33,090 research outputs found
Lower Bounds for Electrical Reduction on Surfaces
We strengthen the connections between electrical transformations and homotopy from the planar setting - observed and studied since Steinitz - to arbitrary surfaces with punctures. As a result, we improve our earlier lower bound on the number of electrical transformations required to reduce an n-vertex graph on surface in the worst case [SOCG 2016] in two different directions. Our previous Omega(n^{3/2}) lower bound applies only to facial electrical transformations on plane graphs with no terminals. First we provide a stronger Omega(n^2) lower bound when the planar graph has two or more terminals, which follows from a quadratic lower bound on the number of homotopy moves in the annulus. Our second result extends our earlier Omega(n^{3/2}) lower bound to the wider class of planar electrical transformations, which preserve the planarity of the graph but may delete cycles that are not faces of the given embedding. This new lower bound follow from the observation that the defect of the medial graph of a planar graph is the same for all its planar embeddings
Stored energies for electric and magnetic current densities
Electric and magnetic current densities are an essential part of
electromagnetic theory. The goal of the present paper is to define and
investigate stored energies that are valid for structures that can support both
electric and magnetic current densities. Stored energies normalized with the
dissipated power give us the Q factor, or antenna Q, for the structure. Lower
bounds of the Q factor provide information about the available bandwidth for
passive antennas that can be realized in the structure. The definition that we
propose is valid beyond the leading order small antenna limit. Our starting
point is the energy density with subtracted far-field form which we obtain an
explicit and numerically attractive current density representation. This
representation gives us the insight to propose a coordinate independent stored
energy. Furthermore, we find here that lower bounds on antenna Q for structures
with e.g. electric dipole radiation can be formulated as convex optimization
problems. We determine lower bounds on both open and closed surfaces that
support electric and magnetic current densities.
The here derived representation of stored energies has in its electrical
small limit an associated Q factor that agrees with known small antenna bounds.
These stored energies have similarities to earlier efforts to define stored
energies. However, one of the advantages with this method is the above
mentioned formulation as convex optimization problems, which makes it easy to
predict lower bounds for antennas of arbitrary shapes. The present formulation
also gives us insight into the components that contribute to Chu's lower bound
for spherical shapes. We utilize scalar and vector potentials to obtain a
compact direct derivation of these stored energies. Examples and comparisons
end the paper.Comment: Minor updates to figures and tex
Stored energies in electric and magnetic current densities for small antennas
Electric and magnetic currents are essential to describe electromagnetic
stored energy, as well as the associated quantities of antenna Q and the
partial directivity to antenna Q-ratio, D/Q, for general structures. The upper
bound of previous D/Q-results for antennas modeled by electric currents is
accurate enough to be predictive, this motivates us here to extend the analysis
to include magnetic currents. In the present paper we investigate antenna Q
bounds and D/Q-bounds for the combination of electric- and magnetic-currents,
in the limit of electrically small antennas. This investigation is both
analytical and numerical, and we illustrate how the bounds depend on the shape
of the antenna. We show that the antenna Q can be associated with the largest
eigenvalue of certain combinations of the electric and magnetic polarizability
tensors. The results are a fully compatible extension of the electric only
currents, which come as a special case. The here proposed method for antenna Q
provides the minimum Q-value, and it also yields families of minimizers for
optimal electric and magnetic currents that can lend insight into the antenna
design.Comment: 27 pages 7 figure
Optimal Design of IPM Motors With Different Cooling Systems and Winding Configurations
Performance improvement of permanent magnet (PM) motors through optimization techniques has been widely investigated in the literature. Oftentimes the practice of design optimization leads to derivation/interpretation of optimal scaling rules of PM motors for a particular loading condition. This paper demonstrates how these derivations vary with respect to the machine ampere loading and ferrous core saturation level. A parallel sensitivity analysis using a second-order response surface methodology followed by a large-scale design optimization based on evolutionary algorithms are pursued in order to establish the variation of the relationships between the main design parameters and the performance characteristics with respect to the ampere loading and magnetic core saturation levels prevalent in the naturally cooled, fan-cooled, and liquid-cooled machines. For this purpose, a finite-element-based platform with a full account of complex geometry, magnetic core nonlinearities, and stator and rotor losses is used. Four main performance metrics including active material cost, power losses, torque ripple, and rotor PM demagnetization are investigated for two generic industrial PM motors with distributed and concentrated windings with subsequent conclusions drawn based on the results
Fundamental bounds on transmission through periodically perforated metal screens with experimental validation
This paper presents a study of transmission through arrays of periodic
sub-wavelength apertures. Fundamental limitations for this phenomenon are
formulated as a sum rule, relating the transmission coefficient over a
bandwidth to the static polarizability. The sum rule is rigorously derived for
arbitrary periodic apertures in thin screens. By this sum rule we establish a
physical bound on the transmission bandwidth which is verified numerically for
a number of aperture array designs. We utilize the sum rule to design and
optimize sub-wavelength frequency selective surfaces with a bandwidth close to
the physically attainable. Finally, we verify the sum rule and simulations by
measurements of an array of horseshoe-shaped slots milled in aluminum foil.Comment: 10 pages, 11 figures. Updated Introduction and Conclusion
Dissipation Factors of Spherical Current Modes on Multiple Spherical Layers
Radiation efficiencies of modal current densities distributed on a spherical
shell are evaluated in terms of dissipation factor. The presented approach is
rigorous, yet simple and straightforward, leading to closed-form expressions.
The same approach is utilized for a two-layered shell and the results are
compared with other models existing in the literature. Discrepancies in this
comparison are reported and reasons are analyzed. Finally, it is demonstrated
that radiation efficiency potentially benefits from the use of internal volume
which contrasts with the case of the radiation Q-factor.Comment: 5 pages, 5 figure
Wetting, roughness and flow boundary conditions
We discuss how the wettability and roughness of a solid impacts its
hydrodynamic properties. We see in particular that hydrophobic slippage can be
dramatically affected by the presence of roughness. Owing to the development of
refined methods for setting very well-controlled micro- or nanotextures on a
solid, these effects are being exploited to induce novel hydrodynamic
properties, such as giant interfacial slip, superfluidity, mixing, and low
hydrodynamic drag, that could not be achieved without roughness.Comment: 28 pages, 14 figures, 4 tables; accepted for publication in Journal
of Physics: Condensed Matte
Mathematical modelling of the catalyst layer of a polymer-electrolyte fuel cell
In this paper we derive a mathematical model for the cathode catalyst layer of a polymer electrolyte fuel cell. The model explicitly incorporates the restriction placed on oxygen in reaching the reaction sites, capturing the experimentally observed fall in the current density to a limiting value at low cell voltages. Temperature variations and interfacial transfer of O2 between the dissolved and gas phases are also included. Bounds on the solutions are derived, from which we provide a rigorous proof that the model admits a solution. Of particular interest are the maximum and minimum attainable values. We perform an asymptotic analysis in several limits inherent in the problem by identifying important groupings of parameters. This analysis reveals a number of key relationships between the solutions, including the current density, and the composition of the layer. A comparison of numerically computed and asymptotic solutions shows very good agreement. Implications of the results are discussed and future work is outlined
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