Search

We report on the discovery and validation of a transiting long-period mini-Neptune orbiting a bright (V = 9.0 mag) G dwarf (TOI 4633; R = 1.05 RSun, M = 1.10 MSun). The planet was identified in data from the Transiting Exoplanet Survey Satellite by citizen scientists taking part in the Planet Hunters TESS project. Modeling of the transit events yields an orbital period of 271.9445 +/- 0.0040 days and radius of 3.2 +/- 0.20 REarth. The Earth-like orbital period and an incident flux of 1.56 +/- 0.2 places it in the optimistic habitable zone around the star. Doppler spectroscopy of the system allowed us to place an upper mass limit on the transiting planet and revealed a non-transiting planet candidate in the system with a period of 34.15 +/- 0.15 days. Furthermore, the combination of archival data dating back to 1905 with new high angular resolution imaging revealed a stellar companion orbiting the primary star with an orbital period of around 230 years and an eccentricity of about 0.9. The long period of the transiting planet, combined with the high eccentricity and close approach of the companion star makes this a valuable system for testing the formation and stability of planets in binary systems., Comment: 24 pages, 16 figures, 4 tables

We present the Citizen Science program Active Asteroids and describe discoveries stemming from our ongoing project. Our NASA Partner program is hosted on the Zooniverse online platform and launched on 2021 August 31, with the goal of engaging the community in the search for active asteroids -- asteroids with comet-like tails or comae. We also set out to identify other unusual active solar system objects, such as active Centaurs, active quasi-Hilda asteroids, and Jupiter-family comets (JFCs). Active objects are rare in large part because they are difficult to identify, so we ask volunteers to assist us in searching for active bodies in our collection of millions of images of known minor planets. We produced these cutout images with our project pipeline that makes use of publicly available Dark Energy Camera (DECam) data. Since the project launch, roughly 8,300 volunteers have scrutinized some 430,000 images to great effect, which we describe in this work. In total we have identified previously unknown activity on 15 asteroids, plus one Centaur, that were thought to be asteroidal (i.e., inactive). Of the asteroids, we classify four as active quasi-Hilda asteroids, seven as JFCs, and four as active asteroids, consisting of one Main-belt comet (MBC) and three MBC candidates. We also include our findings concerning known active objects that our program facilitated, an unanticipated avenue of scientific discovery. These include discovering activity occurring during an orbital epoch for which objects were not known to be active, and the reclassification of objects based on our dynamical analyses., Comment: 35 pages, 5 figures, 3 tables

We have discovered two epochs of activity on quasi-Hilda 2009 DQ118. Small bodies that display comet-like activity, such as active asteroids and active quasi-Hildas, are important for understanding the distribution of water and other volatiles throughout the solar system. Through our NASA Partner Citizen Science project, Active Asteroids, volunteers classified archival images of 2009 DQ118 as displaying comet-like activity. By performing an in-depth archival image search, we found over 20 images from UT 2016 March 8--9 with clear signs of a comet-like tail. We then carried out follow-up observations of 2009 DQ118 using the 3.5 m Astrophysical Research Consortium Telescope at Apache Point Observatory, Sunspot, New Mexico, USA and the 6.5 m Magellan Baade Telescope at Las Campanas Observatory, Chile. These images revealed a second epoch of activity associated with the UT 2023 April 22 perihelion passage of 2009 DQ118. We performed photometric analysis of the tail and find that it had a similar apparent length and surface brightness during both epochs. We also explored the orbital history and future of 2009 DQ118 through dynamical simulations. These simulations show that 2009 DQ118 is currently a quasi-Hilda and that it frequently experiences close encounters with Jupiter. We find that 2009 DQ118 is currently on the boundary between asteroidal and cometary orbits. Additionally, it has likely been a Jupiter family comet or Centaur for much of the past 10 kyr and will be in these same regions for the majority of the next 10 kyr. Since both detected epochs of activity occurred near perihelion, the observed activity is consistent with sublimation of volatile ices. 2009 DQ118 is currently observable until ~mid-October 2023. Further observations would help to characterize the observed activity., Comment: 10 pages, 3 figures

