Over the course of the past several decades, Observational Cosmology has made great progress in establishing a Standard Model of Cosmology: LambdaCDM. This model successfully reproduces and explains a vast array of cosmological observations. These successes notwithstanding, LambdaCDM continues to be plagued by several rather obvious and fundamental issues, including: What is Dark Matter? What causes the acceleration of the expansion of the Universe? Why do different types of measurements of the current expansion rate yield different results? In this personally biased talk I will review some aspects of the current status of these issues.
Biopolymer networks such as collagen are typically well below the isostatic threshold and therefore intrinsically floppy. Yet, when subjected to deformation, even these sub-isostatic networks can undergo a sharp transformation into a rigid state. I will show how this strain-controlled transition constitutes a continuous mechanical phase transition, with clear critical signatures captured by simulations of fibrous networks and experiments on type-I collagen. Using a real-space renormalization approach, we uncover scaling relations between the critical exponents and establish the universality of this transition across different network architectures. I then link this static criticality to dynamics: near the onset of rigidity, nonaffine rearrangements dominate, giving rise to diverging relaxation times, power-law rheology, and a simple quantitative connection between nonaffinity and viscosity.
