Total's responses to global warming

Building upon recent work on other major fossil fuel companies, we report new archival research and primary source interviews describing how Total responded to evolving climate science and policy in the last 50 years. We show that Total personnel received warnings of the potential for catastrophic global warming from its products by 1971, became more fully informed of the issue in the 1980s, began promoting doubt regarding the scientific basis for global warming by the late 1980s, and ultimately settled on a position in the late 1990s of publicly accepting climate science while promoting policy delay or policies peripheral to fossil fuel control. Additionally, we find that Exxon, through the International Petroleum Industry Environmental Conservation Association (IPIECA), coordinated an international campaign to dispute climate science and weaken international climate policy, beginning in the 1980s. This represents one of the first longitudinal studies of a major fossil fuel company's responses to global warming to the present, describing historical stages of awareness, preparation, denial, and delay.

Bonneuil, C., Choquet, P. L., & Franta, B. (2021). Early warnings and emerging accountability: Total’s responses to global warming, 1971–2021. Global Environmental Change, 102386. doi:10.1016/j.gloenvcha.2021.102386

Great number

The Large Numbers hypothesis asserts that all the large dimensionless numbers occurring in Nature are connected with the present epoch, expressed in atomic units, and thus vary with time. It requires that the gravitational constant G shall vary, and also that there shall be continuous creation of matter. The consistent following out of the hypothesis leads to the possibility of only two cosmological models. One of them, which occurs if one assumes that the continuous creation is a multiplication of existing matter, is Einstein’s cylindrical closed Universe. The other, which occurs if one assumes the continuous creation takes place uniformly through the whole of space, involves an approximately flat Minkowski space with a point of origin where the Big Bang occurred.

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Dirac, P. A. M. (1974). Cosmological models and the large numbers hypothesis. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 338(1615), 439-446. doi:10.1098/rspa.1974.0095

John Barrow: Some Generalities About Generality

John D. Barrow - via commons

On 1 December 2014 I had the pleasure of attending a lecture by John David Barrow at the "Enriques" Department of Mathematics in Milano. Very kind person, when I approached him to be able to shake his hand and take a picture of him, he granted me both honors with great simplicity. Unfortunately that photo has now been lost among smartphone changes, perhaps kept in some hard disk stored somewhere, nor did I publish it on one of my social networks, but I still wanted to pay homage to it by offering you the abstract of an article from 2015, the fifth chapter of the book The Philosophy of Cosmology (arXiv):

We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for investigation. We show how simple counting arguments can be used to characterise parts of the general solution of Einstein's equations when various matter fields are present and with different spatial topologies. Applications are described to the problem of singularities, static cosmological models, cosmic no hair theorems, the late-time isotropisation of cosmological models, and the number of parameters needed to describe a general astronomical universe.

The obscure Planet Nine

Planet Nine is an hypothetical plante in Our Souls System. Its existence is inferred by the orbital data of a group of extreme trans-Neptunian objects, that seemed influenced by the presence of an undiscovered planet, or something else. Recently Amir Siraj and Abraham Loeb proposed a new hypothesys: Planet Nine could be a little black hole, about five times more massive than Earth with the dimension of an orange:

Planet Nine has been proposed to potentially be a black hole in the outer solar system. We investigate the accretion flares that would result from impacts of small Oort cloud objects, and find that the upcoming LSST observing program will be able to either rule out or confirm Planet Nine as a black hole within a year. We also find that LSST could rule out or confirm the existence of trapped planet-mass black holes out to the edge of the Oort cloud, indirectly probing the dark matter fraction in subsolar mass black holes and potentially improving upon current limits by orders of magnitude.

Siraj, A., & Loeb, A. (2020). Searching for Black Holes in the Outer Solar System with LSST. ApJL 898 L4 arXiv:2005.12280. doi:10.3847/2041-8213/aba119 (arXiv).

A laser particle accelerator

Particle accelerators are usually associated with large national facilities. Because photons are able to impart momentum to electrons, there are also efforts to develop laser-based particle accelerators. Sapra et al. developed an integrated particle accelerator using photonic inverse design methods to optimize the interaction between the light and the electrons. They show that an additional kick of around 0.9 kilo–electron volts (keV) can be given to a bunch of 80-keV electrons along just 30 micrometers of a specially designed channel. Such miniaturized dielectric laser accelerators could open up particle physics to a number of scientific disciplines.

