scholarly journals Ergodic currents dual to a real tree

2014 ◽  
Vol 36 (3) ◽  
pp. 745-766 ◽  
Author(s):  
THIERRY COULBOIS ◽  
ARNAUD HILION
Keyword(s):  
Free Group ◽  
Outer Space ◽  
Unique Ergodicity ◽  
Real Tree ◽  
Dense Orbits ◽  
A Current

Let $T$ be an $\mathbb{R}$-tree with dense orbits in the boundary of outer space. When the free group $\mathbb{F}_{N}$ acts freely on $T$, we prove that the number of projective classes of ergodic currents dual to $T$ is bounded above by $3N-5$. We combine Rips induction and splitting induction to define unfolding induction for such an $\mathbb{R}$-tree $T$. Given a current ${\it\mu}$ dual to $T$, the unfolding induction produces a sequence of approximations converging towards ${\it\mu}$. We also give a unique ergodicity criterion.

Toric Geometry ofSL2(ℂ) Free Group Character Varieties from Outer Space

2018 ◽  
Vol 70 (2) ◽  
pp. 354-399 ◽  
Author(s):  
Christopher Manon
Keyword(s):  
Free Group ◽  
Outer Space ◽  
Integrable Hamiltonian System ◽  
Outer Automorphism ◽  
Character Variety ◽  
Toric Geometry ◽  
Character Varieties ◽  
Simplicial Space ◽  
Proper Map ◽  
Divisorial Valuations

AbstractCuller and Vogtmann defined a simplicial spaceO(g), calledouter space, to study the outer automorphism group of the free groupFg. Using representation theoretic methods, we give an embedding ofO(g) into the analytification of X(Fg,SL2(ℂ)), theSL2(ℂ) character variety ofFg, reproving a result of Morgan and Shalen. Then we show that every pointvcontained in a maximal cell ofO(g) defines a flat degeneration of X(Fg,SL2(ℂ)) to a toric varietyX(PΓ). We relate X(Fg,SL2(ℂ)) andX(v) topologically by showing that there is a surjective, continuous, proper map Ξv:X(Fg,SL2(ℂ)) →X(v). We then show that this map is a symplectomorphism on a dense open subset of X(Fg, SL2(ℂ)) with respect to natural symplectic structures on X(Fg, SL2(ℂ)) andX(v). In this way, we construct an integrable Hamiltonian system in X(Fg, SL2(ℂ)) for each point in a maximal cell ofO(g), and we show that eachvdefines a topological decomposition of X(Fg, SL2(ℂ)) derived from the decomposition ofX(PΓ) by its torus orbits. Finally, we show that the valuations coming from the closure of a maximal cell inO(g) all arise as divisorial valuations built from an associated projective compactification of X(Fg, SL2(ℂ)).

scholarly journals Assessment of fog and rain induced-attenuation on terrestrial FSO links

2020 ◽  
Vol 4 (1) ◽  
pp. 37-44
Author(s):  
M. O. Ajewole ◽  
P. A. Owolawi ◽  
J. S. Ojo ◽  
R. M. Adetunji
Keyword(s):  
High Speed ◽  
Rain Rate ◽  
Outer Space ◽  
Atmospheric Conditions ◽  
Wireless Communication Network ◽  
5G Network ◽  
Link Margin ◽  
Communication Links ◽  
Atmospheric Channel ◽  
A Current

Launching into the next generation of wireless communication network (5G network) requires secure highdata rate, high speed and huge bandwidth links. With the tremendous increase in broadband users, the existingcommunication systems such as radio frequency (RF) and microwave links cannot meet up with the challenges due totheir link interference and low bandwidth. A current technology that promises such requirements and more is FreeSpace Optical (FSO) communication. The FSO basically involves the transmission of signal-modulated opticalradiation from a transmitter to a receiver through the atmosphere or outer space. It is designed to complement thetraditional fibre optical communication links. However, location-variant atmospheric channel degrades the qualityand performance of an FSO system under severe atmospheric conditions. This paper attempts to assess both fog- andrain-induced attenuation on the performance of FSO link in a terrestrial terrain using measured visibility and rainrate data at Akure, Nigeria. 5-year (2012-2016) archived visibility data and measured rain rate data of 1-minuteintegration time obtained from Nigerian Meteorological Agency (NIMET) and the Department of Physics, FederalUniversity of Technology, Akure respectively, were used to compute the fog- and rain-induced specific attenuationsusing Kruse and Carboneur models. The performance of the FSO system was analyzed through link margin by usingthe parameters of a commercial optical transceiver, Terescope 5000. Findings from this work will be useful for FSOsystem design in the area.

scholarly journals The minimally displaced set of an irreducible automorphism is locally finite

