scholarly journals Finitely many physical measures for sectional-hyperbolic attracting sets and statistical stability

2020 ◽  
pp. 1-28
Author(s):  
VITOR ARAUJO
Keyword(s):  
Vector Field ◽  
Statistical Stability ◽  
Srb Measures ◽  
Attracting Set ◽  
Inner Radius ◽  
Physical Measures ◽  
Almost All ◽  
Uniformly Bounded

Abstract We show that a sectional-hyperbolic attracting set for a Hölder- $C^{1}$ vector field admits finitely many physical/SRB measures whose ergodic basins cover Lebesgue almost all points of the basin of topological attraction. In addition, these physical measures depend continuously on the flow in the $C^{1}$ topology, that is, sectional-hyperbolic attracting sets are statistically stable. To prove these results we show that each central-unstable disk in a neighborhood of this class of attracting sets is eventually expanded to contain a ball whose inner radius is uniformly bounded away from zero.

ON THE GENERALITY OF THE UNFOLDED CHUA'S CIRCUIT

1996 ◽  
Vol 06 (05) ◽  
pp. 801-832 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Topological Conjugacy ◽  
Chua’S Oscillator ◽  
State Observability ◽  
Almost All ◽  
Special Case ◽  
Scalar Nonlinearity

In this paper, we study the generality of Chua's oscillator by deriving a class of vector fields that Chua's oscillator is equivalent to. For the class of vector fields with a scalar nonlinearity, we prove that under certain conditions, two such vector fields are topologically conjugate if the Jacobian matrices at each point have the same eigenvalues and the equilibrium points are matched up. We show how these conditions are related to the complete state observability of a corresponding linear system. These results are used to show that the n-dimensional Chua's oscillator is topologically conjugate to almost every vector field in this class. We comment on the special case when the vector field is piecewise-linear and in particular when the vector field is 2-segment piecewise-linear. These results are illustrated by transforming several systems studied in the literature into equivalent Chua's oscillators. We also extend some of these results to the case of several scalar nonlinearities. As a corollary we prove that almost all piecewise-linear vector fields with parallel boundary planes are topologically conjugate if the boundary planes and equilibrium points are the same and the eigenvalues in corresponding regions are the same. We also give a dual result of topological conjugacy.

Function space topologies defined by sectional integrals and applications to an extremal problem

1980 ◽  
Vol 87 (1) ◽  
pp. 81-96 ◽  
Author(s):  
K. J. Falconer
Keyword(s):  
Extremal Problem ◽  
Final Section ◽  
Convex Set ◽  
Compact Convex ◽  
Unit Vector ◽  
Extremal Values ◽  
Almost All ◽  
Function Space Topologies ◽  
Dimensional Lebesgue Measure ◽  
Uniformly Bounded

Let H(t, θ) be the hyperplane in Rn (n ≥ 2) which is perpendicular to the unit vector θ, and distant t from the origin; that is H(t, θ) = {x ε Rn: x.θ = t}. (Note that H(t, θ) and H(−t, − θ) are the same hyperplane.) If f(x) εℒ1(Rn), we will denote the integral of f with respect to (n − 1)-dimensional Lebesgue measure over H(t, θ) by F(t, θ), termed the projection or sectional integral of f over H(t,θ). By Fubini's theorem, F(t, θ) exists for almost all t for any θ. Throughout this paper we will assume that f(x) has support in X, a compact convex subset of Rn. In Section 2 we examine some of the topologies that may be defined on functions on X in terms of the F(t, θ), and in the remainder of the paper we examine the extremal problem suggested by Croft (4), that of maximizing the integral of f over the set X with the constraint that the F(t, θ) are uniformly bounded above. We examine in particular how the extremal values depend on the convex set X. In the final section the extremal problem is related to a generalization of Bang's plank theorem and the theory of capacities, and several conjectures are proposed.

