232 research outputs found
Controlled nanochannel lattice formation utilizing prepatterned substrates
Solid substrates can be endued with self-organized regular stripe patterns of
nanoscopic lengthscale by Langmuir-Blodgett transfer of organic monolayers.
Here we consider the effect of periodically prepatterned substrates on this
process of pattern formation. It leads to a time periodic forcing of the
oscillatory behavior at the meniscus. Utilizing higher order synchronization
with this forcing, complex periodic patterns of predefined wavelength can be
created. The dependence of the synchronization on the amplitude and the
wavelength of the wetting contrast is investigated in one and two spatial
dimensions and the resulting patterns are discussed. Furthermore, the effect of
prepatterned substrates on the pattern selection process is investigated
Dynamics of a thin liquid film with surface rigidity and spontaneous curvature
The effect of rigid surfaces on the dynamics of thin liquid films which are
amenable to the lubrication approximation is considered. It is shown that the
Helfrich energy of the layer gives rise to additional terms in the
time-evolution equations of the liquid film. The dynamics is found to depend on
the absolute value of the spontaneous curvature, irrespective of its sign. Due
to the additional terms, a novel finite wavelength instability of flat rigid
interfaces can be observed. Furthermore, the dependence of the shape of a
droplet on the bending rigidity as well as on the spontaneous curvature is
discussed.Comment: 4 pages, 5 figure
On the relation between Differential Privacy and Quantitative Information Flow
Differential privacy is a notion that has emerged in the community of
statistical databases, as a response to the problem of protecting the privacy
of the database's participants when performing statistical queries. The idea is
that a randomized query satisfies differential privacy if the likelihood of
obtaining a certain answer for a database is not too different from the
likelihood of obtaining the same answer on adjacent databases, i.e. databases
which differ from for only one individual. Information flow is an area of
Security concerned with the problem of controlling the leakage of confidential
information in programs and protocols. Nowadays, one of the most established
approaches to quantify and to reason about leakage is based on the R\'enyi min
entropy version of information theory. In this paper, we analyze critically the
notion of differential privacy in light of the conceptual framework provided by
the R\'enyi min information theory. We show that there is a close relation
between differential privacy and leakage, due to the graph symmetries induced
by the adjacency relation. Furthermore, we consider the utility of the
randomized answer, which measures its expected degree of accuracy. We focus on
certain kinds of utility functions called "binary", which have a close
correspondence with the R\'enyi min mutual information. Again, it turns out
that there can be a tight correspondence between differential privacy and
utility, depending on the symmetries induced by the adjacency relation and by
the query. Depending on these symmetries we can also build an optimal-utility
randomization mechanism while preserving the required level of differential
privacy. Our main contribution is a study of the kind of structures that can be
induced by the adjacency relation and the query, and how to use them to derive
bounds on the leakage and achieve the optimal utility
On the strange vector form factors of the nucleon in the NJL soliton model
Within the Nambu--Jona--Lasinio model strange degrees of freedom are
incorporated into the soliton picture using the collective approach of Yabu and
Ando. The form factors of the nucleon associated with the nonet vector current
are extracted. The numerical results provide limits for the strange magnetic
moment: . For the strange magnetic form factor of the
nucleon the valence quark and vacuum contributions add coherently while there
are significant cancellations for the strange electric form factor.Comment: 9 pages, one figure, postscript file submitted as uuencoded
compressed fil
The Newsvendor problem: analysis of the cost structure under normally distributed demand
We briefly review selected mathematical models that describe the dynamics of
pattern formation phenomena in dip-coating and Langmuir-Blodgett transfer
experiments, where solutions or suspensions are transferred onto a substrate
producing patterned deposit layers with structure length from hundreds of
nanometres to tens of micrometres. The models are presented with a focus on
their gradient dynamics formulations that clearly shows how the dynamics is
governed by particular free energy functionals and facilitates the comparison
of the models. In particular, we include a discussion of models based on
long-wave hydrodynamics as well as of more phenomenological models that focus
on the pattern formation processes in such systems. The models and their
relations are elucidated and examples of resulting patterns are discussed
before we conclude with a discussion of implications of the gradient dynamics
formulation and of some related open issues
Trust in Crowds: probabilistic behaviour in anonymity protocols
