Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Molecular phylogeography of the Woodland Ringlet (Erebia medusa [Denis and Schiffermüller] 1775) in Europe

Phylogeography is a recent field of biological research that links phylogenetics to biogeography through deciphering the imprint that evolutionary history has left on the genetic structure of extant populations. During the cold phases of the successive ice ages, which drastically shaped species’ distributions since the Pliocene, populations of numerous species were isolated in refugia where many of them evolved into different genetic lineages. My dissertation deals with the phylogeography of the Woodland Ringlet (Erebia medusa [Denis and Schiffermüller] 1775) in Central and Eastern Europe. This Palaearctic butterfly species is currently distributed from central France and south eastern Belgium over large parts of Central Europe and southern Siberia to the Pacific. It is absent from those parts of Europe with mediterranean, oceanic and boreal climates. It was supposed to be a Siberian faunal element with a rather homogeneous population structure in Central Europe due to its postglacial expansion out of a single eastern refugium. An already existing evolutionary scenario for the Woodland Ringlet in Central and Eastern Europe is based on nuclear data (allozymes). To know if this is corroborated by organelle evolutionary history, I sequenced two mitochondrial markers (part of the cytochrome oxydase subunit one and the control region) for populations sampled over the same area. Phylogeography largely relies on the construction of networks of uniparentally inherited haplotypes that are compared to geographic haplotype distribution thanks to recent developed methods such as nested clade phylogeographic analysis (NCPA). Several ring-shaped ambiguities (loops) emerged from both haplotype networks in E. medusa. They can be attributed to recombination and homoplasy. Such loops usually avert the straightforward extraction of the phylogeographic signal contained in a gene tree. I developed several new approaches to extract phylogeographic information in the presence of loops, considering either homoplasy or recombination. This allowed me to deduce a consistent evolutionary history for the species from the mitochondrial data and also adds plausibility for the occurrence of recombination in E. medusa mitochondria. Despite the fact that the control region is assumed to have a lack of resolving power in other species, I found a considerable genetic variation of this marker in E. medusa which makes it a useful tool for phylogeographic studies. In combination with the allozyme data, the mitochondrial genome supports the following phylogeographic scenario for E. medusa in Europe: (i) a first vicariance, due to the onset of the Würm glaciation, led to the formation of several major lineages, and is mirrored in the NCPA by restricted gene flow, (ii) later on further vicariances led to the formation of two sub-lineages in the Western lineage and two sub-lineages in the Eastern lineage during the Last Glacial Maximum or Older Dryas; additionally the NCPA supports a restriction of gene flow with isolation by distance, (iii) finally, vicariance resulted in two secondary sub-lineages in the area of Germany and, maybe, to two other secondary sub-lineages in the Czech Republic. The last postglacial warming was accompanied by strong range expansions in most of the genetic lineages. The scenario expected for a presumably Siberian faunal element such as E. medusa is a continuous loss of genetic diversity during postglacial westward expansion. Hence, the pattern found in this thesis contradicts a typical Siberian origin of E. medusa. In contrast, it corroboratess the importance of multiple extra-Mediterranean refugia for European fauna as it was recently assumed for other continental species.

Top-quark pair production at hadron colliders

In this thesis we investigate several phenomenologically important properties of top-quark pair production at hadron colliders. We calculate double differential cross sections in two different kinematical setups, pair invariant-mass (PIM) and single-particle inclusive (1PI) kinematics. In pair invariant-mass kinematics we are able to present results for the double differential cross section with respect to the invariant mass of the top-quark pair and the top-quark scattering angle. Working in the threshold region, where the pair invariant mass M is close to the partonic center-of-mass energy sqrt{hat{s}}, we are able to factorize the partonic cross section into different energy regions. We use renormalization-group (RG) methods to resum large threshold logarithms to next-to-next-to-leading-logarithmic (NNLL) accuracy. On a technical level this is done using effective field theories, such as heavy-quark effective theory (HQET) and soft-collinear effective theory (SCET). The same techniques are applied when working in 1PI kinematics, leading to a calculation of the double differential cross section with respect to transverse-momentum pT and the rapidity of the top quark. We restrict the phase-space such that only soft emission of gluons is possible, and perform a NNLL resummation of threshold logarithms. The obtained analytical expressions enable us to precisely predict several observables, and a substantial part of this thesis is devoted to their detailed phenomenological analysis. Matching our results in the threshold regions to the exact ones at next-to-leading order (NLO) in fixed-order perturbation theory, allows us to make predictions at NLO+NNLL order in RG-improved, and at approximate next-to-next-to-leading order (NNLO) in fixed order perturbation theory. We give numerical results for the invariant mass distribution of the top-quark pair, and for the top-quark transverse-momentum and rapidity spectrum. We predict the total cross section, separately for both kinematics. Using these results, we analyze subleading contributions to the total cross section in 1PI and PIM originating from power corrections to the leading terms in the threshold expansions, and compare them to previous approaches. We later combine our PIM and 1PI results for the total cross section, this way eliminating uncertainties due to these corrections. The combined predictions for the total cross section are presented as a function of the top-quark mass in the pole, the minimal-subtraction (MS), and the 1S mass scheme. In addition, we calculate the forward-backward (FB) asymmetry at the Tevatron in the laboratory, and in the ttbar rest frames as a function of the rapidity and the invariant mass of the top-quark pair at NLO+NNLL. We also give binned results for the asymmetry as a function of the invariant mass and the rapidity difference of the ttbar pair, and compare those to recent measurements. As a last application we calculate the charge asymmetry at the LHC as a function of a lower rapidity cut-off for the top and anti-top quarks.

