922 research outputs found
Grid-based Decorative Corners
Abstract I explore a space of geometric, decorative corner designs based on paths through a square grid. I discuss the problems of enumerating corners of a given size efficiently, and exploring them interactively in software. I then impose a higher-level connectivity constraint on corners and discuss the effect of this constraint on the mathematical and aesthetic properties of corner designs
A chiral aperiodic monotile
The recently discovered "hat" aperiodic monotile mixes unreflected and
reflected tiles in every tiling it admits, leaving open the question of whether
a single shape can tile aperiodically using translations and rotations alone.
We show that a close relative of the hat -- the equilateral member of the
continuum to which it belongs -- is a weakly chiral aperiodic monotile: it
admits only non-periodic tilings if we forbid reflections by fiat. Furthermore,
by modifying this polygon's edges we obtain a family of shapes called Spectres
that are strictly chiral aperiodic monotiles: they admit only chiral
non-periodic tilings based on a hierarchical substitution system.Comment: 23 pages, 12 figure
An aperiodic monotile
A longstanding open problem asks for an aperiodic monotile, also known as an
"einstein": a shape that admits tilings of the plane, but never periodic
tilings. We answer this problem for topological disk tiles by exhibiting a
continuum of combinatorially equivalent aperiodic polygons. We first show that
a representative example, the "hat" polykite, can form clusters called
"metatiles", for which substitution rules can be defined. Because the metatiles
admit tilings of the plane, so too does the hat. We then prove that generic
members of our continuum of polygons are aperiodic, through a new kind of
geometric incommensurability argument. Separately, we give a combinatorial,
computer-assisted proof that the hat must form hierarchical -- and hence
aperiodic -- tilings.Comment: 89 pages, 57 figures; Minor corrections, renamed "fylfot" to
"triskelion", added the name "turtle", added references, new H7/H8 rules (Fig
2.11), talk about reflection
Flavor Mediation Delivers Natural SUSY
If supersymmetry (SUSY) solves the hierarchy problem, then naturalness
considerations coupled with recent LHC bounds require non-trivial superpartner
flavor structures. Such "Natural SUSY" models exhibit a large mass hierarchy
between scalars of the third and first two generations as well as degeneracy
(or alignment) among the first two generations. In this work, we show how this
specific beyond the standard model (SM) flavor structure can be tied directly
to SM flavor via "Flavor Mediation". The SM contains an anomaly-free SU(3)
flavor symmetry, broken only by Yukawa couplings. By gauging this flavor
symmetry in addition to SM gauge symmetries, we can mediate SUSY breaking via
(Higgsed) gauge mediation. This automatically delivers a natural SUSY spectrum.
Third-generation scalar masses are suppressed due to the dominant breaking of
the flavor gauge symmetry in the top direction. More subtly, the
first-two-generation scalars remain highly degenerate due to a custodial U(2)
symmetry, where the SU(2) factor arises because SU(3) is rank two. This
custodial symmetry is broken only at order (m_c/m_t)^2. SUSY gauge coupling
unification predictions are preserved, since no new charged matter is
introduced, the SM gauge structure is unaltered, and the flavor symmetry treats
all matter multiplets equally. Moreover, the uniqueness of the anomaly-free
SU(3) flavor group makes possible a number of concrete predictions for the
superpartner spectrum.Comment: 17 pages, 7 figures, 2 tables. v2 references added, minor changes to
flavor constraints and a little discussion adde
The long-term evolution of the spin, pulse shape, and orbit of the accretion-powered millisecond pulsar SAX J1808.4-3658
We present a 7 yr timing study of the 2.5 ms X-ray pulsar SAX J1808.4-3658,
an X-ray transient with a recurrence time of ~2 yr, using data from the Rossi
X-ray Timing Explorer covering 4 transient outbursts (1998-2005). We verify
that the 401 Hz pulsation traces the spin frequency fundamental and not a
harmonic. Substantial pulse shape variability, both stochastic and systematic,
was observed during each outburst. Analysis of the systematic pulse shape
changes suggests that, as an outburst dims, the X-ray "hot spot" on the pulsar
surface drifts longitudinally and a second hot spot may appear. The overall
pulse shape variability limits the ability to measure spin frequency evolution
within a given X-ray outburst (and calls previous nudot measurements of this
source into question), with typical upper limits of |nudot| < 2.5x10^{-14} Hz/s
(2 sigma). However, combining data from all the outbursts shows with high (6
