arXiv subjects

Waipot Ngamsaad

Publications and source records attributed to Waipot Ngamsaad.

10 recordsLinked to original sources

arXiv2023

A short-time drift propagator approach to the Fokker-Planck equation

The Fokker-Planck equation is a partial differential equation that describes the evolution of a probability distribution over time. It is used to model a wide range of physical and biological phenomena, such as diffusion, chemical reactions, and population dynamics. Solving the Fokker-Planck equation is a difficult task, as it involves solving a system of coupled nonlinear partial differential equations. In general, analytical solutions are not available and numerical methods must be used. In this research, we propose a novel approach to the solution of the Fokker-Planck equation in a short time interval. The numerical solution to the equation can be obtained iteratively using a new technique based on the short-time drift propagator. This new approach is different from the traditional methods, as the state-dependent drift function has been removed from the multivariate Gaussian integral component and is instead presented as a state-shifted element. We evaluated our technique employing a fundamental Wiener process with constant drift components in both one- and two-dimensional space. The results of the numerical calculation were found to be consistent with the exact solution. The proposed approach offers a promising new direction for research in this area.

physics.comp-ph↗

arXiv2019

Perturbative traveling wave solution for a flux-limited reaction-diffusion morphogenesis equation

In this study, we investigate a porous medium-type flux limited reaction--diffusion equation that arises in morphogenesis modeling. This nonlinear partial differential equation is an extension of the generalized Fisher--Kolmogorov--Petrovsky--Piskunov (Fisher-KPP) equation in one-dimensional space. The approximate analytical traveling wave solution is found by using a perturbation method. We show that the morphogen concentration propagates as a sharp wave front where the wave speed has a saturated value. The numerical solutions of this equation are also provided to compare them with the analytical predictions. Finally, we qualitatively compare our theoretical results with those obtained in experimental studies.

physics.bio-ph↗

arXiv2018

Propagating wave in the flock of self-propelled particles

We investigate the linearized hydrodynamic equations of interacting self-propelled particles in two dimensional space. It is found that the small perturbations of density and polarization fields satisfy the hyperbolic partial differential equations---that admit analytical propagating wave solutions. These solutions uncover the questionable traveling band formation in the flocking state of self-propelled particles. Below the critical noise strength, an unstable disordered state (random motion) undergoes a transient vortex and evolves to an ordered state (flocking motion) as unidirectional traveling waves. There appear two possible longitudinal wave patterns depending on the noise strength, including single band in stable state and multiplebands in unstable state. A comparison of theoretical and experimental studies is presented.

physics.bio-ph↗

arXiv2015

Mechanically-driven spreading of bacterial populations

The effect of mechanical interactions between cells in the spreading of bacterial populations was investigated in one-dimensional space. A continuum-mechanics approach, comprising cell migration, proliferation, and exclusion processes, was employed to elucidate the dynamics. The consequent nonlinear reaction-diffusion-like equation describes the constitution dynamics of a bacterial population. In this model, bacterial cells were treated as rod-like particles that interact with each other through hard-core repulsion, which introduces the exclusion effect that causes bacterial populations to migrate quickly and at high density. The propagation of bacterial density as a traveling wave front over extended times was also analysed. The analytical and numerical solutions revealed that the front speed was enhanced by the exclusion process, which depended upon the cell-packing fraction. Finally, we qualitatively compared our theoretical results with experimental evidence.

physics.bio-ph↗

arXiv2013

Radial propagation in population dynamics with density-dependent diffusion

The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate analytical solution to this equation has been found. It shows that the population density evolves from initial state and propagates as the traveling wave-like for the large time scale. One can be mentioned that, if the distance is insufficient large, the curvature has ineluctable influence on density profile and front speed. In comparison, the analytical solution is in agreement with the numerical solution.

