Active fluids comprise a variety of systems composed of elements immersed in a fluid environment which can convert some form of energy into directed motion; as such they are intrinsically out-of-equilibrium in the absence of any external force. A fundamental problem in the physics of active matter concerns the understanding of how the characteristics of autonomous propulsion and agent-agent interactions determine the collective dynamics of the system. We study numerically the suspensions of self-propelled diffusiophoretic colloids, in (quasi)-2d configurations, accounting for both dynamically resolved solute-mediated phoretic interactions and solvent-mediated hydrodynamic interactions. Our results show that the system displays different scenarios at changing the colloid-solute affinity and it develops a cluster phase in the chemoattractive case. We study the statistics of cluster sizes and cluster morphologies for different magnitudes of colloidal activity. Finally, we provide evidences that hydrodynamics plays a relevant role in the aggregation kinetics and cluster morphology, significantly hindering cluster growth.

The dynamics of active colloids is very sensitive to the presence of boundaries and interfaces which therefore can be used to control their motion. Here we analyze the dynamics of active colloids adsorbed at a fluid-fluid interface. By using a mesoscopic numerical approach which relies on an approximated numerical solution of the Navier-Stokes equation, we show that when adsorbed at a fluid interface, an active colloid experiences a net torque even in the absence of a viscosity contrast between the two adjacent fluids. In particular, we study the dependence of this torque on the contact angle of the colloid with the fluid-fluid interface and on its surface properties. We rationalize our results via an approximate approach which accounts for the appearance of a local friction coefficient. By providing insight into the dynamics of active colloids adsorbed at fluid interfaces, our results are relevant for two-dimensional self assembly and emulsion stabilization by means of active colloids.

Bandelt and Mulder's structural characterization of bipartite distance hereditary graphs 16 asserts that such graphs can be built inductively starting from a single vertex and by re- 17 peatedly adding either pendant vertices or twins (i.e., vertices with the same neighborhood 18 as an existing one). Dirac and Duffin's structural characterization of 2-connected series- 19 parallel graphs asserts that such graphs can be built inductively starting from a single edge 20 by adding either edges in series or in parallel. In this paper we give an elementary proof 21 that the two constructions are the same construction when bipartite graphs are viewed as 22 the fundamental graphs of a graphic matroid. We then apply the result to re-prove known 23 results concerning bipartite distance hereditary graphs and series-parallel graphs and to 24 provide a new class of polynomially-solvable instances for the integer multi-commodity 25 flow of maximum value.

This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures, emerging on the accessible surface of a slab, by means of Active Thermography. In real life, this surface is heated with a laser and its temperature is measured for a time interval by means of an infrared camera. A fundamental step in iterative inversion methods is the numerical solution of the underlying direct mathematical model. Usually, this step requires specific techniques in order to limit an abnormal use of memory resources and computing time due to excessively fine meshes necessary to follow a very thin fracture in the domain. Our contribution to this problem consists in decomposing the temperature of the damaged specimen as a sum of a term (with known analytical form) due to an infinite virtual fracture and the solution of an initial boundary value problem for the heat equation on one side of the fracture (i.e. on a rectangular domain). The depth of the fracture is a variable parameter in the boundary conditions that must be estimated from additional data (usually, measurements of the surface temperature). We apply our method to the detection of simulated cracks in concrete and steel specimens.

A composite specimen, made of two slabs and an interface A is heated through one of its sides S, in order to evaluate the thermal conductance H of A. The direct model consists of a system of Initial Boundary Value Problems completed by suitable transmission conditions. Thanks to the properties of multilayer diffusion, we reduce the problem to the slab between A and S only. In this case evaluating the thermal resistance of A means to identify a coefficient in a Robin boundary condition. We evaluate H numerically by means of Thin Plate Approximation.

A new class of multiscale scheme is presented for micro-hydrodynamic problems based on a dual representation of the fluid observables. The hybrid model is first tested against the classical flow between two parallel plates and then applied to a plug flow within a micrometer-sized striction and a shear flow within a microcavity. Both cases demonstrate the capability of the multiscale approach to reproduce the correct macroscopic hydrodynamics also in the presence of refined grids (one and two levels), while retaining the correct thermal fluctuations, embedded in the multiparticle collision method. This provides the first step toward a novel class of fully mesoscale hybrid approaches able to capture the physics of fluids at the micro- and nanoscales whenever a continuum representation of the fluid falls short of providing the complete physical information, due to a lack of resolution and thermal fluctuations.

We present an extension of the multiparticle collision dynamics method for flows with complex interfaces, including supramolecular near-contact interactions mimicking the effect of surfactants. The new method is demonstrated for the case of (i) short range repulsion of droplets in close contact, (ii) arrested phase separation, and (iii) different pattern formation during spinodal decomposition of binary mixtures.

