arXiv subjects

Gangadhara Boregowda

Publications and source records attributed to Gangadhara Boregowda.

3 recordsLinked to original sources

arXiv2025

Existence and Stability Theory of a Neurologically-Inspired Parabolic PDE Model with a Nonlinear Time-Delayed Boundary Condition

In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a time $τ\geq 0$ in the past. These equations model the production dynamics of a protein species by a single cell, where a feedback mechanism downregulates the protein's production. Furthermore, we analyze the stability of a non-trivial steady-state solution and provide sufficient conditions on the nonlinearity parameter, boundary flux, and time delay that ensure the occurrence of a Hopf bifurcation.

math.DS↗

arXiv2024

High-performance computing for the BGK model of the Boltzmann equation with a meshfree Arbitrary Lagrangian-Eulerian (ALE) method

In this paper, we present high-performance computing for the BGK model of the Boltzmann equation with a mesh-free method. For the numerical simulation of the BGK equation we use an Arbitrary-Lagrangian-Eulerian (ALE) method developed in previous work, where the approximation of spatial derivatives and the reconstruction of a function is based on the weighted least squares method. A Graphics Processing Unit (GPU) is used to accelerate the code. The result is compared with sequential and parallel versions of the CPU code. Two and three-dimensional driven cavity problems are solved, where a speed-up of several orders of magnitude is obtained compared to a sequential CPU simulation.

math.NA↗

arXiv2023

Optimization of probe separation distance and cooling time in multi-probe cryoablation technique by arranging probes in triangular and square pattern-A computational approach

Cryoablation is a minimally invasive and efficient therapy option for liver cancer. Liquid nitrogen was used to kill the unwanted cells via freezing. One of the challenges of cryosurgery is to destroy the complete tumor without damaging the surrounding healthy cells when the tumor is large. To overcome this challenge, multi-cryoprobes were arranged in a polygonal pattern to create a uniform cooling and optimum ablation zone in the tissue. Single, three, and four cryoprobes were placed in the center, triangle, and square patterns to analyze the temperature profile and ablation zone. The results showed that tissue will freeze quickly when cryoprobes are placed in a square pattern. After the treatment of 600 seconds, $99\%$, $96\%$, and $31\%$ of the tumor were killed using four, three, and single cryoprobes, respectively. One of the difficulties in the multi-probe technique is choosing the probe separation distance and cooling time. The volume of the ablation zone, the thermal damage to healthy cells, and the volume of tumor cells killed during the treatment for different probe separation distances of 10 mm, 15 mm, and 20 mm are analyzed. Compared to other settings, a multi-probe technique destroys the entire tumor with the least harm to healthy cells when probes are arranged in a square pattern with a 15 mm space between them.

physics.med-ph↗