2020 ◽  
Vol 55 (2) ◽  
pp. 301-336
Author(s):  
Stefano Francaviglia ◽  
◽  
Armando Martino ◽  
Dionysios Syrigos ◽  
◽  
...  
Keyword(s):  
Free Group ◽  
Outer Space ◽  
General Setting ◽  
Deformation Space ◽  
Train Track ◽  
Free Products ◽  
Deformation Spaces ◽  
Locally Finite ◽  
Irreducible Automorphism

We prove that the minimally displaced set of a relatively irreducible automorphism of a free splitting, situated in a deformation space, is uniformly locally finite. The minimally displaced set coincides with the train track points for an irreducible automorphism. We develop the theory in a general setting of deformation spaces of free products, having in mind the study of the action of reducible automorphisms of a free group on the simplicial bordification of Outer Space. For instance, a reducible automorphism will have invariant free factors, act on the corresponding stratum of the bordification, and in that deformation space it may be irreducible (sometimes this is referred as relative irreducibility).

scholarly journals NON-RIGIDITY OF CYCLIC AUTOMORPHIC ORBITS IN FREE GROUPS

2012 ◽  
Vol 22 (03) ◽  
pp. 1250021 ◽  
Author(s):  
BRIAN RAY
Keyword(s):  
General Theory ◽  
Free Group ◽  
Outer Space ◽  
Free Groups ◽  
Length Function ◽  
Translation Length

We say a subset Σ ⊆ FN of the free group of rank N is spectrally rigid if whenever T1, T2 ∈ cv N are ℝ-trees in (unprojectivized) outer space for which ‖σ‖T1 = ‖σ‖T2 for every σ ∈ Σ, then T1 = T2 in cv N. The general theory of (non-abelian) actions of groups on ℝ-trees establishes that T ∈ cv N is uniquely determined by its translation length function ‖⋅‖T : FN → ℝ, and consequently that FN itself is spectrally rigid. Results of Smillie and Vogtmann, and of Cohen, Lustig and Steiner establish that no finite Σ is spectrally rigid. Capitalizing on their constructions, we prove that for any Φ ∈ Aut (FN) and g ∈ FN, the set Σ = {Φn(g)}n∈ℤ is not spectrally rigid.

scholarly journals ℝ-trees, dual laminations and compact systems of partial isometries

2009 ◽  
Vol 147 (2) ◽  
pp. 345-368 ◽  
Author(s):  
THIERRY COULBOIS ◽  
ARNAUD HILION ◽  
MARTIN LUSTIG
Keyword(s):  
Dynamical System ◽  
Free Group ◽  
Finite Rank ◽  
Partial Isometries ◽  
Minimal Action ◽  
Dense Orbits

AbstractLetFNbe a free group of finite rankN≥ 2, and letTbe an ℝ-tree with a very small, minimal action ofFNwith dense orbits. For any basisofFNthere exists aheart$K_{\CAr}$⊂(= the metric completion ofT) which is a compact subtree that has the property that the dynamical system of partial isometriesai:$K_{\CAr} \cap a_{i} K_{\CAr} \to a_{i}\inv K_{\CAr} \cap K_{\CAr}$, for eachai∈, defines a tree$T_{(K_{\CAn}, \CAr)}$which contains an isometric copy ofTas minimal subtree.

Radiation Damage in Ceramics

1982 ◽  
Vol 40 ◽  
pp. 600-603
Author(s):  
T. E. Mitchell ◽  
M. R. Pascucci ◽  
R. A. Youngman
Keyword(s):  
Radiation Damage ◽  
Outer Space ◽  
Point Of View ◽  
Nuclear Waste Storage ◽  
Waste Storage ◽  
Storage Media ◽  
Transmission Electron ◽  
Fundamental Point ◽  
Small Defect ◽  
Present Understanding

1. Introduction. Studies of radiation damage in ceramics are of interest not only from a fundamental point of view but also because it is important to understand the behavior of ceramics in various practical radiation enyironments- fission and fusion reactors, nuclear waste storage media, ion-implantation devices, outer space, etc. A great deal of work has been done on the spectroscopy of point defects and small defect clusters in ceramics, but relatively little has been performed on defect agglomeration using transmission electron microscopy (TEM) in the same kind of detail that has been so successful in metals. This article will assess our present understanding of radiation damage in ceramics with illustrations using results obtained from the authors' work.

