27 December 2014

On my 2015 wishlist...

...is an e-print server where I can submit my pdf preprint and have it archived as-is, without making me jump through hoops just because someone somewhere thought it would be a good idea to force the authors to provide their publication in some particular format.

Case in point: I've tried storing the preprint of a recent paper (published online in September 2014).

20 December 2014

"Universal" Casimir forces

What is remarkable about the quantum Casimir force between perfect conductors is its very simple formula, which depends only on the geometry and on universal constants. Would this force be the same in the presence of different interactions?

11 December 2014

Cymatics

Great illustration of normal modes in acoustics!


3 December 2014

What science is

I am not satisfied with most definitions of science I've seen so far, either essentialist or enumerative. I think the "social" definition below is much better:

1. Science is what scientists do [1].

It may not be very satisfying, but neither is it as glib as it first appears. Still, I believe it needs some precisions: obviously, not everything scientists do is science. This applies in private life (some scientists are atheists and others are deeply religious) but also to public attitudes: Johannes Stark was an authentic Nazi, but this does not prevent us from studying the Stark effect. Conversely, his scientific achievements do not render Nazism respectable. Then:

2 December 2014

CNRS positions - the 2015 campaign

[Updated with 2015 data]
The 2015 campaign for permanent research positions at the CNRS (Centre national de la recherche scientifique) is officially open. The submission deadline is January 6th 2015. There are 212 open positions at the CR2 level (same as in 2014), 77 CR1 (+11), 253 DR2 (-26) and 2 DR1 (+2).

30 November 2014

Resources on creating scientific graphs

For the data analysis course I'm teaching these days, I've been looking into the best way of plotting the data (classical two-dimensional line or scatterplot). There are surprisingly few resources (or I am surprisingly bad at searching for them!)

The classics:

    The moderns:

    9 November 2014

    Good research practice

    The Ethics Committee of the CNRS has published (in French only, as far as I can see) a Guide for the promotion of truthful and responsible research.

    The guidelines are quite reasonable, but what drew my attention is the front cover: three ladies, a senior researcher, a more junior one and —probably— a PhD student or postdoc are huddled around a multi-well plate, each of them pointing at a different well. Note the micro-pipette in the foreground (shorthand for "this is a biology research lab"). Note also that the boss is in her street clothes and her bare hand is dangerously close to the samples. Maybe one should add to this guide rule 0.1: "Use appropriate protective equipment ?!"

    Borges and Nietzsche

    Borges was influenced by Nietzsche's ideas, in particular his "eternal return" (see The Doctrine of Cycles) and mentions him explicitly in some of his stories (e.g. Deutsches Requiem). What I have only recently realized is that Borges' story Funes the memorious (already mentioned in a previous post) is prefigured in Nietzsche's second Untimely Meditation1:

    Imagine the extremest possible example of a man who did not possess the power of forget­ting at all and who was thus condemned to see everywhere a state of becoming: such a man would no longer believe in his own being, would no longer believe in himself, would see everything flowing asunder in moving points and would lose himself in this stream of becoming: like a true pupil of Heraclitus, he would in the end hardly dare to raise his finger.

    Nietzsche's  has already been invoked in relation with Funes2, but as far as I can tell (I do not have access to the full text of the paper) only with respect to the difficulty of forming general concepts.

    1. Breazeale, D., & Hollingdale, R. J. (1997). Nietzsche: Untimely meditations. Cambridge University Press.
    2. Martin, C. W. (2006). Borges Forgets Nietzsche, Philosophy and Literature 30(1), 265-276.



    2 November 2014

    The politics of disgust

    Right in time for the midterm elections we hear that liberals and conservatives react differently to disgusting images. I find it very surprising, the more so because I have never been able to understand how a single variable can account for so many orthogonal issues (citing from the paper): pacifism/abortion rights/welfare spending/torture of terrorism suspects etc.


    28 October 2014

    Historical event

    This month, after nine years in my current (tenured) position, I finally earned more than the monthly income during my Göttingen postdoc (2002-2005).

    5 October 2014

    The veil of ignorance

    There is something disquieting about Rawls' veil of ignorance position: participants are supposed to set aside their status, their attributes and even their personality in order to found this ideal society, whose first principle enshrines the liberty of conscience and freedom of speech. There may not be a logical contradiction between the two, but I think there is an obvious moral one.

    4 October 2014

    A neural basis for readiness-to-hand ?

