Input Admittance, Directivity and Quality Factor of Biconical Antenna of Arbitrary Cone Angle

New analytical expressions and numerical results for the quality factor and directivity as well as computationally convenient expressions for the input admittance of a symmetrical biconical antenna of arbitrary length $L$ and cone angle $\theta_0$ are presented. The quality factor for a wide-angle biconical antenna is shown to very closely approach the Chu's limit of $Q = (kL)^{-1}\{1+(kL)^{-2}\}$. Numerical calculations based on the analytical formula for antenna admittance confirm the conjecture that Foster's reactance theorem remains invalid even for perfectly conducting antennas. Furthermore, the variation of directivity of a wide-angle biconical antenna is a slowly varying function of its electrical length and is shown to depart significantly from that of a thin cylindrical dipole. <br>

Input Admittance, Directivity and Quality Factor of Biconical Antenna of Arbitrary Cone Angle

New analytical expressions and numerical results for the quality factor and directivity as well as computationally convenient expressions for the input admittance of a symmetrical biconical antenna of arbitrary length $L$ and cone angle $\theta_0$ are presented. The quality factor for a wide-angle biconical antenna is shown to very closely approach the Chu's limit of $Q = (kL)^{-1}\{1+(kL)^{-2}\}$. Numerical calculations based on the analytical formula for antenna admittance confirm the conjecture that Foster's reactance theorem remains invalid even for perfectly conducting antennas. Furthermore, the variation of directivity of a wide-angle biconical antenna is a slowly varying function of its electrical length and is shown to depart significantly from that of a thin cylindrical dipole. <br>

Rectifying curves and geodesics on a cone in the Euclidean 3-space

A twisted curve in the Euclidean 3-space $\mathbb E^3$ is called a rectifying curve if its position vector field always lie in its rectifying plane. In this article we study geodesics on an arbitrary cone in $\mathbb E^3$, not necessary a circular one, via rectifying curves. Our main result states that a curve on a cone in $\mathbb E^3$ is a geodesic if and only if it is either a rectifying curve or an open portion of a ruling. As an application we show that the only planar geodesics in a cone in $\mathbb E^3$ are portions of rulings.

Wicking of a liquid bridge connected to a moving porous surface

We study the coupled problem of a liquid bridge connected to a porous surface and an impermeable surface, where the gap between the surfaces is an externally controlled function of time. The relative motion between the surfaces influences the pressure distribution and geometry of the liquid bridge, thus affecting the shape of liquid penetration into the porous material. Utilizing the lubrication approximation and Darcy’s phenomenological law, we obtain an implicit integral relation between the relative motion between the surfaces and the shape of liquid penetration. A method to control the shape of liquid penetration is suggested and illustrated for the case of conical penetration shapes with an arbitrary cone opening angle. We obtain explicit analytic expressions for the case of constant relative speed of the surfaces as well as for the relative motion between the surfaces required to create conical penetration shapes. Our theoretical results are compared with experiments and reasonable agreement between the analytical and experimental data is observed.

On the theory of one-sided models in spaces with arbitrary cones

The paper presents a way of constructing quasimonotone nonautonomous systems ensuring x-stability of the nonautonomous system. There are described extensions quasimonotone with respect to an arbitrary cone, Perron condition and invariant surface stability under perturbations U-stability on the set of non wandering points is proved to imply u-stability of quasimonotone nonlinear system and exponential u-stability on minimal attraction center provides u-stability of the total systems Examples are available.

On a sufficient optimality condition over convex feasible regions

In this note a sufficient optimality condition is established for nonlinear programming problems over arbitrary cone domains. A Kuhn-Tucker type sufficient condition is established if the programming problem has a pseudoconvex objective function and a convex feasible region.