Dynamics of freely moving plates connected by a shallow liquid bridge

We study the dynamics of freely moving plates connected by a shallow liquid bridge via analytic and experimental methods. The gap between the plates is used as a small parameter within a lubrication approximation, reducing the problem to an Abel equation of the second kind. Analysis of the governing differential equation yields two novel physical phenomena: (1) An impulse-like peak in the force applied by the liquid bridge on the plates, obtained from a uniform asymptotic solution for small capillary numbers. (2) Both linear and non-linear oscillations of the system for the case of surfaces with low wettability, obtained from small perturbations of the system around the equilibrium point. An experimental setup examining the motion of freely moving plates was constructed, yielding experimental data which compared favorably with the analytic results and specifically displayed the predicted oscillations and impulse-like peak of the applied force. The application of the current analysis to the manipulation of solid bodies and possible future research directions are discussed

Region-based memory management for Mercury programs

Region-based memory management (RBMM) is a form of compile time memory management, well-known from the functional programming world. In this paper we describe our work on implementing RBMM for the logic programming language Mercury. One interesting point about Mercury is that it is designed with strong type, mode, and determinism systems. These systems not only provide Mercury programmers with several direct software engineering benefits, such as self-documenting code and clear program logic, but also give language implementors a large amount of information that is useful for program analyses. In this work, we make use of this information to develop program analyses that determine the distribution of data into regions and transform Mercury programs by inserting into them the necessary region operations. We prove the correctness of our program analyses and transformation. To execute the annotated programs, we have implemented runtime support that tackles the two main challenges posed by backtracking. First, backtracking can require regions removed during forward execution to be "resurrected"; and second, any memory allocated during a computation that has been backtracked over must be recovered promptly and without waiting for the regions involved to come to the end of their life. We describe in detail our solution of both these problems. We study in detail how our RBMM system performs on a selection of benchmark programs, including some well-known difficult cases for RBMM. Even with these difficult cases, our RBMM-enabled Mercury system obtains clearly faster runtimes for 15 out of 18 benchmarks compared to the base Mercury system with its Boehm runtime garbage collector, with an average runtime speedup of 24%, and an average reduction in memory requirements of 95%. In fact, our system achieves optimal memory consumption in some programs.Comment: 74 pages, 23 figures, 11 tables. A shorter version of this paper, without proofs, is to appear in the journal Theory and Practice of Logic Programming (TPLP

Effect of shell structure on the fission of sub-lead nuclei

Fission of atomic nuclei often produces mass asymmetric fragments. However, the origin of this asymmetry was believed to be different in actinides and in the sub-lead region [A. Andreyev {\it et al.}, Phys. Rev. Lett. {\bf 105}, 252502 (2010)]. It has recently been argued that quantum shell effects stabilising pear shapes of the fission fragments could explain the observed asymmetries in fission of actinides[G. Scamps and C. Simenel, Nature {\bf 564}, 382 (2018)]. This interpretation is tested in the sub-lead region using microscopic mean-field calculations of fission based on the Hartree-Fock approach with BCS pairing correlations. The evolution of the number of protons and neutrons in asymmetric fragments of mercury isotope fissions is interpreted in terms of deformed shell gaps in the fragments. A new method is proposed to investigate the dominant shell effects in the pre-fragments at scission. We conclude that the mechanisms responsible for asymmetric fissions in the sub-lead region are the same as in the actinide region, which is a strong indication of their universality.Comment: Accepted as a rapid communication by Phys. Rev.

