Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Prenatal diagnosis of a fetal abdominal eventration: a rare congenital abdominal wall defect.

We report a case of abdominal eventration associated with cystic fibrosis, diagnosed by mid-trimester ultrasonography. The defect concerned the abdominal muscles and their aponevrotic sheath, but respected the skin. There was no associated malformation. The outcome was favorable after surgery, and the infant is well at the age of 6 months.

The Flexural Fatigue Strength of Prestressed Steel I-Beams, HR-73, 1962

The purpose of this investigation was to study the flexural fatigue strength of two prestressed steel I-beams which had previously been fabricated in connection with a jointly sponsored project under the auspices of the Iowa State Highway Commission. The beams were prestressed by deflecting them under the action of a concentrated load at the center of a simple span, then welding unstressed high strength steel plates to the top and bottom flanges to retain a predetermined amount of prestress. The beams were rolled sections of A36 steel and the plates were USS "T-1" steel. Each of the two test specimens were subjected to an identical repeated loading until a fatigue failure occurred. The loading was designed to produce stresses equivalent to those which would have occurred in a simulated bridge and amounted to 84 percent of a standard H-15 live load including impact. One of the beams sustained 2,469,100 repetitions of load to failure and the other sustained 2,756,100 cycles. Following the fatigue tests, an experimental study was made to determine the state of stress that had been retained in the prestressed steel beams. This information, upon which the calculated stresses of the test could be superimposed, provided a method of correlating the fatigue strength of the beams with the fatigue information available on the two steels involved.

Live Load Deflections in a Prestressed Steel Beam Bridge, HR-74, 1963

This report describes the measurement of dynamic (live load) deflections in a 240' x 30' three span continuous prestressed steel bridge, skewed 30 degrees. The design assumptions and prestressing procedure are described briefly, and the instrumentation and loading are discussed. The actual deflections are presented in tabular form, and the deflections due to the design live load are calculated. The maximum deflections are presented as a ratio of the span length, and the further use of prestressed steel beams is recommended.

Detection of Steel Corrosion in Bridge Decks and Reinforced Concrete Pavement, HR-156, 1977

The Iowa Department of Transportation initiated this research to evaluate the reliability, benefit and application of the corrosion detection device. Through field testing prior to repair projects and inspection at the time of repair, the device was shown to be reliable. With the reliability established, twelve additional devices were purchased so that this evaluation procedure could be used routinely on all repair projects. The corrosion detection device was established as a means for determining concrete removal for repair. Removal of the concrete down to the top reinforcing steel is required for all areas exhibiting electrical potentials greater than 0.45 Volt. It was determined that the corrosion detection device was not applicable to membrane testing. The corrosion detection device has been used to evaluate corrosion of reinforcing steel in continuously reinforced concrete pavement.

Une carte des zones de cisaillement ductiles des Alpes Centrales

The main deformation structures due to the Tertiary continental collision in the Western Swiss Alps are ductile shear zones. Four main shear zones can be recognized on the structural map, each characterised by a different shear direction. The first D I shear zone with a X I, SE (transverse) stretching direction has been created during the under-thrusting towards the SE of the European plate under the Adriatic plate. This took place mainly by ductile deformation of the upper part of the European continental basement with the formation of the external massifs basement folds and the Penninic foldnappes. The second D II shear zone (Simplon ductile shear zone) is characterized by a XII stretching, dipping from 0 to 30-degrees to the SW (longitudinal stretching). It is approximately 10 km wide, and crosses the Alpine nappes in an oblique direction. It corresponds to a relative SW transport direction of the upper units together with the Adriatic plate. This dextral transpression zone is also responsible for the stretching parallel to the elongation of the Alpine belt. The third D III shear zone is made of mylonites with a steep stretching direction and corresponds to the hanging wall of the Canavese reverse fault. The D IV shear zones, dextral wrench zones combined with underthrusting movement, are characterised by a W and SW stretching direction. They were formed during and after the S facing backfolding which for instance made the Mischabel fold and the Boggioleto fold. Actually it occupies two narrow areas of more ductile rocks between the Mischabel backfold to the N and the Monte Rosa nappe to the S and allong the Canavese Line. These dextral shear zones represent probably the western continuation of the Tonale Line dextral wrench fault. The D I to IV ductile shear zone were formed under greenschist and amphibolite facies conditions during the Tertiary orogenic metamorphism. Their regional distribution is limited to the metamorphic ductile zone representing the deep part of the Alpine belt, between 10 and 30 km depth. The emplacement and orientation of the shear zones was also directed by the geometry of the boundaries of the European and Adriatic plates. The analysis of the superposed Central Alpine shear zones permits thus to propose a model of the history of the relative convergent and wrench movements which took place between the European and Adriatic plates during the Alpine Tertiary continental collision.

Precast Concrete Panel Thickness for Epoxy-Coated Prestressing Strands, Volume 2, HR-353, 1994

