2,583 research outputs found
Combinatorial Games with a Pass: A dynamical systems approach
By treating combinatorial games as dynamical systems, we are able to address
a longstanding open question in combinatorial game theory, namely, how the
introduction of a "pass" move into a game affects its behavior. We consider two
well known combinatorial games, 3-pile Nim and 3-row Chomp. In the case of Nim,
we observe that the introduction of the pass dramatically alters the game's
underlying structure, rendering it considerably more complex, while for Chomp,
the pass move is found to have relatively minimal impact. We show how these
results can be understood by recasting these games as dynamical systems
describable by dynamical recursion relations. From these recursion relations we
are able to identify underlying structural connections between these "games
with passes" and a recently introduced class of "generic (perturbed) games."
This connection, together with a (non-rigorous) numerical stability analysis,
allows one to understand and predict the effect of a pass on a game.Comment: 39 pages, 13 figures, published versio
Glass state of superfluid 3He-A in aerogel
Glass states formed in the superfluid He confined in aerogel are
discussed. If the short range order corresponds to the A-phase state, the glass
state is nonsuperfluid in the long wave length limit. The superfluidity can be
restored by application of a small mass current. Transitions between the
superfluid and nonsuperfluid glass states can be triggered by small magnetic
field and by the change of the tipping angle of magnetization in NMR
experiments.Comment: 6 pages, LaTeX file, no figures, submitted to JETP Letter
Spin susceptibility of the superfluid He-B in aerogel
The temperature dependence of paramagnetic susceptibility of the superfluid
^{3}He-B in aerogel is found. Calculations have been performed for an arbitrary
phase shift of s-wave scattering in the framework of BCS weak coupling theory
and the simplest model of aerogel as an aggregate of homogeneously distributed
ordinary impurities. Both limiting cases of the Born and unitary scattering can
be easily obtained from the general result. The existence of gapless
superfluidity starting at the critical impurity concentration depending on the
value of the scattering phase has been demonstrated. While larger than in the
bulk liquid the calculated susceptibility of the B-phase in aerogel proves to
be conspicuously smaller than that determined experimentally in the high
pressure region.Comment: 10 pages, 4 figures, REVTe
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ranacapa: An R package and Shiny web app to explore environmental DNA data with exploratory statistics and interactive visualizations.
Environmental DNA (eDNA) metabarcoding is becoming a core tool in ecology and conservation biology, and is being used in a growing number of education, biodiversity monitoring, and public outreach programs in which professional research scientists engage community partners in primary research. Results from eDNA analyses can engage and educate natural resource managers, students, community scientists, and naturalists, but without significant training in bioinformatics, it can be difficult for this diverse audience to interact with eDNA results. Here we present the R package ranacapa, at the core of which is a Shiny web app that helps perform exploratory biodiversity analyses and visualizations of eDNA results. The app requires a taxonomy-by-sample matrix and a simple metadata file with descriptive information about each sample. The app enables users to explore the data with interactive figures and presents results from simple community ecology analyses. We demonstrate the value of ranacapa to two groups of community partners engaging with eDNA metabarcoding results
Universal Behaviour of the Superfluid Fraction and Tc of He-3 in 99.5% Open Aerogel
We have investigated the superfluid transition of He-3 in a 99.5% porosity
silica aerogel. This very dilute sample shows behaviour intermediary between
bulk He-3 and He-3 confined to the denser aerogels previously studied. We
present data on both the superfluid transition temperature and the superfluid
density and compare our results with previous measurements. Finally, we show
that the suppression of the superfluid transition temperature and suppression
of the superfluid density of He-3 in aerogel follow a universal relation for a
range of aerogel samples.Comment: 4 pages, 5 figures; 1 new figure, minor change
Heritable Characters in Maize: Accessory Blade
A mutant character in maize brings about the formation of ridge and blade-like outgrowths on the surfaces of leaves. These accessory laminae, which are present on the partially developed leaves in the dormant embryo, arise by re-activation of vertical zones on the immature leaf
Model of Inhomogeneous Impurity Distribution in Fermi Superfluids
The standard treatment of impurities in metals assumes a homogeneous
distribution of impurities. In this paper we study distributions that are
inhomogeneous. We discuss in detail the "isotropic inhomogeneous scattering
model" which takes into account the spatially varying scattering on the scale
of the superfluid coherence length. On a large scale the model reduces to a
homogeneous medium with renormalized parameter values. We apply the model to
superfluid 3He, where porous aerogel acts as the impurity. We calculate the
transition temperature Tc, the order parameter, and the superfluid density.
Both A- and B-like phases are considered. Two different types of behavior are
identified for the temperature dependence of the order parameter. We compare
the calculations with experiments on 3He in aerogel. We find that most of the
differences between experiments and the homogeneous theory can be explained by
the inhomogeneous model. All our calculations are based on the quasiclassical
theory of Fermi liquids. The parameters of this theory for superfluid 3He in
aerogel are discussed.Comment: 14 pages, 9 figures, minor change
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