Willem Marinus Dudok. Progetti urbani per la citta' di Hilversum

Il tema principale affrontato dalla presente ricerca è quello dell’architettura della città; attraverso lo studio dei progetti urbani redatti dall’architetto Willem Marinus Dudok per la città di Hilversum, la tesi vuole confermare l’ipotesi che la costruzione dei “luoghi urbani” collettivi è il fulcro dell’idea di architettura che porta alla costruzione della città. La ricerca si propone di studiare il contributo dato da Dudok al progetto dello sviluppo urbano della città olandese, considerando un arco temporale che va dal 1915, anno in cui l’architetto viene designato a ricoprire la carica di direttore del locale ufficio Lavori Pubblici, al 1954, anno simbolico della sua nomina a cittadino onorario di Hilversum. Il lavoro di ricerca vuole individuare quelle caratteristiche formali e tipologiche, insite nei quartieri progettati dall’architetto olandese, in grado di definire una struttura urbana capace di sostenere un ragionamento architettonico indipendente dal luogo e dal tempo, un ragionamento impostato sulla definizione della forma urbis. Non desidera certo delineare un modello, vista la consapevolezza che ogni progetto ha un proprio luogo e un proprio tempo, cerca di tratteggiare, piuttosto, uno scenario possibile per il progetto urbano, capace di assurgere ad exemplum per la costruzione della città. I progetti analizzati riguardano edifici residenziali e spazi urbani per la collettività; questi rappresentano veri e propri nuclei aggregativi per la costruzione dei complessi di alloggi popolari, dei quali definiscono la scena fissa delle vicende umane. Lo studio di questi quartieri rappresenta, pertanto, il tentativo di decodificare un “modo” di comporre la città dal quale sia possibile estrapolare temi validi e di carattere generale che permettano di formalizzare una serie di utili insegnamenti, tramite i quali poter pensare alla realizzazione della stessa, nella convinzione che “la qualità del progetto consiste nella qualità dei caratteri del tema e nel loro riconoscimento nelle forme dell’architettura”.

Asymmetric drift and halo flattening in disk galaxies

The main result in this work is the solution of the Jeans equations for an axisymmetric galaxy model containing a baryonic component (distributed according to a Miyamoto-Nagai profile) and a dark matter halo (described by the Binney logarithmic potential). The velocity dispersion, azimuthal velocity and some other interesting quantities such as the asymmetric drift are studied, along with the influence of the model parameters on these (observable) quantities. We also give an estimate for the velocity of the radial flow, caused by the asymmetric drift. Other than the mathematical beauty that lies in solving a model analytically, the interest of this kind of results can be mainly found in numerical simulations that study the evolution of gas flows. For example, it is important to know how certain parameters such as the shape (oblate, prolate, spherical) of a dark matter halo, or the flattening of the baryonic matter, or the mass ratio between dark and baryonic matter, have an influence on observable quantities such as the velocity dispersion. In the introductory chapter, we discuss the Jeans equations, which provide information about the velocity dispersion of a system. Next we will consider some dynamical quantities that will be useful in the rest of the work, e.g. the asymmetric drift. In Chapter 2 we discuss in some more detail the family of galaxy models we studied. In Chapter 3 we give the solution of the Jeans equations. Chapter 4 describes and illustrates the behaviour of the velocity dispersion, as a function of the several parameters, along with asymptotic expansions. In Chapter 5 we will investigate the behaviour of certain dynamical quantities for this model. We conclude with a discussion in Chapter 6.