Fluid flows hosting electrical phenomena are the subject of a fascinating and highly interdisciplinary scientific field. In recent years, the extraordinary success of electrospinning and solution-blowing technologies for the generation of polymer nanofibers has motivated vibrant research aiming at rationalizing the behavior of viscoelastic jets under applied electric fields or other stretching fields including gas streams. Theoretical models unveiled many original aspects in the underpinning physics of polymer solutions in jets and provided useful information to improve experimental platforms. This review examines advances in the theoretical description and numerical simulation of polymer solution jets in electrospinning and solution blowing. Instability phenomena of electrical and hydrodynamic origin, which play a crucial role in the relevant flow physics, are highlighted. Specifications leading to accurate and computationally viable models are formulated. Electrohydrodynamic modeling, theories on jet bending instability, recent advances in Lagrangian approaches to describe the jet flow, including strategies for dynamic refinement of simulations, and effects of strong elongational flow on polymer networks are reviewed. Finally, the current challenges and future perspectives in the field are outlined and discussed, including the task of correlating the physics of the jet flows with the properties of relevant materials, as well as the development of multiscale techniques for modeling viscoelastic jets.

Bicontinuous interfacially jammed emulsion gels ("bijels") represent a new class of soft materials made of a densely packed monolayer of solid particles sequestered at the interface of a bicontinuous fluid. Their mechanical properties are relevant to many applications, such as catalysis, energy conversion, soft robotics, and scaffolds for tissue engineering. While their stationary bulk properties have been covered in depth, much less is known about their behavior in the presence of an external shear. In this paper, we numerically study the dynamics of a bijel confined within a three-dimensional rectangular domain and subject to a symmetric shear flow sufficiently intense to break the material. Extensive numerical simulations reveal that the shear flow generally promotes the detachment of a sizable amount of particles from the fluid interface and their accumulation in the bulk. Fluid interfaces undergo large stretching and deformations along the flow direction, an effect that reduces their capability of entrapping particles. These results are supported by a series of quantitative indicators such as (i) curvature of the fluid interface, (ii) spatial distribution of the colloidal particles, and (iii) fluid flow structure within the microchannel. (c) 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

In this paper we describe how to swap two 2 × 2 blocks in a real Schur form and a generalized real Schur form. We pay special attention to the numerical stability of the method. We also illustrate the stability of our approach by a series of numerical tests.

Let X={X1,X2,...,Xm} be a system of smooth vector fields in R^n satisfying the Hörmander's finite rank condition. We prove the following Sobolev inequality with reciprocal weights in Carnot-Carathéodory space G associated to system X (1?BRK(x)dx?BR|u|tK(x)dx)1/t<=CR??1?BR1K(x)dx?BR|Xu|2K(x)dx??1/2, where Xu denotes the horizontal gradient of u with respect to X. We assume that the weight K belongs to Muckenhoupt's class A_2 and Gehring's class G_?, where ? is a suitable exponent related to the homogeneous dimension.

We study an eigenvalue problem involving a fully anisotropic elliptic differential operator in arbitrary Orlicz-Sobolev spaces. The relevant equations are associated with constrained minimization problems for integral functionals depending on the gradient of competing functions through general anisotropic N-functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called \Delta_2-condition. The resulting analysis requires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces.

We introduce non-local dynamics on directed networks through the construction of a fractional version of a non-symmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both directed and undirected graphs, showing the possibility of exploring the network employing random walks with jumps of arbitrary length. We also provide some examples of the applicability of the proposed dynamics, including consensus over multi-agent systems described by directed networks.

Visibility has an encompassing importance in humans' perception of the landscape, since the first encounter with a new environment normally occurs through sight. In historical and archaeological studies, two main methods (i.e., the geometric method and the Geographical Information System [GIS] computation) have been employed to determine the distance from which an object can be recognized. However, neither is exhaustive when applied to a maritime context, where the main factor affecting the visibility radius is weather. To establish how far at sea an object can be seen, and how its visibility would have changed in different weather conditions, we adopted a method from Aerosol Optics based on a well-established mathematical model of the light scattering phenomena. We applied this method to compute the visibility radius in historical studies. To demonstrate its application, we choose to examine the visibility of a key point in both historical and current seafaring, namely Mount Etna (Sicily, Italy), from the Ionian coast of Calabria (Italy). The results obtained by the application of this method have been validated by comparing them with mentions of Mount Etna in both written sources and on-the-ground records.

The computation of matrix functions using quadrature formulas and rational approximations of very large structured matrices using tensor trains (TT), and quantized tensor trains (QTT) is considered here. The focus is on matrices with a small TT/QTT rank. Some analysis of the error produced by the use of the TT/QTT representation and the underlying approximation formula used is also provided. Promising experiments on exponential, power, Mittag-Leffler and logarithm function of multilevel Toeplitz matrices, that are among those which generate a low TT/QTT rank representation, are also provided, confirming that the proposed approach is feasible. (C) 2019 Elsevier B.V. All rights reserved.

