Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Feasibility Study of Strengthening Existing Single Span Steel Beam Concrete Deck Bridges, June 1961

Iowa has the same problem that confronts most states in the United States: many bridges constructed more than 20 years ago either have deteriorated to the point that they are inadequate for original design loads or have been rendered inadequate by changes in design/maintenance standards or design loads. Inadequate bridges require either strengthening or posting for reduced loads. A sizeable number of single span, composite concrete deck - steel I beam bridges in Iowa currently cannot be rated to carry today's design loads. Various methods for strengthening the unsafe bridges have been proposed and some methods have been tried. No method appears to be as economical and promising as strengthening by post-tensioning of the steel beams. At the time this research study was begun, the feasibility of posttensioning existing composite bridges was unknown. As one would expect, the design of a bridge-strengthening scheme utilizing post-tensioning is quite complex. The design involves composite construction stressed in an abnormal manner (possible tension in the deck slab), consideration of different sizes of exterior and interior beams, cover-plated beams already designed for maximum moment at midspan and at plate cut-off points, complex live load distribution, and distribution of post-tensioningforces and moments among the bridge beams. Although information is available on many of these topics, there is miminal information on several of them and no information available on the total design problem. This study, therefore, is an effort to gather some of the missing information, primarily through testing a half-size bridge model and thus determining the feasibility of strengthening composite bridges by post-tensioning. Based on the results of this study, the authors anticipate that a second phase of the study will be undertaken and directed toward strengthening of one or more prototype bridges in Iowa.

Statistical Modeling of the Eye for Multimodal Treatment Planning for External Beam Radiation Therapy of Intraocular Tumors.

PURPOSE: Ocular anatomy and radiation-associated toxicities provide unique challenges for external beam radiation therapy. For treatment planning, precise modeling of organs at risk and tumor volume are crucial. Development of a precise eye model and automatic adaptation of this model to patients' anatomy remain problematic because of organ shape variability. This work introduces the application of a 3-dimensional (3D) statistical shape model as a novel method for precise eye modeling for external beam radiation therapy of intraocular tumors. METHODS AND MATERIALS: Manual and automatic segmentations were compared for 17 patients, based on head computed tomography (CT) volume scans. A 3D statistical shape model of the cornea, lens, and sclera as well as of the optic disc position was developed. Furthermore, an active shape model was built to enable automatic fitting of the eye model to CT slice stacks. Cross-validation was performed based on leave-one-out tests for all training shapes by measuring dice coefficients and mean segmentation errors between automatic segmentation and manual segmentation by an expert. RESULTS: Cross-validation revealed a dice similarity of 95% ± 2% for the sclera and cornea and 91% ± 2% for the lens. Overall, mean segmentation error was found to be 0.3 ± 0.1 mm. Average segmentation time was 14 ± 2 s on a standard personal computer. CONCLUSIONS: Our results show that the solution presented outperforms state-of-the-art methods in terms of accuracy, reliability, and robustness. Moreover, the eye model shape as well as its variability is learned from a training set rather than by making shape assumptions (eg, as with the spherical or elliptical model). Therefore, the model appears to be capable of modeling nonspherically and nonelliptically shaped eyes.

Ion-beam induced oxidation of GaAs and AlGaAs

The oxidation of GaAs and AlxGa1−xAs targets by oxygen irradiation has been studied in detail. It was found that the oxidation process is characterized by the strong preferential oxidation of Al as compared to Ga, and of Ga as compared to As. This experimental observation, which has been accurately quantified by using x‐ray photoelectron spectroscopy, is connected to the different heats of formation of the corresponding oxides. The oxide grown by ion beam oxidation shows a strong depletion in As and relatively low oxidation of As as well. The depletion can be associated with the preferential sputtering of the As oxide in respect to other compounds whereas the low oxidation is due to the low heat of formation. In contrast Al is rapidly and fully oxidized, turning the outermost layer of the altered layer to a single Al2O3 overlayer, as observed by transmission electron microscopy. The radiation enhanced diffusion of oxygen and aluminum in the altered layer explains the large thickness of these altered layers and the formation of Al oxides on top of the layers. For the case of ion‐beam oxidation of GaAs a simulation program has been developed which describes adequately the various growth mechanisms experimentally observed

Whole anterior segment proton beam radiotherapy for diffuse iris melanoma.

