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Colloidal droplets are used in a variety of practical applications. Some of these applications require particles of different sizes. These include medical diagnostic methods, the creation of photonic crystals, the formation of…
We define a family of asymmetric processes for particles on a one-dimensional lattice, depending on a continuous parameter $\lambda \in [0,1] $, interpolating between the completely asymmetric processes [1] (for $\lambda =1$) and the n=1…
Self-similarity has been the paradigmatic picture for the pinch-off of a drop. Here we will show through high-speed imaging and boundary integral simulations that the inverse problem, the pinch-off of an air bubble in water, is not…
Ordinary differential equations are arguably the most popular and useful mathematical tool for describing physical and biological processes in the real world. Often, these physical and biological processes are observed with errors, in which…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
Let $S_\infty=A_\infty\times B_\infty$ be a self-similar product Cantor set in the complex plane, defined via $S_\infty=\bigcup_{j=1}^L T_j(S_\infty)$, where $T_j:\C\to\C$ have the form $T_j(z)=\frac1{L}z+z_j$ and $\{z_1,...,z_L\}=A+iB$ for…
Many models require integrals of high-dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
We re-examine the ordering behavior of a one-dimensional fluid of freely rotating hard needles, where the centers of mass of the particles are restricted to a line. Analytical equations are obtained for the equation of state, order…
The search for new significant peaks over a energy spectrum often involves a statistical multiple hypothesis testing problem. Separate tests of hypothesis are conducted at different locations producing an ensemble of local p-values, the…
The pinch-off dynamics of a Newtonian liquid thread embedded in a viscoplastic medium is investigated using direct numerical simulations and theory. Thread breakup occurs below a nearly universal threshold set by the balance of capillary…
This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…
The motion of flexible fibers through structured fluidic environments is ubiquitous in nature and industrial applications. Most often, their dynamics results from the complex interplay between internal elastic stresses, contact forces and…
Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess,…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
Micro-bubbles are of significant interest due to the long-living signature they leave behind naval ships. In order to numerically model and predict these bubbles in naval applications, subgrid-scale models are required because of the…
In this paper we get an estimate of Favard length of an arbitrary neighbourhood of an arbitrary self-similar Cantor set. Consider $L$ closed disjoint discs of radius $1/L$ inside the unit disc. By using linear maps of smaller disc onto the…
We present experiments on the dynamic buckling and fragmentation of slender rods axially impacted by a projectile. By combining the results of Saint-Venant and elastic beam theory, we derive a preferred wavelength lambda for the buckling…
Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical,…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…