Ivan S. Maksymov, Andrey Pototsky
Then, we neglect viscoelastic damping and obtain a linear model of parametrically excited subharmonic body waves in an elastic fluid-filled cylinder. We follow the approach developed for subharmonic vibrations of a water drop placed on an oscillating solid plate , where natural vibration frequencies of a cylinder squashed by gravity are considered Fig. 5. The degree of squashing is characterised by the indentation depth δ that, in turn, is proportional to the gravity acceleration g. In the co-moving frame of the vibrating plate, the gravity is time-dependent. This means that the effect of the vibration is equivalent to periodically varying the squashing of the cylinder. Therefore, in the linear regime, natural frequencies of the squashed cylinder are periodically modulated, thereby leading to a parametric type of forcing.
To the best of our knowledge, the analysis of the vibrational frequencies of a cylinder supported by a solid plate along its entire length has not been reported. Therefore, we estimate the order of magnitude of the natural frequencies by using the well-known result for a cylinder with freely supported ends [62, 63, 64], as demonstrated below. A comprehensive review of the linear and nonlinear vibration and instabilities of cylindrical shells and plates can be found in [47, 65, 66].
In cylindrical coordinates, the axial u(r, θ), azimuthal v and radial w displacements of the shell of a cylinder with freely supported ends can be written as
where the integers n and m determine the circumferential and the axial vibration modes, respectively. As a representative example, in Fig. 5 we show the first three lowest frequency modes.
For 1, the deviation of vibrational frequencies from those of a circular cylinder is of first order in . This allows us to write the equations of motion for the amplitudes U, V, W as
where x = (U, V, W), J0 is the Jacobian matrix corresponding to the circular cylinder and J1 is its first order correction due to squashing. When the solid plate is vibrated with the frequency ω, its vertical displacement is given by Acos(ωt), where A is the vibrational amplitude. The gravity acceleration in the co-moving frame of reference is g(t) = g(1 + αcos(ωt)), where α = is the dimensionless scaled amplitude. Since viscosity is neglected, we anticipate the onset of the subharmonic vibrations at small amplitude α ≪ 1. In this regime, we obtain from Eq. for the time-dependent squashing . In this limit, Eq. reduces to the three-dimensional Mathieu function
where is the scaled vibration amplitude.
We emphasise that the linear model Eq. can only be used for qualitative estimations of generally nonlinear subharmonic response. Discrepancies with experimental results obtained for real earthworms can be due to viscoelastic damping, nonlinear deformation and twisting of the worm body, as well as due to the assumption of a thin wall elastic cylinder filled with Newtonian fluid used in the model.
The properties of solutions of Eq. are well-known . Parametrically excited instability sets in when 2πf coincides with one of the combination frequencies , where are the eigenvalues of . Because ∼0.04 for E = 1 MPa, we can neglect the term J1 in Eq. as compared with J0, which implies that the natural frequencies ω0i of the gravity squashed worm can be approximated by those of a circular elastic cylinder.
Amongst the three frequencies (ω0) one is typically two orders of magnitude lower than the other two. This lowest frequency ω0 corresponds to the mode with predominantly radial displacement and is given by 
where λm = and In is the modified Bessel function of the first kind of order n.
Considered as a whole, the combination ω0R in Eq. depends on the geometry of the cylinder, the Poisson ratio ν and the ratio of the densities , but is independent of the Young’s modulus E. In Fig. 6, we plot the frequency factor as a function of the axial mode number m for different values of n for a cylinder of length L = 10 cm, shell thickness h = 50 μm, radius R = 5 mm, filled with a fluid with density ρl = ρ = 1100 kg/m3. The first three lowest frequency modes with n = 1, m = 1, n = 2, m = 2 and n = 2, m = 1 are shown in the right panel of Fig. 5 for the sake of illustration.
Analysis of experimental results in light of the predictions of the developed theoretical model. By scanning through all theoretically possible combinations of vibration modes and varying the value of the effective Young’s modulus of the worm, we find the modes involved in the subharmonic response of the worm and plot the respective spatial mode profiles. (a) Frequency factor ω0R plotted as a function of the axial mode number m for the circular elastic cylinder filled with liquid with density ρl. The other parameters are R = 5 mm, L = 10 cm, ρ = ρl = 1100 kg/m3, ν = 0.5 and h = 50 μm. The circumferential mode number n is indicated next to each curve. The two solid horizontal lines correspond to the levels of 38πR and 43πR with E = 8.3 MPa. For E = 8.3 MPa, the mode n = 3, m = 3 is excited at 38 Hz and the mode n = 2, m = 3 is excited at 43 Hz. The frequencies 38 Hz and 43 Hz correspond to the first and the second minimum of the critical vibration amplitude function in Fig. 4. The number of modes N that match the subharmonic resonance criterion as a function of E. From this panel we obtain information about the largest possible values of the Young’s modulus corresponding to the modes at 38 Hz and 43 Hz.
The presented theoretical model can, in general, be used to find the mode profiles corresponding to the resonance frequencies found in the experiment in Fig. 4 by using experimental data for the Young’s modulus E of earthworms as a key input parameter. However, plausible values of E for different worm species are a subject of active debate due to a large range of the reported values and poor understanding of the impact of the cuticle on mechanical properties of worms [53, 60].
