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We study effectively one-dimensional systems that emerge at the edge of a two-dimensional topologically ordered state, or at the boundary between two topologically ordered states. We argue that anyons of the bulk are associated with…
We revise the tight binding approach to strained or curved graphene in the presence of external probes such as Photoemission or Scanning Tunneling Microscopy experiments. We show that extra terms arise in the continuum limit of the tight…
Twisted assemblies of filaments in ropes, cables and bundles are essential structural elements in wide use in macroscopic materials as well as within the cells and tissues of living organisms. We develop the unique, non-linear elastic…
A number of arguments exists that the "minimal" BPS wall width in large N supersymmetric gluodynamics vanishes as 1/N. There is a certain tension between this assertion and the fact that the mesons coupled to the gluino condensate have…
Predicting the rheological behavior of associative polymers bridging colloidal particles into transient networks is fundamentally challenging because the coupled spatiotemporal scales prevent efficient molecular-fidelity modeling. We…
The application of hybrid composites in lightweight engineering enables the combination of material-specific advantages of fiber-reinforced polymers and classical metals. The interface between the connected materials is of particular…
Disordered filamentous networks with compliant crosslinks exhibit a low linear elastic shear modulus at small strains, but stiffen dramatically at high strains. Experiments have shown that the elastic modulus can increase by up to three…
Orbifold compactifications with continuous Wilson lines have very interesting characteristics and as a consequence they are candidates to obtain realistic models. We perform an analysis of the soft supersymmetry-breaking terms arising in…
Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…
We establish non-Hermitian topological mechanics in one dimensional (1D) and two dimensional (2D) lattices consisting of mass points connected by meta-beams that lead to odd elasticity. Extended from the "non-Hermitian skin effect" in 1D…
We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called…
Filamentous bio-materials such as fibrin or collagen networks exhibit an enormous stiffening of their elastic moduli upon large deformations. This pronounced nonlinear behavior stems from a significant separation between the stiffnesses…
We consider an n-dimensional Brownian Motion trapped inside a bounded convex set by normally-reflecting boundaries. It is well-known that this process is uniformly ergodic. However, the rates of this ergodicity are not well-understood,…
We investigate, in a fairly general setting, the limit of large volume equilibrium Gibbs measures for elasticity type Hamiltonians with clamped boundary conditions. The existence of a quasiconvex free energy, forming the large deviations…
Nonintersecting Brownian bridges on the unit circle form a determinantal stochastic process exhibiting random matrix statistics for large numbers of walkers. We investigate the effect of adding a drift term to walkers on the circle…
Two-dimensional random tilings of rhombi can be seen as projections of two-dimensional membranes embedded in hypercubic lattices of higher dimensional spaces. Here, we consider tilings projected from a $D$-dimensional space. We study the…
Using Brownian dynamics, we simulate the fracture of polymer interfaces reinforced by diblock connector chains. We find that for short chains the interface fracture toughness depends linearly on the degree of polymerization $N$ of the…
Bundles of polymer filaments are responsible for the rich and unique mechanical behaviors of many biomaterials, including cells and extracellular matrices. In fibrin biopolymers, whose nonlinear elastic properties are crucial for normal…
We consider a single layer graphene nanoribbon with armchair edges in a longitudinally constant external potential and point out that its transport properties can be described by means of an effective non-Hermitian Hamiltonian. We show that…
We present a numerical method which accurately computes the discrete spectrum and associated bound states of Hamiltonians which model electronic "edge" states localized at boundaries of one and two-dimensional crystalline materials. The…