A computational paradigm

I was posed a question by an anonymous follower whether the following animation could be easily simulated on a computer. 

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In today’s world, lots of research are being aided by using numerical methods. But it is quintessential to note that computational methods alone are not enough to dictate behavior of the natural world. It is with the amalgamation of experiments that it’s beauty exemplifies.

The butterfly effect

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One of the many reasons its hard to predict behavior ( say the weather for instance ) is primarily because of the errors that are induced whilst recording it. 

And these errors evolve with time. Let’s take the trivial example of a double pendulum.

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Notice how a slight variation in initial angle with horizontal axis of the blue pendulum causes a huge aberration in the result.

Flow past a cylinder

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When experiments are carried out under controlled conditions, it is possible to observe and simulate phenomenon.

But like it was pointed out before,the simulation per se is proportional to the accuracy of the instruments used to make the measurements themselves.

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So, yeah it is possible to simulate a system such as the one asked, considering crucial boundary conditions are known to us with considerable precision.

And as the complexity of the problem evolves, the computation time and power required also increases exponentially.

Thanks for asking, Have a great day!

If there is magic on this planet, it is contained in water 😀

It’s that time of the year folks, where quenching your thirst with a cool drink is your top most priority. Beer, Lemonade, whatever is up for grabs. But the last thing you would want is your drink to be warm.

So, let’s look at some hacks to turn that warm beer that you have into a cool scintillation for your body and soul.

Beer Hack #1

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                                  Source : Buzzfeed on YouTube                 

The physics

Compared to air, water is the better thermal conductor.

It is like you have a tennis ball and 2 pipes with different diameters ( one bigger than the ball and other smaller ).

The tennis ball will pass easily through through the larger diameter whereas it will be quite difficult with the smaller one.

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Air is like the smaller pipe – offers higher resistance to the transfer of heat. But water offering lower resistance than air cools the beer faster.


Beer Hack #2

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                                  Source : DaveHax on YouTube    

The physics

An ice cube melting will take up energy, while an ice cube freezing will give off energy. Ergo, for ice to melt, it requires energy

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Here’s how the heat would be exchanged ( without addition of salt ):

Beer —–> Can —–> Water —–>Ice (melts it )

Water( initially > 0°C ) and ice ( initially < 0°C ) continue to exchange heat until they approach equilibrium temperature ( 0°C ).

What happens when you add salt ?

Adding salt lowers the
freezing point i.e . The temperature at which a liquid changes into a
solid. This is 0°C. But the addition of salt makes this drop further
down.

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                                                 Source

Here’s how the heat would be exchanged ( with the addition of salt ):

Beer —–> Can —–> Water( colder ) —–> Ice ( melting )

Water( initially > 0°C ) and ice ( initially < 0°C ) continue to
exchange heat until they approach equilibrium temperature ( in this case < 0°C ).

The water reaches 0°C and continues to drop below it ( w/o freezing ) because the freezing point has been lowered with the addition of salt

Since there is much larger temperature gradient between the can and the water, the heat transfer also increases. This cools down the beer much faster than the former.

Pretty cool huh?


Although this post focuses on beer, it is applicable to any other drink as well. Have fun ! ;D

Where to go next:

Why does salt decrease freezing point?

More Beer hacks

The best things come in small packages (#1)

fuckyeahphysica:

People often brag about Large Hadron Collider as having one of the
most sophisticated Technology in the world. True, but even if you are
living in France, it’s still inaccessible! I believe that accessibility
is the true trait of technology.

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Look around the place that
you are sitting in. Do you see a Ball Point pen lying around in the
vicinity? Chances are that it is, are really high.

Today on FYP, we will
unravel the modest physics that governs it.

The physics

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Behold the ball in a ball point pen!.

To write you glide your pen onto the paper right? So what you are doing is rolling the ball that is present on the pen’s tip.

The ink flows continuously under the influence of gravity from the ink reservoir to the ball.

The ball rolls and the ink gets transferred onto the paper.

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                                          Source Video

Why does the ink not pour out ?

This has everything to do with Surface Tension.

