472 research outputs found
Variational collocation for systems of coupled anharmonic oscillators
We have applied a collocation approach to obtain the numerical solution to
the stationary Schr\"odinger equation for systems of coupled oscillators. The
dependence of the discretized Hamiltonian on scale and angle parameters is
exploited to obtain optimal convergence to the exact results. A careful
comparison with results taken from the literature is performed, showing the
advantages of the present approach.Comment: 14 pages, 10 table
Solution to the Equations of the Moment Expansions
We develop a formula for matching a Taylor series about the origin and an
asymptotic exponential expansion for large values of the coordinate. We test it
on the expansion of the generating functions for the moments and connected
moments of the Hamiltonian operator. In the former case the formula produces
the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We
choose the harmonic oscillator and a strongly anharmonic oscillator as
illustrative examples for numerical test. Our results reveal some features of
the connected-moments expansion that were overlooked in earlier studies and
applications of the approach
Predicting extreme events in a data-driven model of turbulent shear flow using an atlas of charts
Dynamical systems with extreme events are difficult to capture with
data-driven modeling, due to the relative scarcity of data within extreme
events compared to the typical dynamics of the system, and the strong
dependence of the long-time occurrence of extreme events on short-time
conditions.A recently developed technique [Floryan, D. & Graham, M. D.
Data-driven discovery of intrinsic dynamics. Nat Mach Intell ,
1113-1120 (2022)], here denoted as , or CANDyMan, overcomes these difficulties
by decomposing the time series into separate charts based on data similarity,
learning dynamical models on each chart via individual time-mapping neural
networks, then stitching the charts together to create a single atlas to yield
a global dynamical model. We apply CANDyMan to a nine-dimensional model of
turbulent shear flow between infinite parallel free-slip walls under a
sinusoidal body force [Moehlis, J., Faisst, H. & Eckhardt, B. A low-dimensional
model for turbulent shear flows. New J Phys , 56 (2004)], which
undergoes extreme events in the form of intermittent quasi-laminarization and
long-time full laminarization. We demonstrate that the CANDyMan method allows
the trained dynamical models to more accurately forecast the evolution of the
model coefficients, reducing the error in the predictions as the model evolves
forward in time. The technique exhibits more accurate predictions of extreme
events, capturing the frequency of quasi-laminarization events and predicting
the time until full laminarization more accurately than a single neural
network.Comment: 9 pages, 7 figure
Colour superconductivity in finite systems
In this paper we study the effect of finite size on the two-flavour colour
superconducting state. As well as restricting the quarks to a box, we project
onto states of good baryon number and onto colour singlets, these being
necessary restrictions on any observable ``quark nuggets''. We find that
whereas finite size alone has a significant effect for very small boxes, with
the superconducting state often being destroyed, the effect of projection is to
restore it again. The infinite-volume limit is a good approximation even for
quite small systems.Comment: 14 pages RevTeX4, 12 eps figure
Chiral quark-soliton model in the Wigner-Seitz approximation
In this paper we study the modification of the properties of the nucleon in
the nucleus within the quark-soliton model. This is a covariant, dynamical
model, which provides a non-linear representation of the spontaneously broken
SU(2)_L X SU(2)_R symmetry of QCD. The effects of the nuclear medium are
accounted for by using the Wigner-Seitz approximation and therefore reducing
the complex many-body problem to a simpler single-particle problem. We find a
minimum in the binding energy at finite density, a change in the isoscalar
nucleon radius and a reduction of the in-medium pion decay constant. The latter
is consistent with a partial restoration of chiral symmetry at finite density,
which is predicted by other models.Comment: 30 pages, 13 figures; uses REVTeX and epsfi
Relativistic Hamiltonians in many-body theories
We discuss the description of a many-body nuclear system using Hamiltonians
that contain the nucleon relativistic kinetic energy and potentials with
relativistic corrections. Through the Foldy-Wouthuysen transformation, the
field theoretical problem of interacting nucleons and mesons is mapped to an
equivalent one in terms of relativistic potentials, which are then expanded at
some order in 1/m_N. The formalism is applied to the Hartree problem in nuclear
matter, showing how the results of the relativistic mean field theory can be
recovered over a wide range of densities.Comment: 14 pages, uses REVTeX and epsfig, 3 postscript figures; a postscript
version of the paper is available by anonymous ftp at
ftp://carmen.to.infn.it/pub/depace/papers/951
Deep venous thrombosis and abortion: an unusual clinical manifestation of severe form of pectus excavatum
Pectus excavatum is a chest wall malformation with a strong psychological and aesthetic impact. Rarely, pectus excavatum patients can show respiratory or cardiac symptoms occurring mainly during physical exertion. We report a case of a 34-year-old pregnant woman with a severe degree of pectus excavatum who developed serious cardiovascular disease resulting in spontaneous twin abortion at the twenty-first week of gestation. Cardiovascular disease was resolved after open surgical correction of pectus excavatum. This case shows how a tardive diagnosis and a delayed surgical approach for pectus excavatum can lead to severe consequences
Chiral phase properties of finite size quark droplets in the Nambu--Jona-Lasinio model
Chiral phase properties of finite size hadronic systems are investigated
within the Nambu--Jona-Lasinio model. Finite size effects are taken into
account by making use of the multiple reflection expansion. We find that, for
droplets with relatively small baryon numbers, chiral symmetry restoration is
enhanced by the finite size effects. However the radius of the stable droplet
does not change much, as compared to that without the multiple reflection
expansion.Comment: RevTex4, 9 pages, 6 figures, to be published in Phys. Rev.
Insights from Amphioxus into the Evolution of Vertebrate Cartilage
Central to the story of vertebrate evolution is the origin of the vertebrate head, a problem difficult to approach using paleontology and comparative morphology due to a lack of unambiguous intermediate forms. Embryologically, much of the vertebrate head is derived from two ectodermal tissues, the neural crest and cranial placodes. Recent work in protochordates suggests the first chordates possessed migratory neural tube cells with some features of neural crest cells. However, it is unclear how and when these cells acquired the ability to form cellular cartilage, a cell type unique to vertebrates. It has been variously proposed that the neural crest acquired chondrogenic ability by recruiting proto-chondrogenic gene programs deployed in the neural tube, pharynx, and notochord. To test these hypotheses we examined the expression of 11 amphioxus orthologs of genes involved in neural crest chondrogenesis. Consistent with cellular cartilage as a vertebrate novelty, we find that no single amphioxus tissue co-expresses all or most of these genes. However, most are variously co-expressed in mesodermal derivatives. Our results suggest that neural crest-derived cartilage evolved by serial cooption of genes which functioned primitively in mesoderm
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