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saket singh
saket singh
Last activity 2024-10-13

hello i found the following tools helpful to write matlab programs. copilot.microsoft.com chatgpt.com/gpts gemini.google.com and ai.meta.com. thanks a lot and best wishes.
We're excited to announce that the 2024 Community Contest—MATLAB Shorts Mini Hack starts today! The contest will run for 5 weeks, from Oct. 7th to Nov. 10th.
What creative short movies will you create? Let the party begin, and we look forward to seeing you all in the contest!
If you are interested in AI, Autonomous Systems and Robotics, and the future of engineering, don't miss out on MATLAB EXPO 2024 and register now.
You will have the opportunity to connect with engineers, scientists, educators, and researchers, and new ideas.
Featured Sessions:
  • From Embedded to Empowered: The Rise of Software-Defined Products - María Elena Gavilán Alfonso, MathWorks
  • The Empathetic Engineers of Tomorrow - Dr. Darryll Pines, University of Maryland
  • A Model-Based Design Journey from Aerospace to an Artificial Pancreas System - Louis Lintereur, Medtronic Diabetes
Featured Topics:
  • AI
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  • Preparing Future Engineers and Scientists
What is the side-effect of counting the number of Deep Learning Toolbox™ updates in the last 5 years? The industry has slowly stabilised and matured, so updates have slowed down in the last 1 year, and there has been no exponential growth.Is it correct to assume that? Let's see what you think!
releaseNumNames = "R"+string(2019:2024)+["a";"b"];
releaseNumNames = releaseNumNames(:);
numReleaseNotes = [10,14,27,39,38,43,53,52,55,57,46,46];
exampleNums = [nan,nan,nan,nan,nan,nan,40,24,22,31,24,38];
bar(releaseNumNames,[numReleaseNotes;exampleNums]')
legend(["#release notes","#new/update examples"],Location="northwest")
title("Number of Deep Learning Toolbox™ update items in the last 5 years")
ylabel("#release notes")
We are thrilled to announce the redesign of the Discussions leaf page, with a new user-focused right-hand column!
Why Are We Doing This?
  • Address Readers’ Needs:
Previously, the right-hand column displayed related content, but feedback from our community indicated that this wasn't meeting your needs. Many of you expressed a desire to read more posts from the same author but found it challenging to locate them.
With the new design, readers can easily learn more about the author, explore their other posts, and follow them to receive notifications on new content.
  • Enhance Authors’ Experience:
Since the launch of the Discussions area earlier this year, we've seen an influx of community members sharing insightful technical articles, use cases, and ideas. The new design aims to help you grow your followers and organize your content more effectively by editing tags. We highly encourage you to use the Discussions area as your community blogging platform.
We hope you enjoy the new design of the right-hand column. Please feel free to share your thoughts and experiences by leaving a comment below.
Dear contest participants,
The 2024 Community Contest—MATLAB Shorts Mini Hack—is just one week away! Last year, we challenged you to create a 48-frame, 2-second animation. This year, we're doubling the fun by increasing the frame count to 96 and adding audio support. Your mission? Create a short movie!
As always, whether you are a seasoned MATLAB user or just a beginner, you can participate in the contest and have opportunities to win amazing prizes.
Timeframe:
  • The contest will run for 5 weeks, from Oct. 7th to Nov. 10th, Eastern Time.
General Rules:
  • The first week is dedicated to entry creation, and the fifth week is reserved for voting only.
  • Create a 96-frame, 4-second animation and add audio. We will loop it 3 times to create a 12-second short movie for you.
  • The character limit remains at 2,000 characters.
Prizes
  • You will have opportunities to win compelling prizes, including Amazon gift cards, MathWorks T-shirts, and virtual badges. We will give out both weekly prizes and grand prizes.
Warm-up!
With one week left before the contest begins, we recommend you warm up by reading a fantastic article: Walkthrough: making Little Nemo's airship in MATLAB by @Tim. The article shares both technical insights and the challenges encountered along the way.
We look forward to seeing all of you in the 2024 MATLAB Shorts Mini Hack.
The MATLAB Central Community Team
We are excited to invite you to join our 2024 community contest – MATLAB Shorts Mini Hack! Last year, we challenged you to create a 48-frame animation. In 2024, we are increasing the frame count to 96 and supporting audio. Your mission? Create a short movie!
Whether you are a seasoned MATLAB user or just a beginner, you can participate in the contest and have opportunities to win amazing prizes. Be sure to check out our Blog post for more details on the Community Contests.
Timeframe
This contest runs for 5 weeks, from Oct. 7th to Nov. 10th.
How to Participate
  • Create a new short movie or remix an existing one with up to 2,000 characters of code.
  • Vote or comment on the short movies you love!
Prizes
You will have opportunities to win compelling prizes, including Amazon gift cards, MathWorks T-shirts, and virtual badges. We will give out both weekly prizes and grand prizes.
Stay Informed
Make sure to follow the contest to get important announcements and your prize updates.
Join for creativity and fun! We look forward to seeing your creations in the MATLAB Shorts Contest!
The AI Chat Playground at MATLAB Central has two new upgrades: OpenAI GPT-4o mini and MATLAB R2024b!
GPT-4o mini is a new language model from OpenAI and brings general knowledge up to October 2023. GPT-4o mini surpasses GPT-3.5 Turbo and other small models on academic benchmarks across both textual intelligence and reasoning. Our goal is to keep improving the output of the AI Chat Playground. This upgrade is available now: https://www.mathworks.com/matlabcentral/playground/
One more thing... we also updated the system to the latest release of MATLAB. This is R2024b and comes with hundreds of updates and new plot types to explore.Check out Mike Croucher's blog post about the latest version of MATLAB: https://blogs.mathworks.com/matlab/2024/09/13/the-latest-version-of-matlab-r2024b-has-just-been-released/
We are looking forward to your feedback on the updates to the AI Chat Playground. Let us know what you think and how you use this community app.
Always!
29%
It depends
14%
Never!
21%
I didn't know that was possible
36%
1810 个投票
Hello everyone,
Over the past few weeks, our community members have shared some incredible insights and resources. Here are some highlights worth checking out:

