182 research outputs found
Greedy Algorithm for General Biorthogonal Systems
AbstractWe consider biorthogonal systems in quasi-Banach spaces such that the greedy algorithm converges for each x∈X (quasi-greedy systems). We construct quasi-greedy conditional bases in a wide range of Banach spaces. We also compare the greedy algorithm for the multidimensional Haar system with the optimal m-term approximation for this system. This substantiates a conjecture by Temlyakov
Influence of Hydrodynamic Interactions on the Kinetics of Colloidal Particle's Adsorption
The kinetics of irreversible adsorption of spherical particles onto a flat
surface is theoretically studied. Previous models, in which hydrodynamic
interactions were disregarded, predicted a power-law behavior for
the time dependence of the coverage of the surface near saturation.
Experiments, however, are in agreement with a power-law behavior of the form
. We outline that, when hydrodynamic interactions are considered, the
assymptotic behavior is found to be compatible with the experimental results in
a wide region near saturation.Comment: 4 pages, 1 figures, Phys. Rev. Lett. (in press
Scale-dependent behavior of scale equations
We propose a new mathematical framework to formulate scale structures of general systems. Stack equations characterize a system in terms of accumulative scales. Their behavior at each scale level is determined independently without referring to other levels. Most standard geometries in mathematics can be reformulated in such stack equations. By involving interaction between scales, we generalize stack equations into scale equations. Scale equations are capable to accommodate various behaviors at different scale levels into one integrated solution. On contrary to standard geometries, such solutions often reveal eccentric scale-dependent figures, providing a clue to understand multiscale nature of the real world. Especially, it is suggested that the Gaussian noise stems from nonlinear scale interactions.open0
Kinetics of Particles Adsorption Processes Driven by Diffusion
The kinetics of the deposition of colloidal particles onto a solid surface is
analytically studied. We take into account both the diffusion of particles from
the bulk as well as the geometrical aspects of the layer of adsorbed particles.
We derive the first kinetic equation for the coverage of the surface (a
generalized Langmuir equation) whose predictions are in agreement with recent
simulation results where diffusion of particles from the bulk is explicitly
considered.Comment: 4 page
An analytic model for a cooperative ballistic deposition in one dimension
We formulate a model for a cooperative ballistic deposition (CBD) process
whereby the incoming particles are correlated with the ones already adsorbed
via attractive force. The strength of the correlation is controlled by a
tunable parameter that interpolates the classical car parking problem at
, the ballistic deposition at and the CBD model at . The
effects of the correlation in the CBD model are as follows. The jamming
coverage increases with the strength of attraction due to an ever
increasing tendency of cluster formation. The system almost reaches the closest
packing structure as but never forms a percolating cluster which
is typical to 1D system. In the large regime, the mean cluster size
increases as . Furthermore, the asymptotic approach towards the
closest packing is purely algebraic both with as and with as where .Comment: 9 pages (in Revtex4), 9 eps figures; Submitted to publicatio
Moments of unconditional logarithmically concave vectors
We derive two-sided bounds for moments of linear combinations of coordinates
od unconditional log-concave vectors. We also investigate how well moments of
such combinations may be approximated by moments of Gaussian random variables.Comment: 14 page
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