On The Transpose Of A Matrix

Here’s every total solar eclipse happening in your lifetime. Is this year your best chance?

On Aug. 21, a total solar eclipse will be visible from the continental United States. It’ll be the first to traverse coast to coast in nearly a century. Learn more about past and future eclipses: See full graphic.

The dihydrogen monoxide hoax involves calling water by the unfamiliar chemical name “dihydrogen monoxide” (DHMO), and listing some of water’s effects in an alarming manner, such as the fact that it accelerates corrosion and can cause severe burns. The hoax often calls for dihydrogen monoxide to be regulated, labeled as hazardous, or banned. It illustrates how the lack of scientific literacy and an exaggerated analysis can lead to misplaced fears.

The hoax gained renewed popularity in the late 1990s when a 14-year-old student collected anti-DHMO petitions for a science project about gullibility. The story has since been used in science education to encourage critical thinking and avoid the appeal to nature.

Forty-three students favored banning DHMO, six were undecided, and only one correctly recognized that ‘dihydrogen monoxide’ is actually plain old water.

Here’s the information he gave the students:

Dihydrogen monoxide is colorless, odorless, tasteless, and kills uncounted thousands of people every year. Most of these deaths are caused by accidental inhalation of DHMO, but the dangers of dihydrogen monoxide do not end there. Prolonged exposure to its solid form causes severe tissue damage. Symptoms of DHMO ingestion can include excessive sweating and urination, and possibly a bloated feeling, nausea, vomiting and body electrolyte imbalance. For those who have become dependent, DHMO withdrawal means certain death.

Dihydrogen monoxide:

is also known as hydroxl acid, and is the major component of acid rain.

contributes to the “greenhouse effect.”

may cause severe burns.

contributes to the erosion of our natural landscape.

accelerates corrosion and rusting of many metals.

may cause electrical failures and decreased effectiveness of automobile brakes.

has been found in excised tumors of terminal cancer patients.

Contamination is reaching epidemic proportions!

Quantities of dihydrogen monoxide have been found in almost every stream, lake, and reservoir in America today. But the pollution is global, and the contaminant has even been found in Antarctic ice. DHMO has caused millions of dollars of property damage in the midwest, and recently California.

Despite the danger, dihydrogen monoxide is often used:

as an industrial solvent and coolant.

in nuclear power plants.

in the production of styrofoam.

as a fire retardant.

in many forms of cruel animal research.

in the distribution of pesticides. Even after washing, produce remains contaminated by this chemical.

as an additive in certain “junk-foods” and other food products.

Companies dump waste DHMO into rivers and the ocean, and nothing can be done to stop them because this practice is still legal. The impact on wildlife is extreme, and we cannot afford to ignore it any longer!

The American government has refused to ban the production, distribution, or use of this damaging chemical due to its “importance to the economic health of this nation.” In fact, the navy and other military organizations are conducting experiments with DHMO, and designing multi-billion dollar devices to control and utilize it during warfare situations. Hundreds of military research facilities receive tons of it through a highly sophisticated underground distribution network. Many store large quantities for later use.

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Why most metals are silver (but copper and gold aren’t)

If we want to understand what gives a metal its color we first need to understand a little bit about the definition of a metal. Metals are materials that experience metallic bonding - wherein the atoms are so close that there is a veritable “sea of electrons” in the substance. (This is also what makes metals conductors, but that’s another story). Basically each atom donates an electron or two that is free to flow throughout the material, unattached to any particular nucleus. 

This proximity leads to an overlap in the allowed energy levels of electrons (shown in the lower left hand image above); basically the higher empty electronic levels are so close to the uppermost filled levels (also called the Fermi level) that they form an essentially continuous band of allowed energies. 

Now, backtracking a little bit, color in a substance is caused when a material doesn’t absorb a particular wavelength of light. Because of the empty energy levels mentioned above, metals generally can absorb all wavelengths of light in the visible spectrum. This implies that a metal should look black, except that the excited electron can immediately fall back to the state that it came from, emitting exactly the same energy, causing a flat piece of metal to appear reflective. Thus, the reason why most metals are silver. (Also, the flatter a metal, the more reflective, thanks to diffuse vs. specular reflection).

