Central Ellipse Research Articles

Universal Hitting Time Statistics for Integrable Flows

The perceived randomness in the time evolution of “chaotic” dynamical systems can be characterized by universal probabilistic limit laws, which do not depend on the fine features of the individual system. One important example is the Poisson law for the times at which a particle with random initial data hits a small set. This was proved in various settings for dynamical systems with strong mixing properties. The key result of the present study is that, despite the absence of mixing, the hitting times of integrable flows also satisfy universal limit laws which are, however, not Poisson. We describe the limit distributions for “generic” integrable flows and a natural class of target sets, and illustrate our findings with two examples: the dynamics in central force fields and ellipse billiards. The convergence of the hitting time process follows from a new equidistribution theorem in the space of lattices, which is of independent interest. Its proof exploits Ratner’s measure classification theorem for unipotent flows, and extends earlier work of Elkies and McMullen.

Accurate TOF measurement of ultrasonic signal echo from the liquid level based on a 2-D image processing method

The central ellipse algorithm can be employed to measure the time of flight (TOF) of the returned signal in ultrasonic range detection. However, the existing ellipse algorithm is likely to result in a considerable measuring error, because the algorithm simply treats the time corresponding to the vertical axis of the ellipse extracted from the echo signal as the TOF. To improve the measuring accuracy of the TOF, we propose a modified TOF measurement method based on the existing ellipse algorithm, where the Canny operator for edge detection in 2-D image processing is used. first, the ellipse algorithm is utilized to extract the echo pulse from the ultrasonic echo signal, from which a 2-D pulse pattern approximating an elliptical shape is obtained. Then, the Canny operator is applied to detect the boundary of the extracted elliptic pulse. Finally, the maximum gradients of the ellipse edge variation in the second and third quadrants of the coordinate system are calculated, and the TOF can be determined by averaging two time points corresponding to two maximum gradients of the edge change in two quadrants. The relevant experiments demonstrate that the modified method can obtain a more accurate TOF with approximately 30% error reduction.

Observations and three-dimensional ionization structure of the planetary nebula SuWt 2★

The planetary nebula SuWt 2 (PN G311.0+02.4) is an unusual object with a prominent, inclined central emission ellipse and faint bipolar extensions. It has two A-type stars in a proven binary system at the centre. However, the radiation from these two central stars is too soft to ionize the surrounding material leading to a so far fruitless search for the responsible ionizing source. Such a source is clearly required and has already been inferred to exist via an observed temporal variation of the centre-of-mass velocity of the A-type stars. Moreover, the ejected nebula is nitrogen rich which raises question about the mass-loss process from a likely intermediate-mass progenitor. We use optical integral-field spectroscopy to study the emission lines of the inner nebula ring. This has enabled us to perform an empirical analysis of the optical collisionally excited lines, together with a fully three-dimensional photoionization modelling. Our empirical results are used to constrain the photoionization models, which determine the evolutionary stage of the responsible ionizing source and its likely progenitor. The time-scale for the evolutionary track of a hydrogen-rich model atmosphere is inconsistent with the dynamical age obtained for the ring. This suggests that the central star has undergone a very late thermal pulse. We conclude that the ionizing star could be hydrogen deficient and compatible with what is known as a PG 1159-type star. The evolutionary tracks for the very late thermal pulse models imply a central star mass of ∼0.64 M⊙, which originated from an ∼3 M⊙ progenitor. The evolutionary time-scales suggest that the central star left the asymptotic giant branch about 25 000 yr ago, which is consistent with the nebula's age.

