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  1. Empirical rules play a crucial role in industrial and experimental settings for efficiently determining the rheological properties of materials, thereby saving both time and resources. An example is the Cox–Merz rule, which equates the steady-shear viscosity with the magnitude of the complex viscosity obtained in oscillatory tests. This empirical rule provides access to the steady-shear viscosity that is useful for processing conditions without the instabilities associated with experiments at high shear rates. However, the Cox–Merz rule is empirical and has been shown to work in some cases and fail in others. The underlying connection between the different material functions remains phenomenological and the lack of a comprehensive understanding of the rheological physics allows for ambiguity to persist in the interpretation of material responses. In this work, we revisit the Cox–Merz rule using recovery rheology, which decomposes the strain into recoverable and unrecoverable components. When viewed through the lens of recovery rheology, it is clearly seen that the steady-shear viscosity comes from purely unrecoverable acquisition of strain, while the complex viscosity is defined in terms of contributions from both recoverable and unrecoverable components. With recovery tests in mind, we elucidate why the Cox–Merz rule works only in a limited set of conditions and present an approach that could allow for universal comparisons to be made. This work further highlights the significance of recovery rheology by showing how it is possible to extend beyond phenomenological approaches through clear rheophysical metrics obtained by decomposing the material response into recoverable and unrecoverable components.

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    Free, publicly-accessible full text available May 1, 2025
  2. Understanding the yielding of complex fluids is an important rheological challenge that affects our ability to engineer and process materials for a wide variety of applications. Common theoretical understandings of yield stress fluids follow the Oldroyd–Prager formalism in which the material behavior below the yield stress is treated as solidlike, and above the yield stress as liquidlike, with an instantaneous transition between the two states. This formalism was built on a quasi-static approach to the yield stress, while most applications, ranging from material processing to end user applications, involve a transient approach to yielding over a finite timescale. Using stress-controlled oscillatory shear experiments, we show that yield stress fluids flow below their yield stresses. This is quantified through measuring the strain shift, which is the value about which the strain oscillates during a stress-controlled test and is a function of only the unrecoverable strain. Measurements of the strain shift are, therefore, measurements of flow having taken place. These experimental results are compared to the Herschel–Bulkley form of the Saramito model, which utilizes the Oldroyd–Prager formalism, and the recently published Kamani–Donley–Rogers (KDR) model, in which one constitutive equation represents the entire range of material responses. Scaling relationships are derived, which allow us to show why yield stress fluids will flow across all stresses, above and below their yield stress. Finally, derivations are presented that show strain shift can be used to determine average metrics previously attainable only through recovery rheology, and these are experimentally verified.

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    Free, publicly-accessible full text available May 1, 2025
  3. The ability to concisely describe the dynamical behavior of soft materials through closed-form constitutive relations holds the key to accelerated and informed design of materials and processes. The conventional approach is to construct constitutive relations through simplifying assumptions and approximating the time- and rate-dependent stress response of a complex fluid to an imposed deformation. While traditional frameworks have been foundational to our current understanding of soft materials, they often face a twofold existential limitation: i) Constructed on ideal and generalized assumptions, precise recovery of material-specific details is usually serendipitous, if possible, and ii) inherent biases that are involved by making those assumptions commonly come at the cost of new physical insight. This work introduces an approach by leveraging recent advances in scientific machine learning methodologies to discover the governing constitutive equation from experimental data for complex fluids. Our rheology-informed neural network framework is found capable of learning the hidden rheology of a complex fluid through a limited number of experiments. This is followed by construction of an unbiased material-specific constitutive relation that accurately describes a wide range of bulk dynamical behavior of the material. While extremely efficient in closed-form model discovery for a real-world complex system, the model also provides insight into the underpinning physics of the material.

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    Free, publicly-accessible full text available January 9, 2025
  4. We derive an exact upper bound on the epidemic overshoot for the Kermack–McKendrick SIR model. This maximal overshoot value of 0.2984 · · · occurs atR0=2.151. In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics withR0near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

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    Free, publicly-accessible full text available December 1, 2024
  5. Budd, Graham E. (Ed.)

