Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences

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Article
The Standard Model is the theory used to describe the interactions between fundamental particles and fundamental forces. It is remarkably successful at predicting the outcome of particle physics experiments. However, the theory has not yet been completely verified. In particular, one of the most vital constituents, the Higgs boson, has not yet been observed. This paper describes the Standard Model, the experimental tests of the theory that have led to its acceptance and its shortcomings.
 
Article
Although astrobiological or SETI detections are possible, actual invasions of sentient extra-terrestrials or plagues of escaped alien microbes are unlikely. Therefore, an anthropological perspective on the question suggests that in the event of a detection, the vast majority of humanity will be dealing not with extra-terrestrial life itself (whether intelligent or not, local or distant), but with human perceptions and representations of that alien life. These will, inevitably, derive from the powerful influences of culture and individual psychology, as well as from science. It may even be argued that in most detection scenarios, the scientific data (and debates about their interpretation) will be nigh-irrelevant to the unfolding of international public reaction. 'Extra-terrestrial life' will, in short, go wild. From this premise, some key questions emerge, including: what can scientists reasonably do to prepare, and what should their responsibilities be, particularly with respect to information dissemination and public discussions about policy? Then, moving beyond the level of immediate practicalities, we might also ask some more anthropological questions: what are the cultural substrates underneath the inquiries of Western science into extra-terrestrial life? In particular, what are the stories we have been told about discovery of rare life, and about contact with other beings, and do these stories really mean what we think they do? Might a closer look at those narratives help us gain perspective on the quest to find extra-terrestrial life, and on our quest to prepare for the consequences of detection?
 
Article
In the Standard Model (SM) of particle physics, quarks are permanently confined by the strong interaction into bound states called hadrons. The values of some parameters, such as the quark masses and the strengths of the decays of one quark flavour into another, cannot be measured directly and must be deduced from experiments on hadrons. This requires calculations of the strong-interaction effects within the bound states, which are only possible using numerical simulations of quantum chromodynamics (QCD), the quantum field theory of the strong interaction. In conjunction with experimental data from B factories over the next few years, QCD simulations may provide clues to physics beyond the SM. The simulations are computationally intensive and, for the past 20 years, have exploited leading-edge computing technology. This continues today, with a project to develop a 10 Tflops computer for QCD costing less than 1 US dollar per Mflops.
 
1. Schematic diagram of section dependencies 
1. A simple graph with a certain choice for its Laplacian
Article
Sturm's oscillation theorem states that the nth eigenfunction of a Sturm-Liouville operator on the interval has n-1 zeros (nodes) (Sturm 1836 J. Math. Pures Appl. 1, 106-186; 373-444). This result was generalized for all metric tree graphs (Pokorny et al. 1996 Mat. Zametki 60, 468-470 (doi:10.1007/BF02320380); Schapotschnikow 2006 Waves Random Complex Media 16, 167-178 (doi:10.1080/1745530600702535)) and an analogous theorem was proved for discrete tree graphs (Berkolaiko 2007 Commun. Math. Phys. 278, 803-819 (doi:10.1007/S00220-007-0391-3); Dhar & Ramaswamy 1985 Phys. Rev. Lett. 54, 1346-1349 (doi:10.1103/PhysRevLett.54.1346); Fiedler 1975 Czechoslovak Math. J. 25, 607-618). We prove the converse theorems for both discrete and metric graphs. Namely if for all n, the nth eigenfunction of the graph has n-1 zeros, then the graph is a tree. Our proofs use a recently obtained connection between the graph's nodal count and the magnetic stability of its eigenvalues (Berkolaiko 2013 Anal. PDE 6, 1213-1233 (doi:10.2140/apde.2013.6.1213); Berkolaiko & Weyand 2014 Phil. Trans. R. Soc. A 372, 20120522 (doi:10.1098/rsta.2012.0522); Colin de Verdière 2013 Anal. PDE 6, 1235-1242 (doi:10.2140/apde.2013.6.1235)). In the course of the proof, we show that it is not possible for all (or even almost all, in the metric case) the eigenvalues to exhibit a diamagnetic behaviour. In addition, we develop a notion of 'discretized' versions of a metric graph and prove that their nodal counts are related to those of the metric graph.
 
SXMCD peaks and corresponding transitions at the Ti L and O K edges 
Article
We report room-temperature ferromagnetism (FM) in highly conducting, transparent anatase Ti(1-x)Ta(x)O(2) (x∼0.05) thin films grown by pulsed laser deposition on LaAlO(3) substrates. Rutherford backscattering spectrometry (RBS), X-ray diffraction, proton-induced X-ray emission, X-ray absorption spectroscopy (XAS) and time-of-flight secondary-ion mass spectrometry indicated negligible magnetic contaminants in the films. The presence of FM with concomitant large carrier densities was determined by a combination of superconducting quantum interference device magnetometry, electrical transport measurements, soft X-ray magnetic circular dichroism (SXMCD), XAS and optical magnetic circular dichroism, and was supported by first-principles calculations. SXMCD and XAS measurements revealed a 90 per cent contribution to FM from the Ti ions, and a 10 per cent contribution from the O ions. RBS/channelling measurements show complete Ta substitution in the Ti sites, though carrier activation was only 50 per cent at 5 per cent Ta concentration, implying compensation by cationic defects. The role of the Ti vacancy (V(Ti)) and Ti(3+) was studied via XAS and X-ray photoemission spectroscopy, respectively. It was found that, in films with strong FM, the V(Ti) signal was strong while the Ti(3+) signal was absent. We propose (in the absence of any obvious exchange mechanisms) that the localized magnetic moments, V(Ti) sites, are ferromagnetically ordered by itinerant carriers. Cationic-defect-induced magnetism is an alternative route to FM in wide-band-gap semiconducting oxides without any magnetic elements.
 
STM and LEED characterization of epitaxial graphene on Ru(0001) surface. (a) The atomically flat graphene flake extends over the entire Ru(0001) surface. (b) The hexagonal moiré pattern formed owing to lattice mismatch between graphene and Ru substrate. (c) Atomic-resolution image of one unit cell of the moiré pattern. (d) LEED pattern indicates the single crystalline nature of the graphene sheet. (e) Atomic resolution STM image taken at step edges indicates the continuous growth of graphene across whole Ru terraces. (Online version in colour.) 
(a) Large-scale STM image of the kagome lattice of FePc. (b) Zoom-in image showing the details of the kagome lattice of FePc. The unit cell of the kagome lattice is marked with blue solid lines. (c) Structural model of the kagome lattice showing molecular orientation disorder. (d,e) STM images of single-guest FePc and (t-Bu) 4-ZnPc molecules hosted by FePc kagome lattice, respectively. Dashed lines highlight the underlying kagome lattice. (Online version in colour.) 
STM topography of C 60 molecules adsorbed on under-annealed G/Ru surface. (a) Large-area STM image showing C 60 islands and isolated C 60 molecules. Five larger bright protrusions owing to argon gas bubbles are pointed out by the arrows. (b) Low-coverage image showing defect-induced isolated adsorption. (c) Regular moiré pattern of G/Ru. (d) Zoom-in image of the lower left part of (a). Four kinds of typical template surface conditions are distinguished: (I) regular moiré pattern, (II) disordered or imperfect areas, (III) steps and (IV) corrugations. (e) Zoom-in image of the area inside the blue square in (d). (f ) High-pass filtered image of (e). (Online version in colour.) 
(a) The substrate-commensurate growth of C 60 molecules on G/Ru. (b) Zoom-in image of the supramolecular structure. The unit cells of the underlying substrate and molecular lattice are outlined by large and small rhombuses, respectively. (c) STM image showing both substrate-commensurate (lower right, marked with 'A') and substrateincommensurate (upper left, marked with 'B') growth structure of C 60 molecules on G/Ru. The dotted lines in different orientations indicate different molecular domains. (d) Zoom-in image of an incommensurate area. Inset shows its Fourier transformation and the angle between vector q 1 and q 2 is about 26 •. (Online version in colour.) 
Article
We review the way to fabricate large-scale, high-quality and single crystalline graphene epitaxially grown on Ru(0001) substrate. A moiré pattern of the graphene/Ru(0001) is formed due to the lattice mismatch between graphene and Ru(0001). This superstructure gives rise to surface charge redistribution and could behave as an ordered quantum dot array, which results in a perfect template to guide the assembly of organic molecular structures. Molecules, for example iron phthalocyanine and C60, on this template show how the molecule-substrate interaction makes different superstructures. These results show the possibility of constructing ordered molecular structures on graphene/Ru(0001), which is helpful for practical applications in the future.
 
