Durgesh K.

PhD Applied Mathematician | Math Modeling | Scientific Computing

I am a 𝗣𝗵𝗗 𝗔𝗽𝗽𝗹𝗶𝗲𝗱 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗶𝗮𝗻 and 𝗥𝗲𝘀𝗲𝗮𝗿𝗰𝗵 𝗖𝗼𝗻𝘀𝘂𝗹𝘁𝗮𝗻𝘁 specializing in 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝗠𝗼𝗱𝗲𝗹𝗶𝗻𝗴, 𝗦𝗰𝗶𝗲𝗻𝘁𝗶𝗳𝗶𝗰 𝗖𝗼𝗺𝗽𝘂𝘁𝗶𝗻𝗴, 𝗥𝗲𝘀𝗲𝗮𝗿𝗰𝗵 𝗠𝗮𝗻𝘂𝘀𝗰𝗿𝗶𝗽𝘁 𝗥𝗲𝘃𝗶𝗲𝘄, 𝗡𝘂𝗺𝗲𝗿𝗶𝗰𝗮𝗹 𝗠𝗲𝘁𝗵𝗼𝗱𝘀, and 𝗧𝗵𝗲𝗼𝗿𝗲𝘁𝗶𝗰𝗮𝗹 𝗙𝗿𝗮𝗺𝗲𝘄𝗼𝗿𝗸 𝗗𝗲𝘃𝗲𝗹𝗼𝗽𝗺𝗲𝗻𝘁. 𝗜 𝗵𝗲𝗹𝗽 𝗿𝗲𝘀𝗲𝗮𝗿𝗰𝗵𝗲𝗿𝘀, 𝘂𝗻𝗶𝘃𝗲𝗿𝘀𝗶𝘁𝗶𝗲𝘀, 𝗮𝗻𝗱 𝗥&𝗗 𝘁𝗲𝗮𝗺𝘀 𝘁𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺 𝗰𝗼𝗺𝗽𝗹𝗲𝘅 𝘀𝗰𝗶𝗲𝗻𝘁𝗶𝗳𝗶𝗰 𝗶𝗱𝗲𝗮𝘀 𝗶𝗻𝘁𝗼 𝗺𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹𝗹𝘆 𝗿𝗶𝗴𝗼𝗿𝗼𝘂𝘀 𝗺𝗼𝗱𝗲𝗹𝘀, 𝘃𝗮𝗹𝗶𝗱𝗮𝘁𝗲𝗱 𝗰𝗼𝗺𝗽𝘂𝘁𝗮𝘁𝗶𝗼𝗻𝗮𝗹 𝗺𝗲𝘁𝗵𝗼𝗱𝘀, 𝗮𝗻𝗱 𝗽𝘂𝗯𝗹𝗶𝗰𝗮𝘁𝗶𝗼𝗻-𝗿𝗲𝗮𝗱𝘆 𝗿𝗲𝘀𝗲𝗮𝗿𝗰𝗵. Since 2012, I have completed 𝗠𝗼𝗿𝗲 𝘁𝗵𝗮𝗻 𝟭𝟵𝟬 𝗽𝗿𝗼𝗷𝗲𝗰𝘁𝘀 𝗼𝗻 𝗨𝗽𝘄𝗼𝗿𝗸, helping researchers, engineers, independent scholars, universities, startups, and R&D teams solve complex mathematical and computational problems involving 𝗗𝗶𝗳𝗳𝗲𝗿𝗲𝗻𝘁𝗶𝗮𝗹 𝗘𝗾𝘂𝗮𝘁𝗶𝗼𝗻𝘀, 𝗧𝗵𝗲𝗿𝗺𝗼𝗱𝘆𝗻𝗮𝗺𝗶𝗰 𝗦𝘆𝘀𝘁𝗲𝗺𝘀, 𝗖𝗼𝗺𝗽𝘂𝘁𝗮𝘁𝗶𝗼𝗻𝗮𝗹 𝗠𝗼𝗱𝗲𝗹𝗶𝗻𝗴, 𝗡𝘂𝗺𝗲𝗿𝗶𝗰𝗮𝗹 𝗦𝗶𝗺𝘂𝗹𝗮𝘁𝗶𝗼𝗻𝘀, 𝗦𝗰𝗶𝗲𝗻𝘁𝗶𝗳𝗶𝗰 𝗣𝗿𝗼𝗴𝗿𝗮𝗺𝗺𝗶𝗻𝗴, 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝗩𝗮𝗹𝗶𝗱𝗮𝘁𝗶𝗼𝗻, and 𝗣𝘂𝗯𝗹𝗶𝗰𝗮𝘁𝗶𝗼𝗻-𝗥𝗲𝗮𝗱𝘆 𝗥𝗲𝘀𝗲𝗮𝗿𝗰𝗵 𝗦𝘂𝗽𝗽𝗼𝗿𝘁. Recent engagements have included 𝗺𝘂𝗹𝘁𝗶-𝗽𝗵𝗮𝘀𝗲 𝘁𝗵𝗲𝗼𝗿𝗲𝘁𝗶𝗰𝗮𝗹 𝗳𝗿𝗮𝗺𝗲𝘄𝗼𝗿𝗸 𝗿𝗲𝘃𝗶𝗲𝘄𝘀, 𝗵𝗶𝗴𝗵-𝗶𝗺𝗽𝗮𝗰𝘁 𝗷𝗼𝘂𝗿𝗻𝗮𝗹 𝗺𝗮𝗻𝘂𝘀𝗰𝗿𝗶𝗽𝘁 𝗽𝗿𝗲𝗽𝗮𝗿𝗮𝘁𝗶𝗼𝗻, referee-level 𝗺𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝗿𝗲𝘃𝗶𝗲𝘄, 𝘁𝗵𝗲𝗿𝗺𝗼𝗱𝘆𝗻𝗮𝗺𝗶𝗰 𝘀𝘆𝘀𝘁𝗲𝗺 𝗺𝗼𝗱𝗲𝗹𝗶𝗻𝗴, and 𝗺𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝘃𝗮𝗹𝗶𝗱𝗮𝘁𝗶𝗼𝗻 𝗼𝗳 𝗻𝗼𝘃𝗲𝗹 𝘀𝗰𝗶𝗲𝗻𝘁𝗶𝗳𝗶𝗰 𝗰𝗼𝗻𝗰𝗲𝗽𝘁𝘀. I assist