Mercury Wetting and Non-wetting Condensing Research

Mercury wetting and non-wetting condensatio

The Power of General Relativity

We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to $R^{1+\delta}$. This scale-free extension reduces to general relativity when $\delta \to 0$. In order to constrain generalisations of general relativity of this power class we analyse the behaviour of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires $\delta >0$ or $\delta <-1/4$. The stable attractors of the evolution are found. By considering the synthesis of light elements (helium-4, deuterium and lithium-7) we obtain the bound $-0.017<\delta <0.0012.$ We evaluate the effect on the power spectrum of clustering via the shift in the epoch of matter-radiation equality. The horizon size at matter--radiation equality will be shifted by $\sim 1$ for a value of $\delta \sim 0.0005.$ We study the stable extensions of the Schwarzschild solution in these theories and calculate the timelike and null geodesics. No significant bounds arise from null geodesic effects but the perihelion precession observations lead to the strong bound $\delta =2.7\pm 4.5\times 10^{-19}$ assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound $0\leq \delta <7.2\times 10^{-19}$ on theories of this type.Comment: 26 pages and 5 figures. Published versio

Hinode Calibration for Precise Image Co-alignment between SOT and XRT (November 2006 -- April 2007)

To understand the physical mechanisms for activity and heating in the solar atmosphere, the magnetic coupling from the photosphere to the corona is an important piece of information from the Hinode observations, and therefore precise positional alignment is required among the data acquired by different telescopes. The Hinode spacecraft and its onboard telescopes were developed to allow us to investigate magnetic coupling with co-alignment accuracy better than 1 arcsec. Using the Mercury transit observed on 8 November 2006 and co-alignment measurements regularly performed on a weekly basis, we have determined the information necessary for precise image co-alignment and have confirmed that co-alignment better than 1 arcsec can be realized between Solar Optical Telescope (SOT) and X-Ray Telescope (XRT) with our baseline co-alignment method. This paper presents results from the calibration for precise co-alignment of CCD images from SOT and XRT.Comment: 8 pages, 9 figures, accepted for publication in PASJ (Hinode Special issue

The contrasting fission potential-energy structure of actinides and mercury isotopes

Fission-fragment mass distributions are asymmetric in fission of typical actinide nuclei for nucleon number $A$ in the range $228 \lnsim A \lnsim 258$ and proton number $Z$ in the range $90\lnsim Z \lnsim 100$. For somewhat lighter systems it has been observed that fission mass distributions are usually symmetric. However, a recent experiment showed that fission of $^{180}$Hg following electron capture on $^{180}$Tl is asymmetric. We calculate potential-energy surfaces for a typical actinide nucleus and for 12 even isotopes in the range $^{178}$Hg--$^{200}$Hg, to investigate the similarities and differences of actinide compared to mercury potential surfaces and to what extent fission-fragment properties, in particular shell structure, relate to the structure of the static potential-energy surfaces. Potential-energy surfaces are calculated in the macroscopic-microscopic approach as functions of fiveshape coordinates for more than five million shapes. The structure of the surfaces are investigated by use of an immersion technique. We determine properties of minima, saddle points, valleys, and ridges between valleys in the 5D shape-coordinate space. Along the mercury isotope chain the barrier heights and the ridge heights and persistence with elongation vary significantly and show no obvious connection to possible fragment shell structure, in contrast to the actinide region, where there is a deep asymmetric valley extending from the saddle point to scission. The mechanism of asymmetric fission must be very different in the lighter proton-rich mercury isotopes compared to the actinide region and is apparently unrelated to fragment shell structure. Isotopes lighter than $^{192}$Hg have the saddle point blocked from a deep symmetric valley by a significant ridge. The ridge vanishes for the heavier Hg isotopes, for which we would expect a qualitatively different asymmetry of the fragments.Comment: 8 pages, 9 figure

Recovery of the Schwarzschild Metric in Theories with Localized Gravity Beyond Linear Order

We solve the Einstein equations in the Randall-Sundrum framework with a static, spherically symmetric matter distribution on the {\it physical brane} and obtain an approximate expression for the gravitational field outside the source to second order in the gravitational coupling. This expression when confined on the {\it physical brane} coincides with the standard form of the Schwarzschild metric. Therefore, the Randall-Sundrum scenario is consistent with the Mercury precession test of General Relativity.Comment: 17 pages, plain Tex, references added, typos correcte