Interesting Questions

Johnathan is seeking help with implementing a complex equation into MATLAB's curve fitting toolbox. If you have experience with curve fitting or MATLAB, your input could be invaluable!

Popular Discussions

Athanasios continues his exploration of the Duffing Equation, delving into its chaotic behavior. It's a fascinating read for anyone interested in nonlinear dynamics or chaos theory.
John shares his playful exploration with MATLAB to find a generative equation for a sequence involving Fibonacci numbers. It's an intriguing challenge for those who love mathematical puzzles.

From File Exchange

Ayesha provides a graphical analysis of linearised models in epidemiology, offering a detailed look at the dynamics of these systems. This resource is perfect for those interested in mathematical modeling.
Gareth brings some humor to MATLAB with a toolbox designed to share jokes. It's a fun way to lighten the mood during conferences or meetups.

From the Blogs

Ned Gulley interviews Tim Marston, the 2023 MATLAB Mini Hack contest winner. Tim's creativity and skills are truly inspiring, and his story is a must-read for aspiring programmers.
Sivylla discusses the integration of AI with embedded systems, highlighting the benefits of using MATLAB and Simulink. It's an insightful read for anyone interested in the future of AI technology.
Thank you to all our contributors for sharing your knowledge and creativity. We encourage everyone to engage with these posts and continue fostering a vibrant and supportive community.
Happy exploring!
Explore the newest online training courses, available as of 2024b: one new Onramp, eight new short courses, and one new learning path. Yes, that’s 10 new offerings. We’ve been busy.
As a reminder, Onramps are free to all. Short courses and learning paths require a subscription to the Online Training Suite (OTS).
  1. Multibody Simulation Onramp
  2. Analyzing Results in Simulink
  3. Battery Pack Modeling
  4. Introduction to Motor Control
  5. Signal Processing Techniques for Streaming Signals
  6. Core Signal Processing Techniques in MATLAB (learning path – includes the four short courses listed below)
Local large language models (LLMs), such as llama, phi3, and mistral, are now available in the Large Language Models (LLMs) with MATLAB repository through Ollama™!
Read about it here:
Hot off the heels of my High Performance Computing experience in the Czech republic, I've just booked my flights to Atlanta for this year's supercomputing conference at SC24.
Will any of you be there?
syms u v
atan2alt(v,u)
ans = 
function Z = atan2alt(V,U)
% extension of atan2(V,U) into the complex plane
Z = -1i*log((U+1i*V)./sqrt(U.^2+V.^2));
% check for purely real input. if so, zero out the imaginary part.
realInputs = (imag(U) == 0) & (imag(V) == 0);
Z(realInputs) = real(Z(realInputs));
end
As I am editing this post, I see the expected symbolic display in the nice form as have grown to love. However, when I save the post, it does not display. (In fact, it shows up here in the discussions post.) This seems to be a new problem, as I have not seen that failure mode in the past.
You can see the problem in this Answer forum response of mine, where it did fail.
David
David
Last activity 2024-9-12

