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One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices…
This paper reveals a categorical equivalence connecting two distinct quantum logic structures. The first is the orthomodular lattice, an algebraic system designed to formalize the properties of quantum systems. The second is a finitary…
We review recent results on Integrable Discrete Geometry. It turns out that most of the known (continuous and/or discrete) integrable systems are particular symmetries of the quadrilateral lattice, a multidimensional lattice characterized…
Long range order and symmetry in heterogeneous materials architected on crystal lattices lead to elastic and inelastic anisotropies and thus limit mechanical functionalities in particular crystallographic directions. Here, we present a…
Cavity optomechanics enables controlling mechanical motion via radiation pressure interaction, and has contributed to the quantum control of engineered mechanical systems ranging from kg scale LIGO mirrors to nano-mechanical systems,…
We present a scheme for the analytic computation of renormalization functions on the lattice, using a symbolic manipulation computer language. Our first nontrivial application is a new three-loop result for the topological susceptibility.
Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process…
Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose…
Gel-elastomer composites, comprising an active swellable hydrogel and a passive elastomer, are a compelling class of programmable material systems (PMS) capable of shape morphing under multiphysics actuation. The precise design of the…
The rapid evolution of next-generation communications and the Internet of Things (IoT) has catalyzed an urgent demand for governing expansive spatial environments as functional electromagnetic (EM) entities. However, deterministically…
Shape morphing magnetic soft materials, composed of magnetic particles in a soft polymer matrix, can transform shapes reversibly, remotely, and rapidly, finding diverse applications in actuators, soft robotics, and biomedical devices. To…
Configuration-Constrained Tube Model Predictive Control (CCTMPC) offers flexibility by using a polytopic parameterization of invariant sets and the optimization of an associated vertex control law. This flexibility, however, often demands…
Multifunctional lattice materials are of great interest to modern engineering including aerospace, robotics, wave control, and sensing. In this work, we proposed and developed a new class of functional lattice materials called liquid metal…
Ultracold atoms in optical lattices are pristine model systems with a tunability and flexibility that goes beyond solid-state analogies, e.g., dynamical lattice-geometry changes allow tuning a graphene lattice into a boron-nitride lattice.…
The demand for structured light with a reconfigurable spatial and polarization distribution has been increasing across a wide range of fundamental and advanced photonics applications, including microscopy, imaging, sensing, communications,…
Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
Integrated photonic systems provide a flexible platform where artificial lattices can be engineered in a reconfigurable fashion. Here, we show that one-dimensional photonic arrays with engineered losses allow the realization of topological…
In situ robotic automation in construction is challenging due to constantly changing environments, a shortage of robotic experts, and a lack of standardized frameworks bridging robotics and construction practices. This work proposes a…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…