AIM: To report the results of whole anterior segment proton beam radiotherapy (PBR) for diffuse iris melanoma. METHODS: Between 2000 and 2011, 12 patients with iris melanoma received PBR to the entire iris and ciliary body. RESULTS: Patients had a mean age of 57 years and a median follow-up of 3.5 years (range 1-11.6 years). Tumour iris involvement was 1-4 h in five patients, 5-8 h in four and 9-12 h in three. Angle involvement was 6-8 h in five patients and 9-12 h in seven. The visual acuity (VA) before treatment was 6/5-6/6 in six patients, 6/8-6/9 in three and 6/18-6/38 in three. No tumour recurrence occurred during the follow-up period. Glaucoma treatment was required in 11 of 12 patients. The visual acuity at the last follow-up was 6/5-6/9 in five patients, 6/18-6/24 in three, 6/60-1/60 in two and no light perception in two. Four patients developed varying non-severe degrees of limbal stem cell deficiency, which was treatable with conservative measures. CONCLUSIONS: Whole anterior segment PBR is a useful alternative to enucleation for diffuse iris melanoma. Most patients will need treatment for glaucoma and some may require treatment for tear-film instability and/or stem cell failure.

Investigation of Two Bridge Alternatives for Low Volume Roads, Volume 1 of 2 Concept 1: Precast Steel Beam Units, HR-382, 1997

Recent reports have indicated that 23.5% of the nation's highway bridges are structurally deficient and 17.7% are functionally obsolete. A significant number of these bridges are on the Iowa secondary road system where over 86% of the rural bridge management responsibilities are assigned to the counties. Some of the bridges can be strengthened or otherwise rehabilitated, but many more are in need of immediate replacement. In a recent investigation (HR-365 "Evaluation of Bridge Replacement Alternatives for the County Bridge System") several types of replacement bridges that are currently being used on low volume roads were identified. It was also determined that a large number of counties (69%) have the ability and are interested in utilizing their own forces to design and construct short span bridges. In reviewing the results from HR-365, the research team developed one "new" bridge replacement concept and a modification of a replacement system currently being used. Both of these bridge replacement alternatives were investigated in this study, the results of which are presented in two volumes. This volume (Volume 1) presents the results of Concept 1 - Steel Beam Precast Units. Concept 2 - Modification of the Beam-in-Slab Bridge is presented in Volume 2. Concept 1, involves the fabrication of precast units (two steel beams connected by a concrete slab) by county work forces. Deck thickness is limited so that the units can be fabricated at one site and then transported to the bridge site where they are connected and the remaining portion of the deck placed. Since Concept 1 bridge is primarily intended for use on low-volume roads, the precast units can be constructed with new or used beams. In the experimental part of the investigation, there were three types of static load tests: small scale connector tests, "handling strength" tests, and service and overload tests of a model bridge. Three finite element models for analyzing the bridge in various states of construction were also developed. Small scale connector tests were completed to determine the best method of connecting the precast double-T (PCDT) units. "Handling strength" tests on an individual PCDT unit were performed to determine the strength and behavior of the precast unit in this configuration. The majority of the testing was completed on the model bridge [L=9,750 mm (32 ft), W=6,400 mm (21 ft)] which was fabricated using the precast units developed. Some of the variables investigated in the model bridge tests were number of connectors required to connect adjacent precast units, contribution of diaphragms to load distribution, influence of position of diaphragms on bridge strength and load distribution, and effect of cast-in-place portion of deck on load distribution. In addition to the service load tests, the bridge was also subjected to overload conditions. Using the finite element models developed, one can predict the behavior and strength of bridges similar to the laboratory model as well as design them. Concept 1 has successfully passed all laboratory testing; the next step is to field test it.