scholarly journals Constant-roll inflation in the generalized SU(2) Proca theory

2021 ◽  
Author(s):  
Juan Garnica Aguirre ◽  
Luis Gomez Diaz ◽  
Andres Navarro Leon ◽  
Yeinzon Rodriguez Garcia
Keyword(s):  
Vector Field ◽  
Degrees Of Freedom ◽  
Coupling Constants ◽  
Kinetic Term ◽  
De Sitter ◽  
Attraction Basin ◽  
Slow Roll ◽  
Dimensional Phase Space ◽  
Almost All ◽  
New Interactions

Abstract The generalized SU(2) Proca theory (GSU2P for short) is a variant of the well known generalized Proca theory (GP for short) where the vector field belongs to the Lie algebra of the SU(2) group of global transformations under which the action is made invariant. New interesting possibilities arise in this framework because of the existence of new interactions of purely non-Abelian character and new configurations of the vector field that result in spatial spherical symmetry and the cosmological dynamics being driven by the propagating degrees of freedom. We study the two-dimensional phase space of the system that results when the cosmic triad configuration is employed in the Friedmann-Lemaitre-Robertson-Walker background and find an attractor curve whose attraction basin covers almost all the allowed region. Such an attractor curve corresponds to a primordial inflationary solution that has the following characteristic properties: 1.) it is a de Sitter solution whose Hubble parameter is regulated by a generalized version of the SU(2) group coupling constant, 2.) it is constant-roll including, as opposite limiting cases, the slow-roll and ultra slow-roll varieties, 3.) a number of e-folds $N > 60$ is easily reached, 4.) it has a graceful exit into a radiation dominated period powered by the canonical kinetic term of the vector field and the Einstein-Hilbert term. The free parameters of the action are chosen such that the tensor sector of the theory is the same as that of general relativity at least up to second-order perturbations, thereby avoiding the presence of ghost and Laplacian instabilities in the tensor sector as well as making the gravity waves propagate at light speed. This is a proof of concept of the interesting properties we could find in this scenario when the coupling constants be replaced by general coupling functions.

Habitat Association of Klebsiella Species

1985 ◽  
Vol 6 (2) ◽  
pp. 52-58 ◽  
Author(s):  
Susan T. Bagley
Keyword(s):  
Drinking Water ◽  
Gastrointestinal Tract ◽  
Surface Waters ◽  
Industrial Effluents ◽  
Opportunistic Pathogen ◽  
Habitat Associations ◽  
Habitat Association ◽  
Klebsiella Species ◽  
Almost All ◽  
Polluted Waters

AbstractThe genus Klebsiella is seemingly ubiquitous in terms of its habitat associations. Klebsiella is a common opportunistic pathogen for humans and other animals, as well as being resident or transient flora (particularly in the gastrointestinal tract). Other habitats include sewage, drinking water, soils, surface waters, industrial effluents, and vegetation. Until recently, almost all these Klebsiella have been identified as one species, ie, K. pneumoniae. However, phenotypic and genotypic studies have shown that “K. pneumoniae” actually consists of at least four species, all with distinct characteristics and habitats. General habitat associations of Klebsiella species are as follows: K. pneumoniae—humans, animals, sewage, and polluted waters and soils; K. oxytoca—frequent association with most habitats; K. terrigena— unpolluted surface waters and soils, drinking water, and vegetation; K. planticola—sewage, polluted surface waters, soils, and vegetation; and K. ozaenae/K. rhinoscleromatis—infrequently detected (primarily with humans).

