C. P. Snow’s ‘Two Cultures’ from 1959 started a reconciliation movement in the philosophy of science, or at least led to more serious introspection about the nature of disciplinary silos; Science vs Humanities. This trend was to coincide with the post-Newtonian and post-modern revolutions in the sciences and humanities which replaced reductionist perspectives with systemic ones. While much has been written about the two cultures of science and humanities, not enough has been done at institutional scales to mediate these gaps. In this paper, we take a complex systems approach to examine students’ meaning making of their undergraduate program by studying self-reported reflections of several mathematics majors at a public university. Using tools of network theory, we show that even at the college level, teaching and learning is dualistic and most students, if not all, fail to see connections across disciplines. We argue for a more integrated approach to teaching and curriculum design and suggest ways in which such an undertaking can succeed.

In this paper, we examine the phenomenon of collective behavior as it broadly reveals itself in different living and nonliving systems. It has previously been argued that self-organizing behavior that occurs in dissipative systems resembles the kind of collective behavior that is seen in living systems. In this paper, we specifically discuss the evolution of collective behavior, i.e., how a system learns as it engages in a collective, self-organizing activity over time. We specifically look at this phenomenon through the examples of Futbol and chemical flocking of a benzoquinone system, which reveal common patterns of learning that occur in a collective setting. The growth profile of the examples studied reveal the existence of criticality and phase transition which are fundamental traits of such complex systems.

The place of living organisms in the natural world is a nearly perennial question in philosophy and the sciences; how can inanimate matter yield animate beings? A dominant answer for several centuries has been to treat organisms as sophisticated machines, studying them with the mechanistic physics and chemistry that have given rise to technology and complex machines. Since the early 20th century, many scholars have sought instead to naturalize biology through thermodynamics, recognizing the precarious far-from-equilibrium state of organisms. Erwin Bauer was an early progenitor of this perspective with ambitions of “general laws for the movement of living matter”. In addition to taking a thermodynamic perspective, Bauer recognized that organisms are fundamentally behaving systems, and that explaining the physics of life requires explaining the origins of intentionality, adaptability, and self-regulation. Bauer, like some later scholars, seems to advocate for a “new physics”, one that extends beyond mechanics and classical thermodynamic, one that would be inclusive of living systems. In this historical review piece, we explore some of Bauer’s ideas and explain how similar concepts have been explored in modern non-equilibrium thermodynamics and dissipative structure theory. Non-living dissipative structures display end-directedness, self-maintenance, and adaptability analogous to organisms. These findings also point to an alternative framework for the life sciences, that treats organisms not as machines but as sophisticated dissipative structures. We evaluate the differences between mechanistic and thermodynamic perspectives on life, and what each theory entails for understanding the behavior of organisms.

The physical origin of behaviour in biological organisms is distinct from those of non-living systems in one significant way: organisms exhibit intentionality or goal-directed behaviour. How may we understand and explain this important aspect in physical terms, grounded in laws of physics and chemistry? In this article, we discuss recent experimental and theoretical progress in this area and future prospects of this line of thought. The physical basis for our investigation is thermodynamics, though other branches of physics and chemistry have an important role. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

Assessment is an issue that is central to the lives of educators and students alike. At all levels, from programmatic to course-specific, instructors strive to assess in a way that accurately measures achievement or progress relative to one's goals. This paper reports on students' experiences with alternative assessments in our undergraduate mathematics course for non-STEM (Science, Technology, Engineering and Mathematics) majors. The course, Creative Thinking in Mathematics, designed to fulfil the university's general education requirement for mathematics, was recently revised and renamed to highlight the role of creativity in mathematics. In the course, students engage in mathematics using creative approaches and consider how these approaches connect to other disciplines, their career aspirations, and important mathematical discoveries throughout history. This shift in course emphasis necessitated revisions to assessments in ways that mirrored the course's instructional approach. This article describes the alternative assessments, outlines the research study, and reports on the results relative to students' experiences with these assessments, both prior to and during the course, highlighting a need for instructors to reconsider traditional assessments.

