Stability criterion for 1D heat and wave equation for numerical solution
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Pages
Building Particle Tracking Algorithm
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Understanding Navier-Stokes Equation
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Posts
Statistical Moments: Mean, Variance, Skweness and Kurtosis
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Looking at distributions is a daily part of the job for many including me. Here I explain the statistical moments and what they actually `mean’ (no pun indented). Charecterisng a distribution using statistical measures gives us insight on the data; how does the curve look like?, what’s the spread?, symetric or not?, how skewed it is?, markers for multimodality.
Stability criterion for 1D heat and wave equation for numerical solution
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We often run into unstable conditions while solving the heat and wave equations. This report details the proof of the stability criterion for 1D heat and wave equations which then dictates the choice for spatial and temporal intervals.
Python Virtual Environments: A Quick Guide
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Creating Python virtual environments is essential for isolating project-specific dependencies from your system’s global Python installation. This helps prevent version conflicts and ensures that your work does not interfere with other projects or system-level packages.
DEM Simulations Comparing Two Contact Models
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The Discrete Element Method (DEM) models granular materials by simulating particle interactions. This study compares the Cundall-Strack and Hertz-Mindlin contact models, highlighting differences in energy, stiffness, force distribution, and dynamics.
Understanding Navier-Stokes Equation
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I often revisit the Navier-Stokes equation and find myself grappling with the same questions about its structure, underlying assumptions, and the linear algebra concepts I’ve forgotten over time. This summary report provides a clear explanation of the equation’s structure while also serving as a refresher on essential linear algebra and vector calculus concepts.
Building Particle Tracking Algorithm
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An exciting technique in data analysis, chi-squared minimization by convolution allows researchers to accurately identify the positions and sizes of particles in 2D. By comparing observed data with theoretical models and minimizing the difference, this approach offers a precise method for particle tracking and analysis.
publications
Contact network structures and rigidity development in two-dimensional bidisperse suspensions
Published in Journal of Rheology, Volume 70, Issue 2, 2025
In this paper, we analyze the contact network of highly bidisperse (4:1 size ratio) dense suspensions. We observe a remarkable difference in the nature of pair-wise interactions between particles compared to the lower bidisperse case. We also investigate the jamming tendencies and how the system approaches jamming. For the first time ever in a dense suspension we charecterize the anisotropy using the fabric tensor.
talks
Properties of 3D arches in a clogged hopper of soft deformable particles
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We study arches that form during clogging in a 3D system of soft hydrogel particles (bulk modulus 10-30 kPa) in water flowing through a square cross-section tube with a circular outlet. The particles are dyed with a fluorescent dye and a laser sheet is used to locate the particles in 3D when the system clogs. The tube’s dimensions are 7.62 cm x 7.62 cm x 25.4 cm. The mean particle diameter is 1.46 cm. We vary the total number of particles from 80-125 and the diameter of the outlet from 2-3.5 cm. We measure the clogging probability, and the 3D particle positions in the clog to identify 3D arches. We find that the number of particles in the clogged arch depends on the width of the orifice and the number of particles.
Study of rigid clusters in dense bidisperse suspensions under high shear
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Dense non-Brownian suspensions, found in industries like cement and chocolate, exhibit complex flow behavior influenced by shear and particle interactions. Using LF-DEM, we study 2D bidisperse systems, modeling polydispersity and jamming transitions. Employing the pebble game algorithm, we analyze rigidity percolation, particle contacts, and rheology to understand the formation of rigid clusters. Watch the talk here
Rigid structure development in dense mono- and bidisperse suspensions
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Discontinuous shear thickening (DST) in suspensions occurs when stress drives particles into frictional contact networks, setting a threshold for shear-induced contacts. Using an established simulation technique [1], we show that contact networks grow with solid fraction and fluctuate under flow. As jamming nears, rigid clusters emerge with 2D Ising-like critical behavior. We analyze scaling in mono- and bidisperse suspensions (up to a 4:1 size ratio) and examine how shear and normal stresses relate to rigid structure formation.
Rigidity development in dense shear thickened mono- & bi-disperse suspensions
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The onset of shear thickening and, ultimately, jamming occurs due to the formation of large-scale microstructures within the suspension. Although these events are rare, they are significant enough to counterbalance the imposed shear stress in dense suspensions, leading to the development of frictional contact networks that resist further deformation.
teaching
ChE 432: Chemical Reaction Engineering
Undergraduate Course, MR-103, CCNY, 2022
Course Overview
Welcome to Fall 2022! This course, ChE 43200: Chemical Reaction Engineering, this course covers reactor analysis and design for batch, flow, and semibatch reactors, along with homogeneous and heterogeneous reaction systems. Topics include catalysis, reaction mechanisms, heat and mass transfer effects, with applications in the chemical and petrochemical industries.
ChE 22900: Chemical Thermodynamics
Undergraduate Course, NAC 1/203, CCNY, 2023
Course Overview
Welcome to Spring 2023! This course, ChE 22900: Chemical Thermodynamics, explores fundamental concepts in reaction engineering and thermodynamics, including thermodynamic laws, heat engines, steam turbines, and equations of state with phase equilibria.
Intro to MATLAB
Graduate Course, SH-203, CCNY, 2025
As part of the Engineering Analysis (Engr I1100) course, the computer project involves solving differential equations numerically using a programming language of choice (MATLAB is recommended).