Well-Posedness of a Navier-Stokes/Mean Curvature Flow system

We consider a two-phase flow of two incompressible, viscous and immiscible fluids which are separated by a sharp interface in the case of a simple phase transition. In this model the interface is no longer material and its evolution is governed by a convective mean curvature flow equation, which is coupled to a two-phase Navier-Stokes equation with Young-Laplace law. The problem arises as a sharp interface limit of a diffuse interface model, which consists of a Navier-Stokes system coupled with an Allen-Cahn equation. We prove existence of strong solutions for sufficiently small times and regular initial data.Comment: 32 page

Sharp Interface Limits for Diffuse Interface Models with Contact Angle

We consider the sharp interface limit for the Allen-Cahn equation and some variants in a bounded smooth domain in the case of boundary contact. The Allen-Cahn equation is a diffuse interface model since (after a short generation time) solutions typically develop so-called diffuse interfaces, where the solution stays smooth but experiences steep gradients. Moreover, the equation contains a small parameter $\varepsilon>0$ that corresponds to the thickness of the diffuse interfaces. The limit $\varepsilon\rightarrow 0$ is called \enquote{sharp interface limit} because - at least heuristically - the solutions should converge to step functions with the jump set evolving in time according to some sharp interface problem. We show the rigorous sharp interface limit, i.e.~that solutions to the diffuse interface and the sharp interface model are related rigorously. The results are local in time and applicable as long as a smooth solution to the limit problem exists. We consider the following cases: \begin{itemize} \item Convergence of the Allen-Cahn equation with Neumann boundary condition to the mean curvature flow with $90^\circ$-contact angle in any dimension $N\geq 2$. \item Convergence of the vector-valued Allen-Cahn equation involving different choices for the potential and with Neumann boundary condition to the mean curvature flow with $90^\circ$-contact angle in any dimension $N\geq 2$, but without the triple junction situation. For this case we expect that a similar strategy works. We give some comments in this direction. \item Convergence of an Allen-Cahn equation with a non-linear Robin boundary condition to the mean curvature flow with an $\alpha$-contact angle in 2D for $\alpha$ close to $90^\circ$. \end{itemize} For the convergence proofs we use the method of de Mottoni, Schatzman \cite{deMS}, i.e.~we \begin{enumerate} \item Rigorously construct an approximate solution for the diffuse interface model with asymptotic expansions. \item Estimate the difference of the exact and approximate solution to the diffuse interface model with a spectral estimate for a linear operator associated to the model. \end{enumerate} The major novelty in the thesis is the consideration of boundary contact for the diffuse interfaces within the method of \cite{deMS}. Therefore we construct suitable curvilinear coordinates. Based on the latter we rigorously set up the asymptotic expansions. In this process new parameter-dependent elliptic problems on the half space in $\mathbb{R}^2$ appear. For the $90^\circ$-case these problems are solved with a splitting method in exponentially weighted Sobolev spaces. The latter seems not possible for angles $\alpha\neq 90^\circ$ and we use the Implicit Function Theorem with respect to $\alpha$ in this case. Moreover, for the spectral estimate for the Allen-Cahn operator in every case (which is obtained by linearization at the approximate solution) we use a new idea: we construct an approximate first eigenfunction using asymptotic expansions. Then we split the space of $H^1$-functions over the domain into a \enquote{small} explicit space formally approximating the first eigenfunctions and the complementing space. Finally, we analyze the associated bilinear form on every part

Development of Industrial Catalysts for Sustainable Chlorine Production

The heterogeneously catalyzed gas-phase oxidation of HCl to Cl2 offers an energy-efficient and eco- friendly route to recover chlorine from HCl-containing byproduct streams in the chemical industry. This process has attracted renewed interest in the last decade due to an increased chlorine demand and the growing excess of byproduct HCl from chlorination processes. Since its introduction (by Deacon in 1868) and till recent times, the industrialization of this reaction has been hindered by the lack of sufficiently active and durable materials. Recently, RuO2-based catalysts with outstanding activity and stability have been designed and they are being implemented for large-scale Cl2 recycling. Herein, we review the main limiting features of traditional Cu-based catalysts and survey the key steps in the development of the new generation of industrial RuO2-based materials. As the expansion of this technology would benefit from cheaper, but comparably robust, alternatives to RuO2-based catalysts, a nov el CeO2-based catalyst which offers promising perspectives for application in this field has been introduced

Pulse respiration quotient as a measure sensitive to changes in dynamic behavior of cardiorespiratory coupling such as body posture and breathing regime

