1,126 research outputs found
Geometric representation of interval exchange maps over algebraic number fields
We consider the restriction of interval exchange transformations to algebraic
number fields, which leads to maps on lattices. We characterize
renormalizability arithmetically, and study its relationships with a
geometrical quantity that we call the drift vector. We exhibit some examples of
renormalizable interval exchange maps with zero and non-zero drift vector, and
carry out some investigations of their properties. In particular, we look for
evidence of the finite decomposition property: each lattice is the union of
finitely many orbits.Comment: 34 pages, 8 postscript figure
Geometrical Models for Substitutions
International audienceWe consider a substitution associated with the Arnoux-Yoccoz interval exchange transformation (IET) related to the tribonacci substitution. We construct the so-called stepped lines associated with the fixed points of the substitution in the abelianization (symbolic) space. We analyze various projections of the stepped line, recovering the Rauzy fractal, a Peano curve related to work in [Arnoux 88], another Peano curve related to the work of [McMullen 09] and [Lowenstein et al. 07], and also the interval exchange transformation itself
Impacts of changes in groundwater recharge on the isotopic composition and geochemistry of seasonally ice-covered lakes: insights for sustainable management
Lakes are under increasing pressure due to widespread anthropogenic impacts
related to rapid development and population growth. Accordingly, many lakes
are currently undergoing a systematic decline in water quality. Recent
studies have highlighted that global warming and the subsequent changes in
water use may further exacerbate eutrophication in lakes. Lake evolution
depends strongly on hydrologic balance, and therefore on groundwater
connectivity. Groundwater also influences the sensitivity of lacustrine
ecosystems to climate and environmental changes, and governs their
resilience. Improved characterization of groundwater exchange with lakes is
needed today for lake preservation, lake restoration, and sustainable
management of lake water quality into the future. In this context, the aim of
the present paper is to determine if the future evolution of the climate, the
population, and the recharge could modify the geochemistry of lakes (mainly
isotopic signature and quality via phosphorous load) and if the isotopic
monitoring of lakes could be an efficient tool to highlight the variability
of the water budget and quality.
Small groundwater-connected lakes were chosen to simulate changes in water
balance and water quality expected under future climate change scenarios,
namely representative concentration pathways (RCPs) 4.5 and 8.5. Contemporary
baseline conditions, including isotope mass balance and geochemical
characteristics, were determined through an intensive field-based research
program prior to the simulations. Results highlight that future lake
geochemistry and isotopic composition trends will depend on four main
parameters: location (and therefore climate conditions), lake catchment size
(which impacts the intensity of the flux change), lake volume (which impacts
the range of variation), and lake G index (i.e., the percentage of
groundwater that makes up total lake inflows), the latter being the dominant
control on water balance conditions, as revealed by the sensitivity of lake
isotopic composition. Based on these model simulations, stable isotopes
appear to be especially useful for detecting changes in recharge to lakes
with a G index of between 50 and 80 %, but response is non-linear.
Simulated monthly trends reveal that evolution of annual lake isotopic
composition can be dampened by opposing monthly recharge fluctuations. It is
also shown that changes in water quality in groundwater-connected lakes
depend significantly on lake location and on the intensity of recharge
change
Cross sections for geodesic flows and \alpha-continued fractions
We adjust Arnoux's coding, in terms of regular continued fractions, of the
geodesic flow on the modular surface to give a cross section on which the
return map is a double cover of the natural extension for the \alpha-continued
fractions, for each in (0,1]. The argument is sufficiently robust to
apply to the Rosen continued fractions and their recently introduced
\alpha-variants.Comment: 20 pages, 2 figure
Multi-machine scaling of the main SOL parallel heat flux width in tokamak limiter plasmas
As in many of today’s tokamaks, plasma start-up in ITER will be performed in limiter
configuration on either the inner or outer midplane first wall (FW). The massive, beryllium
armored ITER FW panels are toroidally shaped to protect panel-to-panel misalignments,
increasing the deposited power flux density compared with a purely cylindrical surface.
The chosen shaping should thus be optimized for a given radial profile of parallel heat flux,
q in the scrape-off layer (SOL) to ensure optimal power spreading. For plasmas limited
on the outer wall in tokamaks, this profile is commonly observed to decay exponentially
as q q = − exp ( / r λ ) 0 q omp , or, for inner wall limiter plasmas with the double exponential
decay comprising a sharp near-SOL feature and a broader main SOL width, λq
omp. The initial choice of λq
omp
, which is critical in ensuring that current ramp-up or down will be
possible as planned in the ITER scenario design, was made on the basis of an extremely
restricted L-mode divertor dataset, using infra-red thermography measurements on the
outer divertor target to extrapolate to a heat flux width at the main plasma midplane. This
unsatisfactory situation has now been significantly improved by a dedicated multi-machine
ohmic and L-mode limiter plasma study, conducted under the auspices of the International
Tokamak Physics Activity, involving 11 tokamaks covering a wide parameter range with
R = = 0.4–2.8 m, 1 B I 0 p .2–7.5 T, = 9–2500 kA. Measurements of λq
omp
in the database
are made exclusively on all devices using a variety of fast reciprocating Langmuir probes
entering the plasma at a variety of poloidal locations, but with the majority being on the
low field side. Statistical analysis of the database reveals nine reasonable engineering
and dimensionless scalings. All yield, however, similar predicted values of λq
omp
mapped
to the outside midplane. The engineering scaling with the highest statistical significance,
λ = ( / ( )) ( / /κ) − −
q 10 P V W m a R omp tot 3 0.38 1.3
, dependent on input power density, aspect ratio and elongation, yields λq omp = [7, 4, 5] cm for Ip = [2.5, 5.0, 7.5] MA, the three reference limiter plasma currents specified in the ITER heat and nuclear load specifications. Mapped to the inboard midplane, the worst case (7.5 MA) corresponds to λq ~ 57 1 ± 4 imp mm, thus consolidating the 50mm width used to optimize the FW panel toroidal shape.EURATOM 633053Czech Science Foundation GA CR P205/12/2327, GA15-10723S, MSMT LM2011021US Department of Energy DE-FG02- 07ER54917, DE-AC02-09CH11466, DE-FC02-04ER5469
Impacts of changes in groundwater recharge on the isotopic composition and geochemistry of seasonally ice-covered lakes: insights for sustainable management
Lakes are under increasing pressure due to widespread anthropogenic impacts
related to rapid development and population growth. Accordingly, many lakes
are currently undergoing a systematic decline in water quality. Recent
studies have highlighted that global warming and the subsequent changes in
water use may further exacerbate eutrophication in lakes. Lake evolution
depends strongly on hydrologic balance, and therefore on groundwater
connectivity. Groundwater also influences the sensitivity of lacustrine
ecosystems to climate and environmental changes, and governs their
resilience. Improved characterization of groundwater exchange with lakes is
needed today for lake preservation, lake restoration, and sustainable
management of lake water quality into the future. In this context, the aim of
the present paper is to determine if the future evolution of the climate, the
population, and the recharge could modify the geochemistry of lakes (mainly
isotopic signature and quality via phosphorous load) and if the isotopic
monitoring of lakes could be an efficient tool to highlight the variability
of the water budget and quality.