researchers in 𝗘𝘃𝗮𝗹𝘂𝗮𝘁𝗶𝗻𝗴, 𝗦𝘁𝗿𝗲𝘀𝘀-𝗧𝗲𝘀𝘁𝗶𝗻𝗴, and 𝗥𝗲𝗳𝗶𝗻𝗶𝗻𝗴 𝗘𝗺𝗲𝗿𝗴𝗶𝗻𝗴 𝗜𝗱𝗲𝗮𝘀—including 𝗔𝗜-𝗮𝘀𝘀𝗶𝘀𝘁𝗲𝗱 𝗮𝗻𝗱 𝗲𝗺𝗲𝗿𝗴𝗶𝗻𝗴 𝗿𝗲𝘀𝗲𝗮𝗿𝗰𝗵 𝗰𝗼𝗻𝗰𝗲𝗽𝘁𝘀—by identifying logical gaps, assessing internal consistency, developing formal definitions, and translating conceptual frameworks into rigorous mathematical architectures. My work spans 𝗥𝗲𝘀𝗲𝗮𝗿𝗰𝗵 𝗖𝗼𝗻𝘀𝘂𝗹𝘁𝗶𝗻𝗴, 𝗦𝗰𝗶𝗲𝗻𝘁𝗶𝗳𝗶𝗰 𝗦𝗶𝗺𝘂𝗹𝗮𝘁𝗶𝗼𝗻, 𝗝𝗼𝘂𝗿𝗻𝗮𝗹 𝗠𝗮𝗻𝘂𝘀𝗰𝗿𝗶𝗽𝘁 𝗥𝗲𝘃𝗶𝗲𝘄, 𝗧𝗵𝗲𝗼𝗿𝗲𝗺 𝗩𝗲𝗿𝗶𝗳𝗶𝗰𝗮𝘁𝗶𝗼𝗻, 𝗣𝗿𝗼𝗼𝗳 𝗩𝗮𝗹𝗶𝗱𝗮𝘁𝗶𝗼𝗻, 𝗧𝗵𝗲𝗿𝗺𝗼𝗱𝘆𝗻𝗮𝗺𝗶𝗰 𝗠𝗼𝗱𝗲𝗹𝗶𝗻𝗴, 𝗖𝗼𝗺𝗽𝘂𝘁𝗮𝘁𝗶𝗼𝗻𝗮𝗹 𝗣𝗵𝘆𝘀𝗶𝗰𝘀, 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝗙𝗿𝗮𝗺𝗲𝘄𝗼𝗿𝗸 𝗗𝗲𝘃𝗲𝗹𝗼𝗽𝗺𝗲𝗻𝘁, and 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝗩𝗮𝗹𝗶𝗱𝗮𝘁𝗶𝗼𝗻 for advanced scientific and engineering research. Recent collaborations include long-term consulting engagements in mathematical modeling, thermodynamic analysis, referee-level manuscript review, and the formalization of novel theoretical frameworks for publication-quality research. 𝗦𝗘𝗟𝗘𝗖𝗧𝗘𝗗 𝗥𝗘𝗖𝗘𝗡𝗧 𝗣𝗥𝗢𝗝𝗘𝗖𝗧𝗦 𝗔𝗗𝗩𝗔𝗡𝗖𝗘𝗗 𝗠𝗔𝗡𝗨𝗦𝗖𝗥𝗜𝗣𝗧 𝗥𝗘𝗙𝗜𝗡𝗘𝗠𝗘𝗡𝗧 & 𝗣𝗥𝗢𝗢𝗙 𝗩𝗔𝗟𝗜𝗗𝗔𝗧𝗜𝗢𝗡 (𝗖𝗼𝗺𝗽𝗹𝗲𝘁𝗲𝗱) Conducted a 128-hour research consulting engagement supporting an advanced theoretical physics manuscript through proof verification, derivation auditing, referee-risk assessment, logical consistency analysis, and journal-ready LaTeX preparation. 𝗧𝗛𝗘𝗥𝗠𝗢𝗗𝗬𝗡𝗔𝗠𝗜𝗖 𝗦𝗬𝗦𝗧𝗘𝗠 𝗠𝗢𝗗𝗘𝗟𝗜𝗡𝗚 (𝗢𝗻𝗴𝗼𝗶𝗻𝗴) Developing nonlinear thermal-energy balance models with analytical investigation and numerical validation. 