Sapra, N. V., Yang, K. Y., Vercruysse, D., Leedle, K. J., Black, D. S., England, R. J., ... & Byer, R. L. (2020). On-chip integrated laser-driven particle accelerator. Science, 367(6473), 79-83. doi:10.1126/science.aay5734

Abstract: The Universe at Lattice-Fields

Guido, G. and Filippelli, G. (2017) The Universe at Lattice-Fields. Journal of High Energy Physics, Gravitation and Cosmology, 3, 828-860. doi:10.4236/jhepgc.2017.34060.

We formulate the idea of a Universe crossing different evolving phases $U_k^*$ where in each phase one can define a basic field at lattice structure $U_k$ increasing in mass (Universe-lattice). The mass creation in $U_k$ has a double consequence for the equivalence "mass-space": Increasing gravity (with varying metric) and increasing space (expansion). We demonstrate that each phase is at variable metric beginning by open metric and to follow a flat metric and after closed. Then we define the lattice-field of intersection between two lattice fields of base into universe and we analyse the universe in the Nucleo-synthesis phase and in the that of recombination. We show that the phase is built on the intersection of the lattices of the proton and electron. We show $U_H$ [the intersection between proton's anch electron's lattices] to be at variable metric (open in the past, flat in the present and closed in the future). Then, we explain some fundamental aspects of this universe $U_H$: Hubble's law by creating the mass-space in it, its age (13.82 million of Years) as time for reaching the flat metric phase and the value of critic density. In last we talk about dark universe lattice, having hadronic nature, and calculating its spatial step and its density in present phase of [the universe].

For some personal problems, I cannot add the LaTeX figures, so I uploaded them on researchgate.

JMP #58, 4: path integrals and friends

The path integral formulation of quantum mechanics replaces the single, classical trajectory of a system with the sum over an infinity of quantum possible trajectories. To compute this sum is used a functional integral. The most famous interpretation is dued by Richard Feynman. In an Euclidean spacetime we speak about Euclidean path integral:

Bernardo, R. C. S., & Esguerra, J. P. H. (2017). Euclidean path integral formalism in deformed space with minimum measurable length. Journal of Mathematical Physics, 58(4), 042103. doi:10.1063/1.4979797

We study time-evolution at the quantum level by developing the Euclidean path-integral approach for the general case where there exists a minimum measurable length. We derive an expression for the momentum-space propagator which turns out to be consistent with recently developed $\beta$-canonical transformation. We also construct the propagator for maximal localization which corresponds to the amplitude that a state which is maximally localized at location $\xi'$ propagates to a state which is maximally localized at location $\xi"$ in a given time. Our expression for the momentum-space propagator and the propagator for maximal localization is valid for any form of time-independent Hamiltonian. The nonrelativistic free particle, particle in a linear potential, and the harmonic oscillator are discussed as examples.

Other papers from JMP #58, 4, follows:

JMP 58, 3: math paradoxes in quantum mechanics

Facchi, P., & Ligabò, M. (2017). Large-time limit of the quantum Zeno effect Journal of Mathematical Physics, 58 (3) DOI: 10.1063/1.4978851 (arXiv)

If very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect. We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, $t \propto N^\alpha$. The limit survival probability exhibits a sudden jump from $1$ to $0$ at $\alpha = 1/2$, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for $\alpha \geq 1$, the limit probability becomes sensitive to the spectral properties of the initial state and to the arithmetic properties of the measurement periods.

Selvitella, A. (2017). The Simpson’s paradox in quantum mechanics Journal of Mathematical Physics, 58 (3) DOI: 10.1063/1.4977784 (sci-hub)

In probability and statistics, the Simpson’s paradox is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, while the reverse trend appears for the aggregate data. In this paper, we give some results about the occurrence of the Simpson’s paradox in quantum mechanics. In particular, we prove that the Simpson’s paradox occurs for solutions of the quantum harmonic oscillator both in the stationary case and in the non-stationary case. In the non-stationary case, the Simpson’s paradox is persistent: if it occurs at any time $t=\tilde t$, then it occurs at any time $t\not= \tilde t$. Moreover, we prove that the Simpson’s paradox is not an isolated phenomenon, namely, that, close to initial data for which it occurs, there are lots of initial data (a open neighborhood), for which it still occurs. Differently from the case of the quantum harmonic oscillator, we also prove that the paradox appears (asymptotically) in the context of the nonlinear Schrödinger equation but at intermittent times.

