Heat Kernel Bounds for the Laplacian on Metric Graphs of Polygonal Tilings

We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as well as the two dimensional nature of these graphs.Comment: 8 page

TEMPERATURE AND RELATIVITY

We investigate whether inertial thermometers moving in a thermal bath behave as being hotter or colder. This question is directly related to the classical controversy concerning how temperature transforms under Lorentz transformations. Rather than basing our arguments on thermodynamical hypotheses, we perform straightforward calculations in the context of relativistic quantum field theory. For this purpose we use Unruh-DeWitt detectors, since they have been shown to be reliable thermometers in semi-classical gravity. We believe that our discussion helps in definitely clarifying this issue.Comment: 9 pages, 1 figure available upon reques

Ionospheric effects of the solar flares of September 23, 1998 and July 29, 1999 as deduced from global GPS network data

This paper presents data from first GPS measurements of global response of the ionosphere to solar flares of September 23, 1998 and July 29, 1999. The analysis used novel technology of a global detection of ionospheric effects from solar flares (GLOBDET) as developed by one of the authors (Afraimovich E. L.). The essence of the method is that use is made of appropriate filtering and a coherent processing of variations in total electron content (TEC) in the ionosphere which is determined from GPS data, simultaneously for the entire set of visible (over a given time interval) GPS satellites at all stations used in the analysis. It was found that fluctuations of TEC, obtained by removing the linear trend of TEC with a time window of about 5 min, are coherent for all stations and beams to the GPS satellites on the dayside of the Earth. The time profile of TEC responses is similar to the time behavior of hard X-ray emission variations during flares in the energy range 25-35 keV if the relaxation time of electron density disturbances in the ionosphere of order 50-100 s is introduced. No such effect on the nightside of the Earth has been detected yet.Comment: EmTeX-386, 13 pages, 5 figure

The use of GPS-arrays in detecting shock-acoustic waves generated during rocket launchings

This paper is concerned with the form and dynamics of shock-acoustic waves (SAW) generated during rocket launchings. We have developed a method for determining SAW parameters (including angular characteristics of the wave vector, and the SAW phase velocity, as well as the direction towards the source) using GPS-arrays whose elements can be chosen out of a large set of GPS-stations of the global GPS network. The application of the method is illustrated by a case study of ionospheric effects from launchings of launch vehicles (LV) Proton and Space Shuttle from space-launch complexes Baikonur and Kennedy Space Center (KSC) in 1998 and 1999 (a total of five launchings). The study revealed that, in spite of a difference of LV characteristics, the ionospheric response for all launchings had the character of an N - wave corresponding to the form of a shock wave, regardless of the disturbance source (rocket launchings, industrial explosions). The SAW period T is 270--360 s, and the amplitude exceeds the standard deviation of TEC background fluctuations in this range of periods under quiet and moderate geomagnetic conditions by factors of 2 to 5 as a minimum. The angle of elevation of the SAW wave vector varies from 30 degree to 60 degree, and the SAW phase velocity (900-1200 m/s) approaches the sound velocity at heights of the ionospheric F-region maximum.Comment: EmTeX-386, 23 pages, 6 figure

The Time-Energy Uncertainty Relation

The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition of "Time in quantum mechanics") contains minor corrections, new examples and pointers to some additional relevant literatur

Continuity and Stability of Partial Entropic Sums

Extensions of Fannes' inequality with partial sums of the Tsallis entropy are obtained for both the classical and quantum cases. The definition of kth partial sum under the prescribed order of terms is given. Basic properties of introduced entropic measures and some applications are discussed. The derived estimates provide a complete characterization of the continuity and stability properties in the refined scale. The results are also reformulated in terms of Uhlmann's partial fidelities.Comment: 9 pages, no figures. Some explanatory and technical improvements are made. The bibliography is extended. Detected errors and typos are correcte

Early Mississippian sandy siltstones preserve rare vertebrate fossils in seasonal flooding episodes

