The behavior of capillary suspensions at diverse length scales: From single capillary bridges to bulk

Liquid-liquid-solid systems are becoming increasingly common in everyday life with many possible applications. Here, we focus on a special case of such liquid-liquid-solid systems, namely, capillary suspensions. These capillary suspensions originate from particles that form a network based on capillary forces and are typically composed of solids in a bulk liquid with an added secondary liquid. The structure of particle networks based on capillary bridges possesses unique properties compared with networks formed via other attractive interactions where these differences are inherently related to the properties of the capillary bridges, such as bridge breaking and coalescence between adjacent bridges. Thus, to tailor the mechanical properties of capillary suspensions to specific requirements, it is important to understand the influences on different length scales ranging from the dynamics of the bridges with varying external stimuli to the often heterogeneous network structure.     

On the Brauer p-dimension of Henselian discrete valued fields of residual characteristic p > 0

Let $(K,v)$ be a Henselian discrete valued field with residue field $\stackrel{?}{K}$ of characteristic $p>0$, and ${\text{Brd}}_p(K)$ be the Brauer p-dimension of K. This paper shows that ${\text{Brd}}_p(K)\ge n$ if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that ${\text{Brd}}_p(K)=\infty$ if and only if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

Enhanced Power Density of Alcohol Biofuel Cell by Polymer-assisted Crosslinks of 3D Graphene on Carbon Paper as the Bioanode

Herein, we successfully construct the 3D biocompatible graphene through crosslinking 2D graphene nanosheet onto carbon fiber paper with poly(diallyldimethylammonium chloride) (PDDA) as anode of the alcohol biofuel cell. Compared with the bioanode without 3D graphene, the current density and output power of PDDA-graphene-ADH bioanode is increased by 23 % and 41 % at a high concentration of ethanol at pH 8.9, suggesting the stabilization role of graphene in enzyme loading. The study provides us a deep analysis on structures and performances of the bioanode incl. electrochemistry, X-ray photoelectron spectra, and atomic force microscopy images, which is significant to develop the new methods to construct 3D porous electrodes in energy conversion device.     

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in ${\mathbb{R}}^d$ and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.     

Semi-concurrent vector fields in Finsler geometry

In the present paper, we give an answer to a question which is closely related to doubly warped product of Finsler metrics: ‘‘For each n, is there an n-dimensional Finsler manifold $(M,F)$, admitting a non-constant smooth function f on M such that $\frac{\partial f}{\partial x^i}\frac{\partial g^{ij}}{\partial y^k}=0$?”. We relate the preceding mentioned condition to different concepts appeared and studied in Finsler geometry. We introduce and investigate the notion of a semi concurrent vector field on a Finsler manifold. We show that some special Finsler manifolds admitting such vector fields turn out to be Riemannian. We prove that Tachibana's characterization of Finsler manifolds admitting a concurrent vector field leads to Riemannian metrics. Various examples for conic Finsler spaces that admit semi-concurrent vector field are presented.     

INFLUENCE OF FRICTION ON THE MOTION OF BASE WITH AN ECCENTRIC ROTOR

偏心转子惯性力引起的底座运动受到地面摩擦的影响，与光滑情形的理论结果存在定性差异。转子逆时针匀速旋转的惯性力若小于构件总重，则底座随摩擦因子增加而出现连续、一次停顿和两次停顿的振动及完全静止的4种状态。因惯性力对正压力及摩擦力的影响，底座在连续及一次停顿的振动时右向位移较大；而底座跳起时如``蛤蟆夯'则整体向左移动。