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The ethical apparatus: The material-discursive shaping of ethics, autonomy, and the driverless car (2023)

Ganesh, Indira Maya

This research argues that the emergent driverless car, as a kind of autonomous vehicle, is a Foucault-ian ‘ethical apparatus’, working as an epistemic device to materially embody and enable discursive power by generating notions of ‘autonomy’ and ‘ethical decision-making’. The ethical implications of AI, algorithmic, and autonomous technologies are topics of current regulatory and academic concern. This concern relates to the lack of meaningful oversight of black boxes inside AI systems, liabilities for manufacturers, and inadequate frameworks to hold AI-based socio-technical systems to account. One recent artefact, the driverless car, has taken on these concerns quite literally in the shaping of a niche discourse of the ‘ethics of autonomous driving’. Ambitions to produce a fully autonomous vehicle based on AI technologies are constrained by speculative concerns that its decision-making in unexpected accident situations cannot be assumed to protect humans. ‘The ethics of autonomous driving’ evaluates proposals to build ‘ethical machines’ by examining the relationship between structures of human values and moral decision-making, and how they comport to computational architectures for decision-making. This is the first case this work takes up, chiefly organised around an analysis of a thought experiment, the Trolley Problem, and the online game, Moral Machine, that crowdsourced values to suggest approaches to an ‘ethics of autonomous driving’. Rather than evaluate the feasibility or appropriateness of these two approaches, this work attends to the more critical issue that ethics is being proposed in terms of technologies turning on the logics of risk, speculation, and probabilistic correlations that are fundamental to how machine learning makes decisions. The concern in this work is less a normative framework or approach for a better or more appropriate ethics of autonomous driving. Rather, this work argues that what we understand as ‘the ethical’ is being transformed when architected by, through, and for AI/autonomous technologies to become their own regulators. Hence the production of autonomous driving necessitates computational infrastructures that are creating a world legible to and for the navigation of a driverless car. I argue that this is fostering computational governance that has implications for human bodies and social relations, chiefly that conventional approaches to regulation and accountability attend to human values and decision-making rather than computational ones. A second case that this research examines is that of driverless car crashes, to examine how ‘autonomous’ driving requires substantial embodied human knowledge and micro-work. Taken together, these two cases - the ethics of autonomous driving, and crashes - make an argument for how myriad practices of knowledge-production are translating the human world into something legible to the navigational needs of the car, producing changes in the human world through the actions of the car on that basis, and advancing notions of ‘autonomy’. This work concludes with arguments for a critical reconceptualisation of ethics and ethical decision-making in AI/autonomous systems.

Corporate management accounting for sustainable development : A multimethod approach (2023)

Wenzig, Julius

Companies are invited to contribute to the United Nations’ 17 Sustainable Development Goals (SDGs) and sustainability management accounting (SMA) has an important role to play in achieving them. However, if companies are to address the SDGs and linkages beyond organizational boundaries, SMA needs a broader scope than is conventionally assumed. Therefore, I advance a multi-level framework that addresses context, action-formation, and transformative contributions (CAT) in the following directions: first, an innovative systematic method that allows screening company-related SDGs and assessing corporate contributions to selected SDGs is introduced; second, management control systems are integrated to support managers in guiding employee behavior to make contributions to the SDGs; and, third, self-reinforcing mechanisms of the path-dependence theory are incorporated to serve as a guide to identifying barriers to individuals and groups becoming involved in SMA. This advanced CAT framework contributes to corporate practice and research by providing a multilevel framework that offers concrete management guidance for SMA to address the SDGs. It also facilitates analysis of both enabling and inhibiting factors at the organizational level. The advanced CAT framework has several implications for SMA: it promotes backcasting from the SDGs for benchmarking purposes, integrates different social, environmental, and economic issues, facilitates future-oriented action and transformation planning, addresses different layers such as the company as well as individuals and groups within it and enables to identify barriers hindering individuals and groups from becoming involved in SMA.

