193 research outputs found
Finite size effects in Neutron Star and Nuclear matter simulations
In this work we study molecular dynamics simulations of symmetric nuclear
matter using a semi-classical nucleon interaction model. We show that, at
sub-saturation densities and low temperatures, the solutions are
non-homogeneous structures reminiscent of the ``nuclear pasta'' phases expected
in Neutron Star Matter simulations, but shaped by artificial aspects of the
simulations. We explore different geometries for the periodic boundary
conditions imposed on the simulation cell: cube, hexagonal prism and truncated
octahedron. We find that different cells may yield different solutions for the
same physical conditions (i.e. density and temperature). The particular shape
of the solution at a given density can be predicted analytically by energy
minimization. We also show that even if this behavior is due to finite size
effects, it does not mean that it vanishes for very large systems and it
actually is independent of the system size: The system size sets the only
characteristic length scale for the inhomogeneities.
We then include a screened Coulomb interaction, as a model of Neutron Star
Matter, and perform simulations in the three cell geometries. In this case, the
competition between competing interactions of different range produces the well
known nuclear pasta, with (in most cases) several structures per cell. However,
we find that the results are affected by finite size in different ways
depending on the geometry of the cell. In particular, at the same physical
conditions and system size, the hexagonal prism yields a single structure per
cell while the cubic and truncated octahedron show consistent results with more
than one structure per cell. In this case, the results in every cell are
expected to converge for systems much larger than the characteristic length
scale that arises from the competing interactions.Comment: 17 pages, 10 figure
Isoscaling and the nuclear EOS
Experiments with rare isotopes are shedding light on the role isospin plays
in the equation of state (EoS) of nuclear matter, and isoscaling -an
straight-forward comparison of reactions with different isospin- could deliver
valuable information about it. In this work we test this assertion
pragmatically by comparing molecular dynamics simulations of isoscaling
reactions using different equations of state and looking for changes in the
isoscaling parameters; to explore the possibility of isoscaling carrying
information from the hot-and-dense stage of the reaction, we perform our study
in confined and expanding systems. Our results indicate that indeed isoscaling
can help us learn about the nuclear EoS, but only in some range of excitation
energies
Optomechanically induced transparency in membrane-in-the-middle setup at room temperature
We demonstrate the analogue of electromagnetically induced transparency in a
room temperature cavity optomechanics setup formed by a thin semitransparent
membrane within a Fabry-P\'erot cavity. Due to destructive interference, a weak
probe field is completely reflected by the cavity when the pump beam is
resonant with the motional red sideband of the cavity. Under this condition we
infer a significant slowing down of light of hundreds of microseconds, which is
easily tuned by shifting the membrane along the cavity axis. We also observe
the associated phenomenon of electromagnetically induced amplification which
occurs due to constructive interference when the pump is resonant with the blue
sideband.Comment: 5 pages, 4 figure
Topological characterization of neutron star crusts
Neutron star crusts are studied using a classical molecular dynamics model
developed for heavy ion reactions. After the model is shown to produce a
plethora of the so-called "pasta" shapes, a series of techniques borrowed from
nuclear physics, condensed matter physics and topology are used to craft a
method that can be used to characterize the shape of the pasta structures in an
unequivocal way
Optomechanical sideband cooling of a thin membrane within a cavity
We present an experimental study of dynamical back-action cooling of the
fundamental vibrational mode of a thin semitransparent membrane placed within a
high-finesse optical cavity. We study how the radiation pressure interaction
modifies the mechanical response of the vibrational mode, and the experimental
results are in agreement with a Langevin equation description of the coupled
dynamics. The experiments are carried out in the resolved sideband regime, and
we have observed cooling by a factor 350 We have also observed the mechanical
frequency shift associated with the quadratic term in the expansion of the
cavity mode frequency versus the effective membrane position, which is
typically negligible in other cavity optomechanical devices.Comment: 15 pages, 7 figure
Tunable linear and quadratic optomechanical coupling for a tilted membrane within an optical cavity: theory and experiment
We present an experimental study of an optomechanical system formed by a
vibrating thin semi-transparent membrane within a high-finesse optical cavity.
We show that the coupling between the optical cavity modes and the vibrational
modes of the membrane can be tuned by varying the membrane position and
orientation. In particular we demonstrate a large quadratic dispersive
optomechanical coupling in correspondence with avoided crossings between
optical cavity modes weakly coupled by scattering at the membrane surface. The
experimental results are well explained by a first order perturbation treatment
of the cavity eigenmodes.Comment: 10 pages, 6 figure
The Maximal Denumerant of a Numerical Semigroup
Given a numerical semigroup S = and n in S, we
consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >=
0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over
all such factorizations of n. We provide an algorithm for computing the maximum
number of maximal factorizations possible for an element in S, which is called
the maximal denumerant of S. We also consider various cases that have
connections to the Cohen-Macualay and Gorenstein properties of associated
graded rings for which this algorithm simplifies.Comment: 13 Page
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