Read also: Two quantum Simpson's paradoxes

Meng, F., & Liu, C. (2017). Necessary and sufficient conditions for the existence of time-dependent global attractor and application Journal of Mathematical Physics, 58 (3) DOI: 10.1063/1.4978329 (sci-hub)

In this paper, we are concerned with infinite dimensional dynamical systems in time-dependent space. First, we characterize some necessary and sufficient conditions for the existence of the time-dependent global attractor by using a measure of noncompactness. Then, we give a new method to verify the sufficient condition. As a simple application, we prove the existence of the time-dependent global attractor for the damped equation in strong topological space.

Cen, J., Correa, F., & Fring, A. (2017). Time-delay and reality conditions for complex solitons Journal of Mathematical Physics, 58 (3) DOI: 10.1063/1.4978864 (arXiv)

We compute lateral displacements and time-delays for scattering processes of complex multi-soliton solutions of the Korteweg de-Vries equation. The resulting expressions are employed to explain the precise distinction between solutions obtained from different techniques, Hirota’s direct method and a superposition principle based on Bäcklund transformations. Moreover they explain the internal structures of degenerate compound multi-solitons previously constructed. Their individual one-soliton constituents are time-delayed when scattered amongst each other. We present generic formulae for these time-dependent displacements. By recalling Gardner’s transformation method for conserved charges, we argue that the structure of the asymptotic behaviour resulting from the integrability of the model together with its $PT$-symmetry ensures the reality of all of these charges, including in particular the mass, the momentum, and the energy.

Wilming, H., Kastoryano, M., Werner, A., & Eisert, J. (2017). Emergence of spontaneous symmetry breaking in dissipative lattice systems Journal of Mathematical Physics, 58 (3) DOI: 10.1063/1.4978328 (arXiv)

A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analog of such a theory. Specifically, we consider local dissipative dynamics preparing an equilibrium steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes, there exist asymptotically stationary symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation.

JMP 58, 2: quantum abstract

I'm returning with the selections from the Journal of Mathematical Physics. I'm arranging two further post for this series for the next weeks. Stay tuned!

Alhaidari, A., & Taiwo, T. (2017). Wilson-Racah quantum system Journal of Mathematical Physics, 58 (2) DOI: 10.1063/1.4975138 (arXiv)

Using a recent formulation of quantum mechanics without a potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials.

Dorsch, F. (2017). Accumulation rate of bound states of dipoles generated by point charges in strained graphene Journal of Mathematical Physics, 58 (2) DOI: 10.1063/1.4976201 (arXiv)

We consider strained graphene, modelled by the two-dimensional massive Dirac operator, with potentials corresponding to charge distributions with vanishing total charge, non-vanishing dipole moment and finitely many point charges of subcritical coupling constants located in the graphene sheet. We show that the bound state energies accumulate exponentially fast at the edges of the spectral gap by determining the leading order of the accumulation rate.

Physics Education vol.52: Ciênsação and others educational papers

One of the most interesting paper published on the last issue of Physics Education is Ciênsação: gaining a feeling for sciences about a learning repository for high school theachers.
The project born for brazilian schools, but I think that it could be useful for allo teachers in the world. For example in most educational systems there are the same reasons against the introduction of hands-on experiments in classroom:

• lack of time;
• insecurity and lack of training;
• lack of resources and infrastructure.

So the repository Ciênsação propose to all teachers some interesting and simple experiments. It try

(...) to convince teachers that short experiments — which may take just a couple of minutes or even seconds to conduct — can smoothly transit to productive class discussions, in which students simultaneously advance their fact knowledge, deepen their understanding and foster their scientific skills.

If we see some experiments (for example the brief activity about magnetism), we can apreciate the simple integration of the experiment in the usual lesson with few materials.
I think that the phylosophy of Ciênsação is very near to my (past) teaching activities:

The research tasks, around which Ciênsação experiments are built, invite students to actively do science, instead of merely reproducing known results and confirming textbook claims. Giving students a few minutes to pursue such a task autonomously in small groups, allows them not only to experience the excitement of discovery, but also to experience science as a creative activity, as a craft they can master, rather than the privilege of an elite called 'scientists'.

