Jacopo.bertolotti

Author(s): Thomas Hisch, Matthias Liertzer, Dionyz Pogany, Florian Mintert, and Stefan Rotter

The angular emission pattern of a random laser is typically very irregular and difficult to tune. Here we show by detailed numerical calculations that one can overcome the lack of control over this emission pattern by actively shaping the spatial pump distribution. We demonstrate, in particular, how...

[Phys. Rev. Lett. 111, 023902] Published Fri Jul 12, 2013

Benoit Mandelbrot delivered one of the very early 24/7 Lectures. A 24/7 Lecture is a lecture in two parts: first a complete technical description in 24 seconds, second a simple description anyone can understand in 7 words.

At the 2006 Ig Nobel Prize Ceremony, Professor Mandelbrot, who invented the concept of fractals, here spoke on the topic: FRACTALS. His seven-word summary has become a classic definition, against which all others are measured.

Here’s video of that historic moment:

BONUS: The 24/7 Lectures have been a featured part of every Ig Nobel Prize Ceremony since 2001. This year’s ceremony, on September 12, 2013, will include several new 24/7 Lectures, each written and performed by one of the world’s great thinkers.

BONUS: Dany Adams’s classic 24/7 Lecture on BIOLOGY

BONUS: Eric Lander’s classic 24/7 Lecture on THE HUMAN GENOME

BONUS: Other Improbable Research videos

Photons could conceivably decay, but new analysis of the cosmic microwave background shows that a visible wavelength photon is stable for at least 10¹⁸ years.

Published Thu Jul 11, 2013

Trial and error

Nature 499, 7457 (2013). doi:10.1038/499125a

Italian officials should not go ahead with expensive clinical tests of an unproven stem-cell therapy that has no good scientific basis.

Observation of trapped light within the radiation continuum

Nature 499, 7457 (2013). doi:10.1038/nature12289

Authors: Chia Wei Hsu, Bo Zhen, Jeongwon Lee, Song-Liang Chua, Steven G. Johnson, John D. Joannopoulos & Marin Soljačić

The ability to confine light is important both scientifically and technologically. Many light confinement methods exist, but they all achieve confinement with materials or systems that forbid outgoing waves. These systems can be implemented by metallic mirrors, by photonic band-gap materials, by highly disordered media (Anderson localization) and, for a subset of outgoing waves, by translational symmetry (total internal reflection) or by rotational or reflection symmetry. Exceptions to these examples exist only in theoretical proposals. Here we predict and show experimentally that light can be perfectly confined in a patterned dielectric slab, even though outgoing waves are allowed in the surrounding medium. Technically, this is an observation of an ‘embedded eigenvalue’—namely, a bound state in a continuum of radiation modes—that is not due to symmetry incompatibility. Such a bound state can exist stably in a general class of geometries in which all of its radiation amplitudes vanish simultaneously as a result of destructive interference. This method to trap electromagnetic waves is also applicable to electronic and mechanical waves.

By exploiting some exotic acoustic techniques, researchers have built a window that allows the passage of air but not sound

European deal cuts red tape

Nature 499, 7456 (2013). http://www.nature.com/doifinder/10.1038/499018a

Author: Quirin Schiermeier

Horizon 2020 research programme streamlines project reimbursements.

US and UK join forces

Nature 499, 7456 (2013). doi:10.1038/nj7456-117a

Initiative will fund joint research projects in emerging nations.

Reduction of the radiative decay of atomic coherence in squeezed vacuum

Nature 499, 7456 (2013). doi:10.1038/nature12264

Authors: K. W. Murch, S. J. Weber, K. M. Beck, E. Ginossar & I. Siddiqi

Quantum fluctuations of the electromagnetic vacuum are responsible for physical effects such as the Casimir force and the radiative decay of atoms, and set fundamental limits on the sensitivity of measurements. Entanglement between photons can produce correlations that result in a reduction of these fluctuations below the ordinary vacuum level, allowing measurements that surpass the standard quantum limit in sensitivity. The effects of such ‘squeezed states’ of light on matter were first considered in a prediction of the radiative decay rates of atoms in squeezed vacuum. Despite efforts to demonstrate such effects in experiments with natural atoms, a direct quantitative observation of this prediction has remained elusive. Here we report a twofold reduction of the transverse radiative decay rate of a superconducting artificial atom coupled to continuum squeezed vacuum. The artificial atom is effectively a two-level system formed by the strong interaction between a superconducting circuit and a microwave-frequency cavity. A Josephson parametric amplifier is used to generate quadrature-squeezed electromagnetic vacuum. The observed twofold reduction in the decay rate of the atom allows the transverse coherence time, T2, to exceed the ordinary vacuum decay limit, 2T1. We demonstrate that the measured radiative decay dynamics can be used to reconstruct the Wigner distribution of the itinerant squeezed state. Our results confirm a canonical prediction of quantum optics and should enable new studies of the quantum light–matter interaction.

