9,055 research outputs found
Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory
This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Stäckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems
Superintegrable Systems in Darboux spaces
Almost all research on superintegrable potentials concerns spaces of constant
curvature. In this paper we find by exhaustive calculation, all superintegrable
potentials in the four Darboux spaces of revolution that have at least two
integrals of motion quadratic in the momenta, in addition to the Hamiltonian.
These are two-dimensional spaces of nonconstant curvature. It turns out that
all of these potentials are equivalent to superintegrable potentials in complex
Euclidean 2-space or on the complex 2-sphere, via "coupling constant
metamorphosis" (or equivalently, via Staeckel multiplier transformations). We
present tables of the results
Printable Nanoscopic Metamaterial Absorbers and Images with Diffraction-Limited Resolution
The fabrication of functional metamaterials with extreme feature resolution
finds a host of applications such as the broad area of surface/light
interaction. Non-planar features of such structures can significantly enhance
their performance and tunability, but their facile generation remains a
challenge. Here, we show that carefully designed out-of-plane nanopillars made
of metal-dielectric composites integrated in a metal-dielectric-nanocomposite
configuration, can absorb broadband light very effectively. We further
demonstrate that electrohydrodynamic printing in a rapid nanodripping mode, is
able to generate precise out-of-plane forests of such composite nanopillars
with deposition resolutions at the diffraction limit on flat and non-flat
substrates. The nanocomposite nature of the printed material allows the
fine-tuning of the overall visible light absorption from complete absorption to
complete reflection by simply tuning the pillar height. Almost perfect
absorption (~95%) over the entire visible spectrum is achieved by a nanopillar
forest covering only 6% of the printed area. Adjusting the height of individual
pillar groups by design, we demonstrate on-demand control of the gray scale of
a micrograph with a spatial resolution of 400 nm. These results constitute a
significant step forward in ultra-high resolution facile fabrication of
out-of-plane nanostructures, important to a broad palette of light design
applications. nanostructures, important to a broad palette of light design
applications
Superintegrability in a two-dimensional space of nonconstant curvature
A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant (possibly zero) curvature when all the independent integrals are either quadratic or linear in the canonical momenta. In this article the first steps are taken to solve the problem of superintegrability of this type on an arbitrary curved manifold in two dimensions. This is done by examining in detail one of the spaces of revolution found by G. Koenigs. We determine that there are essentially three distinct potentials which when added to the free Hamiltonian of this space have this type of superintegrability. Separation of variables for the associated Hamilton–Jacobi and Schrödinger equations is discussed. The classical and quantum quadratic algebras associated with each of these potentials are determined
Targeting, deployment and loss-tolerance in Lanchester engagements
Existing Lanchester combat models focus on two force parameters: numbers (force size) and per-capita effectiveness (attrition rate). While these two parameters are central in projecting a battle’s outcome, there are other important factors that affect the battlefield: (1) targeting capability, the capacity to identify live enemy units and not dissipate fire on non-targets; (2) tactical restrictions preventing full deployment of forces; and (3) morale and tolerance of losses, the capacity to endure casualties. In the spirit of Lanchester theory, we derive, for the first time, force-parity equations for various combinations of these effects, and obtain general implications and trade-offs. We show that more units and better weapons (higher attrition rate) are preferred over improved targeting capability and relaxed deployment restrictions unless these are poor. However, when facing aimed fire and unable to deploy more than half one’s force it is better to be able to deploy more existing units than to have either additional reserve units or the same increase in attrition effectiveness. Likewise more relaxed deployment constraints are preferred over enhanced loss-tolerance when initial reserves are greater than the force level at which withdrawal occurs
Local estimates for entropy densities in coupled map lattices
We present a method to derive an upper bound for the entropy density of
coupled map lattices with local interactions from local observations. To do
this, we use an embedding technique being a combination of time delay and
spatial embedding. This embedding allows us to identify the local character of
the equations of motion. Based on this method we present an approximate
estimate of the entropy density by the correlation integral.Comment: 4 pages, 5 figures include
Orthogonal, solenoidal, three-dimensional vector fields for no-slip boundary conditions
Viscous fluid dynamical calculations require no-slip boundary conditions.
Numerical calculations of turbulence, as well as theoretical turbulence closure
techniques, often depend upon a spectral decomposition of the flow fields.
However, such calculations have been limited to two-dimensional situations.
Here we present a method that yields orthogonal decompositions of
incompressible, three-dimensional flow fields and apply it to periodic
cylindrical and spherical no-slip boundaries.Comment: 16 pages, 2 three-part figure
Thiol density dependent classical potential for methyl-thiol on a Au(111) surface
A new classical potential for methyl-thiol on a Au(111) surface has been
developed using density functional theory electronic structure calculations.
Energy surfaces between methyl-thiol and a gold surface were investigated in
terms of symmetry sites and thiol density. Geometrical optimization was
employed over all the configurations while minimum energy and thiol height were
determined. Finally, a new interatomic potential has been generated as a
function of thiol density, and applications to coarse-grained simulations are
presented
Harmonic lattice behavior of two-dimensional colloidal crystals
Using positional data from video-microscopy and applying the equipartition
theorem for harmonic Hamiltonians, we determine the wave-vector-dependent
normal mode spring constants of a two-dimensional colloidal model crystal and
compare the measured band-structure to predictions of the harmonic lattice
theory. We find good agreement for both the transversal and the longitudinal
mode. For , the measured spring constants are consistent with the
elastic moduli of the crystal.Comment: 4 pages, 3 figures, submitte
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