scholarly journals On a generalized doubly parabolic Keller–Segel system in one spatial dimension

2015 ◽  
Vol 26 (01) ◽  
pp. 111-160 ◽  
Author(s):  
Jan Burczak ◽  
Rafael Granero-Belinchón
Keyword(s):  
Numerical Analysis ◽  
Upper Bound ◽  
Finite Time ◽  
Chaotic Behavior ◽  
Spatial Dimension ◽  
The Other ◽  
Well Posedness ◽  
Dynamical Properties ◽  
Spatio Temporal ◽  
Time Blowup

We study a doubly parabolic Keller–Segel system in one spatial dimension, with diffusions given by fractional Laplacians. We obtain several local and global well-posedness results for the subcritical and critical cases (for the latter we need certain smallness assumptions). We also study dynamical properties of the system with added logistic term. Then, this model exhibits a spatio-temporal chaotic behavior, where a number of peaks emerge. In particular, we prove the existence of an attractor and provide an upper bound on the number of peaks that the solution may develop. Finally, we perform a numerical analysis suggesting that there is a finite time blowup if the diffusion is weak enough, even in presence of a damping logistic term. Our results generalize on one hand the results for local diffusions, on the other the results for the parabolic–elliptic fractional case.

SPECTRAL APPROXIMATION OF A SCHRÖDINGER TYPE EQUATION

1994 ◽  
Vol 04 (01) ◽  
pp. 49-88 ◽  
Author(s):  
CHRISTINE BERNARDI ◽  
MARIE-CLAUDE PELISSIER
Keyword(s):  
Numerical Analysis ◽  
Type Equation ◽  
Neumann Boundary ◽  
Rectangular Domain ◽  
The Other ◽  
Well Posedness ◽  
Discrete Problem ◽  
Spectral Approximation ◽  
Numerical Tests ◽  
Continuous Problem

This paper deals with a linear Schrödinger type equation in a rectangular domain with mixed Dirichlet-Neumann boundary conditions. The well-posedness of the continuous problem is proved, then a discrete problem is defined by combining a Legendre type spectral method in the first direction and a leap-frog scheme in the other one. The numerical analysis of the discretization is performed and error estimates are given. Numerical tests are presented.

scholarly journals A diffusion equation with localized chemical reactions

1994 ◽  
Vol 37 (1) ◽  
pp. 101-118 ◽  
Author(s):  
John M. Chadam ◽  
Hong-Ming Yin
Keyword(s):  
Global Existence ◽  
Diffusion Equation ◽  
Finite Time ◽  
Diffusion Processes ◽  
Model Problem ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Well Posedness ◽  
Blowup Rate ◽  
Time Blowup

In some chemical reaction–diffusion processes, the reaction takes place only at some local sites, due to the presence of a catalyst. In this paper we study the well-posedness of a model problem of this type. Sufficient conditions are found to ensure global existence and finite time blowup. The blowup rate and the blowup set are also investigated in the case of special nonlinearity.

The Numerical Analysis of the Velocity and Pressure Distribution of the Oil Film in Heavy Hydrostatic Thrust Bearing

2014 ◽  
Vol 541-542 ◽  
pp. 658-662
Author(s):  
Jian Li ◽  
Yuan Chen ◽  
Yang Chun Yu ◽  
Zhu Xin Tian ◽  
Yu Huang
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Pressure Distribution ◽  
Working Conditions ◽  
Thrust Bearing ◽  
Rotation Speed ◽  
The Other ◽  
Surface Load ◽  
Oil Film ◽  
Volume Method

To study the velocity and pressure distribution of the oil film in a heavy hydrostatic thrust bearing, a mathematical model of the velocity is proposed and the finite volume method (FVM) has been used to simulate the flow field under different working conditions. Some pressure experiments were carried out and the results verified the correctness of the simulation. It is concluded that the pressure distribution varies small under different rotation speed when the surface load on the workbench is constant. But the velocity of the oil film is influenced greatly by the rotation speed. When the rotation speed of the workbench is as quick as enough, the velocity of the oil film on one radial side of the pad will be zero, that is to say the lubrication oil will be drained from the other three sides of the recess.