We announce the discovery of a main-belt comet (MBC), 2010 LH15 (alternately designated 2010 TJ175). MBCs are a rare type of main-belt asteroid that display comet-like activity, such as tails or comae, caused by sublimation. Consequently, MBCs help us map the location of solar system volatiles, providing insight into the origins of material prerequisite for life as we know it. However, MBCs have proven elusive, with fewer than 20 found among the 1.1 million known main-belt asteroids. This finding derives from Active Asteroids, a NASA Partner Citizen Science program we designed to identify more of these important objects. After volunteers classified an image of 2010 LH15 as showing activity, we carried out a follow-up investigation which revealed evidence of activity from two epochs spanning nearly a decade. This discovery is timely, with 2010 LH15 inbound towards its 2024 March perihelion passage, with potential activity onset as early as late 2023., Comment: 4 pages, 1 figure

We announce the discovery of activity, in the form of a distinct cometary tail, emerging from main-belt asteroid 2015 VA108. Activity was first identified by volunteers of the Citizen Science project Active Asteroids (a NASA Partner). We uncovered one additional image from the same observing run which also unambiguously shows 2015 VA108 with a tail oriented between the anti-solar and anti-motion vectors that are often correlated with activity orientation on sky. Both publicly available archival images were originally acquired UT 2015 October 11 with the Dark Energy Camera (DECam) on the Blanco 4 m telescope at the Cerro Tololo Inter-American Observatory (Chile) as part of the Dark Energy Camera Legacy Survey. Activity occurred near perihelion and, combined with its residence in the main asteroid belt, 2015 VA108 is a candidate main-belt comet, an active asteroid subset known for volatile sublimation., Comment: 4 pages, 1 figure

We present the discovery of activity emanating from main-belt asteroid 2015 FW412, a finding stemming from the Citizen Science project Active Asteroids, a NASA Partner program. We identified a pronounced tail originating from 2015 FW412 and oriented in the anti-motion direction in archival Blanco 4-m (Cerro Tololo Inter-American Observatory, Chile) Dark Energy Camera (DECam) images from UT 2015 April 13, 18, 19, 21 and 22. Activity occurred near perihelion, consistent with the main-belt comets (MBCs), an active asteroid subset known for sublimation-driven activity in the main asteroid belt; thus 2015 FW412 is a candidate MBC. We did not detect activity on UT 2021 December 12 using the Inamori-Magellan Areal Camera and Spectrograph (IMACS) on the 6.5 m Baade telescope, when 2015 FW412 was near aphelion., Comment: 4 pages, 1 figure

Last year, we reported a perturbative theory of the Casimir-Lifshitz torque between planar biaxially anisotropic materials in the retarded limit [Phys. Rev. Lett. {\bf 120}, 131601 (2018)], which is applied here to study the change of sign and magnitude of the torque with separation distance in biaxial black phosphorus having excess charge carriers. The study is carried out both in vacuum as well as in a background fluid medium. The presence of extra charge carriers and that of an intervening fluid medium are both found to promote enhancement of the magnitude of the torque between identical slabs. The degree of enhancement of the magnitude of torque increases not only with an increased carrier concentration but also with separation distance. In the non-identical case when different planes of anisotropic black phosphorus face each other, owing to the non-monotonic characteristic of the sign-reversal effect of the torque, the enhancement by carrier addition and intervening medium also becomes non-monotonic with distance. In the presence of a background medium, the non-monotonic degree of enhancement of the torque with distance is observed even between identical slabs.