Article
A wealth of intriguing properties emerge in the seemingly simple system composed of the band insulators LaAlO(3) and SrTiO(3) such as a two-dimensional electron gas, superconductivity and magnetism. In this paper, we review the current insight obtained from first principles calculations on the mechanisms governing the behaviour of thin LaAlO(3) films on SrTiO(3)(001). In particular, we explore the strong dependence of the electronic properties on the surface and interface termination, the finite film thickness, lattice polarization and defects. A further aspect that is addressed is how the electronic behaviour and functionality can be tuned by an SrTiO(3) capping layer, adsorbates and metallic contacts. Lastly, we discuss recent reports on the coexistence of magnetism and superconductivity in this system for what they might imply about the electronic structure of this system.
 
Article
There is no consensus as yet to account for the significant presence of water on the terrestrial planets, but suggested sources include direct hydrogen adsorption from the parent molecular cloud after the planets' formation, and delivery of hydrous material via comets or asteroids external to the zone of the terrestrial planets. Alternatively, a more recent idea is that water may have directly adsorbed onto the interstellar dust grains involved in planetary formation. In this work, we use electronic structure calculations based on the density functional theory to investigate and compare the bulk and {010} surface structures of the magnesium and iron end-members of the silicate mineral olivine, namely forsterite and fayalite, respectively. We also report our results on the adsorption of atomic hydrogen at the mineral surfaces, where our calculations show that there is no activation barrier to the adsorption of atomic hydrogen at these surfaces. Furthermore, different surface sites activate the atom to form either adsorbed hydride or proton species in the form of hydroxy groups on the same surface, which indicates that these mineral surfaces may have acted as catalytic sites in the immobilization and reaction of hydrogen atoms to form dihydrogen gas or water molecules.
 
Article
Radio observations of gamma-ray burst (GRB) afterglows are essential for our understanding of the physics of relativistic blast waves, as they enable us to follow the evolution of GRB explosions much longer than the afterglows in any other wave band. We have performed a 3-year monitoring campaign of GRB 030329 with the Westerbork Synthesis Radio Telescopes and the Giant Metrewave Radio Telescope. Our observations, combined with observations at other wavelengths, have allowed us to determine the GRB blast wave physical parameters, such as the total burst energy and the ambient medium density, as well as to investigate the jet nature of the relativistic outflow. Further, by modelling the late-time radio light curve of GRB 030329, we predict that the Low-Frequency Array (30-240 MHz) will be able to observe afterglows of similar GRBs, and constrain the physics of the blast wave during its non-relativistic phase.
 
Article
We present here the analysis of the early and late multiwavelength afterglow emission, as observed by Swift a small robotic telescope, and the VLT. We compare early observations with late afterglow observations obtained with Swift and the VLT and we observe an intense rebrightening in the optical band at about one day after the burst which is not present in the X‐ray band. The lack of detection in X‐ray of such a strong rebrightening at lower energies may be described with a variable external density profile. In such a scenario, the combined X‐ray and optical observations allow us to derive that the matter density located at ∼ 1017 cm from the burst is about a factor of 10 higher than in the inner region. This is the first time in which a rebrightening has been observed in the optical afterglow of a GRB that is clearly absent in the X‐ray afterglow.
 
(a) The normalized lightcurves in different energy bands for GRB 060218; (b) GRB 060218 roughly satisfies the lag–luminosity relation discovered by Norris et al. (2000). From Liang et al. (2006).  
Article
GRB 060218 is a watershed event. Statistically, its detection suggests that there is likely a distinct low-luminosity (LL) population of gamma-ray bursts (GRBs) whose event rate is much higher than that of conventional high-luminosity GRBs. This LL population may give significant contribution to the diffuse neutrino background flux at energies higher than 1016eV. The spectral lag of this burst is very long, and roughly follows the luminosity-lag relation of normal GRBs. This, along with the fact that it follows the Ep-Eiso relation as well, suggests that X-ray flashes (XRFs) are natural extension of GRBs in the softer regime and that GRBs and XRFs share the same radiation physics. We discuss how the broadband data pose strong constraints on possible models of the prompt emission of this GRB.
 
Average normalized approximation error of the Nyström reconstruction of the diffusion maps kernel obtained from the video of figure 3 using different subset selection methods. Sampling according to the determinant yields overall the best performance. Blue circles, uniform sampling (s = 0); red squares, determinantal maximization (s = ∞); black diamonds, determinantal sampling (s = 1).  
Article
In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here, we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nyström extension. We provide a quantitative framework to analyse this procedure, and use it to demonstrate algorithmic performance bounds on a range of practical approaches designed to optimize the landmark selection process. We compare the practical implications of these bounds by way of real-world examples drawn from the field of computer vision, whereby low-dimensional manifold structure is shown to emerge from high-dimensional video data streams.
 
(a) Schematic and (b) image of a six-leg inkjet-printed composite TE device on a flexible PET substrate. 
Temperature dependence of electrical conductivity, Seebeck coefficient and power factor for n-type poly[K x (Niett)]/PVDF/DMSO composite films (a-c) and p-type poly[Cu x (Cu-ett)]/PVDF/DMSO composite films (d-f ) prepared with different drying temperatures. 
The output voltage and short-circuit current of the flexible device. 
Article
In this article, we put forward a simple method for the synthesis of thermoelectric (TE) composite materials. Both n- and p-type composites were obtained by ball-milling the insoluble and infusible metal coordination polymers with other polymer solutions. The particle size, film morphology and composition were characterized by dynamic light scattering, scanning electron microscopy, transmission electron microscopy and energy-dispersive X-ray spectroscopy. The TE properties of the drop-cast composite film were measured at different temperatures. An inkjet-printed flexible device was fabricated and the output voltage and short-circuit current at various hot-side temperatures (Thot) and temperature gradients (ΔT) were tested. The composite material not only highly maintained the TE properties of the pristine material but also greatly improved its processability. This method can be extended to other insoluble and infusible TE materials for solution-processed flexible TE devices.
 
Article
The pure water vapour and water-nitrogen continuum absorption in the 1000 and 2500 cm(-1) atmospheric windows has been studied using a 2 m base-length White-type multi-pass cell coupled with a BOMEM DA3-002 Fourier transform infrared spectrometer. The measurements were carried out at the National Institute of Standards and Technology (NIST, Gaithersburg, MD) over the course of several years (2004, 2006-2007, 2009). New data on the H(2)O:N(2) continuum in the 1000 cm(-1) window are presented and summarized along with the other experimental results and the continuum model. The experimental data reported on the water vapour continuum in these atmospheric windows basically agree with the most reliable laboratory data from the other sources. The MT_CKD (Mlawer-Tobin-Clough-Kneizys-Davies) continuum model significantly departs from the experimental data in both windows. The deviation observed includes the continuum magnitude, spectral behaviour and temperature dependence. In the 2500 cm(-1) region, the model does not allow for the nitrogen fundamental collision-induced absorption (CIA) band intensity enhancement caused by H(2)O:N(2) collisions and underestimates the actual absorption by over two orders of magnitude. The water vapour continuum interpretation as a typical CIA spectrum is reviewed and discussed.
 
