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Well, this is my first time to participate in such community competitions and guess what, I've gone for 4 submissions so far (Feels Great!!)
So I wanna share some tricks that I followed for my first submission named Happy Shaping' ( Go Check it out!!):
1. Dynamic Background Color Change:
- Technique: The background color of the figure window is gradually changed using sine and cosine functions.
- Reason: These trigonometric functions (sin and cos) create smooth, oscillating transitions over time, which gives a fluid effect to the background's color shift.
- Implementation:
Color = [0.1 + 0.5*abs(sin(f/10)), 0.1 + 0.5*abs(cos(f/15)), 0.9 -
0.5*abs(sin(f/20))];
- Benefit: This introduces a smooth, visually appealing animation effect.
2. Smooth Object Motion Using Sine and Cosine:
- Technique: The position and shape of objects are based on trigonometric functions.
- Reason: Using sin(t) and cos(t) ensures that the movement is circular or elliptical, creating continuous and natural motion in animations.
- Implementation (for object position):
x = 10 * cos(t * 2 * pi) * (1 + 0.5 * sin(t * pi));
y = 10 * sin(t * 2 * pi) * (1 + 0.5 * cos(t * pi));
- Benefit: Circular and smooth motions are pleasing and easily controlled by tweaking the frequency and phase of sine/cosine functions.
3. Polygon Shape Changing Over Time:
- Technique: The number of sides of the polygon (sides) changes dynamically based on t.
- Reason: It creates variation in shape, maintaining user interest as the shape transitions from a triangle to a hexagon.
- Implementation:
sides = 3 + round(3 * abs(sin(t)));
- Benefit: This provides dynamic shape transitions over time, keeping the animation non-static.
4. Use of the fill Function for Color-Filled Shapes:
- Technique: The fill function is used to draw a polygon with smoothly changing colors.
- Reason: Filling polygons with varying colors based on time (t) allows for continuous color transitions, adding more complexity to the animation.
- Implementation:
fill(xp, yp, c, 'EdgeColor', 'none');
- Benefit: Combining both color changes and shape changes enhances the visual impact.
5. Consistent Use of hold on and hold off:
- Technique: hold on allows multiple graphic objects to be drawn on the same axes without clearing previous objects.
- Reason: This is crucial for drawing multiple elements (like polygons, circles, and lines) on the same figure.
- Benefit: It helps manage and layer different graphical elements effectively within the same frame.
6. Use of rectangle for a Smooth Ball Motion:
- Technique: The ball's motion is defined by rectangle with a Curvature of [1, 1] to make it circular.
- Reason: Using the rectangle function simplifies the process of drawing a filled circle, and controlling its position and size is intuitive.
- Benefit: It provides a straightforward way to animate circular objects within the plot.
7. Animating the Connection Line:
- Technique: A white dashed line (w--) is drawn between the polygon and the moving ball to show a connection between these objects.
- Reason: This adds interactivity to the scene, as it gives the impression that the polygon and the ball are related or connected in some way.
- Implementation:
plot([x bx], [y by], 'w--', 'LineWidth', 2);
- Benefit: A dynamic element that adds depth and narrative to the animation, guiding the viewer’s attention.
8. Frame Synchronization with Time (f and t):
- Technique: The variable f is used as a frame number, while t = f / 24 creates a link between frame and time.
- Reason: Ensuring smooth and continuous transitions in the animation over time is critical, so f acts as the control for time-based changes in shape, color, and position.
- Benefit: This makes it easy to manage frame rates and time-based updates for the animation.
Over the past week, we have seen many creative and compelling short movies! Now, let the voting begin! Cast your votes for the short movies you love. Authors, share your creations with friends, classmates, and colleagues. Let's showcase the beauty of mathematics to the world!
We know that one of the key goals for joining the Mini Hack contest is to LEARN! To celebrate knowledge sharing, we have special prizes—limited-edition MATLAB Shorts—up for grabs!