The existing analysis of the Crowds anonymity protocol assumes that a participating member is either ‘honest’ or ‘corrupted’. This paper generalises this analysis so that each member is assumed to maliciously disclose the identity of other nodes with a probability determined by her vulnerability to corruption. Within this model, the trust in a principal is defined to be the probability that she behaves honestly. We investigate the effect of such a probabilistic behaviour on the anonymity of the principals participating in the protocol, and formulate the necessary conditions to achieve ‘probable innocence’. Using these conditions, we propose a generalised Crowds-Trust protocol which uses trust information to achieves ‘probable innocence’ for principals exhibiting probabilistic behaviour
Quantitative Information Flow and Applications to Differential Privacy
International audienceSecure information flow is the problem of ensuring that the information made publicly available by a computational system does not leak information that should be kept secret. Since it is practically impossible to avoid leakage entirely, in recent years there has been a growing interest in considering the quantitative aspects of information flow, in order to measure and compare the amount of leakage. Information theory is widely regarded as a natural framework to provide firm foundations to quantitative information flow. In this notes we review the two main information-theoretic approaches that have been investigated: the one based on Shannon entropy, and the one based on Rényi min-entropy. Furthermore, we discuss some applications in the area of privacy. In particular, we consider statistical databases and the recently-proposed notion of differential privacy. Using the information-theoretic view, we discuss the bound that differential privacy induces on leakage, and the trade-off between utility and privac
Thin film dynamics with surfactant phase transition
A thin liquid film covered with an insoluble surfactant in the vicinity of a
first-order phase transition is discussed. Within the lubrication approximation
we derive two coupled equations to describe the height profile of the film and
the surfactant density. Thermodynamics of the surfactant is incorporated via a
Cahn-Hilliard type free-energy functional which can be chosen to describe a
transition between two stable phases of different surfactant density. Within
this model, a linear stability analysis of stationary homogeneous solutions is
performed, and drop formation in a film covered with surfactant in the lower
density phase is investigated numerically in one and two spatial dimensions
Continuation for thin film hydrodynamics and related scalar problems
This chapter illustrates how to apply continuation techniques in the analysis
of a particular class of nonlinear kinetic equations that describe the time
evolution through transport equations for a single scalar field like a
densities or interface profiles of various types. We first systematically
introduce these equations as gradient dynamics combining mass-conserving and
nonmass-conserving fluxes followed by a discussion of nonvariational amendmends
and a brief introduction to their analysis by numerical continuation. The
approach is first applied to a number of common examples of variational
equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including
certain thin-film equations for partially wetting liquids on homogeneous and
heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal
equations. Second we consider nonvariational examples as the
Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard
equations and thin-film equations describing stationary sliding drops and a
transversal front instability in a dip-coating. Through the different examples
we illustrate how to employ the numerical tools provided by the packages
auto07p and pde2path to determine steady, stationary and time-periodic
solutions in one and two dimensions and the resulting bifurcation diagrams. The
incorporation of boundary conditions and integral side conditions is also
discussed as well as problem-specific implementation issues
Colloquium: Mechanical formalisms for tissue dynamics
The understanding of morphogenesis in living organisms has been renewed by
tremendous progressin experimental techniques that provide access to
cell-scale, quantitative information both on theshapes of cells within tissues
and on the genes being expressed. This information suggests that
ourunderstanding of the respective contributions of gene expression and
mechanics, and of their crucialentanglement, will soon leap forward.
Biomechanics increasingly benefits from models, which assistthe design and
interpretation of experiments, point out the main ingredients and assumptions,
andultimately lead to predictions. The newly accessible local information thus
calls for a reflectionon how to select suitable classes of mechanical models.
We review both mechanical ingredientssuggested by the current knowledge of
tissue behaviour, and modelling methods that can helpgenerate a rheological
diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and
tissue scale ("inter-cell") contributions. We recall the mathematical framework
developpedfor continuum materials and explain how to transform a constitutive
equation into a set of partialdifferential equations amenable to numerical
resolution. We show that when plastic behaviour isrelevant, the dissipation
function formalism appears appropriate to generate constitutive equations;its
variational nature facilitates numerical implementation, and we discuss
adaptations needed in thecase of large deformations. The present article
gathers theoretical methods that can readily enhancethe significance of the
data to be extracted from recent or future high throughput
biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few
corrections to the published version, all in Appendix D.2 devoted to large
deformation
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