The canonical subgroup: a "subgroup-free" approach

Beyond the crucial role they play in the foundations of the theory of overconvergent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is essential to understand various ``numerical'' aspects of the canonical subgroup, and in particular, the precise extent of its overconvergence. We develop a theory of canonical subgroups for a general class of curves (including the unitary and quaternionic Shimura curves), using formal and rigid geometry. In our approach, we use the common geometric features of these curves rather than their (possible) specific moduli-theoretic description.Comment: 16 pages, 1 figur

Canonical Subgroups over Hilbert Modular Varieties

We obtain new results on the geometry of Hilbert modular varieties in positive characteristic and morphisms between them. Using these results and methods of rigid geometry, we develop a theory of canonical subgroups for abelian varieties with real multiplication.Comment: 56 page

First record of the Indo-Pacific species Iphione muricata Savigny in Lamarck, 1818 (Polychaeta: Iphionidae) from the Mediterranean Sea, Israel

The Indo-Pacific scaleworm Iphione muricata was observed and caught in the Mediterranean Sea along the coast of Israel. Morphological and molecular diagnostic characters of the species are discussed. This is the first record of this alien species in the Mediterranean Sea, and its previous reports in the Suez Canal suggest its introduction via Lessepsian migration

The Mechanical Coupling of Fluid-Filled Granular Material Under Shear

The coupled mechanics of fluid-filled granular media controls the physics of many Earth systems, for example saturated soils, fault gouge, and landslide shear zones. It is well established that when the pore fluid pressure rises, the shear resistance of fluid-filled granular systems decreases, and, as a result, catastrophic events such as soil liquefaction, earthquakes, and accelerating landslides may be triggered. Alternatively, when the pore pressure drops, the shear resistance of these geosystems increases. Despite the great importance of the coupled mechanics of grain-fluid systems, the basic physics that controls this coupling is far from understood. Fundamental questions that must be addressed include: what are the processes that control pore fluid pressurization and depressurization in response to deformation of the granular skeleton? and how do variations of pore pressure affect the mechanical strength of the grains skeleton? To answer these questions, a formulation for the pore fluid pressure and flow has been developed from mass and momentum conservation, and is coupled with a granular dynamics algorithm that solves the grain dynamics, to form a fully coupled model. The pore fluid formulation reveals that the evolution of pore pressure obeys viscoelastic rheology in response to pore space variations. Under undrained conditions elastic-like behavior dominates and leads to a linear relationship between pore pressure and overall volumetric strain. Viscous-like behavior dominates under well-drained conditions and leads to a linear relationship between pore pressure and volumetric strain rate. Numerical simulations reveal the possibility of liquefaction under drained and initially over-compacted conditions, which were often believed to be resistant to liquefaction. Under such conditions liquefaction occurs during short compactive phases that punctuate the overall dilative trend. In addition, the previously recognized generation of elevated pore pressure under undrained compactive conditions is observed. Simulations also show that during liquefaction events stress chains are detached, the external load becomes completely supported by the pressurized pore fluid, and shear resistance vanishe

Balancing adaptivity and customisation : in search of sustainable personalisation in cultural heritage

Personalisation for cultural heritage aims at delivering to visitors the right stories at the right time. Our endeavour to determine which features to use for adaptation starts from acknowledging what forms of personalisation curators value as most meaningful. Working in collaboration with curators we have explored the different features that must be taken into account: some are related to the content (multiple interpretation layers), others to the context of delivery (where and when), but some are idiosyncratic (“match my mood”, “something that is relevant to my life”). The findings reveal that a sustainable personalization needs to accurately balance: (i) support to curators in customising stories to different visitors; (ii) algorithms for the system to dynamically model aspects of the visit and instantiate the correct behaviour; and (iii) an active role for visitors to choose the type of experience they would like to have today

Implications of longitudinal ridges for the mechanics of ice-free long runout landslides

The emplacement mechanisms of long runout landslides across the Solar System and the formation mechanisms of longitudinal ridges associated with their deposits remain subjects of debate. The similarity of longitudinal ridges in martian long runout landslides and terrestrial landslides emplaced on ice suggests that an icy surface could explain both the reduction of friction associated with the deposition of long runout landslides and the development of longitudinal ridges. However, laboratory experiments on rapid granular flows show that ice is not a necessary requirement for the development of longitudinal ridges, which instead may form from convective cells within high-speed flows. These experiments have shown that the wavelength (S) of the ridges is 2-3 times the thickness (T) of the flow, which has also been demonstrated at field scale on a tens-of-kilometre martian long runout landslide. Here, we present the case study of the 4-km-long, ice-free El Magnifico landslide in Northern Chile which exhibits clear longitudinal ridges, and show for the first time on a terrestrial landslide that the S/T ratio is in agreement with the scaling relationship found for both laboratory rapid granular flows and a previously measured martian long runout landslide. Several outcrops within the landslide allow us to study internal sections of the landslide deposit and their relationship with the longitudinal ridges in order to shed light on the emplacement mechanism. Our observations include interactions without chaotic mixing between different lithologies and the presence of meters-sized blocks that exhibit preserved original bedding discontinuities. We associate these observations with fluctuations in stress, as they are qualitatively similar to numerically modelled rapid granular slides, which were suggested, to some degree, to be associated with acoustic fluidization. Our results suggest that 1) the mechanism responsible for the formation of longitudinal ridges is scale- and environment-independent; 2) while the internal structures observed do not necessarily support a mechanism of convective-style motion, their interpretation could also point to a mechanism of internal deformation of the sliding mass derived from pattern-forming vibrations. Our novel observations and analysis provide important insights for the interpretation of similar features on Earth and Mars and for discerning the underlying mechanisms responsible for the emplacement of long run out landslides

Stimulated wave of polarization in spin chains

Stimulated wave of polarization, triggered by a flip of a single spin, presents a simple model of quantum amplification. Previously, it has been found that such wave can be excited in a 1D Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field. Here we explore models with more realistic Hamiltonians, in particular, with natural dipole-dipole interactions. Results of simulations for 1D spin chains and rings with up to nine spins are presented.Comment: 15 pages, 5 figure

Longitudinal ridges imparted by high-speed granular flow mechanisms in martian landslides

The presence of longitudinal ridges documented in long runout landslides across our solar system is commonly associated with the existence of a basal layer of ice. However, their development, the link between their occurrence and the emplacement mechanisms of long runout landslides, and the necessity of a basal ice layer remain poorly understood. Here, we analyse the morphometry of longitudinal ridges of a martian landslide and show that the wavelength of the ridges is 2–3 times the average thickness of the landslide deposit, a unique scaling relationship previously reported in ice-free rapid granular flow experiments. We recognize en-echelon features that we interpret as kinematic indicators, congruent with experimentally-measured transverse velocity gradient. We suggest that longitudinal ridges should not be considered as unequivocal evidence for presence of ice, rather as inevitable features of rapid granular sliding material, that originate from a mechanical instability once a kinematic threshold is surpassed