The Disk Detective citizen science project recently released a new catalog of disk candidates found by visual inspection of images from NASA's Wide-Field Infrared Survey Explorer (WISE) mission and other surveys. We applied this new catalog of well-vetted disk candidates to search for new members of nearby young stellar associations (YSAs) using a novel technique based on Gaia data and virtual reality (VR). We examined AB Doradus, Argus, $\beta$ Pictoris, Carina, Columba, Octans-Near, Tucana-Horologium, and TW Hya by displaying them in VR together with other nearby stars, color-coded to show infrared excesses found via Disk Detective. Using this method allows us to find new association members in mass regimes where isochrones are degenerate. We propose ten new YSA members with infrared excesses: three of AB Doradus (HD 44775, HD 40540 and HD 44510), one of $\beta$ Pictoris (HD 198472), two of Octans-Near (HD 157165 and BD+35 2953), and four disk-hosting members of a combined population of Carina, Columba and Tucana-Horologium: CPD-57 937, HD 274311, HD 41992, and WISEA J092521.90-673224.8. This last object (J0925) appears to be an extreme debris disk with a fractional infrared luminosity of $3.7 \times 10^{-2}$. We also propose two new members of AB Doradus that do not show infrared excesses: TYC 6518-1857-1 and CPD-25 1292. We find HD 15115 appears to be a member of Tucana-Horologium rather than $\beta$ Pictoris. We advocate for membership in Columba-Carina of HD 30447, CPD-35 525, and HD 35841. Finally, we propose that three M dwarfs, previously considered members of Tuc-Hor are better considered a separate association, tentatively called ``Smethells 165''., Comment: 26 pages; 17 figures, 3 tables. Accepted for publication in AAS Journals

WISEA J080822.18-644357.3, an M star in the Carina association, exhibits extreme infrared excess and accretion activity at an age greater than the expected accretion disk lifetime. We consider J0808 as the prototypical example of a class of M star accretion disks at ages $\gtrsim 20$ Myr, which we call ``Peter Pan'' disks, since they apparently refuse to grow up. We present four new Peter Pan disk candidates identified via the Disk Detective citizen science project, coupled with \textit{Gaia} astrometry. We find that WISEA J044634.16-262756.1 and WISEA J094900.65-713803.1 both exhibit significant infrared excess after accounting for nearby stars within the 2MASS beams. The J0446 system has $>95\%$ likelihood of Columba membership. The J0949 system shows $>95\%$ likelihood of Carina membership. We present new GMOS optical spectra of all four objects, showing possible accretion signatures on all four stars. We present ground-based and \textit{TESS} lightcurves of J0808 and 2MASS J0501-4337, including a large flare and aperiodic dipping activity on J0808, and strong periodicity on J0501. We find Pa$\beta$ and Br$\gamma$ emission indicating ongoing accretion in near-IR spectroscopy of J0808. Using observed characteristics of these systems, we discuss mechanisms that lead to accretion disks at ages $\gtrsim20$ Myr, and find that these objects most plausibly represent long-lived CO-poor primordial disks, or ``hybrid'' disks, exhibiting both debris- and primordial-disk features. The question remains: why have gas-rich disks persisted so long around these particular stars?, Comment: 25 pages, 17 figures. Accepted for publication in the Astrophysical Journal

The Disk Detective citizen science project aims to find new stars with excess 22-$\mu$m emission from circumstellar dust in the AllWISE data release from the Wide-field Infrared Survey Explorer (WISE). We evaluated 261 Disk Detective objects of interest with imaging with the Robo-AO adaptive optics instrument on the 1.5m telescope at Palomar Observatory and with RetroCam on the 2.5m du Pont telescope at Las Campanas Observatory to search for background objects at 0.15''-12'' separations from each target. Our analysis of these data lead us to reject 7% of targets. Combining this result with statistics from our online image classification efforts implies that at most $7.9\% \pm 0.2\%$ of AllWISE-selected infrared excesses are good disk candidates. Applying our false positive rates to other surveys, we find that the infrared excess searches of McDonald et al. (2012), McDonald et al. (2017), and Marton et al. (2016) all have false positive rates $>70\%$. Moreover, we find that all thirteen disk candidates in Theissen & West (2014) with W4 signal-to-noise >3 are false positives. We present 244 disk candidates that have survived vetting by follow-up imaging. Of these, 213 are newly-identified disk systems. Twelve of these are candidate members of comoving pairs based on \textit{Gaia} astrometry, supporting the hypothesis that warm dust is associated with binary systems. We also note the discovery of 22 $\mu$m excess around two known members of the Scorpius-Centaurus association, and identify known disk host WISEA J164540.79-310226.6 as a likely Sco-Cen member. Thirty-one of these disk candidates are closer than $\sim 125$ pc (including 27 debris disks), making them good targets for direct imaging exoplanet searches., Comment: 23 pages, eight figures. Accepted for publication in the Astrophysical Journal. SEDs and machine-readable tables will be available in the ApJ online version