Immediate breast reconstruction using autologous skin graft associated with breast implant

Immediate breast reconstruction with skin graft is still little mentioned in the literature. Follow-up studies regarding the technique aspects are particularly scarce. The objective was to detail immediate breast reconstruction using autologous skin graft. Patients (n=49) who underwent mastectomies and autologous immediate breast reconstruction with skin graft associated with a breast implant at A. C. Camargo Hospital (São Paulo, Brazil) between January 2007 and July 2010 were included. Information on clinical data, technique details and clinical outcome were prospectively collected. Following mastectomy, the autologous full-thickness skin graft was obtained through an inframammary fold incision along the contralateral breast in most patients. The skin graft was placed on the surface of the pectoralis major muscle after adjustments to conform to the mastectomy defect. A minimum of 10-month follow-up period was established. Patients' age ranged from 35 to 55 years and all received a silicone gel textured surface implant to obtain the necessary breast mound. The mean surgical time was 45min, and the mean amount of skin resection was 4.5cm in the largest diameter. Follow-up ranged from 10 to 35 months (median 23). All patients had silicone-gel textured surface implants to perform the breast mound reconstruction. No complications were observed in 87.8% of reconstructions. Forty-six patients (94%) had no complaints about the donor-site aesthetics. The result was a breast mound with a central ellipse of healed skin graft. Three (6%) poor results were observed. Thirty-six patients (67%) reported the results as good or very good. Our results lead us to conclude that autologous skin graft provided a reliable option in immediate breast reconstruction to skin-sparing mastectomy defects. The technique accomplished a single-stage implant breast reconstruction when there is inadequate skin coverage.

Reemergence of Rabies in Chhukha District, Bhutan, 2008

From January through July 2008, rabies reemerged in the Chhukha district of southwestern Bhutan. To clarify the distribution and direction of spread of this outbreak, we mapped reported cases and conducted directional tests (mean center and standard deviational ellipse). The outbreak resulted in the death of 97 animals (42 cattle, 52 dogs, and 3 horses). Antirabies vaccine was given free of charge to ≈674 persons suspected to have been exposed. The outbreak spread south to north and appeared to follow road networks, towns, and areas of high human density associated with a large, free-roaming, dog population. The outbreak was controlled by culling free-roaming dogs. To prevent spread into the interior of Bhutan, a well-coordinated national rabies control program should be implemented in disease-endemic areas.

Explaining historical urban development using the locations of mosques: A GIS/spatial statistics-based approach

Religious buildings, including temples, churches, synagogues and mosques have always been one of the integral components of the urban layout. This paper aims to answer the question whether the historical spatial development of a large-size city can be approximated using historical geographical and categorical data pertaining to its places of worship. We use data for 525 mosques built in Izmir, Turkey, over the years 1550–2008 and maps of built-up areas for the same period. Based on the results of GIS/spatial statistics-based analyses using the three basic measures of spatial statistics (mean center, weighted mean center and standard deviational ellipse), we conclude that the spatial distribution of mosques is a close proxy of urban development. Thus, location data for places of worship, often available and accessible, can be used to derive historical urban development over a given period.

Haptic Feature Extraction

This study examined the process by which the shape of a haptically explored object is synthesized from the geometric characteristics of simpler constituent elements, such as arcs and ellipses. Subjects traced the outlines of virtual objects by means of whole arm movements. Each object consisted of the union of a large central ellipse and two smaller circles, extending upward and outward from the top left and right sides of the base. The sizes of the two circles and the eccentricity of the elliptical base were varied. After exploring the object's contour in the absence of vision, subjects reproduced the sensed shape by means of freehand drawing. Speed and force were modulated during the exploratory phase in a manner that suggested that subjects reacted to rather than predicted changes in curvature. Also, subjects typically devoted more time to exploring the part of the contour encompassing the two smaller circles. During drawing, individual features of the explored shape were reproduced with varying degrees of fidelity. Aspects related to the size and location of the smaller circles were reproduced better than was the eccentricity of the ellipse forming the base. Since subjects spent proportionally less time exploring the base, these results suggest that subjects selectively focused attention to regions of high spatial contrast and that the exploratory strategy introduced distortions in the haptically sensed shapes.