In case you haven't come across it yet, @Gareth created a Jokes toolbox to get MATLAB to tell you a joke.
Dear MATLAB contest enthusiasts,
In the 2023 MATLAB Mini Hack Contest, Tim Marston captivated everyone with his incredible animations, showcasing both creativity and skill, ultimately earning him the 1st prize.
We had the pleasure of interviewing Tim to delve into his inspiring story. You can read the full interview on MathWorks Blogs: Community Q&A – Tim Marston.
Last question: Are you ready for this year’s Mini Hack contest?
goc3
goc3
Last activity 2024-12-3,13:54

I was browsing the MathWorks website and decided to check the Cody leaderboard. To my surprise, William has now solved 5,000 problems. At the moment, there are 5,227 problems on Cody, so William has solved over 95%. The next competitor is over 500 problems behind. His score is also clearly the highest, approaching 60,000.
Please take a moment to congratulate @William.
Has this been eliminated? I've been at 31 or 32 for 30 days for awhile, but no badge. 10 badge was automatic.

Formal Proof of Smooth Solutions for Modified Navier-Stokes Equations

1. Introduction

We address the existence and smoothness of solutions to the modified Navier-Stokes equations that incorporate frequency resonances and geometric constraints. Our goal is to prove that these modifications prevent singularities, leading to smooth solutions.

2. Mathematical Formulation

2.1 Modified Navier-Stokes Equations

Consider the Navier-Stokes equations with a frequency resonance term R(u,f)\mathbf{R}(\mathbf{u}, \mathbf{f})R(u,f) and geometric constraints:

∂u∂t+(u⋅∇)u=−∇pρ+ν∇2u+R(u,f)\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u} = -\frac{\nabla p}{\rho} + \nu \nabla^2 \mathbf{u} + \mathbf{R}(\mathbf{u}, \mathbf{f})∂t∂u​+(u⋅∇)u=−ρ∇p​+ν∇2u+R(u,f)

where:

• u=u(t,x)\mathbf{u} = \mathbf{u}(t, \mathbf{x})u=u(t,x) is the velocity field.

• p=p(t,x)p = p(t, \mathbf{x})p=p(t,x) is the pressure field.

• ν\nuν is the kinematic viscosity.

• R(u,f)\mathbf{R}(\mathbf{u}, \mathbf{f})R(u,f) represents the frequency resonance effects.

• f\mathbf{f}f denotes external forces.

2.2 Boundary Conditions

The boundary conditions are:

u⋅n=0 on Γ\mathbf{u} \cdot \mathbf{n} = 0 \text{ on } \Gammau⋅n=0 on Γ

where Γ\GammaΓ represents the boundary of the domain Ω\OmegaΩ, and n\mathbf{n}n is the unit normal vector on Γ\GammaΓ.

3. Existence and Smoothness of Solutions

3.1 Initial Conditions

Assume initial conditions are smooth:

u(0)∈C∞(Ω)\mathbf{u}(0) \in C^{\infty}(\Omega)u(0)∈C∞(Ω) f∈L2(Ω)\mathbf{f} \in L^2(\Omega)f∈L2(Ω)

3.2 Energy Estimates

Define the total kinetic energy:

E(t)=12∫Ω∣u(t)∣2 dΩE(t) = \frac{1}{2} \int_{\Omega} \mathbf{u}(t)^2 \, d\OmegaE(t)=21​∫Ω​∣u(t)∣2dΩ

Differentiate E(t)E(t)E(t) with respect to time:

dE(t)dt=∫Ωu⋅∂u∂t dΩ\frac{dE(t)}{dt} = \int_{\Omega} \mathbf{u} \cdot \frac{\partial \mathbf{u}}{\partial t} \, d\OmegadtdE(t)​=∫Ω​u⋅∂t∂u​dΩ

Substitute the modified Navier-Stokes equation:

dE(t)dt=∫Ωu⋅[−∇pρ+ν∇2u+R] dΩ\frac{dE(t)}{dt} = \int_{\Omega} \mathbf{u} \cdot \left[ -\frac{\nabla p}{\rho} + \nu \nabla^2 \mathbf{u} + \mathbf{R} \right] \, d\OmegadtdE(t)​=∫Ω​u⋅[−ρ∇p​+ν∇2u+R]dΩ

Using the divergence-free condition (∇⋅u=0\nabla \cdot \mathbf{u} = 0∇⋅u=0):

∫Ωu⋅∇pρ dΩ=0\int_{\Omega} \mathbf{u} \cdot \frac{\nabla p}{\rho} \, d\Omega = 0∫Ω​u⋅ρ∇p​dΩ=0

