227,386 research outputs found
Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: lattice-Boltzmann simulations
By means of a three-dimensional amphiphilic lattice-Boltzmann model with
short-range interactions for the description of ternary amphiphilic fluids, we
study how the phase separation kinetics of a symmetric binary immiscible fluid
is altered by the presence of the amphiphilic species. We find that a gradual
increase in amphiphile concentration slows down domain growth, initially from
algebraic, to logarithmic temporal dependence, and, at higher concentrations,
from logarithmic to stretched-exponential form. In growth-arrested
stretched-exponential regimes, at late times we observe the self-assembly of
sponge mesophases and gyroid liquid crystalline cubic mesophases, hence
confirming that (a) amphiphile-amphiphile interactions need not be long-ranged
in order for periodically modulated structures to arise in a dynamics of
competing interactions, and (b) a chemically-specific model of the amphiphile
is not required for the self-assembly of cubic mesophases, contradicting claims
in the literature. We also observe a structural order-disorder transition
between sponge and gyroid phases driven by amphiphile concentration alone or,
independently, by the amphiphile-amphiphile and the amphiphile-binary fluid
coupling parameters. For the growth-arrested mesophases, we also observe
temporal oscillations in the structure function at all length scales; most of
the wavenumbers show slow decay, and long-term stationarity or growth for the
others. We ascribe this behaviour to a combination of complex amphiphile
dynamics leading to Marangoni flows.Comment: 16 pages, 13 figures. Accepted for publication in Phys. Rev. E.
(Replaced for the latest version, in press.) Higher-quality figures can be
sent upon reques
Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems
Characterizing the work statistics of driven complex quantum systems is
generally challenging because of the exponential growth with the system size of
the number of transitions involved between different energy levels. We consider
the quantum work distribution associated with the driving of chaotic quantum
systems described by random matrix Hamiltonians and characterize exactly the
work statistics associated with a sudden quench for arbitrary temperature and
system size. Knowledge of the work statistics yields the Loschmidt echo
dynamics of an entangled state between two copies of the system of interest,
the thermofield double state. This echo dynamics is dictated by the spectral
form factor. We discuss its relation to frame potentials and its use to assess
information scrambling.Comment: 11+6pp, 5 figures. v3: version accepted for publication in Quantu
Adaptive, locally-linear models of complex dynamics
The dynamics of complex systems generally include high-dimensional,
non-stationary and non-linear behavior, all of which pose fundamental
challenges to quantitative understanding. To address these difficulties we
detail a new approach based on local linear models within windows determined
adaptively from the data. While the dynamics within each window are simple,
consisting of exponential decay, growth and oscillations, the collection of
local parameters across all windows provides a principled characterization of
the full time series. To explore the resulting model space, we develop a novel
likelihood-based hierarchical clustering and we examine the eigenvalues of the
linear dynamics. We demonstrate our analysis with the Lorenz system undergoing
stable spiral dynamics and in the standard chaotic regime. Applied to the
posture dynamics of the nematode our approach identifies
fine-grained behavioral states and model dynamics which fluctuate close to an
instability boundary, and we detail a bifurcation in a transition from forward
to backward crawling. Finally, we analyze whole-brain imaging in
and show that the stability of global brain states changes with oxygen
concentration.Comment: 25 pages, 16 figure
Asynchronous growth and competition in a two-sex age-structured population model
Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states
Growing dust grains in protoplanetary discs - III. vertical settling
TM acknowledges the support of a Swinburne Special Studies Programme. GL is grateful to the Australian Research Council for funding via Discovery project grant DP1094585, and acknowledges funding from the European Research Council for the FP7 ERC advanced grant project ECOGAL. JFG's research was conducted within the Lyon Institute of Origins under grant ANR-10-LABX-66.We aim to derive a simple analytic model to understand the essential properties of vertically settling growing dust grains in laminar protoplanetary discs. Separating the vertical dynamics from the motion in the disc mid-plane, we integrate the equations of motion for both a linear and an exponential grain growth rate. Numerical integrations are performed for more complex growth models. We find that the settling efficiency depends on the value of the dimensionless parameter γ , which characterizes the relative efficiency of grain growth with respect to the gas drag. Since γ is expected to be of the same order as the initial dust-to-gas ratio in the disc (≃10−2), grain growth enhances the energy dissipation of the dust particles and improves the settling efficiency in protoplanetary discs. This behaviour is mostly independent of the growth model considered as well as of the radial drift of the particles.Publisher PDFPeer reviewe
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