On a mathematical model of age-cycle length structured cell population with non-compact boundary conditions

This paper focuses on development of a new mathematical model and its analytical solution for buckling analysis of elastic columns weakened simultaneously with transverse open cracks and partial longitudinal delamination. Consequently, the analytical solution for buckling loads is derived for the first time. The critical buckling loads are calculated using the proposed analytical model. A parametric study is performed to investigate the effects of transverse crack location and magnitude, length and degree of partial longitudinal delamination, and different boundary conditions on critical buckling loads of weakened columns. It is shown that the critical buckling loads of weakened columns can be greatly affected by all the analyzed parameters. Finally, the presented results can be used as a benchmark solution.

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A Branching Process to Characterize the Dynamics of Stem Cell Differentiation

10.1101/016295 ◽

2015 ◽

Cited By ~ 1

Author(s):

david miguez

Keyword(s):

Mathematical Model ◽

Cell Cycle ◽

Stem Cell ◽

Cycle Length ◽

Branching Process ◽

Stem Cell Differentiation ◽

Stem Cell Population ◽

Mathematical Framework ◽

Average Cell ◽

Cell Cycle Length

The understanding of the regulatory processes that orchestrate stem cell maintenance is a cornerstone in developmental biology. Here, we present a mathematical model based on a branching process formalism that predicts average rates of proliferative and differentiative divisions in a given stem cell population. In the context of vertebrate spinal neurogenesis, the model predicts complex non-monotonic variations in the rates of pp, pd and dd modes of division as well as in cell cycle length, in agreement with experimental results. Moreover, the model shows that the differentiation probability follows a binomial distribution, allowing us to develop equations to predict the rates of each mode of division. A phenomenological simulation of the developing spinal cord informed with the average cell cycle length and division rates predicted by the mathematical model reproduces the correct dynamics of proliferation and differentiation in terms of average numbers of progenitors and differentiated cells. Overall, the present mathematical framework represents a powerful tool to unveil the changes in the rate and mode of division of a given stem cell pool by simply quantifying numbers of cells at different times.

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Influence of Nano-Fluid Lubrication On Single Porous-Layered Journal Bearing: A Hypothetical Approach

10.21203/rs.3.rs-225735/v1 ◽

2021 ◽

Author(s):

BIPLAB BHATTACHARJEE ◽

PRASUN CHAKRABORTI ◽

KISHAN CHOUDHURY

Keyword(s):

Mathematical Model ◽

Boundary Conditions ◽

Micropolar Fluid ◽

Journal Bearing ◽

Performance Characteristics ◽

Published Data ◽

Nano Fluid ◽

Nano Lubricant ◽

Output Characteristics ◽

Modified Darcy’S Law

Abstract In this article a mathematical model of single layered nano-fluid lubricated PJB (porous journal bearing) has been formulated. The nano-lubricant's impact on the efficiency of said journal bearing has been studied using modified Darcy's law and boundary conditions. The different nanoparticles often used as an additive in industrial lubricating oils improve their viscosity significantly. The brief description of dimensionless performance characteristics of the investigated bearing was obtained by the use of the nano-lubricant's modified Krieger-Dougherty viscosity model. The observations revealed that the output characteristics are substantially improved by using nano-lubricant. The present study was validated by comparing the findings of recently published data with micropolar fluid and was found to be completely compatible since data with nano-lubricant are still unavailable.

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A Mathematical Model for Bone Cell Population Dynamics of Fracture Healing Considering the Effect of Energy Dissipation

10.1007/978-3-030-42707-8_3 ◽

2021 ◽

pp. 33-52

Author(s):

Mahziyar Darvishi ◽

Hooman Dadras ◽

Mohammad Mahmoodi Gahrouei ◽

Kiarash Tabesh ◽

Dmitry Timofeev

Keyword(s):

Mathematical Model ◽

Population Dynamics ◽

Energy Dissipation ◽

Fracture Healing ◽

Cell Population ◽

Bone Cell ◽

Cell Population Dynamics

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Lamb waves in multilayered media: 3D and 6D formalisms

E3S Web of Conferences ◽

10.1051/e3sconf/20199703003 ◽

2019 ◽

Vol 97 ◽

pp. 03003

Author(s):

Anna Avershyeva ◽

Sergey Kuznetsov

Keyword(s):

Mathematical Model ◽

Boundary Conditions ◽

Fundamental Matrix ◽

Elastic Anisotropy ◽

Lamb Waves ◽

Stratified Media ◽

Multilayered Media ◽

Different Types ◽

Secular Equations ◽

Fundamental Matrices

A mathematical model for analyzing Lamb waves propagating in stratified media with arbitrary elastic anisotropy is worked out. The model incorporates a combined Fundamental Matrix (FM) and Modified Transfer Matrix (MTM) methods. Multilayered unbounded plates with different types of boundary conditions imposed on the outer surfaces are considered. Closed form fundamental matrices and secular equations for dispersion relations are derived.

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