Investigation of Two Bridge Alternatives for Low Volume Roads - Phase II Volume 1 of 2 Concept 1: Steel Beam Precast Units, TR-410, 2000

This project continues the research which addresses the numerous bridge problems on the Iowa secondary road system. It is a continuation (Phase 2) of Project HR-382, in which two replacement alternatives (Concept 1: Steel Beam Precast Units and Concept 2: Modification of the Benton County Beam-in-Slab Bridge) were investigated. In previous research for concept 1, a precast unit bridge was developed through laboratory testing. The steel-beam precast unit bridge requires the fabrication of precast double-tee (PCDT) units, each consisting of two steel beams connected by a reinforced concrete deck. The weight of each PCDT unit is minimized by limiting the deck thickness to 4 in., which permits the units to be constructed off-site and then transported to the bridge site. The number of units required is a function of the width of bridge desired. Once the PCDT units are connected, a cast-in-place reinforced concrete deck is cast over the PCDT units and the bridge railing attached. Since the steel beam PCDT unit bridge design is intended primarily for use on low-volume roads, used steel beams can be utilized for a significant cost savings. In previous research for concept 2, an alternate shear connector (ASC) was developed and subjected to static loading. In this investigation, the ASC was subjected to cyclic loading in both pushout specimens and composite beam tests. Based on these tests, the fatigue strength of the ASC was determined to be significantly greater than that required in typical low volume road single span bridges. Based upon the construction and service load testing, the steel-beam precast unit bridge was successfully shown to be a viable low volume road bridge alternative. The construction process utilized standard methods resulting in a simple system that can be completed with a limited staff. Results from the service load tests indicated adequate strength for all legal loads. An inspection of the bridge one year after its construction revealed no change in the bridge's performance. Each of the systems previously described are relatively easy to construct. Use of the ASC rather than the welded studs significantly simplified the work, equipment, and materials required to develop composite action between the steel beams and the concrete deck.

Strengthening of an Existing Continuous-Span, Steel-Beam, Concrete-Deck Bridge by Post-Tensioning, HR-308, 1990

The need to upgrade a large number of understrength and obsolete bridges in the U.S. has been well documented in the literature. Through several Iowa DOT projects, the concept of strengthening simple-span bridges by post-tensioning has been developed. The purpose of the project described in this report was to investigate the use of post-tensioning for strengthening continuous composite bridges. In a previous, successfully completed investigation, the feasibility of strengthening continuous, composite bridges by post-tensioning was demonstrated on a laboratory 1/3-scale-model bridge (3 spans: 41 ft 11 in. x 8 ft 8 in.). This project can thus be considered the implementation phase. The bridge selected for strengthening was in Pocahontas County near Fonda, Iowa, on County Road N28. With finite element analysis, a post-tensioning system was developed that required post-tensioning of the positive moment regions of both the interior and exterior beams. During the summer of 1988, the strengthening system was installed along with instrumentation to determine the bridge's response and behavior. Before and after post-tensioning, the bridge was subjected to truck loading (1 or 2 trucks at various predetermined critical locations) to determine the effectiveness of the strengthening system. The bridge, with the strengthening system in place, was inspected approximately every three months to determine any changes in its appearance or behavior. In 1989, approximately one year after the initial strengthening, the bridge was retested to identify any changes in its behavior. Post-tensioning forces were removed to reveal any losses over the one-year period. Post-tensioning was reapplied to the bridge, and the bridge was tested using the same loading program used in 1988. Except for at a few locations, stresses were reduced in the bridge the desired amount. At a few locations flexural stresses in the steel beams are still above 18 ksi, the allowable inventory stress for A7 steel. Although maximum stresses are above the inventory stress by about 2 ksi, they are about 5 ksi below the allowable operating stress; therefore, the bridge no longer needs to be load-posted.

Strengthening of Existing Single Span Steel Beam and Concrete Deck Bridges, HR-238, Part 1, 1983