sigma) significance that the pulsar is undergoing long-term spin down at a rate
nudot = (-5.6+/-2.0)x10^{-16} Hz/s, with most of the spin evolution occurring
during X-ray quiescence. We discuss the possible contributions of magnetic
propeller torques, magnetic dipole radiation, and gravitational radiation to
the measured spin down, setting an upper limit of B < 1.5x10^8 G for the
pulsar's surface dipole magnetic field and and Q/I < 5x10^{-9} for the
fractional mass quadrupole moment. We also measured an orbital period
derivative of Pdot = (3.5+/-0.2)x10^{-12} s/s. This surprising large Pdot is
reminiscent of the large and quasi-cyclic orbital period variation observed in
the so-called "black widow" millisecond radio pulsars, supporting speculation
that SAX J1808.4-3658 may turn on as a radio pulsar during quiescence. In an
appendix we derive an improved (0.15 arcsec) source position from optical data.Comment: 22 pages, 10 figures; accepted for publication in Ap
SUSY Stops at a Bump
We discuss collider signatures of the "natural supersymmetry" scenario with
baryon-number violating R-parity violation. We argue that this is one of the
few remaining viable incarnations of weak scale supersymmetry consistent with
full electroweak naturalness. We show that this intriguing and challenging
scenario contains distinctive LHC signals, resonances of hard jets in
conjunction with relatively soft leptons and missing energy, which are easily
overlooked by existing LHC searches. We propose novel strategies for
distinguishing these signals above background, and estimate their potential
reach at the 8 TeV LHC. We show that other multi-lepton signals of this
scenario can be seen by currently existing searches with increased statistics,
but these opportunities are more spectrum-dependent.Comment: 23 pages, 7 figures, 3 tables. V2: spectrum discussion corrected,
most of the changes are in Sec. 2. Benchmarks, analysis and conclusions
unchanged. References adde
The X-ray Position and Optical Counterpart of the Accretion-Powered Millisecond Pulsar XTE J1814-338
We report the precise optical and X-ray localization of the 3.2 ms
accretion-powered X-ray pulsar XTE J1814-338 with data from the Chandra X-Ray
Observatory as well as optical observations conducted during the 2003 June
discovery outburst. Optical imaging of the field during the outburst of this
soft X-ray transient reveals an R = 18 star at the X-ray position. This star is
absent (R > 20) from an archival 1989 image of the field and brightened during
the 2003 outburst, and we therefore identify it as the optical counterpart of
XTE J1814-338. The best source position derived from optical astrometry is R.A.
= 18h13m39.s04, Dec.= -33d46m22.3s (J2000). The featureless X-ray spectrum of
the pulsar in outburst is best fit by an absorbed power-law (with photon index
= 1.41 +- 0.06) plus blackbody (with kT = 0.95 +- 0.13 keV) model, where the
blackbody component contributes approximately 10% of the source flux. The
optical broad-band spectrum shows evidence for an excess of infrared emission
with respect to an X-ray heated accretion disk model, suggesting a significant
contribution from the secondary or from a synchrotron-emitting region. A
follow-up observation performed when XTE J1814-338 was in quiescence reveals no
counterpart to a limiting magnitude of R = 23.3. This suggests that the
secondary is an M3 V or later-type star, and therefore very unlikely to be
responsible for the soft excess, making synchroton emission a more reasonable
candidate.Comment: Accepted for publication in ApJ. 6 pages; 3 figure
A Light Stop with Flavor in Natural SUSY
The discovery of a SM-like Higgs boson near 125 GeV and the flavor texture of
the Standard Model motivate the investigation of supersymmetric quiver-like BSM
extensions. We study the properties of such a minimal class of models which
deals naturally with the SM parameters. Considering experimental bounds as well
as constraints from flavor physics and Electro-Weak Precision Data, we find the
following. In a self-contained minimal model - including the full dynamics of
the Higgs sector - top squarks below a TeV are in tension with b->s{\gamma}
constraints. Relaxing the assumption concerning the mass generation of the
heavy Higgses, we find that a stop not far from half a TeV is allowed. The
models have some unique properties, e.g. an enhancement of the h->
b\bar{b},\tau\bar{{\tau}} decays relative to the h->\gamma{\gamma} one, a
gluino about 3 times heavier than the stop, an inverted hierarchy of about 3-20
between the squarks of the first two generations and the stop, relatively light
Higgsino neutralino or stau NLSP, as well as heavy Higgses and a W' which may
be within reach of the LHC.Comment: LaTeX, 22 pages, 4 figures; V2: references adde
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