Della vicenda Stamina si è già scritto tutto, o quasi. In particolare si è parlato, in questi giorni, del presunto plagio delle immagini dall’articolo di Elena Schegelskaya inserite nelle domande di brevetto presentate da Stamina. Ma soprattutto dei rinvii ripetutamente richiesti da Davide Vannoni per fornire al ministero il protocollo per la sperimentazione della terapia a base di staminali. Quasi paradossale, a questo proposito, l’intervista rilasciata da Vannoni questa mattina a Radio24, nella trasmissione di Alessandro Milan, in cui confusamente parla di semplificazione e di standardizzazione di un protocollo che non si sa bene se e quando sarà consegnato al ministero. Il link all’intervista è questo, se volete farvene un’idea. (L’intervista, per inciso, è negli ultimi venti minuti del programma.)

Al di là delle critiche già espresse da molti altri, molto più competenti di me, c’è una frase di Vannoni che mi ha colpito. E precisamente questa: «Visto che avevo in mano una terapia che pensavo funzionasse, ho cercato di applicarla, salvando delle persone». Senza aspettare, dunque, i lunghi processi di validazione cui sono sottoposte le terapie mediche prima di poter accedere alla pratica clinica.

E questo mi ha fatto venire in mente una vecchia storia. Siamo nel 1932, alla fine di marzo, quando il magnate newyorchese Eben M. Byers muore nella sua sontuosa dimora, vittima di una malattia che da 18 mesi ne devastava il corpo, corrodendo lo scheletro finché le ossa avevano iniziato a scheggiarsi. Amici e parenti contattano i più celebri luminari dell’epoca per sapere se Byers sia morto a causa di una malattia contagiosa, mentre le autorità istituiscono un’inchiesta, e le conclusioni preliminari dell’autopsia vengono pubblicate dal «New York Times»: «Avvelenamento da radio».

La tragedia di Byers è iniziata nel 1927, in seguito a una dolorosa frattura che gli impediva di muovere disinvoltamente un braccio per praticare l’amato golf. È un medico di Pittsburgh a consigliargli una specialità messa a punto un paio d’anni prima dal «dottor» William A. Bailey, funambolico titolare del Bailey Radium Laboratory, con sede nel New Jersey. Il Radithor, d’altra parte, è descritto dal produttore come cura per la dispepsia, l’ipertensione, l’impotenza e almeno altre 150 malattie «del sistema endocrino», recitano i depliant. E, sul mercato da appena due anni, ha già un considerevole successo, dato anche il prezzo oltraggioso per l’epoca. Di fatto, si tratta di acqua contenente forti dosi di radio, l’elemento scoperto da Marie e Pierre Curie meno di trent’anni prima e che dà il nome alla radioattività.

Tra il 1925 e il 1930 Bailey venderà 400.000 confezioni di Radithor, ma pure altri produttori – anche in Europa – si buttano sul neonato mercato dei prodotti medici a base di radio, sebbene le autorità sanitarie comincino ad accumulare dati sul fatto che anche piccole quantità di sostanze radioattive possono avere effetti negativi sulla salute. Nessuno però sembra preoccuparsene, e la Food and Drug Administration, che aveva un potere sicuramente meno esteso di oggi, poteva dare avvertimenti ma non intraprendere azioni legali. È dunque la Federal Trade Commission, nel 1928, a incaricare una commissione d’inchiesta di intraprendere una ricerca sulle presunte virtù curative del Radithor. E finalmente, il 19 dicembre 1931, emana un’ordinanza che intima al Bailey Radium Laboratory di interrompere la vendita del preparato.