(a) The 22-pole ion trap scheme. In the radial direction, ions are confined by the radiofrequency field, created by two sets of 11 poles (RFa and RFb) precisely mounted on opposite sides (f = 18 MHz, V 0 = 19 V for H + , V 0 = 26 V for He + ). The entrance and exit electrodes (EN and EX) are used to open and close the trap with electrostatic barriers of some tens of meV. (b) Typical decrease of the relative number of trapped H + ions due to reactions with H 2. The number density of H 2 has been varied from 10 12 to 10 14 cm −3 , leading to decay time constants between many minutes and 2.5 s. (Online version in colour.)
Formation of He + 2 dimers via the He + + 2 He reaction. Filled circles show the measured temperature dependence of k 3 (T ) used as a thermometer in the trap, as proposed in Gerlich [17]. The inverted triangles indicate previous results obtained using a selected ion drift tube by Böhringer et al. [18] and triangles show a ring electrode trap by Gerlich, at low temperatures [12]. The dashed line extrapolates Böhringer's fit. (Online version in colour.)  
Apparent binary association rate coefficient k * for T 22PT = 11 K, circles, and 22 K, squares (averaged over many measurements). In order to extract information on radiative and ternary association, the density has been varied over a wide range. The data have been fitted with k * = k r + k 3 [H 2 ]. The dashed and the dashed-dotted lines show the individual contributions. The surprising observation that the ternary association rate coefficient is the same for both temperatures while radiative association becomes faster with decreasing temperature is discussed in the text. (Online version in colour.)
Temperature dependences of k r and k 3 . The solid circles are the results from the fits shown in figure 3. (a) k 3 (T ) was measured at two densities (squares, 8 × 10 12 cm −3 ; triangles, 1.6 × 10 13 cm −3 ). The results have been corrected individually for contribution from radiative association. The apparent increase of k 3 with T is within the overall uncertainty of the data. (b) k r (T ) was measured at a density of 9 × 10 11 cm −3 . The results have been corrected individually for contributions from ternary association. The uncorrected values are plotted as open symbols. The dashed line indicates a T −1 law, the dashed-dotted a T −2 law. (Online version in colour.)  
Article
Formation of via association of H(+) with H(2) has been studied at low temperatures using a 22-pole radiofrequency trap. Operating at hydrogen number densities from 10(11) to 10(14) cm(-3), the contributions of radiative, k(r), and ternary, k(3), association have been extracted from the measured apparent binary rate coefficients, k*=k(r)+k(3)[H(2)]. Surprisingly, k(3) is constant between 11 and 22 K, (2.6±0.8)×10(-29) cm(6) s(-1), while radiative association decreases from k(r)(11 K)=(1.6±0.3)×10(-16) cm(3) s(-1) to k(r)(28 K)=(5±2)×10(-17) cm(3) s(-1). These results are in conflict with simple association models in which formation and stabilization of the complex are treated separately. Tentative explanations are based on the fact that, at low temperatures, only few partial waves contribute to the formation of the collision complex and that ternary association with H(2) may be quite inefficient because of the 'shared proton' structure of .
 
Article
New W isotope data for lunar metals demonstrate that the Moon formed late in isotopic equilibrium with the bulk silicate Earth (BSE). On this basis, lunar Sr isotope data are used to define the former composition of the Earth and hence the Rb-Sr age of the Moon, which is 4.48+/-0.02Ga, or 70-110Ma (million years) after the start of the Solar System. This age is significantly later than had been deduced from W isotopes based on model assumptions or isotopic effects now known to be cosmogenic. The Sr age is in excellent agreement with earlier estimates based on the time of lunar Pb loss and the age of the early lunar crust (4.46+/-0.04Ga). Similar ages for the BSE are recorded by xenon and lead-lead, providing evidence of catastrophic terrestrial degassing, atmospheric blow-off and significant late core formation accompanying the ca 100Ma giant impact. Agreement between the age of the Moon based on the Earth's Rb/Sr and the lead-lead age of the Moon is consistent with no major losses of moderately volatile elements from the Earth during the giant impact. The W isotopic composition of the BSE can be explained by end member models of (i) gradual accretion with a mean life of roughly 35Ma or (ii) rapid growth with a mean life of roughly 10Ma, followed by a significant hiatus prior to the giant impact. The former assumes that approximately 60 per cent of the incoming metal from impactors is added directly to the core during accretion. The latter includes complete mixing of all the impactor material into the BSE during accretion. The identical W isotopic composition of the Moon and the BSE limits the amount of material that can be added as a late veneer to the Earth after the giant impact to less than 0.3+/-0.3 per cent of ordinary chondrite or less than 0.5+/-0.6 per cent CI carbonaceous chondrite based on their known W isotopic compositions. Neither of these on their own is sufficient to explain the inventories of both refractory siderophiles such as platinum group elements and rhenium, and volatiles such as sulphur, carbon and water.
 
Article
Double-docking self-assembled monolayers (DDSAMs), namely self-assembled monolayers (SAMs) formed by molecules possessing two docking groups, provide great flexibility to tune the work function of metal electrodes and the tunnelling barrier between metal electrodes and the SAMs, and thus offer promising applications in both organic and molecular electronics. Based on the dispersion-corrected density functional theory (DFT) in comparison with conventional DFT, we carry out a systematic investigation on the dual configurations of a series of DDSAMs on an Au(111) surface. Through analysing the interface electronic structures, we obtain the relationship between single molecular properties and the SAM-induced work-function modification as well as the level alignment between the metal Fermi level and molecular frontier states. The two possible conformations of one type of DDSAM on a metal surface reveal a strong difference in the work-function modification and the electron/hole tunnelling barriers. Fermi-level pinning is found to be a key factor to understand the interface electronic properties.
 
Article
A simple model of the thermal dihalogenation of a silicon surface by an adsorbate, Br-R-Br, is described for the first time. The model consists of a pair of silyl radicals (SiH(3)), treated by density functional theory, placed a distance d apart. Two adsorbates were considered, one with R = benzene and one with R = biphenyl. The Br...Br internuclear separation (r(Br, Br)) in 1,4-dibromobenzene is 6.6 A, whereas that in 4,4'-dibromobiphenyl is 10.9 A. In the former case the model yields a (most-favourable) 'critical' separation d* approximately 10.2 A, corresponding to the lowest-energy barrier, and in the latter case d* approximately 13.8 A. The dangling-bond separations, d, were restricted to values present at an Si(111)7 x 7 surface. The critical values, d*, exceeded the corresponding value of r(Br, Br) in the intact adsorbate in each case by ca. 3.5 A, corresponding to ca. 93% of the van der Waals molecular size. This is approximately the observed increase in separation of a pair of halogen atoms in reactions at a Si surface, as compared with the separation in the parent molecule. If the dangling bonds at the surface are too close to one another (d < d*), the adsorbate molecules' charge cloud extends too far for a favourable interaction, whereas if the dangling bonds are too far apart (d < d*) the adsorbate's charge cloud cannot reach them. When the second reagent is a peg-board, the factors governing chemical reactivity are more exposed to view.
 
Article
The 125th anniversary of Osborne Reynolds' seminal publication on the transition to turbulence in pipe flow offers an opportunity to survey our understanding of the nature of the transition. Dynamical systems concepts, computational methods and dedicated experiments have helped to elucidate some of Reynolds' observations and to extract new quantitative characteristics of the transition. This introduction summarizes some of the developments and indicates how the various papers in this volume contribute to an improved understanding of Reynolds' observations.
 