Rethinking incumbent firms in sustainability-oriented industry transitions (2023)

Hübel, Charlott

This dissertation deals with the increasingly recognized role of incumbent firms in advancing sustainability-oriented industry transitions. Incumbent firms are understood as firms-in-industries, which are embedded in established market structures and thereby contrast new entrant firms. The purpose of this research is twofold. First, to provide empirical evidence of barriers to and success factors of incumbent-driven industry transitions. Second, to unify hitherto dispersed descriptions of transition-related firm behaviour in a new understanding of incumbent firms in industry transitions. To this end, theoretical concepts are discussed and extended on the basis of different empirical studies in the German meat industry. The meat industry serves as suitable research setting due to its diverse sustainability challenges, ranging from climate change and pollution to animal welfare and public health, as well as its current developments towards sustainable protein alternatives. The meat context also offers opportunities to delve into individual-level processes influencing transition-related behaviour. The main contribution of this dissertation is a Multi Embeddedness Framework (MEF) that details processes and outcomes of integrated incumbent firm behaviour, including passive, reactive and proactive behaviors. The framework acknowledges the diversity in incumbent firm behaviors within industries and firms and provides new insights into transition-related behaviors at firm and individual level. With regard to the latter, the potential of learning about and from innovative start-up firms as well as shared sensemaking processes are discussed. The contents of this dissertation provide valuable contributions to the transition literature as well as important management implications with regard to the stimulation and promotion of proactive behaviors

Linking biodiversity, nature‘s contributions to people, and good quality of life: insights from tropical dry secondary forests in Mexico (2023)

Santillán Carvantes, Patricia

One of the key challenges of our era is to halt biodiversity loss and foster the sustainable use of nature. The Sustainable Development Goals (SDGs) recognize the importance of the inextricable link between social and ecological systems and human quality of life (QoL) and biodiversity. Therefore, understanding the feedback and interactions between biodiversity, nature’s contributions to people (NCP), and QoL plays a central role in advancing toward sustainability. In this context, the social-ecological systems (SES) approach has advanced on the subject, particularly in recent decades; however, much remains to be done to comprehensively understand these relationships and interactions, especially at local decision-making scales. In this thesis, through the lenses of the SES approach, I investigate connections between biodiversity, NCP, and QoL in a tropical dry forest (TDF) on the Western coast of Mexico. This place is one of the best-known Neotropical TDF and has been the focus of SES research in the past 20 years, making it an excellent case study for exploring these connections. First, to approach the need for dialogue among different global and local scales and between global and local frameworks, the thesis identifies five key components of the SES dynamics-(1) ecological supply, (2) co-production of NCP, (3) management, (4) demand, and (5) benefits- and three local decision-making scales of analysis- individual plot, smallholder, and land tenure or governance units. A literature review was performed on the social-ecological indicators for the last 11 years in the Chamela-Cuixmala region to operationalize this framework. The representability of the framework shows that research has emphasized the components of NCP co-production (42% of indicators) and SES management (21%). By analyzing SES dynamics through this new framework, we can support the monitoring of NCP and potentially detect regime shifts or radical changes before they happen. The framework is simultaneously context-specific and operationable across global contexts, providing an opportunity to inform discussions on global sustainability from local contexts. Second, this thesis uses social-ecological information to identify social-ecological systems units (SESU) spatially explicitly. A methodology was provided to spatially identify the components of social-ecological systems that environmental conditions and management practices have shaped at three previously stated relevant decision-making scales: plots owned by individuals, plot owners, and governance units. To do so, we identified and characterized: (1) ecological clusters (EC), (2) social-management clusters (SC), and (3) SESU in a TDF in western Mexico. Our findings suggested that decision-makers (ejidatarios, i.e., type of ownership (related to agrarian reform), that in most cases the land allocated is small-smallholders-) are bounded by the topographical characteristics and the public policies that determine communal (or private) governance and the number of resources available to them. The methodology can be applied to other contexts and nested decision-making scales. The spatial identification of these interdependencies is critical for landscape planning since it can contribute to reconciling productive activities and biodiversity conservation. Finally, the thesis examines the self-perceived QoL across the different SESU, finding 48 QoL items, which were grouped into six categories: 1) social capital, 2) economic capital, 3) agency, 4) nature, 5) peasant non-work activities, and 6) government and services; and two additional dimensions referred to obstacles and enablers of QoL. We found that the more land cover transformation, the more enablers, and obstacles of QoL are identified; emphasis was put on economic capital to achieve QoL. As management is intensified and governance fosters individualism across SES, the higher the Current Welfare Index, and the lower the self-perceived material and non-material satisfaction. We discuss the need for governance structures promoting smallholders´ worldviews that move beyond utilitarianism and foster commons. The social-ecological systems approach employed throughout this dissertation contributed towards crosscutting insights; the testing of new frameworks and methodologies represent important steps towards unraveling the connections between biodiversity, NCP, and QoL and contributes to achieving sustainable scenarios such as the ones proposed by the SDGs.