    Researchers in Munich discovered that there is a specific network in the brain for using tools (the paper appeared in The Journal of Neuroscience).
    Heidegger's concept of readiness-to-hand is arguably much more general than the motor skills involved in the use of familiar objects, but I like the idea of a neural basis for a philosophical concept.

    3 October 2014

    Fête de la science 2014

    Notre laboratoire se prépare pour la Fête de la science. Beaucoup d'activités sont prévues pour vendredi et dimanche (10 et 12 octobre), voir le programme. Pour des informations en temps réel suivre @LPS_Orsay.

    25 September 2014

    Solving tan(x) = x

    [UPDATE: 25/09/2014 with the iterative method] This kind of transcendental equation is often encountered in physics. Undergraduate students are usually shown (or asked to draw) the graphical solution:



    The numerical solutions are easily found by an iterative method using a scientific calculator (see below), but how far can one go with only pen and paper?

    Expansion

    Aside from the trivial solution \(x_0 = 0\), one clearly has \( x_k \simeq \frac{(2k +1) \pi}{2}\) (\(k \geq 1 \)), so we can write: \[ x_k = \frac{(2k +1) \pi}{2} - \varepsilon _k, \quad \mathrm{with} \quad \varepsilon _k < 1\] One would like to do an expansion in \( \varepsilon _k\), but of course this will not work for the tangent around its divergence points. We can however use the cotangent, since \( \tan (x_k) = x_k \Rightarrow \cot (x_k) = 1/x_k \). Using standard substitution formulas for the sine and cosine yields: \[\cot \left [ \frac{(2k +1) \pi}{2} - \varepsilon _k \right ] = \tan(\varepsilon _k) \simeq \varepsilon _k \simeq \frac{2}{(2k + 1) \pi}\] where in the last equality we neglected \( \varepsilon _k\) in the denominator. One can include it for a more rigorous treatment. Finally, we have: \[ x_k \simeq \frac{(2k +1) \pi}{2} - \frac{2}{(2k + 1) \pi}, \quad \mathrm{for} \quad k \geq 1 \, ,\] giving for the first three solutions 4.5002, 7.7267, and 10.9046, to be compared with the "exact" values 4.4934…, 7.7253…, and 10.9041…. The quality of the approximation increases with the order \(k\), since \(\varepsilon _k\) decreases (the intersections are closer and closer to the vertical asymptotes).

    Iteration

    Let us rewrite the initial equation by applying the arctangent to both members:
    \[x = \arctan (x) \tag{1}\]
    For the \(k\)-th solution, the initial estimate is: \( x^0_k = \frac{(2k +1) \pi}{2} \). Let us plug it in the right-hand side of Eq. (1) to obtain the first order estimate \( x^1_k\) and then iterate. Note that the arctangent is a multi-valued function, and the standard implementation reduces it to the first branch (the one going through the origin). We are looking for the solution sitting on the \(k\)-th branch, so we need to add \(k \pi\) each time:
    \[x^{i+1}_k = \arctan (x^i_k)  + k \pi \tag{2}\]
     For the first non-trivial solution (\(k = 1\)), the sequence is: 4.71239, 4.50328, 4.49387, 4.49343, 4.49341,... with the second iteration already reaching an excellent precision!

    18 September 2014

    13 September 2014

    False false friends

    Whoever had to evolve between two related languages is familiar with the concept of false friends.
     I would argue that there is a less visible category of terms (or more precisely, of relations between terms) namely similar words that one feels are false friends but that actually have a similar meaning in the two languages: these are false false friends (FFF).
    This is a subjective relation, being a false perception of one speaker.
    For me, when going from French (or Romanian) to English, the FFF are mainly terms of Latin origin for which I am tempted to substitute Saxon words or other Latin terms, but which have no immediate equivalent in Romance languages:
    • salary becomes wages
    • merits deserves
    • evidentobvious
    • hypothesis assumption
    etc. 

    28 August 2014

    RIP, Jacques Friedel (1921-2014)

    Jacques Friedel passed away yesterday. He was among the pioneers of the study of defects in solids and of the electronic structure of matter, one of the founders of my lab and my scientific great-grandfather.


    25 August 2014

    The arbitrariness of words

    (via phys.org) A statistical analysis of English terms, recently published in Phil. Trans. R. Soc. B (free preprint on the corresponding author's site), finds systematic relations between sound and meaning, refuting a pure arbitrariness of the linguistic sign.

