scholarly journals Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
José Francisco Gómez Aguilar ◽  
Margarita Miranda Hernández
Keyword(s):  
Time Domain ◽  
Fractional Diffusion ◽  
Anomalous Behavior ◽  
Space Time ◽  
Advection Equation ◽  
Algebraic Decay ◽  
Physical Relation ◽  
Space And Time ◽  
Fractional Solution ◽  
Fractional Space

An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as0<β,γ≤1for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parametersσxandσtare introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parametersβandγ. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.

scholarly journals Fractional thermal diffusion and the heat equation

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Francisco Gómez ◽  
Luis Morales ◽  
Mario González ◽  
Victor Alvarado ◽  
Guadalupe López
Keyword(s):  
Time Domain ◽  
Time Derivative ◽  
Space Time ◽  
Mathematical Representation ◽  
Alternative Representation ◽  
Complex Processes ◽  
Temporal Derivative ◽  
Dimensional Parameters ◽  
Non Local ◽  
Fractional Space

AbstractFractional calculus is the branch of mathematical analysis that deals with operators interpreted as derivatives and integrals of non-integer order. This mathematical representation is used in the description of non-local behaviors and anomalous complex processes. Fourier’s lawfor the conduction of heat exhibit anomalous behaviors when the order of the derivative is considered as 0 < β,ϒ ≤ 1 for the space-time domain respectively. In this paper we proposed an alternative representation of the fractional Fourier’s law equation, three cases are presented; with fractional spatial derivative, fractional temporal derivative and fractional space-time derivative (both derivatives in simultaneous form). In this analysis we introduce fractional dimensional parameters σ

scholarly journals Integrated field-agent based modelling using the LUE scientific data base

2020 ◽  
Author(s):  
Oliver Schmitz ◽  
Kor de Jong ◽  
Derek Karssenberg
Keyword(s):  
Time Domain ◽  
Data Model ◽  
Space Time ◽  
Environmental Modelling ◽  
Agent Based ◽  
Space And Time ◽  
Physical Data ◽  
Time Domains ◽  
Spatio Temporal ◽  
Temporal Objects

&lt;p&gt;The heterogeneous nature of environmental systems poses a challenge to researchers constructing environmental models. Many simulation models of integrated systems need to incorporate phenomena that are represented as spatially and temporally continuous fields as well as phenomena that are modelled as spatially and temporally bounded agents. Examples include moving animals (agents) interacting with vegetation (fields) or static water reservoirs (agents) as components of hydrological catchments (fields). However, phenomena bounded in space and time have particular properties mainly because they require representation of multiple (sometimes mobile) objects that each exist in a small subdomain of the space-time domain of interest. Moreover, these subdomains of objects may overlap in space and time such as interleaving branches due to tree crown growth. Efficient storage and access of different types of phenomena requires an approach that integrates representation of fields and objects in a single data model.&lt;/p&gt;&lt;p&gt;We develop the open-source LUE data model that explicitly stores and separates domain information, i.e. where phenomena exist in the space-time domain, and property information, i.e. what attribute value the phenomenon has at a particular space-time location, for a particular object. Notable functionalities are support for multiple spatio-temporal objects, time domains, objects linked to multiple space and time domains, and relations between objects. The design of LUE is based on the conceptual data model of de Bakker (2017) and implemented as a physical data model using HDF5 and C++ (de Jong, 2019). Our LUE data model is part of a new modelling language implemented in Python, allowing for operations accepting both fields and agents as arguments, and therefore resembling and extending the map algebra approach to field-agent modelling.&lt;/p&gt;&lt;p&gt;We present the conceptual and physical data models and illustrate the usage by implementing a spatial agent-based model simulating changes in human nutrition. We thereby consider the interaction between personal demand and supply of healthy food of nearby stores as well as the influence of agent's social network.&lt;/p&gt;&lt;p&gt;&lt;br&gt;References:&lt;/p&gt;&lt;p&gt;de Bakker, M. P., de Jong, K., Schmitz, O., &amp; Karssenberg, D. (2017). Design and demonstration of a data model to integrate agent-based and field-based modelling. Environmental Modelling &amp; Software, 89, 172&amp;#8211;189. https://doi.org/10.1016/j.envsoft.2016.11.016&lt;/p&gt;&lt;p&gt;de Jong, K., &amp; Karssenberg, D. (2019). A physical data model for spatio-temporal objects. Environmental Modelling &amp; Software. https://doi.org/10.1016/j.envsoft.2019.104553&lt;/p&gt;&lt;p&gt;LUE source code repository: https://github.com/pcraster/lue/&lt;/p&gt;

Fractional Transmission Line with Losses

2014 ◽  
Vol 69 (10-11) ◽  
pp. 539-546 ◽  
Author(s):  
José Francisco Gómez-Aguilar ◽  
Baleanu Dumitru
Keyword(s):  
Transmission Line ◽  
Numerical Simulations ◽  
Time Domain ◽  
Caputo Derivative ◽  
Physical Relation ◽  
Space And Time ◽  
Two Parameters ◽  
Fractional Equation

AbstractIn this manuscript, the fractional transmission line with losses is presented. The order of the Caputo derivative is considered as 0 < β ≤ 1 and 0 < γ ≤ 1 for the fractional equation in space and time domain, respectively. Two cases are solved, with fractional spatial and fractional temporal derivatives, and also numerical simulations were carried out, where there are taken both derivatives in simultaneous form. Two parameters σx and σt are introduced and a physical relation between these parameters is reported. Solutions in space and time are given in terms of the Mittag-Leffler functions. The classic cases are recovered when β and γ are equal to 1.