SEM Cold Stage Techniques for the Observation of Vegetative and Floral Apices of Oat (Avena sativa L.) Plants

1977 ◽  
Vol 35 ◽  
pp. 590-591
Author(s):  
B. K. Kirchoff ◽  
L.F. Allard ◽  
W.C. Bigelow
Keyword(s):  
Critical Point ◽  
Avena Sativa ◽  
Substantial Improvement ◽  
Fresh Tissue ◽  
Cold Stage ◽  
Critical Point Drying ◽  
Almost All ◽  
Cell Collapse ◽  
Conductive Paint ◽  
Carbon Based

In attempting to use the SEM to investigate the transition from the vegetative to the floral state in oat (Avena sativa L.) it was discovered that the procedures of fixation and critical point drying (CPD), and fresh tissue examination of the specimens gave unsatisfactory results. In most cases, by using these techniques, cells of the tissue were collapsed or otherwise visibly distorted. Figure 1 shows the results of fixation with 4.5% formaldehyde-gluteraldehyde followed by CPD. Almost all cellular detail has been obscured by the resulting shrinkage distortions. The larger cracks seen on the left of the picture may be due to dissection damage, rather than CPD. The results of observation of fresh tissue are seen in Fig. 2. Although there is a substantial improvement over CPD, some cell collapse still occurs.Due to these difficulties, it was decided to experiment with cold stage techniques. The specimens to be observed were dissected out and attached to the sample stub using a carbon based conductive paint in acetone.

Electron microscopy studies of plasma-sprayed materials

1983 ◽  
Vol 41 ◽  
pp. 70-71
Author(s):  
K.R. Subramanian ◽  
A.H. King ◽  
H. Herman
Keyword(s):  
Plasma Spraying ◽  
Substrate Surface ◽  
Flame Temperature ◽  
Ceramic Coatings ◽  
Metallic Substrates ◽  
Hot Plasma ◽  
Almost All ◽  
Plasma Sprayed ◽  
Hostile Environments ◽  
Plasma Spraying Process

Plasma spraying is a technique which is used to apply coatings to metallic substrates for a variety of purposes, including hardfacing, corrosion resistance and thermal barrier applications. Almost all of the applications of this somewhat esoteric fabrication technique involve materials in hostile environments and the integrity of the coatings is of paramount importance: the effects of process variables on such properties as adhesive strength, cohesive strength and hardness of the substrate/coating system, however, are poorly understood.Briefly, the plasma spraying process involves forming a hot plasma jet with a maximum flame temperature of approximately 20,000K and a gas velocity of about 40m/s. Into this jet the coating material is injected, in powder form, so it is heated and projected at the substrate surface. Relatively thick metallic or ceramic coatings may be speedily built up using this technique.

Vacuum System to Minimize the Specimen Contamination of High-Performance EM

1977 ◽  
Vol 35 ◽  
pp. 68-69
Author(s):  
N. Yoshimura ◽  
K. Shirota ◽  
T. Etoh
Keyword(s):  
Electron Microscope ◽  
High Speed ◽  
High Performance ◽  
High Vacuum ◽  
Vacuum System ◽  
Pump System ◽  
Pumping System ◽  
Diffusion Pump ◽  
Almost All ◽  
Cascade Type

One of the most important requirements for a high-performance EM, especially an analytical EM using a fine beam probe, is to prevent specimen contamination by providing a clean high vacuum in the vicinity of the specimen. However, in almost all commercial EMs, the pressure in the vicinity of the specimen under observation is usually more than ten times higher than the pressure measured at the punping line. The EM column inevitably requires the use of greased Viton O-rings for fine movement, and specimens and films need to be exchanged frequently and several attachments may also be exchanged. For these reasons, a high speed pumping system, as well as a clean vacuum system, is now required. A newly developed electron microscope, the JEM-100CX features clean high vacuum in the vicinity of the specimen, realized by the use of a CASCADE type diffusion pump system which has been essentially improved over its predeces- sorD employed on the JEM-100C.