    Of course, such relations have been sought for —and found— ever since Plato (last year, I reviewed on this blog Genette's Mimologics, a great exploration of the topic.) The novelty is the quantitative aspect of the analysis: the authors define phonetic and semantic distances between pairs of terms and then measure the correlation of these distances, which is higher than expected by pure chance. Unfortunately, they give no intuitive illustration for the amplitude of the effect, expressed as an \(r\)-factor. So, finally, how systematic is the English language?

    Another interesting result is that more systematic words are acquired earlier. The authors speculate that systematicity helps language development in its early stages but might hinder it later, when (the vocabulary being larger) it can lead to confusion.

    24 August 2014

    Moments of inertia of triangular prisms

    Now that we have determined the moments of inertia of regular and truncated equilateral triangles, it is time to calculate them for the corresponding right prisms. These bodies, with mass density \(\rho\), can be seen as stacks of infinitesimally thin triangles of thickness \(\text{d}h\) and surface density \(\text{d} \mu = \rho \text{d}h\) (we preserve the notations from the previous posts and introduce the height of the stack, \(H\). The inertia moments of the prisms are denoted by \(P\), instead of \(I\).)
    The centers of mass of these sheets are all situated on \(z\), so the total moment of inertia about this axis is simply the sum of the individual ones. We must simply replace \(\mu\) by \(\rho H\) in (1) and (3):
    \[\begin{array}{ll}
    P_z(L,H) &= \rho H L^4 \frac{\sqrt{3}}{48}\\
    P^{\text{tr}}_z(L,a,H) &= \rho H \frac{\sqrt{3}}{48} [L^4 - 3 a^4 - 12 a^2 (L-a)^2]
    \end{array}\tag{5}\]
    The derivation is slightly more complicated for axis \(y\), since we need to account for the variable distance between it and the centers of mass of the sheets (using, of course, the overworked parallel axis theorem!) Fortunately, we only need the integral \( \displaystyle \int_{-H/2}^{H/2} \text{d}h \, h^2 = \frac{H^3}{12}\) to get:
    \[
    \begin{array}{ll}
    P_y(L,H) &= \rho H L^4 \frac{\sqrt{3}}{96} \left [ 1 + 2 \left ( \frac{H}{L} \right )^2 \right ] \\
    P^{\text{tr}}_y(L,a,H) &= \rho H \frac{\sqrt{3}}{96} \left [ L^4 - 3 a^4 - 12 a^2 (L-a)^2 + 2 H^2 (L^2 - 3 a^2) \right ]\\
     &= \rho H L^4 \frac{\sqrt{3}}{96} \left [ 1 + 2 \left ( \frac{H}{L} \right )^2 - 12 x^2 \left ( (1-x)^2 + \frac{x^2}{4} + \frac{x^2}{2} \left ( \frac{H}{L} \right )^2 \right ) \right ]
    \end{array}\tag{6}\]where \(x = a /L\).

    23 August 2014

    Moment of inertia of a clipped triangle

    After calculating the moment of inertia for an equilateral triangle, let us consider the same shape, but with clipped corners, as in the drawing below:

    We will preserve the notations of the previous post, adding the superscript "tr" for the truncated shape: \(I_{z}^{\text{tr}} (L,a)\) is the moment about the \(z\) axis of the equilateral triangle with side \(L\), clipped by \(a\) at each corner (with \(a \leq L/2\)). We will also use the same strategy, writing the moments of the complete shape as a combination of its four fragments:
    \[I_{z}(L) = I_{z}^{\text{tr}} (L,a) + 3[I_{z}(a)+m(a)d^2] ,\]
    where \(d=(L-a)/\sqrt{3} .\) Using the results obtained for the full triangle immediately yields:
    \[ I_{z}^{\text{tr}} (L,a) = \frac{\sqrt{3}}{48} \mu \left [ L^4 - 3a^4 - 12 a^2 (L-a)^2\right ] \tag{3}\]
    Similarly, from:
    \[I_{y}(L) = I_{y}^{\text{tr}} (L,a)+I_{y}(a) + 2[I_{y}(a)+m(a)(L-a)^2/4]\]
    we get:
     \[ I_{y}^{\text{tr}} (L,a) = \frac{\sqrt{3}}{96} \mu \left [ L^4 - 3a^4 - 12 a^2 (L-a)^2\right ] = I_{z}^{\text{tr}} (L,a)/2 \tag{4}\]
    The clipped shape preserves the threefold symmetry of the original one, so the same conclusion as to the in-plane isotropy of the inertia tensor holds. Also, \( I_{z} = 2  I_{y}\) in both cases; I'm sure there is some elegant way to explain this, but I can't find it.
    A quick check of results (3) and (4) is that \( I_{y,z}^{\text{tr}} (2L,L) = I_{y,z}(L) .\) In this case, one retrieves the situation shown in the illustration to the previous post.

