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We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…
We have developed a dynamic self-consistent field theory, without any adjustable parameters, for unentangled polymer blends under shear. Our model accounts for the interaction between polymers, and enables one to compute the evolution of…
Nanophotonic technologies inherently rely on tailoring light-matter interactions through the excitation and interference of deeply confined optical resonances. However, existing concepts in optical mode engineering remain heuristic and are…
A fundamental challenge in the design of photonic devices, and electromagnetic structures more generally, is the optimization of their overall architecture to achieve a desired response. To this end, topology or shape optimizers based on…
Advances in synthetic methods have spawned an array of nanoparticles and bio-inspired molecules of diverse shapes and interaction geometries. Recent experiments indicate that such anisotropic particles exhibit a variety of 'nonclassical'…
Inverse design of metasurfaces for specific electromagnetic responses requires generating geometries that satisfy stringent spectral constraints while maintaining manufacturability. Conventional design methodologies rely on iterative…
An optimal control strategy is developed to construct nanostructures of desired geometry along line segments by means of directed self-assembly of charged particles. Such a control strategy determines the electric potentials of a set of…
Based on experimental and simulation methods we helped develop, we are advancing mechanistic understanding of how self-assembled NC metamaterials can produce distinctive near- and far-field optical properties not readily achievable in…
Defects in conformal field theories are interesting objects to study from both formal and applied points of view. In this paper, we construct conformal defects in free scalar field CFTs in diverse dimensions. After discussing the possible…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
We present a combined experimental and theoretical study on the role of copolymer architecture in the self-assembly of binary PEO-PCL mixtures in water-THF, and show that altering the chain geometry and composition of the copolymers can…
The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…
The phase behavior of asymmetrically interacting ABC star triblock copolymer melts is investigated by the self-consistent field theory (SCFT). Motivated by the experimental systems, in this study, we focus on the systems in which the…
We study the depletion-induced self-assembly of indented colloids. Using state-of-the-art Monte Carlo simulation techniques that treat the depletant particles explicitly, we demonstrate that colloids assemble by a lock-and-key mechanism,…
In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the…
Polymer-grafted nanoparticles are versatile building blocks that self-assemble into a rich diversity of mesostructures. Coarse-grained molecular simulations have commonly accompanied experiments by resolving structure formation pathways and…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
The pursuit of green methodologies for fabricating optoelectronic devices necessitates the adoption of self-assembly-based strategies to engineer efficient and sustainable platforms. Microbubble lithography (MBL) stands out as a directed…
Predictive high-fidelity finite element simulations of human cardiac mechanics co\-mmon\-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics.…
The dissipative particle dynamics (DPD) simulation method has been shown to be a promising tool to study self-assembly of soft matter systems. In particular, it has been used to study block copolymer (BCP) self-assembly. However, previous…