13,876 research outputs found
Improved bounds on the set A(A+1)
For a subset A of a field F, write A(A + 1) for the set {a(b + 1):a,b\in A}.
We establish new estimates on the size of A(A+1) in the case where F is either
a finite field of prime order, or the real line.
In the finite field case we show that A(A+1) is of cardinality at least
C|A|^{57/56-o(1)} for some absolute constant C, so long as |A| < p^{1/2}. In
the real case we show that the cardinality is at least C|A|^{24/19-o(1)}. These
improve on the previously best-known exponents of 106/105-o(1) and 5/4
respectively
Stellarator bootstrap current and plasma flow velocity at low collisionality
The bootstrap current and flow velocity of a low-collisionality stellarator
plasma are calculated. As far as possible, the analysis is carried out in a
uniform way across all low-collisionality regimes in general stellarator
geometry, assuming only that the confinement is good enough that the plasma is
approximately in local thermodynamic equilibrium. It is found that conventional
expressions for the ion flow speed and bootstrap current in the
low-collisionality limit are accurate only in the -collisionality regime
and need to be modified in the -regime. The correction due to
finite collisionality is also discussed and is found to scale as
Probing the high-density behavior of symmetry energy with gravitational waves
Gravitational wave (GW) astronomy opens up an entirely new window on the
Universe to probe the equations of state (EOS) of neutron-rich matter. With the
advent of next generation GW detectors, measuring the gravitational radiation
from coalescing binary neutron star systems, mountains on rotating neutron
stars, and stellar oscillation modes may become possible in the near future.
Using a set of model EOSs satisfying the latest constraints from terrestrial
nuclear experiments, state of the art nuclear many-body calculations of the
pure neutron matter EOS, and astrophysical observations consistently, we study
various GW signatures of the high-density behavior of the nuclear symmetry
energy, which is considered among the most uncertain properties of dense
neutron-rich nucleonic matter. In particular, we find the tidal polarizability
of neutron stars, potentially measurable in binary systems just prior to
merger, is more sensitive to the high density component of the nuclear symmetry
energy than the symmetry energy at nuclear saturation density. We also find
that the upper limit on the GW strain amplitude from elliptically deformed
stars is very sensitive to the density dependence of the symmetry energy. This
suggests that future developments in modeling of the neutron star crust, and
direct gravitational wave signals from accreting binaries will provide a wealth
of information on the EOS of neutron-rich matter. We also review the
sensitivity of the -mode instability window to the density dependence of the
symmetry energy. Whereas models with larger values of the density slope of the
symmetry energy at saturation seem to be disfavored by the current
observational data, within a simple -mode model, we point out that a
subsequent softer behavior of the symmetry energy at high densities (hinted at
by recent observational interpretations) could rule them in.Comment: 14 pages, 11 figures, 3 tables; submitted to EPJA Special Volume on
Nuclear Symmetry Energ
Resonant conditions for Love wave guiding layer thickness
In this work we report a systematic investigation of polymer overlayer thickness in a Love wave device working at a fundamental frequency of 110MHz and at the 330MHz harmonic. At both frequencies we observe the initial reduction in insertion loss associated with a Love wave device. Significantly, we also observe a series of resonant conditions as the layer thickness is further increased. The separation of these resonances is attributed to an increase in thickness of half of the acoustic wavelength in the polymer
Quantum-state tomography for spin-l systems
We show that the density matrix of a spin-l system can be described entirely
in terms of the measurement statistics of projective spin measurements along a
minimum of 4l+1 different spin directions. It is thus possible to represent the
complete quantum statistics of any N-level system within the spherically
symmetric three dimensional space defined by the spin vector. An explicit
method for reconstructing the density matrix of a spin-1 system from the
measurement statistics of five non-orthogonal spin directions is presented and
the generalization to spin-l systems is discussed.Comment: 10 pages, including 2 tables, minor modifications in section II,
final version for publication in Phys. Rev.
Pulse mode operation of Love wave devices for biosensing applications
In this work we present a novel pulse mode Love wave biosensor that monitors both changes in amplitude and phase. A series of concentrations of 3350 molecular weight poly(ethylene glycol) (PEG) solutions are used as a calibration sequence for the pulse mode system using a network analyzer and high frequency oscilloscope. The operation of the pulse mode system is then compared to the continuous wave network analyzer by showing a sequence of deposition and removal of a model mass layer of palmitoyl-oleoyl-sn-glycerophosphocholine (POPC) vesicles. This experimental apparatus has the potential for making many hundreds of measurements a minute and so allowing the dynamics of fast interactions to be observed
Status and prospects of `bi-large' leptonic mixing
Bi-large patterns for the leptonic mixing matrix are confronted with current
neutrino oscillation data. We analyse the status of these patterns and
determine, through realistic simulations, the potential of upcoming
long-baseline experiment DUNE in testing bi-large \emph{ansatze} and
discriminating amongst them.Comment: 14 pages, 7 figures, numerical results refined, some more discussion
added. Matches published version of Phys. Let.
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