Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations

Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular. The latter is due to the degenerate equations' finite speed of propagation. In this study, a rigours convergence analysis is given for such integrators without assuming any restrictive regularity on the solutions or the domains. The analysis is conducted by first deriving a new variational framework for the domain decomposition, which is applicable to the two standard degenerate examples. That is, the $p$-Laplace and the porous medium type vector fields. Secondly, the decomposed vector fields are restricted to the underlying pivot space and the time integration of the parabolic problem can then be interpreted as an operators splitting applied to a dissipative evolution equation. The convergence results then follow by employing elements of the approximation theory for nonlinear semigroups

Generic IRS in free groups, after Bowen

Let $E$ be a measure preserving equivalence relation, with countable equivalence classes, on a standard Borel probability space $(X,B,\mu)$. Let $([E],d_{u})$ be the the (Polish) full group endowed with the uniform metric. If $F_r = \langle s_1, \ldots, s_r \rangle$ is a free group on $r$-generators and $\alpha \in \operatorname{Hom}(F_r,[E])$ then the stabilizer of a $\mu$-random point $\alpha(F_r)_x$ is a random subgroup of $F_r$ whose distribution is conjugation invariant. Such an object is known as an "invariant random subgroup" or an IRS for short. Bowen's generic model for IRS in $F_r$ is obtained by taking $\alpha$ to be a Baire generic element in the Polish space $\operatorname{Hom}(F_r, [E])$. The "lean aperiodic model" is a similar model where one forces $\alpha(F_r)$ to have infinite orbits by imposing that $\alpha(s_1)$ be aperiodic. In this setting we show that for $r < \infty$ the generic IRS $\alpha(F_r)_x$ is of finite index in $F_r$ a.s. if and only if $E = E_0$ is the hyperfinite equivalence relation. For any ergodic equivalence relation we show that a generic IRS coming from the lean aperiodic model is co-amenable and core free. Finally, we consider the situation where $\alpha(F_r)$ is highly transitive on almost every orbit and in particular the corresponding IRS is supported on maximal subgroups. Using a result of Le-Ma\^{i}tre we show that such examples exist for any aperiodic ergodic $E$ of finite cost. For the hyperfinite equivalence relation $E_0$ we show that high transitivity is generic in the lean aperiodic model.Comment: 15 pages, 1 figur

Aerodynamic instability: A case history

The identification, diagnosis, and final correction of complex machinery malfunctions typically require the correlation of many parameters such as mechanical construction, process influence, maintenance history, and vibration response characteristics. The progression is reviewed of field testing, diagnosis, and final correction of a specific machinery instability problem. The case history presented addresses a unique low frequency instability problem on a high pressure barrel compressor. The malfunction was eventually diagnosed as a fluidic mechanism that manifested as an aerodynamic disturbance to the rotor assembly

Effects of alloying elements on the microstructure and fatigue properties of cast iron for internal combustion engine exhaust manifolds

In the design of exhaust manifolds for internal combustion engines the materials used must exhibit resistance to corrosion at high temperatures while maintaining a stable microstructure. Cast iron has been used for manifolds for many years by auto manufacturers due to a combination of suitable mechanical properties, low cost, and ease of casting. Over time cast iron is susceptible to microstructural changes, corrosion, and oxidation which can result in failure due to fatigue. This thesis seeks to answer the question: “Can observed microstructural changes and measured high temperature fatigue life in cast iron alloys be used to develop a predictive model for fatigue life?” the importance of this question lies in the fact that there is little data for the behavior of cast iron alloys at high temperature. For this study two different types of cast iron, 50HS and HSM will be examined. Of particular concern for the high Si+C cast irons (and Mo in the case of the HSM cast iron) are subsurface microstructural changes that result due to heat treatment including (1) decarburization, (2) ferrite formation, (3) graphitization, (4) internal oxidation of the Si, (5) high temperature fatigue resistance, and (6) creep potential. Initial results obtained include microstructure examination after being exposed to high temperatures, grain size, nodule size, and hardness measurements. The initial examinations concluded that both cast irons performed fairly similarly, although the microstructure of the HSM samples did show slightly better resistance to high temperature as compared to that of the 50HS. Follow on work involved high temperature fatigue testing of these two materials in order to better determine if the newer alloy, HSM is a better choice for exhaust manifolds. Correlations between fatigue performance and microstructure were made and discussed, with the results examined in light of current and proposed models for predicting fatigue performance based on computational methods, to see if any suitable models exist that might be used to assist in designing with these cast alloys

On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients

In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with time-irregular coefficients. In the finite-dimensional case, we consider Carath\'eodory type functions satisfying a one-sided Lipschitz condition. After investigating the well-posedness and the stability properties of the randomized scheme, we prove the convergence to the exact solution with a rate of $0.5$ in the root-mean-square norm assuming only that the coefficient function is square integrable with respect to the temporal parameter. These results are then extended to the numerical solution of infinite-dimensional evolution equations under monotonicity and Lipschitz conditions. Here we consider a combination of the randomized backward Euler scheme with a Galerkin finite element method. We obtain error estimates that correspond to the regularity of the exact solution. The practicability of the randomized scheme is also illustrated through several numerical experiments.Comment: 37 pages, 3 figure

Analysis of the efficiency of wind turbine gearboxes using the temperature variable

The aim of this paper is to evaluate how lubricant selection affects gearbox efficiency and overall energy production by analysing real data from wind farms, monitored and controlled by a Supervisory Control and Data Acquisition (SCADA system). The turbines analysed worked with two or more oil types for the same amount of hours, which allowed to establish relations between the active power curves and wind velocity; oil temperature inside gearboxes and wind velocity; and oil temperature inside gearboxes and active power production. The results of this study evidenced a direct relation between oil characteristics and energy efficiency i.e. gearboxes working with mineral oil perform better then gearboxes working with synthetic oils. Those differences can be significant in terms of active power production. Also, it was observed oil degradation as function of temperature increase, with changes on viscosity, which reveals that temperature behaviour along the active power curve is strongly related to oil' characteristics. (C) 2018 Elsevier Ltd. All rights reserved.Agência financiadora Portuguese Foundation for Science and Technology (FCT) PTDC/AAG-TEC/1710/2014 MONITOR project - Atlantic Area EAPA_333/2016 Portuguese Foundation for Science and Technology under the Portuguese Researchers' Programme 2014 IF/00286/2014/CP1234 Marie Sklodowska-Curie Actions of the European Union's H2020-MSCA-IF-EF-RI-2016/under REA - 748747info:eu-repo/semantics/publishedVersionhttp://creativecommons.org/licenses/by/4.0

R. Ḥasdai Crescas and the Concept of Motivation in Modern Psychology and the Philosophy of Education

The concept of educational motivation refers to the desire to invest time and effort in a particular activity, even when this is difficult, exacts a high price, and may be unsuccessful. Recent decades have seen a growing recognition of the central role of motivation processes in students’ success in their studies and other processes of adaptation. Modern motivation theories attempt to study and explain the psychological processes that motivate human beings—processes associated with arousal, self-intention, and the like. According to these studies, motivation is both a cognitive and an emotional process, because thinking and emotion determine our individual path and desire and mobilize the forces required to turn desire into action. The article looks at the concept of motivation in the philosophy of Hasdai Crescas. It is shown to stand at the center of several of his most important theories, such as love in general and love of God in particular, joy, the purpose of the Torah and precepts, prayer, and even determinism. It is argued that his ideas anticipated various modern theories of motivation that are found in research on the philosophy and psychology of education