Identifying invariant ergodic subsets and barriers to mixing by cutting and shuffling: Study in a birotated hemisphere.

Mixing by cutting and shuffling can be mathematically described by the dynamics of piecewise isometries (PWIs), higher dimensional analogs of one-dimensional interval exchange transformations. In a two-dimensional domain under a PWI, the exceptional set, E[over ¯], which is created by the accumulation of cutting lines (the union of all iterates of cutting lines and all points that pass arbitrarily close to a cutting line), defines where mixing is possible but not guaranteed. There is structure within E[over ¯] that directly influences the mixing potential of the PWI. Here we provide computational and analytical formalisms for examining this structure by way of measuring the density and connectivity of ɛ-fattened cutting lines that form an approximation of E[over ¯]. For the example of a PWI on a hemispherical shell studied here, this approach reveals the subtle mixing behaviors and barriers to mixing formed by invariant ergodic subsets (confined orbits) within the fractal structure of the exceptional set. Some PWIs on the shell have provably nonergodic exceptional sets, which prevent mixing, while others have potentially ergodic exceptional sets where mixing is possible since ergodic exceptional sets have uniform cutting line density. For these latter exceptional sets, we show the connectivity of orbits in the PWI map through direct examination of orbit position and shape and through a two-dimensional return plot to explain the necessity of orbit connectivity for mixing.

Long-term field performance of a conventional and modified bioretention system for removing dissolved nitrogen species in stormwater runoff.

Bioretention systems are efficient at removing particulates, metals, and hydrocarbons from stormwater runoff. However, managing dissolved nitrogen (N) species (dissolved organic N, NH4+, NO2-, NO3-) is a challenge for these systems. This paper reports the results of a long-term field study comparing N removal of: 1) a modified bioretention system that included an internal water storage zone containing wood chips to promote denitrification and 2) a conventional bioretention system. The systems were studied, without and with plants, under varying hydraulic loading rates (HLRs) and antecedent dry conditions (ADCs). Both bioretention designs were efficient at removing NH4+ (83% modified, 74% conventional), while removal of NOx (NO2--N + NO3--N) was significantly higher in the modified system (81% modified, 29% conventional). Results show that the addition of an internal water storage zone promotes denitrification, resulting in lower effluent TN concentrations (<0.75 mg/L modified, ∼1.60 mg/L conventional). The lowest HLR studied, 4.1 cm/h, provided the longest hydraulic retention time in the internal water storage zone (∼3 h) and had the greatest TN removal efficiency (90% modified, 59% conventional). In contrast to prior short-term studies, ADCs between 0 and 13 days did not significantly affect DOC export or TN removal. A short-term study with Florida friendly vegetation indicated that TN removal performance was enhanced in the conventional bioretention system. This field study provides promising results for improving dissolved N removal by modifying bioretention systems to include an internal water storage zone containing wood chips.

Cutting and shuffling a hemisphere: Nonorthogonal axes.

We examine the dynamics of cutting-and-shuffling a hemispherical shell driven by alternate rotation about two horizontal axes using the framework of piecewise isometry (PWI) theory. Previous restrictions on how the domain is cut-and-shuffled are relaxed to allow for nonorthogonal rotation axes, adding a new degree of freedom to the PWI. A new computational method for efficiently executing the cutting-and-shuffling using parallel processing allows for extensive parameter sweeps and investigations of mixing protocols that produce a low degree of mixing. Nonorthogonal rotation axes break some of the symmetries that produce poor mixing with orthogonal axes and increase the overall degree of mixing on average. Arnold tongues arising from rational ratios of rotation angles and their intersections, as in the orthogonal axes case, are responsible for many protocols with low degrees of mixing in the nonorthogonal-axes parameter space. Arnold tongue intersections along a fundamental symmetry plane of the system reveal a new and unexpected class of protocols whose dynamics are periodic, with exceptional sets forming polygonal tilings of the hemispherical shell.

Mixing and the fractal geometry of piecewise isometries.

Mathematical concepts often have applicability in areas that may have surprised their original developers. This is the case with piecewise isometries (PWIs), which transform an object by cutting it into pieces that are then rearranged to reconstruct the original object, and which also provide a paradigm to study mixing via cutting and shuffling in physical sciences and engineering. Every PWI is characterized by a geometric structure called the exceptional set, E, whose complement comprises nonmixing regions in the domain. Varying the parameters that define the PWI changes both the structure of E as well as the degree of mixing the PWI produces, which begs the question of how to determine which parameters produce the best mixing. Motivated by mixing of yield stress materials, for example granular media, in physical systems, we use numerical simulations of PWIs on a hemispherical shell and examine how the fat fractal properties of E relate to the degree of mixing for any particular PWI. We present numerical evidence that the fractional coverage of E negatively correlates with the intensity of segregation, a standard measure for the degree of mixing, which suggests that fundamental properties of E such as fractional coverage can be used to predict the effectiveness of a particular PWI as a mixing mechanism.

A Tire-Sulfur Hybrid Adsorption Denitrification (T-SHAD) process for decentralized wastewater treatment.