For theachers that are intrested to sbmit their teaching activities, there's also a submission form.

Henrique Abreu de Oliveira, M., & Fischer, R. (2017). Ciênsação: gaining a feeling for sciences Physics Education, 52 (2) DOI: 10.1088/1361-6552/aa5430

And now some others interesting papers:

Bioplastic from weaver's broom

At the end of 1980s the researcher Catia Bastioli developed a new bioplastic, Mater-Bi, using corn⁽¹⁾. Since 1989, there were developed a lot of bioplastic, for example the polymer poly(lactic acid)⁽²⁾ or the broom fibers:

Fallico, C., Troisi, S., Molinari, A., and Rivera, M. F.: Characterization of broom fibers for PRB in the remediation of aquifers contaminated by heavy metals, Biogeosciences, 7, 2545-2556, doi:10.5194/bg-7-2545-2010, 2010

The present level of pollution, increasingly involving ground waters, constitutes a serious risk to the environment and also to human health. Therefore the remediation of saturated and unsaturated soils to remove pollutant materials is more and more frequently required. In the present paper, the possibility of removing heavy metals by permeable reactive barrier (PRB) from the groundwater carried out specifically with broom fibers, is investigated.
Once shown the economic benefits deriving from the use of this plant, a hydraulic characterization of the broom fiber mass was performed, determining the permeability and the porosity in correspondence to different levels of compactness of the fibers.
Having verified the effectiveness of removal of some heavy metals by these fibers, the results of some experiments, carried out in the laboratory for this purpose, are shown. These experiments were carried out utilizing broom fibers obtained in different ways and, limitedly to the considered pollutants, showed the high capability of these fibers to reduce their concentrations. The best results were obtained for the broom fibers extracted by a particular chemical-physical process.
Moreover, the behaviour of this fiber with time was investigated, determining the kinetic constant of degradation.

Gabriele, Bartolo, Teresa Cerchiara, Giuseppe Salerno, Giuseppe Chidichimo, Mabel Valeria Vetere, Cosimo Alampi, Maria Caterina Gallucci, Carmela Conidi, and Alfredo Cassano. "A new physical–chemical process for the efficient production of cellulose fibers from Spanish broom (Spartium junceum L.)." Bioresource technology 101, no. 2 (2010): 724-729. doi:10.1016/j.biortech.2009.08.014 (sci-hub)

A novel and efficient method for the extraction of cellulose fibers from Spanish broom (Spartium junceum L.) is presented. The method is based on the sequential combination between an initial chemical stage (alkaline digestion) and a subsequent physical–chemical stage, consisting of compression with hot air in an autoclave followed by rapid decompression (DiCoDe process, digestion–compression–decompression). The alkaline mother liquor deriving from the initial digestion step can be conveniently recycled after centrifugation followed by ultrafiltration. The process is characterized by the production of fibers with excellent physical–chemical properties, such as high mechanical resistance and high elasticity, and rapid production times. The fibers obtained after the DiCoDe process can be further softened and whitened by means of enzymatic digestion.
Fibers were morphologically characterized by scanning electron microscopy (SEM), while their composition and physical–chemical properties were determined by conventional methods, including colorimetry, TAPPI protocols, IR spectroscopy, and X-ray diffractometry.

Cassano, Roberta, Sonia Trombino, Ermelinda Bloise, Rita Muzzalupo, Francesca Iemma, Giuseppe Chidichimo, and Nevio Picci. "New broom fiber (Spartium junceum L.) derivatives: preparation and characterization." Journal of agricultural and food chemistry 55, no. 23 (2007): 9489-9495. doi:10.1021/jf071711k (sci-hub)

In the past decade interest in biopolymers has increased. Attempts were made to prepare new composite systems from biopolymers by binding different synthetic polymers to a biopolymer backbone. This paper reports the synthesis and characterization of derivatized broom fibers to prepare composites with either degradability or fireproofing properties. Synthetic strategies are described for the introduction of polymerizable functional groups or fluorine atoms on the glucose of cellulose chains of broom. The fibers containing polymerizable groups were copolymerized with dimethylacrylamide and styrene and, after that, investigated by optical polarizing microscopy (OPM) and scanning electron microscopy analysis (SEM). The materials containing fluorine were submitted to thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) for the purpose of verifying the fireproofing. Such derivatized biomaterials could be successfully used for applications in agriculture and in the packaging area.

