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Alzheimer’s disease (AD) is characterized in part by the accumulation and spread of amyloid beta proteins in the brain. Recent experiments have revealed that amyloid beta oligomers induce microvascular mural cells to contract, thereby constricting capillaries and increasing resistance to blood flow. Conversely, hypoperfusion promotes amyloid beta production and hinders its clearance, hence creating a pathogenic positive feedback loop. Here, we develop a mathematical model that combines protein–capillary interaction with the prion-like behaviour of amyloid beta. For sufficiently strong interaction, we find that healthy and diseased steady states, both stable, can exist simultaneously, implying that pathogenic protein seeds must exceed a critical threshold in order to trigger disease outbreak. We explore the consequences of this bistability for disease propagation through the brain’s structural connectome network. Finally, in a first attempt to model the AD two-hit vascular hypothesis mathematically, we describe how spatially localized deficits in blood supply, e.g. due to embolic stroke or atherosclerosis of the leptomeningeal vessels, may trigger disease outbreak and propagation. 

Abstract For a given material,controllable deformationsare those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials,universal deformationsare those deformations that are controllable for any material within the class. In this paper, we characterize the universal deformations in compressible isotropic implicit elasticity defined by solids whose constitutive equations, in terms of the Cauchy stress$$\varvec{\sigma }$$ $\sigma$and the left Cauchy-Green strain$$\textbf{b}$$ $b$, have the implicit form$$\varvec{\textsf{f}}(\varvec{\sigma },\textbf{b})=\textbf{0}$$ $f(\sigma ,b)=0$. We prove that universal deformations are homogeneous. However, an important observation is that, unlike Cauchy (and Green) elasticity, not every homogeneous deformation is constitutively admissible for a given implicit-elastic solid. In other words, the set of universal deformations is material-dependent, yet it remains a subset of homogeneous deformations. 

In the field of soft robotics, flexibility, adaptability, and functionality define a new era of robotic systems that can safely deform, reach, and grasp. To optimize the design of soft robotic systems, it is critical to understand their configuration space and full range of motion across a wide variety of design parameters. Here we integrate extreme mechanics and soft robotics to provide quantitative insights into the design of bio-inspired soft slender manipulators using the concept of reachability clouds. For a minimal three-actuator design inspired by the elephant trunk, we establish an efficient and robust reduced-order method to generate reachability clouds of almost half a million points each to visualize the accessible workspace of a wide variety of manipulator designs. We generate an atlas of 256 reachability clouds by systematically varying the key design parameters including the fiber count, revolution, tapering angle, and activation magnitude. Our results demonstrate that reachability clouds not only offer an immediately clear perspective into the inverse problem of control, but also introduce powerful metrics to characterize reachable volumes, unreachable regions, and actuator redundancy to quantify the performance of soft slender robots. 

One of the key problems in active materials is the control of shape through actuation. A fascinating example of such control is the elephant trunk, a long, muscular, and extremely dexterous organ with multiple vital functions. The elephant trunk is an object of fascination for biologists, physicists, and children alike. Its versatility relies on the intricate interplay of multiple unique physical mechanisms and biological design principles. Here, we explore these principles using the theory of active filaments and build, theoretically, computationally, and experimentally, a minimal model that explains and accomplishes some of the spectacular features of the elephant trunk. 

Abstract In linear elasticity, universal displacements for a given symmetry class are those displacements that can be maintained by only applying boundary tractions (no body forces) and for arbitrary elastic constants in the symmetry class. In a previous work, we showed that the larger the symmetry group, the larger the space of universal displacements. Here, we generalize these ideas to the case of anelasticity. In linear anelasticity, the total strain is additively decomposed into elastic strain and anelastic strain, often referred to as an eigenstrain. We show that theuniversality constraints(equilibrium equations and arbitrariness of the elastic constants) completely specify theuniversal elastic strainsfor each of the eight anisotropy symmetry classes. The corresponding universal eigenstrains are the set of solutions to a system of second-order linear PDEs that ensure compatibility of the total strains. We show that for three symmetry classes, namely triclinic, monoclinic, and trigonal, only compatible (impotent) eigenstrains are universal. For the remaining five classes universal eigenstrains (up to the impotent ones) are the set of solutions to a system of linear second-order PDEs with certain arbitrary forcing terms that depend on the symmetry class.