COMPUTER SIMULATION FOR THE CROSSING TIME IN A DIPLOID, ASYMMETRIC, SHARPLY-PEAKED LANDSCAPE IN THE INFINITE POPULATION LIMIT

2013 ◽  
Vol 24 (01) ◽  
pp. 1250091 ◽  
Author(s):  
WONPYONG GILL
Keyword(s):  
Computer Simulation ◽  
Steady State ◽  
Selective Advantage ◽  
Sequence Length ◽  
Initial State ◽  
Infinite Population ◽  
Crossing Time ◽  
Increasing Function ◽  
Fitness Parameter ◽  
Extension Parameter

This study calculated the crossing time in the diploid mutation–selection model in an infinite population limit for various dominance parameters, h, and selective advantages, by switching on a diploid, asymmetric, sharply-peaked landscape, from an initial state which is the steady state in a diploid, sharply-peaked landscape. The crossing time for h < 1 was found to diverge at the critical fitness parameter, which increased with increasing selective advantage and decreased with increasing sequence length. When the sequence length was increased with a fixed extension parameter, there was no crossing time for h < 1 when the sequence length was longer than the critical sequence length, which increased with increasing selective advantage. The crossing time for h ≤ 1 was found to be an exponentially increasing function of the sequence length, and the crossing time for h > 1 became saturated at a long sequence length. The crossing time decreased with increasing selective advantage, mainly because the larger selective advantage caused the increase in relative density of the reversal allele to grow exponentially at an earlier time.

CALCULATION OF THE RELATIVE DENSITY AND THE CROSSING TIME THROUGH THE FITNESS BARRIER IN AN ASYMMETRIC SHARPLY-PEAKED LANDSCAPE

2007 ◽  
Vol 18 (12) ◽  
pp. 1985-1996 ◽  
Author(s):  
KWANG SUNG LEE ◽  
WONPYONG GILL
Keyword(s):  
Relative Density ◽  
Stationary State ◽  
Sequence Length ◽  
Initial State ◽  
Length Increase ◽  
Crossing Time ◽  
State Formula ◽  
Simulation Results ◽  
Increasing Function ◽  
Fitness Parameter

We have calculated the relative density and crossing time through the fitness barrier by switching on an asymmetric sharply-peaked landscape, from the initial state which is the quasispecies in a sharply-peaked landscape. It is found that the increment of the relative density with the reversal sequence is a linearly increasing function of time unless a new stationary state in an asymmetric sharply-peaked landscape is reached. It is also found that the relative density with the reversal sequence at the new stationary state [Formula: see text] is in inverse proportion to the asymmetric parameter when the asymmetric parameter is greater than the saturation asymmetric parameter. We have derived the approximate formulae for the relaxation time, the saturation asymmetric parameter, and the relative density with the reversal sequence [Formula: see text], which nicely fit computer simulation results. It is found that the crossing time diverges at the critical fitness parameter in the asymmetric sharply-peaked landscape, in contrast with the symmetric sharply-peaked landscape where the crossing time scales as a power law in the fitness parameter. It is also found that the critical fitness parameter decreases as the asymmetric parameter and sequence length increase.

scholarly journals Computer simulation for the growing probability of additional offspring with an advantageous reversal allele in the decoupled continuous-time mutation–selection model

2016 ◽  
Vol 27 (06) ◽  
pp. 1650070
Author(s):  
Wonpyong Gill
Keyword(s):  
Computer Simulation ◽  
Continuous Time ◽  
Selective Advantage ◽  
Selection Model ◽  
Sequence Length ◽  
Theoretical Formula ◽  
Fitness Parameters ◽  
Population Sizes ◽  
Fitness Parameter ◽  
Allele Model

This study calculated the growing probability of additional offspring with the advantageous reversal allele in an asymmetric sharply-peaked landscape using the decoupled continuous-time mutation–selection model. The growing probability was calculated for various population sizes, N, sequence lengths, L, selective advantages, s, fitness parameters, k and measuring parameters, C. The saturated growing probability in the stochastic region was approximately the effective selective advantage, [Formula: see text], when [Formula: see text] and [Formula: see text]. The present study suggests that the growing probability in the stochastic region in the decoupled continuous-time mutation–selection model can be described using the theoretical formula for the growing probability in the Moran two-allele model. The selective advantage ratio, which represents the ratio of the effective selective advantage to the selective advantage, does not depend on the population size, selective advantage, measuring parameter and fitness parameter; instead the selective advantage ratio decreases with the increasing sequence length.

CALCULATION OF THE CROSSING TIME THROUGH THE FITNESS BARRIER IN A SYMMETRIC MULTIPLICATIVE LANDSCAPE

2005 ◽  
Vol 16 (01) ◽  
pp. 85-97 ◽  
Author(s):  
DOKYOON KIM ◽  
WONPYONG GILL
Keyword(s):  
Computer Simulation ◽  
Mutation Rate ◽  
Approximate Formula ◽  
Mutation Rates ◽  
Sequence Length ◽  
Crossing Time ◽  
Fitness Parameters ◽  
Time Region ◽  
Simulation Results ◽  
Fitness Parameter

The crossing time through fitness barrier in a symmetric multiplicative landscape is systematically calculated for various mutation rates, fitness parameters, and sequence lengths by using a computer simulation. It is found that the crossing time scales as a power law in the mutation rate and the fitness parameter. It is also found that the crossing time increases exponentially as the sequence length increases. We have obtained the approximate formula, which decribes the asymptotic behavior of the crossing time in the long-crossing-time region, and the improved approximate formula with the correction factor, which nicely fit computer simulation results even below the long-crossing-time region. From the comparison between the approximate formula in the multiplicative landscape and the approximate formula in the sharply-peaked landscape, it is found that both landscapes have the same scaling effect of fitness parameter and mutation rate on the crossing time in the long-crossing-time region.