Environmental governance beyond borders: Governing telecoupled systems towards sustainability (2023)

Coenen, Johanna

Globalization has increased the speed, volume and spatial scale of global flows of people, information, finance, goods and services. Economic globalization is closely linked to the globalization of environmental problems, with the underlying causes and directly visible effects of environmental problems becoming increasingly geographically dispersed. For example, the products consumed in one place can have negative environmental effects in distal places of production. This poses challenges to territorially-based governance systems. Governments do not have legal authority to regulate environmental problems in other jurisdictions, even if their own policies or actions of domestic companies contribute to these problems. Likewise, companies face challenges with overseeing and governing the environmental effects that occur along their supply chains. Nevertheless, state and non-state actors increasingly aim to govern environmental problems outside their jurisdictional and organizational boundaries that arise from long-distance interactions between social-ecological systems – so-called telecoupled systems. This doctoral dissertation analyses the environmental governance of long-distance social-ecological interactions in telecoupled systems in two issue domains: global commodity chains and infrastructure projects as part of China’s Belt and Road Initiative (BRI). Although both domains involve different governance actors, institutions and processes, they both concern the question of how the involved actors develop governance structures and institutional responses to telecoupling. This dissertation aims to contribute to a deeper understanding of how to govern environmental problems that are associated with global flows. Since many multilateral environmental governance initiatives have not yet produced the desired solutions to global problems, particular attention is directed at unilateral state-led governance approaches. This dissertation addresses the questions of (1) how to achieve a spatial fit between the scale of telecoupled systems and the scale of governance institutions, (2) how governance actors exercise agency in governing telecoupled systems, and (3) how state actors can govern the domestic and foreign environmental effects of telecoupled flows. This dissertation draws upon, and contributes to, two fields of research: research on telecoupling and research on global environmental governance. The results show that creating a spatial fit in the governance of global commodity flows is challenging because boundary and resolution mismatches can emerge. Boundary mismatches denote situations where social-ecological problems transcend established jurisdictional boundaries, whereas resolution mismatches refer to governance institutions that have too coarse a spatial resolution to allow them to address the specific aspects of social-ecological problems effectively. No single governance institution is likely to avoid all mismatches, which highlights the need to align multiple governance approaches to effectively govern telecoupled systems. 2 Telecoupled flows are often governed at places where they originate and places where they arrive for processing, final consumption, or investment. If governance in the jurisdiction experiencing the environmental issue is weak, external governance actors can aim to fill this governance gap by introducing due diligence legislation and by promoting sustainability standards in international (trade) relations. State actors often rely on the actions of non-state actors to govern beyond jurisdictional borders. Despite efforts to govern environmental outcomes in distant jurisdictions, it is important to recognize the agency of governments that experience the direct environmental effects of telecoupling. They have great leverage to steer telecoupled systems towards sustainability through the formulation, implementation, monitoring and enforcement of stringent regulatory frameworks, in the context of both commodity supply chains and BRI projects. The findings of this dissertation are relevant for scholars and policy makers interested in what can be termed external environmental governance, which refers to the governance structures and institutions to shape environmental outcomes outside the borders of a given jurisdiction. This dissertation sets

Efficacy of internet-based interventions in the indirect reduction of depressive symptoms (2023)

