Finite conical electrodes, which are of particular interest as probes for imaging of surfaces using scanning electrochemical microscopy (SECM), in kinetic studies and in probing thin films were investigated. Theoretical SECM tip current-distance feedback (approach) curves for a finite conical electrode were calculated by numerical (finite element) analysis and compared to an earlier approximate...

To compare the mechanical effectiveness of a new conical screw design with a conventional cylindrical screw design, the screw insertion time, torque, and pull-out strength of single-pedicle screw and triangulated-pedicle screw constructs of each type of screw were compared in human cadaveric vertebral bodies. The time required to insert the conical screws was less than that required for cylindr...

We describe a natural decomposition of a normal complex surface singularity (X, 0) into its “thick” and “thin” parts. The former is essentially metrically conical, while the latter shrinks rapidly in thickness as it approaches the origin. The thin part is empty if and only if the singularity is metrically conical; the link of the singularity is then Seifert fibered. In general the thin part wil...

Presenting true crossings of adiabatic potential energy surfaces, conical intersections are a paradigm of ultrafast and efficient electronic relaxation dynamics. The same mechanism is shown to apply also for vibrational conical intersections, which may occur when two high-frequency modes (such as OH stretch vibrations) are coupled to low-frequency modes (such as hydrogen bonding modes). By deri...

We consider tessellations of the Euclidean (d− 1)-sphere by (d− 2)-dimensional great subspheres or, equivalently, tessellations of Euclidean d-space by hyperplanes through the origin; these we call conical tessellations. For random polyhedral cones defined as typical cones in a conical tessellation by random hyperplanes, and for their dual cones, we study expectations of certain geometric funct...

Estimating the intrinsic dimension of a high-dimensional data set is a very challenging problem in manifold learning and several other application areas in data mining. In this paper we introduce a novel local intrinsic dimension estimator, conical dimension, for estimating the intrinsic dimension of a data set consisting of points lying in the proximity of a manifold. Under minimal sampling as...

Conical polynomials are defined as certain polynomials in quadratic elements of the universal enveloping algebra of a semisimple symmetric Lie algebra over a field of characteristic zero. These polynomials were used in an earlier paper to describe the conical vectors in certain induced modules. Here it is shown that when the base field is extended to a certain type of nonassociative algebra, th...

We consider a class of semilinear elliptic problems in twoand three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Fréchet differentiable. Applying ...

The null geodesic equations in the Alcubierre warp drive spacetime are numerically integrated to determine the angular deflection and redshift of photons which propagate through the distortion of the “warp drive” bubble to reach an observer at the origin of the warp effect. We find that for a starship with an effective warp speed exceeding the speed of light, stars in the forward hemisphere wil...