1,516 research outputs found
The output distribution of important LULU-operators
Two procedures to compute the output distribution phi_S of certain stack
filters S (so called erosion-dilation cascades) are given. One rests on the
disjunctive normal form of S and also yields the rank selection probabilities.
The other is based on inclusion-exclusion and e.g. yields phi_S for some
important LULU-operators S. Properties of phi_S can be used to characterize
smoothing properties of S. One of the methods discussed also allows for the
calculation of the reliability polynomial of any positive Boolean function
(e.g. one derived from a connected graph).Comment: 20 pages, up to trivial differences this is the final version to be
published in Quaestiones Mathematicae 201
Dynamics of the critical Casimir force for a conserved order parameter after a critical quench
Fluctuation-induced forces occur generically when long-ranged correlations
(e.g., in fluids) are confined by external bodies. In classical systems, such
correlations require specific conditions, e.g., a medium close to a critical
point. On the other hand, long-ranged correlations appear more commonly in
certain non-equilibrium systems with conservation laws. Consequently, a variety
of non-equilibrium fluctuation phenomena, including fluctuation-induced forces,
have been discovered and explored recently. Here, we address a long-standing
problem of non-equilibrium critical Casimir forces emerging after a quench to
the critical point in a confined fluid with order-parameter-conserving dynamics
and non-symmetry-breaking boundary conditions. The interplay of inherent
(critical) fluctuations and dynamical non-local effects (due to density
conservation) gives rise to striking features, including correlation functions
and forces exhibiting oscillatory time-dependences. Complex transient regimes
arise, depending on initial conditions and the geometry of the confinement. Our
findings pave the way for exploring a wealth of non-equilibrium processes in
critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In
certain regimes, our results are applicable to active matter.Comment: 38 pages, 11 figure
Convergence of large deviation estimators
We study the convergence of statistical estimators used in the estimation of
large deviation functions describing the fluctuations of equilibrium,
nonequilibrium, and manmade stochastic systems. We give conditions for the
convergence of these estimators with sample size, based on the boundedness or
unboundedness of the quantity sampled, and discuss how statistical errors
should be defined in different parts of the convergence region. Our results
shed light on previous reports of 'phase transitions' in the statistics of free
energy estimators and establish a general framework for reliably estimating
large deviation functions from simulation and experimental data and identifying
parameter regions where this estimation converges.Comment: 13 pages, 6 figures. v2: corrections focusing the paper on large
deviations; v3: minor corrections, close to published versio
Non-equilibrium forces following quenches in active and thermal matter
Non-equilibrium systems are known to exhibit long-ranged correlations due to
conservation of quantities like density or momentum. This, in turn, leads to
long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a
variety of non-equilibrium settings. Here, we study such forces, which arise
transiently between parallel plates or compact inclusions in a gas of
particles, following a change ("quench") in temperature or activity of the
medium. Analytical calculations, as well as numerical simulations of passive or
active Brownian particles, indicate two distinct forces: (i) The immediate
effect of the quench is adsorption or desorption of particles of the medium to
the immersed objects, which in turn initiates a front of relaxing (mean)
density. This leads to time-dependent {\it density-induced forces}. (ii) A
long-term effect of the quench is that density fluctuations are modified,
manifested as transient (long-ranged) (pair-)correlations that relax
diffusively to their (short-ranged) steady-state limit. As a result, transient
{\it fluctuation-induced forces} emerge. We discuss the properties of
fluctuation-induced and density-induced forces as regards universality,
relaxation as a function of time, and scaling with distance between objects.
Their distinct signatures allow us to distinguish the two types of forces in
simulation data. Finally, we propose several scenarios for their experimental
observation.Comment: - Added Journal reference and DOI - Modified title - Fixed minor
typos - Added plot of Eq. (32) [16 pages, 11 figures
Response of active Brownian particles to shear flow
We study the linear response of interacting active Brownian particles in an
external potential to simple shear flow. Using a path integral approach, we
derive the linear response of any state observable to initiating shear in terms
of correlation functions evaluated in the unperturbed system. For systems and
observables which are symmetric under exchange of the and coordinates,
the response formula can be drastically simplified to a form containing only
state variables in the corresponding correlation functions (compared to the
generic formula containing also time derivatives). In general, the shear
couples to the particles by translational as well as rotational advection, but
in the aforementioned case of symmetry only translational advection is
relevant in the linear regime. We apply the response formulas analytically in
solvable cases and numerically in a specific setup. In particular, we
investigate the effect of a shear flow on the morphology and the stress of
confined active particles in interaction, where we find that the activity as
well as additional alignment interactions generally increase the response.Comment: 13 pages, 4 figure
Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions
In a recent study [Phys. Rev. E \textbf{94}, 022103 (2016)] it has been shown
that, for a fluid film subject to critical adsorption, the resulting critical
Casimir force (CCF) may significantly depend on the thermodynamic ensemble.