Principle of s-SNOM. A focused light beam illuminates the tip region of an AFM, where a sample is approached and scanned to produce a topographic image. By recording the scattered light, here in the backwards direction, an optical image is simultaneously generated. The tip oscillates at the cantilever's mechanical resonance frequency Ω (tapping mode) with the important consequence that the near-field optical signal becomes modulated at harmonics nΩ, allowing an electronic filtering against otherwise overwhelming background scattering coming from the shaft and cantilever.
Sketches of optical layouts for interferometric s-SNOM. (a) Heterodyne system where the frequency in the reference arm of a Mach–Zehnder interferometer is offset by frequency ∆ (80 MHz in Hillenbrand & Keilmann (2000)). (b) Homodyne system where the phase of the reference beam in a Michelson interferometer is alternated between ψ = 0 and 90 @BULLET by mechanical mirror translation.  
Predicted s-SNOM amplitude s3 of various sample materials at two different illumination wavelengths, on a general graph where the abscissa is the real part of the sample's dielectric function, and the imaginary part serves as a parameter (Pt tip with a = 20 nm, ∆z = 20 nm).
Dipolar surface-plasmon-polariton oscillation field pattern of an Au disc (91 nm diameter, 20 nm high) on glass induced at a wavelength of 633 nm. (a) Schematic side view of the incident plane wave Ei and of the particle's eigenfield Ep. (b) Top view of near-field amplitude (upper row) and phase (lower row) for the field's z-component, obtained by exact electrodynamic calculation of the total field 10 nm above the disc as marked by the dashed line in (a). (c) Experimental s-SNOM amplitude E2 and phase ϕ2 images using a carbon nanotube tip as near-field-scattering optical probe.  
Predicted s-SNOM amplitude s3 of various sample materials at two different illumination wavelengths, on a general graph where the abscissa is the real part of the sample's dielectric function, and the imaginary part serves as a parameter (Pt tip with a = 20 nm, ∆z = 20 nm). one 256 pixel line. With this method, the infrared s-SNOM produces simultaneous near-field phase-contrast images and near-field amplitude-contrast images.  
Article
We describe ultraresolution microscopy far beyond the classical Abbe diffraction limit of one half wavelength (lambda/2), and also beyond the practical limit (ca. lambda/10) of aperture-based scanning near-field optical microscopy (SNOM). The 'apertureless' SNOM discussed here uses light scattering from a sharp tip (hence scattering-type or s-SNOM) and has no lambda-related resolution limit. Rather, its resolution is approximately equal to the radius a of the probing tip (for commercial tips, a < 20 nm) so that 10 nm is obtained in the visible (lambda/60). A resolution of lambda/500 has been obtained in the mid-infrared at lambda = 10 microm. The advantage of infrared, terahertz and even microwave illumination is that specific excitations can be exploited to yield specific contrast, e.g. the molecular vibration offering a spectroscopic fingerprint to identify chemical composition. S-SNOM can routinely acquire simultaneous amplitude and phase images to obtain information on refractive and absorptive properties. Plasmon- or phonon-resonant materials can be highlighted by their particularly high near-field signal level. Furthermore, s-SNOM can map the characteristic optical eigenfields of small, optically resonant particles. Lastly, we describe theoretical modelling that explains and predicts s-SNOM contrast on the basis of the local dielectric function.
 
Article
The technical aspects of computer security have fascinated researchers (including the author) for decades. It is, however, beginning to appear that the challenging problems are to do with people, rather than with mathematics or electronics.
 
Article
X-ray astronomy has evolved from a chance beginning 40 years ago to become a major branch of observational astronomy, underpinning a revolution in high-energy astrophysics. The intervening development can be seen in three phases, starting in the 1960s with a decade of pioneering exploration with sounding rockets, and consolidated by further discoveries with a series of dedicated small satellites, led by Uhuru, building up to NASA's HEAO-1 and Einstein Observatory missions in 1978-1981. The remaining years of the last century saw X-ray astronomy become a broad international effort with strong contributions from Europe and Japan balancing a temporary loss of momentum in the NASA programme. A brief account of those early years in X-ray astronomy is given, from a personal (UK) perspective, as an introduction to the review of the current status of the discipline, which was the subject of the Discussion Meeting.
 
Bust of James Clerk Maxwell in ornamental surround located in the picture gallery at Marischal College, Aberdeen, commemorating his tenure there as professor of natural philosophy. The posthumous bronze was commissioned from the sculptor Charles d’Orville Pilkington Jackson to mark the centenary of Clerk Maxwell’s Marischal College appointment. It was executed after a detailed study of all available images of Maxwell by the artist. Photo courtesy of Dr John S. Reid. 
Article
This paper is the preface to a special Issue of Phil. Trans. R. Soc. A reporting selected proceedings of the international conference marking the 150th anniversary of James Clerk Maxwell's professorial debut at Marischal College, Aberdeen. Following an introduction to Marischal College, a brief historical note summarizes Maxwell's life prior to his entering the college as professor of natural philosophy. The preface provides a short summary of the event and overviews the contributed papers devoted to subjects covering a wide range of Maxwell's research interests and their modern developments. The mixture of review and research papers reflects both the fundamental importance and the diverse applicability of Maxwell's works in electromagnetics, colour science, dynamics and kinetics. Acknowledgements are given to the individuals and bodies who made the conference the success that it was.
 
Structural hierarchy of the gecko adhesive system. Images (a,b) provided by Mark Moffett. (a) Ventral view of a tokay gecko (Gekko gecko) climbing a vertical glass surface. (b) Ventral view of the foot of a tokay gecko, showing a mesoscale array of seta-bearing scansors (adhesive lamellae). (c) Microscale array of setae are arranged in a nearly grid-like pattern on the ventral surface of each scansor. In this scanning electron micrograph, each diamond-shaped structure is the branched end of a group of four setae clustered together in a tetrad. (d ) Cryo-SEM image of a single gecko seta (image by S. Gorb and K. Autumn). Note individual keratin fibrils comprising the setal shaft. (e) Nanoscale array of hundreds of spatular tips of a single gecko seta. ( f ) Synthetic spatulae fabricated from polyimide at UC Berkeley in the laboratory of Ronald Fearing using nanomoulding (Campolo et al. 2003). 
Stress versus area in the gecko adhesive hierarchy modified from Autumn (2006b). Open circles represent measurements of adhesion and open squares represent measurements of friction. A JKR model prediction for spatular adhesion (23.6 nN) and the measured value for spatular pull off of 10 nN (Huber et al. 2005a) are too low to explain the 40 mN adhesive force of a single seta. However, our new theoretical analysis of van der Waals (vdW) adhesion and friction ( Tian et al. 2006) suggests that adhesion of a spatula can be increased by two orders of magnitude when the angle of pull is reduced from 908 to 108. The van der Waals model predictions for spatular shear force at 108 pull angle are also consistent with measured values of shear force in single setae. 
Young's modulus (E ) of materials including approximate values of bulk b-keratin and effective modulus (E eff ) of natural setal arrays. Adapted with permission from Autumn et al. (2006c). A value of Ez100 kPa (measured at 1 Hz) is the upper limit of the Dahlquist criterion for tack, which is based on empirical observations of pressure-sensitive adhesives (PSAs; Dahlquist 1969; Pocius 2002). A cantilever beam model (Sitti & Fearing 2003) predicts a value of E eff near 100 kPa, as observed for natural setae and PSAs. It is notable that geckos have evolved E eff close to the limit of tack. This value of E eff may be tuned to allow strong and rapid adhesion, yet prevent spontaneous or inappropriate attachment (Autumn & Hansen 2006). 
To determine the adhesive properties of gecko setae, we measured two-dimensional forces while dragging in both proximal and distal directions. (a) Side view of a gecko toe illustrating the distal ('non-adhesive') and proximal ('adhesive') directions. The distal direction is away from the animal while the proximal direction is towards the animal. (b ) Load-drag-pull (LDP) tests consist of a vertical load (L) to predetermined depth, a directional drag (D) while the vertical position is maintained and finally a vertical pull off (P) removing the adhesive from the surface. Setal arrays dragged in the proximal direction adhere and generate large friction forces. The adhesive force is controlled by friction and is sustained during shear sliding. (c ) Distal dragging of setal arrays results in low friction and a compressive normal force. Setal arrays obey Amontons' law of friction in the distal direction with a coefficient of friction of mz0.25-0.3. 
Article
If geckos had not evolved, it is possible that humans would never have invented adhesive nanostructures. Geckos use millions of adhesive setae on their toes to climb vertical surfaces at speeds of over 1ms-1. Climbing presents a significant challenge for an adhesive in requiring both strong attachment and easy rapid removal. Conventional pressure-sensitive adhesives (PSAs) are either strong and difficult to remove (e.g. duct tape) or weak and easy to remove (e.g. sticky notes). The gecko adhesive differs dramatically from conventional adhesives. Conventional PSAs are soft viscoelastic polymers that degrade, foul, self-adhere and attach accidentally to inappropriate surfaces. In contrast, gecko toes bear angled arrays of branched, hair-like setae formed from stiff, hydrophobic keratin that act as a bed of angled springs with similar effective elastic modulus to that of PSAs. Setae are self-cleaning and maintain function for months during repeated use in dirty conditions. Setae are an anisotropic 'frictional adhesive' in that adhesion requires maintenance of a proximally directed shear load, enabling either a tough bond or spontaneous detachment. Gecko-like synthetic adhesives may become the glue of the future-and perhaps the screw of the future as well.
 
