Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows ...the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.
Water scarcity has received global attention in the last decade as it challenges food security in arid and semi-arid regions, particularly in the Middle East and North Africa. This research assesses ...the possible alleviation of water scarcity by reducing the water footprint in crop production through the application of soil mulching and drip irrigation. The study is the first to do so at catchment scale, taking into account various crops, multi-cropping, cropping patterns, and spatial differences in climate, soil, and field management factors, using field survey and local data. The AquaCrop-OS model and the global water footprint assessment (WFA) standard were used to assess the green and blue water footprint (WF) of ten major crops in the Upper Litani Basin (ULB) in Lebanon. The blue water saving and blue water scarcity reduction under these two alternative practices were compared to the current situation. The results show that the WF of crop production is more sensitive to climate than soil type. The annual blue WF of summer crops was largest when water availability was lowest. Mulching reduced the blue WF by 3.6% and mulching combined with drip irrigation reduced it by 4.7%. The blue water saving from mulching was estimated about 6.3 million m3/y and from mulching combined with drip irrigation about 8.3 million m3/y. This is substantial but by far not sufficient to reduce the overall blue WF in summer to a sustainable level at catchment scale.
Display omitted
•This is the first study on the water saving effect of mulching and drip irrigation at catchment scale.•Mulching and drip irrigation will reduce the blue water footprint in Upper Litani Basin (ULB) by 5%.•Additional measures will be needed to lower the water footprint in the ULB to sustainable level.•Mulching reduces the water footprint of crops more than drip irrigation, but combining is the best.
In gold nanoparticle-enhanced radiotherapy, intravenously administered nanoparticles tend to accumulate in the tumor tissue by means of the so-called permeability and retention effect and upon ...irradiation with x-rays, the nanoparticles release a secondary electron field that increases the absorbed dose that would otherwise be obtained from the interaction of the x-rays with tissue alone. The concentration of the nanoparticles in the tumor, number of nanoparticles per unit of mass, which determines the total absorbed dose imparted, can be measured via magnetic resonance or computed tomography images, usually with a resolution of several millimeters. Using a tumor vasculature model with a resolution of 500 nm, we show that for a given concentration of nanoparticles, the dose enhancement that occurs upon irradiation with x-rays greatly depends on whether the nanoparticles are confined to the tumor vasculature or have already extravasated into the surrounding tumor tissue. We show that, compared to the reference irradiation with no nanoparticles present in the tumor model, irradiation with the nanoparticles confined to the tumor vasculature, either in the bloodstream or attached to the inner blood vessel walls, results in a two to three-fold increase in the absorbed dose to the whole tumor model, with respect to an irradiation when the nanoparticles have already extravasated into the tumor tissue. Therefore, it is not enough to measure the concentration of the nanoparticles in a tumor, but the location of the nanoparticles within each volume element of a tumor, be it inside the vasculature or the tumor tissue, needs to be determined as well if an accurate estimation of the resultant absorbed dose distribution, a key element in the success of a radiotherapy treatment, is to be made.
Feature models have been used since the 90s to describe software product lines as a way of reusing common parts in a family of software systems. In 2010, a systematic literature review was published ...summarizing the advances and settling the basis of the area of automated analysis of feature models (AAFM). From then on, different studies have applied the AAFM in different domains. In this paper, we provide an overview of the evolution of this field since 2010 by performing a systematic mapping study considering 423 primary sources. We found six different variability facets where the AAFM is being applied that define the tendencies: product configuration and derivation; testing and evolution; reverse engineering; multi-model variability-analysis; variability modelling and variability-intensive systems. We also confirmed that there is a lack of industrial evidence in most of the cases. Finally, we present where and when the papers have been published and who are the authors and institutions that are contributing to the field. We observed that the maturity is proven by the increment in the number of journals published along the years as well as the diversity of conferences and workshops where papers are published. We also suggest some synergies with other areas such as cloud or mobile computing among others that can motivate further research in the future.