Ma per Byers è troppo tardi. Chiamato a testimoniare davanti alla commissione nel settembre 1931, non è in condizione di muoversi, e deve ricevere il procuratore incaricato di incontrarlo nella sua residenza. La descrizione è terrificante: Byers riesce a malapena a parlare, ha la testa avvolta da bende, ha subito due interventi chirurgici al volto in cui gli sono state rimosse l’intera mascella, con l’eccezione di due incisivi, e la maggior parte della mandibola.
Con la sua morte, nel 1932, la commissione riprende le indagini, e la Food and Drug Administration dà il via a una campagna per ottenere poteri più ampi. Le associazioni mediche approfittano dell’occasione per denunciare tutte le vendite di specialità medicinali sospette e reclamare leggi per il controllo del radio. Di fatto, i precursori della attuali normative restrittive sulla vendita di prodotti radiofarmaceutici risalgono al caso Byers.

Non solo. Il caso Byers ha offerto un contributo decisivo a porre il principio secondo cui ogni terapia è pericolosa finché non ne venga provata la sicurezza.

Le conclusioni tiratele voi. Io mi limito a osservare che la scienza moderna, e in particolare la scienza medica, funziona così. Non si possono dare a Vannoni le chiavi del Servizio sanitario nazionale – come a volte sembrerebbe pretendere, per esempio quando lamenta che non ci siano esperti scelti da lui nella commissione di valutazione – e facesse un po’ come gli pare. Perché sarebbe fare un passo indietro di almeno un secolo nel modo di intendere la ricerca medica e, in senso più ampio, cancellare ad hoc il principio di precauzione. Sarebbe abdicare al ruolo della Evidence Based Medicine, la medicina fondata sulle prove di efficacia, che non è un impedimento alla tempestività delle cure, ma casomai una conquista della civiltà in nome della sicurezza dei cittadini.

Tre altre piccole note.
La prima: trovo inammissibile che strutture ospedaliere pubbliche abbiano autorizzato la somministrazione della cura Vannoni con l’infusione di cellule staminali senza preoccuparsi di conoscerne la sicurezza e l’efficacia prima di ammetterla nella pratica clinica.
La seconda: mi pare singolare che il Governo e il Parlamento di questa Repubblica abbiano prima dato il via libera al Decreto Balduzzi e poi alla sperimentazione Stamina nelle modalità approvate dalla Camera come se fosse tutto normale, mentre chiedono a gran voce e quasi all’unanimità la clausola di salvaguardia sugli OGM in campo agroalimentare quando questi hanno passato tutte le fasi di sperimentazione e validazione (e ormai di commercializzazione, in altri paesi) che Vannoni vorrebbe saltare a piè pari.
La terza: sarebbe bello che chi, nel mondo della comunicazione, ha alimentato questa vicenda nei modi e nei tempi in cui si è dipanata, strumentalizzando il dolore delle famiglie, si facesse un sacrosanto esame di coscienza, e – per il bene dell’informazione – cambiasse mestiere. O si occupasse d’altro.

Photo credit: Andrea Tedeschi.

Ci ha lasciato Margherita Hack, astrofisica dalla lingua tagliente. Aveva un pregio speciale, oltre a quello di essere riuscita a diventare famosa pur occupandosi di una materia che per molti è del tutto avulsa dalla realtà: quello di dire le cose come stanno, non solo in campo scientifico, con buona pace della convenienza e del politically correct.

Sono poche le persone che hanno il coraggio di dire “io la penso così e te lo dico in faccia; se non ti garba, pazienza” invece di cercare l'accomodamento, il compromesso, la via di mezzo che non scontenta nessuno ma al tempo stesso inevitabilmente non accontenta veramente nessuno. Per questo mi mancherà la sua toscanissima schiettezza.

Margherita Hack era inoltre una delle fondatrici del CICAP e ne è sempre stata uno dei garanti scientifici. Di lei ho un ricordo personale che riassume secondo me perfettamente il suo spirito e il suo lascito: venne a Lugano nel dicembre del 2009 per una lezione pubblica al Liceo Cantonale (foto qui sopra). Sala strapiena per un tema già di per sé accattivante (la scoperta di pianeti extrasolari e la probabilità di vita nell'universo), raccontato con il suo piglio e il suo accento inconfondibili, solo leggermente rallentati dall'età.

Nella sessione di domande alla fine della sua lezione, una persona del pubblico chiese alla Hack cosa ne pensasse dell'esagono gigante che era stato osservato su Saturno. Ci fu un attimo di gelo in sala: quello tipico di quando qualcuno fa una domanda assurda da fufologo (non era affatto così, ma poteva sembrarlo). Lei si fece spiegare cosa fosse quest'esagono, ci pensò su un istante e poi scoppiò in un “BBBBBBBOOOOOOH!” liberatorio che scatenò le risate del pubblico.