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(1) Bastioli, Catia. "Properties and applications of Mater-Bi starch-based materials." Polymer Degradation and Stability 59.1-3 (1998): 263-272. doi:10.1016/S0141-3910(97)00156-0 (sci-hub)
(2) Karamanlioglu, Mehlika, Richard Preziosi, and Geoffrey D. Robson. "Abiotic and biotic environmental degradation of the bioplastic polymer poly (lactic acid): A review." Polymer Degradation and Stability (2017). doi:10.1016/j.polymdegradstab.2017.01.009 (sci-hub)

JMP 58, 1: magnetic monopoles, spacetime and gravity

Just another selection of papers from the Journal of Mathematical Physics. I would start with the folowing paper:

Fine, D., & Sawin, S. (2017). Path integrals, supersymmetric quantum mechanics, and the Atiyah-Singer index theorem for twisted Dirac Journal of Mathematical Physics, 58 (1) DOI: 10.1063/1.4973368

Feynman’s time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure that these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a path integral. Further, the class of Laplacians includes the square of the twisted Dirac operator, which corresponds to an extension of $N = 1/2$ supersymmetric quantum mechanics. General results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the Atiyah-Singer index theorem.

Kováčik, S., & Prešnajder, P. (2017). Magnetic monopoles in noncommutative quantum mechanics Journal of Mathematical Physics, 58 (1) DOI: 10.1063/1.4973503

We discuss a certain generalization of the Hilbert space of states in noncommutative quantum mechanics that, as we show, introduces magnetic monopoles into the theory. Such generalization arises very naturally in the considered model, but can be easily reproduced in ordinary quantum mechanics as well. This approach offers a different viewpoint on the Dirac quantization condition and other important relations for magnetic monopoles. We focus mostly on the kinematic structure of the theory, but investigate also a dynamical problem (with the Coulomb potential).

SphereX: the road to BB-8

BB-8 is the last Star Wars' droid introduced in The Force Awakens. It's a spherical robot with a free-moving head. Now, looking on arXiv, I found the proposal for SphereX, a new spherical robot for planetary explorations:

Wheeled planetary rovers such as the Mars Exploration Rovers (MERs) and Mars Science Laboratory (MSL) have provided unprecedented, detailed images of the Mars surface. However, these rovers are large and are of high-cost as they need to carry sophisticated instruments and science laboratories. We propose the development of low-cost planetary rovers that are the size and shape of cantaloupes and that can be deployed from a larger rover. The rover named SphereX is 2 kg in mass, is spherical, holonomic and contains a hopping mechanism to jump over rugged terrain. A small low-cost rover complements a larger rover, particularly to traverse rugged terrain or roll down a canyon, cliff or crater to obtain images and science data. While it may be a one-way journey for these small robots, they could be used tactically to obtain high-reward science data. The robot is equipped with a pair of stereo cameras to perform visual navigation and has room for a science payload. In this paper, we analyze the design and development of a laboratory prototype. The results show a promising pathway towards development of a field system.

The litle robot was tested under simulated lunar and martian gravity conditions, and the results are encouraging:

It was observed that as angle of separation between grouser decreases there is increase in average speed of robot and the power consumption remains almost constant. A hopping mechanism was developed for the robot that enables the robot to in theory perform unlimited hops. Currently the system is able to perform a hop of 8-10 cm under simulated Martian gravity. Extrapolating this, we would be able to achieve 16-20 cm hop in lunar conditions. The performance of hopping mechanism has to be improved to achieve the stated mission requirements. Based on power consumption for each hop and maximum power available, it was calculated that the robot would be able to produce maximum 208 hops in a single charge and robot would operate for 35 minutes of continuous hopping. The proposed SphereX design shows a promising pathway towards further maturation and testing of the technology in the field.

JMP 57, 12: quantum mechanics for the universe

I will begin to publish posts in a more continuous way, also recovering some drafts that I'm not able to conclude in 2016. For now I propose you a selection of articles from the Journal of Mathematical Physics, vol.57, issue 12:

Andersson, A. (2016). Electromagnetism in terms of quantum measurements Journal of Mathematical Physics, 57 (12) DOI: 10.1063/1.4972287

We consider the question whether electromagnetism can be derived from the theory of quantum measurements. It turns out that this is possible, both for quantum and classical electromagnetism, if we use more recent innovations such as smearing of observables and simultaneous measurability. In this way, we justify the use of von Neumann-type measurement models for physical processes. We apply the operational quantum measurement theory to gain insight into fundamental aspects of quantum physics. Interactions of von Neumann type make the Heisenberg evolution of observables describable using explicit operator deformations. In this way, one can obtain quantized electromagnetism as a measurement of a system by another. The relevant deformations (Rieffel deformations) have a mathematically well-defined "classical" limit which is indeed classical electromagnetism for our choice of interaction.