In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a long-range interaction between them, does not exhibit concentration phenomena typical of spectral rankings which take into account just local interactions. We show that the predictive value of the rankings obtained using our proposals is considerably improved on different real world problems.

We use computer simulations to study the morphology and rheological properties of a bidimensional emulsion resulting from a mixture of a passive isotropic fluid and an active contractile polar gel, in the presence of a surfactant that favours the emulsification of the two phases. By varying the intensity of the contractile activity and of an externally imposed shear flow, we find three possible morphologies. For low shear rates, a simple lamellar state is obtained. For intermediate activity and shear rate, an asymmetric state emerges, which is characterized by shear and concentration banding at the polar/isotropic interface. A further increment in the active forcing leads to the self-assembly of a soft channel where an isotropic fluid flows between two layers of active material. We characterize the stability of this state by performing a dynamical test varying the intensity of the active forcing and shear rate. Finally, we address the rheological properties of the system by measuring the effective shear viscosity, finding that this increases as active forcing is increased-so that the fluid thickens with activity.

The main focus of this paper is the characterization and exploitation of the asymptotic spectrum of the saddle--point matrix sequences arising from the discretization of optimization problems constrained by elliptic partial differential equations. They uncover the existence of an hidden structure in these matrix sequences, namely, they show that these are indeed an example of Generalized Locally Toeplitz (GLT) sequences. They show that this enables a sharper characterization of the spectral properties of such sequences than the one that is available by using only the fact that they deal with saddle--point matrices. Finally, they exploit it to propose an optimal preconditioner strategy for the GMRES, and Flexible--GMRES methods.

Rational Krylov methods are a powerful alternative for computing the product of a function of a large matrix times a given vector. However, the creation of the underlying rational subspaces requires solving sequences of large linear systems, a delicate task that can require intensive computational resources and should be monitored to avoid the creation of subspace different to those required. We propose the use of robust preconditioned iterative techniques to speedup the underlying process. We also discuss briefly how the inexact solution of these linear systems can affect the computed subspace. A preliminary test approximating a fractional power of the Laplacian matrix is included.

Recent years have witnessed a massive push towards reproducible research in neuroscience. Unfortunately, this endeavor is often challenged by the large diversity of tools used, project-specific custom code and the difficulty to track all user-defined parameters. NeuroPycon is an open-source multi-modal brain data analysis toolkit which provides Python-based template pipelines for advanced multi-processing of MEG, EEG, functional and anatomical MRI data, with a focus on connectivity and graph theoretical analyses. Importantly, it provides shareable parameter files to facilitate replication of all analysis steps. NeuroPycon is based on the NiPype framework which facilitates data analyses by wrapping many commonly-used neuroimaging software tools into a common Python environment. In other words, rather than being a brain imaging software with is own implementation of standard algorithms for brain signal processing, NeuroPycon seamlessly integrates existing packages (coded in python, Matlab or other languages) into a unified python framework. Importantly, thanks to the multi-threaded processing and computational efficiency afforded by NiPype, NeuroPycon provides an easy option for fast parallel processing, which critical when handling large sets of multi-dimensional brain data. Moreover, its fiexible design allows users to easily configure analysis pipelines by connecting distinct nodes to each other. Each node can be a Python-wrapped module, a user-defined function or a well-established tool (e.g. MNE-Python for MEG analysis, Radatools for graph theoretical metrics, etc.). Last but not least, the ability to use NeuroPycon parameter files to fully describe any pipeline is an important feature for reproducibility, as they can be shared and used for easy replication by others. The current implementation of NeuroPycon contains two complementary packages: The first, called ephypype, includes pipelines for electrophysiology analysis and a command-line interface for on the fiy pipeline creation. Current implementations allow for MEG/EEG data import, pre-processing and cleaning by automatic removal of ocular and cardiac artefacts, in addition to sensor or source-level connectivity analyses. The second package, called graphpype, is designed to investigate functional connectivity via a wide range of graph-theoretical metrics, including modular partitions. The present article describes the philosophy, architecture, and functionalities of the toolkit and provides illustrative examples through interactive notebooks. NeuroPycon is available for download via github (https://github.com/neuropycon) and the two principal packages are documented online (https://neuropycon.github.io/ephypype/index.html, and https://neuropycon.github.io/graph pype/index.html). Future developments include fusion of multi-modal data (eg. MEG and fMRI or intracranial EEG and fMRI). We hope that the release of NeuroPycon will attract many users and new contributors, and facilitate the efforts of our community towards open source tool sharing and development, as well as scientific reproducibility.