Quantitative Freeze Fracture Studies of Gap Junctions in Somatic Cell Hybrids, Their Parents, and Revertants

1976 ◽  
Vol 34 ◽  
pp. 218-219
Author(s):  
W. J. Larsen ◽  
R. Azarnia ◽  
W. R. Loewenstein
Keyword(s):  
Gap Junctions ◽  
Striated Muscle ◽  
Freeze Fracture ◽  
Cell Movement ◽  
Dye Molecules ◽  
Somatic Cell Hybrids ◽  
Cell Coupling ◽  
Normal Cells ◽  
Mediate Cell ◽  
Almost All

Although the physiological significance of the gap junction remains unspecified, these membrane specializations are now recognized as common to almost all normal cells (excluding adult striated muscle and some nerve cells) and are found in organisms ranging from the coelenterates to man. Since it appears likely that these structures mediate the cell-to-cell movement of ions and small dye molecules in some electrical tissues, we undertook this study with the objective of determining whether gap junctions in inexcitable tissues also mediate cell-to-cell coupling.To test this hypothesis, a coupling, human Lesh-Nyhan (LN) cell was fused with a non-coupling, mouse cl-1D cell, and the hybrids, revertants, and parental cells were analysed for coupling with respect both to ions and fluorescein and for membrane junctions with the freeze fracture technique.

Angular Resolved Electron Spectroscopy with Parallel Recording

1990 ◽  
Vol 48 (2) ◽  
pp. 370-371
Author(s):  
Huang Min ◽  
P.S. Flora ◽  
C.J. Harland ◽  
J.A. Venables
Keyword(s):  
Electron Spectroscopy ◽  
Low Voltage ◽  
Solid Angle ◽  
Detection System ◽  
Voltage Electron ◽  
Cylindrical Mirror ◽  
Inner Radius ◽  
Channel Plate ◽  
And Performance ◽  
Type Detector

A cylindrical mirror analyser (CMA) has been built with a parallel recording detection system. It is being used for angular resolved electron spectroscopy (ARES) within a SEM. The CMA has been optimised for imaging applications; the inner cylinder contains a magnetically focused and scanned, 30kV, SEM electron-optical column. The CMA has a large inner radius (50.8mm) and a large collection solid angle (Ω > 1sterad). An energy resolution (ΔE/E) of 1-2% has been achieved. The design and performance of the combination SEM/CMA instrument has been described previously and the CMA and detector system has been used for low voltage electron spectroscopy. Here we discuss the use of the CMA for ARES and present some preliminary results.The CMA has been designed for an axis-to-ring focus and uses an annular type detector. This detector consists of a channel-plate/YAG/mirror assembly which is optically coupled to either a photomultiplier for spectroscopy or a TV camera for parallel detection.

Analytical Electron Microscopy Study of Second-Phase Particles in 7075 and 7475 Aluminum Alloys

1985 ◽  
Vol 43 ◽  
pp. 348-349
Author(s):  
M. Raghavan ◽  
J. Y. Koo ◽  
J. W. Steeds ◽  
B. K. Park
Keyword(s):  
Aluminum Alloys ◽  
Silicon Oxide ◽  
Analytical Electron Microscopy ◽  
Microscopy Study ◽  
Electron Microscopy Study ◽  
Partial Substitution ◽  
Second Phase ◽  
X Ray ◽  
Second Phase Particles ◽  
Almost All

X-ray microanalysis and Convergent Beam Electron Diffraction (CBD) studies were conducted to characterize the second phase particles in two commercial aluminum alloys -- 7075 and 7475. The second phase particles studied were large (approximately 2-5μm) constituent phases and relatively fine ( ∼ 0.05-1μn) dispersoid particles, Figures 1A and B. Based on the crystal structure and chemical composition analyses, the constituent phases found in these alloys were identified to be Al7Cu2Fe, (Al,Cu)6(Fe,Cu), α-Al12Fe3Si, Mg2Si, amorphous silicon oxide and the modified 6Fe compounds, in decreasing order of abundance. The results of quantitative X-ray microanalysis of all the constituent phases are listed in Table I. The data show that, in almost all the phases, partial substitution of alloying elements occurred resulting in small deviations from the published stoichiometric compositions of the binary and ternary compounds.

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