Small groundwater-connected lakes were chosen to simulate changes in water
balance and water quality expected under future climate change scenarios,
namely representative concentration pathways (RCPs) 4.5 and 8.5. Contemporary
baseline conditions, including isotope mass balance and geochemical
characteristics, were determined through an intensive field-based research
program prior to the simulations. Results highlight that future lake
geochemistry and isotopic composition trends will depend on four main
parameters: location (and therefore climate conditions), lake catchment size
(which impacts the intensity of the flux change), lake volume (which impacts
the range of variation), and lake G index (i.e., the percentage of
groundwater that makes up total lake inflows), the latter being the dominant
control on water balance conditions, as revealed by the sensitivity of lake
isotopic composition. Based on these model simulations, stable isotopes
appear to be especially useful for detecting changes in recharge to lakes
with a G index of between 50 and 80 %, but response is non-linear.
Simulated monthly trends reveal that evolution of annual lake isotopic
composition can be dampened by opposing monthly recharge fluctuations. It is
also shown that changes in water quality in groundwater-connected lakes
depend significantly on lake location and on the intensity of recharge
change
Generalized quasiperiodic Rauzy tilings
We present a geometrical description of new canonical -dimensional
codimension one quasiperiodic tilings based on generalized Fibonacci sequences.
These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual
Penrose and icosahedral tilings. Thanks to a natural indexing of the sites
according to their local environment, we easily write down, for any
approximant, the sites coordinates, the connectivity matrix and we compute the
structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change
Describing the set of words generated by interval exchange transformation
Let be an infinite word over finite alphabet . We get combinatorial
criteria of existence of interval exchange transformations that generate the
word W.Comment: 17 pages, this paper was submitted at scientific council of MSU,
date: September 21, 200
Stacked magma lenses beneath mid-ocean ridges: insights from new seismic observations and synthesis with prior geophysical and geologic findings
Author Posting. © American Geophysical Union, 2021. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Solid Earth 126(4), (2021): e2020JB021434, https://doi.org/10.1029/2020JB021434.Recent multi-channel seismic studies of fast spreading and hot-spot influenced mid-ocean ridges reveal magma bodies located beneath the mid-crustal Axial Magma Lens (AML), embedded within the underlying crustal mush zone. We here present new seismic images from the Juan de Fuca Ridge that show reflections interpreted to be from vertically stacked magma lenses in a number of locations beneath this intermediate-spreading ridge. The brightest reflections are beneath Northern Symmetric segment, from ∼46°42′-52′N and Split Seamount, where a small magma body at local Moho depths is also detected, inferred to be a source reservoir for the stacked magma lenses in the crust above. The imaged magma bodies are sub-horizontal, extend continuously for along-axis lengths of ∼1–8 km, with the shallowest located at depths of ∼100–1,200 m below the AML, and are similar to sub-AML bodies found at the East Pacific Rise. At both ridges, stacked sill-like lenses are detected beneath only a small fraction of the ridge length examined and are inferred to mark local sites of higher melt flux and active replenishment from depth. The imaged magma lenses are focused in the upper part of the lower crust, which coincides with the most melt rich part of the crystal mush zone detected in other geophysical studies and where sub-vertical fabrics are observed in geologic exposures of oceanic crust. We infer that the multi-level magma accumulations are ephemeral and may result from porous flow and mush compaction, and that they can be tapped and drained during dike intrusion and eruption events.This research was supported by NSF OCE 0002488 and 0648303 (LDEO), 0002551 (WHOI), 1658199 and 1357076 (UTIG). S. M. Carbotte was partially supported by Columbia University and J. P. Canales by the Independent Research & Development Program at WHOI
Triangulations and Severi varieties
We consider the problem of constructing triangulations of projective planes
over Hurwitz algebras with minimal numbers of vertices. We observe that the
numbers of faces of each dimension must be equal to the dimensions of certain
representations of the automorphism groups of the corresponding Severi
varieties. We construct a complex involving these representations, which should
be considered as a geometric version of the (putative) triangulations
- …