scholarly journals The Multi-Advective Water Mixing Approach for Transport through Heterogeneous Media

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6562
Author(s):  
Joaquim Soler-Sagarra ◽  
Vivien Hakoun ◽  
Marco Dentz ◽  
Jesus Carrera
Keyword(s):  
Transition Matrix ◽  
Heterogeneous Media ◽  
Transition Probability ◽  
Solute Concentration ◽  
Transition Matrices ◽  
Water Mixing ◽  
Incomplete Mixing ◽  
Space Formulation ◽  
Parcel Method ◽  
Water Parcel

Finding a numerical method to model solute transport in porous media with high heterogeneity is crucial, especially when chemical reactions are involved. The phase space formulation termed the multi-advective water mixing approach (MAWMA) was proposed to address this issue. The water parcel method (WP) may be obtained by discretizing MAWMA in space, time, and velocity. WP needs two transition matrices of velocity to reproduce advection (Markovian in space) and mixing (Markovian in time), separately. The matrices express the transition probability of water instead of individual solute concentration. This entails a change in concept, since the entire transport phenomenon is defined by the water phase. Concentration is reduced to a chemical attribute. The water transition matrix is obtained and is demonstrated to be constant in time. Moreover, the WP method is compared with the classic random walk method (RW) in a high heterogeneous domain. Results show that the WP adequately reproduces advection and dispersion, but overestimates mixing because mixing is a sub-velocity phase process. The WP method must, therefore, be extended to take into account incomplete mixing within velocity classes.

scholarly journals Research on the Combination Method of Temporal Conflict Evidence Based on Transition Matrix

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Bin Wu ◽  
Xiao Yi
Keyword(s):  
Transition Matrix ◽  
Transition Probability ◽  
Evidence Theory ◽  
Research Topic ◽  
Combination Method ◽  
Evidence Based ◽  
Important Research ◽  
Transition Matrices ◽  
Important Research Topic ◽  
Evidence Combination

Conflict evidence combination is an important research topic in evidence theory. In this paper, two kinds of transition matrices are constructed based on the Markov model; one is the unordered transition matrix, which satisfies the commutative law, and the other is the temporal transition matrix, which does not satisfy the commutative law, but it can handle the combination of temporal evidence well. Then, a temporal conflict evidence combination model is proposed based on these two transition matrices. First, the transition probability at the first n time is calculated through the model of unordered transition probability, and then, the transition matrix from the N + 1 time is used to solve the combination problem of temporal conflict evidence. The effectiveness of the transition matrix in the research of conflict evidence combination method is proved by the example analysis.

scholarly journals Probability of Deriving a Yearly Transition Probability Matrix for Land-Use Dynamics

2019 ◽  
Vol 11 (22) ◽  
pp. 6355 ◽  
Author(s):  
Shigeaki F. Hasegawa ◽  
Takenori Takada
Keyword(s):  
Land Use ◽  
Transition Matrix ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Negative Solution ◽  
Transition Matrices ◽  
Positive Elements ◽  
Land Use Dynamics ◽  
Probability Matrices ◽  
Use Studies

Takada’s group developed a method for estimating the yearly transition matrix by calculating the mth power roots of a transition matrix with an interval of m years. However, the probability of obtaining a yearly transition matrix with real and positive elements is unknown. In this study, empirical verification based on transition matrices from previous land-use studies and Monte-Carlo simulations were conducted to estimate the probability of obtaining an appropriate yearly transition probability matrix. In 62 transition probability matrices of previous land-use studies, 54 (87%) could provide a positive or small-negative solution. For randomly generated matrices with differing sizes or power roots, the probability of obtaining a positive or small-negative solution is low. However, the probability is relatively large for matrices with large diagonal elements, exceeding 90% in most cases. These results indicate that Takada et al.’s method is a powerful tool for analyzing land-use dynamics.

Regional household poverty and mobility analysis – a transition probability approach

2020 ◽  
Vol 63 (3) ◽  
pp. 286-302
Author(s):  
Damian Mowczan ◽  
Keyword(s):  
Transition Probability ◽  
General Level ◽  
Transition Matrices ◽  
Equivalent Unit ◽  
Central Statistical ◽  
Per Capita ◽  
Probability Matrices ◽  
General Mobility ◽  
One Year ◽  
The One

