Related papers: Keeping it together: a phase field version of path…
Growing network models with both heterogeneity of the nodes and topological constraints can give rise to a rich phase structure. We present a simple model based on preferential attachment with rewiring of the links. Rewiring probabilities…
Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called XY-mean field model and by the phi^4 lattice model, respectively. For…
We introduce a novel approach for object segmentation from 3D images using modified minimal path Eikonal equation. The proposed method utilizes an implicit constraint - a second order correction to the inhomogeneous minimal path Eikonal -…
An important aspect in categorizing topological phases is whether the system is spinless or spinful, given that these classes exhibit distinct symmetry algebras, leading to disparate topological classifications. By utilizing the projective…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines,…
The morphogenesis of cells and tissues involves an interplay between chemical signals and active forces on their surrounding surface layers. The complex interaction of hydrodynamics and material flows on such active surfaces leads to…
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
Photonic topology optimization is a technique used to find the electric permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common techniques are used: continuous density-based optimizations that…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
Accurate early congestion prediction can prevent unpleasant surprises at the routing stage, playing a crucial character in assisting designers to iterate faster in VLSI design cycles. In this paper, we introduce a novel strategy to fully…
We advance a combined filtered/phase-field approach to topology optimization in the setting of linearized elasticity. Existence of minimizers is proved and rigorous parameter asymptotics are discussed by means of variational convergence…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
Tethering methods allow us to perform Monte Carlo simulations in ensembles with conserved quantities. Specifically, one couples a reservoir to the physical magnitude of interest, and studies the statistical ensemble where the total…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…
Topological insulating phases are primarily associated with condensed-matter systems, which typically feature short-range interactions. Nevertheless, many realizations of quantum matter can exhibit long-range interactions, and it is still…