I recall my interactions with Julian Schwinger, first as a graduate student at Harvard, and then as a postdoc at UCLA, in the period 1968--81, and subsequently. Some aspects of his legacy to physics are discussed., Comment: 15 pages, A Contribution to the Proceedings of the Julian Schwinger Centennial Conference, Singapore, February 2018

The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here this is demonstrated in detail for two different models of the field-potential coupling. here is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully interacting quantum field theories; these terms are finite but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply rising smooth potential., Comment: 19 pages; invited issue of Symmetry on Casimir Interactions

These are reminiscences of my interactions with Julian Schwinger from 1968 through 1981 and beyond., Comment: 17 pages. This will appear in the Centennial edition of J. Schwinger, {\it Quantum Mechanics: Symbolism of Atomic Measurements}, edited by B.-G. Englert

In this paper we continue our program of computing Casimir self-entropies of idealized electrical bodies. Here we consider an electromagnetic $\delta$-function sphere ("semitransparent sphere") whose electric susceptibility has a transverse polarization with arbitrary strength. Dispersion is incorporated by a plasma-like model. In the strong coupling limit, a perfectly conducting spherical shell is realized. We compute the entropy for both low and high temperatures. The TE self-entropy is negative as expected, but the TM self-entropy requires ultraviolet and infrared subtractions, and, surprisingly, is only positive for sufficiently strong coupling. Results are robust under different regularization schemes., Comment: 25 pages, 3 figures

We reply to the "Comment on 'The Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors'" [arXiv:1604.06432]. We believe the comment misrepresents our papers, and fails to provide a plausible resolution to the conflict between theory and experiment., Comment: To appear in Phys. Rev. E

Casimir entropies due to quantum fluctuations in the interaction between electrical bodies can often be negative, either caused by dissipation or by geometry. Although generally such entropies vanish at zero temperature, consistent with the third law of thermodynamics (the Nernst heat theorem), there is a region in the space of temperature and separation between the bodies where negative entropy occurs, while positive interaction entropies arise for large distances or temperatures. Systematic studies on this phenomenon in the Casimir-Polder interaction between a polarizable nanoparticle or atom and a conducting plate in the dipole approximation have been given recently. Since the total entropy should be positive according to the second law of thermodynamics, we expect that the self-entropy of the bodies would be sufficiently positive as to overwhelm the negative interaction entropy. This expectation, however, has not been explicitly verified. Here we compute the self-entropy of an electromagnetic $\delta$-function plate, which corresponds to a perfectly conducting sheet in the strong coupling limit. The transverse electric contribution to the self-entropy is negative, while the transverse magnetic contribution is larger and positive, so the total self-entropy is positive. However, this self-entropy vanishes in the strong-coupling limit. In that case, it is the self-entropy of the nanoparticle that is just sufficient to result in a nonnegative total entropy.

We examine the conditions of validity for the Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic plane mirrors. As in the previously studied case of non-magnetic materials (Guerout et al, Phys. Rev. E 90 042125), we recover the usual expression for the lossy model of optical response, but not for the lossless plasma model. We also show that the modes associated with the Foucault currents play a crucial role in the limit of vanishing losses, in contrast to expectations.

