7,931 research outputs found
Solitaire Clobber
Clobber is a new two-player board game. In this paper, we introduce the
one-player variant Solitaire Clobber where the goal is to remove as many stones
as possible from the board by alternating white and black moves. We show that a
checkerboard configuration on a single row (or single column) can be reduced to
about n/4 stones. For boards with at least two rows and two columns, we show
that a checkerboard configuration can be reduced to a single stone if and only
if the number of stones is not a multiple of three, and otherwise it can be
reduced to two stones. We also show that in general it is NP-complete to decide
whether an arbitrary Clobber configuration can be reduced to a single stone.Comment: 14 pages. v2 fixes small typ
Thermodynamics of nano-spheres encapsulated in virus capsids
We investigate the thermodynamics of complexation of functionalized charged
nano-spheres with viral proteins. The physics of this problem is governed by
electrostatic interaction between the proteins and the nano-sphere cores
(screened by salt ions), but also by configurational degrees of freedom of the
charged protein N-tails. We approach the problem by constructing an appropriate
complexation free energy functional. On the basis of both numerical and
analytical studies of this functional we construct the phase diagram for the
assembly which contains the information on the assembled structures that appear
in the thermodynamical equilibrium, depending on the size and surface charge
density of the nano-sphere cores. We show that both the nano-sphere core charge
as well as its radius determine the size of the capsid that forms around the
core.Comment: Submitte
Violent Relaxation of Indistinguishable Objects and Neutrino Hot Dark Matter in Clusters of Galaxies
The statistical mechanical investigation of violent relaxation (Lynden-Bell
1967) is extended to indistinguishable objects. It is found that,
coincidentally, the equilibrium distribution is the same as that obtained for
classical objects. For massive neutrinos, the Tremaine \& Gunn (1979) phase
space bound is revisited and reinterpretated as the limit indicating the onset
of degeneracy related to the coarse-grained phase space distribution. In the
context of one of the currently most popular cosmological models, the Cold and
Hot Dark Matter (CHDM) model (Primack et al. 1995), the onset of degeneracy may
be of importance in the core region of clusters of galaxies. Degeneracy allows
the neutrino HDM density to exceed the limit imposed by the Tremaine \& Gunn
(1979) bound while accounting for the phase space bound.Comment: AASTeX, 16 pages, 2 EPS figures, uses aas2pp4.sty. Accepted by ApJ
Letter
Attraction between Neutral Dielectrics Mediated by Multivalent Ions in an Asymmetric Ionic Fluid
We study the interaction between two neutral plane-parallel dielectric bodies
in the presence of a highly asymmetric ionic fluid, containing multivalent as
well as monovalent (salt) ions. Image charge interactions, due to dielectric
discontinuities at the boundaries, as well as effects from ion confinement in
the slit region between the surfaces are taken fully into account, leading to
image-generated depletion attraction, ion correlation attraction and
steric-like repulsive interactions. We investigate these effects by employing a
combination of methods including explicit-ion and implicit-ion Monte-Carlo
simulations, as well as an effective interaction potential analytical theory.
The latter incorporates strong ion-image charge correlations, which develop in
the presence of high valency ions in the mixture. We show that the implicit-ion
simulations and the proposed analytical theory can describe the explicit
simulation results on a qualitative level, while excellent quantitative
agreement can be obtained for sufficiently large monovalent salt
concentrations. The resultant attractive interaction between the neutral
surfaces is shown to be significant, as compared with the usual van der Waals
interactions between semi-infinite dielectrics, and can thus play a significant
role at the nano scale.Comment: 9 pages, 4 figure
Quenched Charge Disorder and Coulomb Interactions
We develop a general formalism to investigate the effect of quenched fixed
charge disorder on effective electrostatic interactions between charged
surfaces in a one-component (counterion-only) Coulomb fluid. Analytical results
are explicitly derived for two asymptotic and complementary cases: i)
mean-field or Poisson-Boltzmann limit (including Gaussian-fluctuations
correction), which is valid for small electrostatic coupling, and ii)
strong-coupling limit, where electrostatic correlations mediated by counterions
become significantly large as, for instance, realized in systems with
high-valency counterions. In the particular case of two apposed and ideally
polarizable planar surfaces with equal mean surface charge, we find that the
effect of the disorder is nil on the mean-field level and thus the plates
repel. In the strong-coupling limit, however, the effect of charge disorder
turns out to be additive in the free energy and leads to an enhanced long-range
attraction between the two surfaces. We show that the equilibrium inter-plate
distance between the surfaces decreases for elevated disorder strength (i.e.
for increasing mean-square deviation around the mean surface charge), and
eventually tends to zero, suggesting a disorder-driven collapse transition.Comment: 13 pages, 2 figure
Spectrally resolved single-shot wavefront sensing of broadband high-harmonic sources
Wavefront sensors are an important tool to characterize coherent beams of
extreme ultraviolet radiation. However, conventional Hartmann-type sensors do
not allow for independent wavefront characterization of different spectral
components that may be present in a beam, which limits their applicability for
intrinsically broadband high-harmonic generation (HHG) sources. Here we
introduce a wavefront sensor that measures the wavefronts of all the harmonics
in a HHG beam in a single camera exposure. By replacing the mask apertures with
transmission gratings at different orientations, we simultaneously detect
harmonic wavefronts and spectra, and obtain sensitivity to spatiotemporal
structure such as pulse front tilt as well. We demonstrate the capabilities of
the sensor through a parallel measurement of the wavefronts of 9 harmonics in a
wavelength range between 25 and 49 nm, with up to lambda/32 precision.Comment: 12 pages, 6 figure
Dissipative Hydrodynamics and Heavy Ion Collisions
Recent discussions of RHIC data emphasized the exciting possibility that the
matter produced in nucleus-nucleus collisions shows properties of a
near-perfect fluid. Here, we aim at delineating the applicability of fluid
dynamics, which is needed to quantify the size of corresponding dissipative
effects. We start from the equations for dissipative fluid dynamics, which we
derive from kinetic theory up to second order (Israel-Stewart theory) in a
systematic gradient expansion. In model studies, we then establish that for too
early initialization of the hydrodynamic evolution (\tau_0 \lsim 1 fm/c) or
for too high transverse momentum (p_T \gsim 1 GeV) in the final state, the
expected dissipative corrections are too large for a fluid description to be
reliable. Moreover, viscosity-induced modifications of hadronic transverse
momentum spectra can be accommodated to a significant degree in an ideal fluid
description by modifications of the decoupling stage. We argue that these
conclusions, drawn from model studies, can also be expected to arise in
significantly more complex, realistic fluid dynamics simulations of heavy ion
collisions.Comment: 18 pages, 5 figures, uses revtex4; v2: references added, typos
correcte
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