A geometric analysis of the Lagerstrom model problem

AbstractLagerstrom's model problem is a classical singular perturbation problem which was introduced to illustrate the ideas and subtleties involved in the analysis of viscous flow past a solid at low Reynolds number by the method of matched asymptotic expansions. In this paper the corresponding boundary value problem is analyzed geometrically by using methods from the theory of dynamical systems, in particular invariant manifold theory. As an essential part of the dynamics takes place near a line of non-hyperbolic equilibria, a blow-up transformation is introduced to resolve these singularities. This approach leads to a constructive proof of existence and local uniqueness of solutions and to a better understanding of the singular perturbation nature of the problem. In particular, the source of the logarithmic switchback phenomenon is identified

Dynamic contrast-enhanced MRI in malignant pleural mesothelioma : prediction of outcome based on DCE-MRI measurements in patients undergoing cytotoxic chemotherapy

The malignant pleural mesothelioma (MPM) response rate to chemotherapy is low. The identification of imaging biomarkers that could help guide the most effective therapy approach for individual patients is highly desirable. Our aim was to investigate the dynamic contrast-enhanced (DCE) MR parameters as predictors for progression-free (PFS) and overall survival (OS) in patients with MPM treated with cisplatin-based chemotherapy. Methods: Thirty-two consecutive patients with MPM were enrolled in this prospective study. Pretreatment and intratreatment DCE-MRI were scheduled in each patient. The DCE parameters were analyzed using the extended Tofts (ET) and the adiabatic approximation tissue homogeneity (AATH) model. Comparison analysis, logistic regression and ROC analysis were used to identify the predictors for the patient\u27s outcome. Results: Patients with higher pretreatment ET and AATH-calculated Ktrans and ve values had longer OS (P≤.006). Patients with a more prominent reduction in ET-calculated Ktrans and kep values during the early phase of chemotherapy had longer PFS (P =.008). No parameter was identified to predict PFS. Pre-treatment ET-calculated Ktrans was found to be an independent predictive marker for longer OS (P=.02) demonstrating the most favourable discrimination performance compared to other DCE parameters with an estimated sensitivity of 89% and specificity of 78% (AUC 0.9, 95% CI 0.74-0.98, cut off > 0.08 min-1). Conclusions: In the present study, higher pre-treatment ET-calculated Ktrans values were associated with longer OS. The results suggest that DCE-MRI might provide additional information for identifying MPM patients that may respond to chemotherapy

Singular perturbation analysis of a regularized MEMS model

Micro-Electro Mechanical Systems (MEMS) are defined as very small structures that combine electrical and mechanical components on a common substrate. Here, the electrostatic-elastic case is considered, where an elastic membrane is allowed to deflect above a ground plate under the action of an electric potential, whose strength is proportional to a parameter $\lambda$. Such devices are commonly described by a parabolic partial differential equation that contains a singular nonlinear source term. The singularity in that term corresponds to the so-called "touchdown" phenomenon, where the membrane establishes contact with the ground plate. Touchdown is known to imply the non-existence of steady state solutions and blow-up of solutions in finite time. We study a recently proposed extension of that canonical model, where such singularities are avoided due to the introduction of a regularizing term involving a small "regularization" parameter $\varepsilon$. Methods from dynamical systems and geometric singular perturbation theory, in particular the desingularization technique known as "blow-up", allow for a precise description of steady-state solutions of the regularized model, as well as for a detailed resolution of the resulting bifurcation diagram. The interplay between the two main model parameters $\varepsilon$ and $\lambda$ is emphasized; in particular, the focus is on the singular limit as both parameters tend to zero

Frustrated spin order and stripe fluctuations in FeSe

The charge and spin dynamics of the structurally simplest iron-based superconductor, FeSe, may hold the key to understanding the physics of high temperature superconductors in general. Unlike the iron pnictides, FeSe lacks long range magnetic order in spite of a similar structural transition around 90\,K. Here, we report results of Raman scattering experiments as a function of temperature and polarization and simulations based on exact diagonalization of a frustrated spin model. Both experiment and theory find a persistent low energy peak close to 500cm$^{-1}$ in $B_{1g}$ symmetry, which softens slightly around 100\,K, that we assign to spin excitations. By comparing with results from neutron scattering, this study provides evidence for nearly frustrated stripe order in FeSe.Comment: 12 pages, 12 figure