Untersuchungen zur Wirkung des Ginkgo-biloba-Extraktes EGb 761 auf die Proteinaggregation in der Huntington-Krankheit

Der Ginkgo biloba-Extrakt EGb 761 besteht aus einer Reihe pharmakologisch wirksamer Substanzen, welche gut beschriebene Wirkungen auf verschiedene potentiell zytoprotektive Signalwege ausüben und u.a. antioxidative Wirksamkeit haben. Folglich wurde EGb 761 bisher als eine natürliche Behandlung bei neurodegenerativen Erkrankungen mit zellulärem oxidativen Stress angewendet, einschließlich der Alzheimer-Krankheit (AD). Aufgrund von vielen gemeinsamen Merkmalen zwischen der AD und der Huntington-Krankheit (HD) wurde vermutet, dass EGb 761 eventuell auch positive Wirksamkeit bei der HD aufweisen könnte. rnDie Neuropathologie der HD wird durch pathologische Verlängerung an Glutamin-Wiederholungen im Huntingtin-Protein (polyQ-Protein) verursacht, wodurch es zu Fehlfaltungen im Protein kommt und hierdurch der proteasomale Abbau aberranter Proteine erschwert wird. Somit sollten in der vorliegenden Arbeit die EGb 761-Wirkungen auf die Proteasom-Aktivität und die Proteinaggregation in zellulären Modellen der HD untersucht werden. rnWie die ersten Untersuchungen in nativen HEK293-Zellen ergaben, bewirkte die Behandlung der Zellen mit EGb 761 eine Steigerung der basalen Proteasom-Aktivität sowie des proteasomalen Proteinabbaus und erhöhte die Transkription proteasomaler Gene. Hieraus ergaben sich Untersuchungen in Zellen mit Expressionen pathologischer Varianten von polyQ-Proteinen als zelluläre Modelle der HD. Hierbei konnte festgestellt werden, dass die Expression aberranter polyQ-Proteine eine verminderte zelluläre Proteasom-Aktivität bewirkte. Interessanterweise verursachte EGb 761 eine Abmilderung der pathologisch-induzierten verminderten Proteasom-Aktivität, in dem die EGb 761-Behandlung der Zellen zu einer erhöhten Proteasom-Aktivität, einem verbesserten proteasomalen Proteinabbau, sowie zu einer erhöhten Transkription proteasomaler Gene führte. Da diese EGb 761-Effekte unabhängig von der Expression aberranter polyQ-Proteine waren, demonstrierten diese Ergebnisse eine allgemeine EGb 761-Wirkungen auf die Proteasom-Aktivität. Anhand dieser Ergebnisse sollten anschließend weitere Untersuchungen mit zellulären Modellen der HD die genau Wirkung von EGb 761 auf die Degradation von abnormal verlängerten polyQ-Proteinen sowie auf die Bildung von polyQ-Aggregaten klären. rnHier konnte gezeigt werden, dass die Expression aberranter polyQ-Proteinen zu einer Akkumulation von SDS-resistenten bzw. SDS-unlöslichen, aggregierten polyQ-Proteinen führte, sowie die Bildung von sichtbaren polyQ-Aggregaten in Zellen bewirkte. Hierbei verursachte eine EGb 761-Behandlung der Zellen eine signifikante Verminderung im Gehalt an SDS-resistenten polyQ-Proteinen sowie eine Reduzierung von Aggregat-tragenden Zellen. Zudem konnte gezeigt werden, dass eine pharmakologische Inhibition des Proteasoms in EGb 761-behandelten Zellen, den Gehalt an SDS-unlöslichen polyQ-Proteinaggregate wieder erhöhte und somit den Effekt von EGb 761 aufhob. Folglich zeigten diese Ergebnisse, dass die EGb 761-induzierte Reduzierung der polyQ-Proteinaggregate durch einen effizienteren proteasomalen Abbau von fehlgefalteten, aberranten polyQ-Proteinen bewirkte wurde. rnAufbauend auf diesen Ergebnissen wurde eine experimentell-therapeutische Anwendung von EGb 761 in Modellen der HD in vitro und in vivo überprüft und hierzu primäre humane Fibroblasten sowie transgene C. elegans Würmer mit Expressionen aberranter polyQ-Proteine untersucht. Interessanterweise konnte in vitro und in vivo gezeigt werden, dass die EGb 761-Behandlung auch hier eine Reduzierung von SDS-unlöslichen polyQ-Proteinen bewirkte und zudem eine Reduzierung des pathologisch erhöhten Gehalts an Polyubiquitin-Proteinen bewirkte. Folglich wurde auch hier vermutet, dass EGb 761 einen verbesserten proteasomalen Abbau von polyQ-Proteinen induzierte und dies eine Verminderung der polyQ-Proteinaggregate verursachte. Darüber hinaus führte die EGb 761-Behandlung von seneszenten Fibroblasten zur Reduzierung von altersabhängig erhöhten Mengen von polyQ-Aggregaten, wodurch ein therapeutischer Effekt auf den proteasomalen Abbau der polyQ-Proteine verdeutlicht wurde. Zusätzlich konnte in polyQ-transgenen C. elegans demonstriert werden, dass eine EGb 761-Behandlung die Abmilderung eines typischen pathologischen Phänotyps bewirkte, indem eine polyQ-induzierte verminderte Motilität der Nematoden verbessert wurde und hierdurch eine positive EGb 761-Wirkung auf die Pathologie der HD in vivo dargestellt wurde. rnZusammenfassend konnten in dieser Arbeit neue Wirkungen von EGb 761 in der HD demonstriert werden. Hierbei wurde gezeigt, dass EGb 761 die Aggregation von pathogenen aberranten polyQ-Proteinen in vitro und in vivo reduziert, indem eine effizientere Degradation von polyQ-Proteinen erfolgt. Somit könnte diese Wirkungen von EGb 761 eine potentiell therapeutische Anwendung in der HD und ähnliche neurodegenerativen Erkrankungen darstellen.