These exclusive prizes can only be earned through the MATLAB Shorts Mini Hack contest. Interested? Share your knowledge in the Discussions' general channel (be sure to add the tag 'contest2024') to earn opportunities to win the coveted MATLAB Shorts. You can share various types of content, such as tips and tricks for creating animations, background stories of your entry, or learnings you've gained from the contest. We will select different types of winners each week.
We also have an exciting feature announcement: you can now experiment with code in MATLAB Online. Simply click the 'Open in MATLAB Online' button above the movie preview section. Even better! ‘Open in MATLAB Online’ is also available in previous Mini Hack contests!
We look forward to seeing more amazing short movies in Week 2!
If you like them, please feel free to use them for free.
Try to install MATLAB2024a on Ubuntu24.04. In the image below, the button indicated by the green arrow is clickable, while the button indicated by the red arrow are unclickable, and input field where text cannot be entered, preventing the installation.
Let's say you have a chance to ask the MATLAB leadership team any question. What would you ask them?
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 I go to a paint store, I can get foldout color charts/swatches for every brand of paint. I can make a selection and it will tell me the exact proportions of each of base color to add to a can of white paint. There doesn't seem to be any equivalent in MATLAB. The common word "swatch" doesn't even exist in the documentation. (?) One thinks pcolor() would be the way to go about this, but pcolor documentation is the most abstruse in all of the documentation. Thanks 1e+06 !
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")
As pointed out in Doxygen comments in code generated with Simulink Embedded Coder - MATLAB Answers - MATLAB Central (mathworks.com), it would be nice that Embedded Coder has an option to generate Doxygen-style comments for signals of buses, i.e.:
/** @brief <Signal desciption here> **/
This would allow static analysis tools to parse the comments. Please add that feature!
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.
The MATLAB Central Community Team
See the attached PDF for a higher resolution
Related blogs posts:
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)
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.
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?
As far as I know, starting from MATLAB R2024b, the documentation is defaulted to be accessed online. However, the problem is that every time I open the official online documentation through my browser, it defaults or forcibly redirects to the documentation hosted site for my current geographic location, often with multiple pop-up reminders, which is very annoying!
Suggestion: Could there be an option to set preferences linked to my personal account so that the documentation defaults to my chosen language preference without having to deal with “forced reminders” or “forced redirection” based on my geographic location? I prefer reading the English documentation, but the website automatically redirects me to the Chinese documentation due to my geolocation, which is quite frustrating!
In the past two years, MATHWORKS has updated the image viewer and audio viewer, giving them a more modern interface with features like play, pause, fast forward, and some interactive tools that are more commonly found in typical third-party players. However, the video player has not seen any updates. For instance, the Video Viewer or vision.VideoPlayer could benefit from a more modern player interface. Perhaps I haven't found a suitable built-in player yet. It would be great if there were support for custom image processing and audio processing algorithms that could be played in a more modern interface in real time.
Additionally, I found it quite challenging to develop a modern video player from scratch in App Designer.(If there's a video component for that that would be great)
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BTW,the following picture shows the built-in function uihtml function showing a more modern playback interface with controls for play, pause and so on. But can not add real-time image processing algorithms within it.
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)=∫Ωu⋅∂t∂udΩ
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)=∫Ωu⋅[−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∫Ωu⋅ρ∇pdΩ=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+∫Ωu⋅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∫Ωu⋅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=∫Ωu⋅∂t∂udΩ=−ν∫Ω∣∇u∣2dΩ+∫Ωu⋅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.
isequaln exists to return true when NaN==NaN.
unique treats NaN==NaN as false (as it should) requiring NaN to be replaced if NaN is not considered unique in a particular application. In my application, I am checking uniqueness of table rows using [table_unique,index_unique]=unique(table,"rows","sorted") and would prefer to keep NaN as NaN or missing in table_unique without the overhead of replacing it with a dummy value then replacing it again. Dummy values also have the risk of matching existing values in the table, requiring first finding a dummy value that is not in the table.
uniquen (similar to isequaln) would be more eloquent.
Please point out if I am missing something!