The main objective of this paper was to estimate and analyse transition-probability matrices for all 16 of Poland’s NUTS-2 level regions (voivodeship level). The analysis is conducted in terms of the transitions among six expenditure classes (per capita and per equivalent unit), focusing on poverty classes. The period of analysis was two years: 2015 and 2016. The basic aim was to identify both those regions in which the probability of staying in poverty was the highest and the general level of mobility among expenditure classes. The study uses a two-year panel sub-sample of unidentified unit data from the Central Statistical Office (CSO), specifically the data concerning household budget surveys. To account for differences in household size and demographic structure, the study used expenditures per capita and expenditures per equivalent unit simultaneously. To estimate the elements of the transition matrices, a classic maximum-likelihood estimator was used. The analysis used Shorrocks’ and Bartholomew’s mobility indices to assess the general mobility level and the Gini index to assess the inequality level. The results show that the one-year probability of staying in the same poverty class varies among regions and is lower for expenditures per equivalent units. The highest probabilities were identified in Podkarpackie (expenditures per capita) and Opolskie (expenditures per equivalent unit), and the lowest probabilities in Kujawsko-Pomorskie (expenditures per capita) and Małopolskie (expenditures per equivalent unit). The highest level of general mobility was noted in Małopolskie, for both categories of expenditures.

scholarly journals Casselman’s Basis of Iwahori Vectors and Kazhdan–Lusztig Polynomials

2019 ◽  
Vol 71 (6) ◽  
pp. 1351-1366
Author(s):  
Daniel Bump ◽  
Maki Nakasuji
Keyword(s):  
Representation Theory ◽  
Functional Equations ◽  
Transition Matrix ◽  
Principal Series ◽  
Surprising Result ◽  
Transition Matrices ◽  
Natural Basis ◽  
Series Representations ◽  
The Matrix ◽  
Lusztig Polynomials

AbstractA problem in representation theory of $p$-adic groups is the computation of the Casselman basis of Iwahori fixed vectors in the spherical principal series representations, which are dual to the intertwining integrals. We shall express the transition matrix $(m_{u,v})$ of the Casselman basis to another natural basis in terms of certain polynomials that are deformations of the Kazhdan–Lusztig R-polynomials. As an application we will obtain certain new functional equations for these transition matrices under the algebraic involution sending the residue cardinality $q$ to $q^{-1}$. We will also obtain a new proof of a surprising result of Nakasuji and Naruse that relates the matrix $(m_{u,v})$ to its inverse.

Duality results for block-structured transition matrices

1999 ◽  
Vol 36 (4) ◽  
pp. 1045-1057 ◽  
Author(s):  
Yiqiang Q. Zhao ◽  
Wei Li ◽  
Attahiru Sule Alfa
Keyword(s):  
Transition Matrix ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Transition Kernel ◽  
Transition Matrices ◽  
Duality Results ◽  
Markov Renewal Processes ◽  
The Matrix ◽  
Probabilistic Measures ◽  
Block Structured

In this paper, we consider a certain class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewal process possesses some block-structured property, including repeating rows. Duality conditions and properties are obtained on two probabilistic measures which often play a key role in the analysis and computations of such a block-structured process. The method used here unifies two different concepts of duality. Applications of duality are also provided, including a characteristic theorem concerning recurrence and transience of a transition matrix with repeating rows and a batch arrival queueing model.

ZERO-KNOWLEDGE BLACKBOX TESTING: WHERE ARE THE FAULTS?

2014 ◽  
Vol 25 (02) ◽  
pp. 195-217 ◽  
Author(s):  
ERIC WANG ◽  
CEWEI CUI ◽  
ZHE DANG ◽  
THOMAS R. FISCHER ◽  
LINMIN YANG
Keyword(s):  
Transition Probability ◽  
Quantitative Relationship ◽  
Entropy Rate ◽  
Maximal Entropy ◽  
Test Sequence ◽  
System Specification ◽  
Transition Matrices ◽  
Zero Knowledge ◽  
Entropy Principle ◽  
Probability Matrices

We derive a quantitative relationship between the maximal entropy rate achieved by a blackbox software system's specification graph, and the probability of faults Pnobtained by testing the system, as a function of the length n of a test sequence. By equating “blackbox” to the maximal entropy principle, we model the specification graph as a Markov chain that, for each distinct value of n, achieves the maximal entropy rate for that n. Hence the Markov transition probability matrices are not constant in n, but form a sequence of transition matrices T1,…, Tn. We prove that, for nontrivial specification graphs, the probability of finding faults goes asymptotically to zero as the test length n increases, regardless of the evolution of Tn. This implies that zero-knowledge testing is practical only for small n. We illustrate the result using a concrete example of a system specification graph for an autopilot control system, and plot its curve Pn.