Quantitative analysis of extracapsular extension of metastatic lymph nodes and its significance in radiotherapy planning in head and neck squamous cell carcinoma

We performed a histopathologic analysis to assess the extent of the extracapsular extension (ECE) beyond the capsule of metastatic lymph nodes (LN) in head and neck cancer to determine appropriate clinical target volume (CTV) expansions.

Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Genomic Data Reveal a Complex Making of Humans

In the last few years, two paradigms underlying human evolution have crumbled. Modern humans have not totally replaced previous hominins without any admixture, and the expected signatures of adaptations to new environments are surprisingly lacking at the genomic level. Here we review current evidence about archaic admixture and lack of strong selective sweeps in humans. We underline the need to properly model differential admixture in various populations to correctly reconstruct past demography. We also stress the importance of taking into account the spatial dimension of human evolution, which proceeded by a series of range expansions that could have promoted both the introgression of archaic genes and background selection.

Whither PQL?

Generalized linear mixed models (GLMM) are generalized linear models with normally distributed random effects in the linear predictor. Penalized quasi-likelihood (PQL), an approximate method of inference in GLMMs, involves repeated fitting of linear mixed models with “working” dependent variables and iterative weights that depend on parameter estimates from the previous cycle of iteration. The generality of PQL, and its implementation in commercially available software, has encouraged the application of GLMMs in many scientific fields. Caution is needed, however, since PQL may sometimes yield badly biased estimates of variance components, especially with binary outcomes. Recent developments in numerical integration, including adaptive Gaussian quadrature, higher order Laplace expansions, stochastic integration and Markov chain Monte Carlo (MCMC) algorithms, provide attractive alternatives to PQL for approximate likelihood inference in GLMMs. Analyses of some well known datasets, and simulations based on these analyses, suggest that PQL still performs remarkably well in comparison with more elaborate procedures in many practical situations. Adaptive Gaussian quadrature is a viable alternative for nested designs where the numerical integration is limited to a small number of dimensions. Higher order Laplace approximations hold the promise of accurate inference more generally. MCMC is likely the method of choice for the most complex problems that involve high dimensional integrals.

[Intraoral lipoma in the region of the mental nerve--report of a case and review of the literature]

The intraoral lipoma is a benign, slowly growing, painless soft tissue neoplasia, which can cause esthetic or functional problems for the patient, depending on its size. All parts of the body can be affected, whereas the oral cavity is rarely involved. Clinically, the tumour often exhibits an exophytic growth pattern, a soft consistency, a broad base connected to the underlying tissue, and frequently has a reddish-yellowish colour. Instead of a superficial mucosal involvement, a deep localization in the soft tissues is also possible. Depending on the localization of the tumour, the diagnosis and the resulting therapy can turn out to be a challenge for the clinician. A clear differentiation to malign neoplasias of the fat tissues and other soft tissue expansions is essential. The following case report presents a female patient who is affected by a lipoma in the proximity of the mental nerve. The diagnostic work-up and resulting therapy including a review of the current literature are presented and discussed.