    22 August 2014

    Career advice

    (via Slashdot) Infoworld gives some career advice to young programmers. I'm surprised at how much sense these short observations also make for beginning scientists. OK, maybe point 7 is not that relevant, and point 4 should be rephrased as Do not re-invent the wheel. Otherwise, they are spot-on.

    21 August 2014

    Mass moment of inertia of an equilateral triangle

    As in previous posts, I would like to determine the moments of inertia of a solid body, this time an equilateral triangular prism. I will start in this post by a (very thin) equilateral triangle. The challenge is getting the result in the simplest way, making the most of the symmetry elements and taking advantage of the parallel axis theorem.

    Around the \(z\) axis

    The \(z\) axis goes through the center of mass of the triangle of interest (gray central area of side \(L\) in the illustration above) and is perpendicular to its plane. We denote the corresponding moment by \(I_z(L)\). The moment of the large triangle, with side \(2L\), is \(I_z(2L)\). We can relate these two parameters in two ways:
    • For a given shape and surface mass density, the moment of inertia scales as the size to the fourth power, on dimensional grounds. Thus, \(I_z(2L) = 16 I_z(L)\).
    • The large triangle can also be described as the rigid assembly of the small central triangle and the three adjacent ones. The parallel axis theorem yields:
    \[I_z(2L) = I_z(L) + 3 [I_z(L) + m(L) d^2] \]
    where \(m(L)= \mu L^2 \sqrt{3}/4\) is the mass of the small triangle, with \(\mu\) the surface mass density, and \(d=L/\sqrt{3}\) is the distance between the centers of mass of the side triangles and the \(z\) axis.

    Combining these two expressions for \(I_z(2L)\) immediately yields:
    \[ I_z(L) = \mu L^4 \frac{\sqrt{3}}{48} \tag{1}\]

    Around the \(y\) axis

    The \(y\) axis is contained in the plane of the triangle and goes through its center of mass and one vertex. Using the same strategy as above, we get:
    \[ \left\{
    \begin{array}{ll}
    I_y(2L) &= 16 I_y(L)\\
    I_y(2L) &= 2 I_y(L) + 2 [I_y(L) + m(L) (L/2)^2]
    \end{array} \right. \]
    where on the right-hand side of the second equality the first term corresponds to the central and top triangles (both their centers of mass are on axis \(y\)) and the second one to the side triangles, whose centers are shifted by \(L/2\). Finally:
    \[ I_y(L) = \mu L^4 \frac{\sqrt{3}}{96} = \frac{I_z(L)}{2} \tag{2}\]

    How about the \(x\) axis? To answer this question, we start by noting that there are three equivalent directions within the plane of the triangle: \(y\) and the axes (say, \(y'\) and \(y''\)) going through the other two vertices: \(I_y(L) = I_{y'}(L) = I_{y''}(L)\). This third-order symmetry in a two-dimensional space means that the inertia tensor is in fact isotropic in the plane of the triangle, with the same value \(I_{\bot}(L) = I_{y}(L) = I_{x}(L)\) for any axis in this plane. The inertia tensor is then:
    \[\mathrm{I} = \left (
    \begin{matrix}
    I_{\bot}(L) & 0 & 0 \\
    0 & I_{\bot}(L) & 0 \\
    0 & 0 & I_z(L)
    \end{matrix}
    \right ) \]
    This isotropy of a tensorial property for a system that does not in fact have full rotational symmetry is a very useful result (albeit somewhat counterintuitive). To give only one example from a completely different area of physics: a cubic crystal cannot be birefringent!

    3 August 2014

    Madrid - the Prado Museum

    Fra Angelico's Annunciation
    Fra Angelico's Annunciation (see in high resolution)
    Samuel Menashe's Annunciation is the best comment I can think of. I do not know which version of the Annunciation he was actually referring to: possibly Giovanni di Paolo's, in the National Gallery. He had already written a poem about Paolo's work, but I think his observation corresponds better to Fra Angelico's painting.