Aerts, D., & Sassoli de Bianchi, M. (2016). The extended Bloch representation of quantum mechanics: Explaining superposition, interference, and entanglement Journal of Mathematical Physics, 57 (12) DOI: 10.1063/1.4973356

An extended Bloch representation of quantum mechanics was recently derived to offer a possible (hidden-measurements) solution to the measurement problem. In this article we use this representation to investigate the geometry of superposition and entangled states, explaining interference effects and entanglement correlations in terms of the different orientations a state-vector can take within the generalized Bloch sphere. We also introduce a tensorial determination of the generators of $SU(N)$, which we show to be particularly suitable for the description of multipartite systems, from the viewpoint of the sub-entities. We then use it to show that non-product states admit a general description where sub-entities can remain in well-defined states, even when entangled. This means that the completed version of quantum mechanics provided by the extended Bloch representation, where density operators are also considered to be representative of genuine states (providing a complete description), not only offers a plausible solution to the measurement problem but also to the lesser-known entanglement problem. This is because we no longer need to give up the general physical principle saying that a composite entity exists and therefore is in a well-defined state, if and only if its components also exist and therefore are also in well-defined states.

How to produce stationary wave fields

A cylindrical surface of stationary light from
Zamboni-Rached, M., Recami, E., & Hernández-Figueroa, H. (2005). Theory of "frozen waves": modeling the shape of stationary wave fields Journal of the Optical Society of America A, 22 (11) DOI: 10.1364/JOSAA.22.002465 (arXiv)

On the 15th december, 2005, was published an interesting patent (I found it via Research Gate), Method and apparatus for producing stationary intense wave fields of arbitrary shape by Erasmo Recami, Michel Rached Zamboni, Hugo Enrique Ernandez Figueros, Valerio Abate, Cesar Augusto Dartora, Kleber Suza Nobrega, Marco Mattiuzzi:

Method for producing a stationary wave field of arbitrary shape comprising the steps of defining at least one volume being limited in the direction of the axis of propagation of a beam, of the type $0 \leq z \leq L$; defining an intensity pattern within the said region $0 \leq z \leq L$ by a function $F(z)$, describing the said localized and stationary intensity pattern, which is approximated by means of a Fourier expansion or by a similar expansion in terms of (trigonometric) orthogonal functions; providing a generic superposition of Bessel or other beams highly transversally confined; calculating the maximum number of superimposed Bessel beams the amplitudes, the phase velocities and the relative phases of each Bessel beam of the superposition, and the transverse and longitudinal wavenumbers of each Bessel beam of the superposition.

The invention is based on the following theoretical papers:

How to become a superhero

from Amazing Fantasy by Stan Lee and Steve Ditko

We analyze a collaboration network based on the Marvel Universe comic books. First, we consider the system as a binary network, where two characters are connected if they appear in the same publication. The analysis of degree correlations reveals that, in contrast to most real social networks, the Marvel Universe presents a disassortative mixing on the degree. Then, we use a weight measure to study the system as a weighted network. This allows us to find and characterize well defined communities. Through the analysis of the community structure and the clustering as a function of the degree we show that the network presents a hierarchical structure. Finally, we comment on possible mechanisms responsible for the particular motifs observed.

Gleiser, P. (2007). How to become a superhero Journal of Statistical Mechanics: Theory and Experiment, 2007 (09) DOI: 10.1088/1742-5468/2007/09/P09020 (arXiv)

The Marvel Universe as a real social network

Cover of the first number of Marvel Team-Up, comic book dedicated to the collaborations between Marvel heroes

We investigate the structure of the Marvel Universe collaboration network, where two Marvel characters are considered linked if they jointly appear in the same Marvel comic book. We show that this network is clearly not a random network, and that it has most, but not all, characteristics of "real-life" collaboration networks, such as movie actors or scientific collaboration networks. The study of this artificial universe that tries to look like a real one, helps to understand that there are underlying principles that make real-life networks have definite characteristics.