Here, we extend that study by considering fluid films within the so-called
ordinary surface universality class. We focus on mean-field theory, within
which the OP profile satisfies Dirichlet boundary conditions and produces a
nontrivial CCF in the presence of external bulk fields or, respectively, a
nonzero total order parameter within the film. Our analytical results are
supported by Monte Carlo simulations of the three-dimensional Ising model. We
show that, in the canonical ensemble, i.e., when fixing the so-called total
mass within the film, the CCF is typically repulsive instead of attractive as
in the grand canonical ensemble. Based on the Landau-Ginzburg free energy, we
furthermore obtain analytic expressions for the order parameter profiles and
analyze the relation between the total mass in the film and the external bulk
field.Comment: 22 pages, 15 figures. Version 2: minor corrections; added Journal
referenc
Ballistic propagation of density correlations and excess wall forces in quenched granular media
We investigate a granular gas in a shaken quasi-two-dimensional box in
molecular dynamics computer simulations. After a sudden change (quench) of the
shaking amplitude, transient density correlations are observed orders of
magnitude beyond the steady-state correlation length scale. Propagation of the
correlations is ballistic, in contrast to recently investigated quenches of
Brownian particles that show diffusive propagation [Rohwer et al., Phys. Rev.
Lett., 118, 015702 (2017), Rohwer et al., Phys. Rev. E, 97, 032125 (2018)]. At
sufficiently strong cooling of the fluid the effect is overlaid by clustering
instability of the homogeneous cooling state with different scaling behavior.
We are able to identify different quench regimes. In each regime correlations
exhibit remarkably universal position dependence. In simulations performed with
side walls we find confinement effects for temperature and pressure in
steady-state simulations, and an additional transient wall pressure
contribution upon changing the shaking amplitude. The transient contribution is
ascribed to enhanced relaxation of the fluid in the presence of walls. From
incompatible scaling behavior we conclude that the observed effects with and
without side walls constitute distinct phenomena.Comment: 12 pages 11 figure
Investigating the Use of Element Analysis for Differentiation between the Geographic Origins of Western Cape Wines
The aim of this study was to differentiate between the geographic origins of wines produced in the Western Cape on the basis of their element composition. A total of 96 market-ready red and white wines (Pinotage, Shiraz, Merlot, Cabernet Sauvignon, Sauvignon blanc, Chardonnay and Chenin blanc) were analysed by means of inductively coupled plasma atomic emission spectrometry (ICP-AES). The discriminant methods: stepwise discriminant analysis, canonical discriminant analysis and linear discriminant analysis were applied to the data sets. A classification accuracy of 38% for Pinotage, 55% for Shiraz, 68% for Merlot, 75% for Cabernet Sauvignon, 93% for Sauvignon blanc, 68% for Chardonnay and 100% for Chenin blanc was achieved. Subject to the conditions of this study, it was concluded that differentiation between wines according to geographical origin was possible using the elemental composition
Activated diffusiophoresis
Perturbations of fluid media can give rise to non-equilibrium dynamics, which
may in turn cause motion of immersed inclusions. We consider perturbations
("activations") that are local in space and time, of a fluid density which is
conserved, and study the resulting diffusiophoretic phenomena that emerge at a
large distance. Specifically, we consider cases where the perturbations
propagate diffusively, providing examples from passive and active matter for
which this is expected to be the case. Activations can, for instance, be
realized by sudden and local changes in interaction potentials of the medium,
or by local changes of its activity. Various analytical results are provided
for the case of confinement by two parallel walls. We investigate the
possibility of extracting work from inclusions which are moving through the
activated fluid. Further, we show that a time-dependent density profile,
created via suitable activation protocols, allows for conveyance of inclusions
along controlled and stable trajectories. In contrast, in states with a steady
density, inclusions cannot be held at stable positions, reminiscent of
Earnshaw's theorem of electrostatics. We expect these findings to be applicable
in a range of experimental systems.Comment: 14 pages (12+2), 14 Figure
- …