Analytical Approximations For Sitnikov’s Problem

1995 ◽  
pp. 513-523 ◽  
Author(s):  
Karl Wodnar
Keyword(s):  
Analytical Approximations

scholarly journals Simulation modeling and analysis of primary health center operations

SIMULATION ◽  
2021 ◽  
pp. 003754972110309
Author(s):  
Mohd Shoaib ◽  
Varun Ramamohan
Keyword(s):  
Resource Utilization ◽  
Waiting Times ◽  
Discrete Event ◽  
Simulation Models ◽  
Modeling And Analysis ◽  
Healthcare Facilities ◽  
Event Simulation ◽  
Analytical Approximations ◽  
Primary Health ◽  
Generic Modeling

We present discrete-event simulation models of the operations of primary health centers (PHCs) in the Indian context. Our PHC simulation models incorporate four types of patients seeking medical care: outpatients, inpatients, childbirth cases, and patients seeking antenatal care. A generic modeling approach was adopted to develop simulation models of PHC operations. This involved developing an archetype PHC simulation, which was then adapted to represent two other PHC configurations, differing in numbers of resources and types of services provided, encountered during PHC visits. A model representing a benchmark configuration conforming to government-mandated operational guidelines, with demand estimated from disease burden data and service times closer to international estimates (higher than observed), was also developed. Simulation outcomes for the three observed configurations indicate negligible patient waiting times and low resource utilization values at observed patient demand estimates. However, simulation outcomes for the benchmark configuration indicated significantly higher resource utilization. Simulation experiments to evaluate the effect of potential changes in operational patterns on reducing the utilization of stressed resources for the benchmark case were performed. Our analysis also motivated the development of simple analytical approximations of the average utilization of a server in a queueing system with characteristics similar to the PHC doctor/patient system. Our study represents the first step in an ongoing effort to establish the computational infrastructure required to analyze public health operations in India and can provide researchers in other settings with hierarchical health systems, a template for the development of simulation models of their primary healthcare facilities.

scholarly journals Fluxes and Metabolic Pools as Model Traits for Quantitative Genetics. I. The L-Shaped Distribution of Gene Effects

Genetics ◽  
1999 ◽  
Vol 153 (4) ◽  
pp. 2001-2012 ◽  
Author(s):  
Bruno Bost ◽  
Christine Dillmann ◽  
Dominique de Vienne
Keyword(s):  
Enzyme Activity ◽  
Metabolic Pathways ◽  
Quantitative Traits ◽  
Intrinsic Property ◽  
Gene Effects ◽  
Analytical Approximations ◽  
Mean And Variance ◽  
The Individual ◽  
Metabolic Control Theory ◽  
Control Coefficients

Abstract The fluxes through metabolic pathways can be considered as model quantitative traits, whose QTL are the polymorphic loci controlling the activity or quantity of the enzymes. Relying on metabolic control theory, we investigated the relationships between the variations of enzyme activity along metabolic pathways and the variations of the flux in a population with biallelic QTL. Two kinds of variations were taken into account, the variation of the average enzyme activity across the loci, and the variation of the activity of each enzyme of the pathway among the individuals of the population. We proposed analytical approximations for the flux mean and variance in the population as well as for the additive and dominance variances of the individual QTL. Monte Carlo simulations based on these approximations showed that an L-shaped distribution of the contributions of individual QTL to the flux variance (R2) is consistently expected in an F2 progeny. This result could partly account for the classically observed L-shaped distribution of QTL effects for quantitative traits. The high correlation we found between R2 value and flux control coefficients variance suggests that such a distribution is an intrinsic property of metabolic pathways due to the summation property of control coefficients.

A Simple Analytical Tool for Legged Robot Design

2012 ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Analytical Solutions ◽  
Inverted Pendulum ◽  
Legged Locomotion ◽  
Robot Design ◽  
Slip Model ◽  
Legged Robot ◽  
Biologically Relevant ◽  
Analytical Approximations ◽  
Energy Conserving ◽  
Spring Loaded Inverted Pendulum

Although legged locomotion is better at tackling complicated terrains compared with wheeled locomotion, legged robots are rare, in part, because of the lack of simple design tools. The dynamics governing legged locomotion are generally nonlinear and hybrid (piecewise-continuous) and so require numerical simulation for analysis and are not easily applied to robot designs. During the past decade, a few approximated analytical solutions of Spring-Loaded Inverted Pendulum (SLIP), a canonical model in legged locomotion, have been developed. However, SLIP is energy conserving and cannot predict the dynamical stability of real-world legged locomotion. To develop new analytical tools for legged robot designs, we first analytically solved SLIP in a new way. Then based on SLIP solution, we developed an analytical solution of a hip-actuated Spring-Loaded Inverted Pendulum (hip-actuated-SLIP) model, which is more biologically relevant and stable than the canonical energy conserving SLIP model. The analytical approximations offered here for SLIP and the hip actuated-SLIP solutions compare well with the numerical simulations of each. The analytical solutions presented here are simpler in form than those resulting from existing analytical approximations. The analytical solutions of SLIP and the hip actuated-SLIP can be used as tools for robot design or for generating biological hypotheses.

Heat Transfer in Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

1978 ◽  
Vol 100 (2) ◽  
pp. 224-229 ◽  
Author(s):  
O. T. Hanna ◽  
O. C. Sandall
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Analytical Approximations ◽  
Constant Viscosity ◽  
Dependent Viscosity

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

Analytical approximations to the Lambert W function

2021 ◽  
Author(s):  
Baisheng Wu ◽  
Yixin Zhou ◽  
C.W. Lim ◽  
Huixiang Zhong
Keyword(s):  
Lambert W Function ◽  
Analytical Approximations

Recursive Linearization of Multibody Dynamics and Application to Control Design

1990 ◽  
Author(s):  
Tsung-Chieh Lin ◽  
K. Harold Yae
Keyword(s):  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Control Design ◽  
Numerical Differentiation ◽  
Difficult Problem ◽  
Computational Method ◽  
Computational Error ◽  
Dynamics Modeling ◽  
Analytical Approximations

Abstract The non-linear equations of motion in multi-body dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.

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