Article
The concept that the Antarctic ice sheet changes with eternal slowness has been challenged by recent observations from satellites. Pronounced regional warming in the Antarctic Peninsula triggered ice shelf collapse, which led to a 10-fold increase in glacier flow and rapid ice sheet retreat. This chain of events illustrated the vulnerability of ice shelves to climate warming and their buffering role on the mass balance of Antarctica. In West Antarctica, the Pine Island Bay sector is draining far more ice into the ocean than is stored upstream from snow accumulation. This sector could raise sea level by 1m and trigger widespread retreat of ice in West Antarctica. Pine Island Glacier accelerated 38% since 1975, and most of the speed up took place over the last decade. Its neighbour Thwaites Glacier is widening up and may double its width when its weakened eastern ice shelf breaks up. Widespread acceleration in this sector may be caused by glacier ungrounding from ice shelf melting by an ocean that has recently warmed by 0.3 degrees C. In contrast, glaciers buffered from oceanic change by large ice shelves have only small contributions to sea level. In East Antarctica, many glaciers are close to a state of mass balance, but sectors grounded well below sea level, such as Cook Ice Shelf, Ninnis/Mertz, Frost and Totten glaciers, are thinning and losing mass. Hence, East Antarctica is not immune to changes.
 
Newton's reflecting telescope. 
Newton's sketch of his crucial experiment. 
Newton's colour circle published in Opticks (1704). 
Article
Isaac Newton's reputation was initially established by his 1672 paper on the refraction of light through a prism; this is now seen as a ground-breaking account and the foundation of modern optics. In it, he claimed to refute Cartesian ideas of light modification by definitively demonstrating that the refrangibility of a ray is linked to its colour, hence arguing that colour is an intrinsic property of light and does not arise from passing through a medium. Newton's later significance as a world-famous scientific genius and the apparent confirmation of his experimental results have tended to obscure the realities of his reception at the time. This paper explores the rhetorical strategies Newton deployed to convince his audience that his conclusions were certain and unchallengeable. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Martin Lister and his 'plant' fossils of 1673. (a) Portrait of Martin Lister. (b) Handwritten first page of Martin Lister's letter, as read before the Royal Society on 13 November 1673. (c) Numbered sketches hand drawn by Lister, here showing two fossil 'rock plants' (crinoid stems) from the Carboniferous limestone of Yorkshire, UK, with the specimen on the left showing evidence for 'joynts' (ossicles) 'slipped and out of order'. (d) Carboniferous limestone fossils showing similar features. (e) Numbered sketches by Lister showing lateral and basal views of a 'radix' or 'root' (actually a fossil crinoid calyx), showing the bases of arm-like features (brachia), rows of polygonal plates around the calyx and a portion of the stem with its central canal. (e,f ) Comparable fossil specimens showing similar features. (h) Numbered sketches by Lister showing a 'pentagonous' plate (on the left) and another from Northamptonshire, UK, with sculpture resembling an cidariid echinoid interambulcarum (on the right). (i) A comparable Jurassic echinoid test, adoral view. (Sources: (b,c,e) Copyright The Royal Society; (d,f ,g,i) Oxford University teaching collections.) Scale bar, 50 mm (d,f ,g,i). 
These copper-plate engravings appeared in Lister (1673) as figs. 1-37 of his 'Tab. 1' [1]. They are reversed from his original drawings. Loosely translating his descriptions [1], to make palaeontological meanings clearer, these show the following: 1, a single 'joynt' with very fine and small rays; 2, 'joynt' with 'pith' [central canal] bored through in the manner of a cinquefoil; 3, single oval 'joynt' with scarcely visible rays, and a small point in place of the 'pith'; 4, single 'joynt' with a very large 'pith'; 5, a pack of dislocated 'joynts' kept in the correct order; 6, a very long column having many smooth 'joynts' with the branches broken off; 7, a column with smooth 'joynts' and without branches; 8, the biggest column, with stumps of branches; 9, a smooth column with very smooth and numerous 'joynts'; 10, one of the widest and most deeply 'joynted' pieces of a column; 11, a column with numerous poorly ordered knot-like ornaments; 12, a column with only a single row of 'knots' in the centre of each 'joynt'; 13, a column with three rows of 'knots' on each 'joynt'; 14, a smooth column, with each 'joynt' bearing a single large ridge around the middle; 15, 'joynts' that are alternately raised and depressed; 16, a double facet on the edge of each 'joynt'; 17, alternate 'joynts' bearing edged facets; 18-20, certain other differences noted in the paper, but unclear in the engravings; 21, a column bearing a distinct side branch; 22, a branch broken off from a column; 23, a column shaped like a fruit; 24, a 'sastigium or summitas' [possible echinoid spine]; 25, a root-like 'radix' [crinoid calyx] in lateral view: A shows a 'joynt' remaining 'whence an Entrochos [column] was broken off'; C, E, F, D, show four of the double 'feet' [brachia], the rest being hidden from view; 26, the same 'radix' , seen in plan view: A shows the broken off column; C, B, D, E, F show the five double 'feet' [brachia]; note also the hexangular plates with roughened ornament, 'which incrustrate the stone or cover it all over'; 27, a smaller 'radix' [calyx] with smooth plates and five single 'feet' [brachia]: H, the top stone; I, one of the five 'feet' [brachia]; K, one of the five angular plates which 'incrustate the middle of the stone'; G, the base; also the same stone seen from the side; G, the same with the hollow bottom facing upwards. The following figures are of plates that are supposed to 'incrustate divers roots' [i.e. plates of the crinoid calyx]: 28, a 'pentagonous' plate knotted; 29, a thin-edged, smooth 'pentaganous' plate; 30, an indented 'pentagonous' plate; 31, the Northamptonshire 'pentagonous plate' [possible echinoid interambulacral plate from the Jurassic]; 32, a large 'pentagonous' smooth plate; 33, a 'hexagonous' plate sculpted with 'angles'; 34, a 'hexagonous' plate 'as deep as broad'; 35, 37, oddly shaped plates; 36, a quadrangular plate, ribbed and indented. (Copyright The Royal Society.) 
Three alternative hypotheses available for the interpretation of fossils in 1673. (a) The figured stones hypothesis of Kircher [13]: fossils found in rocks grow under the influence of 'plastic forces' , perhaps including cosmic influences; living invertebrates and algae may also grow by spontaneous generation. This view was preferred by Lister for his fossil molluscs [14-16]. (b) The biogenic hypothesis of Steno [17-19] and Hooke [20]: fossils found in stratified sediments are explicable as the remains of once living organisms; unfamiliar groups (e.g. ammonites, crinoids) may yet be discovered in remote areas or the deeper ocean. This view was hinted at by Lister [1] and explicitly suggested by Ray [21]. (c) The biogenic-extinction hypothesis is similar to (b), except that unfamiliar fossils may now be explained by their extinction [22]. This possibility was actually mentioned by Lister [16] for some of his fossil molluscs. The subsequent addition of evolution [23] then brought thinking towards its modern stance. 
Article
In 1673, Martin Lister explored the preservation of 'St Cuthbert's beads' plus other fossil crinoid remains from approximately 350 Ma Carboniferous limestone in northern England. He used taphonomic evidence (transport, disarticulation, burial and cementation) to infer an origin as petrified plant remains, in contrast with his views expressed elsewhere that fossil mollusc shells could have formed abiogenically, by 'plastic forces' within rock. Lister also observed pentagonal symmetry, now seen as characteristic of living echinoderm skeletons. A postscript from John Ray supports Lister's 'taphonomic' observations and accepts the biogenicity of these fossil 'vegetables'. Ray then concluded with a prophecy, predicting the discovery of comparable living fossils in remote ocean waters. These early discussions compare with current debates about the character of candidate microfossils from the early Earth and Mars. Interesting biomorphs are now tested against the abiogenic null hypotheses, making use of features such as those pioneered by Lister, including evidence for geological context, rules for growth and taphonomy. Advanced techniques now allow us to extend this list of criteria to include the nanoscale mapping of biology-like behaviour patterns plus metabolic pathways. Whereas the science of palaeobiology once began with tests for biogenicity, the same is now true for geobiology and astrobiology. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Hales's apparatus from Vegetable Statics (London 1727). Copyright The Royal Society.
Cavendish’s apparatus from Philosophical Transactions (1766). Copyright The Royal Society. 
Priestley’s apparatus from Experiments and Observations on Different Kinds of Air (London 1774). Copyright The Royal Society. 
Article
Historians of chemistry usually associate the eighteenth century with the Chemical Revolution, but it could just as readily be called 'the century of gases' (or 'airs', as they were called in the eighteenth century). In the early part of the century, the British pneumatic chemists struggled to replace the traditional notion 'Air', understood as an inert chemical element, with the concept of 'air', regarded as the third state of matter, encompassing a wide variety of chemical species. These developments constituted a necessary condition for the Chemical Revolution, which occurred in the latter part of the century. In 'Observations', Priestley took pneumatic chemistry to a new level, with the discovery of eight simple inorganic gases. Motivated by his belief in a benevolent God and a pious utilitarianism, Priestly explored the role of the atmosphere in the balance of nature and the politics of the state, which he linked to the movement of Rational Dissent. He styled himself an 'aerial philosopher' to signal the interdisciplinary nature of his inquiries, which he regarded not as a branch of ordinary chemistry, but as a mode of thought that encompassed physics, chemistry and natural theology. Priestley saw it as a source of principles and secrets of nature more extensive than that of 'gravity itself'. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Her page of sketches accompanying her letter showing the comet against various combinations of stars 'a, b and c'. Copyright The Royal Society. 
The Female Philosopher: Smelling out the Comet, 1790s. (Draper Hill Collection, The Ohio State University Billy Ireland Cartoon Library & Museum.) 
Caroline Herschel by M. G. Tieleman, 1829. Copyright The Royal Society. 
Article