physics.bio-ph↗

arXiv2012

Self-similar dynamics of bacterial chemotaxis

Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical concentration gradient. Here, the dynamics of pattern formation in bacterial colony is investigated theoretically through a continuum model that considers chemotaxis. In the case of the gradient sensed by the bacterium is nearly uniform, the bacterial colony patterns are self-similar, which they look the same at every scale. The scaling law of the bacterial colony growth has been revealed explicitly. Chemotaxis biases the movement of bacterial population in colony trend toward the chemical attractant. Moreover, the bacterial colonies evolve long time as the traveling wave with sharp front.

physics.bio-ph↗

arXiv2012

Self-Similar Solutions to a Density-Dependent Reaction-Diffusion Model

In this paper, we investigated a density-dependent reaction-diffusion equation, $u_t = (u^{m})_{xx} + u - u^{m}$. This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation which is widely used in the population dynamics, combustion theory and plasma physics. By employing the suitable transformation, this equation was mapped to the anomalous diffusion equation where the nonlinear reaction term was eliminated. Due to its simpler form, some exact self-similar solutions with the compact support have been obtained. The solutions, evolving from an initial state, converge to the usual traveling wave at a certain transition time. Hence, it is quite clear the connection between the self-similar solution and the traveling wave solution from these results. Moreover, the solutions were found in the manner that either propagates to the right or propagates to the left. Furthermore, the two solutions form a symmetric solution, expanding in both directions. The application on the spatiotemporal pattern formation in biological population has been mainly focused.

physics.bio-ph↗

arXiv2004

Modeling of the dynamic pole-to-pole oscillations of the min proteins in bacterial cell division: The effect of an external field

One of the most important steps in the developmental process of the bacteria cell at the cellular level is the determination of the middle of the cell and the proper placement of the septum, these being essential to the division of the cell. In E. coli, this step depends on the proteins MinC, MinD, and MinE. Exposure to a constant electric field may cause the bacteria cell division mechanism to change, resulting in an abnormal cytokinesis. To see the effects of an external field e.g., an electric or magnetic field on this process, we have solved a set of deterministic reaction diffusion equations, which incorporate the influence of an electric field. We have found some changes in the dynamics of the oscillations of the min proteins from pole to pole. The numerical results show some interesting effects, which are qualitatively in good agreement with some experimental results.

physics.bio-ph↗

arXiv2004

The dynamics of the min proteins of Escherichia coli under the constant external fields

In E. coli the determination of the middle of the cell and the proper placement of the septum is essential to the division of the cell. This step depends on the proteins MinC, MinD, and MinE. Exposure to a constant external field e.g., an electric field or magnetic field may cause the bacteria cell division mechanism to change resulting in an abnormal cytokinesis. To have insight into the effects of an external field on this process, we model the process using a set of the deterministic reaction diffusion equations, which incorporate the influence of an external field, min protein reactions, and diffusion of all species. Using the numerical method, we have found some changes in the dynamics of the oscillations of the min proteins from pole to pole when compared that of without the external field. The results show some interesting effects, which are qualitatively in good agreement with some experimental results.

q-bio.SC↗

arXiv2004

A one-dimensional Lattice Boltzmann method for modeling the dynamic pole-to-pole oscillations of Min proteins for determining the position of the midcell division plane

Determining the middle of the bacteria cell and the proper placement of the septum is essential to the division of the bacterial cell. In E. coli, this process depends on the proteins MinC, MinD, and MinE. Here, the Lattice Boltzmann method (LBM) is used to study the dynamics of the oscillations of the min proteins from pole to pole. This determines the midcell division plane at the cellular level. The LBM is applied to the set of the deterministic reaction diffusion equations proposed by Howard et. al. [1] to describe the dynamics of the Min proteins. The LBM results are in good agreement with those of Howard et al, and agree qualitatively with the experimental results. Our good results indicate that the LBM can be an alternative computational tool for simulating problems dealing with complex biological system which are described by the reaction-diffusion equations.

q-bio.QM↗