scholarly journals Dynamics from Multivariable Longitudinal Data

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Maria Vivien Visaya ◽  
David Sherwell
Keyword(s):  
Longitudinal Data ◽  
Transition Matrix ◽  
Multivalued Map ◽  
Two Dimensional ◽  
Time Step ◽  
Subshift Of Finite Type ◽  
Mathematical Properties ◽  
Dimensional State Space ◽  
The Right ◽  
Time Information

We introduce a method of analysing longitudinal data in n≥1 variables and a population of K≥1 observations. Longitudinal data of each observation is exactly coded to an orbit in a two-dimensional state space Sn. At each time, information of each observation is coded to a point (x,y)∈Sn, where x is the physical condition of the observation and y is an ordering of variables. Orbit of each observation in Sn is described by a map that dynamically rearranges order of variables at each time step, eventually placing the most stable, least frequently changing variable to the left and the most frequently changing variable to the right. By this operation, we are able to extract dynamics from data and visualise the orbit of each observation. In addition, clustering of data in the stable variables is revealed. All possible paths that any observation can take in Sn are given by a subshift of finite type (SFT). We discuss mathematical properties of the transition matrix associated to this SFT. Dynamics of the population is a nonautonomous multivalued map equivalent to a nonstationary SFT. We illustrate the method using a longitudinal data of a population of households from Agincourt, South Africa.

scholarly journals Numerical simulation of two-dimensional laminar unsteady flow past a right trapezoidal cylinder at low Reynolds number: study of sharpening angle, time step, grid independence and domain size

2018 ◽  
Vol 192 ◽  
pp. 02030
Author(s):  
Sodsai Lamtharn ◽  
Monsak Pimsarn
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Unsteady Flow ◽  
Strouhal Number ◽  
Domain Size ◽  
Two Dimensional ◽  
Time Step ◽  
Flow Past ◽  
The Right ◽  
Grid Independence

Numerical simulation of two-dimensional laminar unsteady flow past a right trapezoidal cylinder at low Reynolds number (Re = 100), zero of the flow approaching angle and sharpening angle of the right trapezoidal of 22.5° with a side ratio B/A = 1 are carried out to provide moreapplicable data for engineering design of barred tee in aspect of structural integrity. A finite volume method, non-uniform meshing with second-order implicit time discretization into eight-node quadratic quadrilateral finite elements is employed. An incompressible flow SIMPLEC code with constant fluid properties is used. The convective terms using a third-order QUICK scheme. The numerical simulation result is compared against the published results of flow past a square cylinder. The effect of sharpening angle on the response of the right trapezoidal cylinder is investigated. A special study of the effects of flow on significant factor for time step, grid independence, blockage ratio, domain size, upstream and downstream extents, size domain next to cylinder and size domain extent are performed systematically. The Strouhal number and RMS lift coefficients of fully saturated flow are calculated. The result shown that increasing of sharpening angle, the Strouhal number is negligible changed whilst the RMS lift coefficients significantly increased.

Equilibrium distribution of block-structured Markov chains with repeating rows

1990 ◽  
Vol 27 (03) ◽  
pp. 557-576 ◽  
Author(s):  
Winfried K. Grassmann ◽  
Daniel P. Heyman
Keyword(s):  
General Theory ◽  
Markov Chains ◽  
Boundary Conditions ◽  
Transition Matrix ◽  
Equilibrium Distribution ◽  
Two Dimensional ◽  
Block Form ◽  
The Right ◽  
Block Structured

In this paper we consider two-dimensional Markov chains with the property that, except for some boundary conditions, when the transition matrix is written in block form, the rows are identical except for a shift to the right. We provide a general theory for finding the equilibrium distribution for this class of chains. We illustrate theory by showing how our results unify the analysis of the M/G/1 and GI/M/1 paradigms introduced by M. F. Neuts.

Equilibrium distribution of block-structured Markov chains with repeating rows

1990 ◽  
Vol 27 (3) ◽  
pp. 557-576 ◽  
Author(s):  
Winfried K. Grassmann ◽  
Daniel P. Heyman
Keyword(s):  
General Theory ◽  
Markov Chains ◽  
Boundary Conditions ◽  
Transition Matrix ◽  
Equilibrium Distribution ◽  
Two Dimensional ◽  
Block Form ◽  
The Right ◽  
Block Structured

In this paper we consider two-dimensional Markov chains with the property that, except for some boundary conditions, when the transition matrix is written in block form, the rows are identical except for a shift to the right. We provide a general theory for finding the equilibrium distribution for this class of chains. We illustrate theory by showing how our results unify the analysis of the M/G/1 and GI/M/1 paradigms introduced by M. F. Neuts.

scholarly journals On local and integrated stress-tensor commutators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys
Keyword(s):  
Stress Tensor ◽  
Free Field ◽  
Virasoro Algebra ◽  
Light Sheet ◽  
Operator Product ◽  
Local Form ◽  
Two Dimensional ◽  
Conformal Embedding ◽  
General Aspects ◽  
The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

scholarly journals A two-dimensional glacier–fjord coupled model applied to estimate submarine melt rates and front position changes of Hansbreen, Svalbard

2018 ◽  
Vol 64 (247) ◽  
pp. 745-758 ◽  
Author(s):  
E. DE ANDRÉS ◽  
J. OTERO ◽  
F. NAVARRO ◽  
A. PROMIŃSKA ◽  
J. LAPAZARAN ◽  
...  
Keyword(s):  
Coupled Model ◽  
Small Scale ◽  
Two Dimensional ◽  
Time Step ◽  
Software Packages ◽  
Front Position ◽  
Circulation Patterns ◽  
Glacier Front ◽  
Order Of Magnitude ◽  
Frontal Ablation

ABSTRACTWe have developed a two-dimensional coupled glacier–fjord model, which runs automatically using Elmer/Ice and MITgcm software packages, to investigate the magnitude of submarine melting along a vertical glacier front and its potential influence on glacier calving and front position changes. We apply this model to simulate the Hansbreen glacier–Hansbukta proglacial–fjord system, Southwestern Svalbard, during the summer of 2010. The limited size of this system allows us to resolve some of the small-scale processes occurring at the ice–ocean interface in the fjord model, using a 0.5 s time step and a 1 m grid resolution near the glacier front. We use a rich set of field data spanning the period April–August 2010 to constrain, calibrate and validate the model. We adjust circulation patterns in the fjord by tuning subglacial discharge inputs that best match observed temperature while maintaining a compromise with observed salinity, suggesting a convectively driven circulation in Hansbukta. The results of our model simulations suggest that both submarine melting and crevasse hydrofracturing exert important controls on seasonal frontal ablation, with submarine melting alone not being sufficient for reproducing the observed patterns of seasonal retreat. Both submarine melt and calving rates accumulated along the entire simulation period are of the same order of magnitude, ~100 m. The model results also indicate that changes in submarine melting lag meltwater production by 4–5 weeks, which suggests that it may take up to a month for meltwater to traverse the englacial and subglacial drainage network.

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

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