1,342 research outputs found
New results related to a conjecture of Manickam and Singhi
In 1998 Manickam and Singhi conjectured that for every positive integer
and every , every set of real numbers whose sum is nonnegative
contains at least subsets of size whose sums are
nonnegative. In this paper we establish new results related to this conjecture.
We also prove that the conjecture of Manickam and Singhi does not hold for
Relaxation dynamics in fluids of platelike colloidal particles
The relaxation dynamics of a model fluid of platelike colloidal particles is
investigated by means of a phenomenological dynamic density functional theory.
The model fluid approximates the particles within the Zwanzig model of
restricted orientations. The driving force for time-dependence is expressed
completely by gradients of the local chemical potential which in turn is
derived from a density functional -- hydrodynamic interactions are not taken
into account. These approximations are expected to lead to qualitatively
reliable results for low densities as those within the isotropic-nematic
two-phase region. The formalism is applied to model an initially spatially
homogeneous stable or metastable isotropic fluid which is perturbed by
switching a two-dimensional array of Gaussian laser beams. Switching on the
laser beams leads to an accumulation of colloidal particles in the beam
centers. If the initial chemical potential and the laser power are large enough
a preferred orientation of particles occurs breaking the symmetry of the laser
potential. After switching off the laser beams again the system can follow
different relaxation paths: It either relaxes back to the homogeneous isotropic
state or it forms an approximately elliptical high-density core which is
elongated perpendicular to the dominating orientation in order to minimize the
surface free energy. For large supersaturations of the initial isotropic fluid
the high-density cores of neighboring laser beams of the two-dimensional array
merge into complex superstructures.Comment: low-resolution figures due to file size restrictions, revised versio
Nonequilibrium steady states in fluids of platelike colloidal particles
Nonequilibrium steady states in an open system connecting two reservoirs of
platelike colloidal particles are investigated by means of a recently proposed
phenomenological dynamic density functional theory [M. Bier and R. van Roij,
Phys. Rev. E 76, 021405 (2007)]. The platelike colloidal particles are
approximated within the Zwanzig model of restricted orientations, which
exhibits an isotropic-nematic bulk phase transition. Inhomogeneities of the
local chemical potential generate a diffusion current which relaxes to a
nonvanishing value if the two reservoirs coupled to the system sustain
different chemical potentials. The relaxation process of initial states towards
the steady state turns out to comprise two regimes: a smoothening of initial
steplike structures followed by an ultimate relaxation of the slowest diffusive
mode. The position of a nonequilibrium interface and the particle current of
steady states depend nontrivially on the structure of the reservoirs due to the
coupling between translational and orientational degrees of freedom of the
fluid
Self diffusion of particles in complex fluids: temporary cages and permanent barriers
We study the self diffusion of individual particles in dense (non-)uniform
complex fluids within dynamic density functional theory and explicitly account
for their coupling to the temporally fluctuating background particles. Applying
the formalism to rod-like particles in uniaxial nematic and smectic liquid
crystals, we find correlated diffusion in different directions: The temporary
cage formed by the neighboring particles competes with permanent barriers in
periodic inhomogeneous systems such as the lamellar smectic state and delays
self diffusion of particles even in uniform systems. We compare our theory with
recent experimental data on the self diffusion of fluorescently labelled
filamentous virus particles in aqueous dispersions in the smectic phase and
find qualitative agreement. This demonstrates the importance of explicitly
dealing with the time-dependent self-consistent molecular field that every
particle experiences.Comment: submitte
Passive Vaporizing Heat Sink
A passive vaporizing heat sink has been developed as a relatively lightweight, compact alternative to related prior heat sinks based, variously, on evaporation of sprayed liquids or on sublimation of solids. This heat sink is designed for short-term dissipation of a large amount of heat and was originally intended for use in regulating the temperature of spacecraft equipment during launch or re-entry. It could also be useful in a terrestrial setting in which there is a requirement for a lightweight, compact means of short-term cooling. This heat sink includes a hermetic package closed with a pressure-relief valve and containing an expendable and rechargeable coolant liquid (e.g., water) and a conductive carbon-fiber wick. The vapor of the liquid escapes when the temperature exceeds the boiling point corresponding to the vapor pressure determined by the setting of the pressure-relief valve. The great advantage of this heat sink over a melting-paraffin or similar phase-change heat sink of equal capacity is that by virtue of the =10x greater latent heat of vaporization, a coolant-liquid volume equal to =1/10 of the paraffin volume can suffice
Three and four current reversals versus temperature in correlation ratchets with a simple sawtooh potential
Transport of Brownian particles on a simple sawtooth potential subjected to
both unbiased thermal and nonequilibrium symmetric three-level Markovian noise
is considered. The new effects of three and four current reversals as a
function of temperature are established in such correlation ratchets. The
parameter space coordinates of the fixed points associated with these current
reversals and the necessary and sufficient conditions for the existence of the
novel current reversals are found.Comment: 4 pages, 5 figures; some changes introduced; accepted for publication
in Physical Review
DNA transport by a micromachined Brownian ratchet device
We have micromachined a silicon-chip device that transports DNA with a
Brownian ratchet that rectifies the Brownian motion of microscopic particles.
Transport properties for a DNA 50mer agree with theoretical predictions, and
the DNA diffusion constant agrees with previous experiments. This type of
micromachine could provide a generic pump or separation component for DNA or
other charged species as part of a microscale lab-on-a-chip. A device with
reduced feature size could produce a size-based separation of DNA molecules,
with applications including the detection of single nucleotide polymorphisms.Comment: Latex: 8 pages, 4 figure
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