arXiv subjects

Sonali Kaushik

Publications and source records attributed to Sonali Kaushik.

4 recordsLinked to original sources

arXiv2022

Existence and density conservation using a non-conservative approximation for Safronov-Dubovski aggregation equation

The paper deals with the global existence and density conservation for the Safronov-Dubovski equation for three different coefficients $ϕ$ such that $ϕ_{i,j} \leq \frac{(i+j)}{\min\{i,j\}}$, $ϕ_{i,j} \leq (i+j)$ and $ϕ_{i,j} \leq (1+i+j)^α$ $\forall$ $i,j \in \mathbb{N}$, $α\in [0,1]$. The non-conservative approximation is applied to study the problem and results such as Helly's selection theorem and the refined version of the De la Vallée-Poussin theorem are implemented to establish the existence of each case of the kernel. The article also focuses on the conditions for the conservation of mass per unit volume for such an equation.

math.AP↗

arXiv2022

A Novel Optimized Decomposition Method for Smoluchowski's Aggregation Equation

The Smoluchowski's aggregation equation has applications in the field of bio-pharmaceuticals \cite{zidar2018characterisation}, financial sector \cite{PUSHKIN2004571}, aerosol science \cite{shen2020efficient} and many others. Several analytical, numerical and semi-analytical approaches have been devised to calculate the solutions of this equation. Semi-analytical methods are commonly employed since they do not require discretization of the space variable. The article deals with the introduction of a novel semi-analytical technique called the optimized decomposition method (ODM) (see \cite{odibat2020optimized}) to compute solutions of this relevant integro-partial differential equation. The series solution computed using ODM is shown to converge to the exact solution. The theoretical results are validated using numerical examples for scientifically relevant aggregation kernels for which the exact solutions are available. Additionally, the ODM approximated results are compared with the solutions obtained using the Adomian decomposition method (ADM) in \cite{singh2015adomian}. The novel method is shown to be superior to ADM for the examples considered and thus establishes as an improved and efficient method for solving the Smoluchowski's equation.

math.NA↗

arXiv2022

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

The article presents the existence and mass conservation of solution for the discrete Safronov-Dubovski coagulation equation for the product coalescence coefficients $ϕ$ such that $ϕ_{i,j} \leq ij$ $\forall$ $i,j \in \mathbb{N}$. Both conservative and non-conservative truncated systems are used to analyse the infinite system of ODEs. In the conservative case, Helly's selection theorem is used to prove the global existence while for the non-conservative part, we make use of the refined version of De la Vallée-Poussin theorem to establish the existence. Further, it is shown that these solutions conserve density. Finally, the solutions are shown to be unique when the kernel $ϕ_{i,j} \leq \text{min}\{i^η,j^η\}$ where $η\in [0,2]$.

math.AP↗

arXiv2022

Theoretical analysis of a discrete population balance model for sum kernel

The Oort-Hulst-Safronov equation, shorterned as OHS is a relevant population balance model. Its discrete form, developed by Dubovski is the main focus of our analysis. The existence and density conservation are established for the coagulation rate $V_{i,j} \leqs (i+j),$ $\forall i,j \in \mathbb{N}$. Differentiability of the solutions is investigated for the kernel $V_{i,j} \leqs i^α+j^α$ where $0 \leqs α\leqs 1$. The article finally deals with the uniqueness result that requires the boundedness of the second moment.

math.AP↗