KOMPJUTORSKI MODEL OCJENJIVANJA KVALITETE ORGANSKIH GNOJIVA

Evaluation of manures, composts and growing media quality should include enough properties to enable an optimal use from productivity and environmental points of view. The aim of this paper is to describe basic structure of organic fertilizer (and growing media) evaluation model to present the model example by comparison of different manures as well as example of using plant growth experiment for calculating impact of pH and EC of growing media on lettuce plant growth. The basic structure of the model includes selection of quality indicators, interpretations of indicators value, and integration of interpreted values into new indexes. The first step includes data input and selection of available data as a basic or additional indicators depending on possible use as fertilizer or growing media. The second part of the model uses inputs for calculation of derived quality indicators. The third step integrates values into three new indexes: fertilizer, growing media, and environmental index. All three indexes are calculated on the basis of three different groups of indicators: basic value indicators, additional value indicators and limiting factors. The possible range of indexes values is 0-10, where range 0-3 means low, 3-7 medium and 7-10 high quality. Comparing fresh and composted manures, higher fertilizer and environmental indexes were determined for composted manures, and the highest fertilizer index was determined for composted pig manure (9.6) whereas the lowest for fresh cattle manure (3.2). Composted manures had high environmental index (6.0-10) for conventional agriculture, but some had no value (environmental index = 0) for organic agriculture because of too high zinc, copper or cadmium concentrations. Growing media indexes were determined according to their impact on lettuce growth. Growing media with different pH and EC resulted in very significant impacts on height, dry matter mass and leaf area of lettuce seedlings. The highest lettuce seedlings with highest mass and leaf area are produced using growing media with pH close to 6 and with EC lower than 2 dSm-1. It could be concluded that conductivity approx. 3 dSm-1 has inhibitory effect on lettuce if pH is about 7 or higher. The computer model shows that raising pH and EC resulted in decreasing growth which could be expressed as increasing stress index. The lettuce height as a function of pH and EC is incorporated into the model as stress function showing increase of lettuce height by lowering EC from 4 to 1 dSm-1or pH from 7.4 to 6. The highest growing media index (8.1) was determined for mixture of composted pig manure and peat (1:1), and lowest (2.3) for composted horse manure and peat (1:2.)Ocjena kvalitete organskih gnojiva (stajska gnojiva, komposti) i supstrata treba sadržavati dovoljno informacija da omogući izbor optimalne upotrebe s proizvodnog i ekološkog aspekta. Cilj je ovoga rada prikaz osnovne strukture modela za determinaciju indeksa ocjenjivanja kvalitete organskih gnojiva i supstrata. Osnovna struktura modela sadrži izbor i interpretaciju vrijednosti indikatora kvalitete te integraciju interpretiranih vrijednosti u nove indekse. Prvi korak uključuje unos podataka i izbor raspoloživih podataka za izračun osnovnih ili dopunskih indikatora, ovisno o indeksima i mogućim uporabama kao gnojivo ili supstrat. U drugom koraku raspoloživi podaci koriste se za izračun izvedenih indikatora kvalitete, a treći korak je integracija interpretiranih vrijednosti u tri nova indeksa: fertilizacijski indeks, indeks supstrata i ekološki indeks. Vrijednosti sva tri indeksa računaju se na temelju tri grupe indikatora: indikatori osnovne vrijednosti, indikatori dopunskih vrijednosti i limitirajući faktori. Raspon vrijednosti sva tri indeksa kreće se od 0-10, pri čemu raspon 0-3 znači nisku, 3-7 srednju, a 7-10 visoku kvalitetu. Usporedbom svježih i kompostiranih stajskih gnojiva, viši fertilizacijski i ekološki indeksi utvrđeni su za kompostirana gnojiva, najviši fertilizacijski indeks utvrđen je za kompostirani separat svinjske gnojovke (9,6), a najniži za svježi goveđi stajski gnoj (3,2). Kompostirana stajska gnojiva imaju visoki ekološki indeks (6,0-10) za konvencionalnu poljoprivredu, ali pojedini nemaju ekološku vrijednost (ekološki indeks = 0) za ekološku poljoprivredu zbog visoke koncentracije cinka, bakra ili kadmija. Indeksi supstrata utvrđeni su prema utjecaju supstrata na rast salate. Supstrati s različitim pHH2O i EC vrijednostima rezultirali su vrlo značajnim utjecajem na visinu presadnica salate, produkciju suhe tvari i površinu lista. Najveće presadnice s najvećom masom i lisnom površinom proizvedene su uporabom supstrata s pHH2O vrijednošću oko 6 i EC vrijednošću ispod 2 dSm-1. Može se zaključiti da konduktivitet oko 3 dSm-1 ima inhibitorni učinak na salatu ukoliko je pH supstrata oko 7 ili viši. Kompjutorski je model pokazao da povećanje pHH2O i EC rezultira smanjenim rastom salate, što se može izraziti kao porast stres indeksa. Visina salate kao funkcija pHH2O i EC ugrađena je u model kao stres funkcija koja pokazuje povećanje salate smanjenjem EC vrijednosti od 4 do 1 dSm-1 ili pHH2O vrijednosti od 7,4 do 6. Najveći indeks supstrata (8,1) utvrđen je za smjesu (1:1) kompostiranog separata svinjske gnojovke i treseta, a najniži (2,3) za smjesu (1:2) kompostiranog konjskog stajskog gnojiva i treseta

