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.

(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)

The triple Klein bottle

Felix Klein was a German mathematician best known for a particularsurface thet he introduced in 18882: the Klein bottle, a non-orientable surface without edge, inside, outside and no boundary (for example a sphere is an orientable surface without boundaries).
In 1995 Alan Bennett, a retired glass-blower, became interested in Klein bottles and was in a unique position to satisfy his curiosity. From simple beginnings his researches produced a variety of beautiful and mathematically sophisticated forms. New discoveries have emerged from his work which formed the inspiration for this display.
This is one of a series of glass Klein bottles made by [the artist] for the Science Museum. It consists of three Klein bottles, one inside another. In the series Alan Bennett made Klein bottles analogous to Mobius strips with odd numbers of twists greater than one.
(via archive.org)

The aircraft of the future

Pierpaolo Lazzarini is an italian designer, who proposed an interesting concept personal aircraft for the future of mobility: I.F.O.

The project is an evolution of the previous U.F.O.

Pi and the Basel's problem

In 1644 the Italian mathematician Pietro Mengoli proposed the so-called Basel's problem, which asked for the exact solution to the square of the sum of the reciprocals of all the natural numbers: $\sum_{n=1}^\infty \frac{1}{n^2} = \frac{1}{1^2} + \frac{1}{2^2} + \cdots$ The solution to the problem came in 1735 thanks to Leonard Euler, at the time at the beginning of his brilliant career as a problem solver. The Swiss mathematician proved that the exact sum of the series is $\pi^2 / 6$.
The Euler's demonstration, published in its final form in 1741, is particularly interesting: Euler supposed that it's possible to apply the rules of the finite polynomials even those endless.
We start with the development in Taylor series for the sine function in 0: $\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots$ Dividing by $x$ both terms, we obtain: $\frac{\sin(x)}{x} = 1 - \frac{x^2}{3!} + \frac{x^4}{5!} - \frac{x^6}{7!} + \cdots$ whose roots are $\pi$, $-\pi$, $2\pi$, $-2\pi$, $3\pi$, $-3\pi$, $\ldots$ By changing the variable as $z = x^2$, the polynomial above becomes: $\frac{\sin(\sqrt{z})}{\sqrt{z}} = 1 - \frac{z}{3!} + \frac{z^2}{5!} - \frac{z^3}{7!} + \cdots$ whose roots are $\pi^2$, $4\pi^2$, $9\pi^2$, $\ldots$
Now, given a polynomial $a_n x^n + \cdots + a_3 x^3 + a_2 x^2 + bx + 1$, for the formulas of Viète, we have that the sum of the reciprocals of its roots has as result $-b$. Applying this result for finished polynomials to infinite polynomial in $z$ above, we get: $\frac{1}{3!} = \frac{1}{6} = \frac{1}{\pi^2} + \frac{1}{4\pi^2} + \frac{1}{9\pi^2} + \frac{1}{16\pi^2} + \cdots$ and so: $\frac{\pi^2}{6} = 1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \cdots = \sum_{n=1}^\infty \frac{1}{n^2}$ It's simple to observe the connection between Mengoli's series and Riemann's zeta $\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}$ with $s=2$.
Last observation: in 1982 on the magazine Eureka, it appeared a rigorous proof of Euler's result signed by John Scholes, although it seems that such a demonstration circulated already to late sixties between Cambridge corridors.

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).

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.