Espaço, Tempo e Modernidade

GEOgraphia ◽  
2009 ◽  
Vol 2 (3) ◽  
pp. 51
Author(s):  
Gilvan Luiz Hansen
Keyword(s):  
Modern Philosophy ◽  
Space Time ◽  
Space And Time ◽  
Time Concepts

Resumo Este artigo é uma discussão introdutória acerca da importância das concepções de espaço e tempo na modernidade. O objetivo deste texto é enfatizar os aspectos teóricos e práticos dos conceitos de espaço e tempo, mediante a apresentação de três perspectivas de interpretação desta questão na filosofia desenvolvida na modernidade. Palavras-chave: Modernidade, Espaço, Tempo, Filosofia Moderna, J. Habermas.Abstract This article is an introductory debate about the importance of space and time conceptions in modernity. The objective from this text is emphasize the theoretical and practical aspects of space and time concepts, by presentation of three interpretation perspectives of this question in the philosophy developed in modernity. Keywords: Modernity, Space, Time, Modern Philosophy, J. Habermas.

Samuel Beckett's Debt to Aristotle: Cosmology, Syllogism, Space, Time

2010 ◽  
Vol 22 (1) ◽  
pp. 181-195 ◽  
Author(s):  
Anthony Cordingley
Keyword(s):  
Trinity College ◽  
Space Time ◽  
Formal Logic ◽  
Trinity College Dublin ◽  
Space And Time ◽  
Creative Transformation ◽  
Cosmic Order

This essay argues for the presence of Aristotelian ideas of cosmic order, syllogism, space and time in Beckett's . It accounts for how such ideas impact upon the novel's 'I' as he attempts to offer a philosophical 'solution' to his predicament in an underworld divorced from the revolving heavens. Beckett's study of formal logic as a student at Trinity College, Dublin and his private study of philosophy in 1932 is examined in this light; particularly his “Philosophy Notes,” along with some possible further sources for his knowledge. The essay then reveals a creative transformation of Aristotelian ideas in which led to formal innovations, such as the continuous present of its narrative.

scholarly journals Spatial and space-time correlations in systems of subpopulations with genetic drift and migration.

Genetics ◽  
1993 ◽  
Vol 133 (3) ◽  
pp. 711-727
Author(s):  
B K Epperson
Keyword(s):  
Population Genetics ◽  
Time Correlation ◽  
Space Time ◽  
Spatial Correlations ◽  
Gene Frequencies ◽  
Migration Patterns ◽  
Migration Rates ◽  
Space And Time ◽  
Time Correlations ◽  
And Migration

Abstract The geographic distribution of genetic variation is an important theoretical and experimental component of population genetics. Previous characterizations of genetic structure of populations have used measures of spatial variance and spatial correlations. Yet a full understanding of the causes and consequences of spatial structure requires complete characterization of the underlying space-time system. This paper examines important interactions between processes and spatial structure in systems of subpopulations with migration and drift, by analyzing correlations of gene frequencies over space and time. We develop methods for studying important features of the complete set of space-time correlations of gene frequencies for the first time in population genetics. These methods also provide a new alternative for studying the purely spatial correlations and the variance, for models with general spatial dimensionalities and migration patterns. These results are obtained by employing theorems, previously unused in population genetics, for space-time autoregressive (STAR) stochastic spatial time series. We include results on systems with subpopulation interactions that have time delay lags (temporal orders) greater than one. We use the space-time correlation structure to develop novel estimators for migration rates that are based on space-time data (samples collected over space and time) rather than on purely spatial data, for real systems. We examine the space-time and spatial correlations for some specific stepping stone migration models. One focus is on the effects of anisotropic migration rates. Partial space-time correlation coefficients can be used for identifying migration patterns. Using STAR models, the spatial, space-time, and partial space-time correlations together provide a framework with an unprecedented level of detail for characterizing, predicting and contrasting space-time theoretical distributions of gene frequencies, and for identifying features such as the pattern of migration and estimating migration rates in experimental studies of genetic variation over space and time.

scholarly journals Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

2021 ◽  
Vol 11 (8) ◽  
pp. 3421
Author(s):  
Cheng-Yu Ku ◽  
Li-Dan Hong ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Wei-Po Huang
Keyword(s):  
Porous Media ◽  
Time Domain ◽  
Numerical Solutions ◽  
Space Time ◽  
Two Dimensional ◽  
Transient Flows ◽  
Layered Porous Media ◽  
Time Marching ◽  
Time Basis ◽  
Marching Scheme

In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

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