65,972 research outputs found
On a conjecture about enumerating -free posets
Recently, Kitaev and Remmel posed a conjecture concerning the generating
function for the number of unlabeled -free posets with respect to number
of elements and number of minimal elements. In this paper, we present a
combinatorial proof of this conjecture
Anti-Swarming: Structure and Dynamics of Repulsive Chemically Active Particles
Chemically active Brownian particles with surface catalytic reactions may
repel each other due to diffusiophoretic interactions in the reaction and
product concentration fields. The system behavior can be described by a
`chemical' coupling parameter that compares the strength of
diffusiophoretic repulsion to Brownian motion, and by a mapping to the
classical electrostatic One Component Plasma (OCP) system. When confined to a
constant-volume domain, Body-Centered Cubic crystals spontaneously form from
random initial configurations when the repulsion is strong enough to overcome
Brownian motion. Face-Centered Cubic crystals may also be stable. The `melting
point' of the `liquid-to-crystal transition' occurs at for
both BCC and FCC lattices
Anisotropic swim stress in active matter with nematic order
Active Brownian Particles (ABPs) transmit a swim pressure to the container boundaries, where is the drag coefficient,
is the swim diffusivity and is the uniform bulk number density
far from the container walls. In this work we extend the notion of the
isotropic swim pressure to the anisotropic tensorial swim stress
, which is related to the
anisotropic swim diffusivity . We demonstrate this
relationship with ABPs that achieve nematic orientational order via a bulk
external field. The anisotropic swim stress is obtained analytically for dilute
ABPs in both 2D and 3D systems, and the anisotropy is shown to grow
exponentially with the strength of the external field. We verify that the
normal component of the anisotropic swim stress applies a pressure
on a wall
with normal vector , and, through Brownian dynamics simulations,
this pressure is shown to be the force per unit area transmitted by the active
particles. Since ABPs have no friction with a wall, the difference between the
normal and tangential stress components -- the normal stress difference --
generates a net flow of ABPs along the wall, which is a generic property of
active matter systems
The curved kinetic boundary layer of active matter
The finite reorient-time of swimmers leads to a finite run length and
the kinetic accumulation boundary layer on the microscopic length scale
on a non-penetrating wall. That boundary layer is the microscopic
origin of the swim pressure, and is impacted by the geometry of the boundary
[Yan \& Brady, \textit{J. Fluid. Mech.}, 2015, \textbf{785}, R1]. In this work
we extend the analysis to analytically solve the boundary layer on an
arbitrary-shaped body distorted by the local mean curvature. The solution gives
the swim pressure distribution and the total force (torque) on an arbitrarily
shaped body immersed in swimmers, with a general scaling of the curvature
effect
Growth mechanism of nanostructured superparamagnetic rods obtained by electrostatic co-assembly
We report on the growth of nanostructured rods fabricated by electrostatic
co-assembly between iron oxide nanoparticles and polymers. The nanoparticles
put under scrutiny, {\gamma}-Fe2O3 or maghemite, have diameter of 6.7 nm and
8.3 nm and narrow polydispersity. The co-assembly is driven by i) the
electrostatic interactions between the polymers and the particles, and by ii)
the presence of an externally applied magnetic field. The rods are
characterized by large anisotropy factors, with diameter 200 nm and length
comprised between 1 and 100 {\mu}m. In the present work, we provide for the
first time the morphology diagram for the rods as a function of ionic strength
and concentration. We show the existence of a critical nanoparticle
concentration and of a critical ionic strength beyond which the rods do not
form. In the intermediate regimes, only tortuous and branched aggregates are
detected. At higher concentrations and lower ionic strengths, linear and stiff
rods with superparamagnetic properties are produced. Based on these data, a
mechanism for the rod formation is proposed. The mechanism proceeds in two
steps : the formation and growth of spherical clusters of particles, and the
alignment of the clusters induced by the magnetic dipolar interactions. As far
as the kinetics of these processes is concerned, the clusters growth and their
alignment occur concomitantly, leading to a continuous accretion of particles
or small clusters, and a welding of the rodlike structure.Comment: 15 pages, 10 figures, one tabl
Diquark in Nona-quark States
We study the nonaquark states and which are reported
by KEK-PS (Phys.Lett. B597 (2004) 236; nucl-ex/0310018) by means of the quark
model with diquark correlation. The nonaquark states form
SU(3) multiplets.
The flavor wave functions of all the nonaquark states are constructed through
the standard tensor technique. The mass spectrum is studied by using
Gell-Mann-Okubo mass formula. Some nonaquark mass sum rules are obtained. We
further investigate the decay of and under the
assumption of "fall-apart" mechanism. It has been found that the main decay
mode is rather than which is consistent with
experiment. Also we have uniquely determine the flavor wave function of
which belong to -plet with the quantum number
. Whereas the exotic states can belong to either
-plet or -plet. In the exact limit, both and
belong to -plet with negative parity. We predict that its flavor
structure can be determined by measuring the branch fractions of its decay
channels. The experiments to check this prediction are expected.Comment: 23 pages, 8 figures, to appear in Phys. Rev.
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