Dynamic changes of cardiac conduction during rapid pacing

Slow conduction and unidirectional conduction block (UCB) are key mechanisms of reentry. Following abrupt changes in heart rate, dynamic changes of conduction velocity (CV) and structurally determined UCB may critically influence arrhythmogenesis. Using patterned cultures of neonatal rat ventricular myocytes grown on microelectrode arrays, we investigated the dynamics of CV in linear strands and the behavior of UCB in tissue expansions following an abrupt decrease in pacing cycle length (CL). Ionic mechanisms underlying rate-dependent conduction changes were investigated using the Pandit-Clark-Giles-Demir model. In linear strands, CV gradually decreased upon a reduction of CL from 500 ms to 230-300 ms. In contrast, at very short CLs (110-220 ms), CV first decreased before increasing again. The simulations suggested that the initial conduction slowing resulted from gradually increasing action potential duration (APD), decreasing diastolic intervals, and increasing postrepolarization refractoriness, which impaired Na(+) current (I(Na)) recovery. Only at very short CLs did APD subsequently shorten again due to increasing Na(+)/K(+) pump current secondary to intracellular Na(+) accumulation, which caused recovery of CV. Across tissue expansions, the degree of UCB gradually increased at CLs of 250-390 ms, whereas at CLs of 180-240 ms, it first increased and subsequently decreased. In the simulations, reduction of inward currents caused by increasing intracellular Na(+) and Ca(2+) concentrations contributed to UCB progression, which was reversed by increasing Na(+)/K(+) pump activity. In conclusion, CV and UCB follow intricate dynamics upon an abrupt decrease in CL that are determined by the interplay among I(Na) recovery, postrepolarization refractoriness, APD changes, ion accumulation, and Na(+)/K(+) pump function.

Molecular characterization of HOXA13 polyalanine expansion proteins in hand-foot-genital syndrome

We report on a father and daughter with hand-foot-genital syndrome (HFGS) with typical skeletal and genitourinary anomalies due to a 14-residue polyalanine expansion in HOXA13. This is the largest (32 residues) polyalanine tract so far described for any polyalanine mutant protein. Polyalanine expansion results in protein misfolding, cytoplasmic aggregation and degradation; however, HOXA13 polyalanine expansions appear to act as loss of function mutations in contrast to gain of function for HOXD13 polyalanine expansions. To address this paradox we examined the cellular consequences of polyalanine expansions on HOXA13 protein using COS cell transfection and immunocytochemistry. HOXA13 polyalanine expansion proteins form cytoplasmic aggregates, and distribution between cytoplasmic aggregates or the nucleus is polyalanine tract size-dependent. Geldanamycin, an Hsp90 inhibitor, reduces the steady-state abundance of all polyalanine-expanded proteins in transfected cells. We also found that wild-type HOXA13 or HOXD13 proteins are sequestered in HOXA13 polyalanine expansion cytoplasmic aggregates. Thus, the difference between HOXA13 polyalanine expansion loss-of-function and HOXD13 polyalanine expansion dominant-negative effect is not the ability to aggregate wild-type group 13 paralogs but perhaps to variation in activities associated with refolding, aggregation or degradation of the proteins.

