Related papers: The two-handed tile assembly model is not intrinsi…
Topological Interlocking assemblies are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are constrained only by its permanent contact with other blocks and the frame. In the…
We present fast simulation methods for the self-assembly of complex shapes in two dimensions. The shapes are modeled via a general boundary curve and interact via a standard volume term promoting overlap and an interpenetration penalty. To…
Structural system identification in the presence of thermal loads is challenging, as unmeasured or poorly modeled thermal effects can mask or mimic damage, leading to unreliable conclusions. This work presents an optimization-driven,…
Fragile materials ranging from sand to fire-retardant to toothpaste are able to exhibit both solid and fluid-like properties across the jamming transition. Unlike ordinary fusion, systems of grains, foams and colloids jam and cease to flow…
The two-dimensional (2D) Hubbard model has long attracted interest for its rich phase diagram and its relevance to high-$T_c$ superconductivity. However, reliable finite-temperature studies remain challenging due to the exponential…
Heat transport in two-dimensions is fundamentally different from that in three dimensions. As a consequence, the thermal properties of 2D materials are of great interest, both from scientific and application point of view. However, few…
Jamming is a common feature of out of equilibrium systems showing slow relaxation dynamics. Here we review our efforts in understanding jamming in granular materials using experiments and computer simulations. We first obtain an estimation…
We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectangles whose corresponding sides have no non-trivial common…
Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model…
We study the Renyi and entanglement entropies for free 2d CFT's at finite temperature and finite size, with emphasis on their properties under modular transformations of the torus. We address the issue of summing over fermion spin…
We investigate motion planning algorithms for the assembly of shapes in the \emph{tilt model} in which unit-square tiles move in a grid world under the influence of uniform external forces and self-assemble according to certain rules. We…
We demonstrate an efficient and accurate, general-purpose first-principles blueprint for calculating anharmonic vibrational free energy and predicting structural phase transition temperatures of solids. Thermodynamic integration is…
Accurately capturing and simulating multiscale systems is a formidable challenge, as both spatial and temporal scales can span many orders of magnitude. Rigorous upscaling methods not only ensure efficient computation, but also maintains…
Additive manufacturing holds more potential to enable the development of ceramic-based components. Ceramics offer high resistance to heat, high fracture toughness, and are extremely corrosion resistant. Thus, ceramics are widely used in…
We consider a certain tiling problem of a planar region in which there are no long horizontal or vertical strips consisting of copies of the same tile. Intuitively speaking, we would like to create a dappled pattern with two or more kinds…
We investigate the problem of assembling general shapes and patterns in a model in which particles move based on uniform external forces until they encounter an obstacle. While previous work within this model of assembly has focused on…
We present a minimal model for simulating dynamics of assorted lipid assemblies in a computationally efficient manner. Our model is particle-based and consists of coarse-grained beads put together on a modular platform to give generic…
The quantum thermalization of the Jaynes-Cummings (JC) model in both equilibrium and non-equilibrium open-system cases is sdudied, in which the two subsystems, a two-level system and a single-mode bosonic field, are in contact with either…
Understanding and synthesizing realistic 3D hand-object interactions (HOI) is critical for applications ranging from immersive AR/VR to dexterous robotics. Existing methods struggle with generalization, performing well on closed-set objects…
We study a class of 2D non-equilibrium Ising models based on competing dynamics induced by contact with heat-baths at two different temperatures. We make a comparative study of the non-equilibrium versions of Metropolis, heat bath/Glauber…