Related papers: Structural Landscapes in Geometrically Frustrated …
Recent studies of concentrated solid solutions have highlighted the role of varied solute interactions in the determination of a wide variety of mesoscale properties. These solute interactions emerge as spatial fluctuations in potential…
The Landau-de Gennes model of liquid crystals is a functional acting on wave functions (order parameters) and vector fields (director fields). In a specific asymptotic limit of the physical parameters, we construct critical points such that…
We introduce a class of $n$-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be…
Composed of microscopic layers that stack along one direction while maintaining fluid-like positional disorder within layers, smectics are excellent systems for exploring topology, defects and geometric memory in complex confining…
We investigate bulk thermodynamic and microscopic structural properties of amorphous solids in the framework of the phase-field crystal (PFC) model. These are metastable states with a non-uniform density distribution having no long-range…
Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of 1-form is the local…
It is difficult to relate the properties of liquids and glasses directly to their structure because of complexity in the structure which defies precise definition. The potential energy landscape (PEL) approach is a very insightful way to…
We mathematically model Smectic-A (SmA) phases with a modified Landau-de Gennes (mLdG) model. The orientational order of the SmA phase is described by a tensor-order parameter $\mathbf{Q}$, and the positional order is described by a real…
How useful it is to think about the potential energy landscape of a complex many-body system depends in large measure on how direct the connection is to the system's dynamics. In this paper we show that, within what we call the potential…
We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles --- the Wasserstein geometry --- which allows the deterministic…
A theoretical analysis of surface fluctuations of a freely standing thermotropic smectic-A liquid crystal film is provided, including the effects of viscous hydrodynamics. We find two surface dynamic modes (undulation and peristaltic). For…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
Translating the complex, multi-dimensional data from simulations of biomolecules to intuitive knowledge is a major challenge in computational chemistry and biology. The so-called "free energy landscape" is amongst the most fundamental…
We present a three-dimensional lattice-gas model with trivial thermodynamics, but nontrivial dynamics. The model is characterized by each particle having its own random energy landscape. The equilibrium dynamics of the model were…
Many problems in physics, material sciences, chemistry and biology can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. Well-known examples include phase transitions of…
Polymorphism rationalizes how processing can control the final structure of a material. The rugged free-energy landscape and exceedingly slow kinetics in the solid state have so far hampered computational investigations. We report for the…
The concept of geometrical frustration in condensed matter physics refers to the fact that a system has a locally preferred structure with an energy density lower than the infinite ground state. This notion is however often used in a…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
In this work, phase diagrams of a modified two-mode phase-field crystal (PFC) that show two-dimensional (2D) and three-dimensional (3D) crystallographic structures were determined by utilizing a free energy minimization method. In this…
Glass-forming systems, which are characterized by a highly disordered energy landscape, have been studied in physics by a simulation-based state space aggregation. The purpose of this article is to develop a path-independent approach within…