    18 July 2014

    French research grants - the 2014 campaign

    The main research funding organization in France is the ANR: "Agence Nationale de la Recherche" (national research agency). Every year, it finances a variable number of projects, in all scientific fields.

    The results for 2014 were announced today, and the presentation text (in French only) is very upbeat: the success rate of 28% is more than 11% higher than that of 2013 ! A historical increase, one might conclude.

    Unlike last year, however, the 2014 selection was done in two steps, and the 28% figure only accounts for the second one. The first step had already selected only 33% of the initial submissions, reducing the overall success rate to 9.4%. The only historical event is that this value dipped below 10% for the first time in the ten years since the ANR was created.

    I make two predictions:
    • The 9.4% figure will never appear in official documents.
    • The 2015 campaign will consist of three steps, the last of which will select 100% of the projects that made it through the second round. 

      [UPDATE 19/07/2014] : For comparison, I plotted below the yearly success rates and total amounts distributed by the ANR since 2005.


        11 July 2014

        Reproducible experiments

        Yesterday evening, after having spent my day trying (and failing) to reproduce somebody's published research, I stumbled (via Soylent News) upon a psychologist's essay on "the emptiness of failed replications". Jason Mitchell, psychology professor at Harvard, states that failing to replicate somebody else's experiment does not represent a meaningful scientific contribution. Well, thank you, Prof. Mitchell !

        All jokes aside, it took me quite some time to parse the text, and even more time to realize that this difficulty is likely due to the implicit assumptions that I brought from my own field of work (experimental physics), which are quite different from those of the author, an experimental psychologist. Ultimately, I learned more from trying to separate these two viewpoints than from the text itself, which makes a rather simplistic argument.

        The argument

        Mitchell's main point appears to be that one cannot learn from negative arguments, since not finding something cannot prove it doesn't exist. This sounds entirely reasonable, and is certainly true in the case of the "black swan" example the author uses, but is completely wrong in usual scientific experiments: learning that the correlation between two variables is zero (within the uncertainty) is as strong a result as saying that it is significant and positive. Of course, the first outcome is less likely to lead to a high-profile paper.

        The assumptions

        A basic assumption in physical sciences is that of "homogeneity": the outcome of an experiment should not depend on its location, time or the personality of the scientist. Mitchell does not address this point directly, but seems to imply that getting all the details right for precisely replicating an experiment is next to impossible. He then blames this on the replicators' lack of some sort of "core competence". This is a valid point: if Nature is the same everywhere but the experimentalists are sloppy, their results will of course differ. From this I would however draw two uncomfortable conclusions:
        1. This sloppiness may just as well affect the initial experiment as the attempt to reproduce it.
        2. It also undermines an entire field of study if there is no way of distinguishing careful scientists from the careless (or incompetent) ones.
        In "tabletop" physics, replicating an experiment is relatively cheap1. It is also crucial: our research builds on someone else's results, and very often the replication is a necessary step before being able to go further. Chemists sometime spend weeks or months in order to reproduce published protocols. Needless to say, this is not done to prove the original author wrong ! Neither of these points seems to apply in psychology, as presented by Mitchell.

        Finally, I find quite strange Mitchell's attitude that replicating experiments is almost morally wrong: "One senses either a profound naiveté or a chilling mean-spiritedness at work." This goes beyond mere scientific debate and sounds more like responding to a personal offense.



        1. Even in large scale experiments, reproducing the results may be necessary, albeit very expensive. A good example is the search for the Higgs boson, with the two experiments, ATLAS and CMS, working side-by-side but without communicating (see for instance Jon Butterworth's "Smashing Physics".)

        6 July 2014

        ILCC2014: days four and five

        The plenary lectures of these last two days were given by chemists (Carsten Tschierske and Tadashi Kato) and they were both impressive for the results but also for the huge amount of work these clearly required.

        Overall, I think the scientific level was higher than two years ago, maybe because of the smaller number of oral presentations: there were only three parallel sessions (four on Tuesday) compared to five in Mainz. Finally, the next (26th) edition of the ILCC will take place at Kent State!

        5 July 2014

        Lost (and found) in translation

        On the plane back from Dublin I received all of 18 grams of mini-breadsticks. Fortunately, the packaging was more interesting than the contents:


        In English, the production place was a plant (industrial), while in French it was a workshop (atelier) with a hint of craftsmanship. The Italian term stabilimento (factory, but also establishment) is a bit more general. Unless, of course, I'm giving too much importance to these nuances. See my post on untranslatable concepts.

