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Topology optimization (TO) has experienced a dramatic development over the last decades aided by the arising of metamaterials and additive manufacturing (AM) techniques, and it is intended to achieve the current and future challenges. In…
Permitting multiple materials within a topology optimization setting increases the search space of the technique, which facilitates obtaining high-performing and efficient optimized designs. Structures with multiple materials involving…
Given a closed, orientable surface of constant negative curvature and genus $g \ge 2$, we study the topological entropy and measure-theoretic entropy (with respect to a smooth invariant measure) of generalized Bowen--Series boundary maps.…
Utilizing synthetic dimensions generated by spatial or temporal modulation, topological pumping enables the exploration of higher-dimensional topological phenomena through lower-dimensional physical systems. In this letter, we propose a…
We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, $b(y)$, is assumed to be small compared to the scale of the heterogeneities, $L$, but finite. For such "weakly"…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
A numerical algorithm to compute the topological entropy of multimodal maps is proposed. This algorithm results from a closed formula containing the so-called min-max symbols, which are closely related to the kneading symbols. Furthermore,…
While a variety of fundamental differences are known to separate two-dimensional (2D) and three-dimensional (3D) fluid flows, it is not well understood how they are related. Conventionally, dimensional reduction is justified by an \emph{a…
We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
Thermal fluctuations are not large enough to lead to state changes in granular materials. However, such materials do achieve reproducible bulk properties, suggesting that they are controlled by an underlying statistical mechanics analogous…
We characterize the different morphologies adopted by a drop of liquid placed on two randomly oriented fibers, which is a first step toward understanding the wetting of fibrous networks. The present work reviews previous modeling for…
Entropy production is a universal measure of irreversibility and energy dissipation in physical, chemical, and biological systems operating far from equilibrium. However, quantifying and spatiotemporally localising it in complex processes…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
Topological techniques are powerful tools for characterizing the complexity of many dynamical systems, including the commonly studied area-preserving maps of the plane. However, the extension of many topological techniques to higher…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
In microfluidics, varying wetting properties, expressed in terms of the local slip length, can be used to influence the flow of a liquid through a device. We study flow past surfaces on which the slip length is modulated in stripes. We find…