This article presents ideas and narratives of an experiment on the concept of energy developed for an honors seminar on energy and a mechanics course. We argue that energy is an idea best taught in an interdisciplinary manner. While most physics courses explore ideas such as mechanical energy and conservation of energy, it is imperative that a more practical view of energy as fuel be addressed since this has particular relevance to our students ’future. We believe energy cannot be discussed without talking about entropy and that a proper introduction to energy can only be made by simultaneously discussing the idea of entropy. In this article, we present one lab activity related to carbon emissions from bicycling, designed to help elucidate this idea through the use of conceptual metaphors and embodied learning. The learning goals of the activity were to encourage students to understand that energy and entropy are intricately related and to have students gain a deeper understanding of the concepts by considering and discussing ways in which they apply to different contexts. We discuss the rationale, implementation, and outcomes of the activity. Additional informationNotes on contributorsMika MunakataAshwin Vaidya (vaidyaa@montclair.edu) and Mika Munakata (munakatam@montclair.edu) are professors in the Department of Mathematics, Montclair State University in Montclair, New Jersey.Ashwin VaidyaAshwin Vaidya (vaidyaa@montclair.edu) and Mika Munakata (munakatam@montclair.edu) are professors in the Department of Mathematics, Montclair State University in Montclair, New Jersey.Dirk VanderkleinDirk Vanderklein (vanderkleid@montclair.edu) is a professor in the Department of Biology, Montclair State University in Montclair, New Jersey.

In this paper, we discuss some well-known experimental observations on self-organization in dissipative systems. The examples range from pure fluid flow, pattern selection in fluid–solid systems to chemical-reaction-induced flocking and aggregation in fluid systems. In each case, self-organization can be seen to be a function of a persistent internal gradient. One goal of this article is to hint at a common theory to explain such phenomena, which often takes the form of the extremum of some thermodynamic quantity, for instance the rate of entropy production. Such variational theories are not new; they have been in existence for decades and gained popularity through the Nobel Prize-winning work of theorists such as Lars Onsager and Ilya Prigogine. The arguments have evolved since then to include systems of higher complexity and for nonlinear systems, though a comprehensive theory remains elusive. The overall attempt is to bring out examples from physics, chemistry, engineering, and biology that reveal deep connections between variational principles in physics and biological, or living systems. There is sufficient evidence to at least raise suspicion that there exists an organization principle common to both living and non-living systems, which deserves deep attention.

The simulation of multiphysics problems is a popular research area—and one of the potential concerns too—for researchers studying a wide range of quantifiable systems. For one, reduced order mechanical models are often the best way to deduce inferences about physically complex systems. Obtaining numerical solutions to the differential equations underpinning reduced order models can become computationally expensive, especially as complexity grows. Many multiphysical computations can be limited by this burden. Machine learning (ML) offers tools which can avoid the prohibitive computational expense when making predictions on traditional multiphysics models. However, deep ML techniques needed to properly simulate complex systems require large amounts of data, thus revisiting the computational expense of training on numerically derived data and/or observational challenges of training with empirical data. Instead, ML techniques can be trained by reinforcing or integrating the understood physics of the system. Such a physics-informed approach to machine learning leverages the understood physical qualities of the system for the creation of more accurate and efficient ML models. This work presents an example of physics-informed machine learning that alleviates the common costs associated with multiphysical modeling, with dependable accuracy. More specifically, the problem discussed here is an example of automatic training dataset generation for an informed ML approach to modeling Amyloid-β fibril aggregation.

This study aims to computationally identify the detailed mechanisms of the adhesion process of mucin and foreign bodies in the human tear film subject to the blinking motion of eyelid. The results give us a clue about the role of mucus as a protective agent for the ocular surface and its role in diseases such as dry eye syndrome (DES). We propose a multi-phase model which models the tear film as an inhomogeneous fluid comprising of a mixture of an aqueous layer in which mucin particles are exponentially distributed in the direction normal to corneal surface. We model the mucin adherence to any immersed foreign object, and its overall clearance through the blinking motion of the eyelid. The motions of mucin in the flow are solved by a force balance equation which accounts for the macroscopic interactions between the fluid and the body. The clearance rates of the foreign particle are explored under various conditions with different varying mechanical properties of mucin such as its adhesion force, distribution profile, as well as its viscosity. Our parametric study shows that a condition for higher clearance rate requires (i) greater mucin population in the entire region of tear film, i.e., larger viscosity, (ii) an optimal mucin distribution profile, and (iii) normal physiologic adhesion force between mucin and immersed particles.