Heckendorf, Hanna

Depressive disorders are highly prevalent mental disorders associated with an enormous individual and societal burden. The efficacy of both; treatment and prevention of depression have been meta-analytically demonstrated. Over the past two decades, an increasing number of internet-based interventions for depression has been developed and their efficacy was also metaanalytically shown. However, the uptake of such interventions – despite all the suggested advantages of internet-based interventions – is still rather low. The stigma still associated with “depression” may be one major barrier also to internet-based interventions. To overcome this barrier and potentially increase uptake, the paradigm of indirect interventions has been proposed recently. Indirect interventions primarily address common mental health problems, which are presumed to be less stigmatizing, and are suggested to reduce depressive symptoms indirectly. Targeting common mental health problems that are transdiagnostic risk factors for depression and other mental disorders – such as stress or repetitive negative thinking – seems especially promising. This dissertation evaluated the efficacy of three different internet-based interventions that can be regarded as indirect interventions to reduce depression since they primarily targeted risk factors for depression. For this purpose three registered randomized controlled trials were conducted. In addition to assessing the efficacy of the interventions regarding the primary outcomes, the efficacy to reduce depression and further secondary outcomes was studied. In Study I (N = 200) the efficacy of an internet-based stress management intervention (iSMI), which was adapted and tailored to career starting teachers, was compared to a waitlist control group (WLG). The participants of the intervention group (IG) reported significant reductions on the primary outcome perceived stress at post-intervention (T2), ΔWLG-IG = 3.5, d = 0.52, 95% CI [0.24, 0.80], and threemonth follow-up (3-MFU), d = 0.49, 95% CI [0.21, 0.77]. Furthermore, it was shown that the intervention indirectly also reduced depression at T2, d = 0.66, 95% CI [0.38, 0.94], and 3-MFU, d = 0.47, 95% CI [0.19, 0.75], nad produced significant clinically meaningful reductions of depression with a number needed to treat (NNT) of 3.9 at T2. The effects were sustained at an extended 6-MFU. Besides efficacy, the feasibility to complement the iSMI with a newly developnedte rinet-based classroom management training was shown. Moreover, mediation analyses corroborated the role of problem- and emotion-focused coping skills in the intervention’s effect on stress and the indirect effect of the intervention on depression through stress. Study II (N = 262) demonstrated the efficacy of an internet- and app-based gratitude intervention on the reduction of primary assessed repetitive negative thoughts at T2, ΔWLG-IG = 6.6, d = 0.61, 95% CI [0.36, 0.86], and 3-MFU, d = 0.75, 95% CI [0.50, 1.00], as compared to a WLG. The participants of the IG also reported significantly reduced depressive symptoms at T2, d = 0.38, 95% CI [0.13, 0.62], and 3-MFU, d = 0.40, 95% CI [0.15, 0.64], with significant clinically meaningful effects with an NNT of 4.3 at T2. The effects were sustained at an extended 6-MFU. Besides efficacy, mediation analyses showed that repetitive negative thinking mediated the gratitude intervention’s effect on depression. Finally, Study III N( = 351) showed that an interneta-sbed intervention, tackling worries at the beginning of the COVID-19 pandemic, was effective as compared to an active mental health advice group. At T2, two weeks after randomization, the IG reported significantly reduecveedl sl on the primary outcome worry as compared to controΔlsW, LG-IG = 5.0, d = 0.38, 95% CI [0.17, 0.59]. Participants of the IG also reported significantly reduced levels of depression at T2, d = 0.47, 95% CI [0.26, 0.68], with significant clinically meaningful reductions with an NNT of 3.6. The extended follow-ups in the IG indicated that the improvements from baseline were sustained until the 2-MFU and the 6-MFU. In a mediation analysis, worry was shown to mediate the intervention’s effect on depression. Across all three studies a reliable deterioration of depression was occasionally observed ranging from 3% to 5% in the IGs and from 5% to 12% in the control groups at T2. In summary, the studies in this dissertation demonstrated the efficacy of various indirect interventions focusing on rather common psychological problems to indirectly reduce depressive symptoms. The extent to which depression severity could be reduced is comparable to reductions found within participants with comparable baseline depression severity, in internetbased interventions directly addressing depressive symptoms. Indirect interventions are suggested to increase the uptake of interventions that reduce depressive symptoms, since they might be perceived as less stigmatizing and might broaden the range of interventions to choose from. Future research needs to compare indirect interventions for depression with direct interventions in head-to-head studies regarding uptake, efficacy and potential harmful effects. The indirect interventions examined in this dissertation could then complement the existing range of care for depression and thereby contribute to a reduction of the treatment gap and the burden of disease associated with depression.