In this letter, we focus on the size effect of granular column collapses, which are potentially connected to the dynamics of complex geophysical flows, even if the link between microscopic structures ...of granular assemblies and their macroscopic behaviors is still not well understood. Using the spheropolyhedral discrete element method (DEM), we show that the column radius/grain size ratio has a strong influence on the collapse behavior. A finite‐size analysis, which is inspired by a phase transition around an inflection point, is performed to obtain a general scaling equation with critical exponents for runout distances. We further link the size effect with the strong force network and formalize a correlation length scale that exponentially scales with the effective aspect ratio. Such a scaling solution shows similarities with the percolation problem of two‐dimensional random networks and can be extended to other similar natural and engineering systems.
Plain Language Summary
We aim to understand the size effect in granular column collapses. Geophysical hazards, such as landslides, debris flows, pyroclastic flows, and rock avalanches, occur frequently worldwide, and it is difficult to predict their initiation and dynamical behavior. Many geophysical flows can be considered as granular materials, where interaction between particles matters. However, it is difficult to upscale a grain‐scale particle interaction to a large‐scale predicting tool to capture the behavior of many complex granular flows. This paper starts from the collapse of granular columns, a fundamental problem often used to investigate the mobility of granular materials, and carefully navigates to examine the runout behaviors of columns with different sizes, so that we can obtain a better picture of how different system sizes lead to different collapsing scenarios. We further analyzed the characteristic length scale associated with the collapse of granular columns, and the strong force network presenting at the beginning of the collapse, to understand better what drives the size effect of granular systems, and what we can gain from this research to predict the behavior of geophysical flows.
Key Points
Granular column collapses show a significant size effect with respect to runout distances and phase transitions
The size effect can be further associated with the strong force networks and early stage characteristic length scales
We draw similarities between granular column collapses and dome‐collapse pyroclastic flows
This work aims to study the interplay between the Wilson-Cowan model and connection matrices. These matrices describe cortical neural wiring, while Wilson-Cowan equations provide a dynamical ...description of neural interaction. We formulate Wilson-Cowan equations on locally compact Abelian groups. We show that the Cauchy problem is well posed. We then select a type of group that allows us to incorporate the experimental information provided by the connection matrices. We argue that the classical Wilson-Cowan model is incompatible with the small-world property. A necessary condition to have this property is that the Wilson-Cowan equations be formulated on a compact group. We propose a
-adic version of the Wilson-Cowan model, a hierarchical version in which the neurons are organized into an infinite rooted tree. We present several numerical simulations showing that the
-adic version matches the predictions of the classical version in relevant experiments. The
-adic version allows the incorporation of the connection matrices into the Wilson-Cowan model. We present several numerical simulations using a neural network model that incorporates a
-adic approximation of the connection matrix of the cat cortex.
A
bstract
In this article, we establish in a rigorous mathematical way that Koba-Nielsen amplitudes defined on any local field of characteristic zero are bona fide integrals that admit meromorphic ...continuations in the kinematic parameters. Our approach allows us to study in a uniform way open and closed Koba-Nielsen amplitudes over arbitrary local fields of characteristic zero. In the regularization process we use techniques of local zeta functions and embedded resolution of singularities. As an application we present the regularization of
p
-adic open string amplitudes with Chan-Paton factors and constant
B
-field. Finally, all the local zeta functions studied here are partition functions of certain 1
D
log-Coulomb gases, which shows an interesting connection between Koba-Nielsen amplitudes and statistical mechanics.
We construct
p
-adic Euclidean random fields
Φ
over
Q
p
N
, for arbitrary
N
, these fields are solutions of
p
-adic stochastic pseudodifferential equations. From a mathematical perspective, the ...Euclidean fields are generalized stochastic processes parametrized by functions belonging to a nuclear countably Hilbert space, these spaces are introduced in this article, in addition, the Euclidean fields are invariant under the action of certain group of transformations. We also study the Schwinger functions of
Φ
.
PDF
