Casimir energy of Sierpinski triangles

Using scaling arguments and the property of self-similarity we derive the Casimir energies of Sierpinski triangles and Sierpinski rectangles. The Hausdorff-Besicovitch dimension (fractal dimension) of the Casimir energy is introduced and the Berry-Weyl conjecture is discussed for these geometries. We propose that for a class of fractals, comprising of compartmentalized cavities, it is possible to establish a finite value to the Casimir energy even while the Casimir energy of the individual cavities consists of divergent terms.Comment: 7 pages, 5 figures, minor typos correcte

Analytical and Numerical Verification of the Nernst Theorem for Metals

In view of the current discussion on the subject, an effort is made to show very accurately both analytically and numerically how the Drude dispersion model gives consistent results for the Casimir free energy at low temperatures. Specifically, for the free energy near T=0 we find the leading term to be proportional to T^2 and the next-to-leading term proportional to T^{5/2}. These terms give rise to zero Casimir entropy as T approaches zero, and is thus in accordance with Nernst's theorem.Comment: 19 pages latex, 3 figures. v4: Figures updated. This is the final version, accepted for publication in Physical Review

Energy demand and yield enhancement for roof mounted photovoltaic snow mitigation systems

publishedVersio

Magnetic field inversions at 1 AU: comparisons between mapping predictions and observations

Large-scale magnetic field configurations are important for the transport of solar wind strahl electrons, which are suprathermal and directed along the field outward from the Sun. Strahl electrons are routinely used to infer not only the field configurations between the Sun and Earth but also local field structures, i.e., field inversions, where the magnetic field is locally folded back or inverted. Using solar wind data from ACE observations and a 2-D data-driven solar wind model with nonzero azimuthal magnetic field at the solar wind source surface, magnetic field lines are mapped between the Sun and Earth and beyond, in the solar equatorial plane. Standard verification metrics are used to assess, for five solar rotations at different phases of solar cycle 23, the performance of the mapping predictions for observed inversions, which are inferred from solar wind suprathermal electrons and magnetic fields measured by ACE. The probability of detection is consistently ≈0.70 across the different phases. The success ratio, the Hanssen-Kuipers skill score, and the Heidke skill score are ≈0.55–0.70 for the four rotations in the rising, solar maximum, and declining phases, but ≈0.35–0.60 for the rotation near solar minimum, during which almost half of the samples have undetermined field configurations. Our analyses confirm the persistence of inversions throughout solar cycle 23, suggest for most observed inversions a solar/coronal origin at the wind's source surface or below, and predict that inversions should be less common for larger heliocentric distance r ∼> 3 AU than for smaller r

Vanishing of Gravitational Particle Production in the Formation of Cosmic Strings

We consider the gravitationally induced particle production from the quantum vacuum which is defined by a free, massless and minimally coupled scalar field during the formation of a gauge cosmic string. Previous discussions of this topic estimate the power output per unit length along the string to be of the order of $10^{68}$ ergs/sec/cm in the s-channel. We find that this production may be completely suppressed. A similar result is also expected to hold for the number of produced photons.Comment: 10 pages, Plain LaTex. Minor improvements. To appear in PR

Casimir energy, dispersion, and the Lifshitz formula

Despite suggestions to the contrary, we show in this paper that the usual dispersive form of the electromagnetic energy must be used to derive the Lifshitz force between parallel dielectric media. This conclusion follows from the general form of the quantum vacuum energy, which is the basis of the multiple-scattering formalism. As an illustration, we explicitly derive the Lifshitz formula for the interaction between parallel dielectric semispaces, including dispersion, starting from the expression for the total energy of the system. The issues of constancy of the energy between parallel plates and of the observability of electrostrictive forces are briefly addressed.Comment: 11 pages, no figure

Ultrathin Metallic Coatings Can Induce Quantum Levitation between Nanosurfaces

There is an attractive Casimir-Lifshitz force between two silica surfaces in a liquid (bromobenze or toluene). We demonstrate that adding an ultrathin (5-50{\AA}) metallic nanocoating to one of the surfaces results in repulsive Casimir-Lifshitz forces above a critical separation. The onset of such quantum levitation comes at decreasing separations as the film thickness decreases. Remarkably the effect of retardation can turn attraction into repulsion. From that we explain how an ultrathin metallic coating may prevent nanoelectromechanical systems from crashing together.Comment: 4 pages, 5 figure

Retardation turns the van der Waals attraction into Casimir repulsion already at 3 nm

Casimir forces between surfaces immersed in bromobenzene have recently been measured by Munday et al. Attractive Casimir forces were found between gold surfaces. The forces were repulsive between gold and silica surfaces. We show the repulsion is due to retardation effects. The van der Waals interaction is attractive at all separations. The retardation driven repulsion sets in already at around 3 nm. To our knowledge retardation effects have never been found at such a small distance before. Retardation effects are usually associated with large distances