Study of water use and supply in the district of Independencia, Peru

Peru is a developing country with abundant fresh water resources, yet the lack of infrastructure leaves much of the population without access to safe water for domestic uses. The author of this report was a Peace Corps Volunteer in the sector of water & sanitation in the district of Independencia, Ica, Peru. Independencia is located in the arid coastal region of the country, receiving on average 15 mm of rain annually. The water source for this district comes from the Pisco River, originating in the Andean highlands and outflowing into the Pacific Ocean near the town of Pisco, Peru. The objectives of this report are to assess the water supply and sanitation practices, model the existing water distribution system, and make recommendations for future expansion of the distribution system in the district of Independencia, Peru. The assessment of water supply will be based on the results from community surveys done in the district of Independencia, water quality testing done by a detachment of the U.S. Navy, as well as on the results of a hydraulic model built in EPANET 2.0 to represent the distribution system. Sanitation practice assessments will be based on the surveys as well as observations from the author while living in Peru. Recommendations for system expansions will be made based on results from the EPANET model and the municipality’s technical report for the existing distribution system. Household water use and sanitation surveys were conducted with 84 families in the district revealing that upwards of 85% store their domestic water in regularly washed containers with lids. Over 80% of those surveyed are drinking water that is treated, mostly boiled. Of those surveyed, over 95% reported washing their hands and over 60% mentioned at least one critical time for hand washing when asked for specific instances. From the surveys, it was also discovered that over 80% of houses are properly disposing of excrement, in either latrines or septic tanks. There were 43 families interviewed with children five years of age or under, and just over 18% reported the child had a case of diarrhea within the last month at the time of the interview. Finally, from the surveys it was calculated that the average water use per person per day is about 22 liters. Water quality testing carried out by a detachment of the U.S. Navy revealed that the water intended for consumption in the houses surveyed was not suitable for consumption, with a median E. coli most probable number of 47/100 ml for the 61 houses sampled. The median total coliforms was 3,000 colony forming units per 100 ml. EPANET was used to simulate the water delivery system and evaluate its performance. EPANET is designed for continuous water delivery systems, assuming all pipes are always flowing full. To account for the intermittent nature of the system, multiple EPANET network models were created to simulate how water is routed to the different parts of the system throughout the day. The models were created from interviews with the water technicians and a map of the system created using handheld GPS units. The purpose is to analyze the performance of the water system that services approximately 13,276 people in the district of Independencia, Peru, as well as provide recommendations for future growth and improvement of the service level. Performance evaluation of the existing system is based on meeting 25 liters per person per day while maintaining positive pressure at all nodes in the network. The future performance is based on meeting a minimum pressure of 20 psi in the main line, as proposed by Chase (2000). The EPANET model results yield an average nodal pressure for all communities of 71 psi, with a range from 1.3 – 160 psi. Thus, if the current water delivery schedule obtained from the local municipality is followed, all communities should have sufficient pressure to deliver 25 l/p/d, with the exception of Los Rosales, which can only supply 3.25 l/p/d. However, if the line to Los Rosales were increased from one to four inches, the system could supply this community with 25 l/p/d. The district of Independencia could greatly benefit from increasing the service level to 24-hour water delivery and a minimum of 50 l/p/d, so that communities without reliable access due to insufficient pressure would become equal beneficiaries of this invaluable resource. To evaluate the feasibility of this, EPANET was used to model the system with a range of population growth rates, system lifetimes, and demands. In order to meet a minimum pressure of 20 psi in the main line, the 6-inch diameter main line must be increased and approximately two miles of trench must be excavated up to 30 feet deep. The sections of the main line that must be excavated are mile 0-1 and 1.5-2.5, and the first 3.4 miles of the main line must be increased from 6 to 16 inches, contracting to 10 inches for the remaining 5.8 miles. Doing this would allow 24-hour water delivery and provide 50 l/p/d for a range of population growth rates and system lifetimes. It is expected that improving the water delivery service would reduce the morbidity and mortality from diarrheal diseases by decreasing the recontamination of the water due to transport and household storage, as well as by maintaining continuous pressure in the system to prevent infiltration of contaminated groundwater. However, this expansion must be carefully planned so as not to affect aquatic ecosystems or other districts utilizing water from the Pisco River. It is recommended that stream gaging of the Pisco River and precipitation monitoring of the surrounding watershed is initiated in order to begin a hydrological study that would be integrated into the district’s water resource planning. It is also recommended that the district begin routine water quality testing, with the results available to the public.

OPTIMAL SHAPE IN ELECTROMAGNETIC SCATTERING BY SMALL ASPHERICAL PARTICLES

We consider the question of optimal shapes, e.g., those causing minimal extinction among all shapes of equal volume. Guided by the isoperimetric property of a sphere, relevant in the geometrical optics limit of scattering by large particles, we examine an analogous question in the low frequency (electrostatics) approximation, seeking to disentangle electric and geometric contributions. To that end, we survey the literature on shape functionals and focus on ellipsoids, giving a simple proof of spherical optimality for the coated ellipsoidal particle. Monotonic increase with asphericity in the low frequency regime for orientation-averaged induced dipole moments and scattering cross-sections is also shown. Additional physical insight is obtained from the Rayleigh-Gans (transparent) limit and eccentricity expansions. We propose connecting low and high frequency regime in a single minimum principle valid for all size parameters, provided that reasonable size distributions of randomly oriented aspherical particles wash out the resonances for intermediate size parameters. This proposal is further supported by the sum rule for integrated extinction.