Related papers: Resolving topological obstructions to vectorial st…
Coherent light-matter interactions have recently extended their applications to the ultrafast control of magnetization in solids. An important but unrealized technique is the manipulation of magnetization vector motion to make it follow an…
This work presents a rigorous mathematical formulation for topology optimization of a macrostructure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly…
Orbital angular momentum (OAM), a topological degree of freedom of light, is theoretically invariant under continuous deformations; yet, its physical observability degrades precipitously in complex media, creating a fundamental…
Skyrmions are topologically protected quasiparticles, originally studied in condensed-matter systems and recently in photonics, with great potential in ultra-high-capacity information storage. Despite the recent attention, most optical…
A transformation optics approach was used to derive a general method for designing electromagnetic devices able to manipulate the wave vectors in the specific manner required by the functionality of the device. While the wave paths inside…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
High-order optical vortices are inherently unstable, as they tend to split up under perturbation to a series of vortices with unity charge. Control over the perturbation opens up a new degree of freedom to control and tune their location in…
Surface Stokes and Navier-Stokes equations are used to model fluid flow on surfaces. They have attracted significant recent attention in the numerical analysis literature because approximation of their solutions poses significant challenges…
Optical topologies in the form of Skyrmions have attracted significant interest of late, where their integer Skyrmion number has been shown to be robust to complex media. Here we create the first fractional Skyrmions by structuring light as…
A topology optimization problem in a phase field setting is considered to obtain rigid structures, which are resilient to external forces and constructable with additive manufacturing. Hence, large deformations of overhangs due to gravity…
In this theoretical work, we propose an all-optical method for fast, precise manipulation of two-dimensional multilayers by transferring orbital angular momentum from phase-structured light (e.g. vortex beams) to a 2D material flake. We…
Precise manipulation of small objects using light holds transformative potential across diverse fields. While research in optical trapping and manipulation predominantly relies on the attraction of solid matter to light intensity maxima,…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
Speckle patterns are ubiquitous in optics and have multiple applications for which the control of their spatial correlations is essential. Here, we report on a method to engineer speckle correlations behind a scattering medium through the…
The discovery of correlated phases in twisted moir\'e superlattices accelerated the search for low-dimensional materials with exotic properties. A promising approach uses engineered substrates to strain the material. However, designing…
Navigating an arbitrary-shaped ground robot safely in cluttered environments remains a challenging problem. The existing trajectory planners that account for the robot's physical geometry severely suffer from the intractable runtime. To…
Time-variant systems have recently garnered considerable attention due to their unique potentials in manipulating electromagnetic waves. Here, a novel class of topological spacetime crystals is introduced, with a traveling-wave modulation…
The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…
Control over the physical properties of materials is ubiquitously required in many fields. One means by which this can be achieved is controlling the internal structure of multi-component materials with an eye to enhancing mechanical…