FES-supported standing up by independent control of three global variables - a modelling study

According to the work of Jacobs [1], we propose to control standing-up by applying independent controllers of three global variables (length l and orientation ϕ of the vector between ankle and body center of mass (CoM) and the orientation θ of the trunk). Furthermore, we propose to control l by modulating the activation of mono-articular muscles and to control ϕ and θ by modulating the activation of biarticular muscles (see also [1]). This division of tasks between mono-and biarticular muscles was found in postural control in cats [2]. Our simulations indicate that effective and well co-ordinated standing up may be achieved using this concept, allowing for a range of initial postures and arm support forces

Classical magnetotransport of inhomogeneous conductors

We present a model of magnetotransport of inhomogeneous conductors based on an array of coupled four-terminal elements. We show that this model generically yields non-saturating magnetoresistance at large fields. We also discuss how this approach simplifies finite-element analysis of bulk inhomogeneous semiconductors in complex geometries. We argue that this is an explanation of the observed non-saturating magnetoresistance in silver chalcogenides and potentially in other disordered conductors. Our method may be used to design the magnetoresistive response of a microfabricated array.Comment: 12 pages, 13 figures. Minor typos correcte

Morfološke značajke i učestalost akcesorne desne jetrene vene - procjena pomoću kompjutorizirane tomografije

In the liver, there are many vascular variants, which are important in liver surgery, the presence of accessory right hepatic veins (aRHVs) in particular. Th eir frequency, number and diameter vary considerably. Detailed imaging diagnostics with computed tomography (CT) should be undertaken before surgery. The aim of our study was to examine the characteristics of aRHVs and their demographic correlations. Th e study included data on 188 patients that underwent CT examination of the abdomen with contrast media, 103 men (54.8%) men and 85 (45.2%) women, mean age 63.1}14.3 (range, 21-94) years. The measurements of hepatic veins were carried out on CT images, which were obtained from the Clinical Institute of Radiology, University Medical Centre of Ljubljana. Forty-five of 142 patients had at least one aRHV: one aRHV in 37 (26.1%) cases, two aRHVs in seven (4.9%) cases, and three aRHVs in one (0.7%) case. Th e incidence of aRHV was between 24% and 39.3% (mean, 31.7%) and of more than one aRHV between 2.3% and 10.3% with 95% confi dence interval (CI). Based on the test of proportions, the proportion of cases with inferior aRHV of at least 7 mm was between 7.2% and 18.1% with 95% CI. Th e mean distance between the aRHV and the main RHV confl uences into the inferior vena cava was 3.73 cm (between 3.32 cm and 4.13 cm, 95% CI). The proportion of cases with confl uence distance of at least 4 cm was between 21.6% and 49.5% in cases with at least one aRHV. In cases with more than one aRHV, the distance between the middle aRHV and the main RHV ranged from 1.90 cm to 4.32 cm (95% CI). Th e T-test of independent samples showed no eff ect of age on the incidence of accessory veins (p=0.18), and the test of differences of interests showed no impact of sex (p=0.75). Evaluation of the incidence and diameter of aRHVs is of great importance for safe surgical procedure. Th eir presence can change the surgeon\u27s decision in 10%-20% of cases when employing appropriate imaging technique. CT examination, which is easily accessible and minimally invasive for patients, was successful in only 80% cases, when using standard protocol for CT scanning.U jetri postoji mnoštvo krvožilnih varijanata koje su važne u kirurgiji jetre, osobito prisutnost akcesornih desnih jetrenih vena (aDJV). Njihova učestalost, broj i promjer uvelike se razlikuju. Prije kirurškog zahvata treba provesti detaljnu slikovnu dijagnostiku kompjutoriziranom tomografi jom (CT). Cilj ovoga istraživanja bio je ispitati značajke aDJV i njihove demografske korelacije. Istraživanje je obuhvatilo podatke 188 bolesnika podvrgnutih pretrazi pomoću CT abdomena s kontrastnim sredstvom, 103 (54,8%) muškarca i 85 (45,2%) žena, srednje dobi 63,1}14,3 (raspon dobi 21-94) godine. Mjerenje jetrenih vena provedeno je na snimkama CT dobivenim od Kliničkog zavoda za radiologiju Kliničkog bolničkog centra Ljubljana. Najmanje jednu aDJV imalo je 45 od 142 bolesnika: jedna aDJV utvrđena je u 37 (26,1%), dvije aDJV u 7 (4,9%) slučajeva i tri aDJV u jednom (0,7%) slučaju. Incidencija aDJV procijenjena je na 24%-39,3% (srednja vrijednost 31,7%), a za više od jedne aDJV na 2,3%-10,3%, uz 95%-tni interval pouzdanosti (95% CI). Prema testu proporcija je proporcija slučajeva donje aDJV od najmanje 7 mm procijenjena na 7,2%-18,1%, uz 95% CI. Srednja udaljenost između aDJV i sjecišta s glavnom DJV u donju šuplju venu bila je 3,73 (raspon 3,32-4,13) cm, uz 95% CI. Proporcija slučajeva sa sjecištem udaljenim najmanje 4 cm bila je 21,6%-49,5% u skupini slučajeva s najmanje jednom aDJV. U skupini slučajeva s više od jedne aDJV udaljenost između srednje aDJV i glavne DJV bila je 1,90-4,32 cm (95% CI). T-test nezavisnih uzoraka pokazao je da dob nema učinka na incidenciju aDJV (p=0,18), a testiranje razlika pokazalo je da ni spol nema takav učinak (p=0,75). Procjena incidencije i promjera aDJV veoma je važna za siguran kirurški zahvat. Njihova prisutnost može promijeniti kirurgovu odluku u otprilike 10%-20% slučajeva, uz primjenu dobre tehnike slikovnog prikaza. Pretraga pomoću CT kao lako dostupne i za bolesnika minimalno invazivne tehnike bila je uspješna u samo 80% slučajeva kad se primijenio standardni postupnik skeniranja pomoću CT

