Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Polygonal cracks in the seasonal semi-translucent CO2 ice layer in Martian polar areas

In this paper, we use morphological and numerical methods to test the hypothesis that seasonally formed fracture patterns in the Martian polar regions result from the brittle failure of seasonal CO2 slab ice. The observations by the High Resolution Imaging Science Experiment (HiRISE) of polar regions of Mars show very narrow dark elongated linear patterns that are observed during some periods of time in spring, disappear in summer and re-appear again in the following spring. They are repeatedly formed in the same areas but they do not repeat the exact pattern from year to year. This leads to the conclusion that they are cracks formed in the seasonal ice layer. Some of models of seasonal surface processes rely on the existence of a transparent form of CO2 ice, so-called slab ice. For the creation of the observed cracks the ice is required to be a continuous media, not an agglomeration of relatively separate particles like a firn. The best explanation for our observations is a slab ice with relatively high transparency in the visible wavelength range. This transparency allows a solid state green-house effect to act underneath the ice sheet raising the pressure by sublimation from below. The trapped gas creates overpressure and the ice sheet breaks at some point creating the observed cracks. We show that the times when the cracks appear are in agreement with the model calculation, providing one more piece of evidence that CO2 slab ice covers polar areas in spring.

Modeling of ore-forming and geoenvironmental systems: Roles of fluid flow and chemical reaction processes

Ore-forming and geoenviromental systems commonly involve coupled fluid flowand chemical reaction processes. The advanced numerical methods and computational modeling have become indispensable tools for simulating such processes in recent years. This enables many hitherto unsolvable geoscience problems to be addressed using numerical methods and computational modeling approaches. For example, computational modeling has been successfully used to solve ore-forming and mine site contamination/remediation problems, in which fluid flow and geochemical processes play important roles in the controlling dynamic mechanisms. The main purpose of this paper is to present a generalized overview of: (1) the various classes and models associated with fluid flow/chemically reacting systems in order to highlight possible opportunities and developments for the future; (2) some more general issues that need attention in the development of computational models and codes for simulating ore-forming and geoenviromental systems; (3) the related progresses achieved on the geochemical modeling over the past 50 years or so; (4) the general methodology for modeling of oreforming and geoenvironmental systems; and (5) the future development directions associated with modeling of ore-forming and geoenviromental systems.

Experimental validation of a nonlinear μ FE model based on cohesive-frictional plasticity for trabecular bone

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

Modeling asteroid collisions and impact processes

As a complement to experimental and theoretical approaches, numerical modeling has become an important component to study asteroid collisions and impact processes. In the last decade, there have been significant advances in both computational resources and numerical methods. We discuss the present state-of-the-art numerical methods and material models used in "shock physics codes" to simulate impacts and collisions and give some examples of those codes. Finally, recent modeling studies are presented, focussing on the effects of various material properties and target structures on the outcome of a collision.

Numerical study of Anderson localization of terahertz waves in disordered waveguides

We present a numerical study of electromagnetic wave transport in disordered quasi-one-dimensional waveguides at terahertz frequencies. Finite element method calculations of terahertz wave propagation within LiNbO3 waveguides with randomly arranged air-filled circular scatterers exhibit an onset of Anderson localization at experimentally accessible length scales. Results for the average transmission as a function of waveguide length and scatterer density demonstrate a clear crossover from diffusive to localized transport regime. In addition, we find that transmission fluctuations grow dramatically when crossing into the localized regime. Our numerical results are in good quantitative agreement with theory over a wide range of experimentally accessible parameters both in the diffusive and localized regime opening the path towards experimental observation of terahertz wave localization.

Numerical model of the human cornea based on stromal microstructure: identification of mechanical properties for two age groups

The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

Operator variability using different polishing methods and surface geometry of a nanohybrid composite

This study evaluated the operator variability of different finishing and polishing techniques. After placing 120 composite restorations (Tetric EvoCeram) in plexiglassmolds, the surface of the specimens was roughened in a standardized manner. Twelve operators with different experience levels polished the specimens using the following finishing/polishing procedures: method 1 (40 ?m diamond [40D], 15 ?m diamond [15D], 42 ?m silicon carbide polisher [42S], 6 ?m silicon carbide polisher [6S] and Occlubrush [O]); method 2 (40D, 42S, 6S and O); method 3 (40D, 42S, 6S and PoGo); method 4 (40D, 42S and PoGo) and method 5 (40D, 42S and O). The mean surface roughness (Ra) was measured with a profilometer. Differences between the methods were analyzed with non-parametric ANOVA and pairwise Wilcoxon signed rank tests (?=0.05). All the restorations were qualitatively assessed using SEM. Methods 3 and 4 showed the best polishing results and method 5 demonstrated the poorest. Method 5 was also most dependent on the skills of the operator. Except for method 5, all of the tested procedures reached a clinically acceptable surface polish of Ra?0.2 ?m. Polishing procedures can be simplified without increasing variability between operators and without jeopardizing polishing results.