Avrebbe potuto lanciarsi in congetture ed elucubrazioni per non fare la figura di quella che non conosceva l'argomento, ma invece preferì dire le cose esattamente com'erano: non ne sapeva nulla e non aveva problemi ad ammetterlo. Nella scienza si fa così.

Questa sincera ammissione, così lontana dalla boria dei tanti personaggi politici e parascientifici che hanno un'opinione su tutto e dicono qualunque sequenza di parole pseudocasuali pur di apparire in TV, invece di tenere la bocca umilmente chiusa, è stata per me la lezione migliore di quell'incontro: avere il coraggio di dire “non lo so”.

La sfida, per noi che restiamo, è essere all'altezza di questo semplice esempio.

BOOYA

Jakob Rosenkrantz de Lasson, Jesper Mørk, Philip Trøst Kristensen
We present a numerical formalism for solving the Lippmann–Schwinger equation for the electric field in three dimensions. The formalism may be applied to scatterers of different shapes and embedded in different background media, and we develop it in detail for the specific case of spherical ... [J. Opt. Soc. Am. B 30, 1996-2007 (2013)]

My government (I’m in the UK) recently said that children here should learn up to their 12 times table by the age of 9. Now, I always believed that the reason why I learned my 12 times table was because of the money system that the UK used to have—12 pennies in a shilling. Since that madness ended with decimalization the year after I was born, by the late 1970s when I had to learn my 12 times table, it already seemed to be an anachronistic waste of time.

To find it being given new emphasis nearly 40 years later struck me as so odd that I thought I should investigate it a little more mathematically. Here is what I concluded.

Let’s start with a basic question: exactly why do we use times tables at all? (This is the kind of question my work on computerbasedmath.org has me asking a lot!)

I am going to claim that there are three basic reasons:

1) To directly know the answer to common multiplication questions.
2) To enable multiplication algorithms.
3) To enable approximate multiplication.

Let’s look at those in turn.

1) This reason is important. There are lots of small multiplication problems in day-to-day life, and there is no doubt that knowing the answer to these is useful. But knowing ANY answer to ANY question is useful. What’s so special about multiplying 1 to 12? Why stop at the 12 times table—why not learn 13, 14, 15, 16, and 17 times tables? Why not learn your 39 times table? As the table number goes up, the amount to learn increases as a square of the number while the commonality of encountering a problem that uses that table goes down. “Knowing” the answer to all possible questions is a big task and not worth the effort. This, after all, is why math was invented, so that we don’t have to know the answers to all possible calculations, but instead have a way to work them out when needed. We must draw a line somewhere and then move to a more algorithmic approach. The question is where.

2) There are many fancy computation algorithms, but most of us learn “multiplying in columns,” which involves operating on one digit at a time while managing number place and carrying overflows on to the next column. I still use it sometimes myself. By definition it needs the 0–9 times tables (and implicitly understanding the 10 times table), since it only takes one digit at a time, but any single digit could come up. Knowledge of 11 and 12 times tables is completely irrelevant. If this was the only consideration, we have a clear argument for where to draw our line—at the 10 times table. You can’t manage on less, and more is of no use.

3) But there is another useful algorithm, which is approximating numbers to a few significant digits. This might make a case for drawing the line higher.

Take as an example 7,203 x 6,892. If I want to know that exactly, then I reach for Mathematica (or if I absolutely have to, I reach for pencil and paper to apply multiplication in columns). But often I just need a rough answer, so I mentally convert this to 7,000 x 7,000 = 7 x 7 x 1,000 x 1,000 = 49,000,000. More formally I am converting the numbers the nearest approximation of the form k x 10ⁿ where k ∈ {the set of numbers for which I know times tables}. Then I use the times tables on the remaining significant digits and implicitly use the 10 times table to get the magnitude right. In this case the real answer is:

7203×6892

49643076

Giving me an error of 1.2%—good enough for lots of applications. Now if I knew my 72 times table, I could have made this 7,200 x 6,900 = 49,680,000. Only a 0.07% error.

So, now our “where do I draw the line” question becomes “how much better is a typical approximate calculation if I know up to the 12 times table compared to only knowing my 10 times table?” Let’s investigate. First I need to automate the process of approximating using a given lead number.

And extend that to finding the best approximation, if we have a choice of lead numbers.

For example, if I know only up to my 4 times table, then the best approximation for 18,345 is 20,000.

Now our approximate product is just the product of the best approximations of each number.