For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which break time-reversal symmetry. These forces are typically very small, unless the bodies are nearly touching, and consequently such effects have never been observed, although lateral Casimir forces have been seen for corrugated surfaces. Partly because of the lack of contact with phenomena, theoretical predictions for the frictional force between parallel plates, or between a polarizable atom and a metallic plate, have varied widely. Here we review the history of these calculations, show that theoretical consensus is emerging, and offer some hope that it might be possible to experimentally confirm this phenomenon of dissipative quantum electrodynamics., Comment: 12 pages, 2 figures

Casimir friction between a polarizable particle and a semi-infinite space is a delicate physical phenomenon, as it concerns the interaction between a microscopic quantum particle and a semi-infinite reservoir. Not unexpectedly, results obtained in the past about the friction force obtained via different routes are sometimes, at least apparently, wildly different from each other. Recently, we considered the Casimir friction force for two dielectric semi-infinite plates moving parallel to each other [J. S. H{\o}ye and I. Brevik, Eur. Phys. J. D {\bf 68}, 61 (2014)], and managed to get essential agreement with results obtained by Pendry (1997), Volokitin and Persson (2007), and Barton (2011). Our method was based upon use of the Kubo formalism. In the present paper we focus on the interaction between a polarizable particle and a dielectric half-space again, and calculate the friction force using the same basic method as before. The new ingredient in the present analysis is that we take into account radiative damping, and derive the modifications thereof. Some comparisons are also made with works from others. Essential agreement with the results of Intravaia, Behunin, and Dalvit can also be achieved using the modification of the atomic polarizability by the metallic plate., Comment: 15 pages; clarifying remarks supplied throughout the text, especially in Appendix A; title changed. Version to appear in J. Phys. A: Math. Theor

Starting from the earlier notions of stationary action principles, we show how Julian Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements in nonequilibrium situations is described. The variational formulation of quantum field theory and the development of source theory constitute the latter part of this work. In this document, derived from Schwinger's lectures over four decades, the continuity of concepts, such as that of Green's functions, becomes apparent., Comment: 116 pages, submitted to SpringerBriefs. Very substantially updated version of 1402.3762, with new chapters on Quantum Field Theory and Source Theory

In some recent experiments the distinction between synthetic magnetic monopoles and Dirac monopoles has been blurred. A case in point is the work in a letter by Ray {\it et al.} [arXiv:1408.3133] in which a beautiful experiment is reported but claims with regard to Dirac monopoles are misleading., Comment: 2 pages

Negative entropy has been known in Casimir systems for some time. For example, it can occur between parallel metallic plates modeled by a realistic Drude permittivity. Less well known is that negative entropy can occur purely geometrically, say between a perfectly conducting sphere and a conducting plate. The latter effect is most pronounced in the dipole approximation, which is reliable when the size of the sphere is small compared to the separation between the sphere and the plate. Therefore, here we examine cases where negative entropy can occur between two electrically and magnetically polarizable nanoparticles or atoms, which need not be isotropic, and between such a small object and a conducting plate. Negative entropy can occur even between two perfectly conducting spheres, between two electrically polarizable nano-particles if there is sufficient anisotropy, between a perfectly conducting sphere and a Drude sphere,and between a sufficiently anisotropic electrically polarizable nano-particle and a transverse magnetic conducting plate., Comment: 15 pages, 13 figures, to be published in JPCM special issue on Casimir forces; revision includes small clarifications and additional references

We carefully re-examine the conditions of validity for the consistent derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors. We recover the usual expression for the lossy Drude model, but not for the lossless plasma model. We give an interpretation of this new result in terms of the modes associated with the Foucault currents which play a role in the limit of vanishing losses, in contrast to common expectations., Comment: Accepted in Phys. Rev. E

Starting from the earlier notions of stationary action principles, we show how Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory., Comment: 49 pages, 8 figures, submitted to EPJ H

Several years ago we demonstrated that the Casimir energy for perfectly reflecting and imperfectly reflecting parallel plates gravitated normally, that is, obeyed the equivalence principle. At that time the divergences in the theory were treated only formally, without proper regularization, and the coupling to gravity was limited to the canonical energy-momentum-stress tensor. Here we strengthen the result by removing both of those limitations. We consider, as a toy model, massless scalar fields interacting with semitransparent ($\delta$-function) potentials defining parallel plates, which become Dirichlet plates for strong coupling. We insert space and time point-split regulation parameters, and obtain well-defined contributions to the self- energy of each plate, and the interaction energy between the plates. (This self-energy does not vanish even in the conformally-coupled, strong-coupled limit.) We also compute the local energy density, which requires regularization near the plates. In general, the energy density includes a surface energy that resides precisely on the boundaries. This energy is also regulated. The gravitational interaction of this well-defined system is then investigated, and it is verified that the equivalence principle is satisfied., Comment: 14 pages, 4 figures