Systematic review of medication safety assessment methods

Purpose The accuracy, efficiency, and efficacy of four commonly recommended medication safety assessment methodologies were systematically reviewed. Methods Medical literature databases were systematically searched for any comparative study conducted between January 2000 and October 2009 in which at least two of the four methodologies—incident report review, direct observation, chart review, and trigger tool—were compared with one another. Any study that compared two or more methodologies for quantitative accuracy (adequacy of the assessment of medication errors and adverse drug events) efficiency (effort and cost), and efficacy and that provided numerical data was included in the analysis. Results Twenty-eight studies were included in this review. Of these, 22 compared two of the methodologies, and 6 compared three methods. Direct observation identified the greatest number of reports of drug-related problems (DRPs), while incident report review identified the fewest. However, incident report review generally showed a higher specificity compared to the other methods and most effectively captured severe DRPs. In contrast, the sensitivity of incident report review was lower when compared with trigger tool. While trigger tool was the least labor-intensive of the four methodologies, incident report review appeared to be the least expensive, but only when linked with concomitant automated reporting systems and targeted follow-up. Conclusion All four medication safety assessment techniques—incident report review, chart review, direct observation, and trigger tool—have different strengths and weaknesses. Overlap between different methods in identifying DRPs is minimal. While trigger tool appeared to be the most effective and labor-efficient method, incident report review best identified high-severity DRPs.

Prevalence of asymptomatic and electrically undetectable intracardiac inside-out abrasion in silicon-coated Riata® and Riata® ST implantable cardioverter-defibrillator leads

BACKGROUND: Recently, several cases of symptomatic and/or electrically detectable intracardiac inside-out abrasions in silicon-coated Riata® and Riata® ST leads have been described. However, the prevalence in asymptomatic patients with unremarkable implantable cardioverter defibrillator (ICD) interrogation is unknown. The aim of this study was to determine the prevalence of asymptomatic and electrically undetectable intracardiac inside-out abrasion in silicon-coated Riata® and Riata® ST leads. METHODS: All 52 patients with an active silicone-coated Riata® and Riata® ST lead followed up in our outpatient clinic were scheduled for a premature ICD interrogation and a biplane chest radiograph. When an intracardiac inside-out abrasion was suspected, this finding was confirmed by fluoroscopy. RESULTS: Mean time since implantation was 71±18months. An intracardiac inside-out abrasion was confirmed by fluoroscopy in 6 patients (11.5%). Mean time from lead implantation to detection of intracardiac inside-out abrasion was 79±14months. In all patients with an intracardiac inside-out abrasion, ICD interrogation showed normal and stable electrical parameters. Retrospectively, in 4 of these 6 patients, a coronary angiography performed 25±18months before diagnosis of intracardiac inside-out abrasion already showed the defect. Despite undetected intracardiac inside-out abrasion, 2 of these 4 patients experienced adequate antitachycardia pacing and ICD-shocks. ICD leads were replaced in all 6 patients. CONCLUSIONS: The prevalence of asymptomatic intracardiac inside-out abrasion in silicon-coated Riata® and Riata® ST leads is higher than 10% when assessed by fluoroscopy, and most intracardiac inside-out abrasions are not detectable by ICD interrogation.

