Scrat and the Stevin law

The pressure in a fluid depends only by the deep $h$ and the density of the fluid $\rho_f$: \[p = \rho_f h g\] where $g$ is the gravity.
We could consider also the generalized stevin law \[p = \rho_f h g + p_0\] where $p_0$ is the atmospheric pressure at sea level, but in order to explain the starting sequence in the following animation the first equation is sufficient.

Thanks to Leonardo Petrillo (twitter, GPlus)

A new sustainability model for Open Access

PeerJ is a new proposal in the world of the scientific journals with Open Access licenses. They write:

First, the tax payers deserve free access to research they've paid for. "They won't understand it" is not a valid excuse. Neither is calling Open Access an unsustainable model.
Second, the research community greatly benefits from unencumbered access to the research. And it helps the individual authors rapidly gain credit and revise their work. PeerJ is striving to make research a living process, not a set in stone PDF.

This philosophy is very good and resume all critical points in the OA model proposed by the great publishers. And it seems that this new model will be applied:

PeerJ is establishing a new sustainability model. Researchers will be able to purchase Lifetime Memberships, starting at just $99, giving them the rights to publish their articles in our peer reviewed journal. All published articles are made freely available to the public. Subscription fees made sense in a pre-Internet world, but now they just slow the progress of science. It's time to change that.

In this way each researchers, also in Africa, for example, can afford to support Open Access.
I hope that this is not a dream.

Thanks to OggiScienza.

Maurice Sendak and the atomics for the millions

Attention: the post was updated after the first publication.

Atomics for the millions by Maxwell Leigh Edinoff and Hyman Ruchlis was the first book illustrated by Maurice Sendak.
In this post I propose you some illustration from the book that I found on the blog Collection children's books:

I choise some illustrations from the post. In particular, after the Einstein's portrait, the following two: in the first we can see the dance of the atoms: they bound with others in order to compose molecules. In the second there is a brief pictoric description of the radiation (left) and of the core of a nuclear power:

But the last, I think represents the story of the mankind, and, in this way, the only choice for our destiny seems logic. Or not?

Thanks to Peppe Liberti

The void theory

On tumblr, one of my reader, frankietwohats, ask me the following question:

Can I ask you a random question? I can't remember the name of a theory that argued that the universe wasn't expanding, but instead was stretching. Do you happen to know of it/it's name? It came up in conversation today (well, universe expansion did) and I want to look into it more.

I don't know if this is the theory that you intend, but after a briefly research on Google, i find th Void theory. About it, Esther Inglis-Arkell writes on io9:

There was a time that the earth was considered the center of the universe. Then it got knocked out of the way by the sun, and ever since then the astronomer's mantra was, "We are nothing special." The part of the universe the earth resides in can't be any different than any other part. It's not unique, or remarkable, or even out of the ordinary. Void Theory contradicts all that. Instead of sitting in a typical part of the universe, the earth sits in an unusually empty part; a void. The universe isn't expanding due to some mysterious force. It's just that when light comes from a denser part of the universe and trips across the void, it is altered to make it look like the universe is expanding. Since this exansion is the same when observed from any part of the earth, the earth has to be roughly at the center of this void. Suddenly, the observable universe is geocentric again.

But... what is the void theory?

This diagram reveals changes in the rate of expansion since the universe's birth 15 billion years ago. The more shalow the curve, the faster the rate of expansion. The curve changes noticeably about 7.5 billion years ago, when objects in the universe began flying apart as a faster rate. Astronomers theorize that the faster expansion rate is due to a mysterious, dark force that is pulling galaxies apart.

First of all, following Clifton, Ferreira and Land⁽¹⁾, we must remember that our picture of the universe is based on the following two principles: the spacetime is dynamical, obeying to the Einstein's equations; the Universe is homogeneous and isotropic on large scales, that is a generalisation of the Copernican Principle that the Earth is not in a central, specially favored position.
Now, the exact solution of Einstein's equations was provided by Lemaitre-Tolman-Bondi spacetime \[\text{d} s^2 = -\text{d} t^2 + \frac{Y'^2}{1-K} \text{d} r^2 + Y^2 \text{d} \Omega\] In this model there are four free parameters: the density at the origin, the density and radius at the midpoint, and the radius at which we match to Einstein-de Sitter spacetime⁽²⁾. Instead the void model:

is completely specfied by the radial profile, the Hubble rate at the void centre today, $H_0$, the radiation density today, which is fixed by the CMB mean temperature, $T_0 = 2.725 K$, and the baryon fraction $f_b = \frac{\rho_b}{\rho_m}$. Outside the void we asymptote to EdS.

The curvature for three different types of voids

The checklist for reading (and writing) science news

Emily Willingham (also on Field of Science) writes a little how to read science news. Because I'm a scientific blogger, this checklist could be useful in order to write better posts. In particular I would emphasize the following paragraphs:

What is the basis of the article? Science news originates from several places. Often it's a scientific paper. These papers come in several varieties. The ones that report a real study--lots of people or mice or flies, lots of data, lots of analysis, a hypothesis tested, statistics done--is considered "original research." Those papers are the only ones that are genuinely original scientific studies. Words to watch for--terms that suggest no original research at all--are "review," "editorial," "perspective," "commentary," "case study" (these typically involve one or only a handful of cases, so no statistical analysis), and "meta-analysis." None of these represents original findings from a scientific study. All but the last two are opinion. Also watch for "scientific meeting" and "conference." That means that this information was presented without peer review at a scientific meeting. It hasn't been vetted in any way.