The autorotation and energy harvesting potential of bladeless turbine models are tested in a confined water stream with Reynolds numbers from 20 K to 40 K. Mini bladeless turbine models of various geometrical shapes are 3D-printed using plastic material with low printing density. Experiments were performed using a commercial closed-loop water tank capable of delivering fine incremental speed up to a maximum of 60 cm/s. The cross-cylinder models with low density appear to demonstrate autorotation at high Reynolds numbers. Other turbine models demonstrate either stagnation or oscillation for a wide range of Reynolds numbers. For the cross-cylinder models, the autorotation phenomenon appears to be promoted at lower average flow speed when an upstream asymmetrical obstacle is introduced in the stream. The rotation per minute and energy potential (voltage and current) of the autorotating model are increased with the Reynolds number.

We study the motion of a rigid sphere falling in a two-layer stratified fluid under the action of gravity in the potential flow regime. Experiments at a moderate Reynolds number of approximately 20 to 450 indicate that a sphere with the precise critical density, higher than the bottom layer density, can display behaviors such as bounce or arrestment after crossing the interface. We experimentally demonstrate that such a critical sphere density increases linearly as the bottom fluid density increases with a fixed top fluid density. Additionally, the critical density approaches the bottom layer fluid density as the thickness of density transition layer increases. We propose an estimation of the critical density based on the potential energy. With assuming the zero layer thickness, the estimation constitutes an upper bound of the critical density with less than 0.043 relative difference within the experimental density regime 0.997 g/cm^3 ∼ 1.11 g/cm^3 under the zero layer thickness assumption. By matching the experimental layer thickness, we obtain a critical density estimation with less than 0.01 relative difference within the same parameter regime.

SARS-CoV-2 continues to upend human life by posing novel threats related to disease spread and mutations. Current models for the disease burden of SARS-CoV-2 consider the aggregate nature of the virus without differentiating between the potency of its multiple strains. Hence, there is a need to create a fundamental modeling framework for multi-strain viruses that considers the competing viral pathogenic pathways. Alongside the consideration that other viral pathogens may coexist, there is also a need for a generalizable modeling framework to account for multiple epidemics (i.e., multi-demics) scenarios, such as influenza and COVID-19 occurring simultaneously. We present a fundamental network thermodynamics approach for assessing, determining, and predicting viral outbreak severity, which extends well-known standard epidemiological models. In particular, we use historical data from New York City’s 2011–2019 influenza seasons and SARS-CoV-2 spread to identify the model parameters. In our model-based analysis, we employ a standard susceptible–infected–recovered (SIR) model with pertinent generalizations to account for multi-strain and multi-demics scenarios. We show that the reaction affinities underpinning the formation processes of our model can be used to categorize the severity of infectious or deceased populations. The spontaneity of occurrence captured by the change in Gibbs free energy of reaction (∆G) in the system suggests the stability of forward occurring population transfers. The magnitude of ∆G is used to examine past influenza outbreaks and infer epidemiological factors, such as mortality and case burden. This method can be extrapolated for wide-ranging utility in computational epidemiology. The risk of overlapping multi-demics seasons between influenza and SARS-CoV-2 will persist as a significant threat in forthcoming years. Further, the possibility of mutating strains requires novel ways of analyzing the network of competing infection pathways. The approach outlined in this study allows for the identification of new stable strains and the potential increase in disease burden from a complex systems perspective, thereby allowing for a potential response to the significant question: are the effects of a multi-demic greater than the sum of its individual viral epidemics?