And the relative error can be found from the difference compared to the accurate answer.

For example, working out 549 x 999 when you only know up to your 10 times table will give you a little over an 8% error.

Now, let’s take “typical calculation” to mean a calculation involving uniformly distributed numbers between 1 and 1 million and take the “typical” error to be the average of 100,000 such calculations.

The typical error if you know up to your 10 times table is 9.4%.

But if you know up to your 12 times table, it is only 8.2%.

Here is the error as a function of how many of your times tables you have learned.

Interestingly, most of the improvement happens by the time you know your 7 times table. The odd bump at 10 is because the ability to approximate relies implicitly on knowing your 10 times table already (to be able to handle the trailing zeros).

We can work out how much relative improvement there is in the typical error for each extra table learned.

So the relative benefit gradually drops, in a cyclic way.

But the improvement in error from 9% to 8% comes at a price. Knowing up to your 10 times table requires recollection of 100 facts (OK, 55, if you assume symmetry). But knowing up to your 12 times table is 144 facts. Improving the error from 9.3% of the result to 8.1% is a relative improvement of 12% in the size of the error. But to achieve that you need to memorize 40% more information. That seems like a losing proposition.

Let’s look at the relative improvement in outcome, per extra fact memorized.

The “return on effort” drops very rapidly toward the 10 times table and then barely improves. It seems like a fairly compelling case for stopping our rote learning at 10. Indeed, if times tables were only for estimating, we would get the best return per effort by just looking at the orders of magnitude and using only the 1 and 10 times tables!

Of course numbers are not uniformly distributed. If you are in egg production, 6s and 12s probably come up a lot, just as they will if you happen to be a dealer in pre-decimal British coins! Context issues like these are hard to quantify, but one issue that is general is Benford’s law, which occurs in many real-world datasets. It says that if you look at real-life datasets that cover several orders of magnitude (e.g. populations of communities, or people’s debts, or file sizes on your computer), then the numbers are more likely to start with a 1 than with a 2, and more likely to start with a 2 than a 3, and so on. I don’t know if anyone has studied the distribution of second digits, so I will assume that is uniform. So here is a function that generates “real-world” numbers.

We can now repeat our analysis on these more realistic numbers.

Using these less uniform numbers gives poorer performance (making you more likely to need accurate computation rather than approximation). Improvement can still be achieved by knowing more tables, and this could be taken as an argument for learning beyond 12, but not when you take into account the return per extra fact learned, which makes an even stronger argument for stopping at 10.

If you really are intent on some extra rote learning, there are better ways to spend your effort than learning 11 and 12 times tables. Learning all permutations of 1 to 10 together with 15 and 25 gives a better average result than 1 to 12 (since they more evenly approximate the numbers with a lead digit of 1 or 2).

Or, as Chris Carlson suggested to me, learn the near reciprocals of 100 (2 x 50 = 100, 3 x 33 = 99, 4 x 25 = 100, 5 x 20 = 100, 6 x 17 = 102, etc.), as they come up a lot. I would expect that learning squares and powers of 2 is also probably more useful than 11 and 12 times tables.

With no prospect of the pre-decimal money system returning, I can only conclude that the logic behind this new priority is simply, “If learning tables up to 10 is good, then learning them up to 12 is better.” And when you want to raise standards in math, then who could argue with that? Unless you actually apply some math to the question!

Download this post as a Computable Document Format (CDF) file.

Simulations show that you can learn the meaning of words rapidly if you assume that every object has only one word associated with it.

Published Fri Jun 21, 2013

Author(s): Ariel Amir, Jacob J. Krich, Vincenzo Vitelli, Yuval Oreg, and Yoseph Imry

When sound waves travel through a disordered solid, vibrational modes above a certain threshold frequency can become localized and stop propagating. Theorists present a minimal model that predicts the critical frequency separating the localized and propagating modes in dimensions above two and explores how the transition relates to the level of disorder in the solid and its dimensionality.

[Phys. Rev. X 3, 021017] Published Mon Jun 24, 2013

Author(s): B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk

Here we demonstrate a novel surface plasmon polariton (SPP) microscope which is capable of imaging below the optical diffraction limit. A plasmonic lens, generated through phase-structured illumination, focuses SPPs down to their diffraction limit and scans the focus with steps as small as 10 nm. Th...