The Phase I research, Iowa Department of Transportation (IDOT) Project HR-214, "Feasibility Study of Strengthening Existing Single Span Steel Beam Concrete Deck Bridges," verified that post-tensioning can be used to provide strengthening of the composite bridges under investigation. Phase II research, reported here, involved the strengthening of two full-scale prototype bridges - one a prototype of the model bridge tested during Phase I and the other larger and skewed. In addition to the field work, Phase II also involved a considerable amount of laboratory work. A literature search revealed that only minimal data existed on the angle-plus-bar shear connectors. Thus, several specimens utilizing angle-plus-bar, as well as channels, studs and high strength bolts as shear connectors were fabricated and tested. To obtain additional shear connector information, the bridge model of Phase I was sawed into four composite concrete slab and steel beam specimens. Two of the resulting specimens were tested with the original shear connection, while the other two specimens had additional shear connectors added before testing. Although orthotropic plate theory was shown in Phase I to predict vertical load distribution in bridge decks and to predict approximate distribution of post-tensioning for right-angle bridges, it was questioned whether the theory could also be used on skewed bridges. Thus, a small plexiglas model was constructed and used in vertical load distribution tests and post-tensioning force distribution tests for verification of the theory. Conclusions of this research are as follows: (1) The capacity of existing shear connectors must be checked as part of a bridge strengthening program. Determination of the concrete deck strength in advance of bridge strengthening is also recommended. (2) The ultimate capacity of angle-plus-bar shear connectors can be computed on the basis of a modified AASHTO channel connector formula and an angle-to-beam weld capacity check. (3) Existing shear connector capacity can be augmented by means of double-nut high strength bolt connectors. (4) Post-tensioning did not significantly affect truck load distribution for right angle or skewed bridges. (5) Approximate post-tensioning and truck load distribution for actual bridges can be predicted by orthotropic plate theory for vertical load; however, the agreement between actual distribution and theoretical distribution is not as close as that measured for the laboratory model in Phase I. (6) The right angle bridge exhibited considerable end restraint at what would be assumed to be simple support. The construction details at bridge abutments seem to be the reason for the restraint. (7) The skewed bridge exhibited more end restraint than the right angle bridge. Both skew effects and construction details at the abutments accounted for the restraint. (8) End restraint in the right angle and skewed bridges reduced tension strains in the steel bridge beams due to truck loading, but also reduced the compression strains caused by post-tensioning.

Strengthening of Existing Single Span Steel Beam and Concrete Deck Bridges, HR-238, Part II, 1985

The unifying objective of Phases I and II of this study was to determine the feasibility of the post-tensioning strengthening method and to implement the technique on two composite bridges in Iowa. Following completion of these two phases, Phase III was undertaken and is documented in this report. The basic objectives of Phase III were further monitoring bridge behavior (both during and after post-tensioning) and developing a practical design methodology for designing the strengthening system under investigation. Specific objectives were: to develop strain and force transducers to facilitate the collection of field data; to investigate further the existence and effects of the end restraint on the post-tensioning process; to determine the amount of post-tensioning force loss that occurred during the time between the initial testing and the retesting of the existing bridges; to determine the significance of any temporary temperature-induced post-tensioning force change; and to develop a simplified design methodology that would incorporate various variables such as span length, angle-of-skew, beam spacing, and concrete strength. Experimental field results obtained during Phases II and III were compared to the theoretical results and to each other. Conclusions from this research are as follows: (1) Strengthening single-span composite bridges by post-tensioning is a viable, economical strengthening technique. (2) Behavior of both bridges was similar to the behavior observed from the bridges during field tests conducted under Phase II. (3) The strain transducers were very accurate at measuring mid-span strain. (4) The force transducers gave excellent results under laboratory conditions, but were found to be less effective when used in actual bridge tests. (5) Loss of post-tensioning force due to temperature effects in any particular steel beam post-tensioning tendon system were found to be small. (6) Loss of post-tensioning force over a two-year period was minimal. (7) Significant end restraint was measured in both bridges, caused primarily by reinforcing steel being continuous from the deck into the abutments. This end restraint reduced the effectiveness of the post-tensioning but also reduced midspan strains due to truck loadings. (8) The SAP IV finite element model is capable of accurately modeling the behavior of a post-tensioned bridge, if guardrails and end restraints are included in the model. (9) Post-tensioning distribution should be separated into distributions for the axial force and moment components of an eccentric post-tensioning force. (10) Skews of 45 deg or less have a minor influence on post-tensioning distribution. (11) For typical Iowa three-beam and four-beam composite bridges, simple regression-derived formulas for force and moment fractions can be used to estimate post-tensioning distribution at midspan. At other locations, a simple linear interpolation gives approximately correct results. (12) A simple analytical model can accurately estimate the flexural strength of an isolated post-tensioned composite beam.