Imaging Jupiter's Aurora at Visible Wavelengths

On November 9, 1996 and again on April 2, 1997, the Galileo spacecraft's Solid State Imaging (SSI) camera targeted the northern auroral region of Jupiter. These observations represent (i) the first spatially resolved images of the jovian auroral oval either at visible wavelengths or on the nightside of the planet, (ii) the first image at visible wavelengths of an auroral footprint of the Io Flux Tube (IFT), (iii) the first unambiguous detection at visible wavelengths of auroral emission on the jovian limb, and (iv) the first images of the aurora with spatial resolution below 100 km per pixel (46 and 35 km, respectively). Relative to many prior expectations, the visible aurora is (i) lower in altitude, (ii) associated with magnetic field lines that cross the equator closer to the planet, and (iii) more variable in time and space. The 1996 images used a clear (broadband) filter, while the 1997 images used both the clear filter and five narrower filters over wavelengths ranging from violet to 968 nm. The filtered images imply that the visible auroral emission contains atomic hydrogen lines, although there is also a continuum component. We were able to position the aurora in three-dimensional space and found the limb emission to be ∼240 km above the surface of a standard (P≈ 1 bar) reference ellipsoid. Our most accurate analysis of the equatormost part of the oval placed it at 54.5° planetocentric latitude and 168° west longitude. Combined with the latest magnetic field models, our results imply that the particles that cause the aurora originate in Jupiter's equatorial plane ∼13RJfrom the center of the planet. The oval was brighter and wider in the 1996 images than in the 1997 images. The broadband radiance of a typical place on the oval as seen directly overhead varied from ∼80 kR in 1997 to ∼300 kR in 1996. Our estimates of the full width of the oval varied from under 500 km to over 8000 km, partly depending on the signal-to-noise ratio of the image. The radiated power per unit length along the oval ranged from ∼60 to ∼700 W/m, with the associated radiated power from the entire oval varying from ∼109to ∼9 × 1010W. Appreciable auroral emission also occurred both north and south of the main oval. One image contains the northern footprint of the IFT, which appears as a central ellipse with a tail of emission that lies downstream with respect to the plasma flow past Io. The central ellipse is ∼1200 km downstream by ∼500 km cross stream. The IFT is comparable in brightness to the nearby auroral oval (∼250 kR) and has a total radiated power of ∼3 × 108W.

Mantle plume origin for the Bushveld and Ventersdorp magmatic provinces

Geochemical and isotopic data demonstrate that the parental magma of the lower zone of the Bushveld complex has been contaminated by the crust. Magmas similar in composition are identified in the Ventersdorp Supergroup, but these magmas are part of a series which includes members that are free of crustal contamination. Primary mantle melts can therefore be identified and their conditions of origin have been determined. The depth of origin is between 18 and 40 km. The presence of mantle, at such shallow depths in an intracratonic setting, is only explicable if a mantle diapir temporarily intruded the crust up to the base of the strong middle and upper crustal layer. Crustal melting and contamination occurred at the top of the diapir. In the Ventersdorp, crustal melts failed to impede the passage of mantle melts to the surface. In the Bushveld, mantle melts were impeded and only intruded outside the central ellipse of the crustal melts.

Computation of thermal residual stresses in optic fibers

We propose an analytic method of determining all the components of the residual stress tensor in optic fibers. The method is based on solving a plane problem for a cylindrical structure with singular stresses. We obtain closed-form solutions of the problem in the case of a piecewise-constant distribution of free deformations that model the presence of inclusions in the fiber with different values of the thermal coefficient of expansion. We also consider inclusions with cross sections in the shape of a circle, a central ellipse and a central annular sector. We describe the results obtained on this basis in the computation of residual thermal stresses.

Pattern formation and handedness in the cytoskeleton of human platelets.

