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Elastic transmission eigenvalues and their computation via the method of fundamental solutions
(2020)
A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach.
There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost.
Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different.
A second-order L-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970–986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.
The successful implementation and continuous development of sustainable corporate-level solutions is a challenge. These are endeavours in which social, environmental, and financial aspects must be weighed against each other. They can prove difficult to handle and, in some cases, almost unrealistic. Concepts such as green controlling, IT, and manufacturing look promising and are constantly evolving. This paper aims to achieve a better understanding of the field of corporate sustainability (CS). It will evaluate the hypothesis by which Corporate Sustainability thrives, via being efficient, increasing the performance, and raising the value of the input of the enterprises to the resources used. In fact, Corporate Sustainability on the surface could seem to contradict the idea, which supports the understanding that it encourages the reduction of the heavy reliance on the use of natural resources, the overall environmental impact, and above all, their protection. To understand how the contradictory notion of CS came about, in this part of the paper, the emphasis is placed on providing useful insight to this regard. The first part of this paper summarizes various definitions, organizational theories, and measures used for CS and its derivatives like green controlling, IT, and manufacturing. Second, a case study is given that combines the aforementioned sustainability models. In addition to evaluating the hypothesis, the overarching objective of this paper is to demonstrate the use of green controlling, IT, and manufacturing in the corporate sector. Furthermore, this paper outlines the current challenges and possible directions for CS in the future.
This publication is intended to present the current state of research on the rebound effect. First, a systematic literature review is carried out to outline (current) scientific models and theories. Research Question 1 follows with a mathematical introduction of the rebound effect, which shows the interdependence of consumer behaviour, technological progress, and interwoven effects for both. Thereupon, the research field is analysed for gaps and limitations by a systematic literature review. To ensure quantitative and qualitative results, a review protocol is used that integrates two different stages and covers all relevant publications released between 2000 and 2019. Accordingly, 392 publications were identified that deal with the rebound effect. These papers were reviewed to obtain relevant information on the two research questions. The literature review shows that research on the rebound effect is not yet comprehensive and focuses mainly on the effect itself rather than solutions to avoid it. Research Question 2 finds that the main gap, and thus the limitations, is that not much research has been published on the actual avoidance of the rebound effect yet. This is a major limitation for practical application by decision-makers and politicians. Therefore, a theoretical analysis was carried out to identify potential theories and ideas to avoid the rebound effect. The most obvious idea to solve this problem is the theory of a Steady-State Economy (SSE), which has been described and reviewed.
Rapid development of virtual and data acquisition technology makes Digital Twin Technology (DT) one of the fundamental areas of research, while DT is one of the most promissory developments for the achievement of Industry 4.0. 48% percent of organisations implementing the Internet of Things are already using DT or plan to use DT in 2020. The global market for DT is expected to grow by 38 percent annually, reaching USD16 billion by 2023. In addition, the number of participating organisations using digital twins is expected to triple by 2022. DTs are characterised by the integration between physical and virtual spaces. The driving idea for DT is to develop, test and build our devices in a virtual environment. The objective of this paper is to study the impact of DT in the automotive industry on the new marketing logic. This paper outlines the current challenges and possible directions for the future DT in marketing. This paper will be helpful for managers in the industry to use the advantages and potentials of DT.
This paper uses a quantitative analysis to examine the interdependence and impact of resource rents on socio-economic development from 2002 to 2017. Nigeria and Norway have been chosen as reference countries due to their abundance of natural resources by similar economic performance, while the ranking in the Human Development Index differs dramatically. As the Human Development Index provides insight into a country’s cultural and socio-economic characteristics and development in addition to economic indicators, it allows a comparison of the two countries. The hypothesis presented and discussed in this paper was researched before. A qualitative research approach was used in the author’s master’s thesis “The Human Development Index (HDI) as a Reflection of Resource Abundance (using Nigeria and Norway as a case study)” in 2018. The management of scarce resources is an important aspect in the development of modern countries and those on the threshold of becoming industrialised nations. The effects of a mistaken resource management are not only of a purely economic nature but also of a social and socio-economic nature. In order to present a partial aspect of these dependencies and influences this paper uses a quantitative analysis to examine the interdependence and impact of resource rents on socio-economic development from 2002 to 2017. Nigeria and Norway have been chosen as reference countries due to their abundance of natural resources by similar economic performance, while the ranking in the Human Development Index differs significantly. As the Human Development Index provides insight into a country’s cultural and socio-economic characteristics and development in addition to economic indicators, it allows a comparison of the two countries. This paper found out in a holistic perspective that (not or poorly managed) resource wealth in itself has a negative impact on socio-economic development and significantly reduces the productivity of the citizens of a state. This is expressed in particular for the years 2002 till 2017 in a negative correlation of GDP per capita and HDI value with the share respectively the size of resources in the GDP of a country.
