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I am investigating gravity-driven liquid films flowing over a corrugated substrate with an extended WIBL model, and the base solution is strictly periodic. The next step is a full Floquet stability analysis of that periodic state so I can identify the short-wave instability noses and the curious stability islands created by the substrate’s geometry. All governing equations and parameter ranges are ready; what I still need is a clean, reproducible Floquet framework that extracts the multipliers for each wavenumber and returns clear stability maps. You are free to work in MATLAB, Python (NumPy/SciPy), or Julia as long as the code is well commented and numerically robust—spectral collocation or a high-order finite-difference approach is fine as long as convergence is demonstrated. Deliverables • A runnable script or notebook that assembles the monodromy matrix for the periodic WIBL coefficients and computes the Floquet multipliers across user-defined parameter grids • Plots that highlight the predicted instability noses and stability islands, ready for publication (vector format preferred) • A concise technical note summarising the formulation, numerical method, verification checks, and how to reproduce the figures Acceptance criteria: the dominant multiplier spectrum must match my reference case within 1 % and the code must complete a typical parametric sweep (200 wavenumbers × 50 Reynolds numbers) in under 10 minutes on a standard laptop. Feel free to suggest efficiency tweaks or alternative numerical schemes if they improve accuracy without sacrificing clarity.
Project ID: 40198716
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Dear Sir/Madam, I have experience with Floquet stability analysis and numerical modeling of periodic fluid-flow systems. I’m confident I can build a clear, reproducible framework to compute Floquet multipliers and generate stability maps for your periodic WIBL solution. Let’s connect in the chatbox to discuss the project further, including the budget and timeline. To know more about my experience, let's talk in a freelancer call, and I can share more details and sample works in the chatbox. I am ready to work with you, please connect in the chatbox for further discussions. Thank You. Dr. Divya.
₹1,500 INR in 2 days
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With my team at Prime Code Tech, we harness the full power of Python and its libraries like NumPy and SciPy to deliver robust, scalable, and reproducible scientific computing solutions. My experience with managing complex projects coupled with my proficiency in spectral collocation and high-order finite-difference approaches ensures your Floquet stability analysis for film flow will be addressed with utmost professionalism. The code we provide in either MATLAB, Python (NumPy/SciPy), or Julia will be well-commented, numerically solid, and binary pish for fast parametric sweeps. We always strive to exceed our client's expectations, demonstrated by our ability to run typical parametric sweep with 50 Reynolds numbers and 200 wavenumbers within 10 minutes on a standard laptop. I guarantee an accuracy of the dominant multiplier spectrum within 1% tolerance from your reference case. Apart from the technical expertise and efficiency, what sets us apart is our collaborative approach. I don't just build digital solutions; I become a technology partner invested in achieving your business targets. If there are opportunities to enhance efficiency or improve alternatives without compromising clarity, I would proactively suggest such optimizations for your project. Engaging me for this task isn't just an addition of a freelancer but acquiring a partner dedicated to bringing innovation, scale, and measurable growth to your project.
₹1,000 INR in 5 days
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This project is right in my wheelhouse. I can deliver a clean, fully reproducible Floquet stability framework for your periodic WIBL base state, designed specifically to resolve short-wave instability noses and geometry-induced stability islands with high numerical fidelity. I’ll formulate the linearised perturbation equations around the strictly periodic solution and construct the monodromy operator using a robust spectral collocation (Fourier–Chebyshev) or high-order finite-difference scheme, with convergence checks built in. Floquet multipliers will be computed efficiently across wavenumber–Reynolds grids, with careful attention to conditioning and time-integration accuracy so the dominant spectrum matches your reference within the 1% tolerance. Deliverables will include a well-commented MATLAB or Python implementation, publication-ready vector plots highlighting instability regions, and a concise technical note detailing the formulation, numerical method, validation, and reproduction steps. I’ll also optimise the sweep (matrix reuse, vectorisation, parallelisation where appropriate) to ensure a 200×50 parameter study runs comfortably under your 10-minute target on a standard laptop.
₹1,050 INR in 7 days
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Hi there, You’re absolutely in the RIGHT PLACE. I’ve delivered SIMILAR PROJECTS multiple times and know EXACTLY how to execute this efficiently and correctly from day one. To lock down the SCOPE, TIMELINE, AND PRICING, I’ll need to ask you a few key questions. Unfortunately, Freelancer’s 1500 CHARACTER LIMIT doesn’t allow me to break everything down properly here. Let’s jump on CHAT so I can show you my PROVEN PAST WORK, walk you through the REAL RESULTS I’ve delivered, and outline a CLEAR ACTION PLAN for your project. You’ll immediately see why my approach is DIFFERENT and EFFECTIVE. If you’re serious about getting this done RIGHT, I’m ready to move forward. Looking forward to CONNECTING and WINNING TOGETHER. Cheers, Mayank B
₹1,050 INR in 7 days
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Drawing from my 4+ years of experience working as a Python expert, I offer you a unique blend of numerically robust and efficient code. I am confident in my ability to deliver a clean, reusable Floquet framework that will not only scale gracefully as you explore large parameter grids but also complete a typical parametric sweep swiftly on standard hardware. Moreover, being well-versed in machine learning, I am adept at optimizing code for improved accuracy without compromising clarity, and if need be, I can suggest viable efficiency tweaks or alternative numerical schemes to suit your specific purposes. I understand the importance of documentation for reproducibility and publication readiness. Therefore, alongside the runnable script or notebook that performs the monodromy matrix assembling and Floquet multipliers calculation, I commit to providing detailed, well-commented code that thoroughly elucidates the formulation and numerical methods employed. Furthermore, I'll include comprehensive verification checks to ensure the accuracy of the predicted instability noses and stability islands. Additionally, my familiarity with working on time-bound projects will guarantee on-time delivery without compromising quality. As your project demands a high level of technical expertise in computational fluid dynamics.
₹1,000 INR in 5 days
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