The cytoskeletal patterns of human platelets spread on a glass surface are analyzed. F-actin is arranged in patterns of parallel microfilaments, microfilaments forming triangles, or microfilaments radiating tangentially from a central ellipse or circle. Vinculin, a cytoskeletal protein, is located at both ends of the filaments. In platelets with tangentially radiating microfilaments, vinculin patches are aligned on the branches of a two-armed spiral. The spirals are always left-handed. Talin and two integrins (gpIIb-IIIa, vitronectin receptor), proteins usually associated with focal contacts in tissue culture cells, are not concentrated at the ends of microfilaments in human platelets. It is suggested that the distribution of vinculin is due to competitive aggregation of vinculin close to the inner leaflet of the ventral plasma membrane and that sites of cytoskeleton-membrane linkage are important for generating supramolecular asymmetries of biological systems.

A Detailed Model of the Distribution of Synchrotron Emission in the Galactic Disk

A technique for separating the radio continuum emission of the Galaxy into its thermal and nonthermal components has been recently developed by Broadbent, Haslam and Osborne (1989). In this the thermal component is identified by its detailed correlation with the 60 μm infrared emission as observed by IRAS after the subtraction of zodiacal light and the HI-associated dust emission. This technique has been applied to the 408 MHz allsky survey of Haslam et al. (1982). A model of the distribution of synchrotron emissivity in the galactic disk has then been derived including information on the other tracers of spiral structure (HI, CO and giant HII regions) in order to account in detail for the observed nonthermal emission. The spiral arm pattern has two pairs of arms emanating from a central ellipse. The function describing the underlying variation of synchrotron emissivity with galactocentric radius is zero at the centre, rises to a sharp peak and then falls off slowly beyond 3 kpc. Using a scale length of the variation of cosmic ray electron density derived from γ-ray observations, we find that the scale length of the magnetic field variation must be as long as 22 kpc. This agrees with the scale length derived assuming equipartition between energy densities of magnetic field and cosmic rays. The variation of emissivity with height above the plane deduced by Phillipps et al. (1981) when included in our model gives good fits to the observed cuts across the plane. We have modelled the variation of the galactic magnetic field across a spiral arm as a gaussian. In order to fit the peaks in the galactic plane profile σ=0.2 kpc and a maximum compression of the field in the arm of 3.5:1 is required. These parameters are compatible with the results of N-body simulations of spiral arm formation which treat gas clouds as the unit particles. A detailed description of the model is about to be submitted for publication.

An approximation to the integral of the circular Gaussian distribution over an offset ellipse

and zero elsewhere. The two special cases mentioned below have received a good deal of attention, comprehensive bibliographies will be found in [1] and [2]. If a -b, there is no loss of generality in taking k = 0, and extensive tables exist fo the offset circle integral. For the central ellipse, h = k = 0, the integral can be deduced from that for the offset circle using a result given in [2]. An efficient method for the general case, based on Gaussian quadrature and the use of a table for Erf (x), has been described in [3] and [4]. Tables for P of limited extent will be found in [5] and [6], while an extensive table in inverse form is given in [4]. The purpose of this note is to describe an approximation, accurate to 3 decimal places, and suitable for an electronic computer. This does not employ a table of Erf (x), and is thus more compact in termis of computer storage than the method of [3]. A comparison of computing times is given in Section 3. The method is equivalent to a quadrature formula requiring the evaluation of the exponential at 3a'(a + 1) + 1 points for an ellipse of semi-major axis a, where a is the integral part of (a + 0.5). Increasing the number of evaluations by a factor of 4 reduces the maximum error to 0.0001 for semi-major axes less than 8 units. The average number of evaluations can be reduced considerably by neglecting terms where the index of the exponential falls below a prescribed value, since the number now depends on h, k and tends to zero as they increase. The basis of the method is the diffuse target concept, used in a number of weapon studies, e.g. in [7]. The function f is approximated by

Poloměr setrvačnosti a centrální ellipsa

Poloměr setrvačnosti a centrální ellipsa