Investigation of Two Bridge Alternatives for Low Volume Roads Volume 2 of 2 Concept 2: Beam In Slab Bridge, HR-382, 1997

Recent reports have indicated that 23.5% of the nation's highway bridges are structurally deficient and 17.7% are functionally obsolete. A significant number of these bridges are on the Iowa secondary road system where over 86% of the rural bridge management responsibilities are assigned to the counties. Some of the bridges can be strengthened or otherwise rehabilitated, but many more are in need of immediate replacement. In a recent investigation (HR-365 "Evaluation of Bridge Replacement Alternatives for the County Bridge System") several types of replacement bridges that are currently being used on low volume roads were identified. It was also determined that a large number of counties (69%) have the ability and are interested in utilizing their own forces to design and construct short span bridges. After reviewing the results from HR-365, the research team developed one "new" bridge replacement concept and a modification of a replacement system currently being used. Both of these bridge replacement alternatives were investigated in this study, the results of which are presented in two volumes. This volume (Volume 2) presents the results of Concept 2 - Modification of the Beam-in-Slab Bridge. Concept 1 - Steel Beam Precast Units is presented in Volume 1. Concept 2 involves various laboratory tests of the Beam-in-Slab bridge (BISB) currently being used by Benton County and several other Iowa counties. In this investigation, the behavior and strength of the BISB were determined; a new method of obtaining composite action between the steel beams and concrete was also tested. Since the Concept 2 bridge is primarily intended for use on low-volume roads, the system can be constructed with new or used beams. In the experimental part of the investigation, there were three types of laboratory tests: push-out tests, service and ultimate load tests of models of the BISB, and composite beam tests utilizing the newly developed shear connection. In addition to the laboratory tests, there was a field test in which an existing BISB was service load tested. An equation was developed for predicting the strength of the shear connection investigated; in addition, a finite element model for analyzing the BISB was also developed. Push-out tests were completed to determine the strength of the recently developed shear connector. A total of 36 specimens were tested, with variables such as hole diameter, hole spacing, presence of reinforcement, etc. being investigated. In the model tests of the BISB, two and four beam specimens [L=9,140 mm (30 ft)] were service load tested for behavior and load distribution data. Upon completion of these tests, both specimens were loaded to failure. In the composite beam tests, four beams, one with standard shear studs and three using the shear connection developed, were tested. Upon completion of the service load tests, all four beams were loaded to failure. The strength and behavior of the beams with the new shear connection were found to be essentially the same as that of the specimen with standard shear studs.

Investigation of Two Bridge Alternatives for Low Volume Roads - Phase II Volume 2 of 2, Concept 2: Beam in Slab Bridge, TR-410, 2000

This project continues the research which addresses the numerous bridge problems on the Iowa secondary road system. It is a continuation (Phase 2) of Project HR-382, in which two replacement alternatives (Concept 1: Steel Beam Precast Units and Concept 2: Modification of the Benton County Beam-in-Slab Bridge) were investigated. In previous research for concept 1, a precast unit bridge was developed through laboratory testing. The steel-beam precast unit bridge requires the fabrication of precast double-tee (PCDT) units, each consisting of two steel beams connected by a reinforced concrete deck. The weight of each PCDT unit is minimized by limiting the deck thickness to 4 in., which permits the units to be constructed off-site and then transported to the bridge site. The number of units required is a function of the width of bridge desired. Once the PCDT units are connected, a cast-in-place reinforced concrete deck is cast over the PCDT units and the bridge railing attached. Since the steel beam PCDT unit bridge design is intended primarily for use on low-volume roads, used steel beams can be utilized for a significant cost savings. In previous research for concept 2, an alternate shear connector (ASC) was developed and subjected to static loading. In this investigation, the ASC was subjected to cyclic loading in both pushout specimens and composite beam tests. Based on these tests, the fatigue strength of the ASC was determined to be significantly greater than that required in typical low volume road single span bridges. Based upon the construction and service load testing, the steel-beam precast unit bridge was successfully shown to be a viable low volume road bridge alternative. The construction process utilized standard methods resulting in a simple system that can be completed with a limited staff. Results from the service load tests indicated adequate strength for all legal loads. An inspection of the bridge one year after its construction revealed no change in the bridge's performance. Each of the systems previously described are relatively easy to construct. Use of the ASC rather than the welded studs significantly simplified the work, equipment, and materials required to develop composite action between the steel beams and the concrete deck.