LIQUID LEAD-BISMUTH EUTECTIC AS A COOLANT IN GENERATION IV NUCLEAR REACTORS AND IN HIGH TEMPERATURE SOLAR CONCENTRATOR APPLICATIONS: CHARACTERISTICS, CHALLENGES, ISSUES

Heavy liquid metals have found a wide range of application in energy conversion systems, due to their beneficial thermal properties, especially their low melting points and their capability of operating at higher temperatures without boiling. In addition, the neutronic properties of various liquid metals make them attractive for fusion as well as in Generation IV nuclear reactors. Lately, concentrated solar power (CSP) systems have developed an interest in this technology, calling for temperatures up to 800 oC. The main challenge in realizing engineering scale units is to find proper structural materials that can withstand the corrosion and provide mechanical strength at operation conditions. Lead-Bismuth Eutectic (LBE) is one of the main candidate coolants for liquid metal cooled reactors and solar thermal power applications due to its physical properties such as good thermal conduction, low thermal expansion and melting point, non-violent reactivity to water and low neutron absorption. However, the key limiting factor for LBE usage is the fact of its high corrosiveness to steels and other structural materials. In this work, the results of our systematic materials study in liquid LBE and its alternatives are presented. Various potential structural materials were exposed to LBE, Rose’s metal (Pb-Bi-Sn) and Pb-Bi-Zn eutectic, in static corrosion tests. Post corrosion characterization was conducted by micro-structural analysis (SEM/EDS, X-ray diffraction, Raman spectroscopy) and preferential corrosion mechanisms were evaluated.Heavy liquid metals have found a wide range of application in energy conversion systems, due to their beneficial thermal properties, especially their low melting points and their capability of operating at higher temperatures without boiling. In addition, the neutronic properties of various liquid metals make them attractive for fusion as well as in Generation IV nuclear reactors. Lately, concentrated solar power (CSP) systems have developed an interest in this technology, calling for temperatures up to 800 oC. The main challenge in realizing engineering scale units is to find proper structural materials that can withstand the corrosion and provide mechanical strength at operation conditions. Lead-Bismuth Eutectic (LBE) is one of the main candidate coolants for liquid metal cooled reactors and solar thermal power applications due to its physical properties such as good thermal conduction, low thermal expansion and melting point, non-violent reactivity to water and low neutron absorption. However, the key limiting factor for LBE usage is the fact of its high corrosiveness to steels and other structural materials. In this work, the results of our systematic materials study in liquid LBE and its alternatives are presented. Various potential structural materials were exposed to LBE, Rose’s metal (Pb-Bi-Sn) and Pb-Bi-Zn eutectic, in static corrosion tests. Post corrosion characterization was conducted by micro-structural analysis (SEM/EDS, X-ray diffraction, Raman spectroscopy) and preferential corrosion mechanisms were evaluated