Flood-generated sandy siltstones are under-recognised deposits that preserve key vertebrate (actinopterygians, rhizodonts, and rarer lungfish, chondrichthyans and tetrapods), invertebrate and plant fossils. Recorded for the first time from the lower Mississippian Ballagan Formation of Scotland, more than 140 beds occur throughout a 490 m thick core succession charac-terised by fluvial sandstones, palaeosols, siltstones, dolostone ‘cementstones’ and gypsum from a coastal–alluvial plain setting. Sandy siltstones are described as a unique taphofacies of the Ballagan Formation (Scotland, UK);they are matrix-supported siltstones with millimetre-sized siltstone and very fine sandstone lithic clasts. Common bioclasts include plants and mega-spores, fish, ostracods, eurypterids and bivalves. Fossils have a high degree of articulation compared with those found in other fossil-bearing deposits, such as conglomerate lags at the base of fluvial channel sandstones. Bed thickness and distribution varies throughout the formation, with no stratigraphic trend. The matrix sediment and clasts are sourced from the reworking of floodplain sediments including desiccated surfaces and palaeosols. Secondary pedogenic modification affects 30% of the sandy siltstone beds and most (71%) overlie palaeosols or desiccation cracks. Sandy siltstones are interpreted as cohesive debris flow deposits that originated by the over-bank flooding of rivers and due to localised floodplain sediment transport at times of high rainfall; their association with palaeosols and desiccation cracks indicates seasonally wet to dry cycles throughout the Tournaisian. Tetrapod and fish fossils derived from floodplain lakes and land surfaces are concentrated by local erosion and reworking, and are preserved by deposition into temporary lakes on the floodplain; their distribution indicates a local origin, with sediment transported across the floodplain in seasonal rainfall episodes. These deposits are significant new sites that can be explored for the preservation of rare non-marine fossil material and provide unique insights into the evolution of early terrestrial ecosystems

A new Mississippian tetrapod from Fife, Scotland, and its environmental context

The Visean stage of the Mississippian was a time of rapid tetrapod diversification which marks the earliest appearance of temnospondyls, microsaurs and the limbless aïstopods. Tetrapod finds from this stage are very rare and only a dozen sites are known worldwide. Here we announce the discovery of a new Visean site in Fife, Scotland, of Asbian age, and from it describe a new species of the baphetoid Spathicephalus. These specimens represent the oldest known baphetoid by three million years, yet belong to the most specialized members of the clade. Unlike typical baphetoids with large marginal teeth and palatal fangs characteristic of early tetrapods, spathicephalids had very broad flattened heads with a dentition consisting of a large number of small, uniform teeth. Spathicephalids were probably one of the earliest tetrapod groups to use suction feeding on small, aquatic prey. Palynological and sedimentological analysis indicates that the new fossil bed was deposited in a large, stratified, freshwater lake that became increasingly saline

Quantum gates with neutral atoms: Controlling collisional interactions in time dependent traps

We theoretically study specific schemes for performing a fundamental two-qubit quantum gate via controlled atomic collisions by switching microscopic potentials. In particular we calculate the fidelity of a gate operation for a configuration where a potential barrier between two atoms is instantaneously removed and restored after a certain time. Possible implementations could be based on microtraps created by magnetic and electric fields, or potentials induced by laser light.Comment: 10 pages, 3 figure

Reinterpreting the age of the uppermost ‘Old Red Sandstone’ and Early Carboniferous in Scotland

In Scotland, the base of the Ballagan Formation has traditionally been placed at the first grey mudstone within a contiguous Late Devonian to Carboniferous succession. This convention places the Devonian–Carboniferous boundary within the Old Red Sandstone (ORS) Kinnesswood Formation. The consequences of this placement are that tetrapods from the Ballagan Formation were dated as late Tournaisian in age and that the ranges of typically Devonian fish found in the Kinnesswood Formation continued into the Carboniferous. The Pease Bay specimen of the fish Remigolepis is from the Kinnesswood Formation. Comparisons with its range in Greenland, calibrated against spores, show it was Famennian in age. Detailed palynological sampling at Burnmouth from the base of the Ballagan Formation proves that the early Tournaisian spore zones (VI and HD plus Cl 1) are present. The Schopfites species that occurs through most of the succession is Schopfites delicatus rather than Schopfites claviger. The latter species defines the late Tournaisian CM spore zone. The first spore assemblage that has been found in Upper ‘ORS' strata underlying the Ballagan Formation (Preston, Whiteadder Water), contains Retispora lepidophyta and is from the early latest Famennian LL spore zone. The spore samples are interbedded with volcaniclastic debris, which shows that the Kelso Volcanic Formation is, in part, early latest Famennian in age. These findings demonstrate that the Ballagan Formation includes most of the Tournaisian with the Devonian–Carboniferous boundary positioned close to the top of the Kinnesswood Formation. The Stage 6 calcrete at Pease Bay can be correlated to the equivalent section at Carham, showing that it represents a time gap equivalent to the latest Famennian glaciation(s). Importantly, some of the recently described Ballagan Formation tetrapods are older than previously dated and now fill the key early part of Romer's Gap