For a few select metals, like copper and gold, the absorption and emission of photons are noticeably dependent on wavelength across the visible part of the spectrum. The graph in the lower right image above shows the reflectance of aluminum, silver, and gold, including wavelengths in the infrared and ultraviolet. Aluminum is pretty reflective overall, and silver is highly reflective in the visible region (about 400 to 700 nm), but gold clearly absorbs wavelengths about 500 nm or below. Thus, it most strongly reflects yellow, giving it its characteristic appearance. 

Sources: (first image), 2 (second image), 3 (third image), 4

In mathematics there is a concept known as ‘Conformal Mapping’ which allows you convert a given shape to a completely different one by making a transformation.

In the joukowski transform you take all the points on a circle and apply the following transform:

And the resulting transformed points resemble an aerofoil shape. Pretty cool huh ?

** Conformal mappings are a really cool topic in complex analysis but also equally extensive. If you want to know more about them click here

Just imagine a world full of beautiful stained glass windows which also generate electricity…

[Oxford Photovoltaics]

But that’s not all it can do. Microsoft and NASA teamed up to “bring” you, yes you, to Mars.

Follow @the-future-now

Alloys: Wood’s Metal

Also known as Lipowtiz’s alloy as well as the commercial names of Cerrobend, Bendalloy, Pewtalloy, and MCP 158 among others, Wood’s metal is a bismuth alloy consisting of 50% bismuth, 26.67% lead, 13.33% tin, and 10% cadmium by weight. Named for the man who invented it, a Barnabas Wood, Wood’s metal was discovered/created by him in 1860.

Wood’s metal is both a eutectic and a fusible alloy, with a low melting temperature of approximately 70 °C (158 °F). While none of its individual components have a melting temperature of less than 200 °C, a eutectic alloy can be considered as a pure (homogeneous) substance and always has a sharp melting point. If the elements in a eutectic compound or alloy are not as tightly bound as they would be in the pure elements, this leads to a lower melting point. (Eutectic substances can have higher melting points, if its components bind tightly to themselves.)

Useful as a low-temperature solder or casting metal, Wood’s metal is also used as valves in fire sprinkler systems. Thanks to its low melting temperature, Wood’s metal melts in the case of a fire and thanks to the bismuth it is made from, the alloy also shrinks when it melts (bismuth, like water ice, is one of the few substances to do so) which is the key to setting off the sprinkler system. Wood’s metal is also often used as a filler when bending thin walled metal tubes: the filler prevents the tube from collapsing, then can be easily removed by heating and melting the Wood’s metal. Other applications include treating antiques, as a heat transfer medium in hot baths, and in making custom shaped apertures and blocks for medical radiation treatment.

With the addition of both lead and cadmium, however, Wood’s metal is considered to be a toxic alloy. Contact with bare skin is thought to be harmful, especially once the alloy has melted, and vapors from cadmium containing alloys are also quite dangerous and can result in cadmium poisoning. A non-toxic alternative to Wood’s metal is Field’s metal, composed of bismuth, tin, and indium.

Sources: ( 1 - image 4 ) ( 2 - image 2 ) ( 3 ) ( 4 )

Image sources: ( 1 ) ( 3 )

More Than You Ever Wanted to Know About Mechanical Engineering, Part 33: Stress Concentrations With Fluctuating Stresses

There’s one last complication to consider with fluctuating stresses. When we looked at the case of fully reversed stresses (that is, σ_m = 0, σ_a ≠ 0) we found a fatigue stress concentration factor based on the stress concentration factor for a static situation.

With a fluctuating stress, the situation is a little different. Since the mean stress is non-zero, the part is always under some kind of load. We can consider the effects of this constant mean stress separately from the effects of the momentary alternating stress and assign them a separate fatigue stress concentration factor, which we’ll call K_fm.

Let’s think about what’s actually physically happening to a part being subjected to a fluctuating stress. Let’s say we’re dealing with a plate with a slot in it subjected to fluctuating tension.

There’s obviously a large stress concentration at the slot that we’ll have to take into account.

There’s three different scenarios which can occur here. The first is that the maximum stress the plate sees (the largest value of combined mean and alternating stress, taking stress concentrations into account) never approaches the yield strength of the material. The plate just stretches and contracts elastically. This isn’t really any different from our previous situation with fatigue stress concentration factors - we can use the K_f factor we got earlier here.

