Related papers: Landscape of kinetically trapped binary assemblies
A one-dimensional system of two trapped bosons which interact through a contact potential is studied using the optimized configuration interaction method. The rapid convergence of the method is demonstrated for trapping potentials of convex…
Composite materials are used across engineering applications for their superior mechanical performance, a result of efficient load transfer between the structure and matrix phases. However, the inherently two-dimensional structure of…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular…
Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…
Rational design strategies for self-assembly require a detailed understanding of both the equilibrium state and the assembly kinetics. While the former is starting to be well understood, the latter remains a major theoretical challenge,…
This study presents a framework for optimizing the two-dimensional (2D) placement of electric motorcycle powertrain elements, accounting for the position, the orientation and geometric irregularities. Specifically, we construct a 2D…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
Multiple dissipative self-assembly protocols designed to create novel structures or to reduce kinetic traps have recently emerged. Specifically, temporal oscillations of particle interactions have been shown effective at both aims, but…
In this thesis we study the framework of asymptotic Hodge theory and its applications in both the string landscape and the landscape of 2d integrable field theories. We show how this mathematical framework allows for a general…
Intrinsically disordered proteins (IDPs) are important for biological functions. In contrast to folded proteins, molecular recognition among certain IDPs is "fuzzy" in that their binding and/or phase separation are stochastically governed…
Patchy colloids with highly directional interactions are ideal building blocks to control the local arrangements resulting from their spontaneous self-organization. Here we propose their use, combined with substrates and nonequilibrium…
Combinatorial rigidity theory seeks to describe the rigidity or flexibility of bar-joint frameworks in R^d in terms of the structure of the underlying graph G. The goal of this article is to broaden the foundations of combinatorial rigidity…
We present a symmetry-based exhaustive approach to explore the structural and compositional richness of two-dimensional materials. We use a ``combinatorial engine'' that constructs potential compounds by occupying all possible Wyckoff…
We unravel the existence and stability properties of one-dimensional droplets arising in genuine two-component particle imbalanced bosonic mixtures under the influence of a weak harmonic confinement. A plethora of miscible droplet phases is…
We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…
Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other…
Composites with high strength and high fracture resistance are desirable for structural and protective applications. Most composites, however, suffer from poor damage tolerance and are prone to unpredictable fractures. Understanding the…