The Disk Detective citizen science project recently released a new catalog of disk candidates found by visual inspection of images from NASA's Wide-field Infrared Survey Explorer mission and other surveys. We applied this new catalog of well-vetted disk candidates to search for new members of nearby young stellar associations (YSAs) using a novel technique based on Gaia data and virtual reality (VR). We examined AB Doradus, Argus, β Pictoris, Carina, Columba, Octans-Near, Tucana–Horologium, and TW Hya by displaying them in VR together with other nearby stars, color coded to show infrared excesses found via Disk Detective. Using this method allows us to find new association members in mass regimes where isochrones are degenerate. We propose 10 new YSA members with infrared excesses: three of AB Doradus (HD 44775, HD 40540 and HD 44510), one of β Pictoris (HD 198472), two of Octans-Near (HD 157165 and BD+35 2953), and four disk-hosting members of a combined population of Carina, Columba, and Tucana–Horologium: CPD-57 937, HD 274311, HD 41992, and WISEA J092521.90-673224.8. This last object (J0925) appears to be an extreme debris disk with a fractional infrared luminosity of 3.7 × 10−2. We also propose two new members of AB Doradus that do not show infrared excesses: TYC 6518-1857-1 and CPD-25 1292. We find HD 15115 appears to be a member of Tucana–Horologium rather than β Pictoris. We advocate for membership in Columba–Carina of HD 30447, CPD-35 525, and HD 35841. Finally, we propose that three M dwarfs, previously considered members of Tucana–Horologium are better considered a separate association, tentatively called "Smethells 165."

Julian Schwinger (1918--1994), founder of renormalized quantum electrodynamics, was arguably the leading theoretical physicist of the second half of the 20th century. Thus it is not surprising that he made contributions to gravity theory as well. His students made major impacts on the still uncompleted program of constructing a quantum theory of gravity. Schwinger himself had no doubt of the validity of general relativity, although he preferred a particle-physics viewpoint based on gravitons and the associated fields, and not the geometrical picture of curved spacetime. This note provides a brief summary of his contributions and attitudes toward the subject of gravity., Comment: 6 pages, no figures; revised version has changed title, clarifications, and additional references

The Casimir effect between metal surfaces has now been well-verified at the few-percent level experimentally. However, the temperature dependence has never been observed in the laboratory, since all experiments are conducted at room temperature. The temperature dependence for the related Casimir-Polder force between an atom and a bulk material has, in contrast, been observed between a BEC and a silica substrate, with the environment and the silica held at different temperatures. There is a controversy about the temperature dependence for the force between metals, having to do with the magnitude of the linear temperature term for both low and high temperature, the latter being most prominent at large distances. There are also related anomalies pertaining to semiconductors. The status of this controversy, and of the relevant experiments, are reviewed in this report., Comment: 8 pages, 4 figures, extended version of presentation at Frontiers of Quantum and Mesoscopic Thermodynamics, Prague, July 2011. Revision corrects some errors in references and minor typographic errors. arXiv admin note: substantial text overlap with arXiv:quant-ph/0605005

New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a point-splitting regulator, which amounts to evaluation of the cylinder kernel. The correct Weyl divergences, depending on the volume, surface area, and the edges, are obtained, which is strong evidence that the counting of modes is correct. Because there is no curvature, the finite part of the quantum energy may be unambiguously extracted. Cubic, rectangular parallelepipedal, triangular prismatic, and spherical geometries are also revisited. Dirichlet and Neumann boundary conditions are considered for all geometries. Systematic behavior of the energy in terms of geometric invariants for these different cavities is explored. Smooth interpolation between short and long prisms is further demonstrated. When scaled by the ratio of the volume to the surface area, the energies for the tetrahedra and the prisms of maximal isoareal quotient lie very close to a universal curve. The physical significance of these results is discussed., Comment: 27 pages, 11 figures