Long before women were allowed to become Fellows of the Royal Society, or obtain university degrees, one woman managed to get her voice heard, her discovery verified and her achievement celebrated. That woman was Caroline Herschel, who, as this paper will discuss, managed to find ways to fit comet discoveries into her domestic life, and present them in ways that were socially acceptable. Caroline lived in a time when strict rules dictated how women (and men) should behave and present themselves and their work. Caroline understood these rules, and used them carefully as she announced each discovery, starting with this comet which she found in 1786. Caroline discovered her comets at a time when astronomers were mainly concerned with position, identifying where things were and how they were moving. Since her discoveries, research has moved on, as astronomers, using techniques from other fields, and most recently sending experiments into space, have learned more about what comets are and what they can tell us about our solar system. Caroline's paper marks one small, early step in this much bigger journey to understand comets. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Images are figs. 1 (left) and 9 (right) of Davy's paper [11]. The left hand image represents the safe lantern with its airfeeder and chimney furnished with safety metallic canals. It contains about a quart of air. The sides are of horn or glass, made air tight by putty or cement. (A) is the lamp through which the circular air-feeding canals pass: they are 3 concentric hollow cylinders, distant from each other 1/26 of an inch: the smallest is 2 1/2 inches in circumference; their depth is 2 inches. (B) is the chimney containing 4 such canals, the smallest 2 inches in circumference: above it is a hollow cylinder, with a cap to prevent dust from passing into the chimney. (C) is the hole for admitting oil. (D) is a long canal containing a wire by which the wick is moved or trimmed. (E) is the tube forming a connection between the reservoir of oil and the chamber that supplies the wick with oil. (F) is the rim round the bottom of the lantern to enable it to bear motion. Davy's fig. 9 (right) is a metallic gauze safe lamp. (A) shows the three screens of metallic gauze or flame sieves. (B) indicates wires for trimming the wick. Copyright The Royal Society. 
The final form of the safety lamp. Fig. 11 in [11]. Copyright The Royal Society. 
Photo of the silver-gilt salver sent to Humphry Davy by the Tsar of Russia. (From R. King's booklet on Humphry Davy, published by the Royal Institution, 1978.) 
Article
In the period between 1815 and 1818, Sir Humphry Davy read four papers to the Royal Society and published a monograph dealing with a safety lamp for coal miners, all of which record in detail the experimental work that he carried out, with his assistant Michael Faraday, so as to determine how to prevent catastrophic accidents in coal mines by the explosion of fire-damp (methane) in the presence of a naked flame. This article describes the key experiments that he performed at the Royal Institution and some of the subsequent trials made in the coal mines of the north of England. It begins, however, with an account of Davy's prior achievements in science before he was approached for help by the clergymen and doctors in the Gateshead and Newcastle upon Tyne areas. There is little doubt that the Davy lamp, from the 1820s onwards, transformed the coal industry worldwide. It also profoundly influenced the science of combustion, and in the words of a pioneer in that field, W. A. Bone, FRS, 'There is no better model of logical experimental procedure, accurate reasoning, philosophical outlook and fine literary expression.' It is a remarkable fact that it took Davy essentially only two weeks from the time he was given samples of fire-damp to solve the problem and to devise his renowned miner's safety lamp. A brief account is also given of the contemporaneous invention of a safety lamp by George Stephenson, and of some of Davy's subsequent accomplishments. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Portrait of Davies Gilbert. Copyright The Royal Society. 
The Menai Suspension Bridge; from the book by William Provis [17]. Drawn by G. Arnold and engraved by R. G. Reeve. Courtesy of the Institution of Civil Engineers. 
A portion of Gilbert's text [1], assembled from pages 203, 204 and 212. The y-axis, not shown, goes to the right from point A. Copyright The Royal Society. 
Article
Davies Gilbert's work on the catenary is notable on two counts. First, it influenced Thomas Telford in formulating his final design for the Menai Strait suspension bridge (1826); and second, it established for the first time the form of the 'catenary of equal strength'. The classical catenary is a uniform flexible chain or cable hanging freely under gravity between supports. The 'catenary of equal strength' is the form of a cable whose cross-sectional area is made proportional to the tension at each point, so that the tensile stress is uniform throughout. In this paper I provide a sketch of the lives and achievements of Gilbert and Telford, and of their interaction over the Menai Bridge. There follows a commentary on Gilbert's 1826 paper, and on his two related publications; and a brief sketch of the earlier history of the catenary. I then describe the development of the suspension bridge up to the present time. Finally, I discuss relations between mathematical analysts and practical engineers. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Faraday’s induction ring (1831). Image courtesy of the Royal Society/Science and Society Picture Library. 
Faraday’s spinning disc—generating a continuous electric current in a conducting disc as it spins between two poles of a powerful permanent magnet. This diagram is from Faraday’s original paper [9]. Copyright The Royal Society. 
This is a page from Faradays’ notebook written on 26 March 1832 (RI MS F/2/C, p. 147). It reads: ‘The mutual relation of electricity, magnetism and motion may be represented by three lines at right angles to each other, any one of which may represent any one of these points and the other two lines the other points. Then if electricity be determined in one line and motion in another, magnetism will be developed in the third; or if electricity be determined in one line and magnetism in another, motion will occur in the third. Or if magnetism be determined first then motion will produce electricity or electricity motion. Or if motion be the first point determined, Magnetism will evolve electricity or electricity magnetism. Reproduced by courtesy of the Royal Institution of Great Britain. 
Article
The history of science is filled with examples of key discoveries and breakthroughs that have been published as landmark texts or journal papers, and to which one can trace the origins of whole disciplines. Such paradigm-shifting publications include Copernicus' De revolutionibus orbium coelestium (1543), Isaac Newton's Philosophiæ Naturalis Principia Mathematica (1687) and Albert Einstein's papers on relativity (1905 and 1915). Michael Faraday's 1832 paper on electromagnetic induction sits proudly among these works and in a sense can be regarded as having an almost immediate effect in transforming our world in a very real sense more than any of the others listed. Here we review the status of the subject-the relationship between magnetism and electricity both before and after Faraday's paper and delve into the details of the key experiments he carried out at the Royal Institution outlining clearly how he discovered the process of electromagnetic induction, whereby an electric current could be induced to flow through a conductor that experiences a changing magnetic field. His ideas would not only enable Maxwell's later development of his theory of classical electromagnetism, but would directly lead to the development of the electric dynamo and electric motor, two technological advances that are the very foundations of the modern world. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
James Prescott Joule. Copyright The Royal Society. 
One of Joule's original paddle-wheel assemblies. (Courtesy of the Science Museum, London.) 
Article
James Joule played the major role in establishing the conservation of energy, or the first law of thermodynamics, as a universal, all-pervasive principle of physics. He was an experimentalist par excellence and his place in the development of thermodynamics is unarguable. This article discusses Joule's life and scientific work culminating in the 1850 paper, where he presented his detailed measurements of the mechanical equivalent of heat using his famous paddle-wheel apparatus. Joule's long series of experiments in the 1840s leading to his realisation that the conservation of energy was probably of universal validity is discussed in context with the work of other pioneers, notably Sadi Carnot, who effectively formulated the principle of the second law of thermodynamics a quarter of a century before the first law was accepted. The story of Joule's work is a story of an uphill struggle against a critical scientific establishment unwilling to accept the mounting evidence until it was impossible to ignore. His difficulties in attracting funding and publishing in reputable journals despite the quality of his work will resonate with many young scientists and engineers of the present day. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Watercolour by Jemima Wedderburn showing children playing on the frozen loch at St Mary's Isle near the family home at Glenlair on 23 December 1853. In the background, the adults are seen curling. (Courtesy of The Maxwell at Glenlair Trust and James Clerk Maxwell Foundation.) 
Maxwell's diagram from the Philosophical Magazine of 1861 showing the rotating vortices represented by hexagons and the idle wheels between them [18, plate V, fig. 2]. 
Translation table from Maxwell's notation to unrationalized units. quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Article
Maxwell's great paper of 1865 established his dynamical theory of the electromagnetic field. The origins of the paper lay in his earlier papers of 1856, in which he began the mathematical elaboration of Faraday's researches into electromagnetism, and of 1861-1862, in which the displacement current was introduced. These earlier works were based upon mechanical analogies. In the paper of 1865, the focus shifts to the role of the fields themselves as a description of electromagnetic phenomena. The somewhat artificial mechanical models by which he had arrived at his field equations a few years earlier were stripped away. Maxwell's introduction of the concept of fields to explain physical phenomena provided the essential link between the mechanical world of Newtonian physics and the theory of fields, as elaborated by Einstein and others, which lies at the heart of twentieth and twenty-first century physics. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Sir George Stokes’ initial response to the request to review Osborne Reynolds’ paper. Copyright The Royal Society. 
Part of the joint response of Sir George Stokes and Professor Lamb to Professor Reynolds Paper. Copyright The Royal Society. 
Osborne Reynolds at approximately the time of the 1895 paper. Copyright The University of Manchester. 
Article
Reynolds' paper sought to explain the change in character of flow through a pipe from laminar to turbulent that his earlier experiments had shown to occur when the dimensionless group that today bears his name exceeded approximately 2000. This he did by decomposing the velocity into mean and fluctuating components and noting how the average kinetic energy generation and dissipation rates changed with Reynolds number. The paper was only grudgingly accepted by two very distinguished referees and initially raised little external interest. As years went by, however, the averaged form of the equations of motion, known as the Reynolds equations (which were an intermediate stage in Reynolds' analysis) became the acknowledged starting point for computing turbulent flows. Moreover, some 50 years after his paper, a refinement of his strategy for predicting transition was also successfully taken up. For some engineering problems, the continual rapid growth of computing resources has meant that more detailed approaches for computing turbulent flow phenomena can nowadays be employed. However, this growth of computing power likewise makes possible a Reynolds-averaging strategy for complex flow systems in industry or the environment which formerly had to adopt less comprehensive analyses. Thus, Reynolds' approach may well remain in use throughout the present century. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Article
A week after our meeting, we received the very sad news that Britton Chance had passed away on 16th November 2010, in Philadelphia, aged 97. Britton was an extraordinary scientist who made an enormous impact in so many areas of biochemistry and biophysics. He was a leading figure in biomedical
 
