5,315 research outputs found
Universality of temperature distribution in granular gas mixtures with a steep particle size distribution
Distribution of granular temperatures in granular gas mixtures is
investigated analytically and numerically. We analyze space uniform systems in
a homogeneous cooling state (HCS) and under a uniform heating with a
mass-dependent heating rate . We demonstrate that
for steep size distributions of particles the granular temperatures obey a
universal power-law distribution, , where the exponent
does not depend on a particular form of the size distribution, the
number of species and inelasticity of the grains. Moreover, is a
universal constant for a HCS and depends piecewise linearly on for
heated gases. The predictions of our scaling theory agree well with the
numerical results
Short time heat diffusion in compact domains with discontinuous transmission boundary conditions
We consider a heat problem with discontinuous diffusion coefficientsand
discontinuous transmission boundary conditions with a resistancecoefficient.
For all compact -domains with a
-set boundary (for instance, aself-similar fractal), we find the first term
of the small-timeasymptotic expansion of the heat content in the complement
of, and also the second-order term in the case of a regularboundary.
The asymptotic expansion is different for the cases offinite and infinite
resistance of the boundary. The derived formulasrelate the heat content to the
volume of the interior Minkowskisausage and present a mathematical
justification to the de Gennes'approach. The accuracy of the analytical results
is illustrated bysolving the heat problem on prefractal domains by a finite
elementsmethod
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Spray Fabrication of Layer-by-Layer Antimicrobial N-Halamine Coatings
Antimicrobial coatings in which the active agent (e.g. N-halamine) can regenerate activity represent a promising way to prevent microbial cross-contamination. A reported method for applying coatings containing antimicrobial N-halamines is layer-by-layer (LbL) application of polyelectrolytes, which form N-halamines upon cross-linking. Prior reports on dip layer-by-layer (LbL) fabrication have demonstrated the potential of this coating technology; however, spray LbL fabrication would enable more rapid coating and represents a more commercially translatable application technique. In this work, dip and spray LbL methods were used to coat polypropylene (PP) with N-halamine containing bilayers consisting of cross-linked polyethylenimine (PEI) and poly(acrylic acid) (PAA). Further experimentation with spray LbL fabrication used naturally occurring polyelectrolytes, chitosan and alginate. Materials were characterized using atomic force microscopy (AFM), ellipsometry, contact angle, fourier transform infrared spectroscopy, a chlorine content assay, and a dye assay for amine quantification. All methods of coating application exhibited a 99.999% (5-log) reduction against Listeria monocytogenes with application time for spray LbL taking less than 10% of the time required for dip LbL. Spray LbL fabrication of N-halamines is a rapid and inexpensive method to fabricate rechargeable antimicrobial surfaces
Peller's problem concerning Koplienko-Neidhardt trace formulae: the unitary case
We prove the existence of a complex valued -function on the unit circle,
a unitary operator U and a self-adjoint operator Z in the Hilbert-Schmidt class
, such that the perturbated operator does not belong to the
space of trace class operators. This resolves a problem of Peller
concerning the validity of the Koplienko-Neidhardt trace formula for unitaries
Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae
A formula for the norm of a bilinear Schur multiplier acting from the
Cartesian product of two copies of the
Hilbert-Schmidt classes into the trace class is established in
terms of linear Schur multipliers acting on the space of
all compact operators. Using this formula, we resolve Peller's problem on
Koplienko-Neidhardt trace formulae. Namely, we prove that there exist a twice
continuously differentiable function with a bounded second derivative, a
self-adjoint (unbounded) operator and a self-adjoint operator such that
f(A+B)-f(A)-\frac{d}{dt}(f(A+tB))\big\vert_{t=0}\notin \mathcal S^1. $
Multistage Voting Model with Alternative Elimination
The voting process is formalized as a multistage voting model with successive
alternative elimination. A finite number of agents vote for one of the
alternatives each round subject to their preferences. If the number of votes
given to the alternative is less than a threshold, it gets eliminated from the
game. A special subclass of repeated games that always stop after a finite
number of stages is considered. Threshold updating rule is proposed. A computer
simulation is used to illustrate two properties of these voting games
A magnetic liquid deformable mirror for high stroke and low order axially symmetrical aberrations
We present a new class of magnetically shaped deformable liquid mirrors made
of a magnetic liquid (ferrofluid). Deformable liquid mirrors offer advantages
with respect to deformable solid mirrors: large deformations, low costs and the
possibility of very large mirrors with added aberration control. They have some
disadvantages (e.g. slower response time). We made and tested a deformable
mirror, producing axially symmetrical wavefront aberrations by applying
electric currents to 5 concentric coils made of copper wire wound on aluminum
cylinders. Each of these coils generates a magnetic field which combines to
deform the surface of a ferrofluid to the desired shape. We have carried out
laboratory tests on a 5 cm diameter prototype mirror and demonstrated defocus
as well as Seidel and Zernike spherical aberrations having amplitudes up to 20
microns, which was the limiting measurable amplitude of our equipmentComment: To appear in Optics Expres
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