scholarly journals Observables in terms of connection and curvature variables for Einstein’s equations with two commuting Killing vectors

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150350
Author(s):  
P. Kordas
Keyword(s):  
Transition Matrix ◽  
Momentum Density ◽  
Transition Matrices ◽  
Einstein’S Equations ◽  
Integrals Of Motion ◽  
Einstein's Equations ◽  
Killing Vectors ◽  
Klein Gordon ◽  
Quantum Operators ◽  
Energy And Momentum

Einstein’s equations with two commuting Killing vectors and the associated Lax pair are considered. The equations for the connection A ( ς , η , γ )= Ψ , γ Ψ −1 , where γ the variable spectral parameter are considered. A transition matrix T = A ( ς , η , γ ) A −1 ( ξ , η , γ ) for A is defined relating A at ingoing and outgoing light cones. It is shown that it satisfies equations familiar from integrable PDE theory. A transition matrix on ς = constant is defined in an analogous manner. These transition matrices allow us to obtain a hierarchy of integrals of motion with respect to time, purely in terms of the trace of a function of the connections g , ς g −1 and g , η g −1 . Furthermore, a hierarchy of integrals of motion in terms of the curvature variable B = A , γ A −1 , involving the commutator [ A (1), A (−1)], is obtained. We interpret the inhomogeneous wave equation that governs σ = lnN , N the lapse, as a Klein–Gordon equation, a dispersion relation relating energy and momentum density, based on the first connection observable and hence this first observable corresponds to mass. The corresponding quantum operators are ∂/∂ t , ∂/∂ z and this means that the full Poincare group is at our disposal.

MARKOV CHAIN AS A MATHEMATICAL MODEL OF BUILDING STRUCTURE WORKING UNDER LOAD

2017 ◽  
Vol 7 (1) ◽  
pp. 4-8
Author(s):  
Andrey N. DAVYDOV
Keyword(s):  
Mathematical Model ◽  
Markov Chain ◽  
Transition Matrix ◽  
Transition Probability ◽  
Probabilistic Method ◽  
External Factors ◽  
Numerical Characteristic ◽  
Building Structure ◽  
Structure Transition ◽  
Reliability Performance

Markov process as a probabilistic method for evaluation of the reliability of constructions is considered. The essence of the building structure transition from one state to another, from the infl uence of external factors is disassembled. The transition matrix as an analytical model of Markov chains to evaluate the reliability of the building structure is analyzed. Transition probability as a numerical characteristic of a mathematical model of the Markov chain is considered. A mathematical model of a building structure under load is described. Formulation of the problem to determine the assessment of the reliability performance of the building structure is proposed.

scholarly journals Computable bounds of an 𝓁²-spectral gap for discrete Markov chains with band transition matrices

2016 ◽  
Vol 53 (3) ◽  
pp. 946-952
Author(s):  
Loï Hervé ◽  
James Ledoux
Keyword(s):  
Convergence Rate ◽  
Markov Chains ◽  
Spectral Radius ◽  
Spectral Gap ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Geometric Ergodicity ◽  
Transition Matrices ◽  
Essential Spectral Radius ◽  
Band Transition

AbstractWe analyse the 𝓁²(𝜋)-convergence rate of irreducible and aperiodic Markov chains with N-band transition probability matrix P and with invariant distribution 𝜋. This analysis is heavily based on two steps. First, the study of the essential spectral radius ress(P|𝓁²(𝜋)) of P|𝓁²(𝜋) derived from Hennion’s quasi-compactness criteria. Second, the connection between the spectral gap property (SG2) of P on 𝓁²(𝜋) and the V-geometric ergodicity of P. Specifically, the (SG2) is shown to hold under the condition α0≔∑m=−NNlim supi→+∞(P(i,i+m)P*(i+m,i)1∕2<1. Moreover, ress(P|𝓁²(𝜋)≤α0. Effective bounds on the convergence rate can be provided from a truncation procedure.

Cheeger inequalities for absorbing Markov chains

2016 ◽  
Vol 48 (3) ◽  
pp. 631-647
Author(s):  
Gary Froyland ◽  
Robyn M. Stuart
Keyword(s):  
Markov Chains ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Transition Matrices ◽  
Stochastic Transition ◽  
Absorbing Markov Chains ◽  
Second Eigenvalue

Abstract We construct Cheeger-type bounds for the second eigenvalue of a substochastic transition probability matrix in terms of the Markov chain's conductance and metastability (and vice versa) with respect to its quasistationary distribution, extending classical results for stochastic transition matrices.

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