Development of process to remove oligomers and suppress their formation in aging fuels by adsorbing the precursors of their aging procedure using adsorbents (2023)

Kpan, Jerome Desire Aliekabaa

The research described in this dissertation focuses on developing a process to remove oligomers and suppress their formation by intercepting the aging procedure's precursors using adsorbents when biodiesel and its blends are used as fuel. There has been the search for various energy sources due to the increasing awareness of the depletion of fossil fuel resources, environmental issues, and more urgently is the need to mitigate climate change. Biodiesel has become more attractive in recent times (Daming et al. 2012, Abdullah et al., 2007) as an alternative fuel. Biodiesel, a methyl ester of vegetable oil, is a renewable, low environmental impact, green alternative fuel for diesel engines (EU Regulation, 2012, Ghosh and Dutta, 2012). In addition to its renewable status, biodiesel, compared to fossil fuel, has advantages such as its biodegradability, reduced exhaust emissions, higher cetane number, lubricity, and safer distribution and storage due to its higher flash point (Pereira et al. 2015, Monyem and Van Gerpen, 2001). Biodiesel fuel is chemically fatty acid methyl ester (FAME) derived from different plant oils. It varies slightly in molecular structures due to the degree of unsaturation of the fatty acids in the different sources compared to conventional diesel fuel (Pereira et al. 2015, 2013, Sharma and Singh, 2009). Biodiesel fuels contain significant amounts of esters of oleic, linoleic, or linolenic acids, which influence their oxidative stability. A small percentage of more highly unsaturated fatty compounds have a disproportionately strong effect in reducing oxidation stability and promoting oligomers formation. The oxidation products of the biodiesel in the engine sump influence the degradation of the lubrication oil.

Modeling the decreasing intervention effect in digital health: a computational model to predict the response for a walking intervention (2023)

Gotzian, Lisa

In past digital health interventions, an issue has been that participants drop out over time which is referred to as the ”law of attrition” (Eysenbach, 2005). Based on this, we propose that though initially, participants respond to the intervention, there is a hypothesized second diminishing e↵ect of an intervention. However, we suggest that on top, there is a third e↵ect. Independent of the individual notification or nudge, people could build the knowledge, skills and practice needed to independently engage in the behavior themselves (schraefel and Hekler, 2020). Using behavioral theory and inspired by prior animal computational models of behavior, we propose a dynamical computational model to allow for a separation of intervention and internalization. It is targeted towards the specific case of the HeartSteps intervention that could not explain a diminishing immediate effect of the intervention, second hypothesized e↵ect, while a person’s overall steps remained constant, third e↵ect (Klasnja et al., 2019). We incorporate a habituation mechanism from learning theory that can account for the immediate diminishing e↵ect. At the same time, a reinforcement mechanism allows participants to internalize the message and engage in behavior independently. The simulation shows the importance of a participant’s responsiveness to the intervention and a sufficient recovery period after each notification. To estimate the model, we use data from the HeartSteps intervention (Klasnja et al., 2019; Liao et al., 2020), a just-in-time adaptive intervention that sent two to five walking suggestions per day. We run a Bayesian estimation with Stan in R. Additional validation tests are needed to estimate the accuracy of the model for di↵erent individuals. It could however serve as a template for future just-intime adaptive interventions due to its generic structure. In addition, this model is of high practical relevance as its derived dynamics can be used to improve future walking suggestions and ultimately optimize notification-based digital health interventions.

Assessing transdisciplinary research in sustainability science (2023)

