The need for more and more accurate gravitational-wave templates requires taking into account all possible contributions to the emission of gravitational radiation from a binary system. Therefore, working within a multipolar-post-Minkowskian framework to describe the gravitational-wave field in terms of the source multipole moments, the dominant instantaneous effects should be supplemented by hereditary contributions arising from nonlinear interactions between the multipoles.

We numerically study the translocation dynamics of double emulsion drops with multiple close-packed inner droplets within constrictions. Such liquid architectures, which we refer to as HIPdEs (high-internal phase double emulsions), consist of a ternary fluid, in which monodisperse droplets are encapsulated within a larger drop in turn immersed in a bulk fluid.

The linear-order effects of radiation-reaction on the classical scattering of two point masses, in general relativity, are derived by a variation-of-constants method. Explicit expressions for the radiation-reaction contributions to the changes of 4-momentum during scattering are given to linear order in the radiative losses of energy, linear-momentum, and angular momentum. The polynomial dependence on the masses of the 4-momentum changes is shown to lead to nontrivial identities relating the various radiative losses.

In network analysis, many community detection algorithms have been developed. However, their implementation leaves unaddressed the question of the statistical validation of the results. Here, we present robin (ROBustness In Network), an R package to assess the robustness of the community structure of a network found by one or more methods to give indications about their reliability.

Searching and retrieving information from the Web is a primary activity needed to monitor the development and usage of Web resources. Possible benefits include improving user experience (e.g. by optimizing query results) and enforcing data/user security (e.g. by identifying harmful websites). Motivated by the lack of ready-to-use solutions, in this paper we present a flexible and accessible toolkit for structure and content mining, able to crawl, download, extract and index resources from the Web.

We consider a natural generalization of the eigenvalue problem for the Laplacian with homogeneous Dirichlet boundary conditions. This corresponds to look for the critical values of the Dirichlet integral, constrained to the unit Lq sphere. We collect some results, present some counter-examples and compile a list of open problems.

Some recent results on the theory of fractional Orlicz-Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, and criteria for compact embeddings. The limits of these spaces when the smoothness parameter s in (0, 1) tends to either of the endpoints of its range are also discussed. This note is based on the papers [1, 2, 3, 4], where additional material and proofs can be found.

Understanding the fluid-structure interaction is crucial for an optimal design and manufacturing of soft mesoscale materials. Multi-core emulsions are a class of soft fluids assembled from cluster configurations of deformable oil-water double droplets (cores), often employed as building-blocks for the realisation of devices of interest in bio-technology, such as drug-delivery, tissue engineering and regenerative medicine.

Asymptotically convolution Volterra equations are characterized by kernel functions which exponentially decay to convolution ones. Their importance in the applications motivates a numerical analysis of the asymptotic behavior of the solution. Here the quasi-convolution nature of the kernel is exploited in order to investigate the stability of .; / methods for general systems and in some particular cases.

The state-of-the-art deep learning-based object recognition YOLO algorithm and object tracking DeepSORT algorithm are combined to analyze digital images from fluid dynamic simulations of multi-core emulsions and soft flowing crystals and to track moving droplets within these complex flows. The YOLO network was trained to recognize the droplets with synthetically prepared data, thereby bypassing the labor-intensive data acquisition process.