To prevent the reduction of muscle mass and loss of strength coming along with the human aging process, regular training with e.g. a leg press is suitable. However, the risk of training-induced injuries requires the continuous monitoring and controlling of the forces applied to the musculoskeletal system as well as the velocity along the motion trajectory and the range of motion. In this paper, an adaptive norm-optimal iterative learning control algorithm to minimize the knee joint loadings during the leg extension training with an industrial robot is proposed. The response of the algorithm is tested in simulation for patients with varus, normal and valgus alignment of the knee and compared to the results of a higher-order iterative learning control algorithm, a robust iterative learning control and a recently proposed conventional norm-optimal iterative learning control algorithm. Although significant improvements in performance are made compared to the conventional norm-optimal iterative learning control algorithm with a small learning factor, for the developed approach as well as the robust iterative learning control algorithm small steady state errors occur.
The Rothman–Woodroofe symmetry test statistic is revisited on the basis of independent but not necessarily identically distributed random variables. The distribution-freeness if the underlying distributions are all symmetric and continuous is obtained. The results are applied for testing symmetry in a meta-analysis random effects model. The consistency of the procedure is discussed in this situation as well. A comparison with an alternative proposal from the literature is conducted via simulations. Real data are analyzed to demonstrate how the new approach works in practice.
We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.
The established Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic is investigated for partly not identically distributed data. Surprisingly, it turns out that the statistic has the well-known distribution-free limiting null distribution of the classical criterion under standard regularity conditions. An application is testing goodness-of-fit for the regression function in a non parametric random effects meta-regression model, where the consistency is obtained as well. Simulations investigate size and power of the approach for small and moderate sample sizes. A real data example based on clinical trials illustrates how the test can be used in applications.
The application of mathematical optimization methods for water supply system design and operation provides the capacity to increase the energy efficiency and to lower the investment costs considerably. We present a system approach for the optimal design and operation of pumping systems in real-world high-rise buildings that is based on the usage of mixed-integer nonlinear and mixed-integer linear modeling approaches. In addition, we consider different booster station topologies, i.e. parallel and series-parallel central booster stations as well as decentral booster stations. To confirm the validity of the underlying optimization models with real-world system behavior, we additionally present validation results based on experiments conducted on a modularly constructed pumping test rig. Within the models we consider layout and control decisions for different load scenarios, leading to a Deterministic Equivalent of a two-stage stochastic optimization program. We use a piecewise linearization as well as a piecewise relaxation of the pumps’ characteristics to derive mixed-integer linear models. Besides the solution with off-the-shelf solvers, we present a problem specific exact solving algorithm to improve the computation time. Focusing on the efficient exploration of the solution space, we divide the problem into smaller subproblems, which partly can be cut off in the solution process. Furthermore, we discuss the performance and applicability of the solution approaches for real buildings and analyze the technical aspects of the solutions from an engineer’s point of view, keeping in mind the economically important trade-off between investment and operation costs.
Nacre-mimetic nanocomposites based on high fractions of synthetic high-aspect-ratio nanoclays in combination with polymers are continuously pushing boundaries for advanced material properties, such as high barrier against oxygen, extraordinary mechanical behavior, fire shielding, and glass-like transparency. Additionally, they provide interesting model systems to study polymers under nanoconfinement due to the well-defined layered nanocomposite arrangement. Although the general behavior in terms of forming such layered nanocomposite materials using evaporative self-assembly and controlling the nanoclay gallery spacing by the nanoclay/polymer ratio is understood, some combinations of polymer matrices and nanoclay reinforcement do not comply with the established models. Here, we demonstrate a thorough characterization and analysis of such an unusual polymer/nanoclay pair that falls outside of the general behavior. Poly(ethylene oxide) (PEO) and sodium fluorohectorite form nacre-mimetic, lamellar nanocomposites that are completely transparent and show high mechanical stiffness and high gas barrier, but there is only limited expansion of the nanoclay gallery spacing when adding increasing amounts of polymer. This behavior is maintained for molecular weights of PEO varied over four orders of magnitude and can be traced back to depletion forces. By careful investigation via X-ray diffraction and proton low-resolution solid-state NMR, we are able to quantify the amount of mobile and immobilized polymer species in between the nanoclay galleries and around proposed tactoid stacks embedded in a PEO matrix. We further elucidate the unusual confined polymer dynamics, indicating a relevant role of specific surface interactions.