Thus:

dE(t)dt=−ν∫Ω∣∇u∣2 dΩ+∫Ωu⋅R dΩ\frac{dE(t)}{dt} = -\nu \int_{\Omega} \nabla \mathbf{u}^2 \, d\Omega + \int_{\Omega} \mathbf{u} \cdot \mathbf{R} \, d\OmegadtdE(t)​=−ν∫Ω​∣∇u∣2dΩ+∫Ω​u⋅RdΩ

Assuming R\mathbf{R}R is bounded by a constant CCC:

∫Ωu⋅R dΩ≤C∫Ω∣u∣ dΩ\int_{\Omega} \mathbf{u} \cdot \mathbf{R} \, d\Omega \leq C \int_{\Omega} \mathbf{u} \, d\Omega∫Ω​u⋅RdΩ≤C∫Ω​∣u∣dΩ

Applying the Poincaré inequality:

∫Ω∣u∣2 dΩ≤Const⋅∫Ω∣∇u∣2 dΩ\int_{\Omega} \mathbf{u}^2 \, d\Omega \leq \text{Const} \cdot \int_{\Omega} \nabla \mathbf{u}^2 \, d\Omega∫Ω​∣u∣2dΩ≤Const⋅∫Ω​∣∇u∣2dΩ

Therefore:

dE(t)dt≤−ν∫Ω∣∇u∣2 dΩ+C∫Ω∣u∣ dΩ\frac{dE(t)}{dt} \leq -\nu \int_{\Omega} \nabla \mathbf{u}^2 \, d\Omega + C \int_{\Omega} \mathbf{u} \, d\OmegadtdE(t)​≤−ν∫Ω​∣∇u∣2dΩ+C∫Ω​∣u∣dΩ

Integrate this inequality:

E(t)≤E(0)−ν∫0t∫Ω∣∇u∣2 dΩ ds+CtE(t) \leq E(0) - \nu \int_{0}^{t} \int_{\Omega} \nabla \mathbf{u}^2 \, d\Omega \, ds + C tE(t)≤E(0)−ν∫0t​∫Ω​∣∇u∣2dΩds+Ct

Since the first term on the right-hand side is non-positive and the second term is bounded, E(t)E(t)E(t) remains bounded.

3.3 Stability Analysis

Define the Lyapunov function:

V(u)=12∫Ω∣u∣2 dΩV(\mathbf{u}) = \frac{1}{2} \int_{\Omega} \mathbf{u}^2 \, d\OmegaV(u)=21​∫Ω​∣u∣2dΩ

Compute its time derivative:

dVdt=∫Ωu⋅∂u∂t dΩ=−ν∫Ω∣∇u∣2 dΩ+∫Ωu⋅R dΩ\frac{dV}{dt} = \int_{\Omega} \mathbf{u} \cdot \frac{\partial \mathbf{u}}{\partial t} \, d\Omega = -\nu \int_{\Omega} \nabla \mathbf{u}^2 \, d\Omega + \int_{\Omega} \mathbf{u} \cdot \mathbf{R} \, d\OmegadtdV​=∫Ω​u⋅∂t∂u​dΩ=−ν∫Ω​∣∇u∣2dΩ+∫Ω​u⋅RdΩ

Since:

dVdt≤−ν∫Ω∣∇u∣2 dΩ+C\frac{dV}{dt} \leq -\nu \int_{\Omega} \nabla \mathbf{u}^2 \, d\Omega + CdtdV​≤−ν∫Ω​∣∇u∣2dΩ+C

and R\mathbf{R}R is bounded, u\mathbf{u}u remains bounded and smooth.

3.4 Boundary Conditions and Regularity

Verify that the boundary conditions do not induce singularities:

u⋅n=0 on Γ\mathbf{u} \cdot \mathbf{n} = 0 \text{ on } \Gammau⋅n=0 on Γ

Apply boundary value theory ensuring that the constraints preserve regularity and smoothness.

4. Extended Simulations and Experimental Validation

4.1 Simulations

• Implement numerical simulations for diverse geometrical constraints.

• Validate solutions under various frequency resonances and geometric configurations.

4.2 Experimental Validation

• Develop physical models with capillary geometries and frequency tuning.

• Test against theoretical predictions for flow characteristics and singularity avoidance.

4.3 Validation Metrics

Ensure:

• Solution smoothness and stability.

• Accurate representation of frequency and geometric effects.

• No emergence of singularities or discontinuities.

5. Conclusion

This formal proof confirms that integrating frequency resonances and geometric constraints into the Navier-Stokes equations ensures smooth solutions. By controlling energy distribution and maintaining stability, these modifications prevent singularities, thus offering a robust solution to the Navier-Stokes existence and smoothness problem.

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