This final report for Phase 1 of the research on epoxy-coated, prestressing strands in precast prestressed concrete (PC) panels has been published in two volumes. Volume 1--Technical Report contains the problem description, literature review, and survey results; descriptions of the test specimens, experimental tests, and analytical models; discussions of the analytical and experimental results; summary, conclusions, and recommendations; list of references; and acknowledgments. Volume 2--Supplemental Report contains additional information in the form of appendix material for Volume 1 on the questionnaires, strand forces, geometry of the specimens, concrete crack patterns that formed in the strand transfer length and strand development length specimens, concrete strains in the strand transfer length specimens, and load-point deflections and strand-slip measurements for the strand development length specimens. Appendix A contains the questionnaires that were sent to the design agencies and precast concrete producers. A summary of the results to the questions on the surveys are given as the number of respondents who provided the same answers and as paraphrased comments from the respondents. Appendix B contains graphs of strand force versus time, strand force versus temperature, and strand force versus strand cutting sequence for the concrete castings. Appendix C contains figures that show the location of each specimen in the prestress bed, the geometrical configurations for the strand transfer length (T-type) specimens and strand development length (D-type) specimens, and the concrete cracks that developed in some of the T-type specimens when they were prestressed. Appendix D contains figures that show the concrete cracks that developed in the D-type specimens during the strand development length tests. For each of these tests, the sequence of the failure for the specimen is specified. Appendix E contains graphs of concrete strain versus distance from the end of the T-type specimens that were instrumented with internal embedment strain gages. Appendix F contains graphs of load versus load-point deflection and load versus strand-slip for the strand development length tests of the D-type specimens.

Corrosion of Steel in CRCP, HR-1004, 1975

The Materials and Research Departments cooperated in planning and performing Research Project HR-1004 during the summer of 1974. The Research Department agreed to accept responsibility for the final report; it has been delayed because of our efforts to obtain a maximum amount of information from the data by means of various statistical analyses. This memorandum contains all of the data, hopefully in a manner that will permit you to proceed with your consideration of an experimental project using cathodic protection for the CRCP steel. A more detailed report will be prepared at a later date.

Evaluation of Stainless Steel Culvert Pipe in Mahaska County, Iowa, HR-2001

Corrosion of culvert pipe in Iowa in general is not a serious problem. However, it is potentially significant in some local areas. An opportunity to make a limited durability study of stainless steel pipe was presented when a local fabricating company expressed interest in a cooperative field experiment. The potential of stainless steel pipe is to reduce maintenance costs that are incurred through replacement and upkeep. A new stainless steel material, Allegheny Metal MF-1, was used in a partial fabrication demonstration and later these demonstration sections were delivered to the selected field site for placement.

Preliminary Report on the Installation of Stainless Steel Culvert Pipe in Mahaska County, Iowa, HR-2001, 1967

At the request of Mr. Arnold E. Levine, of the Levine Company, Centerville, Iowa, the Iowa State Highway Commission was asked to observe the partial fabrication of two stainless steel culvert pipes and later the Commission was asked if they would like to study their durability. These pipes were fabricated April 12, 1967 in Des Moines, Personnel of the Design and Materials Department were at the fabrication, but no Research people were present. The idea for the installation was conceived and a site selected after which the project was turned over to the Research Engineer. The stainless steel pipes presumably contained the new Allegheny Metal, MF-1, whose composition is shown in Appendix A. The primary aim of the stainless steel pipe is to reduce long term costs that are incurred through replacement and upkeep. The MF-1 has a theoretical life of infinity.

Evaluation of Long-Term Field Performance of Cold In-Place Recycled Roads: Field and Laboratory Testing, TR-502, 2007

Cold in-place recycling (CIR) has become an attractive method for rehabilitating asphalt roads that have good subgrade support and are suffering distress related to non-structural aging and cracking of the pavement layer. Although CIR is widely used, its use could be expanded if its performance were more predictable. Transportation officials have observed roads that were recycled under similar circumstances perform very differently for no clear reason. Moreover, a rational mix design has not yet been developed, design assumptions regarding the structural support of the CIR layer remain empirical and conservative, and there is no clear understanding of the cause-effect relationships between the choices made during the design/construction process and the resulting performance. The objective of this project is to investigate these relationships, especially concerning the age of the recycled pavement, cumulative traffic volume, support conditions, aged engineering properties of the CIR materials, and road performance. Twenty-four CIR asphalt roads constructed in Iowa from 1986 to 2004 were studied: 18 were selected from a sample of roads studied in a previous research project (HR-392), and 6 were selected from newer CIR projects constructed after 1999. This report describes the results of comprehensive field and laboratory testing for these CIR asphalt roads. The results indicate that the modulus of the CIR layer and the air voids of the CIR asphalt binder were the most important factors affecting CIR pavement performance for high-traffic roads. For low-traffic roads, the wet indirect tensile strength significantly affected pavement performance. The results of this research can help identify changes that should be made with regard to design, material selection, and construction in order to improve the performance and cost-effectiveness of future recycled roads.

Evaluation of Long-Term Field Performance of Cold In-Place Recycled Roads: Summary Report, TR-502, 2007

Cold in-place recycling (CIR) has become an attractive method for rehabilitating asphalt roads that have good subgrade support and are suffering distress related to non-structural aging and cracking of the pavement layer. Although CIR is widely used, its use could be expanded if its performance were more predictable. Transportation officials have observed roads that were recycled under similar circumstances perform very differently for no clear reason. Moreover, a rational mix design has not yet been developed, design assumptions regarding the structural support of the CIR layer remain empirical and conservative, and there is no clear understanding of the cause-effect relationships between the choices made during the design/construction process and the resulting performance. The objective of this project is to investigate these relationships, especially concerning the age of the recycled pavement, cumulative traffic volume, support conditions, aged engineering properties of the CIR materials, and road performance. Twenty-four CIR asphalt roads constructed in Iowa from 1986 to 2004 were studied: 18 were selected from a sample of roads studied in a previous research project (HR-392), and 6 were selected from newer CIR projects constructed after 1999. This report summarizes the results of a comprehensive program of field distress surveys, field testing, and laboratory testing for these CIR asphalt roads. The results of this research can help identify changes that should be made with regard to design, material selection, and construction in order to lengthen the time between rehabilitation cycles and improve the performance and cost-effectiveness of future recycled roads.