Swarthmore College

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    Existence Of Maximal And Minimal Weak Solutions And Dinite Difference Approximations For Elliptic Systems With Nonlinear Boundary Conditions

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    We establish the existence of maximal and minimal weak solutions between ordered pairs of weak sub- and super-solutions for a coupled system of elliptic equations with quasimonotone nonlinearities on the boundary. We also formulate a finite difference method to approximate the solutions and establish the existence of maximal and minimal approximations between ordered pairs of discrete sub- and super-solutions. Monotone iterations are formulated for constructing the maximal and minimal solutions when the nonlinearity is monotone. Numerical simulations are used to explore existence, nonexistence, uniqueness and non-uniqueness properties of positive solutions. When the nonlinearities do not satisfy the monotonicity condition, we prove the existence of weak maximal and minimal solutions using Zorn’s lemma and a version of Kato’s inequality up to the boundary

    ‘Earth System Engineers’ And The Cumulative Impact Of Organisms In Deep Time

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    Understanding the role of humans as ‘ecosystem engineers’ requires a deep-time perspective rooted in evolutionary history and the fossil record. However, no conceptual framework exists for studying the rise of ecosystem engineering in deep time, requiring us to consider effects that fall outside the scope of traditional definitions. Here, we present a new framework applicable to both modern and ancient engineering-type effects. We propose a new term – ‘Earth system engineering’ – to describe biological processes that alter the structure and function of planetary spheres, and which combines core tenets of ecosystem engineering, niche construction, and legacy effects. We illustrate this framework using the fossil record, and show how it can be applied across the tree of life, and throughout Earth history

    Review Of The Unrealizable: Towards A Politics Of Ontology By G. Agamben, Translated By A. Toscano

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    Agamben’s The Unrealizable, ably translated from the Italian by Toscano, is a genealogical excavation of (allegedly) fundamental dichotomies underpinning Western philosophical thought, especially as they pertain to what Agamben calls a ”politics of ontology.” The distinctions between essence and existence or the possible and the real are meticulously developed in the thought of the ancients, the medievals, Marx, and Hegel. There is much to learn here. That said, this reviewer was not fully convinced by the argument that the “splitting of being” has led to the “ontological-political machine of the West,” without which the advancements of Western scientific and technological progress would have been impossible, nor Agamben\u27s further claim that this “splitting” penetrates deeply into how societies are organized, how power is used, and how the actions of individuals and collectives are controlled. Agamben concentrates almost exclusively on the developments of distinctions made by philosophers—Plato, Avicenna, Kant, Marx, Hegel—ignoring many other non-philosophical developments. Additionally, Agamben’s investigations stop at the end of the 19th century, with the exception of Walter Benjamin and Michel Foucault. This is a worthy read for those interested in the origins of problematic distinctions and some contemporary thought along the lines of Foucault. Summing Up: Recommended. Graduate students and faculty

    In Sickness and In Health: Care and Complacency in Aid Efforts for Migrant Youth in Eastern France

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    This thesis examines the perspectives of educators working with unaccompanied migrant minors (MNAs) in eastern France, focusing on how they perceive and navigate the care system and creates their own communities of care within the gaps of the bureaucratic French system. Through qualitative analysis, it explores how educators interpret the structural challenges MNAs face, including access to healthcare, social integration, and legal protections. By centering educators’ voices, this study highlights their role as intermediaries between MNAs and the French system that determines their access to essential services. It interrogates how these professionals negotiate institutional constraints, advocate for the well-being and growth of MNAs, and challenge policies that fail to account for the ever-changing needs of young migrants. Ultimately, this thesis underscores the necessity of a more inclusive, holistic framework that recognizes MNAs not just as legal subjects but as individuals with diverse care experiences that need a place and accompaniment in order to be cultivated

    Exploring Learning Possibilities in the Museum: Contrasting Cases

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    While learning is generally difficult to describe, this is especially true in the case of museum learning. Museums can be classified as “free-choice” learning environments where individuals have greater agency over with what and how deeply they engage. Given the diversity of visitor backgrounds and interests, this freedom lends itself to a wide set of learning possibilities. There have been several attempts to capture the evasiveness of free-choice learning, one of which is Falk and Dierking’s Contextual Model of Learning (CML) (Falk & Dierking, 2012. This model aims to synthesize the myriad of different factors that may contribute to visitor learning across three overlapping contexts—physical, sociocultural, and personal—to situate learning within the broader visitor experience. While the CML examines learning possibilities from the top down, affordances approach this discussion from a bottom-up perspective. The design principle of affordance explains how a given object is “usable,” and this helps dictate the physical interactions that can occur. Ultimately, neither of these theories alone is sufficient for fully encapsulating free-choice learning. To remedy this conceptual gap, I combine the CML and affordances in an attempt to more completely describe the experience of visitor learning in a free-choice setting. In the present study, I examine learning possibilities at two science museums in Philadelphia, which were specifically chosen as “contrasting cases.” I consider how real and perceived affordances either support or constrain learning practices across the three contexts of the CML. This analysis leads me to suggest an additional context to the model: the historical context. The proposed historical context aims to more explicitly unite the two theoretical approaches and explain the origins of free-choice learning possibilities

    Using Physics Simulations To Find Targeting Strategies In Competitive Tenpin Bowling

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    A new approach to finding the ideal location for a bowler to target on a bowling lane is demonstrated. To model bowling ball behavior, a system of six coupled differential equations is derived using Euler’s equations for a rotating rigid body. The numerical solution to the equations of motion shows the path of the ball on the lane, demonstrates the phases of ball motion, and is ultimately used to output a plot that displays the optimal initial conditions for the shot trajectory that leads to a strike for a typical competitive bowler. When the bowler is modeled to be imperfect and some variance is included into the shot trajectory, it is shown that some targeting strategies lead to higher strike rates due to the “miss room” created from the inhomogeneity of the friction surface that results from the oil pattern

    Toward alleviating the ₀ and ₈ tensions with early dark energy-dark matter drag

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    Early dark energy, an additional component of dark energy active in the decade of redshift before recombination, has emerged as one of the most effective models at reducing the “₀ tension” between direct measurement of the Hubble parameter ₀ in the late Universe and the Λ CDM prediction when calibrated on Planck. However, it requires a slight increase in the dark matter density cdm and primordial tilt that worsens the “₈ tension” between measurements of weak gravitational lensing at low redshifts and the Planck/Λ⁢CDM prediction. Using a phenomenological fluid model, we investigate whether the inclusion of a drag term between dark matter and early dark energy can compensate for the effect of the increase in power at small-scales, such that both ₀ and ₈ tensions are simultaneously alleviated. We find that this works if the drag term is dynamically relevant in the post-recombination universe. However, a drag term active before or just around the time at which the early dark energy contribution to the energy density is maximum is significantly constrained due to its impact on the matter perturbations before recombination, and the subsequent modifications to the cosmic microwave background power spectra

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