[Phys. Rev. Lett. 110, 266804] Published Wed Jun 26, 2013

A micrometre-scale Raman silicon laser with a microwatt threshold

Nature 498, 7455 (2013). doi:10.1038/nature12237

Authors: Yasushi Takahashi, Yoshitaka Inui, Masahiro Chihara, Takashi Asano, Ryo Terawaki & Susumu Noda

The application of novel technologies to silicon electronics has been intensively studied with a view to overcoming the physical limitations of Moore’s law, that is, the observation that the number of components on integrated chips tends to double every two years. For example, silicon devices have enormous potential for photonic integrated circuits on chips compatible with complementary metal–oxide–semiconductor devices, with various key elements having been demonstrated in the past decade. In particular, a focus on the exploitation of the Raman effect has added active optical functionality to pure silicon, culminating in the realization of a continuous-wave all-silicon laser. This achievement is an important step towards silicon photonics, but the desired miniaturization to micrometre dimensions and the reduction of the threshold for laser action to microwatt powers have yet to be achieved: such lasers remain limited to centimetre-sized cavities with thresholds higher than 20 milliwatts, even with the assistance of reverse-biased p–i–n diodes. Here we demonstrate a continuous-wave Raman silicon laser using a photonic-crystal, high-quality-factor nanocavity without any p–i–n diodes, yielding a device with a cavity size of less than 10 micrometres and an unprecedentedly low lasing threshold of 1 microwatt. Our nanocavity design exploits the principle that the strength of light–matter interactions is proportional to the ratio of quality factor to the cavity volume and allows drastic enhancement of the Raman gain beyond that predicted theoretically. Such a device may make it possible to construct practical silicon lasers and amplifiers for large-scale integration in photonic circuits.

Heat-transport mechanism mediated by near-field interactions in plasmonic nanostructures networks is shown to be analogous to a generalized random-walk process. Existence of superdiffusive regimes is demonstrated both in linear ordered chains and in three dimensional random networks by analyzing the asymptotic behavior of the corresponding probability distribution function. We show that the spread of heat in these networks is described by a type of L\'{e}vy flight. The presence of such anomalous heat transport regimes in plasmonic networks opens the way to the design of a new generation of composite materials able to transport heat faster than the normal diffusion process in solids.

A phase relation observed in ensemble measurements of photosynthetic proteins is borne out at the single-molecule level.

Authors: Richard Hildner, Daan Brinks, Jana B. Nieder, Richard J. Cogdell, Niek F. van Hulst

Dense electron-positron streams, similar to those found in astrophysical jets, can be made using a relatively simple tabletop laser setup.

Published Thu Jun 20, 2013

Computing: The quantum company

Nature 498, 7454 (2013). http://www.nature.com/doifinder/10.1038/498286a

Author: Nicola Jones

D-Wave is pioneering a novel way of making quantum computers — but it is also courting controversy.

Anisotropic leaky-mode modulator for holographic video displays

Nature 498, 7454 (2013). doi:10.1038/nature12217

Authors: D. E. Smalley, Q. Y. J. Smithwick, V. M. Bove, J. Barabas & S. Jolly

Every holographic video display is built on a spatial light modulator, which directs light by diffraction to form points in three-dimensional space. The modulators currently used for holographic video displays are challenging to use for several reasons: they have relatively low bandwidth, high cost, low

Article

The fabrication of three-dimensional nanoscale structures is important to nanophotonic applications where light is guided and controlled. The optical beam lithography scheme developed by Gan and colleagues enables the fabrication of three-dimensional structures with feature sizes down to 9 nm.

Nature Communications doi: 10.1038/ncomms3061

Authors: Zongsong Gan, Yaoyu Cao, Richard A. Evans, Min Gu

Hey geeks! Join my drawathon.

Franco Battaglia and Thomas F. George
A guide on tensors is proposed for undergraduate students in physics or engineering that ties directly to vector calculus in orthonormal coordinate systems. We show that once orthonormality is relaxed, a dual basis, together with the contravariant and covariant components, naturally emerges. Manip ... [Am. J. Phys. 81, 498 (2013)] published Mon Jul 01, 2013.

Author(s): Els Heinsalu, Emilio Hernández-Garcia, and Cristóbal López

The competition between two ecologically similar species that use the same resources and differ from each other only in the type of spatial motion they undergo is studied. The latter is assumed to be described either by Brownian motion or Lévy flights. Competition is taken into account by assuming t...

[Phys. Rev. Lett. 110, 258101] Published Tue Jun 18, 2013

Thanks to your contributions I will be doing a drawathon Wednesday. My first with a tablet.

Author: Marc Kirschner