Jahn, Stephanie Verena

Given the complex, dynamic, and urgent problems that sustainability science addresses, research approaches are required that not only improve the understanding of sustainability challenges, but also to support action for sustainable development. In this context, transdisciplinary research has established as an approach that aims not only to generate new knowledge, but also to promote the societal relevance and application of research findings through direct collaboration of scientists and societal stakeholders from different fields in integrative research processes. Despite its increasing prevalence in the field, there remains a gap between theoretical ideal-typical models of transdisciplinary research and its actual application within sustainability science. While scholars generally agree that transdisciplinary research is societally effective, there is scattered and partly conflicting evidence on which aspects of transdisciplinary research foster societal impact. Moreover, the extent to which transdisciplinary research contributes to scientific progress is largely unexplored. This thesis aims to contribute to a better understanding of the actual implementation of transdisciplinary research in sustainability science. Following three aims, this work likes to (1.) contribute to the measurability of transdisciplinary research processes as well as their societal and academic outputs and impacts, to (2.) demarcate transdisciplinary research from other modes of research in sustainability science and to (3.) identify and examine the determinants that shape the contribution of transdisciplinary research to societal action for sustainable development and to scientific knowledge production. To serve these aims a mixed methods approach is applied that combines strong quantitative elements with in-depth qualitative analyses that integrate the perspectives of practitioners. This thesis provides a broad set of indicators to describe and assess transdisciplinary research that translate theoretical concepts form transdisciplinarity theory into observable variables. The indicators offer a holistic perspective on transdisciplinary research by representing research mode characteristics, societal as well as scientific outcomes of research projects and their specific context. To theoretically demarcate transdisciplinary research from other forms of research, a narrative literature review first elaborates the differences between ‘normal science’, political use of scientific knowledge and transdisciplinarity in their underlying logics of problem definition, knowledge production and research utilization. Subsequently, these concepts were compared with perspectives and expectations of practitioners in the forest sector on integrative research settings, showing that practitioner perspectives align the most with conceptualizations of political use of scientific knowledge. Moreover, a cluster analysis of data from 59 research projects identified five research modes that empirically demarcate ideal-typical transdisciplinary research from other research modes within sustainability science: (1) purely academic research, (2.) practice consultation, (3.) selective practitioner involvement, (4.) ideal-typical transdisciplinary research and (5.) practice-oriented research. Based on this finding, transdisciplinary research can be characterized as an intensive, but balanced involvement of practitioners. It incorporates not only the needs and goals of the practitioners but also their norms and values. Ideal-typical transdisciplinary research goes beyond mere consultatory research approaches and must be distinguished from what is conceptualized as applied research. Regression analysis of 81 research projects and statistical group comparisons of the five research mode clusters show that societal and academic outputs and impacts vary with specific project characteristics and combinations of project characteristics defined as research modes. The findings indicate that more interactive research modes reach more societal impacts. In particular, the involvement of practitioners in early project phases and the targeted dissemination of the research results positively affect societal impacts. This finding also aligns with practitioner expectations on integrative research and research utilization, provided by qualitative analysis. Moreover, the quantitative results show that scientific outputs and impacts decrease with the intensity of interactions, indicating a trade-off between societal and scientific outcomes and impacts. Overall, the empirical results of this thesis support the claimed effectiveness of transdisciplinary research in providing societally relevant, applicable knowledge and encourage further funding of transdisciplinary research by funding agencies. The relationships discovered in this study between research mode characteristics and societal as well as academic outputs and impacts can help researchers design and reflect on their research and can inform funding agencies in the design of project calls and research programs. However, the observed lower academic outputs and impacts of more integrative research modes raise the question of how to further strengthen the systematic documentation and accessibility of the results of transdisciplinary sustainability research. Additionally, the observed trade-off between societal and academic impacts of transdisciplinary research highlights the need for strategies to mediate between the dual aim of transdisciplinary research to contribute to societal problem solving and scientific knowledge production. Keywords: transdisciplinarity, sustainability science, transdisciplinary research, societal impact, scientific impact, research mode, research evaluation

A probabilistic view on transport and mixing in closed and open flows (2023)

Klünker, Anna

The computational analysis and the optimization of transport and mixing processes in fluid flows are of ongoing scientific interest. Transfer operator methods are powerful tools for the study of these processes in dynamical systems. The focus in this context has been mostly on closed dynamical systems and the main applications have been geophysical flows. In this thesis, we consider transport and mixing in closed flow systems and in open flow systems that mimic technical mixing devices. Via transfer operator methods, we study the coherent behavior in closed example systems including a turbulent Rayleigh-Bénard convection flow and consider the finite-time mixing of two fluids. We extend the transfer operator framework to specific open flows. In particular, we study time-periodic open flow systems with constant inflow and outflow of fluid particles and consider several example systems. In this case, the transfer operator is represented by a transition matrix of a time-homogeneous absorbing Markov chain restricted to finite transient states. The chaotic saddle and its stable and unstable manifolds organize the transport processes in open systems. We extract these structures directly from leading eigenvectors of the transition matrix. For a constant source of two fluids in different colors, the mass distribution in the mixer and its outlet region converges to an invariant mixing pattern. In parameter studies, we quantify the degree of mixing of the resulting patterns by several mixing measures. More recently, network-based methods that construct graphs on trajectories of fluid particles have been developed to study coherent behavior in fluid flow. We use a method based on diffusion maps to extract organizing structures in open example systems directly from trajectories of fluid particles and extend this method to describe the mixing of two types of fluids.

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