the general origin of chaos for these systems.
Further, a molecular dynamics study has been carried out for the calculation of diusion coecients of active species in the Belousov-Zhabotinsky reaction,
namely HBrO2 and Ce(III), by means of mean square displacement and velocity autocorrelation function. These data have been used for a deeper comprehension of the hydrodynamic competition observed between diusion and convective motions for the stability of the system.</br
A Finite-Time Thermodynamics of Unsteady Fluid Flows
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Turbulent fluid has often been conceptualized as a transient thermodynamic phase. Here, a finite-time thermodynamics (FTT) formalism is proposed to compute mean flow and fluctuation levels of unsteady incompressible flows. The proposed formalism builds upon the Galerkin model framework, which simplifies a continuum 3D fluid motion into a finite-dimensional phase-space dynamics and, subsequently, into a thermodynamics energy problem. The Galerkin model consists of a velocity field expansion in terms of flow configuration dependent modes and of a dynamical system describing the temporal evolution of the mode coefficients. Each mode is treated as one thermodynamic degree of freedom, characterized by an energy level. The dynamical system approaches local thermal equilibrium (LTE) where each mode has the same energy if it is governed only by internal (triadic) mode interactions. However, in the generic case of unsteady flows, the full system approaches only partial LTE with unequal energy levels due to strongly mode-dependent external interactions. The FTT model is first illustrated by a traveling wave governed by a 1D Burgers equation. It is then applied to two flow benchmarks: the relatively simple laminar vortex shedding, which is dominated by two eigenmodes, and the homogeneous shear turbulence, which has been modeled with 1459 modes
Mathematical and physical ideas for climate science
The climate is a forced and dissipative nonlinear system featuring nontrivial dynamics on a vast range of spatial and temporal scales. The understanding of the climate's structural and multiscale properties is crucial for the provision of a unifying picture of its dynamics and for the implementation of accurate and efficient numerical models. We present some recent developments at the intersection between climate science, mathematics, and physics, which may prove fruitful in the direction of constructing a more comprehensive account of climate dynamics. We describe the Nambu formulation of fluid dynamics and the potential of such a theory for constructing sophisticated numerical models of geophysical fluids. Then, we focus on the statistical mechanics of quasi-equilibrium flows in a rotating environment, which seems crucial for constructing a robust theory of geophysical turbulence. We then discuss ideas and methods suited for approaching directly the nonequilibrium nature of the climate system. First, we describe some recent findings on the thermodynamics of climate, characterize its energy and entropy budgets, and discuss related methods for intercomparing climate models and for studying tipping points. These ideas can also create a common ground between geophysics and astrophysics by suggesting general tools for studying exoplanetary atmospheres. We conclude by focusing on nonequilibrium statistical mechanics, which allows for a unified framing of problems as different as the climate response to forcings, the effect of altering the boundary conditions or the coupling between geophysical flows, and the derivation of parametrizations for numerical models
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