scholarly journals Detecting Tourism Typologies of Regional Destinations Based on Their Spatio-Temporal and Socioeconomic Performance: A Correlation-Based Complex Network Approach for the Case of Greece

2021 ◽  
Vol 2 (1) ◽  
pp. 113-139
Author(s):  
Dimitrios Tsiotas ◽  
Thomas Krabokoukis ◽  
Serafeim Polyzos
Keyword(s):  
Network Analysis ◽  
Complex Network ◽  
Community Detection ◽  
Optimization Algorithm ◽  
Spatial Dimension ◽  
Economic Dimension ◽  
Complex Network Analysis ◽  
Time Period ◽  
Time Patterns ◽  
Spatio Temporal

Within the context that tourism-seasonality is a composite phenomenon described by temporal, geographical, and socio-economic aspects, this article develops a multilevel method for studying time patterns of tourism-seasonality in conjunction with its spatial dimension and socio-economic dimension. The study aims to classify the temporal patterns of seasonality into regional groups and to configure distinguishable seasonal profiles facilitating tourism policy and development. The study applies a multilevel pattern recognition approach incorporating time-series assessment, correlation, and complex network analysis based on community detection with the use of the modularity optimization algorithm, on data of overnight-stays recorded for the time-period 1998–2018. The analysis reveals four groups of seasonality, which are described by distinct seasonal, geographical, and socio-economic profiles. Overall, the analysis supports multidisciplinary and synthetic research in the modeling of tourism research and promotes complex network analysis in the study of socio-economic systems, by providing insights into the physical conceptualization that the community detection based on the modularity optimization algorithm can enjoy to the real-world applications.

scholarly journals Spatio-Temporal Changes of Urban Forests and Planning Evolution in a Highly Dynamical Urban Area: The Case Study of Wrocław, Poland

Forests ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 17 ◽  
Author(s):  
Justyna Jaworek-Jakubska ◽  
Maciej Filipiak ◽  
Adam Michalski ◽  
Anna Napierała-Filipiak
Keyword(s):  
World War Ii ◽  
Urban Forest ◽  
Urban Forests ◽  
Spatial Dimension ◽  
Temporal Changes ◽  
City Centre ◽  
Socialist Economy ◽  
Urban Green Spaces ◽  
Spatio Temporal ◽  
The City

Knowledge about urban forests in Poland is still limited, as it is primarily based on aggregate, formal data relating to the general area, ignoring the spatial dimension and informal green areas. This article describes and analyses spatio-temporal changes in the actual urban forest resources in Wrocław in 1944–2017, which covers the first period of the city’s rebuilding after its destruction during World War II and its development during the nationalised, centrally-planned socialist economy, as well as the second period of intensive and only partly controlled growth under conditions of market economy. The study is based on current and historical orthophotomaps, which were confronted with cartographic data, as well as planning documents. We found that between 1944 and 2017, the percentage contribution of informal woodlands increased tenfold (from 0.5 to 4.9% of the present total area of the city). The area occupied by such forests has grown particularly during the most recent years of the city’s intensive development. However, the forests have been increasingly fragmented. During the first period, new forest areas were also created in the immediate vicinity of the city centre, while during the second one, only in its peripheral sections. The post-war plans regarding the urban green spaces (UGS), including the current plan, are very conservative in nature. On the one hand, this means no interference with the oldest, biggest, and most valuable forest complexes, but on the other hand, insufficient consideration of the intensive built-up area expansion on former agriculture areas. Only to a limited extent did the above-mentioned plans take into account the informal woodlands, which provide an opportunity for strengthening the functional connectivity of landscape.

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