CROSSING TIME THROUGH THE FITNESS BARRIER IN AN ASYMMETRIC MULTIPLICATIVE OR ADDITIVE LANDSCAPE IN THE MUTATION-SELECTION MODEL

2011 ◽  
Vol 22 (11) ◽  
pp. 1293-1307 ◽  
Author(s):  
WONPYONG GILL
Keyword(s):  
Continuous Time ◽  
Finite Population ◽  
Selection Model ◽  
Sequence Length ◽  
Continuous Time Model ◽  
Time Model ◽  
Discrete Time Model ◽  
Infinite Population ◽  
Crossing Time ◽  
Extension Parameter

This study examines the dependence of crossing time on sequence length for a finite population in an asymmetric multiplicative, or additive, landscape with a positive asymmetric parameter and a fixed extension parameter in three types of mutation-selection model: the coupled discrete-time model, the coupled continuous-time model, and the decoupled continuous-time model. The crossing times for a finite population in the three types of mutation-selection model began to deviate from the crossing times for an infinite population at a critical sequence length. It then increased exponentially as a function of sequence length in the stochastic region where the sequence length was much longer than the critical sequence length. The exponentially increasing rates of the crossing times in the three types of mutation-selection model were similar to each other. These rates were decreased by increasing the asymmetric parameter. Once the asymmetric parameter reached a certain limit the crossing times for the three models in the stochastic region could not be decreased further by increasing the asymmetric parameter past this limit.

Molecular Dynamics Study of Cohesionless Granular Materials: Size Segregation by Shaking

1993 ◽  
Vol 07 (09n10) ◽  
pp. 1865-1872 ◽  
Author(s):  
Toshiya OHTSUKI ◽  
Yoshikazu TAKEMOTO ◽  
Tatsuo HATA ◽  
Shigeki KAWAI ◽  
Akihisa HAYASHI
Keyword(s):  
Molecular Dynamics ◽  
Steady State ◽  
Specific Gravity ◽  
Pressure Gradient ◽  
Granular Materials ◽  
Buoyancy Force ◽  
Temporal Evolution ◽  
Particle Radius ◽  
Size Segregation ◽  
Increasing Function

The Molecular Dynamics technique is used to investigate size segregation by shaking in cohesionless granular materials. Temporal evolution of the height h of the tagged particle with different size and mass is measured for various values of the particle radius and specific gravity. It becomes evident that h approaches the steady state value h∞ independent of initial positions. There exists a threshold of the specific gravity of the particle. Below the threshold, h∞ is an increasing function of the particle size, whereas above it, h∞ decreases with increasing the particle radius. The relaxation time τ towards the steady state is calculated and its dependence on the particle radius and specific gravity is clarified. The pressure gradient of pure systems is also measured and turned out to be almost constant. This suggests that the buoyancy force due to the pressure gradient is not responsible to h∞.

Dynamic Stability of an Impact System Connected With Rock Drilling

1969 ◽  
Vol 36 (4) ◽  
pp. 743-749 ◽  
Author(s):  
C. C. Fu
Keyword(s):  
Computer Simulation ◽  
Exact Solution ◽  
Steady State ◽  
Asymptotic Stability ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
External Excitation ◽  
Rock Drilling ◽  
Impact System ◽  
Number Of Cycles

This paper deals with asymptotic stability of an analytically derived, synchronous as well as nonsynchronous, steady-state solution of an impact system which exhibits piecewise linear characteristics connected with rock drilling. The exact solution, which assumes one impact for a given number of cycles of the external excitation, is derived, its asymptotic stability is examined, and ranges of parameters are determined for which asymptotic stability is assured. The theoretically predicted stability or instability is verified by a digital computer simulation.

The Numerical Analysis of Temperature Field During Moveable Induction Heating of Steel Plate

2012 ◽  
Vol 28 (02) ◽  
pp. 73-81
Author(s):  
Xue-biao Zhang ◽  
Yu-long Yang ◽  
Yu-jun Liu
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Numerical Model ◽  
Induction Heating ◽  
Temperature Difference ◽  
Steel Plate ◽  
Heating Process ◽  
Quasi Steady State ◽  
Initial State ◽  
Plate Temperature

In shipyards, hull curved plate formation is an important stage with respect to productivity and accuracy control of curved plates. Because the power and its distribution of induction heat source are easier to control and reproduce, induction heating is expected to be applied in the line heating process. This paper studies the moveable induction heating process of steel plate and develops a numerical model of electromagneticthermal coupling analysis and the numerical results consistent with the experimental results. The numerical model is used to analyze the temperature changing rules and the influences on plate temperature field of heating speed of moveable induction heating of steel plate, and the following conclusions are drawn. First, the process of moveable induction heating of steel plate can be divided into three phases of initial state, quasi-steady state, and end state. The temperature difference between the top and bottom surfaces of the steel plate at the initial state is the biggest; it remains unchanged at the quasi-steady state and it is the smallest at the end state. Second, obvious end effect occurs when the edges of the steel plate are heated by the inductor, which causes a decrease in temperature difference between the top and bottom surfaces of the steel plate that is unfavorable for formation of pillow shape plates. Third, with the increase of heating speed, the temperature difference between the top and bottom surfaces of the steel plate increases gradually.

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