We discuss the thermodynamics behind self-organizing Benzoquinone (BQ) particles on air-water interface. Experiments (Satterwhite-Warden et al., 2015; Chen et al., 2019; Satterwhite-Warden et al., 2019) reveal that BQ particles undergo rapid transient flocking behavior as they move around on the liquid surface. Flocks are seen to vary in size and their formation and stability appears to be dependent upon their shape. It is hypothesized that self organization of particles is a result of surface tension gradients in the two dimensional liquid surface resulting from the slow dissolution of the BQ particles. The current paper uses a mass-action kinetic framework to study the flocking of particles. Two dynamical models, with and without a reservoir, are proposed and analyzed through the thermodynamic lens of free energy, which informs us about dominant and spontaneous 'reactions' or flock formations in the system. Results of the model are in good agreement with experiment, revealing that irregular shaped BQ particles do indeed show far greater propensity to form flocks compared with regularly shaped particles and validating the mass-action framework as an appropriate tool to investigate this system. (C) 2021 Elsevier B.V. All rights reserved.

The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton’s formulation of the principle of least action typically only accounts for conservative forces, but can be reformulated to include non-conservative forces such as friction by using the approach suggested by Wang and co-workers (Lin and Wang, 2014; Wang, 2015). However, it turns out that this modified action is dependent upon the nature and amount of damping in the system and the optimality argument fails to hold for sufficiently large values of the damping coefficient. In this paper, we specifically investigate the modified action principle for the cases of a linearly and cubically damped, nonlinear pendulum.

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject [...]

Abstract This paper describes the development and implementation of course modules intended to encourage creative thinking in an undergraduate general education mathematics course. The modules were designed to address the characteristics of creativity outlined in the literature through explorations of mathematics relevant to non-mathematics majors. A general description of the modules, as well as specifics about two lessons is provided. Student work, including journal entries, surveys, and class assignments, provide evidence that this intentional focus on creativity in mathematics challenged students’ conceptions about mathematics, allowed them to reconsider the mathematics familiar to them in new ways, and engaged them in meaningful collaborations. Interviews of instructors revealed that they, too, engaged in creative processes as they planned the course and thought about innovative ways to engage students with mathematics. The course modules have been shared with other faculty teaching the course and will eventually be adapted for use in other mathematics courses, including those for STEM majors. Implications and future avenues for implementation and research are discussed.

In this paper we hypothesize that education, especially at the scale of curriculum, should be treated as a complex system composed of different ideas and concepts which are inherently connected. Therefore, the task of a good teacher lies in elucidating these connections and helping students make their own connections. Such a pedagogy allows students to personalize learning and strive to be 'creative' and make meaning out of old ideas. The novel contribution of this work lies in the mathematical approach we undertake to verify our hypothesis. We take the example of a precalculus course curriculum to make our case. We treat textbooks as exemplars of a specific pedagogy and map several texts into networks of isolated (nodes) and interconnected concepts (edges) thereby permitting computations of metrics which have much relevance to the education theorists, teachers and all others involved in the field of education. We contend that network metrics such as average path length, clustering coefficient and degree distribution provide valuable insights to teachers and students about the kind of pedagogy which encourages good teaching and learning.

Aggregation of amyloid-β (Aβ) peptides is a significant event that underpins Alzheimer's disease (AD). Aβ aggregates, especially the low-molecular weight oligomers, are the primary toxic agents in AD pathogenesis. Therefore, there is increasing interest in understanding their formation and behaviour. In this paper, we use our previously established results on heterotypic interactions between Aβ and fatty acids (FAs) to investigate off-pathway aggregation under the control of FA concentrations to develop a mathematical framework that captures the mechanism. Our framework to define and simulate the competing on- and off-pathways of Aβ aggregation is based on the principles of game theory. Together with detailed simulations and biophysical experiments, our models describe the dynamics involved in the mechanisms of Aβ aggregation in the presence of FAs to adopt multiple pathways. Specifically, our reduced-order computations indicate that the emergence of off- or on-pathway aggregates are tightly controlled by a narrow set of rate constants, and one could alter such parameters to populate a particular oligomeric species. These models agree with the detailed simulations and experimental data on using FA as a heterotypic partner to modulate the temporal parameters. Predicting spatio-temporal landscape along competing pathways for a given heterotypic partner such as lipids is a first step towards simulating scenarios in which the generation of specific ‘conformer strains’ of Aβ could be predicted. This approach could be significant in deciphering the mechanisms of amyloid aggregation and strain generation, which are ubiquitously observed in many neurodegenerative diseases.