        3 July 2014

        ILCC2014: day three

        Not too much science today, so I finally got to see the Book of Kells:


        Like any respectable paper, the exhibition even has a "Materials and Methods" section!
        In the afternoon, tour of the Guinness storehouse, one of the few places in Dublin where gravity points upwards.


        1 July 2014

        ILCC 2014: day two

        Not too many events today (at least in the sessions I attended). Two highlights:
        •  Very nice talk by Sin-Doo Lee about surface patterning using micron-sized nanoparticles
        • I wasn't there, but it seems that Ivan Dozov's talk on twist-bend nematics was very appreciated (and led to lively discussion afterwards.)

        Spin 1/2

        I finally realized that the USB connector is a spin-1/2 object. For me, it works like this:
        • Try to plug it in: it doesn't work.
        • Turn by 180°: it doesn't work.
        • Turn again by 180°: it finally works!
        Clearly, it takes (at least) two full turns to bring it back to the initial oriention!

        30 June 2014

        ILCC 2014: day one

        The 25th International Liquid Crystal Conference (ILCC 2014) opened today at the Trinity College Dublin. There are over 600 participants (only 24 of them from France). The organization seems a bit less meticulous than two years ago in Mainz, but the food is definitely better!

        On the scientific side, modulated nematics (such as the twist-bend phase) are clearly the hot topic. There are also many talks on nanocomposites. Geographically, the Ljubljana groups (both at the University and the Jožef Stefan Institute) are very strong, and their collaborations with the Boulder teams of Noel Clark and Ivan Smalyukh look very fruitful, after Slobodan Žumer's talk this afternoon.


        29 June 2014

        How scientific is forensic science?

        [UPDATE 19/04/15:] Similar problems affect forensic hair matches.

        A recent New Yorker article discusses the use of cell-phone call records in criminal trials, and in particular the precision with which a user can be located. Unsurprisingly, this precision is much lower than claimed by some prosecutors and, when overestimated, can lead to wrongful convictions.

        Some days ago I read [via Soylent News and Slate] about a 2009 report of an NAS Committee: Strengthening Forensic Science in the United States: A Path Forward. The Slate article also mentions the numerous convictions overturned by DNA tests and draws bleak conclusions about the current state of forensics (in the US, at least.) How did we get here?

        One obvious answer is that the courts of law are ill-equipped to deal with scientific subtleties (in the same way scientists are not prepared to interpret fine legal points.) In particular, it is quite difficult for judges to identify sound scientific evidence (although some standards do exist) and to assess its reliability. A very useful introduction to this point is "How Science Works", by David Goodstein, in Reference Manual on Scientific Evidence (2nd ed.)

        Another possible reason is the lack of a "checks and balances" mechanism. Scientific results (important ones, at least) are scrutinized by an entire community, with similar expertise and resources as the authors. During trial, evidence introduced by the prosecution should be questioned by experts for the defendant, but the latter may not have the necessary resources. This disparity is even stronger in the case of plea bargains (as in the New Yorker story), where the evidence is never actually introduced.



        28 May 2014

        Mass moment of inertia of a spherocylinder

        [UPDATE 22/08/2014: Corrected a misprint in the formula for \(I_x\). See comment below.]
        Using the moments of inertia calculated in the previous post for the hemisphere (and taking for granted those of the cylinder), we can now determine those of a spherocylinder.
        The height of the cylinder is \(h\), while its radius (and that of the spherical caps) is \(R\).
        \(I_z\) is easy to determine by summing the corresponding moments of the cylinder and of the two hemispheres: \(I_z= \rho \, m_c \frac{R^2}{2} + 2 \rho \, m_h \frac{2}{5} R^2\). Developing \(m_c\) and \(m_h\) and introducing the aspect ratio \(\gamma = 1+ \frac{h}{2R}\) yields:
        \[I_z = \pi \rho R^5 \left [ (\gamma -1) + \frac{8}{15} \right ] \]

        25 May 2014

        Mass moment of inertia of a hemisphere

        I recently had to calculate the moments of inertia of various solid bodies (e. g. the spherocylinder). They can be obtained starting from the definition; this is the kind of calculation described in papers as "tedious but straightforward". I tried to simplify the process as much as possible, using the symmetry properties of the objects and the parallel axis theorem. The latter is of course useful for "composite" objects (combinations of simple units) but, less intuitively, also for sections of such units, as we'll see below for the (solid) hemisphere.