Resolving Crystallites in Zirconium Oxide Films

1969 ◽  
Vol 27 ◽  
pp. 140-141
Author(s):  
R.A. Ploc
Keyword(s):  
Electron Microscope ◽  
Inelastic Scattering ◽  
Zirconium Oxide ◽  
Oxide Films ◽  
Optic Axis ◽  
Objective Lens ◽  
Microscope Objective ◽  
Linear Optic ◽  
A Current ◽  
Microscope Objective Lens

The optic axis of an electron microscope objective lens is usually assumed to be straight and co-linear with the mechanical center. No reason exists to assume such perfection and, indeed, simple reasoning suggests that it is a complicated curve. A current centered objective lens with a non-linear optic axis when used in conjunction with other lenses, leads to serious image errors if the nature of the specimen is such as to produce intense inelastic scattering.

Structure of Palladium Single-Crystal Films Prepared by Flash Evaporation onto (001) NaCl Substrates

1970 ◽  
Vol 28 ◽  
pp. 456-457
Author(s):  
L. E. Murr ◽  
G. Wong
Keyword(s):  
Single Crystal ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
High Rate ◽  
Flash Evaporation ◽  
Optimum Load ◽  
Single Crystal Films ◽  
Crystal Films ◽  
A Current

Palladium single-crystal films have been prepared by Matthews in ultra-high vacuum by evaporation onto (001) NaCl substrates cleaved in-situ, and maintained at ∼ 350° C. Murr has also produced large-grained and single-crystal Pd films by high-rate evaporation onto (001) NaCl air-cleaved substrates at 350°C. In the present work, very large (∼ 3cm2), continuous single-crystal films of Pd have been prepared by flash evaporation onto air-cleaved (001) NaCl substrates at temperatures at or below 250°C. Evaporation rates estimated to be ≧ 2000 Å/sec, were obtained by effectively short-circuiting 1 mil tungsten evaporation boats in a self-regulating system which maintained an optimum load current of approximately 90 amperes; corresponding to a current density through the boat of ∼ 4 × 104 amperes/cm2.

Novel magneto-optical recording materials: Bi-substituted garnet films

1991 ◽  
Vol 49 ◽  
pp. 776-777
Author(s):  
Takao Suzuki ◽  
Hossein Nuri
Keyword(s):  
Grain Size ◽  
Amorphous Film ◽  
Nitrogen Atmosphere ◽  
Optical Recording ◽  
Garnet Film ◽  
Media Noise ◽  
Garnet Films ◽  
Order Of Magnitude ◽  
A New Technique ◽  
A Current

For future high density magneto-optical recording materials, a Bi-substituted garnet film ((BiDy)3(FeGa)5O12) is an attractive candidate since it has strong magneto-optic effect at short wavelengths less than 600 nm. The signal in read back performance at 500 nm using a garnet film can be an order of magnitude higher than a current rare earth-transition metal amorphous film. However, the granularity and surface roughness of such crystalline garnet films are the key to control for minimizing media noise.We have demonstrated a new technique to fabricate a garnet film which has much smaller grain size and smoother surfaces than those annealed in a conventional oven. This method employs a high ramp-up rate annealing (Γ = 50 ~ 100 C/s) in nitrogen atmosphere. Fig.1 shows a typical microstruture of a Bi-susbtituted garnet film deposited by r.f. sputtering and then subsequently crystallized by a rapid thermal annealing technique at Γ = 50 C/s at 650 °C for 2 min. The structure is a single phase of garnet, and a grain size is about 300A.

Facet Topography and Dislocation Structure as a Possible Source for Electrical Heterogeneity in [001] TILT Bicrystals of YBa2Cu3O7-δ

1996 ◽  
Vol 54 ◽  
pp. 338-339
Author(s):  
I-Fei Tsu ◽  
D.L. Kaiser ◽  
S.E. Babcock
Keyword(s):  
Grain Boundary ◽  
Critical Current Density ◽  
Critical Current ◽  
Current Density ◽  
Electromagnetic Properties ◽  
Length Scale ◽  
Density Values ◽  
Current Densities ◽  
Applied Fields ◽  
A Current

A current theme in the study of the critical current density behavior of YBa2Cu3O7-δ (YBCO) grain boundaries is that their electromagnetic properties are heterogeneous on various length scales ranging from 10s of microns to ˜ 1 Å. Recently, combined electromagnetic and TEM studies on four flux-grown bicrystals have demonstrated a direct correlation between the length scale of the boundaries’ saw-tooth facet configurations and the apparent length scale of the electrical heterogeneity. In that work, enhanced critical current densities are observed at applied fields where the facet period is commensurate with the spacing of the Abrikosov flux vortices which must be pinned if higher critical current density values are recorded. To understand the microstructural origin of the flux pinning, the grain boundary topography and grain boundary dislocation (GBD) network structure of [001] tilt YBCO bicrystals were studied by TEM and HRTEM.

Sign in / Sign up

Export Citation Format

Share Document