Nitrogen discharges from decentralized wastewater treatment (DWT) systems contribute to surface and groundwater contamination. However, the high variability in loading rates, long idle periods and lack of regular maintenance presents a challenge for biological nitrogen removal in DWT. A Tire-Sulfur Hybrid Adsorption Denitrification (T-SHAD) process was developed that combines nitrate (NO3(-)) adsorption to scrap tire chips with sulfur-oxidizing denitrification. This allows the tire chips to adsorb NO3(-) when the influent loading exceeds the denitrification capacity of the biofilm and release it when NO3(-) loading rates are low (e.g. at night). Three waste products, scrap tire chips, elemental sulfur pellets and crushed oyster shells, were used as a medium in adsorption, leaching, microcosm and up-flow packed bed bioreactor studies of NO3(-) removal from synthetic nitrified DWT wastewater. Adsorption isotherms showed that scrap tire chips have an adsorption capacity of 0.66 g NO3(-)-N kg(-1) of scrap tires. Leaching and microcosm studies showed that scrap tires leach bioavailable organic carbon that can support mixotrophic metabolism, resulting in lower effluent SO4(2-) concentrations than sulfur oxidizing denitrification alone. In column studies, the T-SHAD process achieved high NO3(-)-N removal efficiencies under steady state (90%), variable flow (89%) and variable concentration (94%) conditions.

Inner ear anomalies and conductive hearing loss in children with Apert syndrome: an overlooked otologic aspect.

OBJECTIVE: To identify the occurrence of inner ear structural anomalies and conductive hearing loss (CHL) in children with Apert syndrome. STUDY DESIGN: Retrospective review. SETTING: Pediatric tertiary referral center. PATIENTS: Twenty pediatric patients with Apert syndrome were found; all patients (38/40 ears) had inner ear anomalies. INTERVENTION(S): Computerized tomography of the head/temporal bone, pure-tone (including air and bone conduction) audiometry, and tympanometry. MAIN OUTCOME MEASURE(S): Imaging demonstrating inner ear anomalies, including malformations of the cochlea, dilated vestibule, and/or semicircular canal; audiologic findings of air-bone gap(s). RESULTS: Hearing loss was found in 90% of the patients with Apert syndrome, and 80% of them had CHL. Air-bone gaps were found at all frequencies, with larger gaps at low frequencies. Fifty percent (20/40) of the ears had better than 0 dB hearing level bone conduction thresholds at 250 and/or 500 Hz. Normal middle ear pressure and mobility were found in all ears with intact eardrum. Inner ear anomalies were found in all patients, and 90% of them had bilateral involvement. Most frequently observed inner ear anomalies were dilated vestibule, malformed lateral semicircular canal, and cochlear dysplasia. CONCLUSION: Children with Apert syndrome may present with significant CHL that cannot be explained by minor middle ear pathologies alone. This conductive loss may be, at least partially, attributed to the inner ear anomalies; however, these structural anomalies are usually not recognized in these patients. Failure to close air-bone gap after surgical intervention may raise the suspicion of inner ear anomalies, and computed tomographic scan of the temporal bone can provide definitive proof.

Atmospheric pressure photoionization. II. Dual source ionization.

In this paper we describe results based on the combination of atmospheric pressure photoionization (APPI) with atmospheric pressure chemical ionization (APCI) and electrospray ionization (ESI). The main purpose of combining more than one ionizer is to extend the range of compounds that can be simultaneously analyzed. Three modes of operation are presented; use of either ionizer, simultaneous use of two ionizers, and rapid switching between ionizers during a single chromatographic run. The dual ionizer configurations only minimally affect the performance of either ionizer relative to the standard single-ionizer sources. However, it is observed that the operation of both ionizers together does not typically give the sum signal from either source operating alone. For APCI/APPI the signal can range from less than that of either source alone to the sum of the two individual sources. For ESI/APPI, we observed large suppressions of the ESI multiply-charged signal of proteins when the APPI source was on. These behaviors are presumed to be due to the interaction of the initially formed ions by both sources and attests to the importance of ion-molecule reactions that occur during and after the primary ionization events. We give examples of compounds that are preferentially ionized by either APPI, APCI or ESI and present thermochemical arguments based on molecular structure and functionality to explain this behavior. The dual source is also shown to be able to operate in negative ion mode opening up the potential to conduct wide ranging chemical analyses.

The diagnosis of congenital adrenal hyperplasia in the newborn by gas chromatography/mass spectrometry analysis of random urine specimens.

Definitive neonatal diagnosis of congenital adrenal hyperplasia (CAH) is frequently complicated by normal 17-hydroxyprogesterone levels in 21-hydroxylase-deficient patients, residual maternal steroids, and other interfering substances in neonatal blood. In an effort to improve the diagnosis, we developed a gas chromatography/mass spectrometry method for simultaneous measurement of 15 urinary steroid metabolites as early as the first day of life. Furthermore, we developed 11 precursor/product ratios that diagnose and clearly differentiate the four enzymatic deficiencies that cause CAH. Random urine samples from 31 neonatal 21-hydroxylase-deficient patients and 59 age-matched normal newborns were used in the development. Additionally, samples from two 11 beta-hydroxylase-deficient patients and one patient each for 17 alpha-hydroxylase and 3 beta-hydroxysteroid dehydrogenase deficiencies were used. The throughput for one bench-top gas chromatography/mass spectrometry instrument is 20 samples per day. Thus, this method affords an accurate, rapid, noninvasive means for the differential diagnosis of CAH in the newborn period without the need for invasive testing and ACTH stimulation.