The Classical Model

2009 ◽  
pp. 159-174
Author(s):  
Farrokh K. Langdana
Keyword(s):  
Classical Model

A semi-classical model of regular inflationary cosmology

2021 ◽  
pp. 100823
Author(s):  
Biplab Paik ◽  
M.Yu. Khlopov ◽  
Mehedi Kalam ◽  
Saibal Ray
Keyword(s):  
Classical Model ◽  
Inflationary Cosmology

scholarly journals An Incompressible Polymer Fluid Interacting with a Koiter Shell

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Dominic Breit ◽  
Prince Romeo Mensah
Keyword(s):  
Moving Boundary ◽  
Classical Model ◽  
Elastic Shell ◽  
Planck Equation ◽  
Navier Stokes ◽  
Flexible Shell ◽  
Navier Stokes Equation ◽  
Shell System ◽  
Forward Equation ◽  
Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

scholarly journals The limits of normal approximation for adult height

2021 ◽  
Author(s):  
Sergei A. Slavskii ◽  
Ivan A. Kuznetsov ◽  
Tatiana I. Shashkova ◽  
Georgii A. Bazykin ◽  
Tatiana I. Axenovich ◽  
...  
Keyword(s):  
Complex Traits ◽  
Adult Height ◽  
Normal Approximation ◽  
Classical Model ◽  
Model Complexity ◽  
Test Case ◽  
Genetic Studies ◽  
Quantitative Genetic ◽  
Profound Influence ◽  
Log Normal

AbstractAdult height inspired the first biometrical and quantitative genetic studies and is a test-case trait for understanding heritability. The studies of height led to formulation of the classical polygenic model, that has a profound influence on the way we view and analyse complex traits. An essential part of the classical model is an assumption of additivity of effects and normality of the distribution of the residuals. However, it may be expected that the normal approximation will become insufficient in bigger studies. Here, we demonstrate that when the height of hundreds of thousands of individuals is analysed, the model complexity needs to be increased to include non-additive interactions between sex, environment and genes. Alternatively, the use of log-normal approximation allowed us to still use the additive effects model. These findings are important for future genetic and methodologic studies that make use of adult height as an exemplar trait.

A new look at the simple epidemic process

1979 ◽  
Vol 16 (01) ◽  
pp. 198-202 ◽  
Author(s):  
L. Billard ◽  
H. Lacayo ◽  
N. A. Langberg
Keyword(s):  
Waiting Times ◽  
Classical Model ◽  
Epidemic Models ◽  
Underlying Structure ◽  
Epidemic Process ◽  
Insight Into ◽  
New Look

Classical epidemic models have invariably proved to be mathematically intractable. By considering the distribution of the number of infectives in a simple epidemic process as a convolution of exponential waiting times, the solution to the classical model is obtained easily giving more insight into the underlying structure. The idea can be extended to other simple epidemic models.

Dynamical Analysis of bantam-Regulated Drosophila Circadian Rhythm Model

2014 ◽  
Vol 24 (12) ◽  
pp. 1450161 ◽  
Author(s):  
Ying Li ◽  
Zengrong Liu
Keyword(s):  
Circadian Rhythm ◽  
Crucial Role ◽  
Target Genes ◽  
Classical Model ◽  
Dynamical Analysis ◽  
Biological Processes ◽  
Biological Mechanisms ◽  
Environmental Perturbations ◽  
Dynamical Behaviors ◽  
Important Regulator

MicroRNAs (miRNAs) interact with 3′untranslated region (UTR) elements of target genes to regulate mRNA stability or translation, and play a crucial role in regulating many different biological processes. bantam, a conserved miRNA, is involved in several functions, such as regulating Drosophila growth and circadian rhythm. Recently, it has been discovered that bantam plays a crucial role in the core circadian pacemaker. In this paper, based on experimental observations, a detailed dynamical model of bantam-regulated circadian clock system is developed to show the post-transcriptional behaviors in the modulation of Drosophila circadian rhythm, in which the regulation of bantam is incorporated into a classical model. The dynamical behaviors of the model are consistent with the experimental observations, which shows that bantam is an important regulator of Drosophila circadian rhythm. The sensitivity analysis of parameters demonstrates that with the regulation of bantam the system is more sensitive to perturbations, indicating that bantam regulation makes it easier for the organism to modulate its period against the environmental perturbations. The effectiveness in rescuing locomotor activity rhythms of mutated flies shows that bantam is necessary for strong and sustained rhythms. In addition, the biological mechanisms of bantam regulation are analyzed, which may help us more clearly understand Drosophila circadian rhythm regulated by other miRNAs.

scholarly journals Bearing and Range Estimation Algorithm for Buried Object in Underwater Acoustics

2009 ◽  
Vol 2009 ◽  
pp. 1-4
Author(s):  
Dong Han ◽  
Caroline Fossati ◽  
Salah Bourennane ◽  
Zineb Saidi
Keyword(s):  
Underwater Acoustics ◽  
Classical Model ◽  
Acoustic Scattering ◽  
Estimation Algorithm ◽  
Signal Classification ◽  
Music Algorithm ◽  
Range Estimation ◽  
Multiple Signal Classification ◽  
Buried Objects ◽  
Buried Object

A new algorithm which associates (Multiple Signal Classification) MUSIC with acoustic scattering model for bearing and range estimation is proposed. This algorithm takes into account the reflection and the refraction of wave in the interface of water-sediment in underwater acoustics. A new directional vector, which contains the Direction-Of-Arrival (DOA) of objects and objects-sensors distances, is used in MUSIC algorithm instead of classical model. The influence of the depth of buried objects is discussed. Finally, the numerical results are given in the case of buried cylindrical shells.

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