In this sense the use of Researchblogging is very useful for readers for two reasons: first of all the reader can know the blogger's seriousness, and secondary the widget can say the origin of the researches telled in the post.

Look at the original source of the information. Google is your friend. Is the original source a scientific journal? At the very least, especially for original research, the abstract will be freely available. A news story based on a journal paper should provide a link to that abstract, but many, many news outlets do not do this--a huge disservice to the interested, engaged reader. At any rate, the article probably includes the name of a paper author and the journal of publication, and a quick Google search on both terms along with the subject (e.g., autism) will often find you the paper. If all you find is a news release about the paper--at outlets like ScienceDaily or PhysOrg--you are reading marketing materials. Period. And if there is no mention of publication in a journal, be very, very cautious in your interpretation of what's being reported.

ScienceDaily usually proposes also the link the paper (or to the draft version) also when it isn't in the original press release. In general ScienceDaily and PhysOrg reprint the press release written by the university or by the research team, and if you want read the original press release you can use Google.
I published press release in two cases: in the first case I published the text sended me by a friend about the results of his team research. In the second, recent case I publish some paragraphs from the original press release published on web, embedding some original paragraphs.
In general I try to publish original posts, but sometimes I cannot write post such that, so I use the abstracts (that I publish especially on posterous) or the press release on this blog. Instead on tumblr I use this solution for the quick posts.
Another warranty for the readers are the science blog networks, like FoS: they are generally constituted by researchers and theachers that tell science with passion and competence.
And, in conclusion:

Ask a scientist. Twitter abounds with scientists and sciencey types who may be able to evaluate an article for you. I receive daily requests via email, Facebook, and Twitter for exactly that assistance, and I'm glad to provide it. Seriously, ask a scientist. You'll find it hard to get us to shut up. We do science because we really, really like it. It sure ain't for the money.

In this case I simply share my twitter account, @ulaulaman, and my GPlus account, Gianluigi Filippelli, but if you want ask something or submit a post, you can use also the tumblr form.

Best regards to all, and read science!

A universe from nothing

I would share with you a talk by Lawrence Krauss, physics and writer (The Physics of Star Trek) about the universe:

Thanks to Fabio De Sicot (twitter, Google Plus)

A flat torus in three dimensional space

Vincent Borrelli, Said Jabrane, Francis Lazarus and Boris Thibert realize for the first time the image of a 3d flat torus. But, what is a flat torus? In a mathematical point of view is a torus without gaussian curvature everywhere. For example: in a 3d space, you can bend a sheet of paper in a cylinder, but you cannot embed it in a torus without stretching the paper itself. But, if you live in a 2d space, a flat torus is a surface like the pacman labirint: you can enter in the right side of the paper and exit behind you from the left side:

We can define a flat torus starting from a couple of real numbers $u$, $v$ such that $u, v \in ]0, 2 \pi]$⁽¹⁾: \[(u, v) \rightarrow \frac{1}{\sqrt{2}} \left ( \cos (u+v), \sin (u+v), \cos (u-v), \sin (u-v) \right )\] The following is the best visualization of a flat torus before Borelli-Jabrane-Lazarus-Thibert:

The mathematical problem around the flat torus was challenged by Nash and Kuiper in 1950s:

Nash and Kuiper proved the existence of a representation that does not perturb the lenghts in the square flat torus. For a long time, this existence remained a challenge for the imagination of mathematicians. But proving and showing should sometimes be clearly distinguished in Mathematics. This is well explained by the thief allegory: Let us assume that a group of people is gathered around a jewel in a closed room. Let us further suppose that the light is turned off for a moment and that the jewel has disappeared when the light is again turned on. We then have the proof that a robber is hiding among the attendance but he can not be exhibited. Although the proofs of Nash and Kuiper are much more than an «existential» trap, their proofs do not provide a sufficiently explicit procedure that would allow for visualization or simply for a mental picture of a square flat torus.⁽²⁾

Between 70s and 80s the Abel Prize Gromov extracted a method from the work of Nash and Kuiper, proposing the so called convex integration, a very useful tool. Indeed it

(...) does not only yield the existence of a solution, it also provides us with an effective construction.⁽²⁾

Starting from this method, Borelli, Jabrane, Lazarus and Thibert realize an algorithm in order to picture the flat torus.

Mathematicians were puzzled by the works of Nash and Kuiper. These works could indeed prove the existence of objects whose regularity was problematic, if not paradoxical. They had to be smooth and rough at the same time... In effect, the mathematical analysis of the images reveals a surface belonging to two antagonist worlds; the smooth surfaces and the fractals,infinitely broken. When zooming in, we invariably observe ripples at smaller and smaller scales. Each ripple - called a corrugation – appears smooth when viewed alone, but the accumulation of those creates an object with a rough and fractal aspect.⁽²⁾

And in conclusion

Demonstrating that convex integration can be implemented open new perspectives in applied mathematics, notably for solving differential systems originating from Physics and Biology.
More specifically, our images reveal a class of objects whose structure lies inbetween smooth surfaces and fractals. Such objects could play a central rôle for shape analysis. They could also resolve some unexplained paradoxes.⁽²⁾

---

Read also Wikipedia | phys.org

---

(1) The Flat Torus in the Three-Sphere
(2) A flat torus in three dimensional space (pdf) | Hevea Project

---

Borrelli, V., Jabrane, S., Lazarus, F., & Thibert, B. (2012). Flat tori in three-dimensional space and convex integration Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.1118478109