arXiv subjects

Kavinda Jayawardana

Publications and source records attributed to Kavinda Jayawardana.

8 recordsLinked to original sources

arXiv2026

Exponential Sigmoid Equation for Modelling Cell Growth in a Confined Space, Log-Normal Distribution for Modelling Cell Area Distribution of Dense Colonies and Other Methods

Based on the growth patterns of 166 CHO monoclones observed over a 15 day period, we show that the standard population growth in a confined space equation, i.e. the sigmoid/logistic function, is alone does not capture the complex behaviour of the cell growth in a confined space. Thus, combining the sigmoid function and the exponential of the sigmoid function, we present a more accurate model for modelling cell growth in a confined space. We also present a working algorithm to obtain population growth variables (growth capacity, growth time and growth rate), model the growth patterns of the CHO monoclones, and we include subset of the dataset, along with a sample python script for the reader to replicate the results. Furthermore, we derive a model for cell confluence growth in a confined space, numerically model the confluence and present the reader with a working algorithm. With Kolmogorov-Smirnov analysis conducted on the area of the CHO monoclones, we show that the cell area of the incipient population is normally distributed, the sparse cell population is gamma distributed and the dense colony population is log-normally distributed. Thus, we further derive models for the mean, the standard deviation, the coefficient of variation and the inverse coefficient of variation for the log cell area growth in a confined space, numerically model them and present the reader with working algorithms. Finally, based on the growth patterns of another 48 CHO monoclones observed over a 16 day period, and their titer and viability measurements, we find the correlation coefficients with our calculated growth variables, and titer and viability measurements, and show that our derived growth variables can be used to predict the productivity and the health of a cell. Thus, we conclude our study by demonstrating that the productivity and the health of a cell (also the overall population) are interdependent.

q-bio.QM↗

arXiv2023

A Shell Bonded to an Elastic Foundation and the Existence of Optimal Elastic and Geometric Conditions for the Membrane Case

In this article, we derive a mathematical model for a shell (i.e. a thin elastic body) bonded to an elastic foundation by modifying Koiter's linear shell equations. We prove the existence and the uniqueness of solutions, and we explicitly derive the governing equations and the boundary conditions for the general case. Finally, with numerical modelling and asymptotic analysis, we show that there exist optimal values for the Young's modulus, the Poisson's ratio and the thickness of the shell (relative to the elastic foundation), and the radius of curvature of the contact region such that the planar solution derived by the shell model (i.e. the membrane case, where stretching effects are dominant) results in a good approximation of the thin body. It is often regarded in the field of stretchable and flexible electronics that the planar solution is mostly accurate when the thin body (i.e. the shell or the membrane) is relatively stiffer (i.e. has a high Young's modulus) than the thicker foundation. As far as we are aware, this is the first analysis showing that for a membrane (or the planar solution of a shell) bonded to an elastic foundation, higher stiffness (relative to the elastic foundation's stiffness) alone would not guarantee a more accurate solution.

math.AP↗

arXiv2023

A Shell Frictionally Coupled to an Elastic Foundation and a Comparison Against the Two-Body Coulomb's Law of Static Friction

In this article, we derive a model for a shell that is frictionally coupled to an elastic foundation. We use Kikuchi and Oden's model for Coulomb's law of static friction to derive a displacement-based static-friction law for a shell on an elastic foundation model, and we prove the existence and the uniqueness of solutions with the aid of the work of Kinderlehrer and Stampacchia. For numerical analysis, we modify Kikuchi and Oden's model for Coulomb's law of static friction to model a full two-body contact problem in curvilinear coordinates. Our numerical results indicate that if the shell has a relatively high Young's modulus or has a relatively high Poisson's ratio, and the contact region has a high coefficient of friction or has a high radius of curvature, then the displacement field of the foundation predicted by both models are in better agreement. As far as we are aware, this is the first derivation of a displacement-based friction law and a two-body 3D elasticity contact problem with friction in the literature.

physics.class-ph↗

arXiv2023

A Generalisation of the Capstan Equation and a Comparison Against Kikuchi and Oden's Model for Coulomb's Law of Static Friction

