298 research outputs found
High purity nanoparticles exceed stoichiometry limits in rebox chemistry: the nano way to cleaner water
A potentially cheaper and more effective way of cleaning wastewater has been discovered by scientists
at Nazarbayev University and the University of Brighton researching nanotechnology [1]. It is well
established that when particles are reduced to the nanoscale unexpected effects occur. Silver, for example,
interacts with mercury ions in a fixed ratio of atoms (stoichiometry), typically 2:1, which presents a limit
that has never been exceeded. In this project we used an alternative chemical procedure based on modified
quartz sand to immobilise silver nanoparticles (NPs) with control over their size. We found that when the
size of the silver NPs decreased below 35 nm the amount of mercury ions reacting with silver increased
beyond the long-held limit and rose to a maximum of 1:1.2 for 10 nm sized silver
High purity nanoparticles exceed stoichiometry limits in rebox chemistry: the nano way to cleaner water
A potentially cheaper and more effective way of cleaning wastewater has been discovered by scientists
at Nazarbayev University and the University of Brighton researching nanotechnology [1]. It is well
established that when particles are reduced to the nanoscale unexpected effects occur. Silver, for example,
interacts with mercury ions in a fixed ratio of atoms (stoichiometry), typically 2:1, which presents a limit
that has never been exceeded. In this project we used an alternative chemical procedure based on modified
quartz sand to immobilise silver nanoparticles (NPs) with control over their size. We found that when the
size of the silver NPs decreased below 35 nm the amount of mercury ions reacting with silver increased
beyond the long-held limit and rose to a maximum of 1:1.2 for 10 nm sized silver
Ergodic directions for billiards in a strip with periodically located obstacles
We study the size of the set of ergodic directions for the directional
billiard flows on the infinite band with periodically placed
linear barriers of length . We prove that the set of ergodic
directions is always uncountable. Moreover, if is rational
the Hausdorff dimension of the set of ergodic directions is greater than 1/2.
In both cases (rational and irrational) we construct explicitly some sets of
ergodic directions.Comment: The article is complementary to arXiv:1109.458
Rotation sets of billiards with one obstacle
We investigate the rotation sets of billiards on the -dimensional torus
with one small convex obstacle and in the square with one small convex
obstacle. In the first case the displacement function, whose averages we
consider, measures the change of the position of a point in the universal
covering of the torus (that is, in the Euclidean space), in the second case it
measures the rotation around the obstacle. A substantial part of the rotation
set has usual strong properties of rotation sets
Rotor interaction in the annulus billiard
Introducing the rotor interaction in the integrable system of the annulus
billiard produces a variety of dynamical phenomena, from integrability to
ergodicity
Observable Optimal State Points of Sub-additive Potentials
For a sequence of sub-additive potentials, Dai [Optimal state points of the
sub-additive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573] gave a method
of choosing state points with negative growth rates for an ergodic dynamical
system. This paper generalizes Dai's result to the non-ergodic case, and proves
that under some mild additional hypothesis, one can choose points with negative
growth rates from a positive Lebesgue measure set, even if the system does not
preserve any measure that is absolutely continuous with respect to Lebesgue
measure.Comment: 16 pages. This work was reported in the summer school in Nanjing
University. In this second version we have included some changes suggested by
the referee. The final version will appear in Discrete and Continuous
Dynamical Systems- Series A - A.I.M. Sciences and will be available at
http://aimsciences.org/journals/homeAllIssue.jsp?journalID=
Linearization of Cohomology-free Vector Fields
We study the cohomological equation for a smooth vector field on a compact
manifold. We show that if the vector field is cohomology free, then it can be
embedded continuously in a linear flow on an Abelian group
Visualizing Spacetime Curvature via Gradient Flows I: Introduction
Traditional approaches to the study of the dynamics of spacetime curvature in
a very real sense hide the intricacies of the nonlinear regime. Whether it be
huge formulae, or mountains of numerical data, standard methods of presentation
make little use of our remarkable skill, as humans, at pattern recognition.
Here we introduce a new approach to the visualization of spacetime curvature.
We examine the flows associated with the gradient fields of invariants derived
from the spacetime. These flows reveal a remarkably rich structure, and offer
fresh insights even for well known analytical solutions to Einstein's
equations. This paper serves as an overview and as an introduction to this
approach.Comment: 10 pages twocolumn revtex 4-1 two figures. Final form to appear in
Phys Rev
Recurrence and algorithmic information
In this paper we initiate a somewhat detailed investigation of the
relationships between quantitative recurrence indicators and algorithmic
complexity of orbits in weakly chaotic dynamical systems. We mainly focus on
examples.Comment: 26 pages, no figure
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