标题： 半解析方法在涉及聚集和破碎过程的群体平衡模型中的应用：比较研究 显示英文标题

标题： Semi-Analytical Methods for Population Balance models involving Aggregation and Breakage processes: A comparative study

摘要： 种群平衡模型通常整合基本的核函数，包括求和、凝结和布朗凝聚核函数。 这些核函数在多个学科领域中展现出广泛的应用价值，如气溶胶物理、化学工程、天体物理学、制药科学和数学生物学，用于阐明粒子动力学。 本研究的目的是改进当前方法得出的半解析解，以解决非线性凝聚和耦合凝聚-破碎种群平衡方程。 本文提出了一种基于同伦分析方法（HAM）的独特半解析方法，用于求解纯凝聚和耦合凝聚-碎片化种群平衡方程，这是一种积分-偏微分方程。 通过分解非线性算子，我们研究了如何利用收敛控制参数，以加快所提出方法中HAM解向精确值的收敛速度。 显示英文摘要

摘要： Population balance models often integrate fundamental kernels, including sum, gelling and Brownian aggregation kernels. These kernels have demonstrated extensive utility across various disciplines such as aerosol physics, chemical engineering, astrophysics, pharmaceutical sciences and mathematical biology for the purpose of elucidating particle dynamics. The objective of this study is to refine the semi-analytical solutions derived from current methodologies in addressing the nonlinear aggregation and coupled aggregation-breakage population balance equation. This work presents a unique semi-analytical approach based on the homotopy analysis method (HAM) to solve pure aggregation and couple aggregation-fragmentation population balance equations, which is an integro-partial differentia equation. By decomposing the non-linear operator, we investigate how to utilize the convergence control parameter to expedite the convergence of the HAM solution towards its precise values in the proposed method.