R. Alberich, J. Miro-Julia, & F. Rossello (2002). Marvel Universe looks almost like a real social network arXiv arXiv: cond-mat/0202174v1

Postcards from Pluto

The New Horizons mission has provided a lot of observations about Pluto, the farthermost known celestial object in our Solar System. Thanks to these observations, astronomers can now describe some interesting Pluto's characteristics.

The Pluto system is surprisingly complex, comprising six objects that orbit their common center of mass in approximately a single plane and in nearly circular orbits. (...)
All four of Pluto's small moons are highly elongated objects with surprisingly high surface reflectances (albedos) suggestive of a water-ice surface composition. Kerberos appears to have a double-lobed shape, possibly formed by the merger of two smaller bodies. Crater counts for Nix and Hydra imply surface ages of at least 4 billion years. Nix and Hydra have mostly neutral (i.e., gray) colors, but an apparent crater on Nix's surface is redder than the rest of the surface; this finding suggests either that the impacting body had a different composition or that material with a different composition was excavated from below Nix's surface. All four small moons have rotational periods much shorter than their orbital periods, and their rotational poles are clustered nearly orthogonal to the direction of the common rotational poles of Pluto and Charon.

Some geometrical aspects of 3- and 4-spaces

A couple of abstracts about the geomtery of space:

Historically, there have been many attempts to produce the appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's quaternions, Gibbs' vector system using the dot and cross products. We illustrate however, that Clifford's geometric algebra (GA) provides the most elegant description of physical space. Supporting this conclusion, we firstly show how geometric algebra subsumes the key elements of the competing formalisms and secondly we show how it provides an intuitive representation and manipulation of the basic concepts of points, lines, areas and volumes. We also provide two examples where GA has been found to provide an improved description of two key physical phenomena, electromagnetism and quantum theory, without using tensors or complex vector spaces. This paper also provides pedagogical tutorial-style coverage of the various basic applications of geometric algebra in physics.

James M. Chappell, Azhar Iqbal & Derek Abbott (2011). Geometric Algebra: A natural representation of three-space, arXiv: 1101.3619v3

We indicate that Heron's formula (which relates the square of the area of a triangle to a quartic function of its edge lengths) can be interpreted as a scissors congruence in 4-dimensional space. In the process of demonstrating this, we examine a number of decompositions of hypercubes, hyper-parallelograms, and other elementary 4-dimensional solids.

J. Scott Carter & David A. Mullens (2015). Some Elementary Aspects of 4-dimensional Geometry, arXiv: 1504.01727v1

There's also a minimalistic introduction to euclidean planes.

Water on Mars

"Our quest on Mars has been to 'follow the water', in our search for life in the universe, and now we have convincing science that validates what we've long suspected. This is a significant development, as it appears to confirm that water -- albeit briny -- is flowing today on the surface of Mars."

John Grunsfeld from the press release. The abstract of the paper follows:

Determining whether liquid water exists on the Martian surface is central to understanding the hydrologic cycle and potential for extant life on Mars. Recurring slope lineae, narrow streaks of low reflectance compared to the surrounding terrain, appear and grow incrementally in the downslope direction during warm seasons when temperatures reach about 250–300 K, a pattern consistent with the transient flow of a volatile species. Brine flows (or seeps) have been proposed to explain the formation of recurring slope lineae, yet no direct evidence for either liquid water or hydrated salts has been found4. Here we analyse spectral data from the Compact Reconnaissance Imaging Spectrometer for Mars instrument onboard the Mars Reconnaissance Orbiter from four different locations where recurring slope lineae are present. We find evidence for hydrated salts at all four locations in the seasons when recurring slope lineae are most extensive, which suggests that the source of hydration is recurring slope lineae activity. The hydrated salts most consistent with the spectral absorption features we detect are magnesium perchlorate, magnesium chlorate and sodium perchlorate. Our findings strongly support the hypothesis that recurring slope lineae form as a result of contemporary water activity on Mars.

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Ojha, L., Wilhelm, M., Murchie, S., McEwen, A., Wray, J., Hanley, J., Massé, M., & Chojnacki, M. (2015). Spectral evidence for hydrated salts in recurring slope lineae on Mars Nature Geoscience DOI: 10.1038/ngeo2546