But suppose the yield strength is exceeded. What happens then? If the maximum stress is greater than the yield strength, then the plate must deform plastically at that point of maximum stress - the slot must widen. If the slot is wider, then the stress concentration is relieved - there’s more room for movement before the geometry stops you. If other words, the fatigue stress concentration factor is lessened.

If it’s just your maximum stress that exceeds the yield strength but your minimum stress is still below it, this localized yielding will be one-sided - you’ll get a slot that’s widened on one side, but you’ll still have some overall mean stress. If this is the case, you base your stress concentration factor on the relationship of the mean and alternating stresses to the yield strength.

If both your minimum and maximum stresses exceed the yield strength of the material, you get a situation where you’ve widened the slot as far as you can without actually breaking the part on both sides and you’re experiencing a stress of magnitude equal to the yield strength at either extreme of the fluctuation. Since you now have a fluctuation with equal and opposite extremes, your mean stress is zero - the mean fatigue stress concentration factor is zero. The scenario is now one of fully reversed loading and the mean stress drops right out of it.

The ocean is where the aliens live.

Transcript under the cut.

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That Time We Flew Past Pluto…

Two years ago today (July 14), our New Horizons spacecraft made its closest flyby of Pluto…collecting images and science that revealed a geologically complex world. Data from this mission are helping us understand worlds at the edge of our solar system.

The spacecraft is now venturing deeper into the distant, mysterious Kuiper Belt…a relic of solar system formation…to reach its next target. On New Year’s Day 2019, New Horizons will zoom past a Kuiper Belt object known as 2014 MU69.

The Kuiper Belt is a disc-shaped region of icy bodies – including dwarf planets such as Pluto – and comets beyond the orbit of Neptune. It extends from about 30 to 55 Astronomical Units (an AU is the distance from the sun to Earth) and is probably populated with hundreds of thousands of icy bodies larger than 62 miles across, and an estimated trillion or more comets.

Nearly a billion miles beyond Pluto, you may be asking how the spacecraft will function for the 2014 MU69 flyby. Well, New Horizons was originally designed to fly far beyond the Pluto system and explore deeper into the Kuiper Belt. 

The spacecraft carries extra hydrazine fuel for the flyby; its communications system is designed to work from beyond Pluto; its power system is designed to operate for many more years; and its scientific instruments were designed to operate in light levels much lower than it will experience during the 2014 MU69 flyby.

What have we learned about Pluto since its historic flyby in 2015?

During its encounter, the New Horizons spacecraft collected more than 1,200 images of Pluto and tens of gigabits of data. The intensive downlinking of information took about a year to return to Earth! Here are a few things we’ve discovered:

Pluto Has a Heart

This image captured by New Horizons around 16 hours before its closest approach shows Pluto’s “heart.” This stunning image of one of its most dominant features shows us that the heart’s diameter is about the same distance as from Denver to Chicago. This image also showed us that Pluto is a complex world with incredible geological diversity.

Icy Plains

Pluto’s vast icy plain, informally called Sputnik Planitia, resembles frozen mud cracks on Earth. It has a broken surface of irregularly-shaped segments, bordered by what appear to be shallow troughs.

Majestic Mountains

Images from the spacecraft display chaotically jumbled mountains that only add to the complexity of Pluto’s geography. The rugged, icy mountains are as tall as 11,000 feet high.

Color Variations

This high-resolution enhanced color view of Pluto combines blue, red and infrared images taken by the New Horizons spacecraft. The surface of tPluto has a remarkable range of subtle color variations. Many landforms have their own distinct colors, telling a complex geological and climatological story.

Foggy Haze and Blue Atmosphere

Images returned from the New Horizons spacecraft have also revealed that Pluto’s global atmospheric haze has many more layers than scientists realized. The haze even creates a twilight effect that softly illuminates nightside terrain near sunset, which makes them visible to the cameras aboard the spacecraft.

Water Ice

New Horizons detected numerous small, exposed regions of water ice on Pluto. Scientists are eager to understand why water appears exactly where it does, and not in other places.

Stay updated on New Horizons findings by visiting the New Horizons page. You can also keep track of Pluto News on Twitter via @NASANewHorizons.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com