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The motion of microstructural interfaces is important in modeling materials that undergo twinning and structural phase transformations. Continuum models fall into two classes: sharp-interface models, where interfaces are singular surfaces;…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
Myocardial motion and deformation are rich descriptors that characterize cardiac function. Image registration, as the most commonly used technique for myocardial motion tracking, is an ill-posed inverse problem which often requires prior…
The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric…
The physics of behavior seeks simple descriptions of animal behavior. The field has advanced rapidly by using techniques in low dimensional dynamics distilled from computer vision. Yet, we still do not generally understand the rules which…
Molecular-scale interactions between solvated macromolecules and solid surfaces govern a large number of processes, from biology to engineering. Yet, despite extensive characterization at the macroscopic level, our molecular understanding…
Topological phenomena typically govern the behavior of delocalized waves, giving rise to robust transport in electronic, photonic, and mechanical systems. Whether similar principles can directly control the motion of a localized particle,…
There has been increasing experimental evidence of non-affine elastic deformation mechanisms in biological soft tissues. These observations call for novel constitutive models which are able to describe the dominant underlying…
Active matter research focuses on the emergent behavior among interacting self-propelled particles. Unification of seemingly disconnected paradigms -- active phase-separation of repulsive discs and collective motion of self-propelled rods…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
Quantum self-oscillatory phases are ubiquitous in driven-dissipative systems. Classically, each phase is defined by its flow pattern and how stationary sets organize phase space (e.g. fixed points and limit cycles), with transitions…
The dynamical characterization of proteins is crucial to understand protein function. From a microscopic point of view, protein dynamics is governed by the local atomic interactions that, in turn, trigger the functional conformational…
How DNA is mapped to functional proteins is a basic question of living matter. We introduce and study a physical model of protein evolution which suggests a mechanical basis for this map. Many proteins rely on large-scale motion to…
Local action principles on a manifold $\M$ are invariant (if at all) only under diffeomorphisms that preserve the boundary of $\M$. Suppose, however, that we wish to study only part of a system described by such a principle; namely, the…
This review is a tutorial for scientists interested in the problem of protein structure prediction, particularly those interested in using coarse-grained molecular dynamics models that are optimized using lessons learned from the energy…
We study the geometric properties of the energy landscape of coarse-grained, off-lattice models of polymers by endowing the configuration space with a suitable metric, depending on the potential energy function, such that the dynamical…
The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for…
The geometry and topology of the region in which a director field is embedded impose limitations on the kind of supported orientational order. These limitations manifest as compatibility conditions that relate the quantities describing the…
Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional…
The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon…