Related papers: Distributed branch points and the shape of elastic…
A characteristic feature of the Earth is that diffuse thermal convection in the mantle produces localized deformation at the surface: Plate Tectonics. However, modelling this phenomenon remains a challenge, due to inability to simulate…
We introduce two notions of hyperbolicity for not necessarily K\"ahler $n$-dimensional compact complex manifolds $X$. The first, called {\it balanced hyperbolicity}, generalises Gromov's K\"ahler hyperbolicity by means of Gauduchon's…
Let $S$ be a closed oriented surface of genus at least $2$. Using the parameterisation of the deformation space of globally hyperbolic maximal anti-de Sitter structures on $S \times \mathbb{R}$ by the cotangent bundle over the Teichm\"uller…
Topological defects in graphene, dislocations and grain boundaries, are still not well understood despites the considerable number of experimental observations. We introduce a general approach for constructing dislocations in graphene…
The surface curvature of membranes, interfaces, and substrates plays a crucial role in shaping the self-assembly of particles adsorbed on these surfaces. However, little is known about the interplay between particle anisotropy and surface…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
Soft and frangible materials that remodel under flow can give rise to branched patterns shaped by material properties, boundary conditions, and the time scales of forcing. We present a general theoretical framework for emergent branching in…
In this paper, we propose a distributed algorithm, called Directed-Distributed Gradient Descent (D-DGD), to solve multi-agent optimization problems over directed graphs. Existing algorithms mostly deal with similar problems under the…
Given a weighted graph $G=(V,E,w)$, a partition of $V$ is $\Delta$-bounded if the diameter of each cluster is bounded by $\Delta$. A distribution over $\Delta$-bounded partitions is a $\beta$-padded decomposition if every ball of radius…
Disordered hyperuniform systems are exotic states of matter that completely suppress large-scale density fluctuations like crystals, and yet possess no Bragg peaks similar to liquids or glasses. Such systems have been discovered in a…
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
In this paper, we present a 2D numerical model developed to simulate the dynamics of soft, deformable particles. To accommodate significant particle deformations, the particle surface is represented as a narrow shell composed of mass points…
This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…
When granular materials with interstitial liquid bridges are sheared in a split-bottom cell, a localized shear band develops, accompanied by a surface elevation. Cohesion, governed by the surface tension of the interstitial liquid, enhances…
We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…
The behavior of annealed branched polymers near adsorbing surfaces plays a fundamental role in many biological and industrial processes. Most importantly single stranded RNA in solution tends to fold up and self-bind to form a highly…
Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces have been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. Here, we report for the first…
Given $\alpha \in (0, \infty)$ and $r \in (0, \infty)$, let ${\cal D}_{r, \alpha}$ be the disc of radius $r$ in the hyperbolic plane having curvature $-\alpha^2$. Consider the Poisson point process having uniform intensity density on ${\cal…
Controlling the spatial distribution of liquid droplets on surfaces via surface energy patterning can be used to control material delivery to specified regions via selective liquid/solid wetting. While studies of the equilibrium shape of…
We present a generic framework for modelling three-dimensional deformable shells of active matter that captures the orientational dynamics of the active particles and hydrodynamic interactions on the shell and with the surrounding…