In this article, we extend the capstan equation to non-circular geometries. We derive a closed form solution for a membrane with a zero Poisson's ratio (or a string with an arbitrary Poisson's ratio) supported by a rigid prism (at limiting-equilibrium case and in steady-equilibrium case) or supported by a rigid general cone (at limiting-equilibrium case only). Our models indicate that the stress profile of the elastic body depends on the change in curvature of the rigid obstacle at the contact region. As a comparison, we extend Kikuchi and Oden's model for Coulomb's law of static friction to curvilinear coordinates, and conduct numerical experiments to examine the properties of Coulomb's law of static friction implied by Kikuchi and Oden's model in curvilinear coordinates and implied by our generalised capstan equation. Our numerical results indicate that for a fixed coefficient of friction, the frictional force is independent of the Young's modulus of the elastic body, and increasing the curvature, increasing the Poisson's ratio and decreasing the thickness of the elastic body increases the frictional force. Our analysis also shows that for given a tension ratio, the coefficient of friction inferred by each model is different, indicating that the implied-coefficient of friction is model dependent.

physics.class-ph↗

arXiv2021

A Critical Study of Baldelli and Bourdin's On the Asymptotic Derivation of Winkler-Type Energies From 3D Elasticity

In our analysis, we show that Baldelli and Bourdin's work is only valid when describing the behaviour of a film bonded to an elastic pseudo-foundation, where Poisson's ratios of both bodies are in between -1 and 0 or in between 0 and 0.5 (where both Poisson's ratios are sufficiently away from 0 and 0.5), and with an asymptotic condition that is different to what the authors present. We also show that, for all Poisson's ratios, the authors' phase diagram is four-dimensional and not two-dimensional. Also, due to the Poisson's ratio dependence, the asymptotic scalings that the authors present are insufficient to derive their proposed models. Furthermore, the authors' scaling of the displacement field implies that their method cannot be applicable to films (or strings) with planar loading, unless the normal displacement is zero. Finally, by deriving a Winkler foundation type solution for a plate supported by an elastic pseudo-foundation via the method implied by the authors, we show that the authors' method cannot be applied to plates due to the structure of the overlying body (i.e. the limits of integration of the plate) and the foundation (i.e. planar-stress free condition of the foundation), unless planar displacement field is identically zero. Despite the limitations of the authors' work, we highlight its strength by showing that unlike the classical derivation of the Winkler foundation equation, Baldelli and Bourdin's approach does not violate the volume conversation laws or violate the governing equations of mathematical elasticity.

cond-mat.soft↗

arXiv2021

A Critical Study of Howell et al.'s Nonlinear Beam Theory

In our analysis, we show that Howell et al.'s nonlinear beam theory does not depict a representation of the Euler-Bernoulli beam equation, nonlinear or otherwise. The authors' nonlinear beam theory implies that one can bend a beam in to a constant radius of deformation and maintain that constant radius of deformation with zero force. Thus, the model is disproven by showing that it is invalid when the curvature of deformation is constant, while even the linear Euler-Bernoulli beam equation stays perfectly valid under such deformations. To conclude, we derive a nonlinear beam equation by using Ciarlet's nonlinear plate equations and show that our model is valid for constant radius of deformations.

physics.class-ph↗

arXiv2021

A Critical Study of Cottenden et al.'s An Analytical Model of the Motion of a Conformable Sheet Over a General Convex Surface in the Presence of Frictional Coupling

In our analysis, we show that what Cottenden et al. accomplish is the derivation of the ordinary capstan equation, and a solution to a dynamic membrane with both a zero-Poisson's ratio and a zero-mass density on a rigid right-circular cone. The authors states that the capstan equation holds true for an elastic obstacle, and thus, it can be used to calculate the coefficient of friction between human skin and fabrics. However, using data that we gathered from human trials, we show that this claim cannot be substantiated as it is unwise to use the capstan equation (i.e. belt-friction models in general) to calculate the friction between in-vivo skin and fabrics. This is due to the fact that such models assume a rigid foundation, while human soft-tissue is deformable, and thus, a portion of the applied force to the fabric is expended on deforming the soft-tissue, which in turn leads to the illusion of a higher coefficient of friction when using belt-friction models.

physics.med-ph↗

arXiv2021

A Critical Study of Efrati et al.'s Elastic Theory of Unconstrained non-Euclidean Plates

In our analysis, we show that Efrati et al.'s publication is inconsistent with the mathematics of plate theory. However it is more consistent with the mathematics of shell theory, but with an incorrect strain tensor. Thus, the authors' numerical results imply that a thin object can be stretched substantially with very little force, which is physically unrealistic and mathematically disprovable. All the theoretical work of the authors, i.e. nonlinear plate equations in curvilinear coordinates, can easily be rectified with the inclusion of both a sufficiently differentiable diffeomorphism and a set of external loadings, such as an external strain field.

physics.class-ph↗