Article
Looked at in a simplistic way, aerosols have counteracted the warming effects of greenhouse gases (GHG) over the past century. This has not only provided some 'climate protection', but also prevented the true magnitude of the problem from becoming evident. In particular, it may have resulted in an underestimation of the sensitivity of the climate system to the effect of GHG. Over the present century, the role of aerosols in opposing global warming will wane, as there are powerful policy reasons to reduce their emissions and their atmospheric lifetimes are short in contrast to those of the GHG. On the other hand, aerosols will continue to play a role in regional climate change, especially with regard to the water cycle. The end of significant climate protection by atmospheric aerosols, combined with the potentially very high sensitivity of the climate system, makes sharp and prompt reductions in greenhouse gas emissions, especially CO2, very urgent.
 
The 16-inch lens and large coelostat (on the left) and the smaller 4-inch telescope in a square box (on the right), with its much smaller coelostat on location at Sobral, Brazil. (Courtesy of the Science Museum, London.) 
The radial deflections of the positions of seven stars observed by the 4-inch telescope at Sobral as a function of distance from the centre of the Sun. The scale on the abscissa is the inverse of the distance from the centre of the Sun. The dotted line shows the Newtonian prediction and the central heavy solid line shows the expectation of the General Theory of Relativity. The upper light solid line shows a best-fit to the deflection of the seven stars by the Sun. Image from [19] (Copyright The Royal Society). 
Measurement of the coefficient (1 + γ )/2 from light deflection and time delay measurements [26]. In General Relativity, the value of γ is 1. The upper part of the diagram shows how the precision of the experiments has improved since the pioneering experiments of 1919. The lower part of the diagram shows the corresponding improvements in the limits to deviations from General Relativity from the Shapiro time delay experiments. (Courtesy of Prof. Clifford Will.) 
A Hubble Space Telescope image of the central region of the rich cluster of galaxies Abell 2218, showing the prominent arcs centred on the massive core of the cluster. The circular images are the gravitationally lensed images of a very distance background galaxy. The core of the cluster acts as a gravitational lens. (Courtesy of NASA, ESA and the Space Telescope Science Institute, Baltimore, MD, USA.) 
Article
The famous eclipse expedition of 1919 to Sobral, Brazil, and the island of Principe, in the Gulf of Guinea, led by Dyson, Eddington and Davidson was a turning point in the history of relativity, not only because of its importance as a test of Einstein's General Theory of Relativity, but also because of the intense public interest which was aroused by the success of the expedition. The dramatic sequence of events which occurred is reviewed, as well as the long-term impact of its success. The gravitational bending of electromagnetic waves by massive bodies is a subject of the greatest importance for contemporary and future astronomy, astrophysics and cosmology. Examples of the potential impact of this key tool of modern observational astronomy are presented. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Article
The nature of statistics has changed over time. It was originally concerned with descriptive 'matters of state'-with summarizing population numbers, economic strength and social conditions. But during the course of the twentieth century its aim broadened to include inference-how to use data to shed light on underlying mechanisms, about what might happen in the future, about what would happen if certain actions were taken. Central to this development was Ronald Fisher. Over the course of his life he was responsible for many of the major conceptual advances in statistics. This is particularly illustrated by his 1922 paper, in which he introduced many of the concepts which remain fundamental to our understanding of how to extract meaning from data, right to the present day. It is no exaggeration to say that Fisher's work, as illustrated by the ideas he described and developed in this paper, underlies all modern science, and much more besides. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Article
![Graphic][1] The Royal Society Theo Murphy International Scientific Meeting Quantum-coherent energy transfer: implications for biology and new energy technologies was one of the last scientific meetings attended by Bob Silbey, who died on 27 October 2011. As always, he brought his
 