To circumvent the lack of experimental data, we reanalyse our experimental results in Fig. 4 in light of the predictions of the developed model Eqs. In particular, we establish which of the theoretically possible vibrational modes could be excited at a given value of E. Here, we vary the value of E in a range bounded by two critical values – the effective bulk Young’s modulus of the worm from  and the locally measured stiffness of the cuticle [60, 61]. Whereas the exact values of E are yet to be confirmed experimentally, it has already been established that E would be a function of the thickness of the cuticle60 and that it would approach 200 … 400 MPa  in a limiting case of the mechanical properties of the worm defined solely by the cuticle.
Naturally, the thickness and stiffness of the cuticle vary for different species of worms and they are also likely to vary from one animal to another within the same species group. Indeed, in our experiments we established that Eisenia fetida earthworms appear to be slightly stiffer when palpated as compared with the other species tested in this work. However, this difference alone cannot result in an order of magnitude discrepancy in the values of E.
Anna Henschel. The Good, the Weird and the Hilarious Scientific Papers
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Parachutes and presumptions
Unsurprisingly, the researchers didn’t manage to recruit anyone, so they had to compromise with conducting their trial comparing the effectiveness of parachutes when people jumped from small, stationary planes, from roughly a meter above the ground. Of course, the parachutes were not more effective than the empty backpacks in preventing injury and death. The point of this study is, as the authors eloquently point out, to showcase the fact that many randomized controlled trials are very biased in their recruitment, which reduces the applicability of trial results to practice. They finally conclude that we can confidently recommend that individuals jumping from [a] small stationary aircraft on the ground do not require parachutes, individual judgment should be exercised when applying these findings at higher altitudes.
There are many more examples of funny and ingenious papers like these ones out there, but to list them all would go beyond the scope of this post. While many of these articles make you laugh, such as a recent paper on marine ecosystems, which is entirely designed in the style of a graphic novel, they also make you think about important issues in science and the way science is done. In the end, we hopefully learn something, in addition to being entertained, for example by the description of scientific misconduct through Dante’s Nine Circles of Hell.
Bennett, C.M., Miller, M.B., & Wolford, G.L. Neural correlates of interspecies perspective taking in the post-mortem Atlantic Salmon: an argument for multiple comparisons correction. Neuroimage, 47, S125.
Thébaud, O., Link, J.S., Kohler, B., Kraan, M., López, R., Poos, J.J., … & Handling editor: Howard Browman. Managing marine socio-ecological systems: picturing the future. ICES Journal of Marine Science, 74, 1965 — 1980.
Yeh, R.W., Valsdottir, L.R., Yeh, M.W., Shen, C., Kramer, D.B., Strom, J.B., … & Nallamothu, B.K. Parachute use to prevent death and major trauma when jumping from aircraft: randomized controlled trial. BMJ, 363, k5094.
The text is published by University of Glasgow PGR BLOG
Anna Henschel. Science has a Mean Girls Problem
Recently, some scientists were engaged in a heated debate on Twitter. This, per se, is nothing new. If a fairy would die every time scientists politely insult each other on social media, they would constantly be dropping out of the sky. However, this debate hit closer to home than the usual arguments on the interpretation of p-values, Frequentist versus Bayesian statistics and programming languages.
The subtle bullying in the 2004 instant classic Mean Girls took place in an analogue world. Since then, we have left high school and entered the digital realms — where the spirit of the Plastics lives on.
This most recent Twitter discussion was sparked when the British Education Secretary Damian Hinds remarked that a degree in Psychology would be of low value, as some statistics suggested that graduates would not be able to repay their student loans within the first 5 years of completing their education. This echoed the tune of a familiar song: there seems to be an implicit pecking order of what is considered the most important and legit kind of science.
How did we get here?
In the fictional world Hinds refers to, the classic STEM subjects, such as Physics, Mathematics and Medicine rank at the very top. Then come the less hard sciences, the Social Sciences, Arts and Humanities. I remember attending an inspiring talk from someone outside of Psychology, which they defensively prefaced with:
I have not been around long enough to witness this rank order emerge, but I can imagine it started around the same time we began developing systematic approaches for how we do science. Maybe William James, one of the founding fathers of Psychology, was already struggling with being taken seriously by the wider scientific community when he first described the principles according to which we still teach today.
Whenever I venture outside of my small area of expertise, I encounter people who, with great passion, share their thoughts and their enthusiasm for a topic they are investigating. Sometimes the problem is so intricate that it can be challenging to communicate to a non-academic audience, why this thing is so exciting. However, this should not be the case for fellow academics. As humans, we have a unique ability to empathize with others — regardless of their scientific specialization.
I can empathize with any researcher passionate about their subject, I can feel the pain of anyone who has worked for a long time on a difficult question and celebrate with colleagues outside of my lab who experience the joy that comes from discovering something new. For me, and I would argue any scientist, this should not be a big leap to make.
Just because a certain field of research is rooted in other norms and methodologies, it cannot be considered ‘lesser than’ or ‘unimportant’. Even more, I want to advocate for the idea that we can benefit from learning about other scientific disciplines and can be inspired by an idea which at first glance may appear completely unrelated to our own research.