    Sponge-grade Archaeocyatha were early Cambrian biomineralizing metazoans that constructed reefs globally. Despite decades of research, many facets of archaeocyath palaeobiology remain unclear, making it difficult to reconstruct the palaeoecology of Cambrian reef ecosystems. Of specific interest is how these organisms fed; previous experimental studies have suggested that archaeocyaths functioned as passive suspension feeders relying on ambient currents to transport nutrient-rich water into their central cavities. Here, we test this hypothesis using computational fluid dynamics (CFD) simulations of digital models of select archaeocyath species. Our results demonstrate that, given a range of plausible current velocities, there was very little fluid circulation through the skeleton, suggesting obligate passive suspension feeding was unlikely. Comparing our simulation data with exhalent velocities collected from extant sponges, we infer an active suspension feeding lifestyle for archaeocyaths. The combination of active suspension feeding and biomineralization in Archaeocyatha may have facilitated the creation of modern metazoan reef ecosystems.

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    Free, publicly-accessible full text available November 1, 2024
  6. Aliovalent substitutions lead to bond disorder and low lattice thermal conductivities in half-Heusler thermoelectrics.

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    Free, publicly-accessible full text available November 7, 2024
  7. Free, publicly-accessible full text available July 22, 2024
  8. Graphene oxide (GO) has attracted attention in materials science and engineering due to its large aspect ratio and dispersibility in polar solvent including water. It has recently been applied to direct-ink-writing (DIW) printing to realize the fabrication of three-dimensional structures, suggesting a wide variety of potential applications. Without post-processing, DIW printing requires yield stress fluids to fully build three-dimensional objects. The key properties of these inks are the yield stress and the viscoelastic properties during yielding. DIW ink rheology has therefore received significant interest in materials science, as well as mechanical and chemical engineering. Despite this interest, the yielding process has not been clearly elucidated and understanding yielding remains an outstanding problem. In this study, we discuss the yielding behavior of GO colloids via oscillatory rheology by decomposing the total strain into the recoverable and unrecoverable parts through iterative experimental techniques. The recoverable and unrecoverable responses represent viscoelastic solid and plastic properties, respectively, and they are used to determine the averaged storage and dissipation of energies. By mapping these contributions, we more clearly elucidate the yielding behavior of the GO colloids and suggest guidelines for energy efficiency. Beyond the specific lessons learned regarding the DIW-relevant rheology of GO colloids, our study contributes to an evolving development of material-centric and energy-focused methods for understanding the out-of-equilibrium rheological physics associated with the yielding of soft materials.

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    Free, publicly-accessible full text available June 1, 2024
  9. Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature, and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described by nonlinear dynamical systems, often display complex parameter dependence and exhibit bifurcations. The dynamics of heterogeneous spatially extended systems passing through bifurcations are still relatively poorly understood, yet recent theoretical studies and experimental data highlight the resulting complex behaviors and their relevance to real-world applications. We explore the consequences of spatial heterogeneities passing through bifurcations via two examples strongly motivated by applications. These model systems illustrate that studying heterogeneity-induced behaviors in spatial systems is crucial for a better understanding of ecological transitions and functional organization in brain development. 
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    Free, publicly-accessible full text available July 19, 2024
  10. Infectious diseases may cause some long-term damage to their host, leading to elevated mortality even after recovery. Mortality due to complications from so-called ‘long COVID’ is a stark illustration of this potential, but the impacts of such post-infection mortality (PIM) on epidemic dynamics are not known. Using an epidemiological model that incorporates PIM, we examine the importance of this effect. We find that in contrast to mortality during infection, PIM can induce epidemic cycling. The effect is due to interference between elevated mortality and reinfection through the previously infected susceptible pool. In particular, robust immunity (via decreased susceptibility to reinfection) reduces the likelihood of cycling; on the other hand, disease-induced mortality can interact with weak PIM to generate periodicity. In the absence of PIM, we prove that the unique endemic equilibrium is stable and therefore our key result is that PIM is an overlooked phenomenon that is likely to be destabilizing. Overall, given potentially widespread effects, our findings highlight the importance of characterizing heterogeneity in susceptibility (via both PIM and robustness of host immunity) for accurate epidemiological predictions. In particular, for diseases without robust immunity, such as SARS-CoV-2, PIM may underlie complex epidemiological dynamics especially in the context of seasonal forcing.

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    Free, publicly-accessible full text available July 12, 2024