Article
![Graphic][1] Dr Steve Wilkins passed away shortly after the end of this meeting. He was one of the truly great pioneers in the area of phase-contrast X-ray imaging, and it is no coincidence that he was invited to give the opening talk at the conference. As well as a scientist of exceptional
 
Article
Prof. Dame Kathleen Lonsdale was one of the two first female Fellows of the Royal Society, having originally been a student of that great British scientist and Nobel Laureate William Henry Bragg. She came to fame initially for her solution of the crystal structure of hexamethyl benzene, thus demonstrating that the benzene ring was flat, of considerable importance to organic chemistry, where it had been proposed before but without proof. This was at a time when the solution of crystal structures was in its infancy, and in its day this work was considered a triumph. As a rare example then of a female physicist, Lonsdale became interested in various aspects of the diffraction of X-rays, and in particular published an important paper on a form of diffraction in which a strongly divergent source was used rather than the usual highly collimated beam. The photographs thus obtained showed a series of arcs and circles, whose positions were so sensitive that they could be used to determine the quality of crystals such as diamond, and even to calculate their lattice dimensions, and hence carbon-carbon bond lengths, to hitherto extraordinary precision. Lonsdale also became known not just as a scientist but as a peace activist and an active member of the Society of Friends. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Article
This issue is dedicated to Peter Hornby and to Ioannis Vardoulakis, friends, colleagues and mentors. Peter Hornby died in June 2009 and Ioannis Vardoulakis in September 2009 while this issue was being prepared. Peter and Ioannis were inaugural members of the Australian Commonwealth Scientific and
 
Article
The key ideas presented in the classic paper 'The growth of crystals and the equilibrium structure of their surfaces' by W. K. Burton, N. Cabrera and F. C. Frank, published in Philosophical Transactions A in 1951, are summarized and put in the context of both the state of knowledge at the time of publication and the considerable amount of work since that time that has built on and developed these ideas. Many of these developments exploit the huge increase in the capabilities of computer modelling that complement the original analytic approach of the paper. The dearth of relevant experimental data at the time of the original publication has been transformed by the application of increasingly sophisticated modern methods of surface science. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
Article
During the weekend of Saturday 31 January to Sunday 1 February 1953, a storm tide raged across the northwest European shelf and flooded the low-lying coastal areas of the countries around the North Sea. The peak high waters occurred during the night and the storm surprised many people in their sleep. The resulting disaster in terms of loss of life and damage to infrastructure was enormous. In the Netherlands, 1836 people fell victim to the flood; in the UK and Belgium, the casualties were 307 and 22, respectively. The large number of fatalities in the Netherlands was related to the fact that much of the affected area is below sea-level.This paper focuses on the case of the Netherlands. It discusses the history of land reclamation, and the fact that living in low-lying areas protected by dykes, often below sea-level, is an accepted fact of life in the Netherlands. The historical approach to dyke maintenance is then outlined, and the state of the dykes in the early twentieth century and after the war is discussed. The characteristics of the storm and the flood are discussed, along with people's experiences of the first hours and days following the flood. The impact of this human stress has often been lasting--many survivors continue to live with daily memories of the flood. Attention is given to the large-scale rescue and relief efforts, the closure of the dykes during the following nine months and the concept of the Delta Plan, designed to prevent such a large-scale disaster ever happening again. Although the 1953 storm was indeed a low probability event leading to very high storm-induced water-levels, and occurred in combination with spring tide, several arguments are presented that explain why this flood turned into a disaster of such a large scale. Equally, the question is raised whether the disaster could have been prevented. The paper concludes by noting the importance of awareness and preparedness in order to prevent a future storm threat of this scale turning into a disaster of the scope of the Big Flood of 1953.
 
Article
Waves and sea levels have been modelled for the storm of 31 January-1 February 1953. Problems in modelling this event are associated with the difficulty of reconstructing wind fields and validating the model results with the limited data available from 50 years ago. The reconstruction of appropriate wind fields for surge and wave models is examined. The surges and waves are reproduced reasonably well on the basis of tide-gauge observations and the sparse observational information on wave heights. The maximum surge coincided closely in time with tidal high water, producing very high water levels along the coasts of the southern North Sea. The statistics of the 1953 event and the likelihood of recurrence are also discussed. Both surge and wave components were estimated to be approximately 1 in 50 year events. The maximum water level also occurred when the offshore waves were close to their maximum. The estimation of return period for the total water level is more problematic and is dependent on location. A scenario with the 1953 storm occurring in 2075, accounting for the effects of sea level rise and land movements, is also constructed, suggesting that sea level relative to the land could be 0.4-0.5m higher than in 1953 in the southern North Sea, assuming a rise in mean sea level of 0.4m.
 
Article
The Big Flood was the worst natural disaster to befall Britain during the twentieth century, and the scale of its human impact was due to the lack of adequate disaster preparedness. The 307 deaths on land were caused by drowning or from the effects of exposure. Two-thirds occurred in four clusters along the shoreline and mainly comprised inhabitants of post-war prefabricated buildings, bungalows and chalets, with the highest mortality among the elderly. The emergency response was spontaneous and community led, with the main search and rescue completed before central government became involved. No individuals or agencies were blamed for the neglected state of the flood defences or the absence of warnings, along with the post-war shortage of adequate housing, which were the main causes of vulnerability. The media played a limited role, and television was in its infancy. Mental health impacts were either self-limiting or failed to be articulated in a society recovering from the Second World War. The major mitigating factors included the empathetic response of people, locally and nationally, as well as the availability of armed forces personnel based in East Anglia, whose actions played a decisive part in the battle against the sea. The major legacies of the Big Flood were a coastal flood forecasting system, a more scientific approach to sea defences and the building of the Thames barrier.
 
Article
![Graphic][1] A detailed biography of Vadim Kuznetsov has already been published in [Sahi (2006)][2]. In this brief note, I shall concentrate on his scientific activity. Vadim's career as a mathematician can be set in three distinct periods. 1. Leningrad (1986–1993). 2. The travelling
 
The fit of the continents around the Atlantic [24]. Copyright The Royal Society. 
Article
In the 1960s, geology was transformed by the paradigm of plate tectonics. The 1965 paper of Bullard, Everett and Smith was a linking transition between the theories of continental drift and plate tectonics. They showed, conclusively, that the continents around the Atlantic were once contiguous and that the Atlantic Ocean had grown at rates of a few centimetres per year since the Early Jurassic, about 160 Ma. They achieved fits of the continental margins at the 500 fathom line (approx. 900 m), not the shorelines, by minimizing misfits between conjugate margins and finding axes, poles and angles of rotation, using Euler's theorem, that defined the unique single finite difference rotation that carried congruent continents from contiguity to their present positions, recognizing that the real motion may have been more complex around a number of finite motion poles. Critically, they were concerned only with kinematic reality and were not restricted by considerations of the mechanism by which continents split and oceans grow. Many of the defining features of plate tectonics were explicit or implicit in their reconstructions, such as the torsional rigidity of continents, Euler's theorem, closure of the Tethyan ocean(s), major continental margin shear zones, the rapid rotation of small continental blocks (Iberia) around nearby poles, the consequent opening of small wedge-shaped oceans (Bay of Biscay), and misfit overlaps (deltas and volcanic piles) and underlaps (stretched continental edges). This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
 
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