In this research we explored the (homeo)dynamic character of cardiorespiratory coupling (CRC) under the influence of different body posture and breathing regimes. Our tool for it was the pulse respiration quotient (PRQ), representing the number of heartbeat intervals per breathing cycle. We obtained non-integer PRQ values using our advanced Matlab® algorithm and applied it on the signals of 20 healthy subjects in four conditions: supine position with spontaneous breathing (Supin), standing with spontaneous breathing (Stand), supine position with slow (0.1 Hz) breathing (Supin01) and standing with slow (0.1 Hz) breathing (Stand01).Main results: Linear features of CRC (in PRQ signals) were dynamically very sensitive to posture and breathing rhythm perturbations. There are obvious increases in PRQ mean level and variability under the separated and joined influence of orthostasis and slow (0.1 Hz) breathing. This increase was most pronounced in Stand01 as the state of joint influences. Importantly, PRQ dynamic modification showed greater sensitivity to body posture and breathing regime changes than mean value and standard deviation of heart rhythm and breathing rhythm. In addition, as a consequence of prolonged supine position, we noticed the tendency to integer quantization of PRQ (especially after 14 min), in which the most common quantization number was 4:1 (demonstrated in other research reports as well). In orthostasis and slow breathing, quantization can also be observed, but shifted to other values. We postulate that these results manifest resonance effects induced by coupling patterns from sympathetic and parasympathetic adjustments (with the second as dominant factor).Significance: Our research confirms that cardiorespiratory coupling adaptability could be profoundly explored by precisely calculated PRQ parameter since cardiorespiratory regulation in healthy subjects is characterized by a high level of autonomic adaptability (responsiveness) to posture and breathing regime, although comparisons with pathological states has yet to be performed. We found Stand01 to be the most provoking state for the dynamic modification of PRQ (cardiorespiratory inducement). As such, Stand01 has the potential of using for PRQ tuning by conditioning the cardiorespiratory autonomic neural networks, e.g., in the cases where PRQ is disturbed by environmental (i.e., microgravity) or pathologic conditions

Successful haemofiltration therapy in severe phenobarbital overdose

In the 19th century, barbiturates were first-line treatment as hypnotic and anticonvulsants, then gradually replaced by agents with a safer clinical profile. However, its ongoing use in Australian veterinary medicine and steadfast prescriptions in developing countries/our migrant population, still contributes to overdoses.We present a case of a middle-aged man with a life-threatening phenobarbital overdose. Haemofiltration was trialled, causing a rapid fall in phenobarbital levels and a speedy recovery. Through a review of the literature, treatment options of barbiturate overdose presentations will be discussed. It is imperative clinicians are aware of barbiturate’s mechanism and its enhanced elimination through extracorporeal treatment

Falls Risk, Circadian Rhythms and Melatonin: Current Perspectives

Aging is associated with weakening of the circadian system. The circadian amplitude of most physiological variables is reduced, while the circadian phase becomes more labile and tends to occur earlier with advancing age. As the incidence of falls in older persons could follow circadian variations, a better understanding of conditions in which falls occur can lead to the implementation of countermeasures (such as adjusting the scheduling of hospital staff, or changing the timing of anti-hypertensive medication if falls are related to undesirable circadian patterns of blood pressure and/or heart rate). This includes knowing the times of the day, days of the week, and times of the year when falls are more likely to occur at home or in the hospital. Additionally, the links between aging processes and factors associated with an increased risk of developing autonomic dysfunction are well established. A strong association between heart rate variability indexes and aging has been shown. Circadian rhythms of autonomous nervous system activity may play important role for maintenance of orthostatic tolerance. Whether one is concerned with disease prediction and prevention or maintenance of healthy aging, the study of circadian rhythms and the broader time structure underlying physiopathology is helpful in terms of screening, early diagnosis and prognosis, as well as the timely institution of prophylactic and/or palliative/ curative treatment. Timing the administration of such treatment as a function of circadian (and other) rhythms also could lead to reduction of falls in older persons. Finally, a prominent circadian rhythm characterizes melatonin, which peaks during the night. The circadian amplitude of melatonin decreases as a function of age, raising the questions whether such a decrease in the circadian amplitude of melatonin relates to a higher risk of falls and, if so, whether melatonin supplementation may be an effective countermeasure. This narrative review assesses the relationships between fall risk and the potential role circadian rhythms and melatonin play in mitigating this risk. We aim to provide healthcare workers adequate information about fall risk in older persons, including the potential role of the circadian rhythms and/or melatonin, as well as to lay foundations for future fall prevention interventional studies.Fil: Goswami, Nandu. University of Graz; AustriaFil: Abulafia, Carolina Andrea. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires". Instituto de Investigaciones Biomédicas. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas; ArgentinaFil: Vigo, Daniel Eduardo. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires". Instituto de Investigaciones Biomédicas. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas; ArgentinaFil: Moser, Maximilian. University of Graz; AustriaFil: Cornelissen, Germaine. University of Minnesota; Estados UnidosFil: Cardinali, Daniel Pedro. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires". Instituto de Investigaciones Biomédicas. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas; Argentin

A Measure of Obesity: BMI versus Subcutaneous Fat Patterns in Young Athletes and Nonathletes

Although the body mass index (BMI, kg/m2) is widely used as a surrogate measure of adiposity, it is a measure of excess weight, rather than excess body fat, relative to height. The BMI classification system is derived from cut points obtained from the general population. The influence of large muscle mass on BMI in athletes and young adults may misclassify these individuals as overweight and obese. Therefore, the use of subcutaneous adipose tissue topography (SAT-Top) may be more effective than BMI in assessing obesity in physically active people and young adults. The purposes of this study were 1) to describe the relationship between the BMI and SAT-Top of young athletes and nonathletes, and 2) to determine the accuracy of the BMI as a measure of overweight. Height, weight, BMI and SAT-Top were determined in 64 males (25.0±6.7) and 42 females (24.8±7.0), who were subsequently separated into two even groups (athletes and nonathletes). The optical Lipometer device was applied to measure the thickness of subcutaneous adipose tissue (SAT).While BMI was similar, male athletes showed a 50.3% lower total SAT thickness compared to their male nonathlete controls. Even though female athletes had significantly higher BMI and weight scores, their total SAT thickness was 34.9% lower than their nonathlete controls. These results suggest subcutaneous fat patterns are a better screening tool to characterize fatness in physically active young people