2,830 research outputs found
Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians
The quartic H\'enon-Heiles Hamiltonian passes the Painlev\'e test for
only four sets of values of the constants. Only one of these, identical to the
traveling wave reduction of the Manakov system, has been explicitly integrated
(Wojciechowski, 1985), while the three others are not yet integrated in the
generic case . We integrate them by building
a birational transformation to two fourth order first degree equations in the
classification (Cosgrove, 2000) of such polynomial equations which possess the
Painlev\'e property. This transformation involves the stationary reduction of
various partial differential equations (PDEs). The result is the same as for
the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases,
a general solution which is meromorphic and hyperelliptic with genus two. As a
consequence, no additional autonomous term can be added to either the cubic or
the quartic Hamiltonians without destroying the Painlev\'e integrability
(completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200
On reductions of some KdV-type systems and their link to the quartic He'non-Heiles Hamiltonian
A few 2+1-dimensional equations belonging to the KP and modified KP
hierarchies are shown to be sufficient to provide a unified picture of all the
integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.Comment: 12 pages, 3 figures, NATO ARW, 15-19 september 2002, Elb
Boundary theories of critical matchgate tensor networks
Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states whose site-averaged ground state properties match the translation-invariant critical Ising model. In this work, we substantially sharpen this relationship by deriving disordered local Hamiltonians generalizing the critical Ising model whose ground and low-energy excited states are accurately represented by the matchgate ansatz without any averaging. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model based on layers of the hyperbolic lattice, breaking the conformal symmetries of the critical Ising model in a controlled manner. We provide a direct identification of correlation functions of ground and low-energy excited states between the disordered and translation-invariant models and give numerical evidence that the former approaches the latter in the large bond dimension limit. This establishes tensor networks on regular hyperbolic tilings as an effective tool for the study of conformal field theories. Furthermore, our numerical probes of the bulk parameters corresponding to boundary excited states constitute a first step towards a tensor network bulk-boundary dictionary between regular hyperbolic geometries and critical boundary states
The challenge of new gatekeepers for public relations:A comparative analysis of the role of social media influencers for European and Latin American professionals
Theory and particle tracking simulations of a resonant radiofrequency deflection cavity in TM mode for ultrafast electron microscopy
We present a theoretical description of resonant radiofrequency (RF)
deflecting cavities in TM mode as dynamic optical elements for
ultrafast electron microscopy. We first derive the optical transfer matrix of
an ideal pillbox cavity and use a Courant-Snyder formalism to calculate the 6D
phase space propagation of a Gaussian electron distribution through the cavity.
We derive closed, analytic expressions for the increase in transverse emittance
and energy spread of the electron distribution. We demonstrate that for the
special case of a beam focused in the center of the cavity, the low emittance
and low energy spread of a high quality beam can be maintained, which allows
high-repetition rate, ultrafast electron microscopy with 100 fs temporal
resolution combined with the atomic resolution of a high-end TEM. This is
confirmed by charged particle tracking simulations using a realistic cavity
geometry, including fringe fields at the cavity entrance and exit apertures
Materials science experiments in space
The criteria for the selection of the experimental areas and individual experiments were that the experiment or area must make a meaningful contribution to the field of material science and that the space environment was either an absolute requirement for the successful execution of the experiment or that the experiment can be more economically or more conveniently performed in space. A number of experimental areas and individual experiments were recommended for further consideration as space experiments. Areas not considered to be fruitful and others needing additional analysis in order to determine their suitability for conduct in space are also listed. Recommendations were made concerning the manner in which these materials science experiments are carried out and the related studies that should be pursued
Germ-furrow morphology and storage conditions determine the degree of viability of Pinus caribaea pollen
This study has found a correlation between Pinus caribaea pollen morphology and viability. Eighteen different P. caribaea pollen families were screened to determine the effect of environmental conditions during storage on germination. The results indicated that there was a direct decrease in viability with an increase in the age of the pollen, temperature at which the pollen was stored, and exposure to high humidity during storage. Scanning electron microscopy was used to investigate the dimensions of the 18 families. Upon statistical analysis of the dimensional data, the families were found to group into three clusters. Pollen families displaying narrow germ furrows clustered with those displaying wide germ furrows, while those pollen families displaying intermediate germ furrows clustered into a second group. When the clusters were compared with the germination data obtained it was found that the pollen families displaying highest germination percentages fell into the intermediate cluster, while the pollen families displaying low to intermediate germination percentages fell into the narrow/wide cluster
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