        17 May 2014

        Saint-Venant's principle and its relatives - part 2

        In part 1 of this discussion we had concluded that the Laplacian was a "zero-sum game", i.e. that a static modulation along one space dimension was exactly matched by a decay in the perpendicular dimension: \(q_x^2 + q_z^2 = 0\).
        What happens for a time-dependent field distribution? For simplicity, let us assume a purely harmonic dependence: \(f(x,z,t) = F(x,z) \exp(i \omega t)\), with translation invariance along \(y\), where \(f\) stands for a component of the electric or magnetic field (in the scalar wave approximation).
        The field now obeys:
        \begin{equation}
        \label{eq:dalemb}
        \Box \, f = \frac{1}{c^2} \partial _t^2 f(x,z,t) - \underbrace {( \partial _x^2 + \partial _z^2)}_{\Delta} f(x,z,t)= 0
        \end{equation}
        where \(c\) is the speed of light and \(\Delta\) is the Laplacian operator discussed in part 1. The wave operator \(\Box \) is often called d'Alembertian.

        11 May 2014

        The Carvallo paradox - part II

        I mentioned the Carvallo paradox in a previous post. Here, I will give a simpler version and some comments. Consider that, instead of using a spectrometer, we only use the dispersive element (e.g. a prism). After refraction, the signal components (the various colors) are projected onto a perfectly absorbing screen:
        From Wikimedia; under CC-SA 1.0 License.

        Even though the incoming signal \(s(t)\) is of finite length (and thus energy), each component (of infinite length) \(f_i(t)\), where \(s(t)=\sum_i f_i(t)\), has finite and constant power, meaning that over a period of time larger than the duration of the original signal the screen will receive a higher amount of energy (which can in fact be made arbitrarily large). The Carvallo paradox can then be restated as follows:

        1) A finite-length signal is a sum of infinite-length components,
        2) which can be separated and manipulated individually.

        There is obviously a problem with 1) or 2) (or both!), since accepting them would break both causality and energy conservation. Note that invoking quantum mechanics does not solve the paradox: we can envision a similar setup using for instance sound waves.

        Whether 2) is valid or not, the "separation" step is non-trivial, as one can see from the power spectrum of the signal: \(P(\omega) = |\tilde{S}(\omega)|^2 = \left | \sum_i \tilde{F}(\omega)\right |^2\), where the uppercase and tilde combination denote the Fourier transform. On the other hand, the power spectrum after separation (e.g. that absorbed by the screen) is: \(P'(\omega) = \sum_i  \left | \tilde{F}(\omega)\right |^2\). What I called separation thus amounts to decorrelating the various signal components.


        9 May 2014

        21 April 2014

        White laundry no longer #GGGGGG

        One of the unintended consequences of replacing incandescent bulbs with LED lamps (which emit less UV light) is that the fluorescent compounds in washing powder will be less effective in giving the "whiter than white" impression.

        See the (open access) original paper and the discussion at PhysOrg and Gizmodo.

        19 April 2014

        Nanotechnology and sophistry

        The current enthusiasm for everything "nano" sounds like Gorgias' praise for the logos, which:

        ...with the finest and most invisible body achieves the most divine works.


        16 April 2014

        Proposition de thèse

        Nanocages Virales Assemblées Autour de Particules d'Or

         Il n'y a pas de financement assuré pour ce sujet de thèse; les candidats éligibles peuvent postuler à l'École Doctorale Physique en Île de France jusqu'au lundi 28 avril à minuit.

        Les virus se présentent comme des exemples naturels de machines moléculaires combinant des propriétés structurales et fonctionnelles remarquables, très loin d'être égalées par les systèmes synthétiques actuels. Notre objectif est de développer des modèles pour répondre aux problématiques structurales et dynamiques posées par l'auto-assemblage de nanocages virales, et pour concevoir ces dernières avec un degré de sophistication croissant. Les applications potentielles concernent le domaine biomédical, mais aussi les matériaux innovants et la virologie. Nous exploitons au maximum les techniques de pointe et les compétences disponibles dans notre laboratoire (spectrophotométrie, microscopie électronique, diffusion statique de la lumière) ainsi que sur les grands instruments (diffusion des rayons X et des neutrons aux petits angles).