𝗥𝗘𝗦𝗘𝗔𝗥𝗖𝗛 𝗠𝗔𝗡𝗨𝗦𝗖𝗥𝗜𝗣𝗧 𝗥𝗘𝗩𝗜𝗘𝗪 & 𝗧𝗘𝗖𝗛𝗡𝗜𝗖𝗔𝗟 𝗔𝗨𝗗𝗜𝗧 (𝗢𝗻𝗴𝗼𝗶𝗻𝗴) Reviewing advanced mathematics and physics manuscripts for derivation verification, notation consistency, and technical rigor. 𝗠𝗔𝗧𝗛𝗘𝗠𝗔𝗧𝗜𝗖𝗔𝗟 𝗙𝗥𝗔𝗠𝗘𝗪𝗢𝗥𝗞 𝗗𝗘𝗩𝗘𝗟𝗢𝗣𝗠𝗘𝗡𝗧 (𝗢𝗻𝗴𝗼𝗶𝗻𝗴) Evaluating and formalizing novel theoretical concepts, including AI-assisted research ideas, into mathematically defensible frameworks. 𝗦𝗘𝗥𝗩𝗜𝗖𝗘𝗦 ✓ Mathematical Modeling ✓ Thermodynamic & Physical System Modeling ✓ Differential Equations (ODEs, PDEs, Dynamical Systems) ✓ Scientific Computing & Numerical Methods ✓ Research Manuscript Review & Validation ✓ Mathematical Proof Verification ✓ Scientific Programming (Python, MATLAB, Maple, Mathematica, Fortran) ✓ CFD, Heat Transfer & Transport Phenomena ✓ LaTeX, Overleaf & Publication Support ✓ Journal, Thesis & Technical Report Preparation 𝗦𝗢𝗙𝗧𝗪𝗔𝗥𝗘 • Python • MATLAB • Maple • Mathematica • Fortran • COMSOL Multiphysics • ANSYS Fluent • LaTeX • Overleaf 𝗛𝗢𝗪 𝗜 𝗪𝗢𝗥𝗞 Every project begins with a focused milestone—such as a model review, derivation audit, framework evaluation, manuscript assessment, or computational validation—to establish a clear technical roadmap before expanding into larger engagements. If you need support with mathematical modeling, scientific computing, theoretical framework development, thermodynamic analysis, research manuscript review, or publication preparation, feel free to contact me. 𝗗𝗿. 𝗗𝘂𝗿𝗴𝗲𝘀𝗵 𝗞𝘂𝘀𝗵𝗮𝘄𝗮𝗵𝗮 𝗣𝗵𝗗 𝗔𝗽𝗽𝗹𝗶𝗲𝗱 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