A drop of water falling off a tap experiences considerable resistance due to water molecules attracting each other. But eventually the drops are overwhelmed by the weight of water that it falls down,

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             Source

In a narrow diameter tube such as a refill of a ballpoint pen, the ink offers much higher resistance than that of water. Therefore the surface tension wins and holds the ink together.

And also some pens have a safety plugs that aid in this.

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                                                  Source

I feel I must add, in the interest of completeness, that my childhood
research showed that if you remove the tube from the pen casing and suck
on the open end hard enough, the ink will eventually exit through that
open end into your mouth

Ball point pen Hack

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                                                  Source

There are frustrating moments where you know that ink has not fully drained out but yet the pen refuses to write. Well, violently scrubbing it on sheet and shredding the first few pages is a way out of the mess.

But instead try this: Get a lighter or heat source and heat the metal tip. That usually works to loosen up what ever is blocked the ball point.

Why does this happen ?

Generally because the rolling ball has picked up some fibers off the
surface being written on, which gets caught between the ball and the
reservoir, effectively plugging it up


If you thought this post was cool, stay tuned for part-two to be posted tomorrow

fuckyeahphysica:

Why can’t you cycle backwards ?

As a avid cyclist, I have always found it baffling that you can’t cycle backwards

I mean seriously, cant you that to slow the thing down by cycling it backwards or something on that lines. Like what is up with that ?

Behold the Freewheel

Lets lay out the problem in its profound glory

When you pedal the cycle forward, the cycle moves. But when you pedal it backwards, nothing happens!!

This is accomplished by something known as a freewheel that is attached to the rear wheel. It looks like this :

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When you pedal forward, the pawl ( the red part ) engages with the dents on the periphery and the cycle moves forward.

But when you pedal backwards or stop pedaling, the ratchet does not engage with anything, therefore the cycle just remains at its current state of motion.

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Do you hear a “tick” sound every time you spin the wheel anti-clockwise? That’s the pawl just clashing with the dents, producing a ticking sound

Voila! Simple and Elegant


Here’s a diagrammatic representation of the above arrangement.

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Can you slow down the cycle by cycling backwards? Well Yeah! They are accomplished using coaster brakes. If you are interested check’em out.

Have a great day!

EDIT:  biXe Gear lets you cycle forward by pedaling backwards

If I could catch a rainbow

If i could catch a rainbow,

I would just do it for you

And share with you it’s beauty,

On the days you are feeling Blue.

Rainbows are nature’s optical illusion.

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It’s not possible unfortunately to catch a rainbow. They are not objects and are not located at specific distance from the observer that one can physically approach.

Rainbows stems from an optical illusion caused by any water droplets viewed from a
certain angle relative to a light source.

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They are user-specific and everyone sees a different rainbow.

The monochrome rainbow

Not all rainbows that occur in nature are multicolored. Under specific
atmospheric conditions, one can spot the Mono-chrome rainbow i.e It has
only one color.

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                                   PC : rodjonesphotography


Moonbows

A Moonbow / Lunar rainbow /White rainbow  is a
rainbow produced by light reflected off the surface of the moon (as
opposed to direct sunlight) refracting off of moisture-laden clouds in
the atmosphere / from waterfalls.

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                                            PC:

GanMed64


Each of your eyes sees a different rainbow.

Just as no two people see exactly the same rainbow, even if they’re
standing next to each other, the few inches between your eyes make a
difference in what you are viewing. 

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There is no color- indigo ( sort of )

One can distinguish almost all colors in a rainbow but Indigo.

Legend has it that Newton
included indigo because he felt that there should be seven rather than six colors in a rainbow due to his strong religious beliefs.

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Origins of ‘Iris’

The Greeks and Romans thought a rainbow was the path made
by Iris, the goddess of the rainbow, between heaven and earth, linking
gods with humans. “Rainbow” in Latin is arcus iris or arcus pluvius, a “rainy arch”.

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The iris of the eye is named after her, because of its
colour. 

The
Greeks used the word “iris” to describe any coloured circle, such as
the “eye” of a peacock’s tail. The flower called iris gets its name from
the Greek, as does the chemical iridium (Ir), compounds of which are
highly coloured. Iris is also the root of “iridescent”.

Pulsating Rainbows

Place a linear polarizer over the camera whilst capturing a rainbow and you get pulsating rainbows.