PVR recurrence and the timing of silicon oil removal

BACKGROUND: Following vitrectomy for PVR-associated retinal detachment, placement of an encircling band, filling with silicone oil (SO) and successful retinal reattachment, a recurrence of PVR can develop. Retinal redetachment after SO removal is usually due to secondary or residual PVR. We wanted to ascertain whether the anatomical and functional outcomes of surgery in patients with a reattached retina and recurrent PVR can be improved by delaying the removal of SO. PATIENTS AND METHODS: 112 consecutive patients with PVR-associated retinal detachment who had undergone vitrectomy with SO filling, were monitored for at least 6 months after SO removal. Prior to SO removal, the retina posterior to the encircling band had to be completely reattached. Patients who developed PVR after SO filling were divided into two groups according to the duration of SO retention: 12 - 18 months (group 2: n = 48); > 18 months (group 3: n = 21). Individuals without PVR recurrence after SO filling and in whom the SO was consequently removed within 4 - 12 months served as control (group 1: n = 43). Anatomical success, intraocular pressure (IOP) and best-corrected visual acuity (BCVA) served as the primary clinical outcome parameters. RESULTS: Six months after SO removal, the anatomical success rates (86.3 %, 88.8 % and 84.6 %, in groups 1, 2 and 3, respectively; log rank = 0.794) and the BCVAs (p = 0.861) were comparable in the three groups. Mean IOP (p = 0.766), and the frequency of complications such as PVR recurrence (p = 0.936), bullous keratopathy (p = 0.981) and macular pucker (p = 0.943) were likewise similar. Patients in whom SO was retained for more than 18 months had the highest IOPs and required the heaviest dosage with anti-glaucoma drugs. CONCLUSIONS: In patients who develop a recurrence of PVR after vitrectomy and SO filling the surgeon can observe and treat retinal changes for up to 18 months without impairing the anatomical and functional outcomes. The retention of SO for more than 18 months does not improve the anatomical outcome. However, it can impair the functional outcome by precipitating the development of a persisting secondary glaucoma.

Should 3K zoom function be used for detection of pneumothorax in cesium iodide/amorphous silicon flat-panel detector radiographs presented on 1K-matrix soft copies?

The purpose of the study was to evaluate observer performance in the detection of pneumothorax with cesium iodide and amorphous silicon flat-panel detector radiography (CsI/a-Si FDR) presented as 1K and 3K soft-copy images. Forty patients with and 40 patients without pneumothorax diagnosed on previous and subsequent digital storage phosphor radiography (SPR, gold standard) had follow-up chest radiographs with CsI/a-Si FDR. Four observers confirmed or excluded the diagnosis of pneumothorax according to a five-point scale first on the 1K soft-copy image and then with help of 3K zoom function (1K monitor). Receiver operating characteristic (ROC) analysis was performed for each modality (1K and 3K). The area under the curve (AUC) values for each observer were 0.7815, 0.7779, 0.7946 and 0.7066 with 1K-matrix soft copies and 0.8123, 0.7997, 0.8078 and 0.7522 with 3K zoom. Overall detection of pneumothorax was better with 3K zoom. Differences between the two display methods were not statistically significant in 3 of 4 observers (p-values between 0.13 and 0.44; observer 4: p = 0.02). The detection of pneumothorax with 3K zoom is better than with 1K soft copy but not at a statistically significant level. Differences between both display methods may be subtle. Still, our results indicate that 3K zoom should be employed in clinical practice.

Percutaneous coronary interventions in Europe: prevalence, numerical estimates, and projections based on data up to 2004

AIMS: A registry mandated by the European Society of Cardiology collects data on trends in interventional cardiology within Europe. Special interest focuses on relative increases and ratios in new techniques and their distributions across Europe. We report the data through 2004 and give an overview of the development of coronary interventions since the first data collection in 1992. METHODS AND RESULTS: Questionnaires were distributed yearly to delegates of all national societies of cardiology represented in the European Society of Cardiology. The goal was to collect the case numbers of all local institutions and operators. The overall numbers of coronary angiographies increased from 1992 to 2004 from 684 000 to 2 238 000 (from 1250 to 3930 per million inhabitants). The respective numbers for percutaneous coronary interventions (PCIs) and coronary stenting procedures increased from 184 000 to 885 000 (from 335 to 1550) and from 3000 to 770 000 (from 5 to 1350), respectively. Germany was the most active country with 712 000 angiographies (8600), 249 000 angioplasties (3000), and 200 000 stenting procedures (2400) in 2004. The indication has shifted towards acute coronary syndromes, as demonstrated by rising rates of interventions for acute myocardial infarction over the last decade. The procedures are more readily performed and perceived safer, as shown by increasing rate of "ad hoc" PCIs and decreasing need for emergency coronary artery bypass grafting (CABG). In 2004, the use of drug-eluting stents continued to rise. However, an enormous variability is reported with the highest rate in Switzerland (70%). If the rate of progression remains constant until 2010 the projected number of coronary angiographies will be over three million, and the number of PCIs about 1.5 million with a stenting rate of almost 100%. CONCLUSION: Interventional cardiology in Europe is ever expanding. New coronary revascularization procedures, alternative or complementary to balloon angioplasty, have come and gone. Only stenting has stood the test of time and matured to the default technique. Facilitated access to PCI, more complete and earlier detection of coronary artery disease promise continued growth of the procedure despite the uncontested success of prevention.