Exercise training effectively mitigates aging-induced health and fitness impairments. Traditional training recommendations for the elderly focus separately on relevant physiological fitness domains, such as balance, flexibility, strength and endurance. Thus, a more holistic and functional training framework is needed. The proposed agility training concept integratively tackles spatial orientation, stop and go, balance and strength. The presented protocol aims at introducing a two-armed, one-year randomized controlled trial, evaluating the effects of this concept on neuromuscular, cardiovascular, cognitive and psychosocial health outcomes in healthy older adults. Eighty-five participants were enrolled in this ongoing trial. Seventy-nine participants completed baseline testing and were block-randomized to the agility training group or the inactive control group. All participants undergo pre- and post-testing with interim assessment after six months. The intervention group currently receives supervised, group-based agility training twice a week over one year, with progressively demanding perceptual, cognitive and physical exercises. Knee extension strength, reactive balance, dual task gait speed and the Agility Challenge for the Elderly (ACE) serve as primary endpoints and neuromuscular, cognitive, cardiovascular, and psychosocial meassures serve as surrogate secondary outcomes. Our protocol promotes a comprehensive exercise training concept for older adults, that might facilitate stakeholders in health and exercise to stimulate relevant health outcomes without relying on excessively time-consuming physical activity recommendations.
Bacterial cellulose (BC) is a promising material for biomedical applications due to its unique properties such as high mechanical strength and biocompatibility. This article describes the microbiological synthesis, modification, and characterization of the obtained BC-nanocomposites originating from symbiotic consortium Medusomyces gisevii. Two BC-modifications have been obtained: BC-Ag and BC-calcium phosphate (BC-Ca3(PO4)2). Structure and physicochemical properties of the BC and its modifications were investigated by scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), atomic force microscopy (AFM), and infrared Fourier spectroscopy as well as by measurements of mechanical and water holding/absorbing capacities. Topographic analysis of the surface revealed multicomponent thick fibrils (150–160 nm in diameter and about 15 µm in length) constituted by 50–60 nm nanofibrils weaved into a left-hand helix. Distinctive features of Ca-phosphate-modified BC samples were (a) the presence of 500–700 nm entanglements and (b) inclusions of Ca3(PO4)2 crystals. The samples impregnated with Ag nanoparticles exhibited numerous roundish inclusions, about 110 nm in diameter. The boundaries between the organic and inorganic phases were very distinct in both cases. The Ag-modified samples also showed a prominent waving pattern in the packing of nanofibrils. The obtained BC gel films possessed water-holding capacity of about 62.35 g/g. However, the dried (to a constant mass) BC-films later exhibited a low water absorption capacity (3.82 g/g). It was found that decellularized BC samples had 2.4 times larger Young’s modulus and 2.2 times greater tensile strength as compared to dehydrated native BC films. We presume that this was caused by molecular compaction of the BC structure.
Game-based learning is a promising approach to anti-phishing education, as it fosters motivation and can help reduce the perceived difficulty of the educational material. Over the years, several prototypes for game-based applications have been proposed, that follow different approaches in content selection, presentation, and game mechanics. In this paper, a literature and product review of existing learning games is presented. Based on research papers and accessible applications, an in-depth analysis was conducted, encompassing target groups, educational contexts, learning goals based on Bloom’s Revised Taxonomy, and learning content. As a result of this review, we created the publications on games (POG) data set for the domain of anti-phishing education. While there are games that can convey factual and conceptual knowledge, we find that most games are either unavailable, fail to convey procedural knowledge or lack technical depth. Thus, we identify potential areas of improvement for games suitable for end-users in informal learning contexts.