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                                                   Source


Double Rainbows/ Multiple Rainbows

A double rainbow is a phenomenon in which two rainbows appear. They are caused by a double reflection of sunlight inside the raindrops. Similarly multiple rainbows are a possibility as well.

Observe that the colors in the second rainbow are inverted because the light is reflected twice inside the water droplet

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                                             PC: Janbazian


Viral Double Rainbow Video

This video of a man witnessing a double rainbow for the first time went viral,  featuring on numerous popular talk shows. Pure ecstasy!

The full rainbow

Whilst standing on earth, we see rainbows as magical arcs across the sky, but rainbows are full circles. The bottom part of the full circle is usually blocked by the horizon.

Pilots however do not face this difficulty. Under the right sky conditions, pilots are spectators to one of nature’s most beautiful spectacles – The full rainbow.

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                                          PC :
Steve Kaufman

Everything has beauty, but not everyone sees it.

Have a great day!

fuckyeahphysica:

Chain Reaction.

Everyone knows that a line of standing dominos creates a fun chain reaction when you knock the first one over; but did you know you can use increasingly larger dominos and get the same result? 

The setup.

Professor Stephen Morris knocks over a 1-meter tall domino that weighs over 100 pounds by starting with a 5mm high by 1mm thick domino.He uses a size ratio of 1.5, meaning each domino is one and a half times larger than the last one. This is the generally accepted maximum ratio that dominos can have to successfully knock each other over.

Hans Van Leeuwen of Leiden University in the Netherlands, published a paper online showing that, theoretically, you could have a size ratio of up to two. But that’s in an ideal (and probably unrealistic) situation.

Fun fact.

There are 13 dominoes in this sequence. If Professor Morris used 29 dominoes in total, with the next one always being 1.5x larger, the last domino would be the height of the Empire State Building.

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Source: Physics Buzz.

On the cross product

fuckyeahphysica:

Understand the concept and not the definition.

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If you have studied vectors, then the notion of a cross product is something that you might be familiar with.

Although it is taught in many colleges and schools in its mathematical glory, this post aims to supplement the same but with an real-life example.

The cross product

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The magnitude of the cross product is the area of the parallelogram with two sides A and B.

The orientation of the cross product is orthogonal to the plane containing this parallelogram. 

Why on earth is it orthogonal ? Like seriously…

I mean this is one of the burning questions regarding the cross product and yet for some reason, textbooks don’t get to the bottom of this.

It is modeling a real life scenario!!

The scenario being :

When you try to twist a screw inside a block in the clockwise direction like so, the nail moves down and vice versa.

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i.e When you move from the screw from u to v, then the direction of the cross product denotes the direction the screw will move.

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That’s why the direction of the cross product is orthogonal. It’s really that simple 😀

Have a good day!

A2A : Anonymous

fuckyeahphysica:

Exploring the Realms of water – The Leidenfrost effect ( #1 )

The skittering of water droplets of a hot surface that you just witnessed is known as the Leidenfrost Effect.

The effect can be seen as drops of water are sprinkled onto a pan at various times as it heats up. There is no specific temperature, beyond which the Leidenfrost effect kicks in.

Unveiling the mystery.

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The bottom part of the water droplet vaporizes immediately on contact with the hot plate. 

The resulting gas suspends the rest of the water droplet just above it, preventing any further direct contact between the liquid water and the hot plate. 

As steam has much poorer thermal conductivity, further heat transfer between the pan and the droplet is slowed down dramatically. This also results in the drop being able to skid around the pan on the layer of gas just under it.

Mesmerizing, isn’t it ?

(Sources: The Leindenfrost Maze , Strange Water

Hand vs Liquid Nitrogen

This also allows the immersion of your bare hands in Liquid Nitrogen for a few Milli-seconds.

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A thin film layer is formed between your hand ( relatively hot compared to liquid nitrogen ) and the Liquid Nitrogen, which prevents the immediate freezing of your hand.

Do not try this at home.

And don’t ever wear a ring/ any jewelery on your hands if you are attempting this under supervision, as this prevents the formation of the thin film. It doesn’t end well after that.

Have a good day!